The Middle atmosphere

Editors' Note It has been for some time the editorial policy of this journal to publish occasional special issues contai...

Author: S. V. Venkateswaran | N. Sundararaman

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Editors' Note It has been for some time the editorial policy of this journal to publish occasional special issues containing articles which have either been presented at a symposium or are devoted to a topic of recognized current interest. This particular issue contains 29 articles dealing with various aspects of the region of the Earth's atmosphere known as the Middle Atmosphere - a region including the upper stratosphere and the mesosphere and comprising roughly the altitude range between 30 and 90 km. The Middle Atmosphere is a region where radiative, photochemical and dynamical processes are interlinked in intriguing ways. Because of the growing awareness that this region is particularly sensitive to both natural and man-made perturbations, there has been an upsurge of research activity in the present decade in what is essentially an interdisciplinary area. It is the hope of the editors that the articles in this volume will help in giving the reader a glimpse of the scope and nature of the problems, of the extent and current status of the progress achieved, and of what lies ahead in this rapidly developing subject. These articles were solicited by the editors as invited contributions from experts in their respective specialities. In content they represent either original contributions or reviews of accomplished work or, as was left to the choice of the authors, appropriate combinations of both. It is our distinct pleasure to thank the authors for their valuable contributions and their cooperation in meeting an early deadline, as well as the anonymous referees for their pertinent comments. The expert secretarial assistance of Ms. Elizabeth Schwalm has been chiefly instrumental in bringing out this volume on schedule.

Los Angeles and Washington, D.C. August 1979

S. V. VENKATESWARAN N. SUNDARARAMAN Guest Editors

Pageoph, Vol. 118 (1980), Birkh~iuser Verlag, Basel

Solar UV Radiation and its Absorption in the Mesosphere and Stratosphere By MARCELNICOLET1'2) A b s t r a c t - Solar radiation of A > 175 nm and of Lyman-alpha at 121.6 nm is absorbed in the mesosphere and stratosphere by molecular oxygen (A < 242 nm) and also by ozone molecules at A > 200 nm. This paper describes the photodissociation processes resulting from absorption in the Schumann-Runge bands and Herzberg continuum of molecular oxygen and also in the Hartley, Huggins and Chappuis bands of ozone. Special consideration is given to differences between the stratospheric and mesospheric problems.

Key words: Ultraviolet radiation; Photodissociation; Schumann-Runge bands; Herzberg continuum; Ozone bands. L

Introduction

In order to study the photochemical action of solar radiation on stratospheric and mesospheric constituents, it is convenient to divide the solar spectrum in spectral ranges related to the molecular oxygen and ozone absorptions. The radiation of wavelengths less than 100 nm is absorbed by nitrogen and oxygen in the thermosphere; it leads essentially to ionization processes and is, therefore, not considered here. Only X rays of wavelengths less than 1 nm can penetrate into the atmosphere below 100km, and lead indirectly to the dissociation of molecular constituents. The radiation of wavelengths less than 242 nm is absorbed by molecular oxygen and leads to its photodissociation. The principal photodissociation continuum (Schumann-Runge continuum) at A < 175 nm corresponds to a complete absorption of the solar radiation in the thermosphere and will not be considered in this analysis. An important solar line, Lyman-~ at 121.6 nm, is situated in a so-called atmospheric window since the 02 absorption cross section is only of the order of 10-2o cmL Such a radiation is absorbed in the mesosphere. The second important spectral range, between 200 nm and 175 nm, is related to the 0 2 Schumann-Runge band system which includes 18 bands, ( 2 - 0 ) to (19-O), subject to the predissociation process. In this spectral region, the mean absorption cross sections are a function of the temperature and number of O2 absorbing molecules. 1) Ionosphere Research Laboratory, The Pennsylvania State University, University Park, Pa. 16802, USA. 2) Present address: 30 Avenue Den Doorn, B-180 Brussels, Belgium.

4

Marcel Nicolet

(Pageoph,

The absorption, which is essentially a mesospheric process, also plays a role in various stratospheric photodissociations. From 200 to 242 nm, the 02 absorption, which is related to the Herzberg continuum with low absorption cross section (from 10 -24 to 10 -23 cm 2) occurs in the stratosphere. In addition, the ozone absorption must be introduced since this spectral region belongs to the spectral range of the 03 Hartley band. The simultaneous absorption by 02 and 08 must be considered in the stratosphere. In the mesosphere, the 03 absorption is practically negligible since the total number of ozone molecules is very small for low solar zenith angles. At wavelengths less than 310 nm corresponding to the 03 Hartley band, the ozone molecule has its principal absorption which occurs in the stratosphere. Its limit near 310 nm must be determined with precision, since the photodissociation process in the Hartley band, which is

03 + hv(A < 310 n m ) - + O2(1Ag) + O(1D)

(1)

leads to the production of O(~D) atoms responsible, particularly below 50 km, for the production of OH from H20, CH4 and H2, and also of NO from N20. At ~ > 310 nm, the Oa Huggins bands correspond to the limit of its ultraviolet absorption. The spectral range to be considered should be between 310 n m a n d 400 nm since it corresponds also to various limits of the absorption spectrum of H202, H2CO, NO2, N20~, HNO2, HNOa, C1ONO2, HOCI . . . . . In the visible region (410-850 nm), the Chappuis bands play an important role leading to the 03 photodissociation in the lower part of the atmosphere, troposphere and lower stratosphere. At ~ > 300 nm, various effects such as the Rayleigh scattering and the albedo must be introduced. In particular, the photodissociation rates of 03; ratio n(O)/n(03), of NOz, ratio n(NO2)/n(NO), and the absolute concentration of the other constituents absorbing in that spectral region are strongly affected by the Rayleigh scattering and albedo effects. Thus, the photodissociation problem is related to a knowledge of the solar flux and its possible variations in certain spectral regions, the exact determination of the vertical distribution of the atmospheric optical depth of 02 and Oa, the measurement of the absorption cross sections and photodissociation quantum yields for each constituent, and the introduction of the atmospheric conditions related to the radiation scattering and a l b e d o .

H. 02 Absorption The absorption cross section in the Herzberg continuum is known with an accuracy which is not greater than 25~ (Fig. 1). At A > 230 nm the 02 cross section is not known with sufficient precision; but since the ozone absorption is maximum in this

Vol. 118, 1980)

Solar UV Radiation Absorption in Mesosphere and Stratosphere

5

15

.~ ~0

: .....................

o

i?i!!~

02

-

INUUM

.....

g

/

"

= 10 200

I

210

I

,

220 230 WAVELENGTH ( nm )

i

2/,0

Figure 1 Experimental data on 02 absorption cross sections in the Herzberg continuum, x DITCHBURN and YOUNG (1962). (:30GAWA (1971). [] I-IASSONand NICHOLLS (1971). 9 SHARDANANO (1977).

Table 1 Mean value o f solar flux (q, photons cm-2 sec-1); mean cross section (o, cm 2 for 500 c m - 1) and 02 photodissociation coefficients (j, sec- 1) at the top o f the Earth's atmosphere in the spectral range o f the 02 Herzberg continuum (A(A) = average wavelength in A o f the spectral range, + 250 cm- 1) A(A) 2010 2030 2051 2072 2094 2116 2139 2162 2186 2209 2234 2259 2286 2312 2339 2367 2395 2424

q~ 1.44 x 1012 1.80 2.08 2.45 5.09 7.12 9.23 8.42 1.20 • 1013 1.22 1.77 1.60 1.96 1.97 1.70 2.00 1.77 1/2 (2.58)

ao2

j~

1.50 x 10 -23 1.25 1.00 9.80 • 10 -24 9.20 8.50 7.85 7.05 6.15 5.50 4.75 4.05 3.35 2.70 2.20 1.65 1.20 0.75

2.16 • 10 -11 2.25 2.08 2.40 4.68 6.05 7.25 5.94 7.38 6.71 8.4l 6.48 6.57 5.32 3.74 3.30 2.12 9.80 • 10 -12

6

Marcel Nicolet

(Pageoph,

10 Z

N ( O 2 } ~< 2 x J019 C m , O- IO2) = 10~29cm 2 ~2xlO

C~

19 c m 2, l o g TO2 = A l o g N I O ; J . B

~) UJ q

"T" p..

U3 O

n

.

o ~

5x~0 ~

0

m <

I

0.'

10'"

I

i

I

1

I I .r

t0 ~

~

I

I

J ~. tl

,

0 2 MOLECULES

r

I

~

i

~

1 0 7'

10 ~~

(crn -2)

Figure 2 Experimental variation of the Lyman-alpha absorption cross section (cm2) with the optical depth in molecular oxygen, N(O2)(cm2).

part of the ultraviolet spectrum, the numerical error is reduced for the value of the total 02 photodissociation rate. Table 1 shows the variation of the mean absorption cross section based on the experimental data of DITCHBURN and YOUNG (1962), OGAWA (1971), HASSON and NICHOLLS (1971) and SHARDANANDand RAO (1977) and increasing from about 10 -24 cm 2 at 240 nm to 1.5 • 10 -23 cm 2 at 200 nm; this last value involves the 0-0 and 0-1 Schumann-Runge band absorption. The resulting j~(O2) from identical energy spectral ranges (500 c m - 1) shows a rapid increase from 240 nm to 230 nm (Table 1) and also a decrease at k < 210 nm. The problem of the solar flux values will be discussed in Section III. The Lyman-a absorption occurs in the wing of an 02 band and is subject to a temperature effect (CARVER et al., 1977). Its absorption cross section is a function of the temperature and of the 02 optical depth. Figure 2 shows how the absorption cross section varies f r o m 10 -2o cm 2 to 7 x 10 -21 cm 2 at T = 190~ (mesospheric temperature) for optical depths between 0 and 9. Lyman-c~ plays a role in the mesospheric photodissociation rate of several constituents, but particularly of H20, CH4 and CO2. It is responsible for the NO ionization in the mesosphere. Its variation with solar activity will be discussed in Section III. The problem of the 02 photodissociation in the Schumann-Runge band spectral range, and also of its atmospheric absorption has not yet reached its final solution. After various applications of the first experimental results to the atmosphere (HUDSON et al., 1969; KOCKARTS, 1971, 1976; HUDSON and MAHLE, 1972; FANG et al., 1974;

Vol. 118, 1980) Solar UV Radiation Absorption in Mesosphere and Stratosphere i

~

+

7

J

"-, 0 2 and 0 3

"~

tO

85kin

50

13 ~

40

1o 2~

02 MOLECULES

\

25

10~'

(crn 2}

Figure 3

PARK, 1974; MURAMATSU,1975; SHIMAZAKI et al., 1977), new experimental and theoretical results (LEwis et al., 1978; FREDER]CK and HUDSON, 1979; NICOLET and PEETERMANS, 1979) show that still more attention should be given to the accuracy problem. There is general agreement on the molecular constants used for the 02 SchumannRunge bands (cf. FANO et al., 1974) as known from experimental data obtained by ACKERMAN and BIAUM~ (1970) and by BRIX and HERZBERG(1954), and analyzed for the fine structure of the upper level 3Z~.,>0 by BERGEMAN and WOFSu (1972). Additional measurements with still higher resolution would be useful. But precise oscillator strengths and linewidths associated with exact line positions are an absolute necessity for accurate determination of the photodissociation processes, particularly in the mesosphere. From a comparative analysis (NICOLET and PEETERMANS, 1979) of the various parameters involved in the atmospheric 02 absorption, it can be concluded that there is no important direct effect of the Scbumann-Runge band absorption on the total J2 value in the stratosphere. If the ratio (Figure 3) of the photodissociation rate Js~B, resulting from the Schumann-Runge band spectral range of (175 nm < h < 200 nm) to the total photodissociation rate JSRB-H~RC, resulting also from the Herzberg continuum spectral region (175 nm < A < 242 nm) is greater than 80~ for a total number of 02 absorbing molecules N(O2) < 1020 cm-2; it is only between l0 and 15~ in the major part of the stratosphere. Furthermore, the essential fraction of this low percentage is due to bands corresponding to v' < 10. The (2-O), (3-0), (4-0), (5-O), (6-0) and (7-0) bands lead for N(O2) = 5 • 1021 cm -2 (stratopause neighborhood) to about 3, 3, 2.5, 2.5, 1.5 and 1.5~, respectively. Thus, the total error due to incorrect parameters in the Schumann-Runge band system cannot account for the importance of the stratospheric J2 value. On the other hand, any solar activity effect which might be introduced in the calculation of these J2 values for

8

Marcel Nicolet

(Pageoph,

Table 2 Parameters for determination of 02 optical depth Temperat~e:190~

Temperature:230~

Temperature:270~

B~d

~,o

~.1

~,o

~.1

~.o

~.1

19-0 18-0 17-0 16-0 15-0 14-0 13-0 12-0 11-0 10-0 9-0 8-0 7-0 6-0 5-0 4-0 3-0 2-0

-22.2647 -26.2477 -21.5859 -23.1643 -20.5035 -22.2214 -25.9576 -25.7030 -21.2361 -25.0795 -24.1337 -25.3090 -24.0797 -28.8867 -31.0862 - 34.4926 -41.5449 -49.2427

0.4938 0.5914 0.4877 0.5184 0.4512 0.4747 0.5466 0.5480 0.4553 0.5159 0.4957 0.4979 0.4845 0.5697 0.6078 0.6683 0.7963 0.9377

-20.511 -27.0032 -21.5692 -22.9975 -21.2109 -22.3230 -26.4881 -25.4172 -21.9458 -24.1133 -23.2161 -23.4269 -24.7619 -25.3433 -30.5188 -33.6523 -40.7366 -48.8488

0.4552 0.6070 0.4874 0.5160 0.4684 0.4808 0.5608 0.5442 0.4739 0.5009 0.4803 0.4848 0.5012 0.5042 0.6000 0.6549 0.7827 0.9304

-20.5433 -26.8968 -21.5642 -23.0408 -20.0262 --22.1773 -26.1471 -25.9842 -22.4196 -22.6346 -23.6780 -24.0370 -24.3381 -24.9085 -26.9407 - 33.1046 - 39.1489 -46.8581

0.4546 0.6036 0.4871 0.5176 0.4449 0.4807 0.5566 0.5575 0.4873 0.4751 0.4923 0.5015 0.4959 0.4989 0.5346 0.6474 0.7546 0.8944

A < 200 nm could play only a minor role corresponding to its 1070 contribution to the stratospheric photodissociation o f molecular oxygen. In the mesosphere, all S c h u m a n n - R u n g e bands between (2-0) and (19-O) must be considered. As an example, for N ( O 2 ) = 1020 cm -2, at and above 75 km, the (7-0) band corresponds to the m a x i m u m o f the order o f 107o while (2-0) and (15-O) have a less significant role, only between 1 and 2 ~ . It is permissible (see references above), therefore, to use simplified formulas in order to compute the J2 factors of various constituents for their stratospheric absorption. In their analysis, NICOLET and PEETERMANS(1979) have introduced, for the 02 mean optical depth, a polynomial function, N(O2) being the total n u m b e r of 02 molecules (cm - 2). In r(O2)b~nd = ~ d~ [In N(O2)] ~

(2)

~=0

which can be applied to almost all atmospheric problems with only two terms In r(O2)b~nd = do + d l In N(O2).

(3)

A formula with six terms has also been deduced, and leads to a complete agreement with the results of the detailed calculation. The numerical values do and dl are given in Table 2. They can be applied to stratospheric problems without any restriction, but they may require several improvements for mesospheric applications when the physical parameters are known with better accuracy. Nitric oxide is an exception since it

Vol. 118, 1980) Solar UV Radiation Absorption in Mesosphere and Stratosphere

9

requires a specific analysis (CIESLm and NICOLET, 1973; CIESLIK, 1977, 1978; FREDERICK and HUDSON, 1979; NICOLET and CmSLIK, 1979).

IlL The solar flux In the wavelength range of h > 175 nm, which is involved in mesospheric, stratospheric and tropospheric photodissociation processes, it has not yet been possible to identify solar flux variations associated with specific solar activity phenomena. First, fluctuations of the solar constant S = 137 + 1 m W c m - 2 have not been established by direct measurements; only a few of atmospheric phenomena have been associated with the bi-annual variation of 6.6~o in flux due to the variations of the Earth-to-Sun distance variation. Only Lyman-~ at 121.6 nm shows a clear evidence of an association of its intensity with solar activity controlled by identified chromospheric plages. It is not possible to examine here all rocket or satellite measurements made since 1949 (see FRIEDMAN, 1960; WEEKS, 1967; PRINZ, 1974; VIDAL-MADJAR, 1975, 1977). It is clear that a more precise absolute calibration of the total Lyman-~ line flux is still required; on the other hand, the profile measurements (TousEY, 1963; BRUNER and PARKER, 1969; BRUNER and RENSE, 1969; LEMAIRE et al., 1978; ARTZNER, 1978) indicate that the global profile is a variable average profile whose form is determined by various solar features between the center and the limb which are influenced by solar activity. Thus, a mean value of 3 x 1011 photons cm -2 sec -1 (see, for example, THOMAS and ANDERSON, 1976) for the Lyman-~ solar flux at the mean Earth-to-Sun distance is almost a conventional value, since the accuracy cannot be better than + 25~. I f we write q~(Lyman-~) = (3

+

1) x 101~ photons cm -2 sec -~

(4)

we may consider 2 x 10 ~ photons cm -2 sec -1 as a minimum working value and 4 x 1011 photons cm -2 sec -1 as an acceptable maximum value corresponding to quiet Sun and active solar conditions, respectively. There is, therefore, a variation of a factor of the order of 2 over an average solar cycle. As far as the variations of the Lyman-~ intensity associated with short-term fluctuations (27 days, for example) are concerned, it seems reasonable to use as an indication the preliminary empirical relations established by VIDAL-MADJAR (1975). We consider that the Lyman-~ flux variations with solar activity represent the maximum possible differences that can occur in the solar flux at ,~ > 100 nm. Furthermore, there is no astrophysical result leading to such possibilities at ~ > 175 nm, except for a few emission lines of relatively low intensity related to solar plages. However, a recent review by HEATH and THEKAEKARA (1977) describes various observational results obtained between 1964 and 1975 which would indicate a variation of a factor of the order of 2 at 200 nm and not less than 4 +__ 10~ at 300 nm. On the

10

Marcel Nicolet

(Pageoph,

Table 3 Solar flux (q| photons cm -2 sec-a), mean absorption cross section (~MAXcm 2) at T = 230~ and 02 photodissociation coefficients (j, sec- 1) at the top o f the Earth's atmosphere in the spectral range o f the 02 Schumann-Runge bands

02 band

q~

ouAx

19-0 18-0 17-0 16-0 15-0 14-0 13-0 12-0 11-0 10-0 9-0 8-0 7-0 6-0 5-0 4-0 3-0 2-0

1.58 x 101~ 2.23 2.80 3.66 5.18 6.60 8.79 1.03 x 1011 1.43 2.07 2.09 2.56 3.96 4.63 6.38 7.16 1.14 • 1012 1.54

7.52 1.41 1.71 1.64 1.44 1.28 9.91 7.14 4.91 3.17 2.02 1.16 6.06 2.86 1.16 4.05 1.29 3.88

]= x 10 -20 x 10 -19

• 10 -2o

x 10 -21 x 10 -22 x 10 -2a

1.19 • 10 -9 3.14 4.79 6.00 7.46 8.45 8.71 7.35 7.02 6.56 4.22 2.97 2.40 1.32 7.40 • 10 -1~ 2.90 1.47 5.98 • 10 -11

other h a n d , SIMON (1978) and DELABOUDINII~RE et aL (1978) do not reach the conclusion t h a t there is any such variability d u r i n g the 11 year cycle. I n fact, if we examine the o b s e r v a t i o n a l results o b t a i n e d in the ultraviolet region from the first rocket m e a s u r e m e n t s to the last o b s e r v a t i o n a l results, we can see t h a t there is a systematic decrease in the observed values o f this solar ultraviolet flux. F u r t h e r m o r e , if we consider only the m o r e recent o b s e r v a t i o n a l d a t a in the spectral r a n g e o f the 0 2 S c h u m a n n - R u n g e b a n d system (ROTTMAN, 1974; SIMON, 1975; SAMA1N and SIMON, 1976; HEROUX a n d SWIRBALUS, 1976; BRUECKNER et al., 1976), it is clear t h a t the e s t i m a t e d precision in the flux m e a s u r e m e n t is o f the o r d e r o f +_20~. Thus, a n y m e a n value a d o p t e d for this spectral region reflects the lack o f accuracy resulting from the d u b i o u s c h a r a c t e r o f absolute calibrations, and also from the limited precision due to various uncertainties in l a b o r a t o r y a n d a t m o s p h e r i c m e a s u r e m e n t s in this spectral region. Consequently, it must be said that any solar activity effect l e a d i n g to a possible variation o f the solar flux c a n n o t yet be distinguished f r o m differences between various observations, even if they have been analyzed after discussion between observers. There is no clear indication leading to a perfect choice for m e a n o r specific values o f the solar flux in this spectral region leading to the 02 p h o t o d i s s o c i a t i o n. The a d o p t e d numerical values given in Table 3 should be accepted as p r o v i s i o n a l values, since the accuracy c a n n o t be given and the precision c a n n o t be better than _+2 5 ~ . They indicate, however, an increase in the solar flux f r o m 175 nm to 200 nm o f the o r d e r o f a factor o f l0 for identical spectral ranges (Av = 500 c m - 1) a n d o f a b o u t a

Vol. 118, 1980)

Solar UV Radiation Absorption in Mesosphere and Stratosphere l

I

I

X

X

X

&

&

X

X

X

X

I

X

0

XX

9

o~ ~

~l~

X

X

~

~

(

'

X

i

k

X

X

g e~ t

X

X

~

l

~

~ l ~

X

~,

11

12

Marcel Nicolet

(Pageoph,

f a c t o r o f 100 f r o m (19-O) to ( 2 - 0 ) b a n d ranges. Nevertheless, it is n o t excluded that a systematic e r r o r o f 50700 c o u l d exist in a p a r t i c u l a r d o m a i n o f this spectral region. I n a n y case, reference m u s t be m a d e to the o b s e r v a t i o n a l results (BRUECKNER et aL, 1976) on the v a r i a t i o n o f the solar flux in the spectral range o f the S c h u m a n n - R u n g e b a n d s due to solar activity ( a b o u t 5700). I n the region o f the 0 2 H e r z b e r g c o n t i n u u m , 200 n m < A < 242 nm, several a t m o s p h e r i c m e a s u r e m e n t s have been m a d e (see SIMON, 1978). The values a d o p t e d here are b a s e d essentially on d a t a p u b l i s h e d b y BROADrOOT (1972) a n d SIMON (1975) a n d have been given in T a b l e 1 with the related 02 a b s o r p t i o n cross sections for 500 c m - 1 spectral ranges. M o r e observations are needed to i m p r o v e the accuracy o f the a d o p t e d values, even if it seems t h a t the precision is better t h a n at h < 200 nm. I n the spectral region covered by the H a r t l e y b a n d f r o m 242 n m to 310 nm, we have also a d o p t e d r o c k e t d a t a by BROAOFOOT (1972) with the values o b t a i n e d by b a l l o o n m e a s u r e m e n t s (SIMON, 1975) at ,~ > 284 n m in o r d e r to a v o i d certain discrepancies between v a r i o u s o b s e r v a t i o n a l d a t a p a r t i c u l a r l y in the spectral region 200--400 n m (see DE LuIsI, 1975; SIMOr~, 1978). T h e a d o p t e d results (NICOLET, 1975) a r e given in T a b l e 4 with the c o r r e s p o n d i n g O3 cross sections a n d p h o t o d i s s o c i a t i o n rates. Besides, in the ultraviolet region, c o r r e s p o n d i n g to the Huggins bands, it is necessary to i n t r o d u c e in the n u m e r i c a l values a s m o o t h t r a n s i t i o n f r o m a b o u t 300 nm, Table 5 Solar flux (q, photons cm -2 sec -1) with average cross section (o, cm 2 for AA = 5 rim) and 03 photodissociation coefficient (j, sec- 1) in the spectral range o f the 03 Huggins bands, at the top o f the Earth's atmosphere

A(A)

q~

~ros

3100 3150 3200 3250 3300 3350 3400 3450 3500 3550 3600 3650 3700 3750 3800 3850 3900 3950 4000 4050

4.95 • 1014 5.83 6.22 6.96 8.61 8.15 8.94 8.44 8.69 9.14 8,23 1.07 • I0 is 1.08 9.72 1.11 8.98 1.18 9.34 1.69 1.70

1.05 5.23 2.91 1.50 7.78 3.72 1.71 7.46 2.66 1.09 5.49

j~ x 10 -1~ • 10 -20

x 10 -21 x 10 -22 • 10 -23

5.20 3.05 1.81 1.04 6.70 3.03 1.53 6.30 2.31 9.96 4.52

• 10 -5

x 10 -6 x 10 -v • 10 -s

Vol. 118, 1980)

Solar U V Radiation Absorption in Mesosphere and Stratosphere Table 6

Solar flux (q photons c m - 2 s e c -1) with average cross section (%cm 2 for A)t = 5 rim) and 03 photodissociation coefficient (j, sec -1) in the spectral range o f the Chappuis bands )t(nm)

q~

400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530 535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625

1.69 1.70 1.84 1.97 1.95 1.81 1.67 1.98 2.02 2.18 2.36 2.31 2.39 2.38 2.39 2.44 2.51 2.30 2.39 2.48 2.40 2.46 2.49 2.32 2.39 2.42 2.55 2.51 2.49 2.55 2.53 2.54 2.50 2.57 2.58 2.67 2.67 2.70 2.62 2.69 2.63 2.68 2.66 2.59 2.69 2.61

j~(03)

5.35 6.19 7.78 1.18 1.14 1.71 2.25 3.25 4.04 4.90 8.53 8.76 9.70 1.19 1.78 1.94 1.98 2.25 2.93 3.99 3.93 3.71 4.25 5.01 6.50 6.88 7.17 7.83 8.02 8.53 9.70 1.11 1.20 1.27 1.21 1.17 1.16 1.24 1.29 1.30 1.21 1.10 1.05 9.40

x 10 -8

x 10 -7

x 10 -6

x 10 -5

x 10 -6

)t(nm)

q|

j~o(03)

630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720 725 730 735 740 745 750 755 760 765 770 775 780 785 790 795 800 805 810 815 820 825 830 835 840 845 850

2.62 2.62 2.63 2.60 2.55 2.48 2.57 2.61 2.61 2.62 2.62 2.57 2.52 2.60 2.58 2.52 2.51 2.48 2.45 2.48 2.45 2.44 2.39 2.40 2.41 2.40 2.38 2.34 2.32 2.30 2.33 2.34 2.29 2.29 2.27 2.27 2.20 2.22 2.18 2.20 2.14 2.14 2.13 2.09 2.05

8.99 x 10 -6 8.31 7.21 6.79 6.17 5.46 5.19 4.83 4.36 4.03 3.72 3.21 2.82 2.65 2137 2.12 1.93 1.73 1.54 1.41 1.29 1.16 1.07 1.01 9.04 x 10 -7 7.80 6.95 6.46 6.26 6.44 6.64 2.90 5.04 4.17 3.70 3.97 4.18 4.11 3.71 3.34 3.04 3.00 2.98 2.97 2.97

13

14

Marcel Nicolet

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in the range of the spectral limit of observational data obtained by BROADFOOT(1972), to 400 nm where the solar flux data obtained by ARVES~N et al. (1969) can be accepted if the published values are reduced to a lower solar constant value (NICOLET, 1975). Such data for AA = 5 nm are given in Table 5. New measurements of the solar flux between 300 nm and 400 nm would be useful in helping to improve the accuracy of absolute values. Finally, the solar flux which is adopted in the visible region corresponds to the numerical values adjusted to the present value of the solar constant (NICOLET, 1975) and deduced also from observational data published by ARVESEN et al. (1969). They are given in Table 6 with the corresponding values of the 03 photodissociation rates corresponding to the Chappuis bands. Since the experimental cross sections of the 08 visible band are certainly good and are not subject to a temperature effect, the total photodissociation rate J3 (Chappuis) = 3.4 • 10-4 sec- 1 seems to be accurate; the total error ( < + 107o) corresponds to the accuracies of the solar flux observations and of the experimental 03 absorption cross sections. In the region of the 08 Huggins bands, where the temperature effect on the absorption cross section value is significant, new solar observations and laboratory measurements are certainly needed. IV. Photodissociation rates

The spectral distribution of the 02 photodissociation has been discussed in its general form corresponding essentially to two spectral ranges for the mesosphere and stratosphere: the Schumann-Runge band system and Herzberg continuum. The action of Lyman-% with an average value of about 3 • 10 -9 sec-t for its photodissociation coefficient at the mesopause, must be introduced in the upper mesosphere. As far as the ozone is concerned the whole spectrum at 2, > 200 nm must be considered, and at low levels the Rayleigh scattering, atbedo and aerosol effects must be considered particularly on account of their action on the spectral regions of wavelengths greater than 300 nm. We cannot discuss here the behavior of all photodissociation rates, but we may consider only typical examples. A few tables which give the respective percentages Table 7 Photodissociation o f water vapor

N(O2) (cm -2) 1 x 1 x

10 I~ 10 TM

2.5 5 1 • 1020 2.5 5 1 •

1021

Lyman-~ (Line) 70

SRC (Continuum) %

SRB (Bands) 70

58 87 88 88 86 70 27

31 0

11 13 12 12 14 30 73 95

1

Vo1.118,1980)

Solar U V Radiation Absorption in Mesosphere and Stratosphere Table 8

Photodissociation of carbon dioxide

N(O2)

Lyman-a (Line)

SRC (02 continuum)

SRB (02 bands)

(cm- 2)

%

%

%

1 x 1016 1 x 1019

20 96

79 0

2.5 5 1 x 1020 2.5 5

96 96 95 88 53

1 x 1021

2

2.5

0

1 4

4 4 5 12 47 98 100 Table 9 Photodissociation of nitrous oxide

N(O~) (cm -2) 1 x 1016 1 • 1019

SRC (02 continuum)

SRB (02 bands)

Herzberg (02 continuum)

%

%

%

59 0

28 77 63 57 45 40 36 33 25 14 3

13 33 37 43 55 60 64 67 75 86 97

1 x 102~ 1 • 1021 ] • 1022 2.5 5 1 • 1022 2.5 5 1 • 1024

Table 10 Photodissociation of nitric acid

N(O2)

SRB (02 bands)

Herzberg (02 continuum)

Hartley (03 band)

Huggins (03 bands)

(cm- 2)

%

%

%

%

1 • 1016 1 • 1019

49 48 45 40 34 31 28 23 6 0 0

36 37 39 43 54 59 59 53 19 1 0

14 14 15 16 11 8 9 13 28 29 26

1

1 • 1020 1 •

IO 2~

1 • 1022 2.5 5 1 • 10 za 2.5 5 1 • 1024

1 1 1

1 2 4 11 47 69 74

15

16

Marcel Nicolet

(Pageoph,

T a b l e 11

Photodissociation o f carbon tetrachloride N(Os) (cm -2)

SRB (02 bands)

Herzberg (02 continuum)

%

% 67 70 76

1 x 1016

33

1 x 1019

30

1 x 1020 1 x 102t 2.5 5 1 x 1022 2.5 5

24 17 14 12 11 10 10

1 x 102a

10

2.5 5 1 x 1024

83

86 88 89 90 90 90 92 96 99

8 4 1

Table 12

Photodissociation of methyl chloride N(02) (cm -2)

SRB (02 bands)

Herzberg (02 continuum)

%

%

1 • 1018 1 x 1019 1 x 1020 2.5 5 I x 1021 1 • l022 2.5 5 1 x 102a 2.5 5

92 90 88 86 84 82 67 59 52 44 35 21

8 10 12 14 16 19

1 x 102~

5

33

41 48 56 65 79 94

Vol. 118, 1980) Solar UV Radiation Absorption in Mesosphere and Stratosphere

17

T:~ble I3

Trichlorofluoromethane photodissociation N(O2) (cm -2) 1 x 1016 1 x 10TM

1 x 1020 1 x 1021 2.5 5 1 x 1022. 2.5 5 1 x 1023 2.5 5 1 x 102~

SRB (02 bands) ~o

Herzberg (O~ continuum)

%

65

35

63 58 50 46 42 38 32 29 27 20 11

37 42 50 54 58 62 68 71 73 80 89 98

2

Table 14

Dichlorodifluoromethane photodissociation N(02) (cm -~) 1 x 10I6 1 x 1019

1 x 1020 1 x 1021 2.5 5 1 x 1022 2.5 5 1 x 1023 2.5 5 1 x 1024

SRB (02 bands) ~ 93 93 90 87 83 79 75 67 61 53 43 28 8

Herzberg (02 continuum)

% 7 7

10 13 17 21 25 33 39 47 57 72 92

related to the various spectral ranges lead to clear indications a b o u t their specific roles. It is particularly i m p o r t a n t to consider the respective percentages related to the spectral ranges of the 02 S c h u m a n n - R u n g e b a n d system (A < 200 nm) and of the 02 Herzberg c o n t i n u u m (~ > 200 nm). The variation of the solar flux with solar activity m a y be different in these two spectral regions. It is also i m p o r t a n t to consider the variation with altitude, i.e. with the total n u m b e r of 02 molecules. Each constituent has a different behavior.

18

Marcel Nicolet

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REFERENCES ACKERMAN, M. and BIAUME, F. (1970), Structure of the Schumann-Runge bands from the 0-0 to the 13-0 band, J. Mol. Spectr. 35, 73. ARVESEN, J. C., GRIFFIN,R. N., Jr. and PEARSON,B. D. (1969), Determination of extraterrestrial solar spectral irradiance from a research aircraft, Appl. Optics 8, 2215. ARTZNER,G. (t978), The solar H-Lyman-alpha line: Wavelength and profile measurement, Astron. Astrophys. 70, L11. BERGEMAN,T. H. and WOFSY, S. C. (1972), The fine structure of 02(B3~a), Chem. Phys. Letters 15, 104. BRIx, P. and HERZBERG,G. (1954), Fine structure of the Schumann-Runge bands near the convergence limit and the dissociation energy of the oxygen molecule, Canad. J. Phys. 32, 110. BROADFOOT,A. L. (1972), The solar spectrum 2100-2300 ,~, Astrophys. J. 173, 681. BRUECKNER,G. E., BARTOE,J. D. F., MOE, O. K. and VANHOOSIER,M. E. (1976), Absolute solar ultraviolet intensities and their variations with solar activity, Part I: The wavelength region 1750 A-2100.4, Astrophys. J. 209, 935. BRUNER, E. C., Jr. and PARKER,R. W. (1969), Hydrogen geocorona and solar Lyman-alpha line 1. Rocket measurement of the solar line profile, J. Geophys. Res. 74, 107. BRUNER, E. C., Jr. and RENSE, W. A. (1969), Rocket observations of profiles of solar ultraviolet emission lines, Astrophys. J. 157, 417. CARVER,J. H., GIES, H. P., HOBBS, T. I., LEWIS, B. R. and McCoY, D. G. (1977), Temperature dependence of the molecular oxygen photoabsorption cross section near the H Lyman alpha line, J. Geophys. Res. 82, 1955. CIESLIK, S. (1977), Ddtermination expdrimentale des forces d'oseillateur dans les principales bandes des syst~mes fl, ~, o et e de la molkcule NO, Bull. Cl. Sci., Acad. Roy. Belg. 63, 884. CIESLIK,S. (1978), Sections eJ~qcaces d'absorption int~gr~es des tales des bandes ~ et e de la moldcule NO, Bull. C1. Sci., Acad. Roy. Belg. 64, 265. CIESLIK, S. and NICOLET, M. (1973), The aeronomic dissociation of nitric oxide, Planet. Space Sci. 21, 925. I)ELABOUDINIERE,J. P., DONNELLY, R. F., HINTEREGGER,n . E., SCHMIDIKE,G. and SIMON,P. C. (1978), [ntercomparison/compilation of relevant solar flux data related to aeronomy. COSPAR Technique Manual No. 7. DE LuIsI, J. J. (1975), Measurements of the extraterrestrial solar radiant flux from 2981 to 4000/~ and its transmission through the Earth's atmosphere as it is affected by dust and ozone, J. Geophys. Res. 80, 345. DITCHBURN, R. W. and YOUNG, P. A. (1962), The absorption of molecular oxygen between 1850 and 2500 Ar, J. Aim. Terr. Phys. 24, 127. FANG, T. M., WOFSY,S. C. and DALGARNO,A. (1974), Opacity distribution functions and absorption in Schumann-Runge bands of molecular oxygen, Planet. Space Sci., 22, 413. FREDERICK, J. E. and HUDSON, R. D. (1979), Predissociation linewidths and oscillator strengths for the (2-0) to (13-0) Schumann-Runge bands of 02, J. Molec. Spec. 74. FRIEDMAN, H. (1960), The Sun's ionizing radiations, Chap. 4 in Physics of the Upper Atmosphere, ed. J. A. Ratcliffe, Academic Press, New York. HASSON, V. and NICHOLLS,R. W. (1971), Absolute spectral absorption measurements on molecular oxygen from 2640-1920 .~: II. Continuum measurements 2430-1920 A', J. Phys. B. Atomic Molec. Phys. 4, 1789. HEATH, D. H. and THEKAEKARA,M. P. (1977), The solar spectrum between 1200 and 3000/~, p. 193 in The Solar Output and its Variation, ed. O. R. White, Colorado Ass. Univ. Press, Boulder. HEROUX, L. and SWIRBALUS,R. A. (1976), Full-disk solar fluxes between 1230 and 1940 ,~, J. Geophys. Res. 81, 436. HUDSON, R. D., CARTER,V. L. and BREIG, E. L. (1969), Predissociation in the Schumann-Runge band system of 02: laboratory measurements and atmospheric effects, J. Geophys. Res. 74, 4079.

Vol. 118, 1980) Solar UV Radiation Absorption in Mesosphere and Stratosphere

19

HUDSON, R. D. and MAHLE, S. H. (1972), Photodissociation rates of molecular oxygen in the mesosphere and lower thermosphere, J. Geophys. Res. 77, 2902. KOCKARTS, G. (1971), Penetration of solar radiation in the Schumann-Runge bands of molecular oxygen, in Mesospheric Models and Related Experiments, ed. G. Fiocco, Reidel Publ. Cy., Dordrecht-Holland, pp. 160-176. KOCKARTS,G. (1976), Absorption and photodissociation in the Schumann-Runge bands of molecular oxygen in the terrestrial atmosphere, Planet. Space Sci. 24, 589. LEMAIRE,P., CHARRA,J., JOUCHOUX,m., VIDAL~ A., ARTZNER,G. E., VIAL,J. C., BONNET, R. M. and SKUMANICH,A. (1978), Calibrated fill disk solar HI Lyman-a andLyman-[3 profiles, Astrophys. J. 223, L55. LEWIS,B. R., CARVER,J. H., HOBBS,T. I., McCoY, D. G. and GIEs, H. P. F. (1978), Experimentally determined oscillator strengths and linewidths for the Schumann-Runge band system of molecular oxygen. L The (6-0)-(14-0) bands, J. Quant. Spectrosc. Radiat. Transfer 20, 191. MURAMATZtr,H. (I 975), Dissociation rates of oxygen and ozone molecules in the stratosphere and mesosphere, Papers in Met. Geophys. 26, 219. NICOLET, M. (1975), Stratospheric ozone: an introduction to its study, Rev. Geophys. Space Phys. 13, 593. NICOLET, M. and CIESLtK,S. (1979), The atmospheric problem of the nitric oxide dissociation, Planet. Space Sci. (to be published). NICOLET, M. and PEETERMANS, W. (1979), Atmospheric absorption in the 02 Schumann-Runge band spectral range and Oz total photodissociation rates in the stratosphere and mesosphere, Planet. Space Sci. (to be published). OGAWA, M. (1971), Absorption cross sections of 02 and CO2 continua in the Schumann and far-UV regions, J. Chem. Phys. 54, 2550. PARK, J. H. (1974), The equivalent mean absorption cross sections for the 02 Schumann-Runge bands: Application to the H20 and NO photodissociation rates, J. Atm. Sc. 31, 1893. PRINZ, D. K. (1974), The spatial distribution of Lyman-a on the Sun, Astrophys. J. 187, 369. ROTTMAN, G. R. (1974), Disc values of the solar ultraviolet flux, 1150 to 1900 ,~, EOS 56, 1157. SAMAIN, D. and SIMON, P. C. (1976), Solar flux determination in the spectral range 150-210 nm, Solar Phys. 49, 33. SHARDANANDand PRASADRAO, A. D. (1977), Collision-induced absorption of 02 in the Herzberg continuum, J. Quant. Spectrosc. Radiat. Transfer 17, 433. SHIMAZAKI,T., OGAWA,T. and FARRELL,B. C. (March 1977), Simplified methods for calculating photodissociation rates of various molecules in the Schumann-Runge band systems in the upper atmosphere, MASA Tech. Note TN D-8399. SIMON, P. C. (1974), Balloon measurements of solar fluxes between 1960 and 2300 ,~, in Proceedings of the third conference on the climatic impact assessment program (eds. Broderick and Hard), p. 137, DOT-TSC-OST-74-15. SIMON, P. C. (1975), Nouvelles mesures de l'ultraviolet solaire dans la stratosphkre, Bulletin Acad. Roy. Belg., C1. Sci. 61, 399. SIMON, P. C. (1978), Irradiation solar flux measurements between 120 and 400 nm. Current position and future needs, Planet. Space Sci. 26, 355. THOMAS, G. E. and ANDERSON, D. E., Jr. (1976), Global atomic hydrogen density derived from OGO-6 Lyman-a measurements, Planet. Space Sci. 24, 303. TotrsEv, R. (1963), The extreme ultraviolet spectrum of the Sun, Space Sci. Rev. 2, 3. VIDAL-MADJAR, m. (1975), Evolution of the solar Lyman-alpha flux during four consecutive years, Solar Phys. 40, 69. VIDAL-MADJAR,A. (1977), The solar spectrum at Lyman-alpha 1216 A*, p. 123 in The Solar Output and its Variation, ed. O. R. White, Colorado Ass. Univ. Press, Boulder. WEEKS, L. I-I. (1967), Lyman-alpha emission from the Sun near solar minimum, Astrophys. J. 147, 1203. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh~iuser Verlag, Basel

Annual Variation of the Effects of Diffuse Radiation on the Photodissociation of Ozone By PAOLO PETRONCELLI1), GIORGIO FIOCCO 1) a n d ALBERTO MUGNAI 2)

Abstract - Previous work has shown the importance of the diffuse solar field in the photochemistry of atmospheric active species, the solar zenith angle being an effective parameter. In view of the diurnal and seasonal variability of this single quantity, in this paper estimates are presented of the daily-integrated values of the photodissociation coefficient of ozone throughout the year, for a purely molecular atmosphere in the absence of scattering and when the effects of molecular scattering are included, and for an absorbing-scattering turbid atmosphere characterized by two different aerosol loads. Also, different values of the ground albedo have been taken into account. Results are shown for a latitude of 45~ The seasonal dependence is strong at altitudes below 20 km and less marked above 20 km. For an albedo A = 0.3, the inclusion of molecular scattering increases the daily-integrated photodissoeiation coefficients approximately by 20% and 40% at 15 km and by 15% and 22% at 30 kin, at the winter and summer solstice respectively. The presence of a heavy aerosol load modifies these results by a further factor which is approximately - 5 % and 107o at 15 km at the winter and summer solstice respectively, and is approximately constant at 870 throughout the year at 30 kin.

Key words: Ozone; Diffuse radiation influence.

1. I n t r o d u c t i o n

Several a u t h o r s have recently studied the effect o f t h e solar r a d i a t i o n diffused by the m o l e c u l a r a t m o s p h e r e and by the g r o u n d on the p h o t o d i s s o c i a t i o n o f active a t m o s p h e r i c species (e.g. LUTHER a n d GELINAS, 1976; CALLIS et al., 1976; ISAKSEN et al., 1977; KURZEJA, 1977; LUTHER et al., 1978; PITARI a n d VISCONTI, 1979), due to its relevance in stratospheric p h o t o c h e m i c a l modeling. F I o c c o , MU6NAt and FORUZZl (1978, F M F hereafter) and MucNAI, PETRONCELLI a n d F I o c c o (1979, M P F hereafter) have extended these analyses by considering the effects o f the diffuse r a d i a t i o n , respectively on the p h o t o d i s s o c i a t i o n o f Oa and o f NO2, NOa, H N O a and H202, u n d e r c o n d i t i o n s o f a t m o s p h e r i c t u r b i d i t y r a n g i n g f r o m purely m o l e c u l a r to heavy particulate loads, and assuming different values o f the g r o u n d a l b e d o a n d o f the solar zenith angle. The effects o f diffuse r a d i a t i o n are particularly evident a n d are 1) UniversitY., lstituto di Fisica, Roma, Italy. 2) Laboratorio Plasma Spazio, CNR, Frascati, Italy.

Vol. 118, 1980) Effectsof Diffuse Radiation on the Photodissociationof Ozone

21

felt over a wide region of altitudes for those species, such as 03 and NO2, that have appreciable values of the photodissociation cross-section in the visible portion of the spectrum. The physical mechanism encompassed by the analyses of FMF and MPF results from the coupling of two factors, i.e. the ground reflectivity and the scattering and absorption by the overlaying turbid atmosphere. At stratospheric heights, for low values of the ground albedo the presence of the aerosol generally leads, because of scattering, to an increase of the total radiation field thus enhancing the photodissociation; on the other hand, at large values of the albedo the main effect of the aerosols is to attenuate the radiation going into and coming from the ground thus reducing the photodissociation. The contribution of the diffuse solar radiation can be introduced in the analysis with varying degrees of complexity, depending on the amount of detail and accuracy required. Previous work indicates that the solar zenith angle is an important variable, at large angles the effects of atmospheric extinction being conspicuously enhanced. Also it does not appear possible, especially in the case of heavy particulate loads, to deduce daily and seasonal averages of the photodissociation coefficients on the basis of a calculation performed at a fixed zenith angle, and it is necessary, for accurate estimates to go through a detailed integration considering the time variation of the zenith angle. In this paper the daily-integrated photodissociation coefficients of ozone have been calculated, for a standard ozone concentration profile, as a function of the day throughout the year, by utilizing the radiative-transfer numerical procedures described in FMF and MPF. Results are shown for various aerosol loads and for different values of the ground albedo. Four additional sets of calculations have also been performed in order to establish the sensitivity of the daily-integrated photodissociation coefficients to the seasonal variation of the ozone concentration profile.

2. Analysis The theory and computational techniques utilized to obtain the direct and diffuse components of the solar flux, which combine to give the total flux, are described in detail in the previous publications, FMF and MPF. Here it will suffice to say that through a radiative transfer algorithm for a plane-parallel, absorbing-scattering atmosphere (GRANTand HUNT, 1969; WISCOMBF, 1976a,b), we have calculated the direct, diffuse and total flux of solar radiation, Fdir(A, 3A), Fdi~(A, 3A) and Ftot(A, 3A) respectively, in the spectral interval 3A around the wavelength Aand entering a sphere of unit section, as a function of the altitude, z, and of the solar zenith angle~ ~. I-n these computations the solar flux in the spectral interval 3A outside the Earth's atmosphere has been taken from the tabulation of THEKAEKARA(1973) r162 refers to a distance from the Sun of one astronomical unit.

22

Paolo Petroncelli, Giorgio Fioceo, and Alberto Mugnai

(Pageoph,

Thus the photodissociation coefficient of 03 in the spectral interval 8A, J(A, 3A), has been obtained as follows: J(A, 8A) = q(?~, 8A)a(A)

(1)

where a(A), the photodissociation cross-section of Oa averaged in the interval 3A, coincides with the absorption cross-section of 03 averaged in the same spectral interval and q()t, 8~), the average number of photons per unit time in the spectral interval 3Aentering a sphere of unit section, has been obtained from the flux computation as follows: q(A, 8A) = 3a~'(A,3A)/he

(2)

F is generically the solar flux; h and c are Planck's constant and the speed of light respectively. Results are given in this paper integrated over the entire spectral region AAr where the ozone is photodissociated: J(AA~) = ~ S(A, 3~).

(3)

The computations were carried out in the spectral region A~r = 2000-7300 A, because of the large absorbtion by 02 in the upper atmosphere for A < 2000 A, and because the photodissociation of ozone for A > 7300 A was considered negligible. The spectral region A,~r has been subdivided in 112 intervals 3A, corresponding to those utilized from ACKERMAN(1971). Also the absorption cross-sections of 03 have been taken from that publication. As for the determination of the particles optical parameters, i.e. the scattering and the absorption coefficients and the phase function, calculations have been carried out only at 14 wavelengths across AAr because these quantities are slowly-varying with frequency. According to the successive degrees of detail introduced in computing the radiative field, the following values for the photodissociation coefficient can be calculated: Jo: is the photodissociation coefficient due to the direct solar flux for a purely molecular atmosphere in the absence of scattering; Jm: is the photodissociation coefficient due to the total flux, direct and diffuse, when the effects of molecular scattering and ground diffuse reflectivity are included ; Jx: is the photodissociation coefficient taking into account the effects of the molecules, of the ground and of an aerosol load of type x ( x = a, c) according to Table 1. Table 1 Aerosol loads

Case m a c

Troposphere

hazyt)

Stratosphere

no aerosol average*) heavyMt. Agung 0~

*) ELTERMAN (1968) 1") 1V[CCLATCHEYet al. (1970) 5) CADLEet al. (1976)

Vol. 118, 1980) Effects of Diffuse Radiation on the Photodissociation of Ozone

23

The time integration of J performed over a 24 hour interval, taking into account the time-variation of the solar zenith angle x(t), gives the daily integrated value

Lo,m,x(D) = e(D) [ Jo,m,x[x(D,t)] dt J1 d a y

(4)

where D indicates the particular day of the year (D = 0 corresponds to January 1 and D = 364 to December 31) and E(D) is a coefficient accounting for the variation of the Sun-Earth distance. A yearly averaged value for the L's has been also computed as follows: [-'o

m x

' '

1 864 = 365 ~ D=0

L,,,m,.(D).

(5)

In order to single out the effects of atmospheric scattering and ground diffuse reflectivity and further separate the contributions of the aerosol load from those of the molecular atmosphere, results will be presented separately for Lo and for the ratios Lm/Zo and LxlLm, so that Lx will be obtained by the product: Lm L~

L= = Lo Lo L,~"

(6)

A limitation of these computations relates to the assumption of a plane parallel atmosphere in the radiative transfer calculation. Evidently this assumption breaks down for high values of the solar zenith angle and may lead to inaccuracies in the L values when applied to high latitude conditions, particularly during winter. The results shown in this paper refer to a latitude of 45 ~ The flux computations were stopped at a solar zenith angle X = 85~ at X = 90~ the corresponding J values were taken equal to zero and a linear interpolation was adopted in the interval 85 ~ < X<90

o.

As in previous works three values of the ground albedo have been considered, namely A = 0, 0.3, 0.7, covering the range of variation expected for this variable. In particular, the value A = 0.7, typical for snow cover, can be also regarded in a rough but sensitive way as indicative of a low tropospheric cloud layer. The model would certainly benefit by a more accurate characterization of the clouds, but their detailed insertion into the analysis would presently largely add to the complexity of the calculation due to the large variety of their geometries and properties. Elements of control of the atmospheric turbidity are the concentration of aerosols, their characteristics and in particular the imaginary part of their refractive index, all quantities subject to change in the real atmosphere. As regards the aerosol load, we have considered several cases including those analyzed in F M F and MPF but have resolved to present here the results for the situations described in Table 1. Case m has no aerosol and the atmosphere is purely molecular. Case a is based on the attenuation data of ELTERMAN (1968) and is indicative of an average aerosol load. Case c is an example of heavy aerosol load at all heights: the heavy stratospheric

24

Paolo Petroncelli, Giorgio Fiocco, and Alberto Mugnai

". |

X

x x

0.8

Ill

15 km x

\\

(Pageoph,

"-.

----

\

30

km

.c

.... --_O

r.)

x\

O~ 0.2

W I N T E R _ _ \ \1 I

O'

i

i

~

-

5UMMER'-~\\I~ ~---

o

A

9

8

HOURS

AFTER

MIDDAY

Figure 1 Daily variation of the photodissociation coefficients, J~, at the winter and summer solstices at the latitude 45~ and for a surface albedo A = 0.3. Results refer to a purely molecular atmosphere, both in the absence of scattering (x = o) and when the effects of molecular scattering and ground reflectivity are included (x = m), and to an absorbing-scattering turbid atmosphere characterized by a heavy aerosol load as in Table 1 (x = c). Solid lines refer to the height of 15 km and dashed lines to the height of 30 kin.

aerosol layer a r o u n d 20 km is that existing at the latitude o f 0 ~ 300 days after the 1963 Mt. A g u n g eruption, according to CADLE et al. (1976), while the tropospheric profile is based on the hazy attenuation case o f McCLATCHEY et al. (1970). The concentration profiles are depicted in Fig. 1 o f either F M F and M P F and are not reproduced here. The composition o f the particles was assumed to be dust in the troposphere and a mixture o f dust and impure sulphuric acid droplets with a mass ratio 1 to 2 in the stratosphere; their detailed characteristics are given in either F M F and M P F . In the majority of the calculations the quantities related to the molecular atmosphere, including the ozone profile, were considered fixed in time during the year, and only the solar zenith angle x and dilution factor ~ were allowed to change. For these computations the atmospheric data were taken from the U.S. Standard Atmosphere Supplements 1966.

Vol. 118, 1980) Effects of Diffuse Radiation on the Photodissociation of Ozone

25

In an additional series of calculations, which is reported in the final part of this paper, we have tried to establish the range of variability of the photodissociation coefficients, by taking into account the seasonal variation of the ozone concentration profile according to the seasonally adjusted values reported by D~TSCH (1978). The other atmospheric quantities, whose seasonal variation however has only a modest effect, were taken according to the seasonal models of the U.S. Standard Atmosphere Supplements 1966.

3. Time integration of the photodissociation coefficients with constant atmospheric conditions To help in the interpretation of the results let us remember that the J coefficient of ozone in the spectral range from 2000 to 7300 A is obtained by the sum of two components, namely: the Hartley component giving the photolysis in the strongly absorbing region 2000 A < A < 3100 A, and the Huggins-Chappuis component giving the photolysis in the weakly absorbing regions 3100 A < A < 3600 A and 4100 A < A < 7300 A. In the upper stratosphere the Hartley J component prevails, while the Huggins-Chappuis component is increasingly dominant in the lower stratosphere and can be identified with the total J coefficient below about 20 km. We can consider a height H where the two contributions are of equal importance. Typically, in the case m for A = 0 and X = 45~ we get H ~ 35 km (see for instance F M F ) ; while the Hartley J component gives about 92700 of the total at 50 kin. H is generally a slightly increasing function of the angle X and of the albedo A. Figure 1 shows, as a function of the hour of the day, the variation of the photodissociation coefficient for the case o, m, c, at the two heights of 15 km and 30 km f o r A = 0.3. The values for case m are larger than those for case o at both 15 and 30 kin. In fact at those heights, where the main contribution to the J is given by the HugginsChappuis component, the inclusion of molecular scattering leads to an increase of the J coefficient. This is because the attenuation of the direct field by molecular scattering is overcompensated by the contribution of the diffuse field, mainly upcoming from the troposphere and the ground. The greater the solar zenith angle, the more effective the attenuation of the direct field: thus, the effect of compensation is felt less strongly. For case c at 30 km Jis larger than for cases o and m throughout the day. On the other hand, at 15 km it is Jc < Jm and also Jc < Jo for large solar zenith angles: in fact the presence of the heavy aerosol layer around 20 km enhances the diffuse radiation at heights above it, while the large extinction by the layer at grazing angles produces a strong reduction of both the direct and diffuse field below it. From Fig. 1 it is apparent that a different choice of the atmospheric conditions leads to a quite different behaviour of the J's during the day, thus indicating the necessity of performing accurate numerical time-integrations over the length of the

26

Paolo Petroncelli, Giorgio Fiocco, and Alberto Mugnai

(Pageoph,

10z. J

J J II

10

355 0 12 WS. Iwintersolstice)

79 E. (equinoxI

125

I•B

172 $.S. Isummersolstice)

TIME, days Figure 2 Annual variation of the daily-integrated photodissociation coefficient, Lo, for a purely molecular atmosphere in the absence of scattering, shown at five specific heights. The quantities related to the molecular atmosphere are kept constant throughout the year.

day in order to obtain realistic values of the daily-integrated photodissociation coefficients. Introducing now the results of the integrations, Fig. 2 gives, at five specific heights, the values Lo(D) which are used merely as reference. Figure 3 depicts, in a threedimensional presentation, the Lm(z, D)/Lo(z, D) ratios for the three different values of the ground albedo A = 0, 0.3, 0.7. For A = 0, the inclusion of scattering involves a reduction of the photodissociation in the lower troposphere because of extinction, but in the upper troposphere and throughout the stratosphere, where the effects of photodissociation are most important, L increases due to the contribution by the solar radiation scattered by molecules in the lower troposphere, where most of the atmospheric mass is located. When the ground albedo increases, the overall effect is always positive, since the ground diffuse reflectivity does not contribute to Lo; in particular, for A = 0.7 the increase in the L is about 90~ at ground level and exceeds 40~ at 30 km during summer. The increase in photodissociation because of the solar radiation diffused by the ground and b y atmospheric molecules is almost always higher in summer than in winter; moreover, the effects of changes in albedo are felt less strongly in winter than in summer. In fact, in winter, due to the large values of the zenith angle, the direct solar radiation is considerably depleted before reaching the lower troposphere because of molecular scattering, thus diminishing also the contribution to the solar diffused

Vol. 118, 1980) Effects of Diffuse Radiation on the Photodissociation of Ozone

27

,t--0

1.0 i

Y

? "Xr^ 0

......... 6,0~ W.S.

" ........

l E.

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Figure 3 Three-dimensional presentation of the ratios L,,(z, D)/Lo(z, D), as a function of the altitude z and of the day of the year, D. Lm(z, D) is the daily-integrated photodissociation coefficient including the effects of the Rayleigh scattering and of the surface albedo for a purely molecular atmosphere. Results are shown for three values of the albedo A = 0, 0.3, 0.7.

field by the surface reflectivity and by the molecular scattering by low-altitude atmospheric layers. So at a fixed height the greater the surface albedo the greater the seasonal variation in the ratio Lr,/Lo which, however, becomes less and tess dependent on the season at increasing heights. In order to explain such a behaviour in the upper stratosphere we recall that the Hartley J component, where it is of importance, does not practically depend on scattering processes, because the strong absorption of the solar radiation makes both the local attenuation by scattering and the contribution of the upcoming diffuse radiation negligible. Therefore this component in the atmospheric case m is practically the same as in the case o. On the other hand, in the Huggins and Chappuis bands the attenuation due to either absorption or scattering is very weak in the upper stratosphere. As a consequence, above about 30 km the photolytic contribution of the

28

Paolo Petroncelli, Giorgio Fiocco, and Alberto Mugnai

,4--0

'

(Pageoph,

:~ 1.0 )

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:

,

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Figure 4 Three-dimensional presentation of the ratios L=(z, D)/Lm(z, D) for three different values of the surface albedo A and for two aerosol loads (x = a, c) as in Table 1. Lx(z, D) is the daily-integrated photodissociation coefficient including the effects of scattering and absorption by aerosols.

O

Vol. 118, 1980) Effects of Diffuse Radiation on the Photodissociation of Ozone

29

50

E 4O

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Figure 5

Vertical profiles of the percentage deviation

(Lm/Eo

1). 100 for three different values of the

-

surface albedo A./~m and/,o are the yearly averages of Lm(D) and Lo(D) respectively.

upcoming diffuse field, the value of which increases by increasing .4 and decreasing X, is almost constant with respect to height and, furthermore, the contribution of the direct field is practically the same in the case m as in the case o (see, for example, FMF, Figs. 2 and 8). The latter contribution depends weakly on the X angle, while the former is more sensitive to variations in that parameter, because of the already mentioned conspicuous attenuation by the scattering at lower atmospheric levels. Therefore, the more important is the contribution to the J~ by the diffuse part of the Huggins-Chappuis J component, the greater is the difference in the behaviour of arm 50 xx x

x =a

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Figure 6 Vertical profiles of the percentage deviation ( E x / E m - 1)- 100 for three different values of the surface albedo A. [,x and L,~ are the yearly averages of L~,(D) and Lm(D) respectively.

30

Paolo Petroncelli, Giorgio Fiocco, and Alberto Mugnai

(Pageoph,

and Jo when varying the angle X; consequently the seasonal variability of the ratio Lm/Lois larger. As shown, the importance of such contribution decreases at increasing heights and for low values of the albedo. Figure 4 is a composite, three-dimensional representation of the ratios Zx/Zm for the two aerosol cases x --- a, c and for the three values of albedo A = 0, 0.3, 0.7. The ratio Lx/Lmis a correcting factor that can be applied to the previous values of the photodissociation coefficient, obtained for a molecular atmosphere, to account for the presence of an aerosol load. Let us point out that now both terms of this ratio depend effectively on the albedo. The case a, representing the average condition of Elterman, leads to a ratio L,JL,~ which is larger than unity throughout the stratosphere, with the exception of the case A = 0.7 in summer when it is slightly less than 1. The representative surfaces show a deep minimum down to 0.6 at the winter solstice below approximately 4 kin; however, at the summer solstice this extinction effect of the aerosols in the lower troposphere is much less noticeable. The effects of the atmospheric particles on the ozone photodissociation are much more intense when a heavy aerosol distribution according to case c is considered, as shown in the inserts c in Fig. 4, again for the three albedo values A = 0, 0.3, 0.7. In both distributions utilized in these computations the particles are mainly concentrated in two regions: one near the ground and the other in the lower stratosphere. The aerosol layer near the ground, insofar as its effects on the stratosphere are concerned, determines a change of the albedo of the ground-troposphere system. This albedo increases, because of scattering by atmospheric particles, when the surface albedo is low, whereas it decreases, because of the extinction of the radiation going to and coming from the ground, when the surface albedo is high. In any case, such aerosol layer is quite effective when the flux of radiation reaching the lower troposphere is high: thus, for low values of the ground albedo the enhancement of photodissociation in the stratosphere is higher in summer than in winter, whereas increasing the ground albedo produces the ratios Lx/Lmto decrease more in summer than winter. The effects of the stratospheric aerosol layer are quite evident in the reduction of the ratios Lx/Lm inside the layer and below it, with a strong seasonal dependence particularly for the very heavy load represented by case c. Above the stratospheric layer there is generally an increase of the photodissociation coefficient, the ratios LxlLm remaining, however, approximately constant as a function of the day of the year. In order to ascertain whether the inclusion of scattering leads to an overall increase or a decrease of the photodissociation of ozone, yearly averages have been carried out for the quantities studied in this paper. Figure 5 shows the yearly average for the LmlLoratios in the form of percentage variation : the effect of molecular scattering on the photodissociation is always strongly positive in the ozone layer region. More complex are the curves for the L~/Lr, and Lc/Lm ratios, shown in Fig. 6

Vol. 118, 1980) Effects of Diffuse Radiation on the Photodissociation of Ozone

31

again in the form of percentage deviation: the effect of the aerosols on the photodissociation of 03 is generally positive, but for large values of the ground albedo can be negative.

4. Time integration of the photodissociation coefficients with seasonally adjusted atmospheric conditions Some tests were carried out to check the sensitivity of the analysis to seasonal variations of the Oa concentration and other atmospheric parameters. For this purpose we have used four monthly average 03 profiles, interpolated at 45~ from those published by DOTSCH (1978) which refer to the months of January, April, July and October at various latitudes in the northern hemisphere. Diitsch's results are based on all available data measured with chemical sondes combined above 10 mb with Umkehr and BUV satellite data; still the author points out that such data are 'far from satisfactory for use in a quantitative manner in combination with photochemical models' ; however, in spite of this caveat, Diitsch's profiles appear t o represent a comprehensive and consistent set of data to be used for sensitivity tests. Curves in Fig. 7 show the ratios between the seasonally adjusted ozone profiles, n(O3)~eas, and the yearly average standard profile previously utilized, n(O3)~ta, as a function of height. Figure 8 shows the variation of the daily-integrated photodissociation coefficients referring to the seasonally adjusted Oa profiles with respect to the previous results obtained for the standard profile. The curves on the left-hand side present the ratios Lo,~e~(D)ILo,~ta(D) for the four typical days 15 January, 15 April, 15 July and 15 October. Below 25 km the ratios do not deviate substantially from unity, the maximum deviation being less

40,

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n (03) seas/n (03) std Figure 7 Ratios n(Oo),~e~,Un(O~).s~abetween the seasonally adjusted ozone profiles, for the months of January, April, July and October, and the yearly average standard profile, as a function of height.

32

Paolo Petroncelli, Giorgio Fiocco, and Alberto Mugnai ,~

,r

9

1"

'r

T

~

~

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r ! O,

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0 0

Lo, seas/Lo, std

1

2

3

4.

5

O.g

Figure 8 Variation of the daily-integrated photodissociation coefficients for the seasonally adjusted ozone profiles compared to those obtained for the standard profile. The curves on the left-hand side show the ratios Lo,sc~,s/Lo.sta for the four typical days 15 January, 15 April, 15 July and 15 October. The curves on the right-hand side give the quantity/3 defined by equation (7), for the two extreme cases of aerosol load (x = m, c), for the days 15 January and 15 July and for a surface albedo A = 0.3. than 4%; this is not surprising, since in this region photodissociation is mostly due to the Huggins-Chappuis component. Above 25 km the ratios show a consistently decreasing trend with height, at 40 km the deviation being as large as 30%; this result is a consequence of the increasing importance of Hartley J component in the upper stratosphere, coupled with the enhanced 03 concentration at those heights in the seasonally adjusted profiles compared with the standard profile, as shown in Fig. 7. Finally, it should be noticed that the photodissociation happens to be more sensitive to changes in the ozone concentration at those levels where the ozone data are less reliable (DOTSCH, 1978). To indicate the effects of changes of the ozone profile on the photodissociation when the diffuse field is included, we have calculated the ratios Lx,se,,s(D)/Lx,s~a(D) for x = m, a, c. Such ratios do not differ considerably from those shown on the left side of Fig. 8. As an example, on the right side of Fig. 8 we report the results of four computations carried out for the cases x = m and x = c for the days 15 January and 15 July. For the sake of comparison, the curves give the quantity/3, defined as follows: Lx,se~

(1 + / 3 ) ~ .

(7)

Lx,stc, For the albedo considered, A = 0.3,/3 is at most 5%. For A = 0.7, not shown here, the maximum value of/3 obtained is 6.5%, while for A = 0 it is 4%. Such results lead to the conclusion that, as regards the radiative transfer calculations, the insertion of a variable ozone profile has a minor effect compared to the inclusion of the diffuse field, with the exception of the upper stratosphere where the photodissociation is particularly sensitive to the ozone content at those heights. It

Vol. 118, 1980) Effects of Diffuse Radiation on the Photodissociation of Ozone

33

should be noticed however that the variability of the photodisSociation rate due to changes in the ozone profile can be considerable, due to the large variation in n(O3) as shown in Fig. 7.

5. Conclusions

The main conclusion drawn from previous work was that computations of the stratospheric photochemistry aiming at accuracies of a few percent cannot avoid taking into account the diffuse solar field to the extent of including not only the molecular contribution, but also the effects of the aerosols. This work supports such a view and shows that the daily-integrated values of the photodissociation coefficients have a strong variation depending on height, season, aerosol load and ground albedo.

Acknowledgements This research was carried out with partial support from 'Progetti Finalizzati' of Consiglio Nazionale delle Ricerche (CNR) of Italy.

REFERENCES ACKERMAN, M. (1971), in Mesospheric Models and Related Experiments, (G. Fiocco, Ed.), D. Reidel, Dordrecht, 149-159. CADLE, R. D., KIANG, C. S. and Louis, J.-F. (1976), The global scale dispersion of the eruption clouds from major volcanic eruptions, J. Geophys. Res. 81, 3125-3132. CALLIS,L. B., RAMANATHAN,V., BOUGHNER,R. E. and BARKS'fROM,B. R. (1976), The stratosphere: scattering effects, a coupled 1-D model, and thermal balance effects, Proc. Fourth Conference on CIAP, DOT-TSC-OST-75-38, (Eds. T. M. Hard and A. J. Broderick), 224-233. DOTSCH, Iff. U. (1978), Vertical ozone distribution on a global scale, Pure Appl. Geophys. 116, 511-529. ELTER~AN, L. (1968), UV, visible and 1R attenuation for altitudes up to 50 km, 1968, AFCRL Report 68-0153, Environmental Research Paper No. 285, Bedford, Mass. Flocco, G., MUG~qAI,A. and FORLIZZI, W. (1978), Effects of radiation scattered by aerosols on thephotodissociation of ozone, J. Atmos. Terr. Phys. 40, 949-961. GRANT, I. P. and HUNT, G. E. (1969), Discrete space theory o.fradiative transfer. L Fundamentals, Proc. Roy. Soc. Lond. A313, 183-197. ISAKSEN, I. S. A., MIDTB~, K. H., SUNDE, J. and CRUTZEN, P. J. (1977), A simplified method to include molecular scattering and reflection in calculations of photon fluxes and photodissociation rates, Geophys. Norv. 31, 11-26. KURZEJA, R. (1977), Effect of diurnal variations and scattering on ozone in the stratosphere for present day and predicted future chlorine concentrations, J. Atmos. Sci. 34, 1120-I 129. LUTHER, F. M. and GELINAS, R. J. (1976), Effect of molecular multiple scattering and surface albedo on atmospheric photodissociation rates, J. Geophys. Res. 81, 1125-1132. LUTHER, F. M., WUEBBLES,D. J., DUEWER, W. H. and CHANG, J. C. (1978), Effect of multiple scattering on species concentrations and model sensitivity, J. Geophys. Res. 83, 3563-3570.

34

Paolo Petroncelli, Giorgio Fiocco, and Alberto Mugnai

(Pageoph,

MCCLATCHEY,R. A., FENN, R. W., SELBY,J. E. A., GARING,J. S. and VOLZ,F. E. (1970), Optical properties of the atmosphere, AFCRL Report 70-0527, Environmental Research Paper No. 331, Bedford, Mass. MUGNAI,A., PETRONCELLI,P. and FIOCCO, G. (1979), Sensitivity of the photodissociation of NO2, NOa, HNO3 and HzOz to the solar radiation diffused by the ground and by atmospheric particles, J. Atmos. Terr. Phys., 41, 351-359. PITARI, G. and VISCONTI,G. (1979), A simple method to account for Rayleigh scattering effects on photodissociation rates, J. Atmos. Sci., 36, September Issue. THEKAEKARA,M. P. (1973), Solar energy outside the earth's atmosphere, Solar Energy, 14, 109-127. WISCOMBE, W. J. (1976a), Extension of the doubling method to inhomogeneous sources, J. Quant. Spectrosc. Radiat. Transfer 16, 477-489. WISCOMBE, W. J. (1976b), On initialization, error and flux conservation in the doubling method, J. Quant. Spectrosc. Radiat. Transfer 16, 637-658. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh/iuser Verlag, Basel

Remote Sensing of the Middle Atmospheric Aerosol 1'2) By A . L. FYMAT 3) a n d C. B. SMITH 8'4) Summary - This article analyzes the nature of the aerosol information that current or planned spacecraft measurements could contribute toward the required input data for studies of natural anthropogenic influences on the middle atmosphere, and their consequent effects on our weather and climate. The analysis is conducted with particular reference to the solar occultation sounding technique as applied by the SAGE I experiment on the Atmospheric Explorer Mission B spacecraft. Its conclusions should prove to be of use in both the interpretation of the S A G E I data, and in the design of the follow-on mission on the Earth Radiation Budget satellite. Our analysis shows, in particular, that further studies are required in: the choice and number of sounding channels; the data taking sequence in relation to the atmospheric regions probed; the accuracy and vertical resolution of the atmospheric profiling, and their dependence on both the instrument/spacecraft parameters and the data inversion techniques; and the data reduction procedures. Neither of the selected channels is in a one-to-one relationship with an atmospheric constituent; hence, unless further assumptions are introduced, inversion techniques based on such a property are not applicable. The aerosol wavelengths are not satisfactory as they are only sensitive to the large size tail of the aerosol size distribution rather than to the predominant sizes; for these, UV wavelengths would be required. Owing to the change of the Sun's shape due to atmospheric refraction as the Sun either sets or rises, the higher altitudes will be scanned fewer times than the lower altitudes. Also, because transmission approaches rapidly unity above ~40 km, the same high altitudes are more sensitive to measurement errors-errors that will propagate to lower altitude determinations when inverted profiles are reconstructed from the top of the atmosphere. These two factors, combined with the small air mass values at the high altitudes, are the cause of the mathematical ill-conditioning of the inversion problem. They point toward the need for a data-taking sequence strategy that would trade off between data storage and transmission constraints, larger accuracy at the high altitudes, and proper division of the atmosphere in order to overcome the ill-conditioning. Likewise, and as a result of the above considerations, there is a need for a detailed trade off study between data accuracy and vertical resolution of the reconstructed profiles. This should take into account the seasonal and geographical variations in the distribution of atmospheric constituents, as well as a representative statistical set at any given location and time, appropriate error measures and their vertical profiles, and several inversions utilizing as initial guesses profiles that depart from the true ones. It is also shown that the aerosol and ozone number densities cannot be recovered simultaneously without introducing some formula for the aerosol extinction or assumptions on the form of the aerosol size distribution. This problem is not resolved by the addition of sounding channels because each such channel introduces an additional unknown aerosol extinction. Thus, one is led to a separate rather than a simultaneous determination of the various constituents by

1) Invited article for the Special Issue ' T h e Middle Atmosphere,' Journal of Pure and Applied Geophysics. 2) Supported by N A S A Contract NAS 7-100 with the Jet Propulsion Laboratory, sponsored by the Offices of Planetary Atmospheres and Earth Applications. JPL Atmospheres Publication No. 3) Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA. 4) N R C / N A S A Post-doctoral Resident Research Associate.

36

A . L . Fymat and C. B. Smith

(Pageoph,

resorting to complementary measurements. For a future experiment, it is suggested to determine the ozone separately from measurements at a close pair of appropriate wavelengths between which the aerosol extinction varies slowly whereas that of ozone exhibits a rapid variation. A similar technique could also be used for the separate determination of NO2. The relaxation-type of inversion suggested by CHU and MCCORMICK (1979) does not seem to be appropriate because each channel is not sensitive selectively to an individual constituent, the aerosol channels are not sensitive to the important sizes in the distribution, and the sensitivity of the channels to the constituents of interest varies greatly with altitude. In the retrieval of the vertical profiles, the cause of the ill-conditioning of the inversion is identified. Two approaches are suggested for overcoming this problem: (i) build the profile starting from the top of the atmosphere (forward procedure) but with an initial layer of sufficient air mass, or preferably (ii) reconstruct the profile from the lowest altitude reached (backward procedure) with a renormalization at the top of the atmosphere. In this process, the minimization search method (FY~AT, 1976) would appear to be a better technique than the onion-peeling technique, as demonstrated by MILL and DRAYSON(1978). In order to maximize the scientific return of SAGE I, a data inversion procedure is proposed. It assumes that (i) there are no aerosols above ~ 25 km, and no NO2 below this altitude (as suggested by CHU and McCORMICK, 1979), (ii) below N 25 km, ozone (and NO2, if present) could be determined separately, and (iii) the aerosol has a known refractive index at all wavelengths of interest, is assumed to be spherical (or describable in terms of 'equivalent spheres',), and the minimum and maximum radii of its size distribution are known a priori. Under these assumptions, it is possible to retrieve the neutral density, NO2 and 03 profiles above ~ 25 km, by either the forward or the backward procedure described above. Taking into consideration the power law variation of the air density with altitude, it is further possible to reconstruct the corresponding profiles at all the lower altitudes from the determinations in the altitude range ~30--40 kin. Below ~ 25 km, the four SAGE I channels would then all become available for the aerosol inversion. While the profile reconstruction could proceed as for the higher altitudes, the aerosol inversion at each individual altitude presents problems of its own. Results of numerical experiments for aerosol inversion using all four SAGE wavelengths and seven different inversion routines are presented. If good a priori information is available on the sought size distribution solution, reasonably satisfactory inversions can be performed (see line 1 of Table 2, and Fig. 3c and 3d). However, in the absence of such information, there are as many solutions as inversion methods tried, in complete conformity with the well-known ill-conditioning of the problem. Among methods providing physically meaningful solutions, no method could be singled out as preferable to the others. In these inversions, the data were assumed to be exact, and 99~o of the distribution were used. Under different conditions, the nonuniqueness of the inversion would be further compounded. Lastly, based on the present study, a strategy is suggested for the design and data interpretation of a follow-on SAGE-type experiment. Considering the important advantages to this problem presented by forward scattering, as demonstrated by FYMAT and MEASE (i978), a composite (extinction-forward scattering) experiment is recommended for the future experiments. Key words: Solar occultation technique; Analysis of technique; Inversion procedures.

L Introduction T h e Sensitivity o f t h e E a r t h ' s a t m o s p h e r i c state to n a t u r a l a n d a n t h r o p o g e n i c influences is a subject o f c o n t i n u i n g c o n c e r n a m o n g p h y s i c a l scientists a n d t h e p u b l i c at large. T h e c o n c e r n s t e m s f r o m o u r r e a l i z a t i o n t h a t s u c h influences m a y a d v e r s e l y affect o u r w e a t h e r a n d c l i m a t e . S o m e e v e n see p o t e n t i a l f a r - r e a c h i n g t h r e a t s to o u r n a t u r a l h a b i t a t a n d life o n this planet.

Vol. 118, 1980)

Remote Sensing of the Middle AtmosphericAerosol

37

That anthropogenic pollutants could adversely modify the middle atmosphere was dramatically brought to the public's attention at the beginning of this decade by the suggestion that high-flying supersonic aircraft exhaust emissions could alter the stratospheric ozone concentration. A number of other similar suggestions have since been made including Space Shuttle exhaust effluents, NOx emissions and chlorofluoromethanes. A number of major research programs have in consequence been initiated worldwide in attempts to understand the problem posed, and hopefully provide recommendations and guidelines for governmental policy decisions and regulations. Examples of such programs in the U.S. include the Climatic Impact Assessment Program (CIAP) and the Upper Atmospheric Research Satellite Program (UARSP). The latter will in fact represent a major U.S. contribution to the international Middle Atmosphere Program (MAP), an activity planned to continue well into the 1980s. The measurement strategy that has evolved within such programs incorporates the gamut of observational platforms from the ground to balloons, rockets, aircraft and spacecraft. Of particular interest in this article is the nature of aerosol information that current or planned spacecraft measurements could contribute toward the required input data for the above studies. After a brief introduction into the problems attending the remote sensing of aerosol parameters, attention will be focussed on the current Stratospheric Aerosol and Gaseous constituents Experiment (SAGE I) on the Atmospheric Explorer Mission B satellite (CHu 1975; Ct-It~ and MCCORMICK, 1979) for which a follow-on mission (SAGE lI) is being planned during 1983 on the Earth Radiation Budget satellite. Results of extensive inversions of simulated SAGE I data will be presented in order to illustrate the retrievable information and its underlying conditions. A strategy for SAGE II, and subsequent extensions of it, will lastly be suggested. II. Preliminary remarks on the remote sensing problem

Remote sensing by occultation is an important tool for the investigation of the middle atmosphere. The geometry of such an experiment is schematically illustrated in Fig. 1. A multichannel radiometer on the spacecraft measures the extinction of solar radiation as it traverses the Earth's limb during spacecraft sunrise and sunset events. The line-of-sight from the spacecraft to the Sun scans the Earth's atmosphere above the cloud tops (or, possibly, somewhat above the ground under clear sky conditions) providing vertical profiles of the atmospheric transmission at each sounding wavelength. These data can, in principle, be numerically inverted to separate the composite extinctions into their contributions from the active atmospheric constituents in the optical path, and provide the vertical concentration profiles of such constituents. Further, utilizing the spacecraft orbit precession, the global aerosol distribution and its time variability can also be obtained during the lifetime of the experiment. SAGE I applies this principle in an attempt to sound both the aerosol

38

A.L. Fymat and C. B. Smith

(Pageoph, TOWARDSLIH

"~'++

ql

, 9

'(

2~'

m

mln

u'Yo

I0 ~

|

31

3O

~.~2

II'.

Figure I Illustrating the geometry for satellite so|ar occu|tation sounding of the atmosphere.

and the gaseous constituents (air, 03 and NO2). It uses the four sounding channels: ~1 = 0.385/~m, ,X2 = 0.45/zm, ~,8 = 0.60/zm and ,X4 = 1.0/zm. It must be immediately noted that the scientific return of a SAGE-type experiment (and, for that matter, of any remote sensing experiment) will be determined by two main considerations: optimized design of instrumental parameters, and data reduction techniques. Considerable progress in both areas has been accomplished, on the experimental side during the precursor SAM (Stratospheric Aerosol Measurement), SAM II, and ASTP (Apollo-Soyuz Test flight Project) experiments (PEPIN, 1975), and on the theoretical side through a better understanding of the mathematical illconditioning of the inversion problem and the derivation of a number of solution algorithms (DEEPAK, 1977; FYMAT, 1978; TWOMEY, 1978). Nevertheless, important problems remain that further hinder progress in the remote sounding of the middle atmosphere from spacecraft. Here, SAGE I could be used as a basis from which these problems could be studied, and solutions to them developed. The theoretical foundation, instrument design and operation, and possible data inversion techniques for this experiment can be found in CHU and MCCORMICK(1979, hereafter referred to as CM). However, analysis of this work reveals the need for further studies in the following areas: choice and number of wavelength channels, data taking sequence in relation to the atmospheric regions probed, accuracy and vertical resolution of the atmospheric profiling, and their dependence on both the instrument/spacecraft parameters and the data inversion techniques, and the data reduction procedures. This analysis is presented below, and used as a framework for an improvement over the SAGE I concept. We wish first to illustrate a few salient points, postponing a complete discussion to the following section.

Vol. 118, 1980)

Remote Sensing of the Middle Atmospheric Aerosol

39

Let (O = zenith, 4, = azimuth) represent an inertial frame of reference at the spacecraft, S;,(O,~) the spectral solar radiance, T~(O) the atmospheric transmission, R~,(O,(~) the atmospheric refraction, and Fx(O,~) the radiometer's viewing function within the solid angle Ato. Then, the measured irradiance for a sounding channel of passband A~ is provided by:

l~,(O,~ ) = ;zx~ ~o~ F~,R~T~,S~do, dA.

(1)

Using the Bouguer-Beer-Lambert law, we can write:

T;~(hN) = exp (-f

~,(h) du~,(h)),

(2)

where hm the altitude of the tangent height, is now used in place of 0, u is the optical path length of the ray of interest, and the integration is to be carried out along this entire path from the spacecraft to the Sun (see next section). In equation (2), 134 represents a composite factor incorporating absorption from ozone (subscript O) and nitrogen dioxide (N), molecular Rayleigh scattering (M), and aerosol extinction (A): fla =/~a(M) +/3a(N) + ilk(O) +/3a(A).

(3)

Further, for the gases, the corresponding factors are explicitly:

fix(M) = NM~a(M),

~a(N) = NN~z(N),

~(0) = No~,(O),

(4)

where the/3A are cross-sections and N are number densities, and/~z(M) follows the well-known inverse fourth-power variation with wavelength. For aerosols, however, the corresponding expression is fla(A) = NA

/~a(A; ma; r

d*,

(5)

r

w h e r e , is a characteristic dimension of the aerosol, nO) its size distribution between dimensions, = '1 a n d , = *2, and m is its refractive index at the sounding wavelength. If the aerosol is of spherical shape, then , denotes its radius and fla(A) would be provided by the well-known Mie scattering solution. Now: - I f we assume that the only atmospheric constituents of importance are air (neutral density), ozone, nitrogen dioxide and aerosols, and further that aerosols can be modeled by spheres of known refractive index that exhibit a power (Junge) size distribution, we find seven unknowns: the four constituent number densities, the Junge exponent and the lower and upper radii of the distribution. Therefore, a set of wavelengths must be identified such that the corresponding measurements bear enough information on these unknowns so as to permit their retrieval by inversion. Thus, even under the ideal hypotheses considered, additional channels beyond the four listed earlier would be required. Their number would depend on their respective information content, and it would be naive (if not incorrect) to conclude without further study that only three more channels would be needed.

40

A.L. Fymat and C. B. Smith -

(Pageoph,

Even with additional channels, the important problem remains that the aerosol and ozone cannot be recovered simultaneously without introducing some assumption on the aerosol extinction formula or the aerosol size distribution function. Indeed, with each such channel, an additional unknown ~a(A) is introduced into the problem which thus remains underdetermined. However, if the right-side of equation (5) could be expressed simply in terms of a few parameters, for example by an assumption on the value of the extinction integral or on the form of n(~), then, the problem could be rendered determined. Nonetheless, the resulting inferences on the atmosphere made from the data would critically depend on these assumptions, and may not represent physical reality. Instead, we will suggest a way of retrieving 03 and NO2 number densities fairly independently of the aerosol, and the aerosol extinction. We will also discuss the type of aerosol information that can be retrieved from the corresponding extinctions. -The expected accuracy and resolution in the reconstructed vertical profiles will vary with height in the atmosphere. It is not possible to require a nearly uniform accuracy throughout. Rather, this should result from a trade-off between the vertical distributions of the constituent concentrations, the capabilities of the applicable data inversion procedures, and the scientific requirements of disciplines using this information. It will be shown that the source of the mathematical ill-conditioning of the inversion can be traced to the small air mass at the high altitudes, at least in those techniques that build the profiles starting from the top of the atmosphere. Requiring a small vertical resolution at these altitudes will only compound the ill-conditioning and further degrade the resolution at the lower altitudes which are of considerably greater interest. It would seem more judicious to 'tune' the resolution at the approximately desired values at the altitudes of interest and to degrade it at the higher levels in order to defeat the ill-conditioning. Of course, different strategies could be developed for the diverse inversion approaches, and it is only the synthesis of several of them that would dictate the optimal trade-off. - The inversion of the aerosol extinction is a well-known ill-conditioned problem (solution of a first-kind Fredholm integral equation). A family of solutions can be obtained that can all match the data. However, as we will later show, the availability of four wavelengths only for this problem is not sufficient for deriving a reasonable 'effective' solution. The minimal number of channels required remains to be determined from an extensive numerical study utilizing several available algorithms. The 'effective' character of the solution must also be stressed. This means that, while certain properties of the true solution could be recovered, the actual number density and size distribution cannot be obtained. The extent of retrievable aerosol information from both the SAGE data and other independent a priori information remains to be established.

Vol. I 18, 1980)

Remote Sensing of the Middle Atmospheric Aerosol

41

III. Remote sensing by satellite solar occultation We analyze below the different key steps in the solar occultation concept of remote sensing with particular reference to SAGE I. Our aim is to establish the information content of the corresponding data, and to identify ways of possibly enhancing the scientific return of any follow-on experiment,

A. Aerosol models and selection of sounding channels We shall employ the same two aerosol models (background, volcanic) as those in CM. These models were computed for an aerosol consisting of a 75~ solution of sulfuric acid in water (refractive index m = 1.43 assumed to be constant at all wavelengths considered), and exhibiting lognormal size distributions (PIrCNICI( et al., 1976). The background model is characterized by the geometric radius rg = 0.0725/zm and the standard deviation % = 1.86, while the corresponding parameters for the volcanic aerosol are: rg = 0.097/zm and % = 2.02. For both models, the total number density is NA = 10 cm -3. In spite of this choice, in their inversions of simulated SAGE I data, Chu and McCormick assumed the aerosol extinction to be that of a power-law type (see Section III.D below). This is an inconsistent approach that could only be justified if it could be proved that the two distributions are optically equivalent, in the sense that they both yield the same extinction data. To our knowledge, such an equivalence has not been demonstrated. Figure 2 shows the wavelength variations of the individual and the total extinctions at several stratospheric altitudes. It is based on the analysis of Fig. 2 that the SAGE I radiometric channels were selected. Chu and McCormick justified this choice by the following argument: 'The 1.0/zm channel is sensitive primarily to aerosol scattering, the 0.6/~m located at the peak of the ozone Chappuis band provides an ozone measurement, and the remaining two channels provide information on nitrogen dioxide and aerosol short-wavelength scattering properties.' While this may appear to be a logical choice, a closer examination of Fig. 2 and of the aerosol models adopted shows that: No single channel can be associated in a one-to-one relation with an atmospheric constituent. Each channel is contributed to by two or more of the four constituents of interest. Thus, the remote sensing problem must attempt to solve simultaneously for all 'active' constituents. To reduce the number of contributors in any one wavelength requires the introduction of a priori information. For example, in the simplest case at 1.0/zm, the aerosol contribution could be isolated only if it were possible to assess independently that of the neutral density. - From the standpoint of the aerosol sizing problem, and irrespective of the above /3(h) variations, the three aerosol wavelengths (0.385 tzm, 0.45 tzm, 1.0 t~m) are not satisfactory choices. Mie's scattering solution shows that the extinction for -

42

A.L. Fymat and C. B. Smith 1

t

I

I

I

I

I

1

I

(Pageoph, I

I

Z = 10 km

10-1

J ~'~" ~ r162

~ 0.5

0.6

I 0.7

I 0.8

I

T

I

I

I 10-4 0.9 .0 0.3 0.4 WAVELENGTH, /am I

10-I

I

Z = 25 km

Z

I

I

10-1

T

w ] ~- 10-4.3 0.4 O t.) ZO ]

I

Z = 18 km

0.5

I

"~(BACKGROUND;

0.6 0.7

I

I

0.8

0.9

I

I

1.0

Z = 40 km

.,..u 10-1

10-2

10-2

10-3

10-4304050607080910

10"50.3~4

! . ~ . ~ 8

0.9

.0

WAVELENGTH, .am

Figure 2 Extinction coefficients as a function of wavelength at four middle atmospheric altitudes (O = ozone, R = Rayleigh, N = nitrogen dioxide, .4 = aerosol, T = total). The dashed curves at z = 18 km correspond to the two aerosol models employed by Chu and McCormick. All other curves are from Elterman's model. a single particle is a m a x i m u m when the phase-shift parameter p = 2(m - 1) • (2~rr/A) is --~4.08. For the given refractive index, m = 1.43, this yields a relation between A and the aerosol radius to which it is most sensitive: r ~ (3/4)A. Thus, the above three wavelengths are respectively most sensitive to the radii values 0.29/~m, 0.34/~m and 0.75/~m. Figures 3(b) and 4(b) below show that for both aerosol models suggested (background and volcanic) these radii fail on the far end o f the large size tail o f the distribution. Wavelengths as short as possible should therefore be selected in order to enhance the sensitivity of the measurements to smaller radii closer to the modes (0.05-0.06/~m).

Vol. 118, 1980) -

Remote Sensing of the Middle Atmospheric Aerosol

43

In any one channel,/3 also exhibits a variation with z in addition to that with [see Fig. 2]. It takes the form of an altitude modulation that follows faithfully the concentration vertical profiles of the contributors in that wavelength. Here again, independent a priori information on the vertical distributions o f some atmospheric constituents would help considerably in reducing the complexity of the inverse problem. It has been suggested to neglect the aerosols above ,-~25 km and to neglect NO2 below this altitude. This is a useful observation that has served in devising the data inversion scheme suggested by the former authors. However, this may not provide an accurate description of the atmosphere as aerosol incursions into the higher altitudes have been observed from Skylab (ScHUERMAN and GREENBERG, 1974). When such incursions are present and neglected, an aliasing is introduced in the inverted solutions that should be investigated. If it is found to be small, it could perhaps be further reduced by introducing an a priori value for the neglected contribution. Otherwise, the inversion technique would have to be generalized in order to relax the assumption of altitude separation between NO2 and aerosols.

B. Scanning rate of the solar disk There are two types of experimental errors associated with occultation experiments : random noise and pointing e r r o r (inaccurate spacecraft ephemeris data, scanning and tracking errors, spacecraft drift due to residual angular momentum). While some of these errors are difficult to evaluate, they are well understood. Another source of error, not adequately documented, arises from the data acquisition mode during a sunrise (or sunset) event. For example, during sunset, the angular diameter of the sun decreases; its shape also changes from that of a sphere to a flattened ellipsoid as a result of refraction in the atmosphere. This effect is faster at the higher altitudes and much slower below. The phenomenon is well-understood and can be evaluated using available ray tracing techniques. Now, the SAGE radiometer scans the solar disk up and down with respect to the earth's horizon at a predetermined rate. Because of the shrinking rate described above, the scanning frequency of any given altitude will thus not be constant (for example, see Fig. 1 of CM). Hence, there is an important difference between the higher and the lower altitude transmission data: the higher altitudes are scanned fewer times than the lower altitudes. For example, there are 4 measurements across the solar disk at z = 40 km, two of which are near the Sun's limb where further uncertainties are introduced by solar limb darkening. On the other hand, at 20 km there are five such measurements, and seven measurements at 10 kin. Thus, there is less transmission data for the higher layers than the lower ones, and the average transmissions within layers are probably less accurate at the higher levels. The importance of obtaining more accurate transmission data for these high altitudes (above ~ 4 0 kin) can also be inferred from the curves of atmospheric transmission, T(A), versus tangent altitude at the four SAGE I wavelength channels (see, e.g.,

44

A, L. Fymat and C. B. Smith

(Pageoph,

Fig. 4 of CM). These transmissions approach unity rapidly above 40 km (for the atmospheric models assumed in the Figure). Hence, the computed extinction In (l/T) = - I n T is much more sensitive to measurement errors at high altitudes. As we will later show, it is the small air mass at these altitudes that is responsible for the difficulties of data inversion (mathematical ill-conditioning); unfortunately, the fact that they are the least scanned further compounds the problem. One way of avoiding this difficulty usually consists in disregarding the high altitude measurements until sufficiently large air mass values are reached (z ,,~ 50 km). This approach has some merit, but it is a pity to reject data. While data storage and transmission limitations must be kept in mind, other strategies that retain the high altitude data would need to be developed. Also, during the inversion process, errors at the high altitudes will propagate to lower altitudes suggesting that the former altitudes should be scanned more frequently. The development of a strategy for the data taking sequence must involve a trade-off study between the three factors: data storage and transmission constraints, larger accuracy at the high altitudes, a division of the atmosphere into homogeneous spherical shells of sufficient air mass to minimize (or preferably eliminate) the cause of ill-conditioning. This study should further be carried out utilizing a large number of Earth atmosphere models to cover all possible situations likely to be encountered during the period of the experiment. This strategy would have of course some bearing on the vertical resolution of the measurements, especially at the high altitudes.

C. Accuracy and resolution of the vertical profiles Techniques are available for carrying out trade-off studies between the overall data accuracy and the vertical resolution of the retrieved profile (cf. Backus-Gilbert technique). Thus, with the knowledge of the desired resolution, it is possible in principle to prescribe the resulting required data accuracy. This would in turn provide instruction on the experiment design. In the case of SAGE I, the following instrumental parameters have been published: FOV = 0.5 arc-rain which, it is claimed, would provide a 0.5 km vertical resolution with' significantly pOorer vertical resolution for certain conditions and heights'. A target value of I km was adopted from numerical inversions of simulated SAGE data. The accuracies derived from the same inversions have been stated as: 10~o for 03 (from the 0.6 tzm channel) between 12-42 km with better accuracy at the peak of the profile, a few percent for the neutral density from 10 to 40 km, 10~ for aerosols (from the 0.45 t~m and 1.0 t~m channels) between 13 and 24 km, 25~ for NO2 (from the 0.45/zm channel) between 25 and 38 km. However, aside from instrumental considerations and atmospheric inhomogeneities (both along the horizontal and the vertical), the detailed mathematical analysis of the information content of the SAGE data, and its accuracy and vertical resolution on the basis of several independent data inversion schemes need to be carried out. The resolution and accuracies quoted for the extinction factors appear to have been

Vol. 118, 1980)

Remote Sensing of the Middle Atmospheric Aerosol

45

derived from only the modified relaxation technique of inversion using (i) a random noise of 0.5~o and scan rate error of 0.5 arc-rain 'corresponding to twice the worstcase expected performance of the SAGE instrument,' (ii) a statistical set of ten independent simulations, reductions and inversions corresponding to different sets of input profiles, and (iii) and initial guess that corresponds to the true profile solutions. A more comprehensive simulation study would now be needed that would take into account the geographical and seasonal variations in the distribution of the atmospheric constituents, as well as a representative statistical set at any given location and time. Different error measures and their vertical profiles should also be considered rather than a global uncertainty over the entire set of profiles considered, and over the altitude range sounded. Lastly, different initial guesses rather than the actual solutions should be tried. We will show in the next section that the latter consideration will have substantial effects on the inverted solutions.

D. Data inversion techniques used previously The following procedures have been suggested in CM for reduction and interpretation of SAGE I data. After the measured irradiances are related to look angle with respect to the Earth's atmosphere (in terms of tangent altitude) and to the solar disk (in terms of position on the limb darkening curve), they are normalized with respect to measurements at high altitudes where the atmospheric extinction can be considered to be zero. These normalized irradiances are then averaged over 0.5 km thick atmospheric spherical shells in order to improve on the signal-to-noise ratio. They give directly the mean integral transmittance profiles which, by integral inversion, would in .principle provide the desired composite extinction factors of the atmosphere at each of the wavelengths of interest separately [see equation (2)]. These, in turn would require a further inversion to determine the atmospheric parameters of interest separately for each constituent. Alternatively, one can attempt to invert the measurements directly for these parameters in one step. We shall refer to these two approaches as inversion methods No. 1 and No. 2, respectively. We provide in the next section a detailed analysis of these and other possible methods, an outline of the elements of a systematic and comprehensive attack on the problem, and a discussion of the atmospheric parameter information that can (or cannot) be retrieved from the data. Because of the 'double inversion' required by method No. 1, this method appears to have been discarded in spite of its simplicity. Nonetheless, we will show later that, with suitable modifications, this technique should be retained as one possible approach along with the others proposed. Two reasons were advanced for this rejection (i) errors in the first inversion would propagate in the second inversion step. Generally speaking, this is a correct statement; it requires nevertheless a numerical simulation and study in order to assess its magnitude; and (ii) the approach 'does not provide enough flexibility to incorporate a vertical smoothing on the retrieved constituent profiles'. It is not clear why such a constraint would be desirable. While

46

A.L. Fymat and C. B. Smith

(Pageoph,

it is a requirement of the inversion method followed in the reference article, other constraints can be used in the context of different inversion algorithms. In fact, a number of such algorithms should be investigated in their application to this experiment. The same reference article suggests rather the use of method No. 2, but illustrates only retrievals of the extinction profiles, not the number density profiles under the assumptions discussed above. For the gases, this step is straightforward if the relevant absorption and scattering cross-sections and their vertical profiles (including the pressure and temperature dependences) are known [see equations (4)]. The problem is not as simple for the aerosols, however, because the corresponding extinction cross-section and its further dependence o n the size distributions are not known [see equations (5)]. Unlike the gaseous constituents cross-sections, this cross-section varies with the wavelength in a manner that depends on the aerosol refractive index and with particle size distribution (and shape). A careful analysis of this problem leads to the conclusion that the aerosol and ozone number densities for altitudes below 25 km cannot be simultaneously recovered without introducing some formula for the aerosol extinction, or assumptions on the form of the aerosol size distribution and the value of the refractive index. The assumed form of the aerosol extinction may, of course, not be correct and thus produce unknown aliasing effects in the recovered number densities for ozone and aerosols. Chu and McCormick adopted a power-law type (Junge) model for this distribution such that flA()~) = Ah ~ (subscript 'A' denotes aerosols), where A and ~ are unknown parameters, and A involves the aerosol number density and the lower and upper radii values of the distribution. Clearly, there are not enough pieces of information for retrieving the aerosol parameters. This is an intrinsic limitation in the SAGE I experiment using 4 channels. Even with additional channels, it is questionable whether the aerosol and ozone parameters could be retrieved. We provide in the next section a complete discussion of this topic, and show in particular that from this data the aerosol number density cannot be retrieved and even less the size distribution (or distribution parameters). We will also identify the type of a priori information that would be required in order to obtain qualitative information on the number density and properties of the distribution. The inversion procedure suggested for SAGE I data is a modified relaxation approach which has been used in the well-known thermal sounding of the atmosphere. It belongs to the method No. 2 category. Its use has thus been justified: 'it is based on the consideration that each wavelength channel is most sensitive selectively to an individual constituent.' Following our earlier discussion in the context of Fig. 2, it is clear that this is not the case, not only because of the multiple contributions from different atmospheric constituents at each of these wavelengths, but also because the ' aerosol channels' are not sensitive to the important sizes in the distribution. Further, referring to the altitude profiles of fractional extinction due to the constituents at the wavelengths claimed to be most sensitive to them, we immediately note the following: neither aerosol nor NO2 extinction, or both together, account for more than 30-40~o o f the total extinction at '~2 = 0.45/~m, at any altitude, (ii) the h4 = 1.0/~m channel

Vol. 118, 1980)

Remote Sensing of the Middle Atmospheric Aerosol

47

is not responding mainly to aerosols at any altitude, and (iii) the ha = 0.6 tzm channel shows a decreasing response to Oa extinction which crosses the 50~o threshold near 17 km altitude. Hence, the sensitivity of these channels to the constituents of interest varies greatly with the altitude, suggesting that a relaxation method may not be entirely appropriate in the present circumstances, even for the atmospheric model adopted by these authors. This suggestion is further heightened by examination of the constituent absorption and extinction cross-section presented (their Fig. 3) and discussed above (Fig. 2). Figure 9 of the same reference shows the results of 10 simulations plotted as error bars against the assumed extinction altitude profiles of the constituents at 3 of the 4 channels (A1 = 0.385 t~m omitted). There one sees that the accuracy of the inversions is poorest in precisely the altitude regions where the channel is not sensitive to the indicated constituents. There are also instances of significant bias on the log-extinction scale away from the true profiles. These findings are the more remarkable since the true assumed profiles were used in the above simulations. Clearly, therefore, other inversion schemes must be developed and/or tested using prior estimates that depart from the true solution, and their results intercompared.

IV. Inversions of simulated SAGE I data With the imposed restriction to four sounding channels, we set out to provide that reduction and interpretation technique that would maximize the scientific return of the SAGE I data. In light of the problems discussed in the previous section, some fundamental hypotheses have to be made if these data are to be inverted in terms of atmospheric parameters. Nonetheless, these hypotheses must be as few as are strictly required, and must further be physically plausible. They are (i) absence of aerosol excursions above 25 km and of NO2 below this altitude, (ii) below 25 km altitude, ozone (and NO2, if present) could be determined separately, (iii) the aerosol has a known refractive index, is assumed to be spherical (or describable in terms of equivalent spheres) and the minimum and maximum radii of its size distribution are known a priori. The information retrieved from the data is critically dependent on these assumptions, and must be so qualified in any subsequent use. Our solution is described below; it differs in many important aspects from that proposed by Chu and McCormick. A. Nature of the data inversion ill-conditioning The geometry of the extinction experiment is illustrated in Fig. 1, where for simplicity we have considered equidistant homogeneous spherical shells. The layers are numbered from the top of the atmosphere; likewise for the light rays with ray 0 being tangent to this top. Denote by H~m~ (i = 0, l, 2 . . . . ) the shortest distance

48

A. L. Fymat and C. B. Smith

(Pageoph,

Table 1 Ray

Half air mass factor

Constituents amount

0

Mo=M0o=0

U0= Uoo=O

1 2 3

M~ = Mil

u~ provided directly by measurement

M 2 = M 2 z + M,21 M a = M3a + M 8 2 + M ~ I

U3~ = U2~(Mz~IMzD, U32 = U22(M321M22)~ U33

i

M , -~ M f t A~ M t , t _ 1 "~ ' " " ~- M i l

U,',I = Uil(M21lMiz) --> U22

to be determined

point along the ray tangent to the bottom of the shell of number i, and by M~j, U~j and T,j respectively, the air mass, constituent amount, and transmission associated with the ray i in the layer j. Table 1 can be constructed for associating M, and U~ to ray i (all quantities M,0, U~0 and Tio being zero). In the computation of the absorption coefficients with effective pressure and effective temperature, respectively defined by Par = f P d m / f dm and T a , = f T d m / f dm, where d m is the differential air mass, and in the integration performed along the appropriate section of the ray path, single values of Pal and Tar must be assignable to each layer. These will change for different rays intersecting a given layer and must therefore be recomputed for each ray. It is possible to take an average over all rays crossing a given layer (not required), but this point would deserve some justification. In each layer, any ray can be related to the previous one following the relation we have adopted between the U's and the M's. Therefore, in any given layer, say of order k, the constituent amount of interest is that corresponding to the ray bearing the same number, i.e., Uk~. The corresponding transmissions (measurements) can be used to derive these amounts as follows: T ~ 12 ~ Too -= e-r176

-

1

(since the rays are unattenuated outside the Earth's atmosphere)

Tio = e -a(~176 =- 1

Tii/2

-

Tii

=

e -e(i)Uii

T21 ~

e-~(1)u~l

yields U11 from measurement of T~ and a priori knowledge of fi(1). __.

e-l~(1)Ull(M211Mll)

is a known quantity using above determination of Ull T2i yields U22 from measured 7"2.

T i/2 = T22T21 = e -z(2w22 Tal

=

e-B(1)u31

~

e-B(1)U2i(Mai[M21)

is known from earlier determination of U21. 7"32 =

e-/3(2)U32

:

e-B(2)U22(Ma2[M22)

is also known. T~ I2 = T33T32T3~ = e -~3~v3o

T32T3t yields U33 from measurement.

Vol. 118, 1980)

Remote Sensing of the Middle Atmospheric Aerosol

49

Thus, with the assumed slanting relation between U and M, the intermediate amounts UC can be immediately determined, and each successive measurement provides one unknown abundance U~. Thus, working from the top of the atmosphere downward, the problem is in a closed form and its solution can in principle provide the required constituent amounts. Using optical depths, ~-, instead of transmissions, the problem can be simply formulated in matrix form as: 2x = Ug, or, more explicitly: fUll

t\ rr~

0

U21 -+ U=

I

0

0

0

0

0

~(2)

0

0

5.(3)

4 Ual

T8

2

9

(6)

-~

4 rj

U32 --> Uaa

\

~(1)\

0

4

+

/~(j)

I VW In the matrix U, the important elements are the diagonal elements. Any row is determined from the previous rows following the arrows indicated. In the ease of a single absorbing gas, fi would be the absorption cross-section,/3, and U would include the desired number densities of this gas. These determinations start from Ull and the associated air mass Mn. If the latter quantity is small, the divisions by it that are subsequently carried out will yield large optical depths which, in turn, yield small differential transmissions. A chain reaction on the other transmissions sets in. Inaccuracies in M~I will get amplified creating an instability in the problem. These diff• could be avoided by choosing a sufficiently wide layer 1 but at the expense of vertical resolution at the high altitudes. Rather than following the kind of forward recursion just discussed, it may be more advantageous to utilize a backward recursion starting from the atmospheric layer of lowest altitude sounded. This upward building process must end at the highest altitude where the air mass is accurately known. The ratio between this air mass and that determined from the computations could then be used as a normalization constant for the entire profile. Thus, in the case of a single constituent, the cause of the ill-conditioning can be traced to the low air mass at the high altitudes. We have suggested two ways of overcoming it. When several absorbing gases are present, the number densities can no longer be included in U, and the ~'s which must incorporate them are truly absorption

50

A.L. Fymat and C. B. Smith

(Pageoph,

coefficients, not cross-sections. All that one can get is the vertical profile of the composite/3 at each sounding wavelength. This would also be the case if monodispersions of aerosols are also present (providing their refractive index is known). The set of fl's thus determined is the one that enters in the inversion of equations (6) and (7) below. In the case ofpolydispersions of aerosols, the corresponding/3 further depends on the size distribution which is an additional unknown of the problem [see equation (5)]. Providing the high altitude air mass ,problem has been taken care of, the system in equation (6) is already in a convenient form for solution by successive determination of the extinctions/3,(h) at decreasing altitudes. As discussed earlier, the choice of a nonuniform discretization of the atmosphere into layers having more uniform masses does provide an alternative approach which could allow stable direct recovery of extinction profiles independently for each layer, if the altitude layers are suitably selected. The penance to be paid when using such an approach is the coarser vertical resolution at the high altitudes. There are, however, several advantages to this direct method other than its numerical simplicity. First, it does not require prior estimates of the extinction profiles for the constituents. Second, for the absorbing gases, it can make use of the constituents cross-sections for the recovery of the gas number densities;enough channels must remain available for recovery of effective aerosol parameters. This is preferable to the naive assumption that the channels are most sensitive to just one constituent. Third, many wavelengths can be processed independently, whether or not future SAGE wavelengths are at the peak response of any constituent sought.

B. Sounding above 25 km altitude In the case of SAGE I, at each of the altitudes of interest, we can write for the composite extinction factor [see equations (4) and (5)]: [3 = ~N, or

/32 /33

/3~

= [tiM(A2) fiN(h2) /~0(h2) ~/JM(A3) 0 /~o(A3)

\~(~)

o

NN ,

(7a)

No] N.

o

where, as earlier, A1 -- 0.385 tzm, h2 = 0.45 t~m, A3 = 0.6/~m and A4 = 1.0 tzm are the four SAGE I channels. Referring again to Fig. 2 and also to Fig. 4 of CM in which the atmospheric transmission versus tangent altitude is graphed, we see immediately that the sounding channel 3,4 transmits almost all the incident solar radiation. This near-unity transmission renders h4 inefficient as an atmospheric sounding channel. This is rather an advantage than a drawback for, instead of the system (la), we can use the system: /3z /33

= |/3M()tZ) /3U(ZZ) /30(A2) \/~M(A3) 0 L(h3)]

NN . No

(7b)

Vol. 118, 1980)

Remote Sensing of the Middle Atmospheric Aerosol

51

Thus, if the matrix/~ is well-behaved, this system could be inverted uniquely to yield the required number densities at each atmospheric level. The reconstruction, altitude by altitude, of the vertical profiles of these parameters will be discussed below. As indicated earlier, one can use either Method No. 1 or Method No. 2 in arriving at the solution. What is important, however, is that/3M = NM~M follows a power law variation in altitude (see, for example, Fig. 5 of CM which displays the vertical extinction profiles for Rayleigh, 03, NO2 and aerosols). The power exponent is slightly different on either side of ~ 40 km. Thus, only two determinations of the molecular extinction are sufficient for completely characterizing this parameter above this altitude. Likewise, from ,-,40 km down to 10 km, two similar determinations are also sufficient; the latter could be obtained in the range ~ 30-40 km. In summary, in the absence of aerosol incursions above 25 km, it is possible to recover ArM, NN and No from the solution of equation (7b), and to further determine the molecular contribution in the region ~ 10-30 km from that at higher altitudes. This would then reduce the number of unknowns at these lower altitudes for which all of the available sounding channels could be used. In the presence of higher altitude aerosols, the problem is less well determined, as discussed earlier.

B. Sounding below 25 km altitude The molecular extinction contribution having been determined, it could be subtracted from the measurements. The analogue of system (7) would be: -

\

[33 ~M(A3) ] \ ~o(~3)[3A(A3][Na] )

(3)

Even using the above device for determining the molecular density, and solving only for the extinctions, the problem is clearly underdetermined by one order (an additional order would be added if NO2 were present in the lower atmosphere). Indeed, there are five unknowns /~A(;~), /3A(A2), /]A()~a), /3A()q) and No to be recovered from only four measurements. Additional measurements would not resolve this ambiguity because each measurement, say at Z = '~5, would introduce a further unknown /JA(;~5). The only way out of this difficulty is to attempt to retrieve the ozone independently of the aerosol, and to provide as many sounding wavelengths as desired values of the aerosol extinction. For a follow-on experiment, we suggest using a pair of ozone channels between which the ozone extinction is greatly variable while the aerosol extinction variation is relatively negligible. If NO2 were also present, the same technique utilizing a close pair of wavelengths in the absorption band could likewise be used for recovering the number density vertical profile of this constituent. Assuming that this approach is followed, all four channels could be used for the aerosol. We illustrate below in great detail what type of aerosol information (beyond the extinction coefficients) could be extracted from these four wavelength measurements.

(a) 10"1 m:

(~)

(b)

......

'"'1

107

[

VOLCANICA[ ROSOL o SIMULATEDDATA ,~ RECOMFIITEODATA

Z~

'

I''""l

105

PO

~

107

N p - 1,234plcm3 AI= 0 . 7 7 3 ~ 2 1 m 3 -2 V = 0.3|5.M3,ecm3 _

OZ

10_2 ~

' '''"'= Io.[llm 3

:'"l

....

~'"1

, ..,."L

N 9 IO.41~

3

F1 = 0"1310#/~3 A = oJme~2/~ 3

Z 105 0 Z --O 3

V = O+3/ZZj31~t3

~,o

IO3

E~ : IOI uO ~

~a~ e 10-3

o

Z

Z~

G Z

10--~

10-~ 10-4

MINIMUM OEVIAINICE SOLUTION

10.5

,,I , , ...... I , . , ,. 10-2 10-1 10~ PARTICLE RADIUS (MICRONS)

-z--.~--~-O

100 WAVELIENGIH (MICRONS) 107

.Tfl~--l~-rTh,, I N ~ 4,58/m

, , i

,,r,_

g~.'o~

107 J " q

3

#1 = O'O72p/cm3

---

= 0.309p31~n3

' ''"'"1

Z

--

o~

~ U 103 ~, : 10 I

iO-3

MINIMUM HOrH -i ~-SOLUTION -~ 10-5 .. L - - a J _ , ~ . u l ~ - ~ . ~ u d 10-2 10-1 10 PARTICLE RADIUS {MICRONS)

, ,.-rrlr

H0flOTONIC NnN-NEGAT I VE SOLUTION

105

A . 0,~Sp21c.l 3 v

10-2 IO-I PARTICLE RADIUS (MICRONS)

o m U

1o3

~

10

z

lO_a

N = 2g3~l/cm3 Pl "a';'aP/c~:] A = o 96tip2/~m3 v - ~.a3op3/r 3

10-5

J i i,~-,J .... ~. 10-2 10-1 I0 PARTICLE RADIUS (MICROI4S)

,,d)

'

' '"'=1 .... N - 271 4 1 ~ 3

'"

1010

_~ lO"

A = O,461M2km3 v - 0.O93M31~.3

ib6

Io6

~

104

I

=

.

' ' r~nr ....... N = 1114043.1~3 A = ~1.7 p2/m 3

cm

106

V = 0.317p31~ 3

104

~ xxx

102 10 ,0 02

1 0 0 _-

(h)

lO IO N - 43740.1~ 3 p I - 341"Iplcm~ A = 16.2I/J 2/cm~

104

102 10 -1

,

(g)

if) 101R ~ " 1

9 MATRIX INVERSIOfl

9

100

x-

10_1

10 -I

:- ENTROPy 10-3 : SOLUTION x x

- WITH 2

I0 -3 :- SMQ~rIIING --" COt~TRAINIS 10-5 ,-d , ~u~u*l , , iO-2 i0-! 100 PARTICLE RADIUS fMIC~ONS)

o

~.,,I , , ,.,,,,I , .... 10-2 10-1 i0 0 PARTICLE RADIUS (MICRONS) 10-5

Z

~ NON-NEGATiVE

10-3- LEASI ~SQtlARE$ 10_5

~ ~OLUTION I , ,,,,,,,

10-2

10-I

, .,,,

IO0

PARTICLE RADIUS (MICRONS)

-Q.,

o

0

Z

LINEAR "~x i ---PROGRAMMING x WITtl 9

106

106

Z

o

102 100 10-I

D

i0-3 10-5

10 " 10-' IO.`3 PARTICI E RADIUS (MICRONS)

(0

z

MAXIMUM ENVELNPE SOLUIK)N

It ~tJIlUd

lO-~

IO-t

~L~

i~~

PARIlCLE RADIUS {MICRONS)

(i)

Figure 3 Illustrating the results of seven numerical inversion techniques applied to S A G E simulated data ()t = 0.385/,m, 0.45 t,m, 0.60 txm and 1.0/zm) for the reconstruction of the aerosol size distribution. Case of a background aerosol model (log-normal distribution with rg = 0.0725, ag = 1.86 and N

=

10 cm-3).

(a) simulated extinction data and extinctions recomputed from the inverted size distributions. (b) actual size distribution and computed averages (arrows on the abscissa scale indicate sizes most sensitive to S A G E sounding channels). (c) inverse solution using the actual distribution as a prior estimate. (d)-(j) inverse solutions using no prior estimates.

Vol. 118, 1980)

Remote Sensing of the Middle Atmospheric Aerosol

g

dd

~

,.~ 0 ..~

d

E ddd

dd~d

,q. II

d c~ 0

"2 O

O

c5 d d ~

~

~m

rD

o

0

0

O

O

..~

a9

53

54

A.L.

F y m a t a n d C. B. S m i t h

(c)

(b)

(o) 10;" I "'"1

1 0 -I $

'

0 ~J 105

I-., ~10

(Pageoph,

' ' ~1''1

'

~ I 0 7 ! .... I

' I ....

m- IO.O/~3 ~t " ~ A + n 358p2/,:,,,3 v = ofieo.uJlc,.3

z 0 O10-

~

SIZE OISTRIBUu

~0 ~

N

0 0

DEVIANCE SOLUTION MINIMUM

0

Z

' ' ....

~11 - (l.~lgp/cm3 A ~. 0.31Dp21~m3 V - 0.090U31~.3

103

BACKGROUND AEROSOL OSIMULATED DATA AECOMPUTEIDUATA

8 ~ I0 "~

'

N - 10.41~3

I05!

i 103

'

' ' '"'"1

~10-3

x ACTUAL ~ AVERAGE

~IO-:

o ,

10

,

10-~ ,,,~ . . . . . . . ~

,,,,I

10 0

~03

l0 ~

: 3.5/cm

r #1

=0"487'U/crn3 "

: A

= 0.274/.t2/crn 3 = =

x-

3~t.3/c,n3 Pl = 4+3Micro3

:

0.082# 3 / c m

~

1~

A " O.6OIp21cm 3

V = O.102.u3/cm3

3~

I~

x

Z l0 O

IO-I IO0 PARTICLE RADIUS (MICRONS)

u 107

3'

- N

"V"

.IJ.L

I0-2 -IO-I 0O PARTICLE RADIUS (MICROHS)

Z

WAVELENGTtl (MICRONSI

io 3 101

Z

O

~ 10 - I

x x~

m I0MINIMUM NORM

10-3 ~ I O -5

10-3 . MONOTONIC

SOLUTION

~u~

~10

NONNEGATIVE SOLUTION

-5 t,,,I

io - 2

IO-1

, ....... I

(~)

(a)

(0 o~,

~.,

(h)

(g)

IO9

N=43E+/cm3

~o7

tI I " 5.OlplCll+ ] A- I O/~+/r 3 V ~ O 336~31cm 3

A"

~.~ lO3 z O F- 10 LINEAR '~ PROGRNI~ING " . ' 10- WITH . c~ NON-flEGAT I VE

~ ,

101 ~ A TR IX

z

121.g/~21

xxxx = 1.86p I~ ~

1~7

?

1o 5

IO~

m

INVERSION 'IO-I .WITII 2 SMOOTII NG 10-3CONSTRAINTS -51

g2~fig+/~ ..

P i "6o~.p/

_o

m

N -

1~9

o

I0 5 Z

.....

IO -2 I0 -1 tOo PARTICLE RADIUS (MICRONS)

io O

PARTICLE RADIUS (MICRONS)

,,.,I

........

I

o

IO-;-LEAST-SQUARES ~m."7.Lq,N.,

....

IO io-2 IO-I Io o PARTICLE RADIUS (MICRONS)

I

Z

PARTICLE RADIUS (MICRONS)

IO-" ,0-2

IO- I . . . . . I OO PARTICLE RAOIUS (MICRONS)

N - 9~616 I/cm 3 TO91:'''~ ....... ~ ....... m

IO7

p - E&86Plcm3 A + +m+~ 2 /cm3 + k= v - 0,560~z3lcm 3

+++-

g

I0-3

WF 1C,IIT F I) AVERAGE ~.fll l i t ION

. I . . . . 100 10 - ~l0 . . . . . . .10PARIICLE RADIUS (MICRONS)

(;)

c,

1 0 - - E N V E I OI'L +SOLUT1ON

i]

To-:Z

lO--" o-2 IO- I 10O PARTICLE RADIUS (MICRONS)

(i)

Figure 4 S a m e as Fig+ 3 for a v o l c a n i c a e r o s o l m o d e l ( l o g - n o r m a l , r~ = 0.097, % = 2.02, N = 10 c m - 3 ) .

Vol. 118, 1980)

Remote Sensing of the Middle Atmospheric Aerosol

55

D. Numerical experiments for aerosol inversion using four SAGE wavelengths For the following study, we have retained the SAGE I wavelengths, and have assumed that they are all available for the aerosol problem. Our objective was to determine what kind of aerosol information could be retrieved from 4 wavelengths. Our library of inversion routines, developed previously, includes: (i) minimum deviation method, (ii) minimum norm method, (iii) monotonic non-negative method, (iv) matrix inversion method with two-smoothing constraints (as applied by Yamamoto and Tanaka), (v) maximum entropy method (SMtTH, 1978), (vi)linear programming method with non-negative least squares, (vii) weighted-average method, and (viii) minimization search method. We have applied the first seven methods for the two aerosol models (background, volcanic). Our results and conclusions, assuming spherical aerosols of known refractive index, are presented below. Figure 3(a) shows the ' d a t a ' as the variation of extinction coefficient with the four wavelength channels. It also exhibits the extinction recomputed from the inverted size distributions presented in the next Figures and retrieved using each of the seven inversion methods. We also illustrate the maximum envelope solution. All eight results fit exactly the data and, consequently, we have reproduced only one of them. Because of this exact fit, we are confident that our inversions do provide a good test of the information content and parameter estimation at these wavelengths. Figure 3(b) displays the true log-normal model distribution for the background aerosol. The distribution parameters: r~ = geometric radius, % = standard deviation, N = number density, tLa = first moment of the distribution, A = geometrical area of the polydispersion (related to the second moment), and V = polydispersion volume are also shown. The 'average' distribution showing averages at 4 radius values is also indicated for information. The inverted distributions using the different methods are graphed in Figs. 3(c) through 3(j) in which the values of the distribution parameters have been reported and summarized in Table 2. In Fig. 3(c) only, the true distribution was used as a prior estimate, as was done in the inversions illustrated by Chu and McCormick. All other inversions use zero as a prior estimate. Figure 4 displays the corresponding results and information for the volcanic aerosol model. Table 2 illustrates the following points (i) if good a priori information is known about the solution, it is possible to perform reasonably good inversions (see method 1 and Figs. 3c and 4c). If no such information is available, there will be as many solutions as inversion methods tried ; (ii) the Minim u m Deviance method has performed best among all methods applied. Nevertheless, its results are not very accurate; and (iii) in practice, among methods providing physically meaningful solutions, no single method could be preferred to all others. The well-known non-uniqueness of the solution is here well represented. In addition, (iv) the data were assumed to be exact; experimental and numerical noise would add to the uncertainty in the solution; and (v) in all inversions, we further assumed that we knew the values of the minimum and maximum radius of the distribution (0-1.0 t*m in the case studied), and we made

56

A.L. Fymat and C. B. Smith

(Pageoph,

sure that 99~o of the distribution is contained in this interval. In practice, this information is not available a priori and this would further compound the non-uniqueness features of numerical inversions.

V. Proposedstrategyfor follow-on experiments The above analysis of the SAGE I concept has suggested the following possible improvements for follow-on experiments: (i) a different data sequence strategy with a faster scanning rate of the solar disk at the high altitudes where the uncertainty is largest (this is also the source of the mathematical ill-conditioning of the data inversion problem); (ii) additional sounding channels at the shortest possible wavelengths (A < 0.385/~m) that would be more sensitive to the bulk of the aerosol sizes. The determination of the minimal number of such channels remains to be investigated; (iii) a pair of additional ozone sounding channels on the short-or-long-wavelength side of the Chappuis absorption band, or one channel on each side of the band center, or even on the, shorter wavelength Hartley-Huggins band; (iv) possibly different data inversion strategies that utilize not only the near altitude separation between NO2 and aerosol contributions (as proposed in SAGE I) but also the power law variations in both altitude and wavelength of the molecular extinction; and (v) different data inversion methods. These several suggestions could be incorporated in SAGE II and subsequent experiments for a larger and less ambiguous scientific return of the data. With regard to the last suggestion, we have already indicated how the profiles could be reconstructed from the bottom up to the top of the atmosphere. The same idea could be implemented using our minimization search inversion approach (FVMAT, 1976). It has been applied recently by MILL and DRAVSON (1978) for recovering both a constant and a variable CO2 mixing ratio profile from transmittance data with random errors, and for reconstructing CF2CI2 vertical profiles from solar occultation data near 930 cm- 1. Another important improvement would consist in adjoining to the transmission measurement a forward scattering measurement. A complete description of this other technique can be found in FVMAT and MEASE (1978). Our reasons are the following (i) forward scattering is a very efficient sensor of particle size, much more so than scattering at larger angles, (ii) it is not too sensitive to the particle shape or orientation, (iii) it is little sensitive to the particle refractive index, particularly for angles close to the exact forward direction; this influence of the refractive index can be represented fairly simply in terms of the extinction efficiency of the aerosol (FYMAT and MEASE, 1979), (iv) it rests on a completely different physical phenomenon than transmission, and thus can provide an independent confirmation or invalidation of the transmission experiment result, (v) a closed form analytical solution of the data inversion problem is available, and (vi) it utilizes basically the same geometry as the

Vol. 118, 1980)

Remote Sensing of the Middle Atmospheric Aerosol

57

occultation experiment. Extensive numerical tests o f this inverse solution have shown that: - The inversion formula o f FYMAT (1978) for forward scattering enables one to reconstruct the size distribution without a priori modeling of, or information on, the distribution. - Examination o f the integrand only o f the inverse formula, evaluated progressively as the data is being received, provides meaningful instruction as to (i) when to terminate the experiment as it would provide no additional useful data, (ii) whether the dispersion under examination consists o f mono-sized particles, and what is the n u m b e r o f its modes. - A size resolution o f a few tenths o f a micron can be achieved with proper selection o f the forward scattering cone half-width, and by the angular resolution with which this cone is scanned. -Moderately strong r a n d o m and systematic noise values are without serious effect as well as multiple scattering, source non-monochromaticity, instrument bandwidth, and finite field-of-view owing to the great stability o f the inverse solution. - The mode radius seems to be always locatable even with only a few measurements. These several advantages appear to us to be o f such an importance as to warrant the most serious consideration o f a satellite forward scattering experiment.

REFERENCES CHU, W. P., in Inversion Methods in Atmospheric Remote Sounding, (Academic, New York 1977), A. Deepak, Ed. CHtI, W. P. and MCCORMICK,M. P. (1979), Appl. Opt. 18, 1404-1413. DEEPAK, A., ed., Inversion Methods in Atmospheric Remote Sounding (Academic, New York 1977), 505 pp. FYMAT, A. L. (1976), Phys. Earth & Planet, Inter. 12, 273-282. FYMAT, A. L. (1978), Appl. Optics, 17, 1676-1677. FYMAT, A. L. and ZUEV, V. E., eds. Remote Sensing of the Atmosphere: Inversion Methods and Applications (Elsevier, New York 1978), 327 pp. FYraAT, A. L. and MEASE,K. D. (1979), Appl, Opt. (in press). MILL, J. D. and DRAYSON,S. R., in Remote Sensing of the Atmosphere: Inversion Methods and Applications (Elsevier, New York 1978), A. L. Fymat and V. E. Zuev, eds., 123-135. PEPIN, T. J., in Inversion Methods in Atmospheric Remote Sounding (Academic Press, New York 1977), A. Deepak, ed. PINNICK, R. G., ROSEN,J. M. and HOFMANN,D. J. (1976), J. Atmos. Sci. 33, 304. SCHUERMAN,D. and GREENBERG,J. M. (1974), Appl. Opt. SMITH, C. B. (1978), Ph.D. dissertation, Univ. of Calif., San Diego. TWOMEY, S. (1977), Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, New York), 243 pp. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkhiiuser Verlag, Basel

Instantaneous Global Ozone Balance Including Observed Nitrogen Dioxide By SUSAN SOLOMON, HAROLD S. JOHNSTON, MARTA KOWALCZYK, a n d IVAN WILSON1)

Abstract - The catalytic destruction of stratospheric ozone by the oxides of nitrogen is believed to be an important part of the global ozone balance. The lack of sufficient measurements of NOx concentrations has impeded efforts to quantify this process. Recent measurements of stratospheric nitrogen dioxide from ground-based stations as well as aircraft and balloons have provided a first approximation to a global distribution of NO2 vertical columns at sunset. These observed vertical columns have been translated into time-dependent vertical NO2 profiles by means of a one-dimensional atmospheric photochemical model. Using recent observations of air temperature and ozone along with this information, the independent instantaneous (one second) rates of ozone production from oxygen photolysis, P(O3), of ozone destruction from pure oxygen species (Chapman reactions) L(Ox), and of ozone destruction by nitrogen oxides L(NOx) were estimated over the three-dimensional atmosphere. These quantities are displayed as zonal average contour maps, summed over various latitude zones, summed over various altitude bands, and integrated globally between 15 and 45 kin. Although the global summation between 15 and 45 km by no means telIs the complete story, these numbers are of some interest, and the relative values are: P(O3), 100; L(Ox), 15; L(NOx), 45 + 15. It is to be emphasized that this relative NO~ contribution to the integrated ozone balance is not a measure of the sensitivity of ozone to possible perturbations of stratospheric NOx; recent model results must be examined for current estimates of this sensitivity. Key words: NO2 distribution; Ozone destruction by NO~.

1. Introduction The importance of the oxides of nitrogen in affecting the stratospheric ozone balance has been a subject of interest in atmospheric chemistry for several years (CRUTZEN, 1970). Recently, NOXON (1978, 1979) and NOXON et al. (1979) have presented measurements of the stratospheric c o l u m n of nitrogen dioxide, NO2, at n u m e r o u s latitudes and seasons. There are now several NO2 profiles up to the middle stratosphere observed from balloons (ACKERMAN et al., 1975; FONTANELLA et al., 1974; OGAWA, 1979; MURCRAY et al., 1974; HARRIES et al., 1976; EVANS et al., 1977; EVANS et al., 1978; GOLDMAN et al., 1978; DRUMMOND and JARNOT, 1978). DOTscrt (1978) has reviewed all of the available data on the vertical ozone distribu1) Department of Chemistry, University of California, and Materials and Molecular Research Division, Lawrence Berkeley Laboratory, Berkeley, Califoria 94720, USA.

Vol. 118, 1980)

Instantaneous Global Ozone Balance

59

tion measured with chemical sondes and one year of ozone data obtained by backscattered ultraviolet radiation from the Nimbus 4 satellite. We have taken these recent measurements of temperature, ozone, and nitrogen dioxide; and using a photochemical model we have translated the observed NO2 columns to time-dependent vertical profiles, which were then extended to global stratospheric distributions. We then examined the global distribution of the rate of NOx catalyzed destruction of ozone by the method of instantaneous rates. The method of instantaneous rates has been described previously (JOHNSTON and WHITTEN, 1973, 1975; JOHNSTON,1975). Briefly the observed distribution of temperature, oxygen, ozone, and incoming solar radiation outside the atmosphere are used to calculate photolysis rates on a grid containing 1 km vertical intervals, 10~ latitude intervals, and 15~ longitude intervals. Rayleigh scattering and albedo effects are treated by the method of ISAKSENet al. (1976). The concentration of O(3P) is calculated at each grid point using the steady-state approximation. At each grid point three independent components of the global ozone balance were evaluated: (a) The rate of ozone production from the photolysis of oxygen, P(O3), which is 2j[O2] as can be seen from the pair of reactions

net:

O~ + hv(h < 242 nm)---> O + O

(slow)

(O + O 2 + M-->O3 + M) • 2

(fast)

(l)

302 + hv --->203

(b) The rate of ozone destruction by the pure oxygen family of reactions, L(O~), which is 2k[O][O3] on the basis of

net:

03 + hv(uv, vis) --> 02 + O

(fast)

O + 03--> 02 + 02

(slow)

(2)

203 + hv --> 302

(c) The rate of ozone destruction by the oxides of nitrogen, L(NOx), which is 2k'[O][NO2] as can be seen from NO + O a - ~ NO2 + 02

(fast)

03 + hv(uv, vis) --~ 02 + 0

(fast)

(3)

NO2 + O--> NO + 02 net:

203 + hv -+ 302

In each of the above cases the loss or production of ozone resulting from the catalytic cycle is given by the rate determining step in each cycle. One might protest that the Ox, NOx, HO~, and C1X families of reactions are coupled, and as a consequence the ozone production and losses cannot simply be identified as 2j[O~], 2k[O][O3], and 2k'[O][NO2]. It is true that the O~, NO~, HOx, and C1X families are strongly coupled, but it is appropriate to review the nature of the coupling and to note what retains its identity during the interactions. Suppose the

60

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph,

photochemistry of the stratosphere is represented by m chemical species, A1, A~. . . . . Am, and n photolytic and chemical reactions with rate constants, Jl,J2 . . . . . kn, at each grid point of the model. A change in the concentration of a chemical substance As may change the concentrations of many, perhaps all, other species. If changing A~ causes a change in local temperature, all temperature-dependent rate constants would be affected. If changing As causes a change in the ozone profile, the distribution of solar radiation in the atmosphere and the photolytic rate constants j would be altered. As an example, an increase in nitric oxide changes the concentrations of HOx species through the reaction HOO + N O - + HO + NO2 and changes the concentrations of CIX species through the reaction CIO + NO -+ C1 + NO2. Thus the concentrations of various species At are coupled to each other, and by feed-back mechanisms the values of temperature dependent rate constants may be affected. However, there are some things that are not changed when species concentrations are altered, in particular the identity of the n photochemical reactions in the model. The set of photochemical reactions can be expressed in terms of linear combinations of these reactions. With care, a set of linear combinations of reactions can be found such that the net effect of each is either (i) an increase in two molecules of ozone, (ii) a decrease in two molecules of ozone, or (iii) no change in ozone (JOHNSTONand PODOLSKE, 1978). Reactions (1), (2), and (3) represent such linear combinations of reactions. The measured ozone and nitrogen dioxide concentrations are the observed results of all the various coupled chemical processes and of atmospheric transport. At each grid point of the sunlit atmosphere, three components of the ozone balance can be evaluated from 2j[O2]obs, 2k[O]o~1o[O3]obs, and 2k'[O]~c[NO2]ob~. These quantities have been zonally averaged, vertically summed, and expressed as total global rates and as global rates in 5 km altitude bands. In this work, then, we have examined the contributions made by NOx and Ox processes to the natural global ozone balance.

2. Observational data

D~TSCn'S (1978) data were supplied as temperature and ozone partial pressures on a pressure grid from 0.5 to 250 rob, each 10 degrees of latitude from the south to the north pole, and for each month of the year. Data for three months were averaged to give seasonal averages, i.e., March, April, May; spring, etc. For each of the four seasons, the data were converted to ozone mixing ratios and ozone concentrations using the barometric equation to yield altitudes at I km intervals starting from the 250 mb level and interpolating between the given pressure levels. For altitudes below 250 rob, earlier distributions were used (DfOTSCH, 1969; JOHNSTON and WHITTEN, 1973). Examples of the global spring and winter temperature distributions are given in Fig. I. The corresponding ozone mixing ratios (ppbm) and concentrations in units of 1012 molecules cm -3 are presented as Figs. 2 and 3 respectively. The concentration of atomic oxygen was calculated at each grid point of the

Vol. t 18, 1980)

61

Instantaneous Global Ozone Balance TEMPERATURE, K

-L----~-'-~-----'~ 40 ~

26o- ~ 2 5 0

~

5 zo

280 -90 Fell

-60

-50

0

30

60

90-90 -60 Spring Summer

-30

0

30

60

90 Winter

LATITUDE

Figure 1 Temperature in the troposphere and stratosphere. The south pole is - 9 0 ~ and the north pole is 90 ~ One panel is the average of DOTscn's (1978) values for March, April, May; the other is the average of Dec., Jan., Feb.

atmosphere and for each of the four seasons. The orientation of the sun relative to the earth was that for spring and fall equinox and winter and summer solstice. A zonal average of the atomic oxygen concentration over daylight hours was obtained for each grid point of altitude and latitude, and representative results are given in Fig. 4. OZONE MIXING RATIOS (PPMV)

I

t

-90 Fell

-60

-50

0

50

60

60 90 -90 Spring Summer

-30

0

LATITUDE Figure 2 Ozone mixing ratios (parts per million by volume).

30

60

90 Winter

62

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph, OZONE CONCENTRATION, I012 MOLECULES CM"3

50 4O

:30

c~ 20 LO

0

L

-90 Fall

I

I

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J

k

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0

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:30

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I

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-30

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I

0

i

I

50

I

I

I

I

60

I

90 Winter

LATITUDE

Figure 3 Ozone concentration in units of 10TM molecules cm -a. Observational data are now available that give a first approximation to the global distribution of stratospheric NO2 (NoxoN et al., 1979; NoxoN, 1979). The measurements were made from the ground or from aircraft during the twilight period using Rayleigh-scattered sunlight from overhead. This gave changes in the NO2, visible, absorption-spectrum through long optical paths in the stratosphere as the sun moved OXYGEN ATOM CONCENTRATION, MOLECULES CM-3

E hi tm

-

50

F--

;_, 20

IE 3E tE

I

-90 Fell

-60

-30

0

50

60

90-90

-60

-30

0

30

60

Spring Summer LATITUDE

Figure 4 Atomic oxygen concentration, 12 hour, daytime average. 3E9 = 3 x 109.

90

Winter

Vol. 118, 1980)

Instantaneous Global Ozone Balance

63

Table 1 Vertical column of stratospheric nitrogen dioxide in units of 10is molecules cm-2 as read from Figs. 1, 2, 3, and 6 of NOXON (1979)

Season

Noxon Fig.

Date

SP

1

4/75

3/77

10/76

3

F

2

3/77

1

10176

3

Lat. Deg.

NO2 1015

77 N 63 N 48 N 43 N 41 N 37 N 27 N 17 N 12 S 31 S 35 S 65 N 53 N 49 N 40 N 14 S

4.9 2.8 2.8 4.6 3.9 3.7 3.1 2.3 2.2 4.4 5.5 1.9 1.9 2.3 3.9 2.6 2.5 2.6 2.5 2.2 2.1 2.9 3.6 4.2 3.5 3.2 4.0 4.0 5.0 4.5

44 N 42 N 40 N 20 N 65 N 53 N 49 N 40 N

Season

Noxon Fig.

Date

SU

1

7/75

3

W

1

2/77

3

6

2/77

Lat. Deg.

NO2 1015

82 N 76 N 69 N 59 N 53 N 40 N 65 N 53 N 49 N 40 N 57 N 56 N 55 N 52 N 51 N 48 N 47 N 46 N 45 N 44 N 43 N 65 N 53 N 49 N 40 N 56 N 49 N 44 N 40 N 30 N

6.9 6.1 5.3 5.4 5.2 5.7 5.1 4.4 4.6 4.9 1.3 1.2 1.4 1.4 1.1 1.1 2.3 1.9 3.2 3.5 3.8 1.3 1.4 2.7 2.3 1.4 1.1 3.0 3.7 3.8

from 88 ~ to 97 ~ with respect to the vertical. The spectral changes d u r i n g sunset (or sunrise) gave the value of the stratospheric NO2 vertical c o l u m n as p r i m a r y information a n d gave a n estimate of the altitude of m a x i m u m NO2. In this article we interpret N o x o n ' s stratospheric NO2 c o l u m n as being that between 15 and 50 kin. At mid-latitudes, NoxoN et al. (1979) reported AM a n d PM c o l u m n s of nitrogen dioxide as well as the altitude of its m a x i m u m concentration. D u r i n g the day the stratospheric NO2 c o l u m n increases by approximately a factor of two, p r e s u m a b l y as the c o m p o u n d s N205, HNO3, CIONO2, and possibly H O O N O 2 are photolyzed. NoxoN (1979) presented the global behavior of NO2 in a series of figures. As a f u n c t i o n of latitude, his Fig. 1 gave representative m e a s u r e m e n t s of the late a f t e r n o o n vertical c o l u m n of stratospheric NO2. We read these points from the graph a n d listed them in Table 1. I n N o x o n ' s Fig. 2, the NO2 c o l u m n s at Cusco, Peru, 14~ ~vere

64

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph, NITROGEN DIOXIDEVERTICAL COLUMN I0

I

'

I

I

I

l

l

l

I

l

l

l

l

l

I

l

E

g "6 B

0

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6 .E

5:

~~

~

(D I

z

] -90

-60

-30

~

T

I

0 Lotitude

I

I

t

l

30

l 60

90

Figure 5 Observed PM vertical columns of stratospheric nitrogen dioxide, fall-spring: (i) NoxoN (1979), Fig. 1; [] NOXON, Fig. 2; A NOXON, Fig. 3; D. HARRIES e t al. (1976); C. MURCRAY et al. (1974); B. OGAWA (1979); A. ACKERMANet al. (1974). The line is that used as the primary case for this study. Sensitivity studies were made with NO~ columns 2/3 and 4/3 of this line.

given over a nine day period; the late afternoon columns read from the graph are in Table 1. At four stations (40~ 49~ 53~ and 65~ enough data were taken to provide 12 month variation of the NO2 columns, and these data are given as Noxon's Fig. 3. For each of our four seasons (winter solstice, spring equinox, summer solstice and fall equinox), we read the value of the NO2 column from Noxon's smooth NITROGEN DIOXIDE VERTICAL COLUMN OJ

E

u

I0

I

I

I

I

~

I

I

[

I

I

I

I

I

I

I

I

9 8

7 -(D

F F

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OH

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--

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5

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4

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G

A

0

" 9

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0 -90

~

I -60

I

I

[ -30

t

I

I

0 Lalitude

~

I

l 30

I

J

I 60

b 90

Figure 6 O b s e r v e d PM vertical c o l u m n s o f s t r a t o s p h e r i c n i t r o g e n dioxide, w i n t e r - s u m m e r : Q , NOXON (1979), Fig. I; ~ , N o x o N , Fig. 3; O , N o x o N , Fig. 6. G. GOLDMAN et al. (1978); E. EVANS et aL (1977) ; F. EvANs e t al. (1978); H. DRUMMOND a n d J ARNOT (1979). T h e line as d e s c r i b e d in Fig. 5.

Vol. 118, 1980)

Instantaneous Global Ozone Balance

et

Z ~

0

~4 O0

~o r ZZ O0

~

~z

._= ,,4 ~.~

65

66

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph,

curve in his Fig. 3, and these points are included in Table 1. Also the data points in Noxon's Fig. 6 are listed in Table I. For the relatively few NO2 columns observed in the southern hemisphere, (SH), Noxon found a gross symmetry with respect to the corresponding season in the northern hemisphere, (NH). To extend the data base, we reflected all observed points in Table 1 to the other hemisphere with a six month phase shift. The points in Table 1 are plotted in Fig. 5 to represent the observed NO2 stratospheric columns for spring (NH), fall (SH) and in Fig. 6 to represent summer (SH), winter (NH). The vertical distributions of stratospheric nitrogen dioxide as observed from balloons typically go from a lower altitude o f 12 to 20 km to an upper altitude of 28 to 40 km. The profile measured by DRUMMOND and JARYOT (1978) extended from 20 to 50 km. Some of these measurements were made at sunset, some at sunrise, and some at noon. Noxon's stratospheric NO2 columns of Table 1 and Figs. 5 and 6 refer to late afternoon conditions and essentially to the NO2 between 15 and 50 kin, and the column provided by the balloon profiles are not strictly comparable. We filled in the gaps in the lower stratosphere, or upper stratosphere, or both to give extended balloon profiles from 15 to 50 km by using estimates from the photochemical model. In the cases where the balloon profile did not correspond to late afternoon conditions, we ran the photochemical model from sunrise to sunset to obtain a model value for the PM/AMratio for the NO2 column. The values, typically about two, were used to scale the observed column to PM conditions. Table 2 contains the resulting columns from the observed NO~ profiles and the value of the corresponding column scaled as described above. Each balloon study is labeled by a letter A through H in Table 2, and these letters appear as data points on Figs. 5 and 6. Entry A in Fig. 5 is based on ACKEgMAN et al. (1975) from 20 to 36 km, on FONTANELLA et al. (1974) from 15 to 20 kin, and on a model-based extension from 36 to 50 km, and this balloon-based column agrees with or may be somewhat smaller than Noxon's results. At the other extreme, Harries' column is far greater than Noxon's column for the corresponding latitude and season, Fig. 5 (JoHNsToN and PODOLSKE, 1978, pointed out that the NO2 from Harries column destroyed ozone above 30 km much faster than it was produced by sunlight and was probably not representative of general conditions). The other observed PM nitrogen dioxide columns scaled to 15 to 50 km lie somewhat above Noxon's NO2 columns, although in general not more than the + 20~o error that Noxon estimated for his method. Considering both Noxon's results and the balloon results, we derived the lines in Figs. 5 and 6 to use as the present estimate of the global and seasonal stratospheric NO2 columns between t5 and 50 kin. Certain sensitivity studies were carried out where the curves of Figs. 5 and 6 were scaled by the factor 2/3 or by the factor 413. 3. Photochemical model calculations

Originally we intended to treat the NO2 distribution 100~o empirically, using (i) the vertical columns from Figs. 5 and 6, (ii) two as a universal PM/AM ratio with

Vol. 118, 1980)

Instantaneous Global Ozone Balance

67

linear change with time during the day at all altitudes, (iii) Noxon's observed altitudes of maximum NO2, and (iv) a Gaussian function (or = 7 km) derived from balloon measurements to give the vertical NO2 profile. This procedure was carried through for one calculation of global instantaneous rates. Its assumptions were tested against a time-dependent photochemical model, and the assumptions were not sustained. The rate of change of NO2 between AMand PM was found not to be uniform with altitude. Model calculations do not yield an NO2 profile which is Gaussian in shape. The rapid rise in the concentration of O(3P) with increasing altitude, as shown in Fig. 4, causes the maximum rate of the O + NO2 reaction to occur at a higher altitude than the maximum NO2 concentration. In order to evaluate the global contribution of this process to the natural ozone balance, it is essential to know the nitrogen dioxide concentrations at high stratospheric altitudes, where there are few measurements. It was felt that model extrapolation of the N02 profile above the highest altitude of NO2 measurement was more reliable than an empirical extrapolation from the limited set of observations. As a result of these considerations, we decided to take the observed PM vertical columns of NO2 as primary data and to use a photochemical model to establish the PM/AMratio, the change of NO2 during the day, and the vertical distribution of the NO~. The model used includes one-dimensional atmospheric motion and photochemistry; it was obtained from the Lawrence Livermore Laboratory as their 1974 model (CHANG, 1974; CHANG et al., 1974), and we modified it to include additional species and reactions. Twenty species are treated time-dependently (03, O, HO, HOO, H20, H202, N20, NO, NO2, NO3, N205, HNO3, CH4, CO, C1, C10, C1ONO2, HC1, CF2C12, CFC13) and three species are treated by steady-state approximations [O(1D), N, H]. A natural background of 2 ppbv of total chlorine is prescribed, including CF2C12 and CFC13 in lieu of natural CHaC1. The vertical eddy diffusion function of STEWARTand HOFFERT(1975) is used. The differential equations for each atmospheric species are solved using the Gear method. The chemical reactions and rate constants are given in Table 3. Model calculations were performed to obtain reference NO2 profiles for three zones: polar, mid-latitude, and tropical regions. For the mid-latitude region, the model was run, using a constant sun at half intensity, for 30 years. Diitsch's ozone was taken as the initial distribution, and runs were made with four different sets of boundary values for NO and NO~. Each of these runs was followed by three days of diurnal calculations with a maximum time step of 200 sec and where the photolysis rates varied continually according to the computed solar angle and radiation flux. This produced four sets of stratospheric evening NO2 profiles, for which the columns bracketed the range observed by Noxon. From these four profiles we derived linear interpolation factors that gave the NO2 profile at any time of day starting from a given PM vertical column. For tropical and polar regions, we could not expect a one-dimensional eddydiffusion model to give reasonable results. Our goal is not to model ozone but only

68

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph,

I'~

I"~

0

0

0

+

'~

5g

gLg$%%~

~ ~3 2" .............

2222~

~3 oo

.....

~,

, , , o&g~,

9

o

8

+

~9

+

+

o

~:++z6zO=5 ~o O+ +

o++~ zoo o

zos

6tn

e

== += 6 c 7 6++o+= ~ o o=~t

tee

t~

t = t6:~=o

++

:~ c ? l " + ~t +c ~+ =+ od +

o+t:~ O "~ 0+

t+ ~'+s

d o z + + o z z +o+ + ~ + ~ 6 +

+ ~ o + +=+z+=+= d ~ 1 7 6+1+7 6 + o + o+9+ ~ + o ~=~c~++c~====+~+oo+=+c~==

+++oo+++o o6ozzzzz~=uob=b===oooozzzz:=ozzoob~

Vol. 118, 1980)

Instantaneous Global Ozone Balance

oz

69

o,

z

z

z

r~

m

r~

<

<

<

<

<

<

z z z

,..I

~ ~ z

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z a

o

9

~

,...~ "0 o 0

g, o

I

b, z i

> .<

~ +

0

j , 0

N

NN

g;g,,,

O 0

N~ .0

~.. N

~ N

~ ,0 g ; g

g

+

~

zz

Z E 0

0

~ ~ ,--; od ,.-; ~

09

+

N +N

~ & 0. .0. .0

I--: e,i ~ ~ d ed ,--1 eH ~ e,i N

z o

o

g Z

g

~

o ++ o ooO+zo= +g==~+t z +~ o ~tggo+O+

.=

o

g z

~

+9

+

zo

+

o

+o~ to

-~.~ +

zz z zz ~

z

Z

~o ~+ o

++ztOzoz_= ~U~z

c~

9

+

~176176163 ~

c~oc~zzz

Z

~zz

70

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph,

to find the shape of the stratospheric NO2 profile. For this purpose it is worthwhile to re-examine the order of magnitude of the chemical relaxation time for various processes. At all altitudes NO and NO2 attain a steady state, primarily but not exclusively by way of hv (a < 4 0 0 n m )

NOn <

03

> NO

with a relaxation time of about 2 minutes. This rapidly exchanged pair (NOx -NO + NO2) interchanges with Nz05 and CION02 with chemical relaxation times of the order of a day or a few days. NOx interchanges with nitric acid HO NO2 <

hv, H O

> HN03

with altitude-dependent characteristic chemical times of about one week to one month. The chemical and photochemical rate of destruction of NzO in the stratosphere has a characteristic time of a few years, and the stratospheric residence time of NO v (NO + NO2 + HNO3 + C1ONO2 + 2N20~) is likewise a small number of years. From consideration of these relaxation times, we started model calculations in tropical and polar regions with observed profiles of slow species (O3, H20, HNO3), and for various assumed boundary values and initial profiles of NOx we ran the model long enough to obtain a quasi-stationary state among the fast species (O, HO, HOO, H202, NO, NO2, NO3, N205, C1, C10, and C1ONO2). This corresponded to seven days with constant sun at half intensity, followed by three days of 24 hours, time-dependent running of the model. A given NO2 column would be interpolated between two of the late afternoon model columns, and the profiles during the previous day found by backing up in time and by interpolating between the two cases. Two model NO2 profiles at mid-latitude are compared with the observed profile between 20 and 50 km obtained by DRUMMOND and JARNOT (1978) in Fig. 7. Curve A represents the observed NO2 profile at 44~ July, one hour after sunrise, and it corresponds to an integrated stratospheric column of 2.8 • 101~ molecules cm -2 Curve B is a model profile corresponding to an integrated column of 2.4 • 10~5 molecules cm -2, and curve C represents an integrated column of 1.0 • l0 is molecules cm-2. Moderately good agreement is obtained between the observed profile and the model calculations, especially in the important region between 30 and 45 km. In order to further verify the high altitude behavior of the NO2 chemistry which we have obtained from these model calculations, we have conducted a study of the solar proton event of 1972. This event has been previously discussed in detail (HEATH et al., 1977). It has been pointed out that the event introduced large quantities of NO in the polar stratosphere and therefore serves as a test for the theory that NOx catalytically destroys ozone. Since the original study by HEATH et al. (1977) there have been major changes in several important rate constants. With 1978 rate constants (Table 3) we calculate ozone decreases in good agreement with the observed changes obtained by satellite measurements above 35 km. As we show below, this is the

Vol. 118, 1980)

Instantaneous Global Ozone Balance

71

OBSERVED AND CALCULATED NO2 PROFILES 44~ SUMMER, ONE HOUR AFTER SUNRISE 5C

4.*

4C

d -o 35

3C

2~

20 I07 2 5 I08 2 5 I09 2 5 I0 I~ Nitrogen Dioxide Concentretion, Molecules cm -3

Figure 7 Nitrogen dioxide profile between 20 and 50 km as observed by DRUMMOND and line A ; the integrated vertical column is 2.8 x 1015 molecules c m - 2 ; 44~ June after sunrise. Lines B and C represent model NO2 profiles respectively from 2.4 molecules cm -2 between 20 and 50 km, one hour after sunrise. The slant lines are volume.

JARNOT (1978), 1975, one hour and 1.0 x 101~ mixing ratio by

region where the bulk of the NOT catalyzed destruction of ozone occurs, and therefore the agreement obtained in this test case serves as some confirmation of the ability of the model to simulate this chemistry. A more detailed description of our study with particular emphasis on the differences in chemistry as compared to previous work (HEATH et al., 1977; FABIAN et al., 1979) will be presented elsewhere. The model was checked against PM/AM ratios of the observed NO2 concentration (EVANS et al., 1978). Between 20 and 30 km Evans obtained a maximum PM/AMratio of about 2, with lower values below, which varied on successive days. The model gives a PM/AM ratio of 1.8 in the 20 to 30 km region, with lower values below and above 30 kin, which is similar to the observations. This use of a model to translate a given NO2 vertical column into a profile has some uncertainties due to atmospheric transport. If horizontal transport systematically

72

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph,

has a different effect on NOz at different altitudes within a time span of a week or less, then the quasi-steady state obtained by the model among NO, NO2, NzO~ and CIONO2 will be systematically distorted. Nitric acid is a major reservoir for the NOx species, especially in the lower stratosphere. The photochemical relaxation time of HNO3 is about a month in the lower stratosphere, it decreases with altitude, and it becomes short in the upper stratosphere. The 10 day integration time to set up quasi-steady state in tropical and polar regions would be adequate above about 25 km for HNOz but inadequate at substantially lower altitudes. We have examined the sensitivity of our calculation to HNO3 in the tropical region. Measurements of HNO3 have been reported at various latitudes by LAZRUS and GANDRUD (1974), who used a filter collection technique, and by MURCRAY et al. 0975) who reported column measurements above 18 km based on infrared emission. Both authors observe a minimum in tropical regions. Lazrus and Gandrud reported tropical mixing ratios of HNO3 that varied from 0.2 to 0.75 ppbm at 18 kin, Murcray found a column of HNOa ranging from 1.0 to 5.4 • 1015 in the region 20~ to 20~ Between the extremes of these observations, we have investigated the effect of two quite different tropical HNOa profiles produced by changing the initial distribution of HNO3 and running the model for the usual seven plus three days. The results of this test are given below: Case 1

Case 2

Column of HNO3/101~ c m - 2

1.2

5.6

HNOa at 18 km/ppbm

0.36

2.2

Column rate of O + NOz reaction (5: 30 pro)/1012 cm - 2 sec- 1

3.8

4.0

From this study, it appears that the uncertainty in the shape of the NO2 profile as a function of uncertainty in the HNO3 profile is only a matter of about five percent on the inferred rate of the reaction (O + NO2 ~ 02 + NO) in the tropical region.

4. Results of instantaneous rate calculations Before presenting results of instantaneous rate calculations, a comparison and contrast will be given between these calculations and those of an atmospheric model. A model takes a set of chemical species, a list of chemical and photochemical reactions, a theory of atmospheric motions, and a mechanism for handling radiation. The model calculates atmospheric transport, photochemical reactions, and radiative balances. In a model calculation every result depends, with different sensitivity, on almost every parameter of the model. A proper model is a tool for predicting future events, including, for example, the effect of atmospheric perturbations. The observed distributions of ozone, nitrogen dioxide, or other species is brought about by actual atmospheric processes, and the method of instantaneous rates starts

Vol. 118, 1980)

Instantaneous Global Ozone Balance

73

with the measured consequences of real atmospheric motion, photochemistry, and radiation effects. To this extent, the method of instantaneous rates does not need to calculate atmospheric transport. As a consequence of its dependence on observed quantities, this method is concerned with interpreting the existing or past atmosphere and has no power of predicting the future atmosphere. Clearly the predictive role of the model is more valuable than the interpretative role of the method of instantaneous rates, although this method does have some unique and useful features. Calculations are made of the distribution of solar radiation at every grid point, and the rates of some photochemical reactions are calculated at these grid points, The rates of ozone production from 02 photolysis, 2j[O2], of ozone destruction from oxygen species, 2k[O][O3], and of ozone destruction by nitrogen oxides, 2k'[O][NO2], are calculated independently of each other and of other important processes that are occurring. Ozone losses to chlorine species (Cl, CIO) and to water species (H, HO, HOO) are obviously omitted. Also omitted is ozone production or loss to net transport in any given volume element. In an example discussed below, NOx reactions destroy ozone in one region of the atmosphere at a rate five times the rate of photochemical production in that region. In this instance it is obvious that atmospheric transport has supplied ozone to a region that contains little or no solar radiation capable of producing ozone (~ < 242 nm) but that contains abundant visible radiation that dissociates ozone and drives the NO= catalytic cycle. In other instances the relative role of atmospheric transport and photochemistry in affecting local ozone may not be apparent, and Fig. 8 provides a reference map for this purpose. The 'ozone

OZONE

PHOTOCHEMICAL

REPLACEMENT

TIME

50

I0 Y R

Io

0 i -90 Fell

i

I -60

i

i I -30

J

I

I 0

I0 YR

J l

I 30

l

J I 60

l

l I I 90-90 -60 Spring Summer

l

J I -30

I

I

I 0

I

i

I 30

I

I

I 60

s 90 Winter

LATITUDE

Figure 8 Ozone photochemical replacement time, the local ozone concentration (Fig. 3) divided by the local rate of photochemical formation of ozone (Fig. 11).

74

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph,

replacement time' is the local ozone concentration divided by the local rate of oxygen photolysis (1)

~-= [08]/2j[02]

(4)

and this quantity is presented in Fig. 8 where 2j[O2] is the 24 hour average value. The ozone replacement times increase with decreasing altitude from about 10 hours in the upper stratosphere to several years in the lower stratosphere. Vertical transport times in the stratosphere over a 10 km altitude range are more or less a year; horizontal transport times over 10 000 km range are also more or less a year. In these terms, ozone photochemistry is faster than ozone transport only above 25 to 35 km (latitude dependent). About every two weeks solar radiation produces enough ozone, 2j[O2], to equal that in the entire atmosphere. This large gross ozone formation is balanced by equally large ozone-destruction processes. The atmosphere as a whole is a closed system, and ozone transported from one region must eventually be destroyed somewhere. In this section global distributions of ozone formation and of ozone destruction by Ox and NOx are given, but these distributions need to be examined in the light of Fig. 8 and the time-scale of atmospheric motions to determine their magnitude relative to transport. Contour lines for the daytime average nitrogen dioxide concentrations are presented as a function of altitude and latitude and for two seasons in Fig. 9, The corresponding mixing ratios are shown in Fig. 10. The two seasons are spring equinox

NITROGEN DIOXIDE CONCENTRATION, I0 9 MOLECULES CM-3

50

--

I

T

i

1

I

11

l

l

i

l

q

I

I

l

l

~

40

~- 3o 20 I0 Z

-90 Fell

-60

-30

0

50

60

90-90 -60 Spring Summer

-30

0

50

60

90 Winter

LATITUDE

Figure 9 Daytime average nitrogen dioxide concentrations in units of 109 molecules cm -3.

Vol. 118, 1980)

NITROGEN 50

t

75

Instantaneous Global Ozone Balance

I

I

i

I

i

r

I

I

~

I

I

DIOXIDE

t

I

MIXING

:

t

i

l

i

RATIO

l

r

l

l

(PPBV)

l

l

~

i

l

l

l

l

l

l

4O

{'{[(

E G

:5O

~

_=_~~'

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_

5

I0=

0 I i I i -90 -60 Fall

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I I I 0

i

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t 1 I I t I 1 I 60 90-90 -60 Spring Summer

I I ~ I ] I ":50 0

L L t 30

I I t 60 90 Winter

LATITUDE

Figure 10 Daytime average nitrogen dioxide mixing ratios in parts per billion by volume.

(fall, SH; spring, NH) and winter solstice (summer, SH; winter, NH), and all remaining figures in this article are based on these two seasons. The NO2 columns were assumed to be symmetrical between the two hemispheres for corresponding seasons. Temperature and ozone concentration are not symmetrical between the hemispheres. Instantaneous rate calculations were done for the other two seasons, summer solstice RATE

/

OF OZONE

PRODUCTION

FROM

02 PHOTOLYSIS,

MOLECULES CM - 3 S -t

U

___

16E6

~ 20 [0

-90 Fall

-60

-30

0

30

60

90-90 -60 Spring Summer

-:50

0

:50

60

90 Winter

LATITUDE

Figure 11 Rate of ozone production from 02 photolysis, P(O3), 2j[O2], 24 hour average, in units of molecules cm-a s-~.

76

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph,

RATE

OF OZONE D E S T R U C T I O N

BY O x R E A C T I O N S , MOLECULES

50

5

~ i i l jl,

CM " 3 S -I

i i i 1 i , I,

~lll# ' '

2O

-

IO

0

h

I

-90 Foll

I

t

-60

I

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-30

I

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0

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i

i

30

I

60

l

i

Fi

i

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90-90 -60 Spring Summer

i

I

I

I

i

1

-30

l

i

0

I

i

30

i

I

60

I

i

90 Winter

LATITUDE

Figure 12 Rate of ozone destruction by C h a p m a n reactions, L(Ox), 2k[O][O3], 24 hour average, in units of molecules c m - 3 s - 1.

RATIO

OF RATE

OF

OZONE

50

OZONE

DESTRUCTION

FORMATION

r , I T ' %.' ' I ' ' .II3 ' ~-.._.o.25_- - I

r

'

BY

BY

0 x TO

RATE

OF

02 PHOTOLYSIS

' H ~0.2

40

~ 30

I0

0

-90 Foll

~

r

I

-60

~

i

i

-50

,

~

i

0

i

~

I

30

~

i

i

60

~

i

-60 90-90 Spring Summer

-30

O

50

roD

90 Winter

LATITUDE

Figure 13 The ratio of the rate of ozone destruction by Ox to the rate of ozone formation by 02 photolysis. L(O=)/P(Oa) = 2k[Ol[O3]/2j[02].

Vol. 118, 1980)

77

Instantaneous Global Ozone Balance

(winter, SH; summer, NH) and fall equinox (spring, SH; fall, NH), but these results are given here only in summary tabular form. Several features of Noxon's measurements are evident in Figs. 9 and 10: the low tropical NO2 columns, the winter 'cliff' above 50~ and the 'trough' in spring. The altitude of maximum concentration is typically close to 30 kin, and the concentrations at the maximum are usually 1 to 3 • 109 molecules cm -3. The altitude of maximum mixing ratio is about 35 kin, and the values at the maximum are about 6 to 12 ppbv. According to Noxon's (1979) Fig. 2, the altitude of maximum NO~. concentration in the tropics varies between 20 and 28 km, whereas our model places the maximum at about 30 kin. This difference in NO~ heights in the tropics is the major disagreement between our model distribution of NO2 and the indications of Noxon's method. The rate of ozone production, P(Os), from the photolysis of oxygen (1) is given by 2j1[O2]. The distribution of radiation in the Schumann-Runge region was treated by the method of HUDSON and MArILE(1972). The zonal average, or 24 hour average, rate of ozone production is given in Fig. 11. The rate exhibits a broad maximum in the upper stratosphere, and an interesting feature is the large zonal-average value over the summer polar region. The rate of ozone destruction by pure oxygen species, L(Ox) is given (2) by 2k[O][O3], as an excellent approximation. The 24 hour average contours of this rate are shown in Fig. 12. The ratio of the two rates, L(Ox)/P(O3), is given by Fig. 13. Above 42 kin, the loss of ozone due to O~ reactions is about 25~ of the rate of ozone production. This percentage rapidly decreases at lower altitude, reaching a region in the lower tropical stratosphere where ozone is produced 1000 times faster than it is destroyed by Ox RATE OF OZONE DESTRUCTION BY NO x REACTIONS, MOLECULES CM -3 S -i 50

40 E -

bJ (:3

30

1--

'iI,

2o

-90 Fell

i I I i I i i ] i r [ i I [ -60 -30 0 30 60

1 90-90 -60 Spring Summer

-30

0

30

60

90 Winter

LATITUDE

Figure 14 The rate of ozone destruction by NOx, L(NO=) = 2k[O][NO2], in units of molecules crn -a s -1.

78

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph,

reactions. The heavy lines in Fig. 13 outline a region where Ox reactions destroy ozone at a rate comparable to (L/P = 0.5) to much faster than (L/P = 5) ozone is produced by solar radiation. At all four seasons this high fractional ozone destruction occurs in a region where the photochemical production of ozone is very slow. Ozone production from 02 occurs only from solar radiation at wavelengths less than 242 nm, which is strongly filtered by oxygen and ozone. Ozone destruction is brought about by oxygen atoms generated by ozone photolysis, which is driven by visible as well as ultraviolet radiation. Thus ozone, brought to a region by transport, undergoes slow photochemical destruction where the rate of ozone formation from O2 photolysis is essentially zero. The 24 hour average rate of ozone destruction by NOx, L(NO~) = 2k[NO2][O], is given by Fig. 14. The maximum rate of ozone destruction by NO:, occurs at midlatitudes between 30 and 40 km. Ozone is rapidly destroyed by this reaction at the rate of 106 molecules cm -3 s -1 in a band about 15 km wide stretching from pole-topole at the equinox. During the winter solstice, this band is 20 km wide over the summer pole and rapidly falls to zero as one approaches the winter pole. The relative rate of ozone destruction by NOx and ozone production from ozone photolysis is demonstrated by contour maps of the ratio L(NO=)/P(O3), Fig. 15. The heavy lines in this figure enclose the region of rapid rate of ozone destruction by NO~; at one limit of this region NOx destroys ozone half as fast as it is formed and the other extreme L(NOx) is five times as great as P(O3), which implies that NO~ is destroying ozone which was brought there by atmospheric transport from the 'net ozone production region.' In the summer-winter contour map, the zone of 50~ or more ozone destruction lies in a band 10 km wide from the summer pole to 60~ In the fall-spring RATIO OF RATE OF OZONE DESTRUCTION BY NO x TO RATE OF OZONE FORMATION BY 02 PHOTOLYSIS 5O

4O

30

5

~"~H6 o

O.

025 o,~ oo5

2o I0

~-

,

, I

-90 FoI~

-60

i J

I i

-50

I I L , i , J I I I

0

30

60

II

~

5

0

, I i i I I

90-90 -60 Spring Summer

-50

I I i , I L i

0

50

I k

60

90 Winter

LATITUDE

Figure 15 Ratio of ozone destruction by NO~, L(NO~), to ozone production by photolysis of oxygen, P(O3).

Vol. 118, 1980)

79

Instantaneous Global Ozone Balance

case, the region of maximum destruction occurs in two large areas over midlatitudes. Below the altitude of maximum ozone concentration in the tropics (Fig. 3), there is a region of some ozone formation where the rate is greater than 105 molecules cm -a s-1 (Fig. 11), but in this region there is almost no photochemical destruction of ozone by Ox (Fig. 13) or by NOx (Fig. 15). With a reduced number of contour lines, the map of the ratios L(NOx)/P(Os) (Fig. 14) are superimposed on the corresponding contour maps of ozone mixing ratios (Fig. 2) to produce Fig. 16. In region B, between the heavy lines, NO,: destroys ozone at least 50% as fast as it is formed. Points A represent mixing ratio maxima for ozone, and point C represents the maximum rate of 02 photolysis. Region B lies across the region of maximum ozone mixing ratio for summer-winter, and it forms two large areas on each side of the ozone maximum mixing ratio for fall-spring conditions. If on the fall-spring map of Fig. 16 one draws a line from point A to a point 18 km above the north pole, one finds an interesting picture for the possibilities of ozone transport from the photochemically active tropical middle stratosphere to the photochemically inert lower polar stratosphere. From the equator to about 40~ along this line, the rate of ozone production from 02 photolysis is much faster than NOx (or Ox) ozone destruction. Where this line crosses into region B, that of large fractional ozone destruction by NOx, the absolute rate of ozone formation and destruction is low. The part o f region B in Fig. 16 that extends as a narrow band below 20 km and through the troposphere is of no importance. This region involves very slow rates of oxygen photolysis and ozone production (Figs. 8, 11), and the ozone distribution is OZONE

MIXING

RATIOS

(PPMV)

DESTRUCTION

BY

AND

REGION

NITROGEN

OF

HEAVY

OZONE

OXIDES

50

40

~

C~7 s

E

) 0.5

B

! I.O

-

.Q

Z

~- 5 O i i

1

7 ~

-i.o J

:_

20

I0 L(NOx)/P(03)

0 I -90 Fall

J I -60

i

--

, i -30

~ ,

L I 0

~ I i 9 I 30 60

t

i

I I 90-90 -60 Spring Summer

I

t I ~ i i -30 0

,

,

i i 50

i

I I i 60 90 Winter

LATITUDE Figure

16

The ratio L(NO,~)/P(Os), Fig. 14, superimposed on ozone mixing ratios, Fig. 2. A, maximum O3 mixing ratio. B, region of heavy, fast ozone destruction by NO~. C, maximum rate ofO3 production from oxygen photolysis.

80

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph, Table 4

Twenty-four hour average column rates (15 to 45 kin) in units o f 1011 molecules cm- 2 s - 1. Spring NH, fall S H (south pole is - 90 ~

Loss of Oo

Lat.

Prod. Oa 2j [ O ~ 1

O~ 2k[O1[O31

NO,~ 2k[O][NO2l

O:,

NOx

Both

80 70 -60 50 -40 30 -20 - 10 0 10 20 30 40 50 60 70 80

14 33 51 67 81 94 106 112 119 117 110 100 83 67 48 28 9

2 3 5 9 13 14 16 17 16 t6 14 13 12 9 5 3 2

28 20 21 26 49 64 47 36 35 37 45 53 44 39 32 26 20

0.13 0.09 0.11 0.14 0.16 O.15 0.15 0.15 0.13 0.13 0.13 0.13 0.15 0.13 0.11 0.11 0.19

1.95 0.61 0.40 0.39 0.60 0.68 0.44 0.32 0.29 0.31 0.41 0.53 0.53 0.58 0.66 0.93 2.18

2.08 0.70 0.51 0.53 0.76 0.83 0.59 0.47 0.42 0.44 0.54 0.66 0.68 0.71 0.77 1.04 2.37

-

-

-

-

-

Ratio L/P

d o m i n a t e d by a t m o s p h e r i c t r a n s p o r t and by m e t h a n e - N O x s m o g reactions. A b o v e 40 k m the o zo n e mixing ratios decrease with increasing altitude, the direction of oz o n e flux is p r e s u m a b l y upwards, and the ozone destruction rate by N O , also decreases with altitude. In this region ozone destruction by H O x and CIX reactions b e c o m e rapid. T h e relative role o f the pure oxygen species an d the oxides o f nitrogen in the global o zo n e balance is e x a m i n e d in Tables 4 and 5. The 24 h o u r average c o l u m n Table 5 Global-sum column rates over various altitude bands, in units o f lO 29 molecules s- 1. Spring NH, fall S H

Loss of 03

Ratio L/P

Alt. Band km

Prod. 03 2jlO2l

Ox

NO,:

O~

NO:,

Both

45-50 40-45 35-40 30-35 25-30 20-25 15-20 15-45

140.2 171.2 155.4 104.0 43.4 8.8 0.9 484

32.4 42.4 19.0 7.2 2.6 0.52 0.04 72

9.2 45.2 89.2 57.4 i 5.4 1.8 0.12 209

0.23 0.25 0.12 0.07 0.06 0.06 0.04 0.15

0.07 0.26 0.57 0.55 0.35 0.30 0.13 0.43

0.30 0.51 0.69 0.62 0.41 0.36 0.17 0.58

Vol. 118, 1980)

Instantaneous Global Ozone Balance

81

rates between 15 and 45 km for ozone photochemical production P(Os), for ozone destruction by Ox reactions L(Ox), and for ozone destruction by NOx reactions L(NO~) are listed for each latitude between 80~ and 80~ in Table 4. For fall-spring conditions, the rate of ozone production at 80~ or 80~ is very slow (about 10~ of that at the equator), and the destruction rates, L(O~) + L(NO~), are about twice as fast as the photochemical pi'oduction. At mid-latitudes (300-60 ~ the 15 to 45 km column rate of ozone destruction by Ox is about 14~o and that by NOx reactions is about 55~ of the rate of ozone production. In tropical regions the percentages are 14 for L(Ox) and 35 for L(NO~). The global sums of P(Oa), L(Ox), and L(NOx) over various altitude bands of 5 km width are given in Table 5. Between 45 and 50 km the role of NO~ is quite small L(NOx) being only 7 ~ of P(Oa); over this range L(O~) is 23~o of P(O3). Between 40 and 45 km, the Ox and NO~ reactions are about equally important in balancing ozone, and each destroys ozone about 25~ as fast as it is produced. Between 30 and 40 kin, the O~ reactions destroy ozone about I 0 ~ as fast as it is produced, and NO~ destroys about 57~o. Between 25 and 30 kin, L(Ox) is 6~o of P(O3), and L(NO~) is 35~o. Below 25 km both the rate of photochemical production of ozone a n d its destruction by O~ and NO~ become slow. Over the range 15 to 45 km on the global scale (compare JOHNSTON, 1975) the O~ reactions destroy 15~o of the photochemically produced ozone and NO~ reactions destroy 43~ for the fall-spring season. This total percentage of 58 leaves ample room for major effects by HOx and Clx reactions. The global role of NO~ in destroying ozone between 15 and 45 km is explored as a function of season in Table 6. Ozone destruction by NO~ is 43~ of P(Oa) in spring, 50~o in summer, 39~o in fall, and 43Yo in winter of the northern hemisphere. The average of these four seasons is 44~. The inventory of NO2 in the sunlit half of the globe is about 1.3 x 10a4 molecules, with some apparent seasonal changes. A sensitivity study was carried out in which the PM nitrogen dioxide columns of Figs. 5 and 6 were scaled by the factor 2/3 and by the factor 4/3. Some of the results given in Table 7. Noxon estimated his NO2 columns to be accurate to + 20~. We have taken + 33~o in order to embrace most of the balloon soundings and to be

Table 6 Comparison o f four seasons in terms o f global instantaneous rates between 15 and 45 km. The total daytime NOz is summed over the sunlit hemisphere

Season NH

P(03) s - t

Total Daytime NO2

( 1029)

( 1032 )

( 1029 )

L P

SP SU F W

484 449 480 527

146 119 135 134

209 222 187 228

0.43 0.50 0.39 0.43

L(NO:,) s - ~

82

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph, Table 7 Sensitivity test where NO2 columns o f Figures 1 and 2 are scaled by 2/3 and 4/3. Global instantaneous rates between 15 and 45 km

A. Summerin NH. Production ofO3 = 449 x 1020s -1. Loss of Oz from Ox = 75 x 1029s- 1.

Rel. NO2

Total Daytime NO2 molecules

Loss of 03 from NOv s- 1

L

2/3 1 4/3

8.15 (33) 1.19 (34) 1.55 (34)

145 (29) 222 (29) 297 (29)

0.32 0.50 0.66

B. Fall in NH. Production of 03 = 480 x 1029s -1. Loss of Os from Ox = 77 • 1029s-1. 2/3 1 4/3

1.00 (34) 1.35 (34) 1.95 (34)

127 (29) 187 (29) 295 (29)

0.26 0.39 0.61

somewhat conservative. For 2/3 the standard NO2 columns, NOx destroyed 29~ of the global ozone produced from 15 to 45 km; for 4/3, NOx destroyed 63~ of the global ozone produced over this altitude interval. On the basis of the observed NO2 columns, we estimate that the global rate of ozone destruction by NOx is 45 + ! 5 ~ of the rate of ozone formation from oxygen photolysis between 15 and 45 km. However, one should take the rate of ozone destruction by NOx from Figs. 14-16 and Tables 4-6, rather than from the single number 45 + 15~, which is averaged over many different regions. This single number for the effect of nitrogen oxides on stratospheric ozone should be used with great caution. Emphatically, it is not an index for the sensitivity of stratospheric ozone to a perturbation by added NO~. At present, model calculations predict that an increase of stratospheric NOx would decrease ozone in the upper stratosphere, would increase ozone in the lower stratosphere, and would have only a small effect of uncertain sign on the total ozone column (RuNt)EL e t al., 1978). Noxon's measurements and these calculations show that the mid-latitude region is not representative of the global average so far as NO2 column and the NOx rate of ozone destruction is concerned. The concentrations of NO2 and the ozone destruction rates L(NOx) are higher in mid-latitude than in the tropics on one side or in the polar region on the other side. This observation is relevant to the degree that onedimensional photochemical models can be verified by comparison with observations made at mid-latitudes. This study of instantaneous rates omitted several minor sources of ozone formation, ozone destruction by O~, and ozone destruction by NO~ (JOHNSTON and

Vol. 118, 1980)

Instantaneous Global Ozone Balance

83

PODOLSKE, 1978). The most important source of ozone formation that is omitted is that from the methane-NOx smog reaction. This smog reaction is an important local source of ozone below but not above 20 km. The present study is primarily concerned with the fast photochemical formation and destruction of ozone above 25 km, and the smog reactions are slow in this context. Ozone is also destroyed by the reaction o f singlet atomic oxygen with ozone, but this small effect was omitted. Ozone is destroyed by another NOx catalytic cycle starting with the reaction NO2 + 0 3 - + NOa + 02 and rate limited by the photolysis of the nitrate free radical to give nitric oxide, NO3 + h v - + N O + 02. Using GRAHAM and JOHNSTON'S (1978) quantum yields for this reaction, we have found that this cycle destroys 0.03 percent of the ozone produced globally from oxygen photolysis. However from one to 10 km, the globally integrated daytime rate is about 1 • 1028 molecules s -1, which is large enough to be of importance in the troposphere where photochemistry is slow (compare CHAMEIDES and WALKER, 1976). The reaction HOO + NO--~ HO + NO2 is an important mechanism whereby an increase in the concentration of NOx species affects the concentrations of HOx species with consequent changes in a number of reaction rates. This strong coupling between the concentrations of various species does not constitute direct ozone formation or destruction, and this reaction is appropriately not included in the calculations of instantaneous rates where the concentration of NO2 is observed. In this calculation of instantaneous rates, the three quantities P(O3), L(Ox), and L(NOx) are independent and are derived from different sets of atmospheric measurements. There was no need to include the several catalytic cycles whereby HOx and C1X destroy ozone, although if we had enough atmospheric measurements of HOO and of C10 these calculations could be made. The global balance of ozone production against all modes of ozone destruction based on observed key species is a necessary condition for verifying the completeness of mechanisms of stratospheric photochemistry. We look forward to the time when there are sufficient measurements of C10 and HOO in the stratosphere for calculations such as these to be made on the effects of C1X and HOx on the global ozone balance.

Acknowledgments This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, U.S. Department of Energy under contract No. W-7405-Eng-48. We especially thank the Lawrence Livermore Laboratory Atmospheric Kinetics Group for generously giving us a complete copy of their 1974 atmospheric model which we have expanded and up-dated for use here. We are grateful to Professor H. U. Dfitsch for supplying us with tables of atmospheric temperature and ozone data. We are grateful to Dr. J. B. Kerr for sending us tables of data that had appeared only as figures [EVANS et al., 1978].

84

Susan Solomon, Harold S. Johnston, Marta Kowalczyk, and Ivan Wilson (Pageoph, REFERENCES

ACKERMAN, M., FONTANELLA,J. C., FRIMOUT, D., GIRARD, A., LOUISNARD,N. and MULLER, C. (1975), Simultaneous measurements of NO and NO2 in the stratosphere, Planet. Space Sci. 23, 651-660. CHAMEIDES, W. C. and WALKER, J. G. (1976), A time dependent photochemical model for ozone near the ground, J. Geophys. Res. 81, 413-420. CHAN, W. H., USELMAN,W. M., CALVERT,J. G. and SHAW, J. A. (1977), The pressure dependence of the rate constant for the reaction HO + CO ~ H + CO2, Chem. Phys. Lett. 45, 240-243. CHANG, J. S. (1974), Simulations, perturbation and interpretations, Proceedings of the Third Conference on CIAP, U.S. Department of Transportation, DOT-TSC-OST-74-15, 330-341. CHANG, J. S., HINDMARSCH, A. C. and MADSEN, N. K., Simulations of chemical kinetics and transport in the stratosphere, in Stiff Differential Systems, (R. A. Willoughky, ed., Plenum, New York, 1974), pp. 51-65. CONNELL, P. and JOHNSTON,H. S. (1979), The thermal dissociation of NzO~ in Nz, Geophys. Res. Lett. 6, 553-556. Cox, R. A. (1978), Kinetics of HO2 radical reactions of atmospheric interest, Symposium on the Geophysical Aspects and Consequences of Changes in the Composition of the Stratosphere, Toronto, World Meteorological Organization, Publication No. 511. CRUTZEN, P. J. (1970), The influence of nitrogen oxides on the atmospheric ozone content, Quart. J. Roy. Meteorol. Soc. 96, 320-325. DRUMMOND,J. R. and JARNOT, R. E. (1978), Infra-red measurements of stratospheric composition. H. Simultaneous NO and NO2 measurements, Proc. R. Soc. Lond. A 364, 237-254. D~rTSCH, H. U., Atmospheric Ozone and Ultraviolet Radiation, Worm Survey of Climatology, (VoL 4, D. F. Rex, ed., Elsevier Publishing Company, Amsterdam, London, New York, 1969), pp. 383-432. DOTSCH,H..U. (1978), Verticalozone distribution on aglobalscale, Pure Appl. Geophys. 116, 511-529. EVANS, W. F. J., KERR, J. B., MCELROY, C. T., O'BRIEN, R. S., RIDLEY,B. A. and WARDLE,D. I. (1977), The odd nitrogen mixing ratio in the stratosphere, Geophys. Res. Lett. 4, 235-238. EVANS, W. F. J., FAST, H., KERR, J. B., MCELROY, C. T., O'BRIEN, R. S. and WARDLE, D. I. (1978), Stratospheric constituent measurements from project stratoprobe, Symposium on the Geophysical Aspects and Consequences of Changes in the Composition of the Stratosphere, Toronto, World Meteorological Organization, Publication No. 511. FABIAN, P., PYLE, J. A. and WELLS, R. J. (1979), The August 1972 solar proton event and the atmospheric ozone layer, Nature 277, 458-460. FONTANELLA,J. C., GRAMONT, L. and LOUISNARD,N. (1974), Vertical distribution of NO, NOz and HNOa as derived from stratospheric absorption spectra, Proceedings of the Third Conference on CLAP, U.S. Department of Transportation, DOT-TSC-OST-74-15, 454-457, and Appl. Opt. 14, 825-828. GOLDMAN, A., FERNWALD,F. G., WILLIAMS,W. S. and MURCRAY,D. G. (1978), Verticaldistribution of NO2 in the stratosphere as determined from balloon measurements of solar spectra in the 4500/{ region, Geophys. Res. Lett. 5, 320-325. GRAHAM, R. A. and JOHNSTON,H. S. (1978), The photochemistry of N 0 3 and the kinetics of the NzOs-O3 system, J. Phys. Chem. 82, 254-268. HAMPSON, R. F. and GARVIN, D. (1977), Reaction rate and photochemical data for Atmospheric Chemistry, NBS Special Publication 513. I-{ARRIES,J. E., MOSS, D. G., SWANN, N. R. W., NEILL, G. F. and GILDWANG,P. (t976), Simultaneous measurements of HzO, NO2 and HNO3 in the daytime stratosphere from 15 to 35 kin, Nature 259, 300-302. HEATH, D. F., KRUEGER,A. J. and CRUTZEN, P. J. (1977), Solar proton event: Influence on stratospheric ozone, Science 197, 886-889. HOWARD, C. J. (1978), Recent developments in atmospheric HO2 chemistry, Symposium on the Geophysical Aspects and Consequences of Changes in the Composition of the Stratosphere, Toronto, World Meteorological Organization, Publication No. 511.

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HUDSON, R. D. and MAHLE, S. H. (1972), Photodissociation rates of molecular oxygen in the mesosphere and lower thermosphere, J. Geophys. Res. 77, 2902-2914. ISAKSEN,I. S. A., MIDTB6, K., DUNDE, J. and CRUTZEN,P. (1976), A simplified method to include molecular scattering and reflection in calculations of photon fluxes and photodissociation rates, Institute for Geophysics, University of Oslo, Oslo, Norway, Report 20, pp. 1-21. JOHNSTON, H. S. and WmTTEN, G. (1973), Instantaneous photochemical rates in the global stratosphere, Pure Appl. Geophys. 106-108, 1468-1489. JOHNSTON, H. S. and WHn'TEN,G. (1975), Chemical reactions in the atmosphere as studied by the method of instantaneous rates, Int. J. Chem. Kinet., Symposium No. 1, 1-26. JOHNSTON, H. S. (1975), Global ozone balance in the natural stratosphere, Rev. Geophys. Space Phys. 13, 637-649. JOHNSTON, a . S. and PODOLSKE, J. (1978), Interpretations of stratospheric photochemistry, Rev. Geophys. Space Phys. 16, 491-519. LAZRUS, A. L. and GANDRUD, B. W. (1974), Distribution of stratospheric nitric acid vapor, J. Atmos. Sci. 31, 1102-1108. MURCRAY, D. G., GOLDMAN,A., WILLIAMS,W. J., MURCRAY,F. H., BROOKS,J. N., VAN ALLEN, J., STOCKEN,R. N., KOSTERS,J. J., BARKER,D. B. and SNIDER, D. E. (1974), Recent results of stratospheric trace-gas measurements from balloon-borne spectrometers, Proceedings of the Third Conference on CIAP, U.S. Department of Transportation, DOT-TSC-OST-74-15, pp. pp. t84-192. MURCRAY, D. G., BARKER, D. B., BROOKS, J. N., GOLDMAN, A. and WILLIAMS,W. J. (1975), Seasonal and latitudinal variation of the stratospheric concentration of HNO3, Geophys. Res. Lett. 2, 223-225. NoxoN, J. F. (1978), Stratospheric N 0 2 in the antarctic winter, Geophys. Res. Lett. 5, 1021-1022. NOXON, J. F., WHIPPLE,E. C. JR. and HYDE, R. S. (1979), Stratospheric NO2. L observational method and behavior at mid-latitude, J. Geophys. Res. 84, 5047-5066. NOXON, J. F. (1979), Stratospheric NO2. II. Global behavior, J. Geophys. Res. 84, 5067-5076. OGAWA,T. (1979), Private communication. RUNDEL, R. D., BUTLER,D. M. and STOLARSKI,R. S. (1978), Uncertainty propagation in a stratospheric model. 1. Development of a concise stratospheric model, J. Geophys. Res. 83, 3063-3073. STEWART,R. W. and HOFrERT, M. I. (1975), A chemical model of the troposphere and stratosphere, J. Atmos Sci. 32, 195-210. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh~iuser Verlag, Basel

The Stratospheric Sulfate Aerosol Layer: Processes, Models, Observations, and Simulations By R. C. WHITTEN,:t) O. B. TOON,1) and R. P. TURCO2)

Abstract - After briefly reviewing the observational data on the stratospheric sulfate aerosol layer, the chemical and physical processes that are likely to fix the properties of the layer are discussed. We present appropriate continuity equations for aerosol particles, and show how to solve the equations on a digital computer. Simulations of the unperturbed aerosol layer by various published models are discussed and the sensitivity of layer characteristics to variations in several aerosol model parameters is studied. We discuss model applications to anthropogenic pollution problems and demonstrate that moderate levels of aerospace activity (supersonic transport and space shuttle operations) will probably have only a negligible effect on global climate. Finally, we evaluate the possible climatic effect of a ten-fold increase in the atmospheric abundance of carbonyl sulfide.

Key words: Stratosphere; Aerosol layer; Sulfates.

1. I n t r o d u c t i o n

The presence of a sulfate aerosol layer in the lower stratosphere was discovered many years ago by Junge and coworkers (JUNGE et al., 1961) while they were carrying out high altitude radioactivity measurements. The morphology of the layer has subsequently been well established with the aid of a wide range of techniques including balloon-borne diffusion chambers (e.g., JUNGE et al., 1961); high-altitude aircraft equipped with wire impactors (e.g., FERRY and LEM, 1974) or filters (CASTLEMAN et al., 1975); optical particle counters (e.g., HOEMANN et al., 1975a; ROSEN et al., 1975); satellite measurements of sunlight scattered by the layer (e.g., PEPIN and MCCORMICK, 1976); and laser light scattered by the layer (e.g., RUSSELL and HAKE, 1977). The optical properties of aerosols required for experimental and theoretical analysis have been reviewed by CADLE and GRAMS (1975) and by TOON and POLLACK (1976). In the stratosphere, the sulfate aerosol mass-mixing ratio usually displays a maximum at altitudes between 20 and 25 km; the number-mixing ratio of large particles (those with radii greater than about 0.15/zm) behaves similarly. The heights of the mixing-ratio maxima appear to be closely related to the height of the tropopause 1) Space Science Division, Ames Research Center, NASA, Moffett Field, California 94035 USA. 2) R and D Associates, Marina del Rey, California 90291 USA.

Vol. 118, 1980)

The Stratosheric Sulfate Aerosol Layer

87

(HoESIANN et aL, 1974; ROSEN et al., 1975; FARLOWet aL, 1979). Aerosol particle size distributions show large decreases for particles with radii greater than 0.1 tzm, with the ratio of the concentrations of particles with radii greater than about 0.15/zm to those with radii greater than 0.25/zm being about 3 to 5. In contrast to the number mixing ratio of large particles, the number-mixing ratio of total particles falls off rapidly above the tropopause. The layer, which exhibits seasonal, latitudinal, and temporal variability, may be greatly enhanced following volcanic activity (HOEMANN and ROSEN, 1977). The presence of a stratospheric aerosol layer has stimulated the interest of atmospheric scientists and climatologists because of suggestions that it may exert a significant influence on the climate of Earth (LAUB, t970; POLLACt~et aL, 1976a,b; HANSEN et al., 1978). In addition to possible natural enhancements of the layer following strong volcanic activity, there is the concern that man may be inadvertently perturbing the layer. Increasing industrial release of sulfur compounds into the atmosphere, or particulate matter injected at high altitudes by aerospace vehicles, might affect the climate or catalyze heterogeneous chemical reactions that affect global ozone abundances (POLLACK et al., 1976c; CADLE et aL, 1975). As a result, there have been efforts to develop appropriate analytical models to evaluate the effects of perturbations on the layer. JUNGEet al., (1961) first used a one-dimensional diffusion model with particle sedimentation and coagulation to explain the observed fall-off of the total particle mixing ratio with increasing height above the tropopause. Similar models were developed by FRIEDLANDER(196I) and MARTELL(t966). Using a two-dimensional model with a meridional as well as vertical transport, CADLE et al. (1976) and CADLEet al. (1977) investigated the global dispersion of aerosol particles following volcanic activity. Detailed theories describing the photochemical interactions of gaseous sulfur constituents in the atmosphere have been developed over the past decade (e.g., see GRAEDEL,1977, and CALVERTet al., 1978, for reviews of tropospheric sulfur chemistry). Junge and his associates made the original suggestion that the large stratospheric aerosol particles might be formed from gaseous sulfur compounds (JUNGEet al., t961). Subsequent work has focused on two mechanisms leading to sulfate formation from SO2: solution reactions which oxidize sulfur dioxide absorbed by aerosol droplets (ScoTT et al., 1969; FRIEND et aL, 1973), and gas phase reactions which convert SO2 into sulfuric acid vapor (e.g., CASTLEMANet al., 1975; DAVIS and KLAUBER,1975; CRUTZEN, 1976). Sulfuric acid vapor can subsequently condense on aerosol particles. Very recently, it has been suggested that sulfur radicals of the type HSOx, which are intermediaries in the formation of H2SO4, may nucleate rapidly to form new aerosol particles or react rapidly with existing particles (J. P. FRIEND,private communication). Sulfur dioxide gas can be either transported directly into the stratosphere from the troposphere (e.g., HARKER, 1975) or it can form within the stratosphere following the photodecomposition of carbonyl sulfide, and oxidation of the resultant sulfur atoms (CRUTZEN, 1976).

88

R.C. Whitten, 0. B. Toon, and R. P. Turco

(Pageoph,

The principal thrust of recent aerosol model development has been in the direction of a more detailed treatment of physical aerosol processes (e.g., KRITZ, 1975a,b; BURGMEIERand BLIFFORD,1975; CADLEet aL, 1976; ROSENet al., 1978; WHITTENand TERCO, 1976; TURCO et aL, 1976, 1979a; TOON et al., 1979). In the remainder of this paper, we will discuss aerosol microphysical processes and their simulation in aerosol models, the sensitivity of model predictions to aerosol parameters, the agreement of model predictions with observational data, and some possible man-made perturbations of the aerosol layer.

2. Aerosol sources and processes Gaseous sulfur sources and sinks

The only sulfur-bearing gases that appear to be important sources for the stratospheric aerosol layer are sulfur dioxide (SO2), carbonyl sulfide (COS) and carbon disulfide (CSz). The concentrations of other sulfur-bearing gases - such as hydrogen sulfide (H2S) and dimethyl sulfide ((CH3)~S)- are so small and the gases are so reactive in the troposphere with constituents such as OH, that they are negligible as sources of stratospheric sulfur. Although the tropospheric lifetime of sulfur dioxide is estimated to be only a few days (FRIEND, 1973; LEVY, 1974), the amount of SO2 emitted into the troposphere is large enough that it still makes a considerable contribution to stratospheric SO2 through upward transport. Sulfur dioxide is also important as an aerosol source because of the belief that it is injected directly into the stratosphere by large volcanic eruptions (as are H2S and COS, but in lesser amounts). Carbonyl sulfide originates in biological, volcanic, and industrial processes (STOIBERet al., 1971; PEYTON et al., 1976). It has been measured over a wide geographical range, and appears to have a very uniform concentration of about 0.5 ppbv throughout the lower troposphere (SANDALLSand PENKETT, 1977; TORRES et al., 1978). Like other sulfur compounds, COS is attacked by OH: COS + O H ~ C O 2

+HS

and this reaction probably governs its overall atmospheric lifetime. Nonetheless, the rate coefficient is quite small (5.7 x 10 -14 cm 3 sec -1 according to KURYLO, 1978, and 10 -15 cm 3 sec -1 according to ATKmSON et al., 1978) leading to an atmospheric lifetime of about a year; this estimate assumes a mean tropospheric OH concentration of 106 cm -3 (e.g., CAMBELLet al., 1978). On the basis of the geographic uniformity of the COS distribution, a lower limit lifetime value of about { year seems reasonable. The photolysis and subsequent conversion of carbonyl sulfide into sulfuric acid in the stratosphere was first studied by CRUTZEN (1976). Recently INN et al. (1979) detected COS in the stratosphere and measured its vertical distribution (Fig. la). The decrease of COS with increasing height in the stratosphere observed by I~N et al. (1979) is consistent with its photolytic decomposition (calculated using measured

Vol. 118, 1980) 70 1

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The Stratospheric Sulfate Aerosol Layer

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Figure la Typical one-dimensional model profiles for the dominant sulfur gases. Data for COS and SO2 are compared. absorption cross sections) and by reaction with OH, and confirms its role as a sulfur source for aerosols, as proposed by CRUTZrN (1976). If Kurylo's measured rate coefficient for the COS reaction with OH is correct, Inn's observation may place some restrictions on stratospheric OH abundances. This is emphasized in Fig. lb, which shows that the stratospheric sulfur balance (TuRCO et aL, 1979b) is dominated by COS. Sulfur is removed from the stratosphere only by sedimentation of aerosol particles followed by 'rainout' or 'washout' of water-soluble sulfur gases and vapors (e.g., H2SO4) in the troposphere. Rainout and washout of trace gases, although important, are difficult to describe analytically. The usual aeronomic approximation for the precipitation removal of a gaseous species is to specify a decreasing rainout rate with increasing altitude such that the resulting average atmospheric residence time roughly corresponds to one deduced using global mass budget arguments. For example, TURCO et al. (1979a) have adopted an SO2 lifetime against washout (and rainout) of 3 days at the surface, and a linear decrease of the washout rate (the inverse of washout lifetime) to zero at an altitude of 13 kin. The sulfuric acid washout rate is probably larger; TURCO et al. (1979a) assume a lifetime of 12 hours at the surface and a rate

R. C. Whitten, O. B. Toon, and R. P. Turco

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Sulfur Flux, tg S/yr-globe 0.01

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Figure 1b The stratospheric balance of gaseous sulfur and aerosol sulfate in a one-dimensional model. Equivalent sulfur atom fluxes are given. The arrows indicate direction of sulfur flow. decreasing linearly to zero at 13 km. Tropospheric precipitation also acts as a sink for aerosol particles that diffuse downward from the stratosphere (see the following section).

Sulfur chemical processes Table 1 lists an abbreviated set of the chemical reactions and the corresponding rate coefficients for the transformation of COS into H2SO4. Once carbonyl sulfide has reached the stratosphere, it is destroyed by photodecomposition and by reaction with O H ; COS photoabsorption coefficients have been measured by CHou et al. (1976) and BRECKINRIDGEand TAUBE (1970). The observed absorption spectrum,

Vol. 118, 1980) 30

The Stratospheric Sulfate Aerosol Layer I

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illustrated in Fig. 2, when combined with the solar fluxes of ACKERMAN (1971), leads to the daily-averaged COS photodissociation rates given in Table 1. The sulfur atoms so formed react rapidly with molecular oxygen to form SO, which is in turn rapidly oxidized into SO~. Other reactions listed in the table further oxidize the SO2 into SO3 and the SO3 combines with water vapor, whose stratospheric mixing ratios are 3-6 p p m v (HARRIES,1976), to form sulfuric acid. The intermediate sulfur radical HSO3, formed by the reaction of SO2 with OH(R7), can react with 02 to produce HSOs. The H S Q radical can in turn react with nitrogen oxides to yield compounds such as HOSOzONO and HOSO2ONO2 (CALVERTand McQuIGG, 1975) or cluster with water to form hydrates, H S O s . H 2 0 . Because the photochemistry of these species is not well understood, it would be difficult to evaluate their effects on aerosols. However, it is interesting to note that FARLOW et al. (1978) have recently detected nitrogen-bearing sulfate compounds in stratospheric aerosol samples. Moreover, FRIEND (private communication) has apparently detected clustered sulfur radicals initiated by the reaction of SO2 with OH in a laboratory experiment; the radicals appear to combine easily into nuclei which can form water drops in a cloud chamber. As discussed by TURCO et al. (1979a), sufficient information to identify

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The Stratospheric

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R.C. Whitten, O. B. Toon, and R. P. Turco

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the dominant processes for the oxidation of SO2 into H2SO4 does not yet exist. As a result, reaction sequences like that listed in Table I must usually be used. Fortunately, reaction schemes can be readily expanded with advances in sulfur photochemistry. Heterogeneous reactions may also be important. FRIEND et al. (1973), have pointed out that SO2 could react directly with sulfuric acid droplet surfaces to produce additional dissolved sulfates; the process would require the presence in solution of a buffering agent such as ammonium ions. Sulfur radicals, such as HSOa, might also be absorbed or react directly on aerosol surfaces. Again, we have insufficient information to be sure; however, we may reasonably assume that some of the nitrogenbearing sulfates that have been detected are formed by heterogeneous reactions. It is important to mention at this point that extensive sensitivity tests (ToON et aL, 1979) have shown that the precise fate of sulfur radicals formed in the stratosphere may not be critical to the simulation, as long as they eventually stick onto aerosol particles and are chemically transformed into sulfate.

Microphysical processes

Theoretical treatments of nucleation and growth by condensation and coagulation of aqueous sulfuric acid solution droplets under stratospheric conditions are available. It is generally assumed in the literature that the aerosol particles are formed in situ by heterogeneous heteromolecular nucleation of H2SO4 and water vapors onto condensation nuclei or Aitken particles. Recently, CADLE and KIANG (1977) reviewed current scientific knowledge of atmospheric Aitken particles. The Aitken nuclei are assumed to be transported by eddy diffusion from the troposphere to the stratosphere or to be deposited in situ by aircraft or rocket engines. If the stratosphere is supersaturated with respect to an aqueous H2SO4 solution, the Aitken particles are rapidly nucleated in times of the order of 10~ sec or tess, depending on the supersaturation, the nucleus composition and size, and other factors (P. HAMILL, private communication). (Model calculations are quite insensitive to this time as long as it is less than 107 see.) HAMILL et al. (1977a), have shown that under ambient stratospheric conditions, homogeneous nucleation or nucleation onto molecular ions may be slower than the heterogeneous process. However, large ions consisting of a charged core surrounded by a cluster of polar molecules such as H~O, HNOa, and H2SO4 have been detected in the lower stratosphere (ARNOLD and HENSCHEN, 1978); such ions might act as effective nucleation sites for aerosol particles (CAsTLEMAN et aL, 1979). Complexes of sulfur radicals might also act as condensation nuclei in the stratosphere (FmF.ND, private communication). Once nucleated, the droplets grow by heteromolecular condensation of sulfuric acid and water vapors; the nonacidic material of the nucleus becomes a (solid or dissolved) droplet core and remains so until the H2SO4 and H 2 0 are evaporated. Even so, the core surface may remain activated for some time due to incomplete

VoI. 118, 1980)

The Stratospheric Sulfate Aerosol Layer

95

drying. HOPPEL(1976) and HAMILLet al. (1977b), have shown that the droplet growth rate is controlled by the rate of impingement of sulfuric acid molecules, and that the droplet is always in equilibrium with the ambient atmospheric water vapor. If the partial pressure of sulfuric acid vapor surrounding the droplet is greater than the droplet vapor pressure, there is a net uptake of incident H2SO4 molecules; conversely, if the vapor pressure is greater, there is a net loss of H2SO~ from the droplet and evaporation occurs. The droplet simultaneously absorbs or evaporates just enough water vapor to maintain a constant mass fraction of H2SO4 in solution (because the amount of water vapor in the stratosphere is much greater than the amount of H~SO4). Particle coagulation has an effect somewhat similar to condensation in that it causes particle growth. However, it is dissimilar in that it involves droplets rather than single molecules sticking to another droplet. In the stratosphere, where aerosol sizes are usually less than 1 t~m, only coagulation due to Brownian motion need be considered; that is, coagulation due to turbulence and coalescence due to differences in fall velocities can be neglected. The coagulation kernel for particles of different size has been derived by FUCHS (1964); the kernel is a function of the molecular diameters for air and H2SO4, the particle sizes, densities and sticking coefficients, and the kinematic viscosity of air. In modeling coagulation, one should include coagulation of condensation nuclei with droplets, but may omit coagulation of nuclei with nuclei because of the much lower probability of their colliding and sticking to each other in the stratosphere. During sedimentation in the lower atmosphere, droplets are always at or very close to their terminal fall velocities and retain their approximately spherical shape if they do not freeze (because at small velocities, surface tension can maintain a nearspherical shape). Hence, the fall velocities are given very accurately by the StokesCunningham formula (e.g., KASTEN, 1968). The aerosol particles are, of course, also transported by atmospheric motions. For droplet sizes representative of the lower stratosphere, one can, to a very good approximation, assume that the mean particle velocity due to drag by atmospheric motion is equal to the local mean atmospheric velocity.

3. Stratospheric aerosol models Model elements The particle size distribution, which is in general a function of time t, altitude z, and radius r, is described by continuity equation of the form

dn ~-

( ~g) ~n +n V-V+~r -= O-t + V.(nv) +~(gn)

= Sn

(1)

where n is the particle concentration per unit radius (particles cm-3 sec-1), g is the

96

R.C. Whitten, O. B. Toon, and R. P. Turco

(Pageoph,

particle growth rate (cm see-1), SN is the net particle source/sink term due to nucleation, coagulation washout, etc. (particles cm -3 sec-1), and v is the particle velocity. The rate of change of n due to coagulation is given by an expression analogous to the collision integral of gas dynamics which specifies the volume rate at which particles are 'scattered' (i.e., coagulated) into a radial 'element' less the rate of'scattering' out of the element. Then equation (1) can be written

~n ~ (dn) ~--~ + V. (nv) + ~ (gn) = ~-

+ S;

(2)

coag~

the coagulation integral, (dn/dt)ooa~., will be discussed later. A similar continuity equation is satisfied by the condensation nuclei. The spatial flux ~b denoted by (nv) in equation (2) is conveniently decomposed into three parts: a sedimentation flux dps = -v~n~z

(3a)

where vs is the fall velocity and ~z is a vertical unit vector; a flux due to atmospheric bulk motion dpa = v~n

(3b)

where va is the atmospheric bulk velocity; and an eddy flux, representative of sub-grid scale motions

(3c) where na is total atmospheric number density and D i s the eddy diffusion tensor. The growth and evaporation of aerosol droplets affect the concentrations of sulfur-bearing gases in the atmosphere. The rate at which H2SO4 molecules condense on and evaporate from droplet surfaces is determined by the particle growth rate and the total particle surface area available. The net rate at which acid molecules condense onto existing particles can be expressed in the (equivalent chemical kinetic) form

dna dt

P~

-

L~n~,

(4)

where P, and L~ are the specific sulfuric acid production rate (molecules cm-a sec-1) and loss rates (molecules sec- 1), respectively, which may be related to the growth rate g and aerosol concentration n by appropriate integrals over particle sizes. The term dn~/dt also represents the net rate of loss of sulfuric acid from the droplets. Hence, if a model is to be interactive between aerosol and vapor, the terms P~ and L~n~ must be included in the kinetic equation for H2SO4 vapor. As we shall see later, it is important to include these terms because condensation can severely deplete H2S04 vapor in the lower stratosphere, moderating the growth rate of aerosol particles.

Vol. 118, 1980)

The Stratospheric Sulfate Aerosol Layer

97

The model of Junge, Chagnon,and Manson I n their p a p e r r e p o r t i n g the first definitive m e a s u r e m e n t s o f t h e stratospheric aerosols, JUNGE ( t 9 6 I ) also p r e s e n t e d a simple m o d e l t h a t was r e m a r k a b l y c o m p l e t e with respect to i m p o r t a n t phYSical processes in view o f the capabilities o f the c o m p u t e r s o f t h a t era. Specifically, they included t r a n s p o r t by vertical diffusion a n d sedimentation, a n d coagulation. They expressed the vertical flux, ~ o f particles as

et al.

0 ((n) n r~ = -naD exp [-f; (vs/D)dzr] -~z

exp

[f~ (vJD) dz']}

(5)

where D is the vertical c o m p o n e n t (D~z) o f the e d d y diffusion tensor. The steady-state f o r m o f the continuity e q u a t i o n was then solved for the particles u n d e r the a s s u m p t i o n t h a t D is a constant, t h a t vs varies inversely with air density, a n d that there were b o t h

CONCENTRATION, NUMBER cm -3 .01 .1 I 3O

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DOWNWARD DI FFUSI NG PARTICLES

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UPWARD DI FFUSING PARTICLES UPWARD DI F FUSI NG PARTICLES WITH COAGULATION

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1.0

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Figure 3 Vertical profiles of particle concentration calculated for diffusion-sedimentation equilibrium for particles of 0.15/~m radius and 2.0 g cm -a density using the model of JUNGE (1961). The eddy diffusion coefficients, D, are in units of cm 2 sec -I. The dashed curves ( . . . . . ) represent upward diffusion of particles from a constant source at 30 km altitude and an effective sink (washout) at the tropopause. The broken curve ( - - . - - ) represents qualitatively the shift in the dashed ( . . . . . ) curves when coagulation is introduced. The vertical bars and heavy solid line connecting their midpoints represent a profile of particles collected by impactor on November 21, 1959; the measurements are roughly representative of 0.15/~m particles.

et aL

98

R.C. Whitten, O. B. Toon, and R. P. Turco

(Pageoph,

stratospheric and tropospheric sources of particles; the sources were taken into account by fixing the number density at 30 km and 10 km. Some calculated number densities of particles with radii of 0.15 tzm are shown in Fig. 3; the particles of stratospheric origin (see 'b' curves) are assumed to be rapidly removed by washout at the tropopause. As seen in Fig. 3, JUNGEet al. (1961) found that at altitudes below 24 km the predicted vertical distribution of 0.15 tzm particles was in rough qualitative agreement with observational data when an eddy diffusivity of 2000 cm 2 sec-1 was used. Because of computational limitations, they were able to give only a qualitative assessment of the coagulation process for upward-diffusing fine particles. For this case, they used an approximate steady-state expression d2n

D-d~z2+ an 2 = 0,

(6)

where a is a coagulation coefficient, which depends on the particle mean free path, and on the air viscosity and temperature. The solutions have the form 6D n = a(z + Zo)2

(7)

where Zo is an empirical constant. A typical vertical distribution for the upwarddiffusing particles is shown by curve c in Fig. 3. JUNGE et al. (1961), concluded from their studies that sedimentation and diffusion, and particle growth by coagulation satisfactorily describe the evolution of particle distributions in the stratosphere. They also concluded that there are three major populations of stratospheric aerosol particles: those with radii < 0.1/zm, probably of tropospheric origin; those with radii between 0.1 and 1 tLm, most likely formed within the stratosphere, probably by oxidation of SO2 and H2S; and those with radii > 1/zm, of extra-terrestrial origin. We now know (e.g., TURCO et al., 1979a) that particle growth by condensation and shrinkage by evaporation are also important microphysical processes. Nevertheless, the model analysis performed by JUNGEet al. (1961), did identify many of the important sources and processes of stratospheric aerosols and helped to explain several features of their experimental data, particularly the vertical distribution of the' large' particles (i.e., particles with radii between 0.15 and 2 t~m). The model o f Burgmeier and Blifford

BURGMEIERand BLIFFORD(1975) had a rather limited objective in their studies: to simulate the 'aging' of aerosols by coagulation and by growth resulting from surface-gas reactions in the presence of regenerating particle sources. They also calculated mean particle residence times in the absence of particle sources. Then Burgmeier and Blifford sought to estimate changes in particle size distributions as they evolved by growth and sedimentation. The aerosol continuity equation used by

The Stratospheric Sulfate Aerosol Layer

Vol. 118, 1980)

99

Burgmeier and Blifford, -On(r, - t) =

Ot

f

rl21/3

K[(r s - r'~ 113, r']n[(r 3 - r'S) 1Is, t ]n(r', t) Ta r 2

[,rb

x (r ~ --r,,)2/s dr' - n(r, t) Jr K(r, r')n(r', t) dr' a

}r

o~

vs ) n(r, t) - ~(r, t) -~r + S(r, t),

(8)

where n(r, t) is the concentration of particles with radii between r and r + dr, K(r, r') is a coagulation kernel, vs(r) is the sedimentation fall velocity, l is a length parameter characteristic of the layer depth (nominally taken to be 100 m), a is the rate of growth due to the reactions of gases on the particle surface, and S(r, t) is a particle source term. The authors were able to ignore gas phase chemistry because all processes leading to particle formation and growth were implicitly absorbed into the empirical terms S(r, t) and a(r, t). The first integral on the right-hand side of equation (8) accounts for accretion of particles in the size range r, r + dr due to coagulation of smaller particles, and the second integral accounts for coagulative loss of particles in that size range. The source term was so constructed that it returned to the atmosphere a total mass equal to that removed by sedimentation, ensuring the size distribution for the source to be the initial size distribution for the calculation, n(r, 0). The continuity equation was then solved numerically for various forms of the initial concentration and size distribution. Burgmeier and Blifford used the model to study aerosol 'aging' and aerosol residence times by simulating the time evolution of various initial size distributions. Of several such distributions considered, only that of BIGG et al. (1972) was consistent with the residence time of 2 yeats estimated by TELEGADASand LIST (1969) from radioactivity measurements. The authors also concluded that, with sources proportional to the initial size distribution, the spectra of BIGGet al. (1972), and of FRIEND (1966) were capable of maintaining their original forms; on the other hand, the spectrum of JUNGE et al. (1961) became significantly depleted in the small size range. For sources that were not proportional to the initial particle size spectrum, BURGME1ER and BLIFFORD(1975) found a tendency for the spectrum to approach the shape of the source. This behavoir was somewhat stronger with the larger particle concentrations of Bigg et al. than with those of Friend or Junge et al. The time evolution of a ' Bigg' initial spectrum is shown in Fig. 4. (Note that the distribution is expressed in the form dn/d log r.)

The model of Kritz In his Ph.D dissertation, KRITZ (1975a) undertook a somewhat more general analysis of aerosols than those outlined above, particularly with respect to particle formation and growth. In order to simplify the treatment of the aerosol particle

100

R. C. Whitten, O. B. Toon, and R. P. Turco

(Pageoph,

t, days

10

j

10 z

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30

/

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Figure 4 Changes in the size distribution of Bigg over a period of 30 days. Note that the distribution is given by dn/d (log r). (After BURGMHERand BLIFFORD, 1975.) continuity equation, he adopted a Lagrangian formulation

Dn(r, t) Dt

1 rD n(r, t) - ~ 1 n(r, t) + f coag. -- ~ [gn(r, t)] + S(r, t),

(9)

where ~'D and ~-~ are, respectively, the particle residence times against diffusion and sedimentation. The term f coag. represents the coagulation integrals (first two terms

Vol. 118, 1980)

The Stratospheric Sulfate Aerosol Layer

101

on the right-hand side of equations (8)), g is the particle growth rate due to accretion of sulfuric acid molecules by the particle surfaces, and S(r, t) is a source term as in equation (8). Gas phase chemistry was assumed to lead to the formation of sulfur trioxide (SO3) from the oxidation o f other sulphur compounds such as sulfur dioxide (SO2). The S Q molecules were then assumed to either form new aerosol particles (via heteromolecular homogeneous nucleation) or to be accreted by existing aerosol particles. The simulation of diffusion and sedimentation by the use of residence times, while admittedly crude, was acceptable for Kritz's limited study of the rates of aerosol processes. To facilitate solution of the coagulation integrals, Kritz employed the logarithm of the particle mass (log m) rather than radius as the variable of integration. The particle size distribution was divided into a series of bins, i = 1, 2 . . . , s p a n n i n g the particle mass range considered such that the log rn~ were in arithmetic progression. The coagulation integrals were then discretized in a manner similar to that used by TuRco et al. (1979a) and discussed below; the coagulations kernels were computed using formulas given by FucI-IS (1964). With a given size distribution as an initial condition, the populations of the bins were allowed to evolve by time-stepping the finite difference analog of equation (9). Rather than treat growth as a separate process, Kritz incorporated it into the coagulation integral. Heterogeneous nucleation (growth) processes were modeled by including a special size bin whose population was set equal to the ambient concentration of SO3. Coagulation of an SO3 molecule with a particle in any aerosol size bin was assumed to be equivalent to growth, and the ambient SOa concentration adjusted by taking the difference between its rate of formation from SO2 and rate of loss to particles. The formation of new particles via homogeneous processes (the S term in equation (9)) was accounted for by increments to the population of the first aerosol size bin. KRITZ (1975a) used this model to simulate a number of possible scenarios related to the formation of the background stratospheric aerosol in order to determine the effects of various postulated rates and mechanisms of aerosol formation on the particle size spectrum of the resultant aerosol populations. The principal conclusions of the study were that the large particles characteristic of the background stratospheric aerosol layer are formed by the growth of a small population of'pre-existing' Aitken particles, and that a principal factor controlling the final size (and number) of the large particles thus formed is the number of Aitken particles (i.e., growth sites) originally present. However, the model could not distinguish between growth caused by the condensation of SO3 and water vapor on the particles (heterogeneous nucleation) and that resulting from the direct uptake and oxidation of SO2 within the particles (presumably in the presence of NHa, as proposed by FRIEND et al., 1973). Coagulation, while effective in limiting the population of smaller particles (~0.05/x radius), was found to be too slow to be a significant factor in the formation of the large particles or in materially reducing their number. The production of large particles was also found to be relatively insensitive to the rate of aerosol formation, so long as these rates were of the same order or fast relative to the ~ 1-year residence

102

R.C. Whitten, O. B. Toon, and R. P. Turco

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times characteristic of the lower stratosphere. KRITZ(1975b) also tested the possibility that the requisite 'pre-existing' Aitken nuclei population might be produced in the stratosphere via a ' self-limiting' homogeneous heteromolecular nucleation of sulfuric acid-water nuclei but concluded that this was unlikely. The model o f Rosen, Hofmann, and Singh

ROSEN et al. (1978) based their model on solutions to a form of equation (9) in which the residence times are replaced by operators representing eddy diffusion and sedimentation: 9D ~ -~z DnA 1 0 -- -->-

7s

~Z

v~.

n21

(10a) (10b)

Further important approximations were also made: coagulation kernels are independent of particle size, H2SO4 vapor is distributed with a narrow Gaussian profile centered at 20 km, and gas phase chemistry can be neglected. Even with these assumptions, Rosen et al. were able to obtain analytic solutions that were in rough qualitative agreement with observed size distributions and vertical height distributions of aerosols. They found, however, that the predicted condensation nuclei (CN) profile was not in good agreement with observation. When they adjusted the input parameters so as to being the CN profile into better agreement with measurements, other profiles, such as the large particle (radius >0.15/~m) mixing-ratio profile became unacceptable. A search for a reasonable set of parameters that would bring the model into essentially complete agreement with the measurements was unsuccessful. The occurrence of a particle mixing-ratio peak at 20 km was, of course, due largely to the assumption of an H2S04 concentration peak at 20 km. Despite its defects, the model of Rosen et al. represents an improvement over earlier models in that aerosol height and size distributions, as they are affected by coagulation, could be studied in greater detail. The model o f Turco and coworkers

TURCO et al. (1976, 1979a) developed a stratospheric aerosol model which includes the following processes: vertical eddy diffusion, sedimentation, nucleation, vapor condensation and evaporation, coagulation, and interactive sulfur gas phase chemistry. 'Interactive' means that sulfuric acid vapor formed by chemical reactions is coupled to the liquid phase abundance in aerosols through equation (4). Turco et al. consider two classes of particles separately: aerosol droplets and condensation nuclei. They also follow the evolution of core material in the droplets, which consists of accumulated nucleus material. The corresponding set of continuity equations, which have the

Vol. 118, 1980)

The Stratospheric Sulfate Aerosol Layer

103

general form of equation (2), were recast into finite difference equations for computer solution. Because stratospheric aerosol particles can span several orders of magnitude in radius, TuRco et al. (1979a) represented their model size range (radii of 0.001 to 2.56 tzm) with a set of geometrically increasing particle size categories (also see the discussion of Kritz's model). As did JUNGE et al. (1961), Turco et aL combined the particle diffusion and sedimentation terms into the form

~tot~1

Dt~ Oz (~n),

(lla)

where n ~ exp [J~ Vs(z'),az ,]j. /z = na(0)

(1 lb)

Using equations (l l) reduces 'numerical' or artificial diffusion problems which normally arise when sedimentation fluxes are calculated. Artificial diffusion also arises in the finite difference formulation of droplet growth, and a suitable means must be employed to minimize it. In the scheme of TuRco et aL (1979a), the particle population of bin i is given by f T,+1 ni,~ l(r) dr, l

where (12)

n~,~+l(r) = n~,i+l r

During a time step at a given height, the constants h and a are calculated by adjusting them to fit the total particle surface areas in bins i and i + 1, i'espectively. One then finds that the finite difference approximation to the growth term in equation (2) can be written for the ith bin as

en,J -ffl~rowth

n,-1 ~,-1

ni

(13)

~,

where the ~-~are the time-dependent parameters which depend on the mean growth rate of particles in a bin and on bin populations. This approach can effectively inhibit spurious particle growth resulting from 'numerical' diffusion. Lack of computer capacity prohibits a detailed treatment of the size distribution of the cores within each droplet size bin. An alternative approach developed by Turco et al. uses the first and second total core volume moments for the inclusions in each size particle. Continuity equations analogous to equation (2) can be derived for the core volume moments. For coagulation, the assumption of a discrete particle size spectrum gives

104

R . C . Whitten, O. B. Toon, and R. P. Turco

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satisfactory results and is easy to use. In this case, one writes the coagulation loss term in equation (2) as (14)

= -- n, ~ K, jn~( Vff V 0 + ooag, loss

j~;~

and the gain term as

On'+11 ~t

(15)

= n, E K~yny(VJlV~)O,y

= coag. gain

3" ~ i

(o,j = 1 if i ~ j ;

O~j = 89 if i = j ) .

The factor 0ij is a symmetry factor which eliminates double summing in computing self-coagulation rates. The treatment for coagulation of condensation nuclei with droplets is slightly different; the reader is referred to TURCO et al. (1979a) for details. Using the model of TURCO et aL (1979a), TooN et al. (1979) have made some rather extensive comparisons of model predictions with aerosol observations. For example, Fig. la shows model predictions of typical vertical distributions of the dominant sulfur-bearing gases, including the effects of aerosols. The mixing ratio of COS is constant in the troposPhere (which is indicative of a long lifetime in this 40

I

I

I

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SPRING 1973 LATITUDE AVERAGE DATA 35

i

30

E25

'yV

2o

15

10

S I

I

.2

I

I

.4

I

~

.6

I

]

]

.8

i

10

SO4 MASS MIXING RATIO, 10"6/ag/mg AIR

Figure 5 Observed and calculated aerosol sulfate mass mixing ratios (rag SOg/kg air). The observations (LAZRUS and GANDRUD, 1974), made with filters, have been averaged over latitude from pole to pole. The error bars give the extreme values found at individual latitudes.

Vol. 118, 1980) 40

The Stratospheric Sulfate Aerosol Layer I

I

I

I I

I

I

I

I

I

I

...... n

I

1 I

I

I

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JUNGE et al. 1961

.__

KP, S E L A U

-- -- --

PODZIMEK

[]

30

105

etal.

1974

e t al. 1 9 7 5

CADLE AND LANGER 1975 t

ea 1-20

. . . . . ;"

-i:

-

ROSENAND HOFMANN 1977

0

10

% 1%

-

M O D E L RESULTS I

I

1

I I

10

I

I

I

I I

100

I

I

I

I

I

I

1000

I

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I

10,000

TOTAL PARTICLE MIXING RATIO, PARTICLES/mg AIR

Figure 6 Observed and calculated total particle number mixing ratios (particles/rag air). The data were obtained over a period of 15 years by various investigators using condensation chambers. The large spread in the data may be partly due to real differences in aerosol abundances and partly due to different sampling techniques. region) and then decreases uniformly with height above the tropopause. The predictions fit the recent stratospheric measurements of INN et al. (1979) quite well. Sulfur dioxide concentrations decrease rapidly above the tropopause due to upward diffusion and rapid oxidation by OH. Interestingly, SO2 increases in the region where COS is photolyzed, and again at higher altitudes where H2SO4 is photolytically decomposed, although this latter process is speculative because H2SO4 vapor absorption cross sections in the dissociating region below 250 nm are undetermined. Sulfuric acid vapor has an interesting distribution in that its lowest concentrations occur in the vicinity of the aerosol layer. The aerosol particles strongly absorb H2SO4, significantly affecting its local abundance. This result suggests that aerosol models that do not include interactive gas-particle processes for H2SO4 may be quite inaccurate in their predictions for the sulfate layer. Some of the steady-state model predictions of the properties of the ambient stratospheric aerosol layer, and comparisons with experimental data, are shown in Figs. 5 to 9. Interestingly, even though T O O N et al. (1979) did not attempt to tune their model by varying some of the uncertain physical parameters, the predictions for the five aerosol characteristics shown in Figs. 5 to 9 are reasonably good. It is pertinent to note that most of the data employed here were obtained during a volcanically quiescent period in 1973-74. The steady-state model predictions are presumed to represent an average global state for the quiescent aerosol layer.

106

R.C. Whitten, O. B. Toon, and R. P. Turco

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40 SUMMER (~ = O WINTER SPRING MODEL RESULTS

35

30

E ..~

25

E3 II-~ w

20

15

10

51

I 0

I 2

I

I 4

I

I 6

I

I 8

I

I 10

~

I 12

LARGE-PARTICLE (r > 0.15/~m) MIXING RATIO, PARTICLES/mg AIR

Figure 7 Observed and calculated mixing ratios of particles with radii >0.15 /zm. The observations (HoFMANNet aL, 1975a) were made using a light-scattering particle counter. A large number of measurements were made over Wyoming; the mean value and a measure of the standard deviations are presented for different seasons. The sulfate mass-mixing ratios shown in Fig. 5 indicate that the model gives roughly the same amount of sulfate mass in the aerosol layer as has been observed. Predicted and measured total particle mixing ratios in the stratosphere are shown in Fig. 6. The scatter in the experimental data could be indicative of variability in atmospheric vertical transport rates in this case. Figure 7 illustrates that the calculated concentrations of large particles (radii > 0.15 txm) are in accord with a number of stratospheric in situ measurements. Figure 8 shows that the size distribution of the large particles (represented by the concentration ratio of particles with radii >0.15/xm to those with radii >0.25 t~m) are also in agreement with observations. In both Figs. 7 and 8, there is a substantial range of measured values, with the model calculation being generally representative of the data. Finally, the computed particle size distributions at 16 and 20 km are compared

Vol. 118, 1980)

The Stratospheric Sulfate Aerosol Layer 40

I

I

I

9 '1 ~'~

35

t

I

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I

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[

107 I

22 FLIGHTSOVER LARAMIE, WYOMING ~ 32 FLIGHTS WORLDWIDE MODEL RESULTS

30

E 25

/

a I'm I'-

~

/

I I

2o

15

10

0

2 4 6 8 RATIO OF PARTICLES > 0.15 #m RADIUS TO THOSE > 0.25 .um RADIUS

10

Figure 8 Observed and measured concentration ratios of particles with radii >0.15/~m to those with radii > 0.25/zm. The observations (PINNICKet al., 1976) were made with a light-scattering particle counter. Numerous flights were made over Wyoming and worldwide. The average value and a measure of the standard deviation are illustrated. to several empirical size distributions in Fig. 9. Evidently, the model reproduces the observed stratospheric aerosol properties quite well (under volcanically quiescent conditions). Model o f Cadle, Kiang, and Louis CADLE et al. (1976) constructed a two-dimensional (meridional plane) model designed to simulate the global dispersion of volcanic eruption clouds. No processes other than transport by atmospheric motions were included in the model. Hence, particle formation, growth, coagulation, and even sedimentation were ignored. Despite these drastic simplifications, the model proved useful in a qualitative way for assessing the rate and degree of meridional spreading of the injected material from several eruptions. As the material from a simulated equatorial eruption ( A g u n g ) s p r e a d poleward, the predicted altitude of peak concentration steadily decreased, as observed for ambient aerosols (e.g., ROSEN et al., 1975). A simulation of a high-latitude eruption (Bezymainny) suggested that the material will tend to stay at high latitudes until it is eventually lost by downward transport into the troposphere.

108

R.C. Whitten, O. B. Toon, and R. P. Turco

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AT 16 km ___• MODEL RESUL" AT 20 km - - - = EXPONENTIAL -log NORMAL o ZOLD ___ r

r~

10-,V

Z O I,<

10-2

g

IZ O

10-3

8

7\

/i ! \

\

\

O r 10-4

10-5 .01

,1 1.0 R A D I U S , ,um

10

Figure 9 Observed and calculated aerosol size spectra. The calculated spectr a correspond to altitudes of 16and 20 km. The observations are represented by the three analytic functions that are based on close fits to a variety of measured distributions (Too~ and POLLACK,1976; PrNNICKet al., 1976). An r-4 spectrum, typical of tropospheric aerosols, is also shown for comparison.

In order to adequately investigate the time evolution o f a volcanic eruption, a two-dimensional transport model that simulates gas phase chemistry as well as aerosol microphysical processes is necessary. Such a model will also be needed for the analysis and interpretation o f the aerosol data to be obtained by S A G E satellites.

4. Sensitivity of predicted aerosol layer properties to processes and parameters A n aerosol model can be expected to be sensitive in varying degrees to the parameters that set the rates of the various physical processes. Since T o o n e t al. (1979) are, to our knowledge, the only investigators to have carried out a detailed and systematic study of such sensitivities, we restrict our discussion to that work. The aerosol processes studied by T o o n e t al. and a qualitative estimate of the response to parameter variations are listed in Table 2. The interested reader is referred to TOON e t al. (1979) for a complete quantitative discussion o f these variations; we discuss four o f them here in some detail. The various uncertainties that are implicit in aerosol

Vol. 118, 1980)

109

The Stratospheric Sulfate Aerosol Layer

Table 2 Sensitivity of predicted aerosol characteristics to: model processes and parameters

Sedimentation Water vapor growth (omission) Growth (omission) Coagulation (omission) Sulfur source strength Absorption of HSO3 by droplets OH abundance (factor of 3 change) Supply of condensation nuclei Condensation nuclei size distribution Tropospheric residence time Tropopause height Diffusion coefficient Nucleation rate (105 < ~-~ < 107 sec) Increased water vapor content of stratosphere Changes in stratospheric temperature

3 3 2 3 3 3 3 2 3 3 2 1 3 3 3

1 3 1 3 1 3 3 3 3 2 1 2 3 3 2

1 3 1 3 1 3 3 2 3 2 1 2 3 3 1

2 3 1 3 1 3 3 3 3 2 2 3 3 3 2

--1 -1 2 3 -------1

a) Ratio of the number of particles with radius > 0.15 tzm to the number with radius > 0.25 tzm. Key: 1 = very sensitive; sensitivity study calculations differ more than observed variability 2 = moderately sensitive; sensitivity study calculations differ as much as observed variability 3 = insensitive; sensitivity study calculations differ less than the observed variability model calculations are discussed at length by TURCO et al. (1979a) a n d TOON et al. (1979).

Growth and coagulation I n Figs. 10(a-d) the results of the reference model of TURCO et al. (1979a) a n d the calculations of four o b s e r v a b l e s - t o t a l particle n u m b e r mixing ratio, largeparticle n u m b e r mixing ratio, aerosol mass-mixing ratio, and particle size ratio (particles with radii > 0.15/zm to those with radii > 0 . 2 5 / z m ) - are c o m p a r e d with model calculations in which growth and coagulation have been omitted. Omission of growth from a model produces a small increase in the total n u m b e r of particles, partly because the particles are smaller and their rate of sedimentation is slower. The total particle mass a n d the n u m b e r of large particles are, of course, reduced dramatically. G r o w t h itself c a n n o t change the total n u m b e r of particles. It is only because of the effect of particle size o n the sedimentation a n d coagulation processes that a change occurs when growth is omitted. The small residual layer r e m a i n i n g in the n o - g r o w t h case illustrated in Figs. 10(a-d) is mainly a r e m n a n t of the initial conditions r e m a i n i n g after 5 years of simulated decay time. G r o w t h also affects the

110

R. C. Whitten, O. B. Toon, and R. P. Turco

(Pageoph,

//--NO GROWTH

40-

REFERENCE~ MODEL~ ' ~

35-

! /NO COAGULATION

30E tu.25

-

20

-

a 1,-I

,< 15-

NO COAGULATION MODIFIED AITKEN. NUCLEI

i

105

I

I

I

10 100 1000 TOTAL PARTICLEMIXING RATIO, PARTICLES/mgAIR

10,000

Figure 10a Figure 10 Reference model calculations are compared with model calculations in which growth and coagulation are omitted (a-d).

40 -

NO COAGULATION /MODIFIED AITKEN

35 3O E Jig tu'25 Q D 120

...J

'~15 t,

,o[ 5

OAGULATION

I

0

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NO GROWTH MODIFIED AITKEN NUCLEI I

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4 6 8 10 12 14 16 18 20 LARGE PARTICLE(r > 0.15/am) MIXING RATIO, PARTICLES/mgAIR Figure lOb

I

22

J

Vol. 118, 1980)

Ill

The Stratospheric Sulfate Aerosol Layer

35

E 30

20

REFERENCE

1 ~

NO COAGULATION -

MODIFIED AITTKION N

it J

NUCLEI

0

I

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1

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.2

.4

.6

.8

1.0

.I 1.2

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1.4

1.6

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1.8

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SO4 MASS MIXING RATIO, 10 -6 ,ug/mg AIR Figure 10c

NO COAGULATION MODIFIED AITKEN NUCLEI-7

40

NO GROWTH WITH MODIFIED AITKENNUCLEI

35

30

E a

25

I-

~ 20 MODEL 15 NO GROWTH COAGULATION

10 51 0

I

I

I

[

1

I

2 4 6 8 10 12 RATIO OF PARTICLES ~> 0.15 ,um RADIUS TO THOSE >~0.25 #m RADIUS Figure 10d

I 14

112

R.C. Whitten, O. B. Toon, and R. P. Turco

(Pageoph,

particle size ratio, which, in the absence of growth, is determined by the assumed tropospheric core size distribution, as modified by coagulation and sedimentation. Omission of particle coagulation leads to a sharp increase in the total particle mixing ratio, which, but for sedimentation, would be constant with altitude. Coagulation is clearly the dominant process controlling the total number of particles (particularly small ones). Moreover, coagulation affects the mass-mixing ratio, the largeparticle mixing ratio and the particle size ratio, suggesting that it is an important loss process for particles larger than 0.1/~m as well. Without coagulation the large increase in the total number of particles and the total particle surface area causes a diminishment of the sulfuric acid vapor available to grow individual particles. Because the average particle size is decreased, the sedimentation rate is reduced, enhancing particle mass at high altitudes. Also, the acid mass is redistributed from larger to smaller particles, increasing the particle size ratio. To define the role of coagulation more clearly, another calculation omitting coagulation was performed in which the number of condensation nuclei at the tropopause was reduced by a factor of 10 so that the number of particles at 20 km was comparable to the number in the reference model. Figures 10(b-d) show that in this case, coagulation has much less effect on the massmixing ratio, the large-particle mixing ratio and the particle size ratio, once the total number of particles has been reduced to the observed values.

40-35-30--

HUNTEN

ON- CHANG

E

\RE F E R E N C E

-

"'

a I~,,20 - -

"

MODEL

< 15lo-5 103

J

104

105

I

1 I 106

D I F F U S I O N C O E F F I C I E N T , cm2/sec

Figure 11 Diffusion coefficient profiles. Reference: TURCOand WmTTEN(1977); Hunten: JOHNSTONet (1976); Dickinson-Chang: NAS (1976).

aL

Vol. 118, 1980)

The Stratospheric Sulfate Aerosol Layer

113

Figure 12: Reference model calculations are compared with calculations in which tropopause height and diffusion profiles are altered (a-d).

~

4 0 - -

~

~ , [~] ~ [~]

9

t~ 't. I , ~ ,

35--

HUNTEN-E~OY ,~ WARMTEMP. o

~ I.~ =~ II~ u~

30--

17 17kmTROPOPAUSE 9 9 km TROPOPAUSE 9 ERENCEMODEL

E

25

DICKINSON-CHANGEDDY

--

I.-

F- 20 --I

15-10 --

L

5

I

i

I

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10,000

Figure 12a

,o F

9 DICKINSON-CHANGEDDY 0 HUNTEN-EDDY 9 WARM TEMP. [] 17 km TROPOPAUSE ll9km TROPOPAUSE -REFERENCE MODEL

35 30 ~ 25

2

20 15

11 -

0

1

I

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2 4 6 8 10 12 14 LARGE PARTICLE (r> 0.15/~m) MIXING RATIO, PARTICLES/mg AIR Figure 12b

R. C. Whitten, O. B. Toon, and R. P. Turco

114

(Pageoph,

9 DICKINSON-CHANG40

35 ~,,,,,..,,,=lg"~.~..~....~= ~'~l[~ ~ ~ ~

EDDY O HUNTEN-EDDY 9 WARM TEMP. [ ] 17 km TROPOPAUSE m9km TROPOPAUSE REFERENCE MODEL - -

~

30

E " 25 O I--20

15

10

I

I

I

I

1

.2 .4 .6 .8 1.0 SO4 MASS MIXING RATIO, 10-6 ,ug/mg AIR

I 1.2

Figure 12c

Diffusion coefficient and tropopause height Several eddy diffusion coefficients are shown in Fig. 11. Such diffusivities are usually presumed to represent global average rates of vertical transport. They are based on matches of predicted and measured vertical distributions of various tracers such as methane, nitrous oxide, the chlorofluoromethanes F-11 and F-12, and excess carbon-14 from atmospheric nuclear explosions. The diffusion coefficient used in the reference model being discussed here (TuRCO and WmTTEN, 1977; TURCO et al., 1979a; TOON et al., 1979) is a modification of that proposed by WovsY and MCELROY (1973). Two other frequently used diffusion profiles are also shown in Fig. 11; one was proposed by Hunten (JOHNSTON et al., 1976) and the other is attributed to Dickinson and Chang (NAS, 1976). As illustrated in Fig. 11, the Hunten profile has noticeably smaller diffusion coefficients at high altitudes than the reference model, and the Dickinson-Chang profile is much less abrupt at the tropopause than the reference model profile.

Vol. 1t8, 1980)

The Stratospheric Sulfate Aerosol Layer

115

40--

35

30

~ 25 CHANG-

a I-~20 -J

'DY '.

E E

15--

10--

5

0

=/ I

I

I

I

I

2

4

6

8

10

RATIO OF PARTICLES ~>0.15/~m RADIUS

TO THOSE 1>0.25 ~tm RADIUS Figure 12d Figure 12(a) shows that a calculation using the Hunten profile yields many fewer particles at high altitudes than does the reference model because, with the smaller diffusion coeff• sedimentation dominates vertical diffusion. The DickinsonChang profile yields a total particle mixing ratio similar to that of the reference model at high altitudes, but the mixing ratio falls off less strongly than that of the reference model near the tropopause. The mass and large particle mixing ratios are both decreased with either of the alternative diffusion coefficients, due in part to reduced diffusive supplies of sulfur-bearing gases. The smaller diffusion coefficients of the Hunten profile do not bring as much COS to high altitudes, so fewer larger particles are formed and those that are formed are more rapidly removed by sedimentation. Also, the sulfur supply is decreased because slower diffusion below the tropopause allows less SO2 to reach the stratosphere before it is washed out or chemically converted into H2SO~. The Dickinson-Chang diffusion profile yields a shorter residence time for gases and particles just above the tropopause and a longer residence time in the troposphere. Thus, the particles have less opportunity to grow just above the tropopause, and SO2 transported upward from the troposphere is almost completely

116

R.C. Whitten, O. B. Toon, and R. P. Turco

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removed before it reaches 14 km. The Dickinson-Chang profile does not substantially suppress the upward transport of COS, however, so the higher altitude portion of the layer closely resembles the reference model. The diffusion coefficients do not affect the particle size ratio very dramatically. The tropopause height varies with latitude, and displays seasonal and random fluctuations at any given location as welL'Figures 12(a-d) illustrate calculations in which the tropopause has been moved from the reference model altitude of 13 km to altitudes of 9 km and 17 km; the change is performed by moving the reference model diffusion profile (Fig. 11) up or down by 4 kin, while altering the nucleation model so that particles below the tropopause are unaffected. The total particle mixing ratio is strongly modified by changing the tropopause height. The calculation corresponding to the higher tropopause yields fewer total particles near the tropopause than the lower tropopause calculation, although the mixing ratios are similar. Nevertheless, coagulation rapidly depletes the particles above the tropopause in each case, despite the variation of residence time with height. As a result, there are fewer particles at each altitude in the lower "r case. The opposite is true for the large-particle and mass-mixing ratios. The lower tropopause case displays higher mixing ratios and a smaller particle size ratio because (1) the aerosol residence time at a fixed height is increased, thus allowing more growth to occur, and (2) the rate of upward diffusion of COS and SO2 is enhanced by increased concentrations at the tropopause level. 5. Model applications - assessments o f anthropogenic effects on the stratospheric aerosol layer

Man-made perturbations to the stratospheric aerosol layer were first considered during the Climatic Impact Assessment Program (CIAP, 1975), which dealt with possible stratospheric and climatic perturbations caused by supersonic transports (SST's). The CIAP assessment was based on a simple residence time model for an aerosol of fixed size dispersion and a rather crude radiative transfer model. POLLACK et al. (1976c), with the aid of more sophisticated radiative transfer techniques, made improved estimates of the temperature changes at the Earth's surface caused by SST aerosol changes. However, Pollack et al. used several approximations in their aerosol model, which lent considerable uncertainty to their results. More recently, the stratospheric models of ROSEN et al. (1978) and of TURCO et al. (1979a) have been applied in studies of global perturbations of the aerosol layer due to anthropogenic activities. Turco et al., for example, have made assessments of the effects of particulate and gaseous pollutants from SST's and Space Shuttle rocket engines and of the effect on the stratospheric sulfate layer of increasing tropospheric levels of carbonyl sulfide. Although detailed papers on these investigations will be published elsewhere, a brief summary of this work is given below. S S T and space shuttle effects

Supersonic transport engines emit gaseous sulfur oxides and carbonaceous particulates as exhaust constituents. Soot particles add directly to the natural aerosol

Vol. t 18, 1980)

The Stratospheric Sulfate Aerosol Layer

117

loading of the atmosphere, and sulfur gases add indirectly t h r o u g h condensation on existing particles. F o r the gaseous sulfur, we adopt an emission index o f 1 g o f SO2 per kilogram o f fuel (CIAP, 1975) and assume a fleet of 300 aircraft o f advanced design. Estimating that each SST would consume about 38,000 kg fuel/hr and operate 7 hours per day (e.g., see POPPOFF et al., 1978), the fleet would release about 3 x 107 kg o f SO2 per year worldwide, mostly at an altitude o f 20 km, a likely cruise altitude for future SST's (PoPPOFF et al., 1978). The soot emission of a J79-GE-10B jet engine, under conditions similar to those o f SST cruise, is about 0.3 g per kilogram of fuel (NAVAL ENVIRONMENTALPROTECTION SUPPORT SERVICE, 1977). A l t h o u g h the soot emission rate is much smaller than the SO2 emission rate, some o f the soot particles added to the stratosphere could 40

35

300 SST's WITH SO2 AND SOOT EMISSION (1.18 x 106/era 2 > 14 km)

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Figure 13 Supersonic transport effects on large aerosol particles. Calculated steady-state large particle (r > 0.15 tzm) mixing ratios in the stratosphere are shown for 20 km supersonic transport flight, both with and without soot emission. The global exhaust injection rates are: SOx (3 x 107 kg SO2/yr); soot (8 • 106 kgsoot/year). The ambient model large-particle mixing-ratio profile is included for comparison. For each profile, the total stratospheric column concentration of large particles is given in brackets.

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Vot. 118, 1980)

The Stratospheric Sulfate Aerosol Layer NOMINAL SHUTTLE (1.23 x 106/cm 2 ~> 14 km)

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Figure 15 Space shuttle effects on large particles. Calculated steady-state large particle (r > 0.15 ~.m) mixing ratios in the stratosphere are shown for nominal space shuttle operations (corresponding to 60 shuttle launches per year), and 10 times the level of activity, assuming the particulate deposition rate profile described in the text. conceivably grow into large aerosol droplets; soot must therefore be carefully considered. Space Shuttle launch vehicles emit large quantities of aluminum oxide (A1203) particles; the emission rate profile determined by HOFMANN et al. (1975b) has been adopted for the work reported here. The average A1203 particle size spectrum measured by wire and tape impactors and a mobility analyzer in several Titan wakes varied as ~ r - ~ ' s between radii of 0.035 and 5 ~m and decreased rapidly for particles with radii smaller than 0.035/xm. The effect of SST emissions on the large-particle mixing ratio is shown in Fig. 13. The main effect is due to sulfur gas rather than soot emission because the small soot particles coagulate rapidly with aerosol droplets of all sizes while the sulfur-bearing gas is absorbed by all of the existing particles as well. Hence, both the soot and SO2 cause existing particles to grow at a rate determined roughly by the relative mass injected. If the sulfur component of aviation fuel were eliminated, the net effect of soot emission alone on large particles would be quite small. In Fig. 14, the total number of soot particles of each size injected during 1 year of SST flight operations, and the ambient and perturbed particle size distributions, are compared. The soot particles are all injected near an altitude of 20 km where fairly large numbers of acid

120

R . C . Whitten, O. B. Toon, and R. P. Turco

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Vol. 118, 1980)

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121

The effect of planned space shuttle launch traffic on the large aerosol particle concentration in the stratosphere, shown in Fig. 15, would be comparable to that of 300 SST's. It was originally proposed by HOFMANN et al. (1975b) that the small particles emitted by space shuttle engines might act as seeds from which new large particles could be grown in a supersaturated environment. However, Fig. 15 demonstrates the effect to be unimportant because the A12Oa seed particles rapidly coagulate with pre-existing aerosols. Our calculations indicate that the total number of large particles might be increased by only about 20 percent. It is interesting to compare the effects on the aerosol particle Size spectra of SST's and space shuttles (Figs. 14 and 16). The shuttle injects more particles in the range 0.01 to 0.1 ~m, which increases the number of acid droplets near 0.1 t~m by redistributing the available acid mass from larger particles (r > 0.3/~m) to smaller particles (r < 0.3 ~m). This is indicated in Fig. 16 by the crossover of the ambient and perturbed size distributions near 0.3/zm. However, this shift in particle sizes still results in a small net increase in the number of large particles. SST's inject many more very small particles (r < 0.01 t~m) than do space shuttles, but the rate of most of these is coagulation with larger aerosols. To calculate the climatic effects of aerosol layer perturbations, the altitudedependent size spectra predicted by the aerosol model were employed in the 'doubling' routine described by POLLACK et al. (1976c). The doubling calculations are highly accurate multiple scattering computations that explicitly account for solar energy absorption by CO2, Oa, 02, and H20 and absorption and scattering by aerosols in the stratosphere and troposphere. The optical constants of a 75-percent sulfuric acid aqueous solution were used for the droplets and the optical constants of (NH4)2SO4 were used for condensation nuclei. Once the solar energy deposition rate profile is determined, an infrared calculation is performed to achieve radiative-convective equilibrium. This routine uses a numerical approach similar in most respects to that described by POLLACK et al. (1976c) to calculate the infrared radiation emitted and absorbed by H20, CO2, Oa, and aerosols. It differs from that of Pollack et al. in that the routine is iterated until a radiative-convective temperature profile is obtained. Such calculations for a fleet of 300 SST's flying 7 hours per day at an altitude of 20 km suggest a possible temperature decrease of about 3 x 10-3~ The predicted temperature decrease for a space shuttle launch rate of 60 per year is only about 0.1 of that value, or 3 x 10-4~ These estimates, which are to be compared with a rough criterion of temperature change for climate effects of 0.1~ show that likely climatic impact of reasonable-sized fleets of SST's and of planned space shuttle launches are completely negligible. Enhancement o f carbonyl sulfide

In some recent work, TURr et al. (1979b) have estimated that the tropospheric lifetime of COS is ~ 1 yr, and that the present day production rate of COS is about 6 • 106 tonnes yr- t of which approximately half may originate from coal combustion.

122 40

R. C. Whitten, O. B. Toon, and R. P. Turco

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Figure 17 The stratospheric sulfate (SO~.-) mass mixing ratio predicted for ambient and perturbed conditions. A ten-fold enhancement in COS, SO2, and CS2 has been simulated by increasing its surface concentration ten-fold. For several cases treated, the total large particle concentration in the stratosphere (N) and the optical depth of the sulfate layer at 550 nm (T) are given in brackets.

Some important industrial sources of COS whose output may increase substantially in the future are coal gasification and combustion involving the use of more abundant high sulfur coal and petroleum. Figure 17 shows calculations by TURCO et aL (1979b) of the effects of changes in COS, CS2, and SO2 levels in the stratospheric sulfate mixing ratio. The model results indicate a very substantial increase in aerosol mass when COS is increased by a factor of 10. Using the radiative transfer model mentioned above, TURCO et aL (1979b) computed a possible decrease in global average surface temperature of ~0.1~ a change that is on the threshold of climatic significance. It is important to note, however, that COS, like CO2, can also create a 'greenhouse' effect in which the far infrared radiation from Earth is trapped in the lower atmosphere. Such an effect would modify these conclusions by canceling, at least partially, the effect of the increased aerosol loading. In addition, we have not taken into account the effects of emissions of other combustion products such as CO, CO2, and SO2. For example, CO emissions may reduce O H concentrations, leading to a larger build-up of COS. Attempts to suppress SO2 emissions might inadvertently create

4

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larger COS emissions. On the other hand, CO2 build-up would enhance surface temperatures through the greenhouse mechanism.

6. Conclusion

The stratospheric sulfate aerosol layer, discovered nearly two decades ago by JUNGE et al. (1961), has been the subject of numerous and concerted observational and theoretical studies of its properties and morphology since that time. Furthermore, knowledge of the physics and chemistry of aerosols has evolved sufficiently that with the advent of large computers it is now feasible to construct detailed models of the aerosol layer. As an example, the one-dimensional model developed by the authors and their coworkers has been shown to be in good agreement with m a n y of the observed aerosol characteristics, including mass-mixing ratios and size distributions. Assessments have been made of possible climate effects of space shuttle and supersonic transport operations and the conclusion is that for reasonable levels of operation, the estimated changes in surface temperatures are likely to be negligible. Further applications of such models to possible climatic effects of large volcanic eruptions and to the interpretation of satellite (i.e., SAGE) observations of the aerosol layer await the development of physically realistic two-dimensional aerosol models.

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SCOTT, W. D., LAMB, D. and DUFFY, D. (1969), The stratospheric aerosol layer and anhydrous reactions between ammonia and sulfur dioxide, J. Atmos. Sci. 26, 727-733. STOIBER, R. E., LEGGETT, D. C., JENKINS, R. F., MURRMANNand RosE, E. I. (1971), Organic compounds in volcanic gas from Santiaguito volcano, Guatemala, Bull. Geolog. Soc. Amer. 82, 2299-2302. TELEGADAS,K. and LIST, R. J. (1969), Are particulate radioactive tracers indicative of stratospheric motions? J. Geophys. Res. 74, 1339-1350. TOON, O. B. and POLLACK,J. B. (1976), A global average model of atmospheric aerosolsfor radiative transfer calculations, J. Appl. Meteorol. 15, 225-246. TOON, O. B., TURCO,R. P., HAMILL,P., KIANG,C. S. and WHITTEN,R. C. (1979), A one-dimensional model describing aerosol formation and evolution in the stratosphere. IL Sensitivity studies and comparison with observations, J. Atmos. Sci. 36, 718-736. TORRES, A. L., MAROULrS, P. J., GOLDBEgG, A. B. and BANDY, A. R. (1978), Measurements of tropospheric OCS on the 1978 GAMETAG flights, Trans. Amer. Geophys. Union (EOS) 59, 1082. TURCO, R. P., HAMILL, P., TOON, O. B. and WmrrEN, R. C. (1976), A model of the stratospheric sulfate aerosol Atmospheric Aerosols: Their Optical Properties and Effects, A topical meeting on atmospheric aerosols, Williamsburg, Virginia, Dec. 1976, Paper WA4, NASA CP-2004. TURCO, R. P. and WI~ITTEN,R. C., The NASA-Ames Research Center one- and two-dimensional stratospheric models. L The one-dimensional model (NASA Tech. Paper 1002, NTIS, Springfield, Va., 1977), 30 pp. TtrRCO, R. P., HAMILL,P., TOON, O. B., WHITTEN,R. C. and KIANG,C. S. (1979a), A one-dimensional model describing aerosol formation and evolution in the stratosphere. L Physical processes and mathematical analogues, J. Atmos. Sci. 36, 699-717; also see NASA Technical Paper 1362 (NTIS, Springfield, Va., 1979) by the same authors. TuRco, R. P., WnITT~N,R. C., Toorq, O. B., POLLACK,J. B. and HAMILL,P. (1979b), Carbonyl sulfide, stratospheric aerosols, and terrestrial climate, Nature (submitted). WARNEClr P., MARMO,F. F. and SULLIVAN,J. O. (1964), Ultraviolet absorption of SOu: Dissociation energies of $02 and SO, J. Chem. Phys. 40, 1132-1137. W~STENBERG, A. A. and DE HAAS, N. (1969), Atom-molecule kinetics using ESR detection. V. Results for 0 + OCS, O + CS2, O + NO2, and H + C2H4, J. Chem. Phys. 50, 707-719. WESTENBERG, A. A., and DE HAAS, N. (1975), Rate of the reaction 0 + SOz + M ~ SOa + M, J. Chem. Phys. 63, 5411-5415. WHITTEN, R. C. and TURCO, R. P., Gas phase chemistry in the Ames stratospheric aerosol model Atmospheric Aerosols: Their Optical Properties and Effects. A topical meeting on atmospheric aerosols, Williamsburg, Virginia, Dec. 1976, Paper WA3, NASA CP-2004. WOFSY, S. C. and MCELROY, M. B. (1973), On vertical mixing in the upper stratosphere and lower mesosphere, J. Geophys. Res. 78, 2619-2624. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birldaiiuser Verlag, Basel

The Importance of Energetic Particle Precipitation on the Chemical Composition of the Middle Atmosphere By RICHARD MANSERGH THORNE x)

Abstract - An assessment is made of the relative contribution of certain classes of energetic particle precipitation to the chemical composition of the middle atmosphere with emphasis placed on the production of odd nitrogen and odd hydrogen species and their subsequent role in the catalytic removal of ozone. Galactic cosmic radiation is an important source of odd nitrogen in the lower stratosphere but since the peak energy deposition occurs below the region where catalytic removal of 03 is most effective, it is questionable whether this mechanism is important in the overall terrestrial ozone budget. The precipitation of energetic solar protons can periodically produce dramatic enhancement in upper stratospheric NO. The long residence time of NO in this region of the atmosphere, where catalytic interaction with 03 is also most effective, mandates that this mechanism be included in future modelling of the global distribution of 03. Throughout the mesosphere the precipitation of energetic electrons from the outer radiation belt (60~ < A < 70~ can sporadically act as a major local source of odd hydrogen and odd nitrogen leading to observable 03 depletion. Future satellite studies should be directed at simultaneously measuring the precipitation flux and the concomitant atmosphere modification, and these results should be employed to develop more sophisticated models of this important coupling.

Key words: Galactic cosmic rays; Solar proton events; Particle precipitation; Chemistry.

1. I n t r o d u c t i o n

As energetic charged particles enter the Earth's atmosphere they are guided in helical orbits by the geomagnetic field until a collision occurs with an ambient atmospheric constituent. This review will consider the importance of three distinct classes o f precipitation which directly deposit energy into the middle atmosphere; namely galactic cosmic radiation, energetic solar protons and relativistic electron precipitation f r o m the Earth's radiation belts. Figure 1 illustrates the general geomagnetic field configuration and classifies three distinct regions for particle precipitation. Over the polar caps (invariant latitudes A ~> 75 ~ the geomagnetic field lines are generally t h o u g h t to be open and connected to the interplanetary medium. This permits direct access for energetic particles o f solar or galactic origin. The auroral zone (70 ~ < A < 75 ~ is a region of continuous and intense precipitation o f low energy (1-10 keV) particles emanating f r o m the Earth's plasmasheet (e.g. EATHER e t al., 1976; LuI et al., 1977; ASHOUR-ABDALLA and THORNZ, 1978). A l t h o u g h the precipitation fluxes in this 1) Department of Atmospheric Sciences, University of California, Los Angeles, USA.

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Figure 1 A schematic view of the Earth's magnetosphere illustrating the dominant zones of particle precipitation. region are considerably enhanced during geomagnetically disturbed periods (termed magnetospheric substorms) the principal energy deposition is confined to altitudes above 100 km and is therefore of little interest to the middle atmosphere. In the subauroral region (A < 70~ however, energetic particles can be stored and accelerated to very high energies (10 keV to several MeV) before eventual precipitation into the middle atmosphere (in the altitude range between 50--100 km). The typical atmospheric penetration altitude (before substantial energy loss occurs) for vertically incident electrons and protons is shown in Fig. 2 as a function of particle energy. Also indicated is the penetration depth for Bremsstrahlung X-rays which are produced during energetic electron precipitation. Most energy loss by the precipitating particles occurs during slowing down collisions with either free or bound electrons. The high energy primary particles themselves are generally inefficient in dissociating or ionizing the ambient atmospheric constituents. But they produce substantial fluxes of secondary electrons (typically between 10-100 eV) which subsequently transfer a major fraction of the incident energy to the atmosphere. The shape of the secondary electron spectrum and the cross sections for their interaction with the atmosphere are therefore of considerable importance (PORTER et al., 1976). Although incoming ions also experience scattering by the Coulomb field of the atmospheric nuclei (and at high energies can undergo nuclear reactions with the scattering nucleus) their overall angular deflection is generally negligible. This greatly simplifies the computation of energy deposition

130

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Energy (kev) Figure 2 The nominal penetration depth of electrons and protons vertically incident at the top of the atmosphere as a function of particle energy. during ion precipitation. On the other hand, in the case of precipitating electrons, angular scattering is of major importance and the energy degradation must be treated by solving an appropriate diffusion equation which takes both energy loss and angular scattering into account (WENTWORTX~et al., 1959; WALT and McDONALD, 1964; WALT et al., 1968). In addition to providing an important and often dominant ionization source for the middle atmosphere, precipitating particles enhance the production of odd nitrogen and odd hydrogen species. Since these are now accepted as a major catalytic sink for middle atmospheric odd oxygen (O or O~) it is important to quantitatively compare the role of particle precipitation with other sources of these catalytic agents. In Section 2 we review the important chemical process, paying particular attention to the relative production rate of odd nitrogen and odd hydrogen species during ionizing particle precipitation. The next three sections separately review recent studies of the role played by galactic cosmic radiation, solar protons and magnetospheric electrons. An overall comparison of these sources is finally made in Section 6 together with an assessment of the status of our understanding and needs for future studies. 2. Chemical considerations during particle precipitation 2.1. Ionization Although the energy deposition by precipitating particles is usually negligible compared to other sources of middle atmospheric (below 100 km) heating it can provide

Vol. 118, 1980)

Energetic Particle Precipitation

131

the dominant source of ionization and dissociation particularly below the altitude (< 80 kin) where solar UV and X-rays are strongly absorbed. Most of the primary ions produced by particle bombardment (N], 0 3 , N § O +) are rapidly converted to O~by the change exchange reactions N+ + O 2 ~ O +

+N2,

0 § + 0~---+0+ + 0 , N + +O2-+O + +N.

(la) (lb) Oc)

A much smaller fraction (~69/oo according to GUNTON et aL, I977) are converted to NO + by the ion-atom interchange reactions O§ +N2~NO

+ +N,

(2a)

N + +O2~NO

+ +O.

(2b)

Ion mass spectrometer observations (e.g. NARCISIand BAILEY, 1965; JOHANNESEN and KRANKOWOSKI,1972) have shown that while O +2 and NO + remain the dominant ions above 85 km the positive ion composition at lower altitudes is complicated by a sequence of clustering reactions which lead to the dominance of multiply hydrated ions of the type H +(H20),, NO +(H20), and H30 +(H20)~. Electron attachment also becomes of major importance below 80 km yielding O~- as the primary negative ion. This subsequently interacts with minor constituents of the middle atmosphere to produce heavier ions such as COy, NOs-, HCO~- and their hydrated clusters. The reader is referred to SECHRIST,(1972), ROWE et al. (1974), THOMAS(1964), FERGUSON(1974), ARNOLD and KRANKOWSKI(1977) and ROBLEand REES (1977) for a comprehensive review of the complex D-region ion chemistry. It is sufficient to note here that the ion chemistry is strongly dependent on the atmospheric temperature and the composition of minor neutral species such as O, O2('A), NO, HO, HO2 and H20. Furthermore, while NO + (produced by solar Ly ~ radiation) is the dominant primary ion in the mesosphere under quiet conditions, O + accounts for 94~ (REAGANet al., 1978) of the ultimate primary ions produced by particle precipitation. This enrichment of 0 + during precipitation events should in turn modify the ultimate composition of cluster ions throughout the lower D-region.

2.2. The importance of catalytic processes involving odd nitrogen and odd hydrogen It is now well established that the direct removal process for odd oxygen species O + 03 -+ 202

(3)

first proposed by CHAPMAN(1930) can account for only about 20~ (e.g. JOHNSTON, 1974, 1975) of the odd oxygen produced by photodissociation of molecular oxygen. The major loss of odd oxygen from the middle atmosphere is thought to occur as a result of catalytic cycles involving trace constituents (e.g. JOHNSTON and PODOLSKE,

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Figure 3 Reactions important in odd oxygen loss and the odd oxygen production rate 2/(02) taken from McELRoY et aL (1974). The sum of the recombination reaction rates equals the production rate at every altitude consistent with the assumption of photochemical equilibrium. Odd nitrogen provides the dominant 03 loss below 45 km while odd hydrogen predominates above 55 km. 1978 ; THRUSH, 1979). Although chlorine compounds provide an important contribution to the overall odd oxygen removal process (e.g. Sa'OLARSKIand CICZRONZ, 1974; WovsY and MCELROY, 1974; MOL[NA and ROLAND, 1974; CRUTZEN and HOWARD, 1978) of particular interest here are the cycles involving odd nitrogen and odd hydrogen species since these can be significantly modified during intense particle precipitation. Figure 3, taken from MCELROY et al. (1974), illustrates the altitude range over which these species are of major importance. The catalytic cycle involving odd nitrogen is most important within the stratosphere (below ~45 kin), whereas the reactions involving odd hydrogen species predominate throughout the mesosphere (above ~ 55 km). Although the odd nitrogen and hydrogen species are chemically coupled we shall discuss their roles separately in the following two subsections. 2.3. Odd nitrogen chemistry

The catalytic cycle involving odd nitrogen species first discussed by CRUTZE~ (1970, 1971) and JOHNSTON(1971) NO + 0 3 - + NO2 + O~,

(4a)

NO2 + O --~NO + 02,

(4b)

Vol. I 18, 1980)

Energetic Particle Precipitation

133

results in a net odd oxygen removal equivalent to reaction (3) without any change in the overall concentration of either NO or NO2. Thus even though the odd nitrogen species usually have a very low concentration (in comparison to odd oxygen) they can repeatedly act as a sink of odd oxygen. This catalytic cycle, however, is only effective between 25 and 45 km. In the lower stratosphere the odd nitrogen cycle is shortcircuited by the rapid conversion of NO2 into HNOa. OH + N O 2 + M ~ H N O ~ + M while at higher altitudes (above ~ 45 km) NO2 is dissociated NO2 + hv(h < 3 9 5 0 A ) ~ N O + O at a rate faster than its interaction with atomic oxygen (reaction 4b). Several sources of middle atmospheric odd nitrogen have been proposed. The most important source of stratospheric nitric oxide (MCELROYand MCCONNEL, 1971) is due to the reaction between O(1D) atoms produced during the photolysis of 03 (NrcoLET, 1970) and nitrous oxide which has been transported upward from the Earth's surface (BATES and HAYS, 1967) O(1D) + N20 --~ 2NO.

(5a)

Nitric oxide can also be produced by direct photodissociation N20 + hv(h < 2500 A)-+ NO + N

(5b)

but this is thought to be not nearly as important as (5a) because the competing reaction N20 + hv(A < 3 3 7 0 A ) ~ N 2 + O accounts for more than 99~ of N20 photodissociation (PRESTON and BARR, 1971). Using realistic models for the upward diffusion of terrestrial N20, the peak NO production from (5a) has been estimated to occur in the lower stratosphere typically between 24-32 km (MCELROYand McCONNELL, 1971; NICOLET and PEETERMANS, 1972). Odd nitrogen species are also produced as a result of ionic reactions in the D and E regions of the ionosphere (NICOLET, 1965; NORTON and BARTH, 1970; MEIRA, 1971; NARCISI et al., 1972; ORANet al., 1975). The important ionic reactions lead to excited N(2D) atoms which subsequently react with 02 to yield NO N(2D) + 02-+ NO + O.

(6)

This is the major source of NO in the atmosphere above 100 kin. On the other hand, nitrogen atoms which are produced in the ground N(4S) state act as an important sink for odd nitrogen species in the upper mesosphere (>70 kin) and thermosphere (MCELROY et al., 1974; WoFsY, 1974) via the reactions N(4S) + NO ~ N z + O 7 N2 + 02 N(4S) + NO2--+ N20 + O "~N2 + O + O.

134

Richard Mansergh Thorne

(Pageoph,

For a quantitative assessment of this thermospheric source it is therefore critically important to know the relative production rate of these two atomic nitrogen species (e.g. ORAN et al., 1975). Theoretical modeling by STROBELet al. (1970) and STROBEL(1971a, b) suggested the need for a substantial downward flux of NO (1 - 5 x 10s cm -2 sec -1) to account for the observed mesospheric concentrations (BARTH, 1966; MEIRA, 1971). However, the rapid dissociation rate of NO throughout the mesosphere (STROBEL, 1971b, 1972; BRASSEURand NICOLET, 1973) compared to the rate of downward transport indicates that there should be little residual NO flux reaching the stratopause. As a consequence the strong thermospheric source of NO should not affect the chemistry of stratospheric ozone. In general only NO produced by in situ sources (below ~ 60 km) can directly influence the removal of ozone from the lower portion of the middle atmosphere. One possible exception to this is the region of polar night mesosphere where the dissociation rate is low and NO concentrations can therefore build up over a long period of time to levels sufficient to permit significant downward transport into the stratosphere. An important in situ source of odd nitrogen species in the middle atmosphere originates from the ionization and dissociation of molecular nitrogen during energetic particle precipitation. The low energy (~ 10-100 eV) secondary electrons produced by incoming primary particles interact efficiently with N~ to produce both ions and free nitrogen atoms; (7a) N 2+ + 2eS N2 + e- --~ 2N + e(7b) "a N + +N+2e(7c) On the basis of the branching ratios given by DALGARNO(1967), WARNECK(1972) initially suggested that cosmic ray impact should produce odd nitrogen species directly in the stratosphere at a rate 1/3 of that for ion-pair formation. However, a more detailed comparison between the cross-sections for total dissociation (WINTERS, 1966) and dissociative ionization (RAPPet al., 1965), led BRASSEURand NICOLET(1973) and NICOLET (1975) to argue that the total primary production of free nitrogen atoms should be more nearly one nitrogen atom for each ion pair. The charge exchange and ion-atom interchange reactions (lc) and (2a) also provide an additional, though relatively small (HEAPS, 1978), contribution to the overall production of free nitrogen. Detailed computations by PORTERet al. (1976) suggest a net value of 1.27 N atoms per ion pair regardless of whether the energetic primary particles are protons or electrons. These authors also show that the average energy required to create an ion pair in air is essentially independent of the primary particle energy; at least for incident energies above a few hundred eV. The numbers quoted are 34.5 and 35.8 eVfion pair for electron and proton bombardment respectively. In the subsequent reactions leading to nitric oxide production N + 02--~ NO + O N + 03--~ NO + 02

(8a) (8b)

Vol. 118, 1980)

Energetic Particle Precipitation

13 5

the rate constant for (8a) depends critically on whether the free nitrogen atoms are produced in the ground state N(~S) or at the excited N(2D) level. Uncertainties in the actual electronic state of middle atmospheric nitrogen atoms has led to a range of computed values, typically between 1.2 to 1.5, for the production of NO molecules[ion pair (e.g. CRUTZEN et al., 1975; FREDERICK, 1976; HEAPS, 1978). The higher values correspond to when the nitrogen atoms exist primarily in the N(2D) state. One further reaction which could augment the net yield of middle atmospheric odd nitrogen species (e.g. NICOLET, 1975; HEAPS, 1978) is O2 + N2 --->NO + + NO.

(9)

The reaction rate, however, is below detectable levels and has been set at less than 10-15 cm 3 see -1 (FERGUSON,1974). Assuming a rate constant of t0 -16, HEAPS (1978) concluded that the reaction (9) is negligible at stratospheric altitudes but that it could become important in the upper mesosphere and thermosphere under quiet or moderately disturbed conditions. Partially supporting this conjecture, FABIAN et al. (1979) have cited rocket measurements of enhanced NO concentrations during auroral precipitation which require an NO production rate between 2 to 2.5 times the ionization rate. However, for our discussions of the middle atmosphere we shall adopt the more

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136

Richard Mansergh Thorne

(Pageoph,

conservative altitude profile of the ratio between odd nitrogen and ion-pair production shown in Fig. 4 (HEAPS, 1978).

2.4. Odd hydrogen chemistry The importance of odd hydrogen species (H, OH, HO2) in the removal of middle atmospheric ozone was first discussed by BATESand NICOLET (1950). The hydrogen chemistry is particularly complex and a number of catalytic cycles have been identified leading to net odd oxygen removal (e.g. JOrrNSTONand PODOLSKE,1978). The following reactions destroy odd oxygen with no net removal of H O , compounds as a group: HO + Oa-+ H02 + Oz,

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For example the pair of reactions (10a) and (10b) convert 208 into 302 with no net change in the concentration of either odd hydrogen species while (10c) and (10d) or (10a) and (10e) are simply equivalent to the normal Chapman removal process (3). Because of the catalytic nature of these reactions the only way to terminate this removal process for odd oxygen is by the mutual annihilation of the hydroxyl radicals to reform water vapor or H202 via reactions of the type OH + OH--+ H20 + O, OH + H02--+ H20 + 02, HO2 + HO2-+ H202 + 02, H + H02--+ H20 + O. Odd hydrogen species are produced in the middle atmosphere by photodissociation of water vapor H20 + hv--+ H + OH (11) and by reactions involving O(1D) atoms O(13) + H20 --+ 2OH,

(12a)

O(1D) + H2--+ H + OH,

(12b)

o(13) + CH~-+ OH + CH3.

(120

Under quiet conditions photodissociation is the most important source in the upper mesosphere (>60 km) while (12a) predominates throughout the stratosphere. Odd hydrogen species are also produced during the complex ionic reactions leading to cluster ions formation in the D region of the ionosphere (e.g. ROWE et aL, 1974). SWIDER and KENESHEA(1973) first pointed out that this source can become significant

Vol. 118, 1980)

Energetic Particle Precipitation

137

in the mesosphere during intense precipitation events. Following the dominant production of O~ ions during particle bombardment, one hydroxyl radical is released during the initial reactions leading to the formation of H30 + ; O + +O2 +M~O

g + M,

O~ + H20--~ O~-(H20) + 02, O2+(H20) + H20--~ H30 + + OH + 02. A further odd hydrogen species is released during the subsequent recombination of the cluster ions in reactions such as H30+(H20)~ + e- --~ H + (n + 1)H20. The net result is that two odd hydrogen species can be produced for each ion pair. This, however, represents a strict upper limit since some of the initial and intermediate ions will be lost by recombination or charge exchange before the odd hydrogen production can occur. Figure 4 shows the results of recent chemical modeling by HEAPS(1978) for tWO rates of ion pair production. A lower ratio between odd-hydrogen and ion-pair production occurs during more disturbed (Q = 105) conditions due mainly to increased charge exchange with enhanced NO concentrations. The sharp drop off above 80 km reflects the upper level for cluster ion formation. Finally, one should note that rocket measurements by ARNOLD et al. (1977) indicate a transition from hydronium ion clusters to carbonated species in the stratosphere and this could reduce the production of odd hydrogen below 40 kin. Because of the increasing importance of odd nitrogen species at lower altitudes it is therefore unlikely that odd hydrogen will play a significant role in the removal of stratospheric odd oxygen during precipitation events, although it may modify the odd nitrogen and chlorine catalytic cycles (THRUSH, 1979).

3. Galactic cosmic rays

Energetic ions of extra solar system origin arrive at the Earth essentially isotropically. The primary galactic cosmic radiation (GCR) is composed mainly of protons (~ 83~) and alpha particles (~ 12~). As the ions approach the Earth, their trajectories are deflected by the geomagnetic field. The dipole field geometry permits easier access to the polar regions where the geomagnetic field lines are open (Fig. 1). This produces a latitudinal gradient in the precipitating cosmic ray flux particularly for the less energetic components which are more strongly influenced by the Earth's field. The early balloon observations (e.g. BOWENet al., 1938) demonstrated that galactic cosmic radiation is a major ionization source at low altitudes with a peak production rate near the tropopause. While the rate of ionization is relatively constant it does exhibit a slow variation which is out of phase with the solar active cycle (FoRBUSH, 1958; NEHER and ANDERSON, 1962). This has been explained in terms of larger

138

Richard Mansergh Thorne

(Pageoph,

interplanetary densities which reduce the G C R flux near the Earth during peak solar activity. The first suggestion that galactic cosmic rays might act as a significant source of stratospheric nitric oxide was made by WARNECK (1972). More detailed studies by BRASSEUR and NICOLET (1973) and NICOLET (1975) examined the worldwide contribution and concluded that it was relatively minor in comparison to that from the oxidation of terrestrial N20. Figure 5 shows an update of this comparison obtained by using the more recent estimates (Section 2.3) for the rate of N O production, qNo ~ 1.3 q~on. The two curves for the production of N O from N 2 0 are taken from Table 1 of BRASSEUR and NICOLET (1973) and indicate the large range of uncertainty in this source due to its sensitivity on the rate of vertical eddy diffusion and the production of O(1D) atoms. It is nevertheless clear that while galactic cosmic radiation is important in the lower stratosphere, it becomes a relatively minor source of N O in the main catalytic reaction region above 25 km. As such it can have little effect on the global ozone abundance. Ruderman and Chamberlain (1975) have nevertheless argued that the significant variation in the G C R flux over the solar cycle should provide a time varying source for 50

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Vol. 118, 1980)

Energetic Particle Precipitation

139

stratospheric NO and they have attempted to link this with the small (few percent) long term cyclic variations observed in total ozone content (PAETZOLDet al., 1972; ANGELLand KORSHOVER,1973). However, the more recent estimates of higher mean NO density in the stratosphere (JOHNSTON, 1975) and the acknowledged importance of solar proton events (Section 4), which can be expected to produce more NO during solar maximum rather than solar minimum conditions, raises serious doubts over whether GCR produced NO can indeed explain the solar cycle variation of 03. RUDERMANet al. (1976) have subsequently proposed a different destruction scheme for the cycIic variation of 03 involving negative ion chemistry; but this remains to be tested experimentally.

4. Solar proton events

Intense fluxes of energetic protons (10-300 MeV) are released following flare activity on the Sun (MEYERet al., 1956; Li)sT and SrMPSON, 1957). These particles have more or less direct access to the polar cap regions of the Earth's atmosphere and the more energetic components can also penetrate down to invariant latitudes of about 60~ These solar proton events (SPE), which typically last for several days, were initially called polar cap absorption (PCA) events. This term stemmed from the pronounced disturbance to radio communication due to enhanced ionization throughout the polar D-region (BELROSEet al., 1956; ELLISONand REID, 1956; BAILEY,1959; REID, 196t ; WEBBER,1962). The energy spectrum of the primary precipitating protons has subsequently been measured in considerable detail by rocket or satellite instruments (e.g. SVESTKA, 1970, 1972; KING, 1974; REAGANet al., 1978). In addition to providing the dominant source of ionization in the mesosphere and upper stratosphere (ZMtJDAand POTEMRA, 1972) it has recently been recognized that moderate to large solar proton events can also modify the concentrations of minor neutral constituents leading to a decrease in middle atmospheric ozone. The first observational evidence for such an effect was published by WEEKSet al. (1972) who reported factors of 2 to 4 decrease in mesospheric (,~ 50-70 kin) ozone concentration during the 2 November 1969 solar proton event. These measurements were later interpreted by SWIDERand KENESrtEA(1973) in terms of an enhanced production of OH and HO2 as a biproduct of cluster ion chemistry initiated by increased D-region ionization during the particle precipitation (Section 2.4). A later study by CRtJrZENet al. (1975) examined the production of stratospheric NO during three intense solar proton events (November 1960, September 1966 and August 1972). They concluded that the total NO production (below 60 km) during each event was comparable to or larger than the annual yield by GCR for geomagnetic latitudes above 60~. Also, in contrast to the more energetic galactic cosmic rays, the solar protons yield peak NO production in the altitude range above 25 km, namely in the region where catalytic removal of Oa is most effective. For the August 1972 event, the

140

Richard Mansergh Thorne

(Pageoph,

proton precipitation source was even comparable to the most optimistic estimates for the annual yield of stratospheric N O production from the oxidation of N20. CRUTZEN et al. (1975) therefore suggested that it is important to consider the effects of SPE on the spatial and temporal distribution of stratospheric ozone. This conclusion was quantitatively confirmed by FREDERICK (1976) who modeled the changes in middle atmospheric neutral chemistry during two solar proton events. Because of the long residence time for NO produced directly in the stratosphere (i.e. several months at 50 km increasing to over a year below 40 km) by the more energetic solar protons, Frederick suggested that horizontal winds might transport the odd nitrogen species to middle latitudes from the primary source in the polar regions; in such a case solar proton events could influence O3 on a global scale. In the mesosphere, on the other hand, predissociation should cause the excess odd nitrogen to return to the unperturbed values within a few days. Mesospheric Oa concentrations should, in any event, be primarily controlled by the catalytic reactions with odd hydrogen species, and because the removal time for odd hydrogen is typically on the order of an hour (HEAPS, 1978) the concomitant ozone depletion should rapidly recover, following the cessation of intense precipitation. The August 1972 solar proton events were the most intense ever recorded, comprising about 85~o of the energetic proton flux over the entire period of solar cycle 20 (KING, 1974). As an illustration of the intensity of the precipitation Fig. 6, taken from REAGAN et aL (1978), shows the ion production rate at the peak of the event in comparison to other known sources. The extensive observational data taken during the period of the August 1972 events provides a unique opportunity for a detailed study of a 'controlled' modification of the stratospheric neutral constituents. In fact, the

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first observation of a detectable SPE depletion in stratospheric ozone was reported by HEATH et al. (1977), using data from the backscattered ultraviolet experiment on the Nimbus 4 satellite during the August event. Their results are reproduced here in Fig. 7. An abrupt decrease in the zonally averaged concentration of 03 (above the 4-mbar pressure surface) was observed at high latitudes following the solar proton event on 4 August. For latitudes A > 75~ this decrease persisted throughout the month of

142

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August while in the intermediate zone between 55-65 ~ the response was apparently complicated by transport processes. HEATH et al. (1977) were able to adequately simulate the observed polar reductions using a two-dimensional, time-dependent model which included the major photochemical reactions and zonally averaged transport processes. In a more recent study FABIAN et aL (1979) have reported that a better fit to the observations can be obtained by assuming an N O production rate approximately 2.5 times the ionization rate. However, in view of the discussion in Section 2.3, it is difficult to imagine how such a high ratio can occur at stratospheric altitudes. The initial results from a more detailed investigation of the August 1972 events have recently been reported by REAGAN et aL (1978). Using preliminary data from the BUV instrument on the Nimbus 4 satellite they report ozone reductions immediately following the main event on 4 August ranging from up to 50~ near 50 km altitude to 970 near 35 km. This corresponds to a net columnar decrease of 27o in total ozone below 55 km altitude. They further conclude that the ozone depletion over the polar regions should cause a net reduction in the heating rate of 2.5~ at 60 km and 1.3~ at 45 km (the altitude of maximum ozone heating). This tends to support the earlier suggestion by ZEREFOSand CRUTZEN (1975) that the solar proton induced O~ reduction should lead to lower temperatures in the upper stratosphere but allow solar UV to penetrate deeper and thus heat the lower stratosphere. Unfortunately, a direct experimental verification is not possible since the selected chopper radiometer flown

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Vol. 118, 1980)

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on Nimbus 4 had insufficient sensitivity and height resolution to detect the anticipated temperature changes during the August 1972 event. Preliminary results from the simulation of chemical changes following the event (REAGANet al., 1978) are shown in Fig. 8. Odd nitrogen species were considerably enhanced over the ambient levels at all altitudes above 35 km; near 50 km the enhancement was as much as a factor of 45. The production of odd hydrogen species was also significantly increased during the intense precipitation and this was attributed as the primary cause of the initial rapid ozone depletion above 40 km immediately following the event. However, the excess odd hydrogen rapidly decayed following the ionization peak and the mean concentration of atmospheric ozone was thereafter determined by the long term enhancement in odd nitrogen.

5. Relativistic electron precipitation

Satellite observations of the Earth's radiation belts have shown that the energetic outer zone electron population is significantly enhanced during geomagnetically disturbed periods (e.g. PF[TZER and W[NCKLER, 1968; OWENS and FRANK, 1968; RUSSELLand THORNE, 1970; CORON[TI and THORNE, 1973; WEST et al., 1973; LYONS and W]LUAMS, 1975). The injected electrons subsequently interact with naturally generated magnetospheric plasma waves resulting in pitch-angle scattering loss to the atmosphere (ANDRONOV and TRAKHTENGERTS, 1964; KENNEL and PETSCHEK, 1966; KENNEL, 1969 ; ROBERTS, 1969 ; THORNE and KENNEL, 1971 ; LYONSet al., 1971, 1972; LYONS and THORNE, 1972; THORNE, 1974, 1976). As indicated in Fig. 9, this precipitational removal of energetic outer zone electrons can enhance the rate of ionization throughout the mesosphere by several orders of magnitude over the quiet time values.

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144

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Although the electron precipitation flux is most intense during periods of geomagnetic disturbances (e.g. REAGAN, 1977), significantly enhanced mesospheric ionization can persist at middle latitudes for over a week following the stormtime injection of electrons into the radiation belts (LAUTERand KNUTH, 1967; BELROSEand THOMAS, 1968; SPJELDVIKand THORNE, 1975; LARSENet al., 1976, 1977). Of particular interest to our discussion of middle atmospheric chemistry are the class of sporadic (1-3 hr duration) relativistic electron precipitation (REP) events which were first identified by their pronounced disturbance to D-region radio communication at subauroral (60 ~ ~ A ~< 70 ~ latitudes (BAILEYand POMERANTZ,1965; BAILEY,t968). It was later established that these intense events occur during magnetospheric substorm activity (RoSENBERGet al., 1972; LARSENand THOMAS,1974; THORNE and LARSEN,1976), and are caused by strong diffusion scattering of trapped outer zone electrons (THORNE, 1974, 1977a). Although the primary incoming electrons are unable to penetrate below 50 kin, the); produce copious fluxes of energetic Bremsstrahlung X-rays (BERGERand SELTZER, 1972; BERGER et al., 1974; LUHMANN, 1977) which penetrate deep into the stratosphere (see Fig. 2) before undergoing excitation and ionization collisions with the neutral atmosphere. By comparing the long-term energy deposition with that from GCR or SPE, THORNE(1977a, b) has suggested that REP events could be an important source of NO in the mesosphere and upper stratosphere, and as such should be included in further photochemical modeling of the terrestrial ozone layer. The characteristic energy spectrum of the precipitating relativistic electrons has only recently been measured by satellite borne instruments (e.g. VAMPOLA, 1971; REAGAN, 1977; THORNE, 1978). Using this information, the ionization profile for selected events can be obtained by numerical codes which follow the energy deposition through the atmosphere (e.g. WALT et al., 1968; SPJELDVIKand THORNE, t975). In Fig. 10, the ionization rate during two particularly intense REP events has been combined with the cluster ion chemistry results of Fig. 4 (HEAPS, 1978) to obtain the resulting profiles for mesospheric odd-hydrogen production. When compared to the two major quiet time sources of odd hydrogen it is clear that the electron precipitation can provide an important local contribution over a broad altitude range near 70 km. Since the concentration of ozone near this altitude is controlled by odd hydrogen catalytic cycles (Section 2.4) one can anticipate local changes in mesospheric ozone during the relativistic electron precipitation. A numerical simulation of the atmospheric response at 70 km due to both a daytime and night-time REP event (J. DEVORE,personal communication, 1979) is shown in Fig. 11. In each case the energy spectrum of th e precipitating electrons was modeled after the 12 March 1977 event illustrated in Fig. 10 and the event duration was assumed to be 2 hours. The event near midnight caused an immediate increase (by more than a factor of 10) in OH concentration which remained enhanced throughout the night. Catalytic removal of 03 however did not occur until after sunrise due to the low O concentrations at night. Maximum 03 depletion (~ 15~) occurred soon after sunrise

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Figure 11 A numerical simulation of OH and 03 variability at 70 km during relativistic electron precipitation. The shaded areas indicate OH enhancement and 03 depletion relative to normal diurnal variation.

146

Richard Mansergh Thorne

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for comparison. The 1-10~ range in the REP source reflects uncertainties in the frequency of occurrence of energetic electron precipitation. and within a few hours both the OH and 03 concentrations had returned to normal levels. During the dayside REP event the relative OH enhancement was less but Os showed an immediate depletion (reaching a maximum of about 30~) followed by a recovery to normal levels within a few hours after the cessation of precipitation. In addition to the production of short-lived odd hydrogen species, REP events also yield NO molecules which can have a much longer residence time in the atmosphere. A comparison of the annual yield from the sporadic REP events with the two dominant quiet time sources for NO is given in Fig. 12. The 1-10~ range for REP production reflects the present observational uncertainty in the occurrence frequency of REP events (THORNE, 1978). It must be emphasized that the comparison only applies to the localized sub-auroral region (60 < A < 70 ~ which maps into the outer radiation belt. Nevertheless, it is clear that the REP source cannot be ignored since it becomes competitive in the upper stratosphere and is the dominant in situ NO source throughout the mesosphere. 6. Concluding remarks Each of the three classes of precipitation considered in this review appears to play a non-trivial role in the chemistry of certain regions of the middle atmosphere. In the lower stratosphere ( < 20 km) galactic cosmic radiation provides the dominant source of odd nitrogen particularly over the polar regions. However, since the peak GCR precipitation occurs below the altitude where catalytic removal of Oa by odd nitrogen species is most efficient it is questionable whether this process contributes significantly to the terrestrial Oa budget, or whether the observed solar cycle variation of 03 can

Vol. I18, 1980)

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be attributed with the known cyclic variation in GCR precipitation flux. In the upper stratosphere the precipitation of energetic solar protons at high latitude (A > 60 ~ can periodically lead to a dramatic enhancement in the concentration of NO which subsequently leads to a catalytic removal of 03. Because of the long residence time of NO at the injected altitudes, the accumulative injection during these SPE events must be considered in the overall budget of terrestrial 03. Throughout the mesosphere (and extending into the upper stratosphere) the sporadic precipitation of energetic electrons from the outer radiation zone (60 < A < 70) can yield a major local source of both odd hydrogen and odd nitrogen species. Measurable, though short-lived, decreases in mesospheric ozone can be expected during such events, due to enhanced OH production. But in view of the shorter residence times for NO at the altitudes of REP injection it is questionable whether this source will contribute to the long-term budget of middle atmospheric odd nitrogen. Future satellite studies should be aimed at making a direct comparison between the particle precipitation flux and the associated modification of the middle atmosphere at different altitudes during selected events. In particular the contribution by energetic electron precipitation is currently poorly understood. Instrumentation capable of measuring the energy spectrum and pitch-angle distribution of precipitating electrons should be included in future missions to assess the overall impact of this source. More sophisticated models of the atmospheric response to prescribed precipitation events should also be developed. Of particular importance here is the need to include realistic transport processes in conjunction with the anticipated chemical modifications. Only then can one assess the overall importance of particle precipitation on the global scale.

Acknowledgements This work was supported in part by NASA contract NSG 5190 and NSF ATM 7724843. The author wishes to thank John DeVore for simulating the chemical change in the mesosphere during REP events and Leo Andreoli who provided the energy deposition rate and preliminary information on the occurrence of such events using OVl-19 and 533 data made available by A. Vampola.

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NICOLET, M. (1965), Ionospherie processes and nitric oxide, J. Geophys. Res. 70, 691. NICOLET, M. (1970), Aeronomie reactions of hydrogen and ozone, Aeronomica Acta. A79, 1. NICOLET, M. (1975), On theproduction of nitric oxide by cosmic rays in the mesosphere and stratosphere, J. Geophys. Res. 23, 637. NICOLET, M. and PEETERMANS,W. (1972), The production of nitric oxide in the stratosphere by oxidation of nitrous oxide, Ann. Geophys. 28, 751. NORTON, R. B. and BARTH, C. A. (1970), Theory of nitric oxide in the Earth's atmosphere, J. Geophys. Res. 75, 3903. ORAN, E. S., JULIENNE,P. S. and STROBEL,D. F. (1975), The aeronomy ofoddnitrogen in the thermosphere, J. Geophys. Res. 80, 3068. OWENS, Y[. D. and FRANK, L. A. (1968), Electron omnidirectional intensity contours in the Earth's outer radiation zone at the magnetic equator, J. Geophys. Res. 73, 199. PAETZOLD, H. K., PISCALOR, F. and ZSEHORNER, H. (1972), Secular variation of the stratospheric ozone layer over middle Europe during the solar cycles from 1951 to 1972, Nature 240, 106. PrITZER, K. A. and WINCKLER,J. R. (1968), Experimental Observations of a large addition to the electron inner radiation belt after a solar flare event, J. Geophys. Res. 73, 5792. PORTER, H. S., JACKMAN, C. H. and GREEN, A. E. S. (1976), Efficiencies for production of atomic nitrogen and oxygen by relativistic proton impact in air, J. Chem. Phys. 65, 154. PRESTON, K. F. and BARR, R. F. (1971), Primary processes in the pho tolysis of nitrous oxide, J. Chem. Phys. 52, 3347. RAPP, D., ENGLANDER-GOLDEN, D. and GRIGLIA, D. D. (1965), Cross sections for dissociative ionization of molecules by electron impact, J. Chem. Phys. 42, 4081. REAGAN, J. B. (1977), Ionization processes, in Dynamical and chemical coupling of neutral and ionized atmospheres, ed. B. Grandal and J. A. Holtet, p. 145, D. Reidel Pub. Co. REAGAN, J. B., GUNTON, R. C., EVANS,J. E., NIGHTINGALE,R. W., JOHNSON,R. G., IMHOF, W. L. and MEYEROTT, R. E. (1978), Effects of the August 1972 solar particle events on stratospheric ozone, Lockheed Report D630455. REID, G. C. (1961), A study of the enhanced ionization produced by solar protons during a polar cap absorption event, J. Geophys. 66, 4071. ROBERTS, C. S. (1969), Pitch angle diffusion of electrons in the magnetosphere, Rev. Geophys. 7, 305. ROBLE, R. G. and REES, M. H. (1977), Time-dependent studies of the aurora: Effects of particle precipitation on the dynamic morphology of ionospheric and atmospheric properties, Planet. Space Sci. 25, 991. ROSENBERG, T. J., LANZERATTI,L. J., BAILEY, D. K. and PIERSON, J. D. (1972), Energy spectra in relativistic electron precipitation events, J. Atmos. Terr. Phys. 34, 1977. RowE, J. N., MITRA, A. P., FERRARO, A. J. and LEE, H. S. (1974), An experimentalandtheoretical study of the D-region-II. A semi-empirical model for mid-latitude D-region, J. Atmos. Terr. Phys. 36, 755. RUDERMAN, M. A. and CHAMBERLAIN,J. W. (1975), Origin of the sun-spot modulation of ozone: Its implications for stratospheric NO injection, Planet. Space Sci. 23, 247. RUDERMAN, M. A., FOLEY, H. M. and CHAMBERLAIN,J. W. (1976), Eleven year variation inpolar ozone and stratospheric chemistry, Science 192, 555. RUSSELL, C. T. and THORNE, R. M. (1970), On the structure of the inner magnetosphere, Cosmic Electrodynamics 1, 67. SECHRIST, C. F., Jr. (1972), Theoreticalmodels of the D-region, J. Atmos. Terr. Phys. 34, 1565. SPJELDVIK, W. N. and THORNE, R. M. (1975), The cause of storm after effects in the middle latitude D-region, J. Atmos. Terr. Phys. 37, 777. STOLARSKI,R. S. and CICERONE, R. J. (1974), Stratospheric chlorine: A possible sink for ozone, Can. J. Phys. 52, 1610. STROBEL, O. F. (1971a), Diurnal variation of nitric oxide in the upper atmosphere, J. Geophys. Res. 76, 2441. STROaEL, D. F. (1971b), Odd nitrogen in the mesosphere, J. Geophys. Res. 76, 8334. STROBEL,D. F. (1972), Nitric Oxide in the D-region, J. Geophys. Res. 77, 1337. STROBEL, D. F., HUNTEN, D. M. and MCELROY, M. B. (1970), Production and diffusion of nitric oxide, J. Geophys. Res. 75, 4307.

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SVESTKA, Z. (1970), Solar particle events, Space Res. 10, 797. SVESTKA, Z. (1972), Characteristics of strong particle sources on the Sun, Proc. COSPAR Syrup. on Solar Particle Event of November 1969, ed. J. C. Ulwick, Rep. AFCRL-72-0474, p. 1. SWIDER, W. and KENESHEA,T. J. (1973), Decrease of ozone and atomic oxygen in the lower mesosphere during a PCA event, Planet. Space Sci. 21, 1969. THOMAS, L. (1964), Recent developments and outstanding problems in the theory of the D-region, Radio Sci. 9, 121. TnORNE, R. M. (1974), A possible cause of dayside relativistic electron precipitation events, J. Atmos. Terr. Phys. 36, 635. THORNE, R. M. (1976), The structure and stability of radiation belt electrons as controlled by waveparticle interactions, in Magnetospheric particles andfields, ed. B. M. McCormac, p. 157, Reidel Pub. Co., Dordrecht, Holland. THORNE, R. M. (1977a), Influence of relativistic electron precipitation on the lower ionosphere and stratosphere, in Dynamical and chemical coupling between the neutral and ionized atmosphere, ed. B. Grandal and J. A. Holtet, p. 161, D. Reidel Pub. Co. THORNE, R. M. (1977b), Energetic radiation belt electron precipitation : A natural depletion mechanism for stratospheric ozone, Science 21, 287. THORNE, R. M. (1978), The potential role of relativistic electron precipitation as a natural destruction mechanism for middle atmospheric ozone, in Proc. of Joint I A G A / I A M A P Assembly in Seattle, pub. by NCAR. THORNE, R. M. and KENNEL, C. F. (1971), Relativistic electron precipitation during magnetic storm main phase, J. Geophys. Res. 76, 4446. Tr~ORNE, R. M. and Larsen, T. R. (1976), An investigation of relativistic electron precipitation events and their association with magnetospheric substorm activity, J. Geophys. Res. 81, 5501. THRUSH, B. A. (1979), Aspects of the chemistry of ozone depletion, Phil. Trans. Roy. Soc. London A, 290, 505. VAMPOLA, A. L. (1971), Electron pitch-angle scattering in the outer zone during magnetically disturbed times, J. Geophys. Res. 76, 4685. WALT, M. and MACDONALD, W. M. (1964), The influence of the Earth's atmosphere on geomagnetically trapped particles, Rev. Geophys. 2, 543. WALT, M., MACDONALD,W. M. and FRANCIS,W. E. (1968), Penetration ofauroralelectrons into the atmosphere, in Physics of the magnetosphere, ed. B. M. McCormac, p. 534, Reidel Pub. Co., Dordrecht~ Holland. WARNECK, P. (1972), Cosmic radiation as a source of odd nitrogen in the stratosphere, J. Geophys. Res. 77, 6589. WEBBER, W. (1962), The production of free electrons in the ionospheric D layer by solar and galactic cosmic rays and the resultant absorption of radio waves, J. Geophys. Res. 67, 5091. WEEKS, L. H., CUIKA'r R. S. and CORBIN, J. R. (1972), Ozone measurements in the mesosphere during the solar proton event of 2 November 1969, 3. Atmos. Sci. 29, 1138. WENTWORTH, R. C., MACDONALD, W. M. and SINGER,S. F. (1959), Lifetimes of trapped radiation belt particles determined by coulomb scattering, Phys. Fluids 2, 499. WEST, H. I. JR., BUCK, R. M. and WALTON,J. R. (1973), Electron pitch angle distribution throughout the magnetosphere as observed on Ogo 5, J . Geophys. Res. 78, 1064. WINTERS, H. F. (1966), Ionic absorption and dissociation cross sections for nitrogen, J. Chem. Phys. 44, 1472. Worse, S. C. (1974), Atmospheric photochemistry of N, H and CI containing radicals, C.I.A.P. Rep. DOT-TSC-OST-74-15, p. 359. WOFSY, S. C. and MCELRoY, M. B. (1974), HO:~, NOx and CIOx: Their role in atmospheric photochemistry, Can. J. Phys. 52, 1582. ZEREFOS, C. S. and CRtSTZEN, P. J. (1975), Stratospheric thickness variations over the Northern Hemisphere and their possible relation to solar activity, J. Geophys. Res. 80, 5041. ZMUDA, A. J. and POTEMRA,T. A. (1972), Bombardment of the polar cap ionosphere by solar cosmic rays, Rev. Geophys. Space Phys. 10, 981. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh~iuser Vertag, Basel

An Introduction to the Generalized Lagrangian-Mean Description of Wave, Mean-Flow Interaction' By M. E. MCINTYRE z'3)

Abstract-The generalized Lagrangian-mean description is motivated a n d illustrated by means of some simple examples of interactions between waves and mean flows, confining attention for the most part to waves of infinitesimal amplitude. The direct manner in which the theoretical description leads to the wave-action concept and related results, and also to the various 'noninteraction' theorems, more accurately non-acceleration theorems, is brought out as simply as possible. Variational formulations are not needed in the analysis, which uses elementary principles only. The significance of the generalized Eliassen-Palm relations as conservation equations for wave activity is discussed briefly, as is the significance of the temporal nonuniformity of the generalized Lagrangian-mean description for dissipating disturbances. [

Key words: Wave meanh-flow interaction; Non-acceleration theorems; Wave action.

1. Introduction A topic which has fascinated me for a n u m b e r o f years now (so much so that I have rashly u n d e r t a k e n to write a b o o k on it!) is the interaction o f waves and mean flows seen b o t h f r o m a general viewpoint a n d also in c o n n e c t i o n with specific applications including those in stratospheric meteorology. P h e n o m e n a associated with wave t r a n s p o r t processes and n o n l i n e a r rectification have long been familiar in simpler contexts such as a c o u s t i c s - e . g , r a d i a t i o n stress (BRILLOUIN, 1925, 1936), acoustic s t r e a m i n g (LIc~nTHILL, 1978) - b u t the subject has been revitalized by recent evidence t h a t w a v e - i n d u c e d s t r e a m i n g effects t a k e place on a very large scale in the m i d d l e a t m o s p h e r e (e.g. HOLTON, 1975). These do not merely p e r t u r b its general circulation, b u t represent gross features which would otherwise be absent. The clearest e x a m p l e so far d o c u m e n t e d is the quasi-biennial oscillation o f the e q u a t o r i a l zonal wind, h e r e a f t e r ' Q B O ' . A n o t h e r is the sudden warming. There has also been the realiza1) This review article is based on material prepared for a summer colloquium on 'The General Circulation: Theory, Modeling, and Observations' held at the National Center for Atmospheric Research in July 1978 and sponsored by the Advanced Study Program. 2) National Center for Atmospheric Research, Boulder, Colorado 80307, USA. The National Center for Atmospheric Research is sponsored by the National Science Foundation. a) Present affiliation: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, England.

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tion that wave transport effects might maintain the four-day rotation of Venus' outer atmosphere (FELs and LI~DZEN, 1974; PLUMb, 1975) and probably play a role in the history of the Sun's differential rotation (E. A. SPIEGEL, personal communication) and in the acceleration of the solar wind (HOLLWEG, 1978 and refs. therein). Quite independently of those developments, there has been a revival in the literature of some long-standing controversies on theoretical aspects of the subject of wave transport, particularly the celebrated 'Abraham-Minkowski controversy' on electromagnetic wave ' m o m e n t u m ' in fluid or Solid media. This controversy and its less-publicized relatives in acoustics and geophysical fluid dynamics typify certain misconceptions concerning the generalities of the subject, which despite clarifications now available (e.g. PEIERLS, 1976) are still widely perpetuated as the scientific literature proliferates with less and less interdisciplinary communication. (In Section 5 we shall catch a glimpse of how these generalities relate to the fluid-dynamical problems which are of more immediate concern to us here.) It has become increasingly evident in recent years that the underlying theoretical structure of the subject becomes immeasurably clearer if one describes wave disturbances in terms of particle displacements about the mean flow, in place of the more usual eddy velocity fields. There are deep reasons for this, associated for instance with the connection between symmetries and conservation relations (e.g. BRETHERTON, 1979; ANDREWS and MCINTYRE, 1978c). How best to define a disturbance-associated particle displacement for arbitrary, finite-amplitude waves on an arbitrary mean flow is not a trivial question; and it is linked to the equally nontrivial question of how to define the notion of Lagrangian-mean flow in a general manner. However, significant progress has recently been made towards answering these questions, as a result of several lines of work traceable back at least as far as that of FRIEMAN and ROTENBERG (1960) and ECKART (1963), and developed by DEWAR (1970), BRETHERTON(1971, 1979), who was perhaps the first to see the importance of the ideas for geophysical fluid dynamics, SOWARD (1972) (in M H D dynamo theory), GRIMSHAW (1975), and culminating in a very general theory developed and discussed by ANDREWS and MCINTYRE (1978b, hereafter AM; see MCINTYRE, 1979 for further discussion). This theory may be called the GLM ('generalized Lagrangian-mean') theory of wave, mean-flow interaction. It draws together a number of threads in the subject which seem unconnected when viewed more conventionally; and in particular it shows where the Eulerian-mean results of ELIASSEN and PALM (1961), CHARNEY and DRAZIN (1961), DICKINSON (1969), F'EES and L1NDZEN (1974), PLUMB (1975), HOLTON(1974), BOYD (1976) and ANDREWSand M CINTYRE(1976a, 1978a) really come from, and how they are connected with such things as the wave-action concept and the energy-momentum-tensor formalism of theoretical physics (HAYES, 1970; ANDREWS and MCINTYRE, 1978c). Many of these general results emerge in an analytically very simple way. On a more practical level, the G L M theory may help us toward a better understanding of the general circulation of the middle a t m o s p h e r e - o n e in which the

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theoretical description of planetary waves and other departures from the zonal-mean state fits more naturally with observations of tracer motions. Some of the ideas involved are discussed by DUNKERTON (1978) and also in the paper by MATSUNO (1980) in this issue; they have important precedents in the work of RIEHL and FULTZ (1957), KRISHNAMURTI(1961), DANIELSEY (1968), MAHLMAN (1969) and others. Our understanding of how to use the theory in this context is far from complete, however; a discussion of some of the difficulties yet to be overcome is attempted in MCINTYRE (1979). In this review I shall concentrate on some prototypical idealized problems concerning the interaction of waves and mean flows, with a view to bringing out the simplicity and intuitive appeal of the ideas which originally led to the G L M theory. I shall also try to show by example why such problems are intriguing for the fluid dynamicist as well as the meteorologist. The two sub-problems comprising the problem of wave, mean-flow interaction, namely (i) How the waves create or change the mean flow, and (ii) How mean-flow profiles react back on the waves, are both well illustrated by the simple example of two-dimensional internal gravity waves, as was illuminatingly brought out in a recent paper by PLUMB (1977). We use this special example in Sections 2 and 3 in order to motivate a discussion of the more general case of waves involving Coriolis forces - and the power of the G L M theory in dealing with t h e m - which follows in Sections 4 and 5. A closely related topic, discussed briefly in Section 6, is the use of 'generalized Eliassen-Palm relations' in sub-problem (ii); this in turn suggests diagnostics which are likely to prove important for interpreting observational data on planetary waves in the middle atmosphere. Finally, in Section 7 we indicate briefly the ideas involved in the G L M description offinite-amplitude disturbances, and its possible application to the middle atmosphere.

2. Two-dimensional internal gravity waves One class of problems of special meteorological (and astrophysical) interest is that of 'longitudinally symmetric' mean flow, independent of a coordinate x which is either longitude or its cartesian 'channel' equivalent. A special feature of such problem s is that there is no longitudinal mean pressure gradient ~p/~x; thus the fluid is free to accelerate in the x direction in response to the wave effects (sub-problem (i)). The simplest model example is that of two-dimensional internal gravity waves being generated by a slippery, corrugated boundary moving parallel to itself with constant velocity c, as suggested in Fig. 1. It is well known that, if the waves are transient or are being dissipated in some layer oL~ a at the top of the picture, then the mean flow accelerates there. The wave-drag force which the boundary exerts on the fluid is not felt at the boundary, as far as the mean flow is concerned; it is felt at 5r This illustrates the well-known ability of waves to set up a mean stress, whereby the

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iZ/./ Figure 1 Internal gravity waves, being generated in a resting, stably-stratified fluid by a rigidly-moving boundary. The sloping lines are lines of constant phase; the disturbance particle paths are parallel to those lines. The buoyancy frequency N is assumed constant. The dotted line L represents an isentropic surface approximately, and Lo is a fixed, horizontal surface.

effect of a mean force (in this case the horizontal force exerted by the boundary) can be transferred over considerable distances (in this case vertically, up to the layer 5O), In this particular case the mean stress involved is simply the Reynolds stress - p u ' w ' associated with the waves. Its divergence appears as the wave-induced contribution to the mean-flow acceleration ~/~t

= - ~(u' w')/~z -

X,

(2.1 a)

where - )( (the sign is chosen for later convenience) is any mean force per unit mass which might also be present (such as a mean viscous force oc ~2~/~z2). The overbars and primes denote the usual zonal or longitudinal Eulerian average with respect to x, and fluctuations about it. We have assumed a Boussinesq fluid with constant density p. Clearly u'w' > 0 below ~o in the picture (the disturbance velocity being directed parallel to the sloping lines of constant phase because the motion is incompressible), and u'w' = 0 above 5 ~ if there is no disturbance there. Then O(u'w')/Oz has to be nonzero somewhere in between, which is why the mean flow must accelerate there, apart from any additional effect from )(. If the waves were generated not at a boundary but by a moving system of heat sources and sinks in some layer in the interior of the fluid, then total momentum integrated over the whole depth of the fluid would have to be constant, and the mean acceleration at 5O would be accompanied by a corresponding deceleration where the waves are generated. The latter effect has been proposed as a mechanism for maintaining the fast zonal flow observed in Venus' outer atmosphere (FELS and LINDZEN 1974; PLUMB 1975, and refs. therein).

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If we had used the G L M description instead of the conventional one, the analogue of equation (2.1a) would have been

b~./~t = p - t O(~'~p')/~z - X~"

(2.1b)

for small amplitude, almost-plane waves in the same Boussinesq fluid. (This involves some approximation; the corresponding exact equation is (8.7a) of AM, or rather the specialization of that equation to two-dimensional motion with constant gravity and zero rotation; see also AM (8.12).) Here ( )L denotes a mean along a line of fluid particles distorted by the waves, such as the wavy dotted line L in Fig. 1 ; if the motion were exactly adiabatic, L would exactly coincide with an isentropic surface corrugated by the wave motion. The vertical displacement of the fluid particles about their mean position L0 is the quantity ~', whose x-derivative appears, correlated with the disturbance pressure p', on the right of equation (2.1b). In Section 7 I shall say more precisely how the G L M theory defines ( )L and the disturbance-associated particledisplacement vector, of which ~' is the vertical component; the definition will in fact apply to finite-amplitude, arbitrary waves. Note that equation (2.1b) makes immediate physical sense: just as equation (2.1a) can be obtained by considering the mean stress across fixed, horizontal control surfaces like L0, so can equation (2. tb) be obtained by considering the mean horizontal stress - ~xP' exerted by the fluid below the wavy, material surface L upon the fluid above it, via the correlation between negative slope - ~ x and positive pressure anomaly. (This is exactly the same thing as the wave drag of the boundary itself; the boundary can be regarded as a particular case of a material surface L.) Equation (2.1b) and its generalizations turn out, as we shall see in Section 5, to lead to the easiest way of expressing the connection between mean flow changes and wave dissipation, forcing or transience, in cases more general than that of Fig. 1, for instance when a nontrivial mean flow ~(z) is present. The connection is then somewhat less obvious. But first we digress to look a little more closely at some specific phenomena described by equations (2.1a) and (2.1b). These show in yet another way that there is more to the subject of wave, mean-flow interaction than meets the eye!

3. The simplest example of vacillation due to wave, mean-flow interaction." Plumb and McEwan's laboratory analogue of the QBO If the waves in Fig. 1 are dissipating throughout the depth of the fluid, t h e n the height scale D for wave attenuation tends to be proportional to the vertical component wo of the group velocity. For uniform dissipation the mean flow will initially develop as in Fig. 2a [~ oc exp (-z/D)], with the biggest change near the boundary *) z = 0. 4) It should be pointed out here that a contrasting situation can occur in the non-Boussinesq case where the density scale height is comparable with D or smaller: the greatest mean-velocity change may then occur far above the boundary. This point has been made by DUNKERTON(1979a), and by URvu (1980) in this issue.

Vol. 118, 1980) Lagrangian-Mean Description of Wave, Mean-Flow Interaction

(a)

-c

(b)

I

c

(c)

<

(d)

[a

.~-a]

-c

(e)+c

157

(

<

Figure 2 (a), (b): Effect on the mean-flow profile tV(z) of a single internal gravity wave with phase speed +c at two successive times. (c)-(f): effect of two waves with phase speeds _+_c, after PLUMB(1977).

But now sub-problem (ii) comes in: the feedback o f the mean-flow change onto the waves affects D. W h e n the intrinsic phase speed e - ff gets small enough, w~ becomes small too (a fact which we shall use again, and which is easily verified from the dispersion properties o f plane internal gravity waves); therefore D decreases and also becomes a function o f z - we m a y still speak of it as the local height scale for wave d i s s i p a t i o n - a n d it is smallest o f all near z = 0. Clearly this cannot go on forever since there is a limiting situation, shown schematically in Fig. 2b, in which = c at z = 0, and no more waves are generated and no more wave-induced meanflow change takes place. Actually, linear theory must break down near z = 0 before this situation is reached, but the idea is qualitatively right. We are tacitly assuming that viscosity has a negligible effect on the mean flow, especially near z = 0. If we now add to the input o f waves at z = 0 a c o m p o n e n t travelling with equal and opposite phase speed - e , something very interesting happens. (The first theory demonstrating the effect was that of HOLTON and LINDZEN (1972), and our understanding o f it has been greatly improved by the recent work of PLUMB (1977).) Suppose for simplicity that the two waves, with phase speeds + c, have equal amplitudes so that the b o u n d a r y is now executing a standing wave

z = h(x, t) =- a sin k ( x - ct) + a s i n k ( x + ct) = 2a sin k x cos kct;

(3.1)

and suppose moreover that 2kc is less than 0.816 times the b u o y a n c y frequency N o f the stratification. Then not only can the leftward-travelling c o m p o n e n t propagate even if ff = + c, but it can also be shown that the relation between wg and intrinsic horizontal phase speed is strictly monotonic, so that wg and therefore D for the leftward-travelling c o m p o n e n t is necessarily larger, for all values of z, than it was for the rightward-travelling c o m p o n e n t before the mean flow developed. Thus, it is easy to see that the leftward-travelling wave will now induce a negative acceleration ~ / O t t h r o u g h o u t a comparatively deep layer, leading to the appearance o f a

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M.E. McIntyre

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downward-moving zero in the mean velocity profile as shown in Figs. 2c-e. In Fig. 2e, D for the leftward-travelling wave has become small just above the narrow shear layer at the bottom; however, the leftward-travelling wave cannot by itself quite destroy the shear layer because if ~ were to become slightly different from + c at z = 0 the effect of the rightward-travelling wave would reassert itself in a very shallow layer near z = 0. The shear layer must nevertheless get destroyed sooner or later, either because mean viscous effects become dominant (PLUMB, 1977) or, more likely in a real fluid, because the Richardson number becomes small and the shear layer goes turbulent. This will quickly wipe out the shear layer and leave us all of a sudden with something like the profile of Fig. 2 f - i.e. qualitatively like Fig. 2b, but with the sign changed. PLUMB (op. cit.) refers to this transition between the profiles of Figs. 2e and 2f as 'switching'. At this point, we can see that the same sequence of events will take place all over again, with the signs changed. The double feedback loop, sub-problems (i) and (ii), between the mean flow and the dissipating waves, has led to a vacillation cycle in which the mean flow reverses again and again, entirely because of the constant input of waves. Figures 2b-2f qualitatively depict just half this vacillation cycle. That such phenomena unquestionably occur in real fluids has recently been most beautifuUy demonstrated in the laboratory by PLUMB and MCEWAN (1978). They took an annulus of salt-stratified fluid (not rotating) and introduced a standing wave via the motion of a rubber membrane at the bottom, so that equal amounts of clockwise and anticlockwise-travelling waves with periods of a fraction of a minute were generated. The initial conditions involved no mean f l o w - an almost completely symmetrical situation- yet sooner or later substantial mean flows would appear, going through a vacillation cycle just as in Figs. 2b-2f. The initial state is unstable to the vacillation cycle (PLUMB, 1977). The period of the cycle depended of course on the wave amplitude a, but was typically an hour or so. No mean flow developed if the wave amplitude a was too small, owing to the stabilizing effect of mean viscous forces. PLUMB and MCEWAN (personal communication) have produced a moving picture dramatically showing the existence of the mean flow evolving just as suggested in Fig. 2, together with the constant-amplitude standing wave on the boundary which causes the whole sequence of events. As is well known by now (e.g. HOLTON, 1975), there is good evidence that a precisely similar mechanism underlies the quasi-biennial reversal, every 26 months or so, of the zonal mean wind in the equatorial lower stratosphere. (The 26 months (or so!) is thus to do with the amplitudes which the relevant (troposphericallygenerated) waves happen to have - and nothing to do with any 'obvious' periodicity such as the annual cycle as was thought at one time.) Plumb and McEwan's finding that the mechanism is rather easily killed off by viscous diffusion of the mean flow immediately suggests one of the reasons why general circulation models, which tend to have rather large artificial viscosities (as well as resolutions too coarse to describe the waves very well), have not yet succeeded in producing a QBO.

Vol. 118, 1980) Lagrangian-Mean Description of Wave, Mean-Flow Interaction

159

Other, less simple, examples of vacillation cycles due to wave, mean-flow interaction have recently been noted by HOLTON and MASS (1976) and HOLTON and DUNKERTON (1978). The waves involved are extratropical planetary waves. In those examples, which model aspects of the behavior of the wintertime stratosphere in high latitudes, wave transience plays an important role in the vacillation dynamics.

4. Waves involving Coriolis forces

The waves involved in the equatorial Q B O - mainly the equatorial planetary waves, but possibly stationary planetary waves from mid-latitudes as well (ANDREWS and MClNTYRE, t976a, w and refs. therein)- involve Coriolis forces and are structurally more complicated than pure internal gravity waves. It is characteristic of such problems that a description of wave-induced momentum transfer of the type given by equation (2.1b)-a Lagrangian-mean descripti0n-turns out to be more direct than that given by equation (2.1a). The Lagrangian-mean description gives by far the simplest route, for instance, to computing the striking effect of different wave dissipation mechanisms on the latitudinal profiles of ~ / ~ t for equatorial waves (ANDREWS and MCINTYRE, op. cit.), an effect which is really quite arduous to compute, even to leading order, by conventional methods (ibid., 1976b). I shall not repeat the analysis for equatorial waves here, since three different versions are already given elsewhere (in the papers just cited, together with AM w Rather, I want to illustrate and compare both types of description (Eulerian-mean and Lagrangian-mean) by means of the simplest relevant problem, namely that of Fig. 1, but with a Coriolis force added whose x, y and z components are (2~2v, - 2~)u, 0) when the velocity components are u, v, w): ~2 is assumed constant for the moment. In the Boussinesq approximation the linearized disturbance equations may be written, now allowing for three-dimensional motion, and setting the constant reference density p equal to unity, as p

Dtu' + ( ~ - 2f2)v' + ~w' + Px = - X '

(4.1)

D t v ' + 2f2u' + p~ = - Y'

(4.2)

D,w' - O' + p'~ = - Z '

(4.3)

DtO' + O~v' + O~w' = - Q '

(4.4)

t

t

t

ux + v~ + w, = O,

(4.5)

where 0 is the buoyancy acceleration, Dt - ~/Ot + ~ ~/ax the rate of change following the mean flow, the latter being assumed to be of the form (if(y, z), O, O} + O(a2), i.e. directed almost parallel to x. Just as we allowed for a mean viscous or other 'extra' force - . ~ in equation (2.1a), here we permit a correspondingly arbitrary O(a) force - X ' on the right of equation (4.1), together with corresponding

160

M.E.

Mclntyre

(Pageoph,

components Y' and Z ' in equations (4.2), (4.3), and an arbitrary heating rate - Q' in the buoyancy equation (4.4). As with all other primed quantities we have X' = Y' = Z ' = Q' --- 0. The buoyancy frequency N is equal to ~i2 in the present notation. To obtain a physically well-posed problem for the mean flow it is simplest to suppose that the flow is bounded laterally by a pair of vertical walls y = 0, b on which the normal component of velocity vanishes (see Fig. 4 below) implying that = ~' --- 0

on

y = 0, b.

(4.6)

Since the bottom boundary is a rigid surface which is impermeable to the fluid, it is plausible (and in fact true for steady waves) that the Lagrangian-mean vertical velocity is zero there also: ~L = 0

on

z = 0.

(4.7)

We must beware, however, of assuming that the Eulerian-mean velocity ,~ vanishes at z = 0; in fact, for a rigidly-translating, corrugated boundary whose shape is described by a given function z = h'(x - ct, y), where h' = O(a), ~r = 0, and c is a (real) constant as before, it can be shown (for more detail see the accompanying paper ANDREWS, 1980) that = ~(v'h')/~y + O(a 3)

on

z = 0.

(4.8)

This is one of the ways in which the conventional Eulerian-mean description is more complicated than a Lagrangian-mean description. The Eulerian-mean velocity ~, which is an average along a horizontal line such as I in Fig. 3, is associated with a vertical mass flux, into or out of the thin region between l and the actual boundary. That flux must satisfy continuity with a horizontal, O(a 2) mass flux within that region, associated with any tendency for the disturbance velocity to be one way along troughs and the other way along ridges in the boundary (Fig. 3). In fact, such a tendency turns out to be the rule rather than the exception when Coriolis effects matter; for instance if h' is of the form a sin k ( x - ct) then the

1 g

C Figure 3 T h e r e a s o n w h y ~ ~ 0 at z = 0 in t h e r o t a t i n g p r o b l e m . (The f o r w a r d slope o f t h e w a v e crests is correct w h e n N f f = 0z) > 4f22.)

Vol. 118, 1980) Lagrangian-Mean Description of Wave, Mean-Flow Interaction

161

disturbance y-velocity v' for conservative, plane inertio-gravity waves on a uniformly stratified basic state of rest turns out to be in quadrature with the z-velocity w' and therefore in phase with h' at z = 0 (ignoring signs). This can easily be verified (once again Iforlfurtherldetaillsee the/accompanyinglpaper) Iby!setting N 2 = 8~ = constant, z7 = 0u = 0, and X' = 0, Q' = 0, and calculating the structure of elementary planewave solutions ~ exp i(kx + m z - oz) of the linearized disturbance equations (4.t)-(4.5). Other pertinent features of such plane-wave solutions are that O', the disturbance buoyancy acceleration, beingproportional to the vertical displacement ~' through the basic stable stratification tT~,is (like h' at z = 0) in quadrature with the vertical velocity w'; also incompressibility dictates that u' is in phase with w' since equation (4.5) implies that iku' + imw' = 0. Note therefore that u'w', v'O' are nonzero, and u'v', w'O' zero, in a plane inertio-gravity wave. The frequency of such a wave, ~ (= kc), satisfies the well-known dispersion relation

02 = (N2k 2 + 4~'12m2)/(k2 + rn2)

(4.9)

when ~ = 0. (It should be noted that this implies that c 2 must lie between 4~2/k 2 and N2/k ~ for the inertio-gravity waves to be generated.) Coming back to the mean-flow problem, and still assuming that fi = (if, 0, 0) + O(a2), I shall write the mean-flow equations for both the conventional and Lagrangianmean descriptions correct to O(a 2) next to each other for easy comparison, starting with the counterparts to equations (2.1a) and (2.1b): I

O~t+

LO~L./~t

I

+

fi. Vz7 - 2 ~ +

ilL.Vr/L

_

2f2~L +

,,V= - ( u ' v ' ) ~ - ( u : w ' ) ~

(4.10a)

, ,)~ + (~xP )~ = 07xP

(4.10b)

~,

~V/~t + 2raFt + flu + Y = O(a 2) forcing O~L/Ot + 2f~t~ + (~L)y + FL

(4.11a)

O(a 2) forcing

(4.tlb)

O~/~t - 0 + ~ + Z = O(a 2) forcing

(4.12a)

O~"/~t - 0,'" + (~:)~ + Z L

O(a 2) forcing

(4.12b)

00/0t + ~0~ + ~0~ + 0 = -(v'O')~ - (w'O')~

(4.13a)

36L/~t + ~L(OL)u + ~L(6L)z + 0L = ZERO

(4.13b)

G + ~ = 0 +

=

(4.14a) +

--Tw

+

(4.14b)

The explicit form of the O(a ~) forcing on the right of equations (4.11) and (4.12) will not be needed. The terms distinguished by asterisks are those which survive in the

162

M.E. McIntyre

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case of almost-plane inertio-gravity waves on a mean flow that is sufficiently slowlyvarying in space and time. This turns out to imply that the mean flow is approximately geostrophic and hydrostatic, and in particular that the forcing terms on the right of equations (4.11) and (4.12) can be neglected. Time scales for the mean flow must be long compared with both (~)-112 and (2f2) -1. The vertical particle displacement ~' appears as before, and there is now also a particle displacement -q' in the y-direction; equation (4.10b) can be seen at once to be a plausible generalization of equation (2.1b). The Eulerian-mean ' a ' equations are familiar and require no comment; the Lagrangian-mean ' b ' equations are derived succinctly in AM w alternatively it is straightforward (although somewhat tedious) to derive them from the Eulerian-mean or ' a ' equations by applying the formula for the 'Stokes corrections' which are defined as ~s _ ~L _ ~,/~s =/SL _ if, etc., and are given correct to O(a ~) by 17s = ~'. Vu' + 89

+ ~ , ~ , ~ + !r,2;;2~ ,-~,

(4.15)

and similarly for ps or any other Stokes correction, where ~' = (~:, ~7, ~) is the vector particle displacement defined in Section 5 below. Note that the Stokes corrections are O(a 2) wave properties (i.e. can be evaluated to O(a 2) from a linearized wave solution). As explained further in MclNTYRE (1979, w the terms in equation (4.15) involving the second derivatives of ff are not usually mentioned in classical accounts of Stokes corrections; note that in evaluating those terms it is immaterial whether or ~" ( = ~ + O(a2)) appears. Note also that, for consistency with our assumptions that ~ and ~ are O(a 2) (and thus ~L and V~L also), it is expedient to assume that X, Y, Z and O are O(a 2) (and thus X~', yr, and Or~ also). A particularly crucial difference between the two descriptions of mean-flow evolution is the difference between the right-hand sides of equations (4.13a) and (4.13b). The Lagrangian-mean equation (4.13b) has zero wave-induced forcing on the right; and this, incidentally, remains exactly true at finite amplitude. For adiabatic motion (Q = 0) the Lagrangian-mean description says very naturally that the mean buoyancy field /~L(y, Z, t) is simply advected by the Lagrangian-mean flow. This is not so in the Eulerian-mean description; the 'eddy heat flux' terms on the right of equation (4.13a) are not generally zero. So even when the motion is completely adiabatic the equations say (if we are using the Eulerian-mean description) that the mean flow feels a wave-induced heating or cooling! The simplest illustration of this artificiality of the Eulerian-mean description is our model example, in which the waves are supposed to have propagated upwards as far as the layer &P in Fig. 4, either because they are being dissipated there, or because a finite time has elapsed since the bottom boundary started moving. Well below ~ we shall take the waves to have reached a steady state and the motion to be s) Equations (4.10b) through (4.13b) are simply the result of applying the operator ( )L to the corresponding equations for the total flow, using (4.15) with Vp in place of u, and using the basic (exact) result that (Off~St + u. V4,)L = 8~L/Ot + fiL'VqgLfor any ~b(x,t) (AM eq. (2.15)); see also MclrqTYR~, 1979, {}3.

Zl)

Vol. 118, 1980) Lagrangian-Mean Description of Wave, Mean-Flow Interaction

_f /

163

x. t

4-

t

J,

t L

fi--~WAVES Z

t

t Z

J

l,--

CI U'

hi "r

-1 t

Z J,

a /at( -asL/at )

f

Y Figure 4

Left: end view (looking along the x axis) of the inertio-gravity-wave problem. Right: typical profile of the mean acceleration in the longitudinal or x direction. The left-hand picture indicates how the Eulerian-mean meridional circulation f, 9 is closed by a mass flux 'within' the bottom boundary, as suggested in Fig. 3. HR is the Rossby height f2b/N. The time scale for mean-flow changes is assumed much longer than both 1/Q and 1/N. The longitudinal Stokes drift ffL _ ff is negligible in this problem, but not the meridional and vertical Stokes drifts.

conservative, as we originally did in Section 2 - we assume that X ' and Q' are zero there, and also X~ and Q. To keep life as simple as possible we shall assume that = 0 initially, again as in Section 2. We also take the b u o y a n c y frequency N = (0z) 1/2 = constant + O(a 2) for the moment. The simplest kind o f mathematical analysis for the waves (again see the a c c o m p a n y i n g paper for details) makes the usual kind of 'slowly-varying' approximation, in which the plane-wave solution is assumed locally valid. This involves inter alia an assumption that the layer ~ is deep compared with a vertical wavelength and also that s is deep compared to the Rossby height HR = f2b/N. We take h to be of the form a.f(y), sin k(x - ct), w h e r e f ( y ) is a slowly-varying function which vanishes at the side wall y = 0, b. Then it follows from the properties o f plane inertio-gravity waves already noted that the most important term on the right o f the x - c o m p o n e n t o f the Eulerian-mean equation (4.10a) is --(u'w')z and that on the right o f equation (4.13a) is -(v'O')u. The remaining terms are not exactly zero, because plane waves represent only the leading approximation; but in fact it is consistent to neglect them. The response o f the mean flow to the forcing -(v'O')~ together with the forcing represented by the inhomogeneous b o u n d a r y condition (4.8) involves an Eulerian-mean ' s e c o n d a r y circulation' indicated schematically by the arrows in Fig. 4. The picture assumes that the wave amplitude is a m a x i m u m

164

M.E. McIntyre

(Pageoph,

near y = 89 and falls monotonically to zero on either side, so that (v'O')y changes sign once, near y = 89 The mean flow feels an apparent 'heating' on one side of the channel, and 'cooling' on the other. This gives rise to an O(a 2) mean vertical velocity ~ (the asterisked terms in equation (4.13a) are in balance, with Q = 0); moreover this same ~ just satisfies the boundary condition (4.8). By continuity there must then be a mean motion across the channel, i.e. a contribution to g, in the vicinity of the layer ~ where the wave amplitude goes to zero with height. The Coriolis force associated with this O(a 2) contribution to ~ produces a contribution to 8~/8t which is generally comparable with that from the Reynolds stress divergence -(u'w')~ in equation (4.10a). Thus the 'heating' and 'cooling' on the right of equation (4.13a) turns out to be vital to a correct Eulerian description of the vertical momentum transport in this problem, just as in MATSUNO (1971). The problem for the Lagrangian-mean flow is simpler in significant respects; for one thing, there is no Lagrangian-mean flow across any of the boundaries, including the bottom one. This, together with the fact that there is also no forcing on the right of equation (4.13b), means that the Lagrangian-mean vertical velocity is negligible sufficiently far below ~. In a region of steady waves, when Q = 0, the fluid particles merely oscillate about a constant mean level, and have no systematic tendency to migrate up or down. This is no more than might be expected for adiabatic motion in stable stratification; and the Lagrangian-mean description expresses this fact more directly and naturally. Since there is no Lagrangian-mean vertical circulation linking the regions of wave generation and dissipation, and thus no 'Coriolis' contribution to the net wave-induced transport of momentum from one region to the other, the analogue, in the Lagrangian-mean momentum equation (4.10b), of the Reynolds stress in the Eulerian-mean momentum equation (4.10a), gives a more direct description of the momentum transport. This important fact was recognized intuitively by BRETHERTON(1969), and the extent to which the result carries over into exact theory is discussed in AM w It has often been assumed in the literature, for instance in connection with thermodynamical, 'heat-engine versus refrigerator' arguments, that the nonzero value of v'O' signifies a tendency for the waves to transport heat across the channel. It is clear from the foregoing that while this is true, in the sense that equation (4.13a) holds, it is also misleading. For a start, (4.13a) is not the only way of describing the heat budget. B u t more important than the theoretical description chosen is the fact, deducible by solving the problem in any correct description, that there is no tendency at all for the mean temperature actually to rise on one side and fall on the other if we are sufficiently far below ~. In the Eulerian-mean description, the adiabatic heating or cooling associated with ~ compensates the divergence of v'O'. This compensation is intrinsic to the nature of the wave motion, as is underlined by the already-mentioned consideration that individual fluid particles are not being heated or cooled below ~q' because the motion was assumed adiabatic there. In this sense, v'O' and ~ are purely artifacts of the Eulerian-mean description. (Similarly, there is nothing in the slightest

Vol. 118, 1980) Lagrangian-Mean Description of Wave, Mean-Flow Interaction

165

remarkable about v'O' in the lower stratosphere being 'countergradient'. Rather, as was noted earlier, the sign of v'O' for wave-like disturbances depends on the phase relations of the disturbance fields, i.e. on the shapes of particle trajectories, which in turn are determined by the wave dynamics and by which way the waves are propagating not by local gradients I) The right-hand half of Fig. 4 schematically indicates the profile of the mean acceleration O~/gt. If the layer ~ is shallower than the Rossby height HR, then additional contributions dR, ~R to the mean meridional circulation arise in a layer of depth HR centered on ~. These adjust the values of 90/~t and ~/gt in such a way as to keep the thermal-wind equation satisfied; there is ' r o o m ' for such a circulation only in a layer of depth HR. The vertical integral of 2 ~ R is zero; therefore the vertical integral of $g/Ot is unaffected. Further detail concerning the Eulerian-mean problem can be found in ANDREWS (1980) and in MCINTYRE (1977, w Incidentally, if we were to relax our assumption that mean time scales are long compared with (2~) -1, as might sometimes be appropriate in the transient case where the layer ~ moves upwards with velocity wg, then the ~/~t terms would become important in equations (4.11) and the mean response would no longer be confined to within a Rossby height below ~ . In such a case the response would take the form of a pattern of zonally symmetric inertio-gravity waves trailing beneath the moving layer ~. One point we have glossed over so far is the role of the right-hand side of the Lagrangian-mean continuity equation (4.14b). Being in the form of a time derivative, it is zero for the steady, conservative waves below ~ ; but in any case it turns out to be negligible everywhere in our simple problem, e) This is by no means true, however, in all problems of interest: one example is that of equatorial planetary waves. The latitudinal waveguide structure involved makes some of the derivatives on the right of equation (4.14b) important (AM w the same is true of the second derivatives on the right of the expression (4.15) for the Stokes drift, a point to be watched when checking directly that the Eulerian and Lagrangian-mean descriptions do, indeed, give equivalent answers (ibid.). Some further examples where the right-hand side of (4.14b) is i m p o r t a n t - we call this the 'divergence e f f e c t ' - a r e discussed in McIntyre (1973, 1979). A more subtle point is that it is generally necessary for the waves to be conservative as well as steady, in order for the right-hand side of equation (4.14b) to vanish exactly. If the waves are being dissipated by radiative heating and cooling, for example, the wavy material line L in Fig. 1 must be expected to become gradually less and less related to the shapes of nearby isentropic surfaces. Such temporally nonuniform behavior, which is in fact characteristic of any Lagrangian description of real fluid motion, can lead to quantities like the right-hand side of (4.14b) differing from zero even for statistically steady waves; therefore if wave dissipation and transience are both strong the theory does not unequivocally distinguish between the two. In Section -

6) The assumption that wave amplitude varies slowly in y as well as z is used here.

166

M.E. McIntyre

(Pageoph,

7 we shall mention one way of overcoming the temporally nonuniform behavior of ( )L which might prove to be of some practical importance in studies of planetary waves in the stratosphere. The nonuniformity reflects an important physical reality, being intimately bound up with the effects of the waves on the apparent large-scale diffusion of chemical tracers about the Lagrangian-mean motion (e.g. RmNES, 1977; RHIrCESand HOLLAND, 1979; MCINTYRE, 1979).

5. Conservation relations f o r wave activity: wave-action and its relatives

We are now almost in a position to see the connection between mean-flow evolution and wave dissipation, forcing or transience, in a far more general way than before- not depending on any special approximations or mean-flow profiles. This can be done (to the present accuracy, O(aZ)) via either the Eulerian-mean equations (4.10a)-(4.14a) or the Lagrangian-mean equations (4.10b)-(4.14b); but the latter route is a good deal quicker, and appears to be the only feasible route if we want to derive the further generalization to finite amplitude derived and discussed in AM and in MCINTYRE (1979). Either route depends on a fundamental conservation relation whose derivation and general significance I shall now indicate. We shall need all three components ~:', r/', ~' of the disturbance particle displacement ~'(x, t). Correct to O(a), they satisfy ~ = 0 and (with Dt = ~/~t + ~8/~x as before) Dt~'

=

v'

(5.1a)

D~' = w'

(5.1b)

Dt~' = u ~ = u' + ~ ' . V ~ = u' + n ' ~ + ~'u~,

(5.1c)

v.~' = 0

(5.2)

together with

if the fluid is incompressible. The manipulations to get the conservation equation are quite simple, and reminiscent of those involved in the familiar operation of forming a kinetic energy equation. However, instead of taking the scalar product of the momentum equation with velocity, we multiply it scalarly by - ~ ' / ~ x and average (with respect to x). It is convenient first to recast the linearized momentum equations (4.1), (4.2), (4.3) in terms of the quantity u z, which is the longitudinal disturbance velocity for the displaced fluid particle, as evidenced by the correction term ~'-V~ in equation (5.1c). We may call u z the Lagrangian disturbance velocity, correct to O(a). In vector notation with u ~ - (u z, v', w') we have, after a little manipulation in which (4.1), (4.2), (4.3) are added to g'. V{(4.10), (4.11), (4.12)} with O(a 2) terms neglected in the latter three equations,

Dtul + 2~2 x u ~ + ~q' + Vp' + ~', V(Vff) + X ~ = 0

(5.3)

Vol. 118, 1980) Lagrangian-Mean Description of Wave, Mean-Flow Interaction

167

where ~ is a unit vertical vector, and q' - - 0~ - - 0' - ~'0~ - ~'0,.

(5.4a)

The quantity q' is a measure of the departure from adiabatic motion, because it is easy to see from equation (4.4) and g'. V (4.13) that it satisfies D t q ' = Q~

(5.4b)

correct to O(a); we have defined X ~ - X' + ~'.VX and Q~ =- Q' + g'.vO.. Now

~, )

~ ' Dtu z = Dt - - ~ x ut Ox and the last term is u z Ou~/~x by (5.1c), = ~(89

&q'oxD r y ' = D ~ ( - ~ x

~'

+ uzDt -~x' = 0. Similarly v'),

~[ ~' ) e~'Ox1)~w' = L,t~--~ w' 9 Finally -2O~"a3x x u Z = - 2 ~ g ' - ~ x

x Dtg' = 2 g ' . ~ x

(

Dt Ox]

(since ~ ( ~ ' . ~ x Dtg')/Ox = O) = -2

Dt cox] "~'~ X

= Dt

(the end result being half the sum of the second and fourth expressions). Therefore (recalling (5.2)) the result of scalarly multiplying (5.3) by -0~'/c3x and averaging with respect to x is simply

Dtp+

0' ) o~ "x' + -5--fx ~ ' q '' V . - - ~ p , = -~x

(5.5)

0g' ( u l + ~ • g,). Ox

(5.6)

correct to O(a2), where P -=

Of course Dt can be replaced by 0/~t in equation (5.5), V.{ } by -O07'~p')/ay -

168

M.E. McIntyre

(Pageoph,

O(~'~p')/Oz, and 1~.~2 x ~' by -2~q~:~7/ (as in ANDREWS and MCINTYRE 1976a, equation (A15)); but I wanted to exhibit both equation (5.5), and its derivation, in a form suggestive of generalizations for other kinds of averaging. For instance if ( ) were a time average we would have scalarly multiplied equation (5.3) by O~'/Ot, and if ( ) were an ensemble average over some ensemble label a - for instance the phase of the waves if we are using either the ' r a n d o m phase' idea or the slowly-varying, 'two-timing' i d e a - t h e n we would have multiplied equation (5.3) by O~'/ba. In all these cases the foregoing derivation goes through almost word for word. In ANDREWS and MCINTYRE (1978C) it is shown that equation (5.5), with a in place of x and with right-hand side zero, reduces to BRETHERTONand GARRETT'S(1968) form of the waveaction equation under their assumption of slowly-varying, conservative waves. (This incidentally provides a simple yet general derivation of Bretherton and Garrett's equation which does not depend on using a variational p r i n c i p l e - it was previously thought that the variational approach is not only illuminating, but essential.) Thus the wave property p is closely related to the wave-action. However, since p itself arises from spatial, rather than ensemble or phase, averaging - so that conservation of p is associated with translational invariance of the mean flow - p should strictly speaking be called the pseudomomentum, following the usage established in solid-state physics. 7) In the case of slowly-varying waves, it is easy to see (ANDREWS and MCINTYRE, 1978C) that p reduces to Bretherton and Garrett's wave-action times the x component of the wavenumber, k. Coming back now to our problem of wave, mean-flow interaction with its two sub-problems (i) (waves changing mean flow), and (ii) (mean flow influencing waves), we can now see how equation (5.5) plays a role in both. For sub-problem (ii) it evidently comprises a useful tool for both calculating and describing the generation, propagation and dissipation of waves in a given mean zonal flow with arbitrary profiles ~(y, z), O(y, z). (Clearly one wants for this purpose a measure of wave activity which is conserved when the waves are not being dissipated or generated; one could then d r a w ' arrow' pictures of the flux, for instance - perhaps superposed on contours of its divergence - and thus get a direct feel for where (in the meridional (yz) domain) the waves are piling up, or being dissipated. By contrast, the divergence of the usual wave-energy flux p'v', p'w' does not indicate any such thing.) Second, equation (5.5) reveals the basic structure of the mean-flow-evolution sub-problem (i). Putting it together with the Lagrangian-mean-flow equation (4.10b) 7) The distinction between pseudomomentum and momentum, whose conservation is associated with translational invariance of the total problem, mean flow plus waves, has long been recognized in solid-state physics, and has recently proved to be the main key to unravelling the AbrahamMinkowski controversy mentioned in the introduction (PEtERLS, 1976). Surprising as it may seem, the controversy stemmed partly from a failure to recognize that translational invariance of the propagating medium is logically not the same thing as translational invariance of the total problem. Another source of confusion has been the fact that in certain special examples p turns out to be numerically equal to the mean momentum; it happens that the problem of Section 2 is one such example, in the purely transient, conservative case.

Vol. 118, 1980) Lagrangian-Mean Description of Wave, Mean-Flow Interaction

169

we see at once that the right-hand side of that equation can be written (correct, as always, to O(a2)) e p - -b-~-" ~ ' XZ - ~-~ ~ ' q'' ~-7

(5.7)

showing the dependence of the wave-induced forcing upon wave transience, dissipation, or generation (the remarks at the end of Section 4 should be borne in mind). The reason why the results come out this way is again to do with the connection between conservation relations and symmetries, as has been clearly brought out by BRETHERTON (1979) and further discussed in ANDREWS and MCINTYRE (1978C). It turns out that the result of putting equations (4.10b) and (5.5) together can, in the case of conservative waves (X, Q, q' all zero), be derived more directly by applying Kelvin's circulation theorem to a wavy line like L in Fig. 1. The most general form of this idea appears to be that expressed by Theorem I of AM for finite-amplitude waves. However, the argument is not complete without considering the complete set of mean-flow equations (after all, if we have naively forgotten about the right-hand side of equation (4.13a) in the Eulerian-mean problem - not to mention the boundary condition (4.8)- we would have got a completely wrong answer for the effective transfer of mean momentum from the boundary to the layer ~e in Fig. 4!). Nevertheless, there is not much more that need be said, because the right-hand side of equation (4.13b) is zero; and so we have to worry only about the right-hand sides of (4.11b), (4.12b), and (4.14b). The last of these is already in the form of a time derivative. The precise form of the forcing in (4.11b) and (4.12b) is not critical, because those two equations enter the problem for the rate of change of ~ and 0 only in time-differentiated form (cf. ANDREWS and MCINTYRE, 1976a, equations (5.7-8)). That is, since we are interested in solving for the mean-flow tendency at a given moment we may regard

{8~L/~t, 80L/St, ~ffL/Ot, gL, ~L}

(5.8)

as our basic set of dependent variables and take, as our basic complete set of equations, (4.10b), (4.13b) and (4.14b) together with the time derivatives of (4.1 l b) and (4.12b). The right-hand sides of the latter must necessarily take the form of time derivatives ! The foregoing arguments do not depend on any approximations based on almostplane waves or special mean-flow profiles, and demonstrate rather generally how mean-flow acceleration is linked to wave dissipation, generation, and transience, in the sense that all wave-induced forcing terms are either time derivatives, like the first term in (5.7), or explicitly involve departures from conservative motion, like the second and third terms in (5.7). A corollary of the analysis is that for steady, conservative waves there is no mean acceleration, as first shown by CHARNEY and DRAZIN (1961) for quasi-geostrophic waves; and this is sometimes called a 'noninteraction theorem'. Fundamentally speaking it should really be called a 'nonacceleration theorem', however: there is an

170

M.E. McIntyre

(Pageoph,

interaction inasmuch as the right-hand sides of equations (4.11b) and (4.12b) are

not zero when steady waves are present, and this upsets thermal-wind balance statically by O(a2). Such interactions, while not always negligible in a description of the mean flow correct to O(a2), are probably not very important in most meteorological examples; but there are other examples, such as the radiation pressure of sound waves in a box (BR~LLOUrN, 1925), the acceleration of the solar wind by Alfv6n waves (e.g. HOLLWE6, 1978), and 'parametric' transmitters in underwater acoustics, (e.g. MOFF~TT et aL, 1971), where analogous interactions are extremely important. [Note added in proof: Langmuir vortices in the oceanic mixed layer may be another such example, according to a note by S. Leibovich to appear in J. Fluid Mech.]

6. Conservation relations for wave activity: the generalized Eliassen-Palm relation The foregoing results (and various others similarly revealing basic structure in the theory of acoustic and surface gravity waves on nontrivial mean flows; see AM w leave one in no doubt that the description in terms of disturbance-associated particle displacements and Lagrangian means is absolutely fundamental from a theoretical point of view. However, it might still be asked whether the basic conservation relation, equation (5.5), could be manipulated into a form not involving the disturbance particle displacements; this would be convenient for observational studies of stratospheric wave activity, for instance. The answer appears to be ' n o ' ; however one can find a conservation relation, equation (5.5a) of ANDREWS and MCINTYRE (1976a), in which the flux, at least, does not depend on the disturbance displacements. The derivation is given in Appendix A of the same reference, in which the present equation (5.5) appears as equation (A15). The result has the form

--~ + -Zy u'v' - u~ - ~ f +

u' w ' + (ffy - 2 f2) ~ } = D.

(6.1)

Here A is a wave property equal to 19 plus a number of extra terms s) involving ~', and D is another expression involving ~' which, like the right-hand side of the present equation (5.5), is zero for conservative motion (X, Q, q' zero). The flux whose divergence appears in this equation does not involve ~'; it is the fundamental entity arising in the analysis of ELIASSENand PALM (1961). Equation (6.1) and its generalizations to spherical geometry (ANDREWS and MclNTYRE, 1976a, 1978a) may appropriately be called 'generalized Eliassen-Palm relations'. They play a role in the theory of the Eulerian-mean flow comparable to that of equation (5.5) for the Lagrangian-mean flow; and like equation (5.5) can also be used as conservation relations for wave activity. This dual role, in sub-problems (i) and (ii), of the Eliassena) A is minus the lengthy expression within heavy square brackets in equation (5.5a) of ANDREWSand MCINTYRE(1976a), with nonhydrostatic terms added; see p. 2034 of same reference.

Vol. 118, 1980) Lagrangian-Mean Description of Wave, Mean-Flow Interaction

171

Palm flux {u'v'-~v'O'/O~, u'w'+ ( f l y - 2~)v'O'/O~), suggests that it should be regarded for at least some purposes as a more fundamental diagnostic than the associated' wave-energy fluxes' also discussed by Eliassen and Palm. Meridional crosssections of the Eliassen-Palm flux and its divergence calculated from general circulation statistics are presented and discussed by EDMON et al. (1980). One question which such observational cross-sections should help to answer is the question of whether a singular (zero-wind) line for topography-linked planetary waves behaves more like an absorber (as predicted by linear theory and numerical experiment) or a reflector (as predicted by a certain class of idealized non-linear theories, e.g. STEWARTSON(1978), WARN and WARN (1978), B~LAND (1978), TVNG (1979)). Eliassen and Palm pointed out that their flux reduces to {u'v', -2~)v'O'/O~} for quasi-geostrophic waves, and it is interesting to note that in the same approximation it can be shown (e.g. from (5.5a), (5.3b) and (6.24) of ANDREWS and MCINTYRE, 1976a) that A -- ~'~' + 89

_ ~

~,

(6.2)

where 3 is the quasi-geostrophic potential vorticity. 9) The ambiguity between 'transience' a n d ' dissipation' again shows itself in the last term. For the conservative case 2 ' = - ~yV' and so equation (6.2) reduces still further to A -'- _89

(6.3)

A significant consequence is that the rate of change of density A of wave activity, in the generalized Eliassen-Palm relation, becomes the flux of quasi-geostrophic potential vorticity in the y-direction (DIr 1969; BRETnERa'ONand HAIDVOGEL, 1976), because from (6.3) and (5.1a)

~A/Ot = -.~yV'v' = v'~'. 7. The finite-amplitude theory and the temporal nonuniformity The Lagrangian-mean theory becomes even more powerful when extended to finite amplitude, and leads to what appear to be the most general forms both of the theorems on mean-flow evolution (sub-problem (i)) and of the conservation relation for wave activity (sub-problem (ii)). The most fundamental question is how to define the idea of Lagrangian-mean flow fiL and disturbance particle displacement l~'(x, t) at finite amplitude. At first sight there appears to be an infinite number of choices; but it turns out that the following definition is the one which appears to lead to the simplest general theoretical structure for finite-amplitude waves, in some ways just as simple as the O(a 2) Lagrangian-mean theory of Sections 4 and 5. Suppose that there is no disturbance anywhere at some initial time t = to. In 9) An interesting parallel can be found in equation (3.3) of MCINTYREand WEISSMAN(1978), which applies to the two-dimensional problem of Section 2 above.

172

M.E. McIntyre P (a)

AX

y, z _~/[[I\\\\\-,.,,., I g~

(c)

s--"~

(Pagcoph,

- "-_ e !'PP_)__..z//l J'[ I X':...,..c_ . Ro

"

s+~ s

Figure 5 Ways of visualizing the generalized Lagrangian-mean velocity and disturbance particle displacement for disturbances of finite amplitude (see text), after AM.

Fig. 5a, let R0 be a line parallel to the x axis. Fix attention on a row of marked particles which are initially spaced at equal distances Ax along R0, and then watch these particles as they follow the fluid motion. We now refer to a mechanical analogy (which has no dynamical connection with the fluid motion) in which we imagine that a thin, light, rigid rod R initially coincides with R0, but is subsequently free to move while remaining parallel to the x-axis. The position P of a typical particle of fluid whose initial position was P0 is joined to the point PR on R which initially coincided with Po ; the ligaments joining the marked particles to R consist of identical ' elastic bands' such that PR is pulled towards P with a force proportional to the distance PaP, and similarly for the other points. The rod R is imagined to be in static equilibrium under the pull of all the ligaments. Then, in the limit Ax --~ 0, the velocity with which the rod moves is defined to be fiT,; and if x is the current position of P~, g'(x, t) is defined to be the 'elastic-band vector' ps It turns out (see (7.1) below) that fiL is exactly equal to the velocity of the center of mass of a thin tube of fluid initially lying in the x-direction (Fig. 5b). This result was conjectured by MATSUNO (personal communication) on the basis of a calculation for small disturbance amplitude. A corollary of Matsuno's remark is that the vertical Stokes drift ~L _ ~ gives a direct measure of the rate of change of disturbance available potential energy; and this too, is given the status of an exact result by the finite-amplitude theory. The foregoing gives the generalized Lagrangian-mean operator ( )L corresponding to a spatial (longitudinal or zonal) Eulerian mean; the G L M operators corresponding to the time, ensemble or two-timing varieties of Eulerian averaging operators are defined in AM, where the theory is developed in a form which covers all these cases lo) For the corresponding analogy for zonal averaging on the sphere, see

MCINTYRE, 1979, w

Vol. 118, 1980) Lagrangian-Mean Description of Wave, Mean-Flow Interaction

173

at once. Once we possess definitions of ~'(x, t) and fi~'(x, t), we can easily derive finite-amplitude analogues of equation (5.5) which are analytically almost as simple, and lead to much the same consequences, as before. (Full details are given in ANDREWS and MCINTYRE, 1978c.) It should be noted that although the operator ( )L involves averaging along the curve C the average is not uniformly weighted with respect to arc length s along C. The weighting of the average along C can be expressed in terms of the non-uniform thickness of the tube corresponding to C in Fig. 5b, or more accurately in terms of the mass per unit length of the tube, if we want to include the case of fully compressible flow. This is because mass per unit length of C in Fig. 5b is just proportional to number of particles per unit length of C in Fig. 5a, in the limit Ax --~ 0. Thus if d V is an element of volume of the tube C, so that p d V is an element of mass, then the G L M of any quantity ~b(x, t) may be defined as

= fc +pdv/fc

p dV,

(7.1)

in the limit of small tube cross-section (AM w As MATSUNO (1980) and MCINTYRE (1979) both explain, the nonuniform weighting is essential if ( )L is to correspond to Stokes' original concept of Lagrangian averaging when the latter is approximately applicable. The definition (7.1) can be used as it stands for taking averages on a sphere, provided that the quantity q~ being averaged is a scalar. When it is a vector or a tensor, further discussion is needed (MCINTYRE, 1979, w The relation (7.1) is also very suggestive of how to define a 'modified G L M ' independent of initial conditions and therefore not subject to the temporally nonuniform behavior noted at the end of Section 4. This could be a matter of the greatest importance for using the theory to describe the long-term behavior of pollutants and planetary-wave activity in the stratosphere. The idea arose during conversations with T. Dunkerton. Consider a hypothetical motion in which X and Q are zero, for all time, so that the motion is conservative (and has been ever since the initial state of no disturbance). Then, since entropy S and potential vorticity P are both constant following this hypothetical motion, we could have defined our thin material tube C to be a tube bounded by surfaces of constant S and S + AS, and P and P + Ap. (The tube would then have a cross-section approximately in the form of a parallelogram, as suggested in Fig. 5 c - except in the singular case where S and P surfaces coincide.) Now in the real stratosphere S and P are not constant following the motion, because of radiative-photochemical effects and turbulent dissipation; but we could still define a 'modified G L M operator' by (7.1) with the tube C still marked out by the S and P surfaces, 'knowing that the modified G L M theory would have the same mathematical structure as the theory described in AM, apart from the dissipative effects. This effectively provides a continuous re-initialization which eliminates the temporal nonuniformity and expresses the distinction between wave transience and dissipation in an intuitively more satisfactory way.

174

M.E. McIntyre

(Pageoph,

On the other hand the topology of such ' S P tubes' could become complicated during strong disturbances. In studies of individual disturbed episodes it may prove better to use the S P tubes to initialize the (unmodified) G L M theory, during a less disturbed state preceding the episode in question (DUNKERTON, 1979). Whatever procedure is adopted, it will necessarily have to cope in one way or another with the fact that nonuniform behavior in time is a basic feature, in practice, of a description of real fluid motion using Lagrangian ideas in any form. The detailed study of this temporal nonuniformity, and the associated dispersal of fluid particles, is sure to play a key role in understanding exactly how the various 'nonacceleration' and 'nontransport' constraints are broken by real, large-amplitude stratospheric motions.

Acknowledgements

It is a pleasure to thank D. G. Andrews, T. Dunkerton, A. Eliassen, I. Held, B. J. Hoskins, C.-P. Hsu, R. S. Lindzen, J. Mahlman, T. Matsuno and A. Plumb for stimulating discussions or correspondence on some of this material.

REFERENCES ANDREWS,D. G. (1980), On the mean motion induced by transient inertio-gravity waves, Pure and Applied Geophys. 118, 177-188. ANDREWS,D. G. and MCIr~TYRE,M. E. (1976a), Planetary waves in horizontal and vertical shear: the generalized Eliassen-Palm relation and the mean zonal acceleration, J. Atmos. Sci. 33, 2031-2048. ANDREWS,D. G. and MCINTYRE,M. E. (1976b), Planetary waves in horizontal and vertical shear: asymptotic theory for equatorial waves in weak shear, J. Atmos. Sci. 33, 2049-2053. ANDREWS,D. G. and MCINTYRE,M. E. (1978a), Generalized Eliassen-Palm and Charney-Drazin theorems for waves on axisymmetric flows in compressible atmospheres, J. Atmos. Sci. 35, 175185. ANDREWS,D. G. and MClNTYRE,M. E. (1978b), An exact theory o f non-linear waves on a Lagrangian-mean flow, J. Fluid Mech. 89, 609-646. ANDREWS,D. G. and MCINTVRE,M. E. (1978c), On wave-action and its relatives, J. Fluid Mech. 89, 647-664. B~LAND, M. (1978), The evolution o f a nonlinear Rossby wave critical level: effects o f viscosity, J. Atmos. Sci. 35, 1802-1815. BOVD, J. (1976), The noninteraction o f waves with the zonally-averaged flow on a spherical Earth and the interrelationships o f eddy fluxes o f energy, heat and momentum, J. Atmos. Sci. 33, 2285-2291. BRETHERTON,F. P. (1969), Momentum transport by gravity waves, Quart. J. Roy. Meteor. Soc. 95, 213-243. BRETHERTON,F. P. (1971), The general linearized theory o f wave propagation, w Lectures in Applied Mathematics (American Math. Soc.), 13, 61-102. BRETHERTON, F. P. (1979), Conservation o f wave action and angular momentum in a spherical atmosphere, J. Fluid Mech. (to appear). BRETHERTON,F. P. and GARRETT,C. J. R. (1968), Wavetrains in inhomogeneous moving media, Proc. Roy. Soc. A 302, 529-554.

Vol. 118, 1980)

Lagrangian-Mean Description of Wave, Mean-Flow Interaction

175

BRETHERTON, F. P. and HAIl)VOGEL, D. B. (1976), Two-dimensional turbulence above topography. J. Fluid Mech, 78, 129-154. BRILLOUIN, L. (1925), On radiation stresses (in French), Annales de Physique 4, 528-586. BRILLOtrIN, L. (1936), Radiation pressures and stresses (in French), Revue d'Acoustique 5, 99-111. See also BRILLOUIN, L., Tensors in mechanics and elasticity. (Academic - New York 1964). CHARNEY, J. G. and DRAZlN, P. G. (1961), Propagation of planetary-scale disturbances from the lower into the upper atmosphere, J. Geophys. Res. 66, 83-109. DANIELSEN, E. F. (1968), Stratospheric-tropospheric exchange based on radioactivity, ozone and potential vorticity, J. Atmos. Sci., 25, 502-518. DEWAR, R. L. (1970), Interaction between hydromagnetic waves and a time-dependent inhomogeneous medium, Phys. Fluids 13, 2710-2720. DICKINSON, R. E. (1969), Theory of planetary wave-zonal flow interaction, J. Atmos. Sci. 26, 73-81. DUNKERTON, T. (1978), On the mean meridional mass motions of the stratosphere and mesosphere, J. Atmos. Sci. 35, 2325-2333. DUNKEgTON, T. (1979a), On the role of the Kelvin wave in the westerly phase of the semiannual zonal wind oscillation, J. Atmos. Sci. 36, 32-41. DUNKERTON, T. (1979b), Lagrangian-mean theory of wave, mean-flow interaction, with applications to non-acceleration and its breakdown, Revs. Geophys. and Space Phys. (submitted). ECKART, C. (1963), Some transformations of the hydrodynamic equations, Phys. Fluids 6, 1037i04l. EDMON, H. J., HOSKINS, B. J. and MCINTYRE, M. E. (1980), Meridional cross-sections of the Eliassen-Palm flux and its divergence, J. Atmos. Sci. (to be submitted). ELIASSEN, A. and PALM, E. (1961), On the transfer of energy in stationary mountain waves, Geofys. Publ. 22, 3, 1-23. FEES, S. B. and LINDZEr,r, R. S. (1974), The interaction of thermally excited gravity waves with'mean flows, Geophys. Fluid Dyn. 6, 149-191. FRIEMAN, E. and ROTENBERG, M. (1960), On hydromagnetic stability of stationary equilibria, Revs. Mod. Phys. 32, 898-902. GRIMSHAW, R. H. J. (1975), Nonlinear internal gravity waves in a rotating fluid, J. Fluid Mech. 71, 497-512. HAYES, W. D. (1970), Conservation of action andmodal wave action, Proc. Roy. Soc. A 320, 187-208. HOLLWEG, J. V. (1978), Some physical processes in the solar wind, Revs. Geophys. and Space Phys. 16, 689-720. HOL'rON, J. R. (1974), Forcing of mean flows by stationary waves, J. Atmos. Sci. 31, 942-945. HOLTON, J. R. (1975), The dynamic meteorology of the stratosphere and mesosphere, Boston, Massachusetts, American Meteorological Society, 218 pp. HOLTON, J. R. and DUNKERTON,T. (1978), On the role of wave transience and dissipation in stratospheric mean flow vacillations, J. Atmos. Sci. 35, 740-744. HOLTON, J. R. and LINDZEN, R. S. (1972), An updated theory for the quasi-biennial cycle of the tropical stratosphere, J. Atmos. Sci. 29, 1076-1080. HOLTON, J. R. and MASS, C. (1976), Stratospheric vacillation cycles, J. Atmos. Sci. 33, 2218-2225. KRISnNAMURTk Y. N. (1961), The subtropical jet stream of winter, J. Meteorol. 18, 172-191. LIGHTHILL, M. J. (1978), Acoustic streaming, J. Sound Vib. 61, 391-418. MAHLMAN, J. D. (1969), Heat balance and mean meridional circulations in the polar stratosphere during the sudden warming of January 1958, Mon. Wea. Rev. 97, 534-540. MATSUNO, T. (t971), A dynamical model of the stratospheric sudden warming, J. Atraos. Sci. 28, 1479-1494. MATSUNO, T. (1980), Lagrangian motion of air parcels in the stratosphere in the presence of planetary waves, Pure and Applied Geophys. 118, 189-216. MCINTYRE, M. E. (1973), Mean motions and impulse of a guided internal gravity wave packet, J. Fluid Mech. 60, 801-811. MCINTYRE, M. E. (1977), Wave transport in stratified, rotating fluids. Springer Lecture Notes in Physics, 71, 29~314 (ed. E. A. Spiegel and J. P. Zahn). (The statement on p. 303 line 27 is wrong; but see eq. (5.2) on p. 311.)

176

M.E. McIntyre

MCINTYRE, M. E. (1979), Towards a Lagrangian-mean description of stratospheric circulations and chemical transports, Phil. Trans. Roy. Soc. London A, to appear (Middle Atmosphere issue). MCINTYRE,M. E. and WEISSMAN,i . A. (1978), On radiating instabilities and resonant over-reflection, J. Atmos. Sci. 35, 1190-1196. MOFFETT, i . B., WESTERVELT,P. J. and BEYER,R. T. (1971), Large-amplitude pulse propagation a transient effect. II, J. Acoust. Soc. Amer. 49, 339-343. PEIERLS, R. (1976), The momentum of light in a refracting medium, Proc. Roy. Soc. A 347, 475-491. PLUMB,R. A. (1975), Momentum transport by the thermal tide in the stratosphere of Venus, Quart. J. Roy. Met. Soc. 101, 763-776. PLUMB, R. A. (1977), The interaction of two internal waves with the mean flow: implications for the theory of the quasi-biennial oscillation, J. Atmos. Sci. 34, 1847-1858. PLUMB, R. A. and McEWAN, A. D. (1978), The instability of a forced standing wave in a viscous, stratified fluid: A laboratory analogue o f the quasi-biennial oscillation, J. Atmos. Sci. 35, 18271839. RHINES, P. B. (1977), The dynamics of unsteady currents, in The Sea: Ideas and Observations on Progress in the Study of the Seas, Vol. 6, 189-318 (ed. E. D. Goldberg). RHINES, P. B. and HOLLAND, W. R. (1979), A theoretical discussion of eddy-driven mean flows, Dyn. Atmos. Oceans (to appear). RIEHL, H. and FULTZ,D. (1957), Jet stream and long waves in a steady rotating-dishpan experiment: structure of the circulation, Quart. J. Roy. Meteorol. Soc. 83, 215-231. SOWARD, A. M. (1972), A kinematic theory of large magnetic Reynolds number dynamos, Phil. Trans. Roy. Soc. A, 272, 431-462. STEWARTSON,K. (1978), The evolution of the critical layer of a Rossby wave, Geophys. Astrophys. Fluid Dyn. 9, 185-200. TUNG, K. K. (1979), A theory of stationary long waves. Part III: Quasi-normal modes in singular wave-guide, J. Atmos. Sci. 36 (to appear). URYU, M. (1980), Acceleration of mean zonalflows by planetary waves, Pure and Applied Geophys., 118, 661-693. WARN, T. and WARN, H. (1978), The evolution of a nonlinear critical level, Studies in App]. Math. 59, 37-71. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh~iuser Verlag, Basel

On the Mean Motion Induced by Transient Inertio-Gravity Waves By D. G. ANDREWS 1)

Abstract - Using standard 'two-scaling' techniques we calculate the Eulerian- and Lagrangianmean flows induced at Second order in amplitude by small-amplitude, transient, non-dissipative, vertically-propagating inertio-gravity waves on an f-plane. The example is an idealized one, but illustrates a number of important features that are typical of wave, mean-flow interaction in a rotating, stratified fluid. Physical discussion of the solution is given in Section 4 of the review by MCINTYRE(1980), which appears elsewhere in this issue.

Key words: Inertio-gravity waves; Stokes drift; Lagrangian-mean flow. 1. Introduction

In two recent review articles, MCINTYRE (1977, 1980) has discussed general aspects of the theory o f Eulerian- and Lagrangian-mean motions forced by waves in fluids. He gave particular attention to the geophysically important case of a rotating, stratified fluid, and illustrated a n u m b e r of significant features o f the theory by reference to a simple but relevant idealized model - that o f the mean flow forced by transient, non-dissipative, vertically-propagating inertio-gravity waves. A l t h o u g h a qualitative physical description o f the solution was given by McIntyre, it was felt worthwhile to publish a brief outline o f the calculations involved, since it might be time-consuming for the reader to reconstruct them. We therefore supply the mathematical details in this note; physical discussion and interpretation are kept to a minimum, since these aspects are covered in some depth in the above-mentioned reviews. 2. Formulation

We consider an inviscid diffusionless fluid of constant b u o y a n c y frequency N, rotating about the z-axis with constant angular velocity f2 = 0f. The fluid is contained in a channel, between rigid vertical walls at y -- 0, b, and a moving lower b o u n d a r y z = h(x, y, t); it is unbounded above (as z--~ m) and as x---~ + oo. The equations o f motion are taken to be Du D---[ - f v

+ Px = O,

(2.1a)

1) Department of Meteorology, MIT, Cambridge, Massachusetts 02139, USA. Current affiliation: Geophysical Fluid Dynamics Program, Princeton University, Princeton, New Jersey 08540, USA.

178

D . G . Andrews

(Pageoph,

=-= + f u + pu = 0, Dt

(2.1b)

Dw D---7 - 0 + p~ = 0,

(2.1c)

DO D---t + N2w = 0,

(2.1d)

u,: + v u + w~ = 0,

(2.1e)

where u - (u, v, w) is the velocity, 0 is the b u o y a n c y acceleration and p the departure of the pressure f r o m the hydrostatic reference value; the reference density is normalized to unity and D / D t - O/~t + u. V, the material derivative. The b o u n d a r y conditions on the sidewalls are v = 0

on

y = 0, b,

(2.2a)

and on the lower b o u n d a r y Dh w = D----/

on

z = h(x, y, t).

(2.2b)

The upper b o u n d a r y condition is that disturbances vanish as z - + oo at finite times, and the initial state is one of rest, relative to the rotating frame of reference.

3. The amplitude expansion We suppose that at t = 0 a moving topographic disturbance, h, of small amplitude, is switched on; the amplitude is measured by the dimensionless p a r a m e t e r a, where a << 1. Each flow quantity, ( ) , is separated in the usual way into an x-averaged (Eulerian-mean) part, ( ) , and a disturbance part, ( )'. h is chosen such that = 0,

h = h' = O(a);

(3.1)

we then find that each disturbance quantity is O(a) and each mean quantity is O(a~); for example u' = O(a),

~ = O(a2).

(3.2)

At O(a), equations (2.1) linearize to u[ -- fv' + p'~ = 0 ,

(3.3a)

v; + fu' + p'~ = 0 ,

(3.3b)

w ~ - O' +p'~ = 0 ,

(3.3c)

O~ + N2w ' = O,

(3.3d)

Vol. 118, 1980) On the Mean Motion Induced by Transient Inertio-Gravity Waves !

t

t

179 (3.3e)

Ux + Vu + Wz --- O,

and the b o u n d a r y conditions give v' = 0

at

(3.4a)

z = 0,

(3.4b)

on

w' = h~

( )'-~0

y = 0, b,

z-+~

as

(t < ~ ) ;

(3.4c)

the initial condition is that all Eulerian disturbances vanish: ()'=0

for

t<0.

(3.4d)

Correct to O(a2), the x-averaged Eulerian-mean versions of (2.1) are

u t - f v = - ( u v ) ~ - (uw)~, !

vt + f u + f i u = - ( v ~

-

t

t2

t

~'

(3.5a)

)~ - ( v w ) z ,

t

(3.5b)

(w'2L,

(3.5c)

!

~ + p~ = - ( w ' v ' L

-

Ot + N 2 ~ = -(0--7-~)~, - (O'w')~,

(3.5d) (3.5e)

vv + w~ = O.

The O(a 2) m e a n sidewall b o u n d a r y conditions are 9= 0

on

y=

0, b;

(3.6a)

Taylor expansion about z = 0 of the full lower b o u n d a r y condition (2.2b) gives, to O(a2), + h'w'~ = u'h" + v'h'~

on z = 0,

or, using (3.3e) and a little manipulation, = (v'h')u

on z = 0,

(3.6b)

again to O(a2). In general, ~ does not vanish on z = 0; for a physical interpretation of this fact see the accompanying paper by MCIYTYRE (1980). Sufficient upper b o u n d a r y conditions are w, p -+ 0

as

z -+ ~ (t < ~ ) ,

(3.6c)

and initial conditions require that all O(a 2) mean quantities vanish for t < 0.

4. A model p r o b l e m (a) The linearized wave f i e l d

We now choose a particular form ofh(x, y, t) that will permit a simple approximate analytical solution of the linearized equations (3.3), (3.4); this solution represents a transient field of vertically-propagating inertio-gravity waves. Moreover, when this

180

(Pageoph

D . G . Andrews

0,T,l

F, /1

~b o Figure 1 (a) The function G(T) that describes the slow time-modulation of the topography; it starts from zero at T = t = 0, increases smoothly to unity by T = To, and remains constant thereafter. Here To = 2~r~o-1, corresponding to an actual time to = 2rrco-l/z-1, which is much greater than N-1 and f - 1, by (4.6). (b) The cross-channel modulation of the topography, which vanishes at the sidewalls Y = 0, /~b (where b ~ 2~rk-~t, -1) and attains a maximum value aho in mid-channel, h0 being some suitable height scale. o

~o

~

wave solution is substituted into the right o f the Eulerian-mean equations (3.5), (3.6), we shall have no difficulty in finding a corresponding approximate solution o f the latter, representing the forced O(a 2) Eulerian-mean flow. The specific f o r m o f h to be used is h = h' = F ( Y ) G ( T ) c o s ( k x - ~ot)

(4.1)

where T = - tzt,

Y-

fly,

if<< 1.

H e r e / z is a 'two-scaling' or ' W K B ' parameter and T and Y represent 'slow t i m e ' and 'slow length' variables, respectively; F and G are smoothly varying functions, and are depicted schematically in Fig. 1. k is the wavenumber and o~ the frequency o f the sinusoidal topographic corrugations, which move with phase speed c = ~o/k. The amplitude o f the corrugations grows slowly (i.e., on a time-scale to = 2rro~-lff - 1 or a 'slow t i m e ' scale To = 2~roJ-1) f r o m a zero initial value, as described by the function G(T). Use o f a ' m o l l i f i e r ' o f this kind is a standard device that allows us to solve an approximate, but self-consistent, initial-value problem without introducing physically u n i m p o r t a n t transient oscillations. The slow cross-channel variation F ( Y ) is also chosen for mathematical expediency; ' r a p i d ' y-variation (on scales O(2rrk- 1)) would greatly lengthen the subsequent algebra without adding any physical content to the solutions. N o t e that F is taken to be formally O(a) and G to be O(1). Substituting (4.1) into the linearized lower b o u n d a r y condition (3.4b), we find w' = - Re io~FG e~(ex-~t)[1 + O(ff)]

on z = 0,

(4.2)

where the error term arises from the fact that a~ [G(T) e_~t] = ( , i o J G + t~Gr)e -'~t.

(4.3)

Vol. 118, 1980) On the Mean Motion Induced by Transient Inertio-Gravity Waves

181

Motivated by the boundary condition (4.2) we seek solutions to the linearized equations (3.3) of the form (u', d, w', p', O'} = Re {~, 8, ff~,p, 0}F(Y) e~*[1 + O(/,)1,

(4.4)

where the phase r = kx+mz-oat,

m is a vertical wavenumber and the complex amplitudes {~. . . . } are functions only of T and a ' slow height' variable Z-/,z. Such a height variation of the wave amplitude is to be expected intuitively from group velocity considerations, and its self-consistency will be verified below. Note that v' in (4.4) automatically satisfies the sidewall conditions (3.4a), since F = 0 at Y = 0, /xb. At zeroth order in/z we can neglect Y-, Z- and T-derivatives and the O(t*) corrections in (4.4), and make the following identifications in the linearized equations (3.3): ~t = -ioJ,

~,: = ik,

~ = im.

We readily obtain the amplitude functions io) a = - f O,

iwk f m ~'

ff~ -

1~ =

i(N2 - ~ fm 2

0 -

N2k f m ~'

(4.5)

and the dispersion relation oa2 = ( N 2 k ~ + f Z m 2 ) / ( k 2 + m2).

(4.6)

The latter gives Imt as a function of oa and k; the sign of m will be determined below. Note that (4.5) and (4.6) are formally identical to the corresponding relations for yindependent inertio-gravity waves; equation (4.4) shows that the y-variation is trivial, at leading order in/z, with each wave quantity being proportional to the local value of the topographic amplitude factor F(Y). Equation (4.6) also shows that 0)2 must lie between f 2 and N 2 if propagation (m real) is to occur. The boundary condition (4.2), together with the second of (4.5), gives ~(Z = O, T ) = J~k G(T).

(4.7)

One could now proceed to find the (Z, T) dependence of z3, etc. for Z > 0. This would necessitate going to O(/*) in equations (3.3), using relations like (4.3); a calculation of this kind was carried out by ANDREWSand MCINTYRE (1976b), for equatorial waves. However, for present purposes, namely the calculation of the 'wave forcing' terms on the right of the O(a 2) mean equations (3.5), (3.6b), this rather lengthy procedure is unnecessary, since it turns out that we shall need the (Z, T)-dependence

182

D.G. Andrews

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of [1312(or, equivalently of the quantity E t o be defined in (4.10)), but not the (Z, T)dependence of the phase of z3. Moreover the wave-forcing terms in (3.5) and (3.6b) can be evaluated, to leading order in/z, from the O(al~ ~ solutions (4.5) alone, in the present inertio-gravity wave example. This contrasts with the equatorial wave case, where ill-conditioning of u'v' necessitated the calculation of the O(t~) corrections to u' and v', or the use of a 'generalized Eliassen-Palm relation' (cf. ANDREWS and MCINTYRE, 1976a,b; MCINTYRE, 1980). We therefore proceed as follows: first, a wave-energy equation is derived from the linearized equations (3.3) in the usual manner; it is 89 '2 + v '2 + w '2 + O'2/N2)t + (p'v')u + ( p ' w ' ) , = 0.

(4.8)

(Note that in the presence of an O(a ~ basic shear flow, extra terms, involving interaction of the waves and the mean flow, would appear.) The averaged quantities in (4.8) are then expressed in terms of [~3[2, using (4.4), (4.5), (4.6), and identities like p ' w ' = 89Re {/~ff:*}V2.

(4.9)

To leading order in tL we find the wave-energy density E - 89 '2 + v '--'g + w "--g + O'2--/N2) = ~

+ m2) [~(Z, T ) I 2 F 2 ( Y ) , 2f2m 2

(4.10)

and the wave-energy fluxes (4.11)

p' v' = O(t~a2), p'w' =

oak~(N 2 _ f 2 ) . ]z3(Z, T)I2F2(Y). 2 f ~ m ( k = 7 m 2)

(4.12)

If we now define mk2(N 2 f2) o4k2 + m2)2 , _

co = p ' w ' / E =

(4.13)

the equality on the right following from (4.10) and (4.12), we can substitute (4.10)(4.13) into (4.8) and use the facts that cg is independent of Z and that averaged quantities depend only on ( Y, Z, T) to obtain ~E OE ~--~ + r = O(Ixa2)

(4.14)

E = E ( T - Z/cg, Y),

(4.15)

which has the solution

to leading order in t~. (Note, incidentally, that in the presence of a basic O(a ~ shear flow, (4.14) must be replaced by an equation expressing conservation of wave-action; cf. BRETHERTONand GARRETT, 1968.) Using the dispersion relation (4.6) we can verify that % as defined by (4.13),

Vol. 118, 1980)

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183

Z

%T

% ( r - To 1

Eo Figure 2 The vertical distribution of the wave-energy density E ( T - Z/co, Y ) for T > To and fixed Y. In the region 0 < Z < co(T - To), E is independent of Z, taking the value Eo = 89 2 + m2)F~(Y). In the upward-moving 'precursor' .~a (the region G ( T - To) < Z < coT, where the waves are transient) E decreases smoothly from Eo to zero ; it remains zero for Z > coT.

satisfies

cg = 8~/8m, which is the usual definition of the vertical component of group velocity. Thus (4.15) verifies that the wave-energy propagates with the group velocity, as expected, from general arguments, in the absence of a basic mean shear flow. The upper boundary condition (3.4c) is satisfied by choosing the sign of m such that c~ > 0; in particular if N 2 > F , as is usually appropriate for the atmosphere or ocean, we have sgn m = - sgn o~,

(4.16)

from (4.13). It is clear from (4.10) and (4.15) that ]~12 is a function of (T - Z/cg) only; we therefore apply the lower boundary condition (4.7) to relate E to F and G:

E(T-

Z/cg, Y) = 89

2 + m~)F~(Y)G2(T- Z/cg).

(4.17)

The vertical distribution of E is depicted in Fig. 2; we have the following approximate, but self-consistent, picture of the field of inertio-gravity waves: at large times the waves are steady except in a 'precursor' region 56', which propagates upwards with speed G; above 5e no waves are present. The wave amplitude varies slowly with y, and vanishes at the sidewalls.

(b) The O(a 2) Eulerian-mean flow To solve for the O(a 2) Eulerian-mean flow forced by the waves we must substitute the wave solutions, as calculated above, in the forcing terms on the right of (3.5) and (3.6). Under the assumption tL << 1 it transpires that only three of these terms need

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to be calculated explicitly; they are, to leading order in/~, u'w' =

kmE kZ + mZ.

O'v ; =

N2f

(4.18)

kmE

co2 k2 + m2

(4.19)

and v'h'

-

-

z=0

f kmE]z=o = __ o~Z'k2 + m z =

O'v' z=0

Nz

(4.20)

These are obtained from the wave solutions (4.4), (4.5); in (4.18) and (4.19) we invoke (4.10), and in (4.20) we use (4.7), (4. I0), (4.17) and (4.19). Only the orders o f magnitude of the other wave-forcing terms are required, namely u'v'=

O(iza2),

v 'z = O(a2),

w' v'

O(~a2),

O'w' = O(t~aZ).

w '2 = O(a2),~

(4.21)

We now look for solutions {~, o, w, p, 0} of the Eulerian-mean equations which are functions of (Y, Z, T) only; using (4.21) in (3.5) we obtain ~ur - f ~ = - tz(u'w')z + O(IzZaZ),

(4.22a)

tz~r + f ~ + ~py = O(tza2),

(4.22b)

t~r -

(4.22c)

0 + t~pz = O(t,a2),

t~Or + N 2 ~ = -tz(O' v')y + 0(l~2a2),

/~gr + / Z ~ z = O.

(4.22d) (4.22e)

It is convenient to introduce a mean streamfunction ~ such that = -/Z~z,

~ = tz~r.

(4.23a,b)

We n o w take f S z (4.22a) - tz az8 r (4.22b) + / ~ ay~r (4.22c) + ~3r (4.22d)

and use (4.23) to get N2~rY + f 2 ~ z z

--

[ f ( U ~ W r) z z + (O'vr)yy],

(4.24)

at leading order in/z. The upper b o u n d a r y condition (3.6c) requires that ~ become constant at great heights; this constant m a y be set to zero, so -+ 0

as

Z ~ ~

(T < ~ ) ;

(4.25a)

integrating the sidewall conditions (3.6a) down from Z = ~ , using (4.23a), we find = 0

on

Y = O,

t~b,

(4.25b)

and similarly, using (3.4a), (3.6b), (4.20) and (4.23b) = - O'v'/N 2

on

Z = O.

(4.25c)

Vol. 118, 1980) On the Mean Motion Induced by Transient Inertio-Gravity Waves

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Equations (4.24) and (4.25) constitute an elliptic problem for ~, which can easily be solved, given the forcing terms on the right of (4.24) and (4.25c). However, it is convenient first to make the boundary conditions homogeneous by introducing the variable ~*, defined by (4.26)

~b* = 4 ' + O'v'/N2

(cf. ANDREWS and MClNTYRE, 1976a [equations (3.2)] and BoYo, 1976); a physical interpretation of ~* will be given in Section 5. Equations (4.24)-(4.26) now yield N 2 ~ * r + f2~b*z = - f [ u ' w '

~* = 0

on

- fO'v'/N2]zz,

Y = 0, t~b, and at Z = 0, oo.

(4.27) (4.28)

Using (4.6), (4.13), (4.18), and (4.19) we find (4.29)

u'w' - f O ' v ' / N 2 = Ecg/c;

the expression on the left is the vertical component of the Eliassen-Palm flux (ANDREWS and MCINTYRE, 1976a [equation (3.3b)]), correct to O(a2). We now define 6(Y, Z, T) to be the (unique) solution of the elliptic problem

= 0

N2~yu q- f 2 6 z z = --fET/ccg,

(4.30)

on

(4.31)

Y = 0,/zb,

and at Z = 0, oo.

Using (4.14), (4.27) and (4.29) it is then seen that ~* = ~r.

(4.32)

Now the forcing on the right of (4.30) is non-zero only in the precursor region L(' (Fig. 2), where E varies with time. Since the boundary conditions (4.31) are homogeneous we therefore know, from the general properties of Poisson's equation, that (and hence ~*) is significantly different from zero only within a vertical distance or

A Z ~ t~fb/N

A z ~ f b / N =- H~

of s where HR is the Rossby height. We denote this region of significant v by R: see Fig. 3. Note incidentally that if we were also to assume that s is deep compared to HR (cf. URYU, 1974; MCINTYRE, 1980) then R would essentially coincide with 2 ~. We now define - fkm 7 - , o 2 ( k 2 + m2) '

(4.33)

O'v'/N 2 = ~,E;

(4.34)

so that (4.19) becomes

then (4.23), (4.26) and (4.32) give g = 1~TEz - tZjzr,

=

_ izTEy

+

Iz~rT.

(4.35a,b)

186

D. G. Andrews (a)

7

(Pageoph, (b)

2

Figure 3

Schematic diagram of contours of (a) Er and (b) # in the YZ plane, for the case where .s is shallower than a Rossby height. ET is confined entirely to the precursor region L,e,and ~ almost entirely to the region R, which straddles .La and has a vertical scale given by the Rossby height (see text).

For definiteness we choose e > 0, corresponding to boundary corrugations propagating in the positive x-direction; then (4.16)implies that ~, > 0 O f f > 0 ) a n d it can be verified that the waves force an Eulerian-mean meridional circulation (9, ~) in the sense shown on the left of Fig. 4 of MCINTYRE (1980). It should be noted that this Eulerian-mean circulation extends all the way from R to the lower boundary Z = 0; moreover ~ is generally non-zero on the latter, in accordance with the boundary condition (3.6b). We now calculate ff in terms of ~; this can be done by using (4.23a) and (4.26) to eliminate g from (4.22a), and then using (4.29), (4.32) and (4.14); we get fir = ET/c - f ~

or, integrating in T and using the initial condition of no disturbance, ff = E / c - f 6 z .

(4.36)

The presence of ~z here shows that mean accelerations take place not only in the region ca, where the waves are transient, but also in the generally larger region R, as indicated on the right of Fig. 4 of MclNTYRE (1980). Note that in this problem the mean m o m e n t u m ff is not identical to the pseudomomentum, which here equals E/c; see MCINTYRE (t977, 1980). It is straightforward to calculate 0 and fi, also; we omit the details, but remark that 0 = - N2~y and/~ = O(/~- Za2). It should be emphasized that we have been able to give a qualitative description of the O(a 2) Eulerian-mean flow without actually solving equation (4.30) for ~. However, if quantitative answers were required, we would have to specify the precise forms of F ( Y ) and G(T), which would imply E, by (4.17), and thence the forcing term in (4.30).

Vol. 118, 1980) On the Mean Motion Induced by Transient Inertio-Gravity Waves

187

5. Particle displacements, Stokes drifts, and the Lagrangian-mean meridional circulation We define a particle displacement function g' = (~:', ~7', ~'), correct to O(a), by g~ = u,t .

(5.1)

V.~' = 0 .

(5.2)

from (3.3e) and (3.4d) it follows that

The Lagrangian-mean meridional velocity (gL, ~L) and the corresponding Stokes drift (~s, ~s) are given by

(~',, ~ ' ) = (~, ~) + (~, ~ ) = (~, ~) + ~'. v(v', w'),

(5.3)

correct to O(a2). Using (5.2), ~(--) = O, and then (5.1), we obtain

~ = v.(g'v') = (~'v'L + (~'v')~ = ~1~ ,~j~ + (~,v,)~,

(5.4a)

~

(5.4b)

= v.(g'w') = (~'w'L + (~'w3~ = (~'w% + 89

Definitions (5.1) and (5.3) are approximate versions of the exact expressions given by ANDREWS and MCINTYRE (1978), and are valid for small-amplitude waves on an O(a 2) mean flow. They are formally similar to the definitions of LONGUET-HIGGINS (1969) ; see also MCINTYRE (1980, equation (4.15)). By analogy with (4.4) we let (~', ~'} = Re {i, ()F(Y) e'r

+ O(/Q],

(5.5)

where (i, ~} depend on (Z, T). From (5.1) and (4.5) it follows that = i~/co,

~ = i~/co = k~/fm,

(5.6)

to leading order in tz. Putting 13 = 1~3[e% we get W' =

[~lFsi n (~ + =),

~,

k IOlFcos (• + =),

(5.7)

so that to leading order in a and/z the projection in the meridional plane of the orbit of a fluid particle is an ellipse, with vertical and horizontal axes in the ratio ]~ok/fml; using (4.6) and the assumption N 2 > f2, we can show that this ratio is ~ 1 according as w2 ~ N y Using (5.4), (5.6), (4.4) and (4.5), or more general arguments, it can be demonstrated that gs = _l~(O,v,/N2)z,

~s = tz(O,v,/NZ)r,

(5.8)

to leading order in/~; hence by (4.23), (4.26), (4.32) and (5.3), ~L = _ ~ ,

= -/~Yzr,

~L =/z~* = t~yr;

(5.9a) (5.9b)

188

D.G. Andrews

thus, under the present approximations, ~* can be interpreted as a stream-function for the Lagrangian-mean meridional circulation. (Note that by equation (9.4) of ANDREWS and MclNTVRE, 1978, V-a L = O(/~aa2), and is negligible in the present example.) Moreover, (oL, ~L), like ~, but unlike (~7, ~7), is confined to the region R, and in particular ~L, unlike ~, vanishes at Z = 0. This agrees with the general results of Section 4.2 of A~DREWS and MCI~TVRE (1978), since the mean position of the lower boundary is here immobile, to leading order. Other Stokes corrections and Lagrangian-mean quantities can be calculated in a similar manner. It is found that ~s = O(/~ff) and gs = O(/x0) in the present case, and it can be verified that the solutions satisfy the Lagrangian-mean equations (4.10b)(4.14b) of the accompanying paper by MclNXVRE (1980), to leading order in /x. A physical discussion of the differences between the Eulerian-mean and Lagrangianmean descriptions of our example is given in Section 4 of that review. A number of authors have dealt with similar problems to that considered in this paper; we omit references to their publications here, since a fairly detailed bibliography appears in the accompanying paper. 9A c k n o w l e d g e m e n t s

Thanks are due to M. E. Mclntyre for helpful discussions. This paper was written while the author was supported by National Science Foundation grant NSF-g-7620070 ATM. REFERENCES ANDREWS,D. G. and MCINTYRE,M. E. (1976a), Planetary waves in horizontal and vertical shear: the generalized Eliassen-Palm relation and the mean zonal acceleration, J. Atmos. Sci. 33, 203 t -2048. ANDREWS,D. G. and MCINTeRE, M. E. (1976b), Planetary waves in horizontal and vertical shear: asymptotic theory for equatorial waves in weak shear, J. Atmos. Sci. 33, 2049-2053. ANDREWS,D. G. and MclNTVRE,M. E. (1978), An exact theory o f nonlinear waves on a Lagrangianmean flow, J. Fluid Mech. 89, 609-646. BoYt~, J. P. (1976), The noninteraction o f waves with the zonally-averaged flow on a spherical Earth and the interrelationships o f eddy fluxes o f energy, heat and momentum, J. Atmos. Sci. 33, 2285-2291. BRETHERTON,F. P. and GARRETT,C. J. R. (1968), Wavetrains in inhomogeneous moving media, Proc. Roy. Soc. A, 302, 529-554. LONGUET-HIGGXNS,M. S. (1969), On the transport o f mass by time-varying ocean currents, DeepSea Res. 16, 431-447. MClNTYR~, M. E. (1977), Wave transport in stratified, rotating fluids, Springer Lecture Notes in Physics 71, 290-314 (ed. E. A. Spiegel and J. P. Zahn). MCINTVRE, M. E. (1980), An introduction to the generalized Lagrangian-mean description o f wave, mean-flow interaction, Pure appl. Geophys. 118, 152-176. URYU, M. (1974), Mean zonal flows induced by a vertically propagating Rossby wave packet, J. Meteorol. Soc. Japan 52, 481490.

(Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh~iuser Verlag, Basel

Lagrangian Motion of Air Parcels in the Stratosphere in the Presence of Planetary Waves By TAROH MATSUN01)

Abstract-Development of thoughts on tracer transport mechanisms in the stratosphere which lead to new approaches to two-dimensional modeling of the tracer problem is reviewed. Three-dimensional motions of individual air parcels affected by a planetary wave are investigated theoretically, treating a steady, upward propagating wave in a uniform flow. It is shown that trajectories of air parcels are of elliptical form when projected onto the meridional plane and that they have no mean meridional or vertical motion, even though the usual zonal Eulerianmean vertical motion exists. The origin of the difference between the mean air parcel motion and the Eulerian-mean motion is discussed. On the basis of the knowledge of air parcel motion, two approaches to two-dimensional modeling are considered. The generalized Lagrangian mean motion (quasi-zonal weighted mean taken over a meandering material tube), recently introduced by Andrews and McIntyre, is identical with the mean motion of an air parcel in a steady state. Such a mean meridional circulation may be used for advecting a tracer in the meridional plane in a two-dimensional model. The transport effect is represented solely by the advection and an eddy transport does not appear in this scheme, to a first approximation. The finding that trajectories of air parcels are elliptical necessitates a reexamination of the Reed-German eddy diffusivity currently used in two-dimensional chemical-dynamical models. By applying a mixing length type hypothesis, we derive an 'eddy diffusivity' formula for use in Eulerian-mean calculations, which, in the case of a conservative tracer is dominated by an anti-symmetric tensor. The eddy transport due to this anti-symmetric tensor diffusivity is of advective type (not diffusive) and has the effect of taking the Stoke drift effect into account, when used in the usual Eulerian-mean formulation. Key words: Planetary waves; Air parcel trajectories; Eddy transport of tracers; Diffusivity tensor.

1. Introduction T h o u g h the stratosphere has only a small fraction o f the whole mass o f the a t m o s p h ere, its general circulation plays a u n i q u e and i m p o r t a n t role in the circulations o f trace substances, because no precipitation takes place there so that water-soluble substances can be stored there for m o r e than a year w i t h o u t suffering f r o m wash-out and they are redistributed over the globe by the circulation. This circulation is, o f course, crucially i m p o r t a n t for the distributions o f o zo n e and other m i n o r constituents f o r m e d in the stratosphere. Perhaps for this reason m o s t studies o f the stratospheric 1) Geophysical Institute, University of Tokyo, Tokyo, Japan.

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Taroh Matsuno

(Pageoph,

general circulation thus far made have been more or less concerned with the transport of trace substances. In early times when direct observation of the motion in the stratosphere on a global scale was not available, the circulation was inferred from the distributions of ozone and water vapor. BREWER(1949) presented a model of the general circulation of the lower stratosphere based on measurements of water vapor in that part of the atmosphere. In his model the stratospheric air ascends at tropical latitudes crossing the tropopause and then flows toward both poles and descends at middle and high latitudes to merge with the troposphere. This model well explains the dryness of the stratosphere, because all the air entering the stratosphere loses moisture in passing the very cold tropical tropopause. DOBSON(1956) showed that the Same circulation can account for the ozone transport from the tropical to polar region needed to maintain the observed distribution which is much deviated from photochemical equilibrium. MURGATROYD and SINGLETON(1961) estimated the air motion from the results of a radiative heat budget calculation by MURGATROYDand GOODY(1958). In other words they used potential temperature as a tracer and from its source-sink distribution they estimated the required transport. The resulting motion field was essentially the same as the Brewer-Dobson circulation in the lower stratosphere (below 30 kin). The magnitude of vertical motions thus estimated amounts to about 1 mm sec -1. A particular pattern seen in the distributions of radioactive isotopes generated by nuclear explosions (NEWELL, 1963) seems to reflect a transport by the above described circulation, too. Thus the distributions of trace substances in the stratosphere all support the existence of the Brewer-Dobson circulation. Later in the 1960s it became possible to determine the mean circulation in the lower stratosphere on the basis of observational data by using the angular momentum and/or heat balance equations. REED et al. (1963), MIYAKODA(1963), JULIANand LABITZKE (1965), PERRY(1967) and MAHLMAN(1969) investigated the mean meridional circulation in winter time, in connection with sudden stratospheric warmings. The circulation pattern discovered by them was apparently quite different from the Brewer-Dobson model. Namely, there is an upward motion in the polar region as well as in the tropical region, and a descending motion occurs at middle latitudes. VINCENT (1968) made a similar but more extensive analysis and showed that the same circulation pattern prevails not only in mid-winter but from October to March. In summer, the circulation in the lower stratosphere is weak and less clearly organized. Thus the two-cell circulation (in one hemisphere) is now established on observational basis. The magnitude of vertical velocity is scattered from a few to more than ten millimeters per second among the works, possibly owing to the different situations considered. The values obtained by VINCENT (1968) for quiet winters (without drastic warmings) are around 3 mm sec-1 and this may be regarded as a representative value. In recent years a number of attempts have been made to simulate the general circulation of the stratosphere by use of three-dimensional numerical models (MANABE and HUNT, 1968; CLARK, 1970; TRENBERTH, 1973a,b; KASAHARAet al. 1973; KASA-

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Lagrangian Motion of Air Parcels in the Stratosphere

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HARA and SASAMORI,1974; CUNNOLD et al. 1975; MANABE and MAHLMAN,1976; SCHLESINGI~R, 1976). In most of these models the two-cell circulation is reproduced as it is in the real atmosphere under winter conditions, as long as zonally asy~rnetric eddies are allowed to exist (TRENBERTH,1973a). Thus a question may arise. Why did the earlier workers obtain a quite different circulation pattern ? The answer to this question is rather simple. They ignored eddy transport process and attributed all the transport required for explaining the tracer distributions to the effect of a mean meridional circulation. In reality, however, eddy transport is very large especially in middle and high latitudes. The transport of ozone from the subtropics to the polar region was found to be accomplished by eddy action (NEWELL, 1963). In the observational studies cited previously it was found that the eddy heat transport is directed poleward and that its magnitude is much larger than what is required to compensate the radiative heat imbalance. The thermally indirect (at least in winter) cell located at middle and high latitudes can be considered to be forced by this eddy heat transport. These features are confirmed by numerical model studies (lot. cit.). Thus the stratospheric circulation cell at higher latitudes shares a common feature to the tropospheric Ferrel cell and some authors indeed described the former as an upward extension of the latter. There is however, a subtle but crucial difference between the two. In the tropospheric Ferrel cell region, the eddy heat transport is predominant and the effect of the indirect mean circulation is merely a small correction. The essential feature can be understood as down-gradient eddy diffusion of heat. In contrast to this, in the stratospheric case, the eddy heat transport is directed poleward no matter what the basic meridional temperature gradient is; hence it is often counter-gradient. Convergence and divergence of the eddy heat flux cause mean vertical motions as observed, and in the heat balance equation, effects of the eddy flux and of the mean circulation are opposite but nearly equal in magnitude so that net dynamical effect which balances with the radiative heat imbalance is a small residual of the two large counteracting effects. The circumstance can be understood by comparing the observed mean vertical velocity in the middle stratosphere, 3 mm sec -1 (VINCENT, 1968) with that deduced from the radiative imbalance, 1 mm sec -~ (MuRGATROYDand SINGLETON,1961). The latter value may become about one-half according to a recent radlatlon calculation by DOPPLICK (1972). This near cancellation of the effects of the two transport processes has been recognized as a notable feature of the transport mechanism in the stratosphere (MAHLMANand MOXlM, 1978, and references therein). The feature was first clearly seen in the transport of a passive tracer in the numerical experimental study conducted by HUNT and MANABE (1968), in which they proposed a new model of the tracer transport mechanism in the stratosphere to replace the Brewer-Dobson model. Their model, invoking combined actions of both eddy transport and mean meridional cell transport, is much more complicated than Brewer and Dobson's. But so far as the final results are concerned, the behavior of tracers as shown in their paper as time sequences of zonal mean concentration of the tracers (their Figs. 4 and 16), appear

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TarohMatsuno

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rather simple and consistent with the Brewer-Dobson circulation. Then it m a y be natural to seek for some way directly to reach the final result by-passing the intermediate complication. A key lies in the cancellation relation, which is not accidental but an intrinsic property of the present situation. First, unlike its counterpart in the troposphere, the eddy heat transport is not attributable to random eddies, but comes from well-structured planetary waves. As mentioned previously the wave causes poleward eddy heat transport regardless of the pre-existing meridional temperature gradient. This is a n evidence of the definite wave structure. (In this sense, eddy transports by the waves can never be regarded as a turbulent transport or diffusion.) Secondly, the observed mean meridional circulation contains, to a large extent, a component which is forced by this poleward eddy heat transport, so that this part of the mean circulation has a definite relation with the eddy flux. As will be shown later, the two effects are nothing but two aspects of the air parcel motion with an elliptic trajectory (as seen on the meridional plane) associated with planetary waves. The cancellation has been proved implicitly by CHARNEY and DRAZIN (1961) for steady, non-dissipating planetary waves. They showed within the quasi-geostrophic approximation that such waves do not cause tendencies of change in the zonal mean fields by their second-order effects. Since both eddy heat transport and the mean vertical motion caused by it are second-order effects, Charney and Drazin's result implies that temperature changes due to these effects cancel with each other in the zonal mean thermodynamic equation. Recently ANDREWS and MC1NTYRE (1978a) have shown that the cancellation holds exactly for finite amplitude waves (see MCINTYRE, 1980 for review). Therefore if we have some way to subtract the two effects simultaneously from the budget equation, the remainder may behave in a rather simpler manner. This can be accomplished by applying the 'generalized Lagrangian-mean' concept developed by ANDREWS and MCINTYRE (loc. cir.) to the present problem (DUNKERTON, 1978). Namely we consider averaging of any tracer concentration with respect to a curved material tube lying nearly along a latitude circle, instead of taking a simple zonal average along a latitude circle (Eulerian mean). The motion of the center of mass of such a material tube is defined to be the Lagrangian-mean motion. Since the equation for a Lagrangian-mean quantity does not involve eddy fluxes, the rate of change of the quantity following a material tube is determined by the source and sink terms averaged over the tube. Thus the motion deduced by MURGATROYDand SINGLETON (1961), hence the Brewer-Dobson circulation, should be identifiable as a Lagrangianmean meridional circulation, as suggested by KIDA (1977) rather intuitively and as pointed out by DUNKERTON (1978) more clearly. Further discussion of the problem, especially that about potential applicability of this type of circulation to a tracer transport problem is made by M CINTYRE (1979). In the present paper we shall discuss how the two different ways of averaging give different motions, treating a steady upward propagating planetary wave in a uniform flow. First we investigate motions of individual air parcels based on the three-dimen-

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Lagrangian Motion of Air Parcels in the Stratosphere

193

sional velocity field, paying attention to how a mean motion following an air parcel differs from a mean at a fixed point. Then we discuss the connection between the mean motion following an air parcel, and the generalized Lagrangian-mean motion. Though general arguments concerning the problem are available in theoretical literatures (e.g. ANDREWS and MCINTYRE,1978a, MCINTYRE,1980), explicit calculation may be helpful to get an idea about the kinematical reasons for the difference and the cancellation relation. In so doing, we will see that a trajectory of an individual air parcel has an elliptical form when projected onto the meridional plane. This fact necessitates that we modify the form of tensor eddy diffusivity originally proposed by REED and GERMAN (1965), because they postulated that the parcel trajectories are straight lines. Thus we shall derive a new expression for eddy diffusivity which may be used in two-dimensional models of the stratospheric chemistry. After the submission of the present paper, the author's attention was drawn to a recent paper by PLUMB (1979). He treated independently the same problem and came to the same conclusion that eddy transport due to an anti-symmetric diffusivity tensor is indispensable to expressing the non-diffusive Stokes drift's effect in Eulerian formulation of a tracer transport problem. 2. Lagrangian motion of a i r parcels

We shall investigate trajectories of individual air parcels in a situation where a steady upward propagating planetary wave exists and affects the air motion. The situation is very similar to the one treated by MATSUNO and NAKAMURA (1979, referred to as MN hereafter), but we shall consider a wave in a uniform basic flow for which we can obtain explicit solution of parcel trajectories. As in MN we consider an atmosphere on a beta-plane bounded by vertical walls at two latitudes ~) but unbounded in the zonal and vertical directions. The wall condition may be considered to substitute for the constraints at the pone for the poleward side. For the equatorward side the condition has no direct physical counterpart, but it is imposed simply to represent the situation that planetary wave in the real atmosphere is guided along the polar night jet (MATsUNO, 1970; SIMMONS, 1974) and its amplitude vanishes around 30 ~ In what follows, we first obtain a solution of the potential vorticity equation, which expresses a steady upward propagating planetary wave, and then calculate trajectories of air parcels for the given three-dimensional velocity field. The basic equations and a solution

Since we are concerned with planetary waves, the quasi-geostrophic approximation is valid. Further, we neglect friction and diabatic heating. Then using conventional mid-latitude beta-plane cartesian coordinates (with x and y axes directed eastward 2) The arguments are applicable to planetary waves in both hemispheres. But for drawing diagrams and also for explanations, situations in the northern hemisphere are assumed.

194

Taroh Matsuno

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and northward and z = H l n (Po/P) as the vertical coordinate), the vorticity and thermodynamic equations for steady planetary waves embedded in a uniform basic zonal flow are written as

--f(3~-H)W+;Y(4,,V2r f- -0x

u0 ~xx

"~

7z + g 2 w + f J

4,7z

= O,

(2.1)

(2.2)

where V 2 is a horizontal Laplacian operator and J stands for a Jacobian operator with respect to x and y. Other notation is as follows: 4, = perturbation geopotential, u, v, w, = perturbation velocity components in the x, y, z directions, f --- Coriolis parameter (constant), fi = Rossby parameter, H = scale height (constant), N = Brunt-V~iis/il/i frequency (constant); u0 is the basic zonal flow which is assumed to be constant, unless otherwise stated. Eliminating w between (2.1) and (2.2), we obtain the potential vorticity equation in the form U oaq ~+

~ 04, + } j(4,,q) = O,

(2.3)

where q is potential vorticity written as 1 V24, + f (t'3,2 q = f ~v- a@

1 c)

h b--~

(2.4)

(2.3) can be satisfied by any q and r which are related as follows: K2 q = - 7 4'

/3 Kz = Uo--"

(2.5)

A solution which has desired character is 4, = ao

eZf2Hsin ly sin (kx

+ mz),

(2.6)

where k, l and m should satisfy the dispersion relation f 2 ( m2 + ~ -I2 ) • 2= k2 + 12 + ~-~

fl = U-o"

(2.7)

Note that the solution given by (2.6) is an upward propagating wave in the sense of group velocity, and that it is zero at y = 0 and rr/l. The horizontal velocities are determined as geostrophic winds, namely l u -- - ] . a cos k v = ~. a sin

ly sin

ty cos

0,

0,

(2.8) (2.9)

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195

where we write, for simplicity, and

a = ao e z~2n

0 = kx + mz.

The vertical velocity field is determined by inserting the solution given by (2.6) into (2.2); the result is w = ~~oo asinly

(msinO-

t ) k t m 2a f2Ns2i n 2 1 y ~-HCOS0

'

(2.10)

where ~'0 is kuo the intrinsic frequency of the wave. As seen from (2.10), w consists of two parts ; the first term is proportional to the wave amplitude ao and has a wavelike form both in the x and z, while the second term is second order in wave amplitude and does not oscillate in either x or z. This second term comes from the Jacobian in (2.2), and expresses the Eulerian-mean vertical motion forced by the poleward eddy heat flux. Recalling that the wails are located at about 30 ~ and 90 ~ we see that according to the model the mean vertical motion is upward in the region poleward of 60 ~ latitude and downward in the region between 30 ~ and 60 ~. This distribution well resembles what is actually observed (e.g. MIYAKOt)A, 1963). Trajectories o f air parcels

Since we know the three-dimensional velocity field V(x), we can calculate a trajectory of an individual air parcel X(t), from the kinematic relation, dX dt

-

V(Z(t)).

(2.11)

The above equation is implicit for N and it is difficult to solve straightforwardly. Therefore we now assume that the wave amplitude a0 is small. Note that this assumption has not been needed so far. Then expanding both V and N; in powers o f a0 and equating each power, we have the following series of equations, dXo dt

- V0 = uoi,

(2.12)

-

(2.13)

dXz at

V~(>~o),

dX2 -dt

= V2(X0) + X1.VVI(X0),

(2.14)

where i in (2.12) stands for the unit vector in the x-direction, and where the fact Vuo = 0 has been used. In the above, V2 consists only of a vertical component given by the last term of (2.10) and the last term on the right-hand side of (2.14) came from the Taylor expansion of V1 about a point Xo, and therefore gradients of velocity components should be evaluated at the point X0. Such a term appears whenever one treats motion of an individual fluid particle to the second order of wave amplitude.

196

Taroh Matsuno

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Since it is quadratic, it usually contains a non-periodic motion (D.C. component), which is called "Stokes drift" (e.g. LONOUE'r-HiCOINS, 1969) in analogy with the mass transport due to water waves treated by Stokes. For the most general discussion of Stokes drifts, see ANDREWS and MclNTYRE (1978a). We shall now obtain parcel trajectories in the present situation according to (2.12) and (2.14). The zeroth-order velocity is merely a constant flow and a solution of (2.12) is

Xo = (Uot, Yo, Zo),

(2.15)

where Y0 and Z0 are constants and we can make the initial value of the parcel's xcoordinate zero, without loss of generality. The trajectory is just a straight line. Using the first-order velocity fields, i.e., (2.8), (2.9) and the first term of (2.10), we obtain the first-order parcel position as l X1 = f ~ 0 a cos 1Y0 cos 0o,

(2.16)

k Y1 = f~o---~a sin IYo sin 00,

(2.17)

Z1 = - - ~ s a s i n l Y o

mcos0o +

sin0 o ,

(2.18)

where 0o = kuot + mZo. We have set all integration constants zero so that the trajectory approaches the undisturbed one as a0 ~ 0. As can be seen from (2.16) and (2.17) the plan view of this first-order part of the trajectory is an ellipse whose major 9: ..,....;,......,...,.,;r

-.,.......-.-.-,.,,..,

(a)

(b)

C)

()

Y

0 O Figure 1 (a) T h e trajectories o f air parcels on the horizontal (x-y) plane, correct to the first order o f wave a m p l i t u d e . (b) S a m e as (a) but including the second order part. N o t e that the trajectories s h o w Stokes drifts.

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197

Z

-I-Y

~ (b)

Figure 2 (a) Same as Fig. la but as seen on the meridional (y-z) plane. (b) Same as Fig. lb but projection onto the meridional plane. (Motion due to the second order Eulerian-mean velocity is not included.) axis is in the x-direction near both walls and in the y-direction in the middle part of the channel (Fig. la). The sense o f rotation is counter-clockwise in the lower latitude and clockwise in the higher latitudes as shown in Fig. la. Note that these express the parcel trajectories as seen by an observer moving with the zeroth-order motion, u0. What is more important to our problem is the projection o f the trajectory onto the meridional plane. F r o m (2.17) and (2.18) we see that the form of the trajectory is an ellipse on the y - z plane, too. Since the vertical displacement is much smaller than the meridional displacement, the major axis is nearly horizontal and inclined slightly downward towards the pole, as depicted schematically in Fig. 2a. The trajectory can also be viewed as superposition of an ellipse with its major axis in the y direction expressed by the cos 00 term in (2.18), and an inclined straight line (the sin 00 term). Magnitudes of the two components are comparable if we take H = 6 x 103 m and m = 2zr/(6 x 104 m), the latter value being chosen corresponding to the vertical wavelength o f the planetary wave o f zonal wavenumber one. As will be shown later, these two components have different effects on the transport of substances, when the effects are parameterized as eddy diffusion. The inclination ~ o f the straight line as well as that of the major axis of the ellipse is given as c~

f~176

2N2H k

(2.19)

If we take f = 10-4 sec-1, N = 2 x 10-2 sec-1, H = 6 x 103 m , k = (2~/2 x 107m) (zonal wavenumber one along the 60 ~ latitude circle), and u0 = 30 m/sec, we have cz - 5 x 10 -4. This value is (happens to be) very close to those adopted by REED and GERMAN (1965) as the inclination o f parcel trajectories, though the presence of

198

Taroh Matsuno

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an elliptic component necessitate modification of their theory and the results will lead us to a somewhat different interpretation of their results. Next we shall discuss the second-order part of the trajectory, by calculating the right-hand side of (2.14). The second-order parcel velocity in the x-direction is obtained as

dX2

~ul

d--i- = x l - y ; kl 2

~Ul

7 ~ul

+ rl-Ufy + .~l-yi-z

= fcoo a 2 ( - c~

lYo co s2 0o + sin 2 IY0 sin z 0o) + (small term).

(2.20)

Here two terms in the parentheses of the second line correspond to the respective terms in the first line. The contribution from Z~(Sul/~z) turns out to be smaller than the first two by a factor c%/f, which is identified with the Rossby number and is much smaller than unity in the present problem. In the present investigation we shall confine ourselves to discussions of leading order quantities neglecting those smaller terms, unlike URYU (1979) who treated the Lagrangian-mean motion associated with a growing baroclinic wave retaining higher order terms. Our approximation is consistent with the neglect of ageostrophic components in u and v given by (2.8) and (2.9). The Stokes drift in the x-direction, G which is the non-periodic part of (2.20) is written as

kl 2

G = Xz'~V1 -

-a 2 cos 21Yo. 2fcoo

(2.21)

As readily seen from (2.21), the drift is westerly in the middle of the channel and easterly near the both sides. Thus the Lagrangian-mean velocity of individual air parcels exceeds the Eulerian-mean westerly speed in the vicinity of the region where planetary wave amplitude attains the maximum, while the parcel velocity is slower at other latitude zones. Though we have treated a particular wave structure which can be a solution of (2.3), the present result depends only on its horizontal part, which could be a model of quasi-geostrophic wave disturbances of a wider class. Then we may apply the present result to interpretation of the trajectories of constant pressure balloons 3) reported by MOREL and BANDEEN (1973), in which only a part of the Stokes drift [Xz(4!udbx)] was considered for interpretation of the results (see also WEBSTER and CURTIN, 1974). However, in the real situation the basic westerly is not uniform as assumed here but more jet-like. In this case a contribution to Stokes drift of the form Yg(~,2uo/~y~) may become significant as pointed out by ANDREWS and MCINTYRE (1978a, see also MClNTYRE, 1980) and we need a more careful treatment of the problem. It seems to be instructive to look into the kinematical mechanism which brings about the drift G. From the expression given in (2.20), one can immediately see that the first term causes a negative drift while the second term has a positive contribution. The reason can be explained by use of Fig. 3 (as well as Fig. 1) which depicts the 3) It may be applicable to the problem of tracer transports by eddy dominated ocean currents.

Vol. 118, 1980)

Lagrangian Motion of Air Parcels in the Stratosphere iI

'1I

'

\l

/

199

(

/

Figure 3 Horizontal picture of stream lines (thick arrows) and vertical velocity distribution (thin solid lines) for the explanation of Stokes drift (see text). The vertical motion field including the second order effect is also shown by dashed lines. The average of the latter vertical motion taken over a strip between two stream lines (Lagrangian mean) vanishes, while the usual zonal mean vertical motion at a constant y is upward in the northern half and downward in the southern half.

horizontal stream line pattern in the present situation. The distribution of vertical velocity is also shown for the explanation of vertical Stokes drift given later. A very similar diagram has been presented by WALLACE (1978) for discussion o f the same problem but considering an evanescent baroclinic wave. The phase relationship between vertical and meridional velocities is different for a propagating planetary wave from an evanescent wave so that trajectory slopes are different between the two waves. Now let us consider a mean westerly velocity following an air parcel. The air parcel experiences both faster and slower westerly velocities along a stream line but it spends a longer time where the westerly velocity is weaker because total velocity is also weaker there as understood from Fig. 3. Contrarily it spends a shorter time where the westerly is stronger. This effect corresponds to the first term of (2.20). At the same time the air parcel makes a north-south excursion and if we consider a parcel travelling in the southern half of the channel, it experiences a faster (first-order) westerly velocity when it is displaced to the south and a weaker (first-order) easterly velocity when it is displaced to the north as understood from Fig. la, thus obtaining a net westerly drift velocity as indicated in Fig. lb. It is expressed by the second term in (2.20). Both of the two effects mentioned above are very similar to the origin of mass transport in water waves treated by Stokes (hence called Stokes drift). The second-order correction of the meridional velocity of an air parcel is calculated in a similar way and turns out to vanish except for a higher order term in Rossby number i.e., X l . ~ v l = 0, /~s ~

(2.22)

0.

This result depends crucially on the wave amplitude being steady. The second-order vertical velocity consists of two components, the Eulerian-mean vertical velocity and the correction due to displacement as given by (2.14). The former

200

Taroh Matsuno

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has already been obtained as the second term of (2.10). The latter quantity is now calculated as OW1 8W1 ~W1 klm x~ --~- + r~--~-y + z ~ - g 7 = -2fN - 2 a2 sin 21Yo(cos 2 0o + sin 2 00) + (small term).

(2.23) Here three terms on the right-hand side are written to have correspondences to those on the left. Again we see that the two terms due to the horizontal displacements have the same magnitude. They are cooperative in this case, to give only non-periodic part, ~s as klm a2 sin 2l Fo.

(2.24)

The kinematical reasons for the drift can be explained in the same manner as for ~. Namely, if we consider an air parcel travelling in the northern half of the channel it spends more time in the descending regions than in the ascending ones as seen in Fig. 3, and simultaneously it experiences a stronger downward motion when it is displaced to the south but a weaker upward motion when it is displaced to the north, because the wave amplitude decreases with latitudes in this part of the channel (Fig. 2a). Thus both of the two effects cause a net downward drift (see Fig. 2b). Now comparing (2.24) with the second term of (2.10) we see that the two terms are equal in magnitude but opposite in sign so that we have dZ2 --dT-= w2 + ~(l"Vwl = 0.

(2.25)

Thus we understand that individual air parcels do not have a mean motion in the vertical direction, even though they make an up and down motion as given by (2.18). Therefore trajectories of air parcels projected onto the meridional plane remain the same as those shown in Fig. 2a, even if we consider the second-order effects. Since individual air parcels do not make a permanent displacement in the vertical, the mean termperature field is kept unchanged, despite the presence of the Eulerian-mean vertical motion as observed in the real stratosphere. We may say that the cancellation of the eddy heat transport effect and the mean vertical motion effect in the heat budget equation, and hence the Charney-Drazin theorem, appears in the form of (2.25), when viewed from air parcel motion. Since we have demonstrated that parcel trajectories are as depicted in Fig. 2a up to the second order of wave amplitude, it is instructive, conversely, to explain the causes of the eddy heat transport and the Eulerian-mean vertical motions on the basis of these parcels motions. In Fig. 4 the situation is illustrated schematically by drawing parcel trajectories as circles instead of inclined ellipses, for the sake of simplicity. Arrows attached to the circles indicate the direction of parcel motions. The upper semi-circles are drawn as dashed lines to indicate that in these positions

Vol. 118, 1980)

Lagrangian Motion of Air Parcels in the Stratosphere

201

..,..............~.~

:::::::::::::::::::::::::

w<0

w>0

iii!i~iii)iii~iii .............,

!iiiiiiiiiiiiiiiiiiiii~:

iiiiiiiiii!iiiiiiiiiii~ .,..........

,....,

\

!

i/

9

9

kl

%

:i:i:i:i:i:!:?i:!:i:;.

iiiilil}ii;i;ili)i;iiii~ .:.:+:.:.:.:.:.:.:.

::::::::::::::::::::: ?:!:??:?)?i:??..

i~iiiii~ii)iiiii)iiii~i

f

.,.......y....,.... :::::::::::::::::::::

..,..............,.,

.....,.......,......,.. ...................,... ..................... .........,...,......... ............. , . . .

i-~.-".:}::!)))i:ii~i ~!i!!i!i!i!i~!!i~i!i!i! ..............._...

:.:.:.:...,........_

Figure 4 Illustrative diagram to show how the zonal mean vertical motions and the meridional heat transport are caused by circular motion of air parcels. Dashed- and solid-lined parts of a circular air trajectory indicate the air parcel is cooler or warmer than its mean surrounding, respectively.

the air parcels have lower potential temperature than the horizontal average. The lower semi-circles drawn as solid lines show higher potential temperature. Then we can readily understand that a northward eddy heat transport should exist because northward moving parcels have higher potential temperature while southward moving ones have lower potential temperature. As understood from the above explanation, the meridional eddy heat transport originates from the vertical gradient of potential temperature so that the flux vector is perpendicular to the gradient vector. This particular feature of transport by planetary waves was recently pointed out by CLARK and ROGERS (1978) from purely Eulerian viewpoint. By treating the perturbation equation for a conservative tracer with a basic concentration gradient together with the perturbation equation for planetary wave propagation, and obtaining fluxes from the solutions they were able to demonstrate the above described property of tracer transports by planetary waves. On the other hand JONES (1969) made a general discussion of transports of energy and entropy by internal waves, without referring to any specific waves, and using the same diagram as Fig. 4 he pointed out that even if individual fluid particles have no mean motion, eddy transport of entropy can take place in the transverse direction to the basic entropy gradient by elliptic motion of fluid particles. In the preceding discussion we have shown that trajectories of air parcels are really elliptical in the case of an upward propagating planetary wave and confimed the Jones' result explicitly9 Neither JONES (1969) nor CLARK and ROGERS (1978), however, considered divergence or convergence of the eddy fluxes. The former erroneously concluded that the transversegradient flux should be non-divergent. In the present problem, the heat transport is

202

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largest at the center of the channel where the wave amplitude attains a maximum, and the transport decreases toward both sides. This meridional variation of heat transport brings about a convergence and a divergence of the heat flux at higher and lower latitudes, respectively. However these effects are offset by the effect of mean vertical motions shown by thin solid lines. The origin of these motions may be attributed to the same meridional variation of the amplitude of planetary wave. Namely, if we consider the Eulerian-mean vertical motion somewhere in the northern half of the region, upward motion is greater than downward motion at the same latitude and height, because the upward motion is a branch of a larger elliptic trajectory whose center is located at a lower latitude while the downward motion is a branch of a smaller ellipse. In this way we can consistently interpret the poleward eddy heat flux, its divergence, the mean vertical motion and the cancellation relation from the knowledge of the parcel trajectories. Viewing things as described above, one may notice that the Eulerian-mean budget consideration is somewhat artificial. It would be more useful if one can devise some way of taking averages which is more closely connected with individual air parcels. This problem will be discussed in the next section. It will also have been realized that the 'eddy heat transport' is not due to random eddies and hence its nature is not diffusive. For parameterizing the effect in terms of eddy diffusion we need a particular care. This problem will be treated in Section 4. 3. Generalized Lagrangian means

So far we have been concerned with 'Lagrangian motion' of air parcels and calculated specifically a mean velocity of an individual air parcel in the Lagrangian sense, i.e., a time mean of V following a parcel. It is clear that in a steady state a time mean following an air parcel can be replaced by a space mean along the path of the air parcel, a stream line. In fact the Stokes drift can be rewritten in the following way.

~(o,

P

Zo)= j

F

0, yo, Zo).VVl(,o,, Y0,Zo)d,/]

dt

In the first line of (3.1), ~1, the displacement of an individual air parcel is a function of time and is labeled by its initial position, while the perturbation velocity V1 is an Eulerian field variable and its gradient at the current position of the parcel is evaluated to calculate correction of the parcel's velocity due to the displacement at t. In contrast to this, in the second line, ~1 can be regarded as an Eulerian field variable as well as V1 and the integration is performed, in effect, with respect to the Eulerian coordinate x. Thus we can calculate the Stokes drift at a given instant only from spatial structure of the wave. The meaning of Xl(x) is the displacement of an air parcel caused by the wave perturbation which was originally at x in the unperturbed state.

Vol. 118, 1980)

Lagrangian Motion of Air Parcels in the Stratosphere

203

This latter way of calculating Stokes drift, hence Lagrangian-mean velocity, may be applied not only to steady waves but to unsteady waves. This idea leads to the generalized Lagrangian-mean motion considered by ANDREWS and MCINTYRE (1978a). (Their theory covers a wider class of averaging and is applicable to finite amplitude waves.) They developed the theory to describe better the back effect of waves on the mean flow, which has been an object of keen interest among many investigators (e.g. ANDREWS and MCINTYRE, 1978b and references therein) in connection with the 'non-acceleration theorem' first discussed by ELIASSEN and PALM (1961) and CHARNEY and DRAZIN (1961). It should be noted here that the integration given by the second line of (3.1) is a weighted mean of k/1 along a stream line. Namely, the integrand is integrated referring not to the stream line but to the original coordinate. This means that a segment of the stream line is given a weight proportional to the length of the segment at its original position. More physically if we consider a thin material tube with a constant mass per unit length at the unperturbed state, the tube after displacement may have different mass per unit length (being proportional to cross sectional area in the case of an incompressible fluid), which becomes the weight. In the present situation, the weight is proportional to a separation of two neighboring streamlines in Fig. 3. Naturally it is proportional to a time per unit length spent by an air parcel in passing through the streamlines. In short, the generalized Lagrangian mean is a mean over a distorted material tube (ANDREWS and MCINTYRE, 1978a; MCINTVRE, 1979; MA-rSUNO and NAKAMVRA, 1979). Essentially the same averaging procedure was adopted by KIDA (1977) in his numerical model study of Lagrangian general circulation of the atmosphere. A similar but not identical averaging, namely an averaging along a curved jet stream path was considered by RIEHI~ and FULTZ (1957) in their analysis of baroclinic waves in a laboratory model, and their method was applied by MAHLMAN (1969) to an analysis of the vertical motion field in the stratosphere at the time of a sudden warming. He was able to show that the mean vertical motion thus calculated was downward on the pole side and upward on the equator side of the polar night jet, in contrast to the Eulerian-mean (usual zonal mean) vertical velocity field which was directed in just the opposite sense. A qualitatively similar result was obtained by MN theoretically for a simplified model. There is, however, a slight difference between the generalized Lagrangian mean and a simple mean along a stream line. As mentioned previously the former mean is a weighted mean along a stream line. The weight is connected with the longitudinal displacement, as can be understood from the discussion in Section 2. The contribution from this displacement to the Stokes drift, i.e., XI(~V1/?~x), has been shown to be very important in the present problem. The magnitudes of those terms are the same as the magnitudes of the other terms, both in ff~ and ff~. The weight is important because it corresponds to length of time for the individual air parcel to pass through various parts of the path and only by taking this effect into account does the generalized Lagrangian mean become equal (in our case) to a mean following an individual air parcel.

204

Taroh Matsuno

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As mentioned previously, originally the generalized Lagrangian-mean description was devised by ANDREWS and MCINTYRE (1978a) in order to describe the evolution of general mean flows in the presence of wave disturbances. The method should also be suited to treating tracer transport problems as pointed out DUNKERTON(1978) and MN (see also MCINTYRE, 1979 for contemporary development), because for any physical quantity x which is advected conservatively, the budget equation does not contain eddy transport terms and is +

~+

~

~ = 0 L,

(3.2)

where .~L denotes the generalized Lagrangian-mean of a quantity A, and Q represents source of A, if any. As discussed in the previous section, ~L and ~L are quite different from their Eulerian-mean counterparts, ~ and ~, because the latters contain a large part whose effect must be compensated by the eddy transport effect. Equation (3.2) is formally identical with the Eulerian-mean equation in the case of no wave disturbances, which was presumed in the earlier studies of BREWER (1949), DOBSON (1956) and MtJRGATROYDand SINGLETON(1961). DUNKERTON(1978) showed that if A is potential temperature and Q is radiational heating rate, the following approximate balance holds in a steady state, i.e., (ITa - F)w L = O~a,

(3.3)

where F is the vertical temperature gradient, f'a is the adiabatic lapse rate, g/c v. The meridional advection of (potential) temperature is neglected against the vertical advection (cf. HOt.TON, 1975). Then he stated that what MURGATROYDand SINGLETON (1961) obtained, and hence the Brewer-Dobson circulation, is .just the Lagrangianmean meridional circulation. He also estimated the residence time of air mass in the stratosphere, using the fact that ff~Lrepresents the mass flow velocity and showed that the estimated value is very close to that inferred from tracer studies. KIDA (1977) also noted that the relation (3.3) holds qualitatively in his numerical model of the Lagrangian general circulation of the atmosphere. In his case, ~" is the observed motion of center of mass of marked air parcels which were distributed initially on a strip of a width of about 7 ~ latitude on an isobaric surface. He found, however, the observed ~L was too large compared with the value expected from the radiational balance (3.3). Examining his results more carefully we notice that the discrepancy is not so large as he claims (a few times), but the magnitude of ~" (negative everywhere in the calculated domain) is at most twice the value deduced from (3.3). The problem will be discussed shortly. Unfortunately Kida's model was not able to produce planetary waves, because the model is confined to a sector of 60 ~ longitude. Though his Eulerian-mean meridional circulation is utterly different from the Lagrangian-mean counterpart, the former was also different from the observed two-cell circulation. Therefore, for the confirmation of (3.3) for a more realistic situation, a rough analysis of the results of

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10 2 e r a g e e -1

30kin t

...... w

//'-",,,

,"

--~/At ......

wl~,,,i :~/r',~

60"',,, -

0~

III

/ f /

:

/

,

-20 km

. .--.

60~ ......

/

.......

\,

~ . ~ 3 ~ ,'/ '

~" I

7

:! i

Figure 5 Three kinds of vertical velocities taken from the HUNT and MANABE(1968) numerical experiment. Solid line: Vertical velocity of a conservative tracer analyzed from the motion of contour lines of equal mixing ratio. Dashed line: Zonal mean vertical velocity. Chain line: Vertical motion required to balance with net radiational heating. HUNT a n d MANABE'S (1968) numerical e x p e r i m e n t was made. The L a g r a n g i a n - m e a n vertical m o t i o n was estimated from the vertical shift o f c o n t o u r s o f equal concentration o f a conservative t r a c e r presented in their Fig. 16. The vertical m o t i o n to balance with the r a d i a t i o n a l heating was also calculated from the d a t a shown in Fig. 12 o f MANAB~ a n d HvN'r (1968). The two vertical velocities as functions o f latitude are shown in Fig. 5 t o g e t h e r with the E u l e r i a n - m e a n vertical velocity taken from their p a p e r . A p p a r e n t l y the L a g r a n g i a n - m e a n vertical velocities agree fairly well with the velocities expected from r a d i a t i o n a l balance, especially at the 30 km level, while the Eulerian m e a n s are quite different from the o t h e r two. Thus we can confirm that (3.3) holds in this case to a g o o d a p p r o x i m a t i o n . In o t h e r words, w h a t governs m o v e m e n t o f tracers is that p a r t o f the vertical m o t i o n that balances with the radiational heating, even t h o u g h the total E u l e r i a n - m e a n vertical m o t i o n is d o m i n a t e d by a c o m p o n e n t forced by e d d y heating due to p l a n e t a r y waves and the f o r m e r c o m p o n e n t is hidden behind the latter. 4) 4) The model did not include topography or continentality. Therefore stationary planetary waves caused by these effects are not present in the model so that the wave-induced Eulerian-mean vertical motions shown in the diagrams are much weaker than the observed counterparts (in the Northern Hemisphere).

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Now comparing the two results for the 30 km level and for the 20 km level, we easily notice that the agreement of two w's is almost perfect for the upper level while for the lower level ~L deduced from tracer motion deviates systematically to the negative side of wR estimated from the radiative imbalance. A similar tendency was found in Kida's results near the tropopause, as already mentioned. This excess downward motion of the Lagrangian-mean circulation in the lowest part of the stratosphere may be attributed to an additional converging motion toward the troposphere. Lagrangian-mean motions are, surprisingly, divergent even if the fluid is incompressible (McINTYRE, 1973, 1979, 1980; ANDREWS and MCINTYRE, 1978a; NAKAMURA, 1979; URYU, 1979). After ANDREWS and MCINTYRE (1978a) and NAKAMURA (1979), we can explain the origin of this divergence in the following way. Consider a situation where a wave disturbance is growing in a uniform flow. If we imagine that straight lines are marked in the fluid in the direction of the uniform flow at the initial time, they will become similar in shape to the stream lines in Fig. 3. Then the center of mass of the fluid contained between one of the side walls and the nearest marker line is likely to shift toward the middle of the channel, thus causing a convergence in the middle (and a divergence near the walls). 5) A converging flow is a dominant feature of the Lagrangian-mean motion associated with a baroclinic unstable wave treated by URVU (1979). On the contrary if a wave decays, the Lagrangian-mean flow must be divergent in the middle of the channel. In both MANABE and HUNT'S (1968) and KIDA'S (1977) numerical experiments, disturbances are thought to be statistically steady and both growing and decaying phases of disturbances must be included for the long periods for which the Lagrangian means were calculated. However, it is also clear that because of the presence of dissipative effects, decay is not a reverse process of growth and after one life cycle of a baroclinic wave a material tube may remain more spread than its initial state. Complicated non-linear processes involving many wave components may also be a source of the irreversible spread. Indeed in KIDA'S (1977) experiment, initially well localized marker particles diffuse with time in the troposphere. In response to this, the Lagrangianmean circulation in the troposphere is dominated by a converging flow toward the center of the troposphere. Bearing these facts in mind the discrepancy between the Lagrangian-mean vertical velocity derived from tracer movements and the vertical velocity estimated from (3.3), found in the lowest stratosphere, may be attributed to the convergent flow toward the troposphere. From the discussions in the present section one may readily understand that it is rational to adopt the Lagrangian-mean meridional circulation (or something like it) as the transport mechanism for a two-dimensional model of the stratospheric chemistry together with a ' t r u e ' eddy diffusion representing the dispersal of material particles on scales smaller than those discussed explicitly. For this purpose one can deduce the circulation directly from the radiative balance, whose approximate form 5) Rhines (1977) noted the same point in discussing the difference between Eulerian and Lagrangian mean flows for a turbulent field.

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is (3.3). It may also be understood that for doing this, especially if the troposphere is included, the phenomenon of convergence and particle dispersion about the mean flow should be dealt with. Investigations on this are now under way (DuNKERTOS, personal communication; MCINTVRE, 1979). It is very interesting that such a method has already been adopted by PRABAKHARA (1963) in his calculations of photochemical-dynamical equilibrium of ozone, made before the discovery of the two-cell Euterian-mean circulation of the stratosphere. He used a meridional circulation derived from MURGATROYD and SINGLETON'S (t961) results but by reducing its magnitude to 20~o of the original. In view of a recent radiation calculation by DOPPLICK (1972), this value seems to be too small but still within an acceptable limit. Prabakhara's procedure may be justified in terms of Lagrangian means, at least qualitatively; and his result, which showed a remarkable agreement with observation, may be taken to indicate that this way of two-dimensional modeling is adequate.

4. A parameter&ation of eddy transports of tracers by planetary waves As mentioned in Section 1, the usual description of transport mechanisms in the stratosphere from an Eulerian viewpoint invokes both mean meridional circulation and eddy transports by planetary waves. In response to this picture of tracer transport mechanism, in two-dimensional modeling of ozone and other chemical substances the transport effects are represented by advection of the tracer by a mean meridional circulation plus eddy diffusion (e.g. HARWOODand PYLE, 1977 ; HIDALGOand CRUTZEN, 1977). In the Eulerian picture the eddy transport is the principal means by which ozone is transported from the subtropics to the polar region, against the counteracting effect of a mean meridional circulation existing in the region; and therefore its representation would appear to have a crucial importance in the problem. The meridional eddy transports are often countergradient, including the ozone transport, though there is no physical basis for supposing that negative diffusion takes place for a passive tracer. In order to parameterize an eddy transport process having such a nature, REED and GERMAN(1965) proposed an eddy diffusion in the meridional plane with an inclined principal axis of diffusion. MURGATROYD (1965) stated that their method would represent well the tracer movements in the stratosphere. Namely, they hypothesized that owing to large-scale disturbances including planetary waves, individual air parcels move along trajectories which are on a plane inclined downward toward the pole. If the slope of this 'mixing surface' is greater than that of equal mixing-ratio surfaces of a tracer in the case where the mixing ratio of the tracer is increasing with height, mixing on this sloped surface would result in a poleward diffusion of the tracer. In this case, the diffusive flux is not parallel to the gradient. They are nearly perpendicular to each other though the flux is still slightly downgradient. The eddy diffusivity connecting the flux and the gradient then becomes a symmetric tensor. Apparently this method represents the eddy transport in the

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stratosphere to some extent (cf. CLARK and ROGERS, 1978) and by finding empirically a matched pair of a mean meridional circulation and an eddy diffusivity distribution it is now possible to reproduce the latitudinal distribution and the seasonal variation of ozone fairly well by two-dimensional models (e.g. HARWOOD and PYLE, 1977; HIDALGO and CRUTZEN, 1977). In view of the foregoing discussions in Section 2, however, we note that the Reed-German eddy diffusivity is not satisfactory for representing eddy transport by planetary waves in the following points. Firstly, we have no basis to consider that parcel trajectories are such as assumed by REED and GERMAN (1965). On the contrary we have shown that the trajectory of air parcels associated with a planetary wave is an ellipse when projected onto a meridional plane. Secondly, as argued in Section 2, eddy fluxes of tracers due to planetary waves do not have the physical nature of a diffusion. The eddy fluxes are needed just to offset the effect of mean vertical motions and hence they should have the character of advection. If we were to apply the ReedGerman diffusivity to the problem treated in Section 2, the initial stratification would be smoothed gradually with time, whereas in the circumstances assumed the mean stratification should remain unchanged. The intrinsically unsatisfactory nature of such a wholly diffusive parameterization has also been demonstrated by MAHLMAN (1975) from the results of a numerical experiment using a general circulation model. In what follows we shall attempt to derive a new eddy diffusivity (though it will turn out not to be diffusive in nature) on the basis of a knowledge of the parcel trajectories and applying a mixing-length type assumption. We consider the vertical and the meridional eddy fluxes crossing a constant latitude and height. If we know the velocity of air parcels and the mixing ratio of a tracer carried by them, we can evaluate the eddy fluxes. For this purpose, let us consider a set of air parcels which are all at a given latitude and height at a certain instant. We take the point under consideration as the origin of a coordinate in the meridional plane and also let the time t be zero at the instant considered. Then the parcel trajectories are written referring to (2.17) and (2.18), as

Y(t; 9) = ay[sin (~ot + 9) - sin 9],

(4.1)

Z(t; 9) = -a~[cos (oJt + 9) - cos 9] - b~[sin (~ot + 9) - sin 9],

(4.2)

where au is the amplitude of parcel oscillation in the y-direction, and a~ and b~ are those in the z-direction associated with the elliptic and linear components of a trajectory, respectively. 9 is a parameter designating the initial position of the parcel and may be regarded as the same as kxoo where x00 is the initial position of the parcel in the x-direction. Next, we shall assume that a physical quantity X is carried with the air parcels and it changes according to the following equation

dx

1

&- = 7 (~ - X),

(4.3)

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Lagrangian Motion of Air Parcels in the Stratosphere

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where 2 is an environmental value of X, which is solely determined by specifying the position (Y, Z ) in the meridional plane, and T is a time constant parameterizing the adjustment of X to its environment. In usual sense of eddy diffusion ~- is a measure of the time needed for a parcel to merge with the surrounding air, hence 9 is a mixing time. F o r chemically active tracers, we m a y interpret ~ as the photochemical equilibrium value and ~- as a photochemical relaxation time. A formal solution of (4.3) is readily obtained as x(t) =

eCt'-t~/~ ~[ Y ( t ' ) , Z ( t ' ) ] dr'.

(4.4)

Here we shall assume that ~ can be approximated by a linear function in the neighborh o o d of the origin, i.e., if(y, z) = ff~y + :~z,

(4.5)

where ~u and 2z are constants. Such an assumption is c o m m o n l y adopted in the mixing-length theory and is justified if mean gradients are nearly constant over particle orbits. It is this assumption that will read to eddy fluxes proportional to mean gradients. The constant term is set zero, because it has nothing to do with the transport. U p o n rewriting ~ in (4.4) in the form given by (4.5) and then substituting Y ( t ) and Z ( t ) into the rewritten expression we can calculate X(0, so), the value of X carried by an air parcel with label So, at t = 0 as cos So + qb2 sin So) - ~za~(- O2 cos So + q~j sin ~o)

x(O, So) = - ~ a y ( 0 1

+ ~b~(qbl cos So + qb2 sin So), where ~1 and qb2 are 9 l(o)r) - - ~

lfO

- ~ sin ~ot e ~/~ dt = 1 +~~

! ~0 qb2(wr) -- --

(4.6)

2'

(4.7)

O)2T2 COS ~ot e t/* dt + 1 = 1 + o927.2.

(4.8)

On the other hand, we readily obtain the velocity components of the air parcel as v(0, So) = ogay cos so, w(0, so) = o)az sin so - ~ob~cos So.

(4.9) (4.10)

Then making products of X(0, 9) and the two velocity components given above and integrating them with respect to q) (equivalent to zonal averages) we obtain eddy fluxes of X as following, --

vx-

oga~ (jp~y + ~oav (a~qb2 + b~q)~)~, 2

-w-X = ~ogav" t-a~

2-

* 2 + bzq)~)~2y - o9 -~ (a~ + b 2 ) O - ~ .

(4. l l) (4.12)

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Taroh Matsuno

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Since (4.11) and (4.12) represent a linear relation between the flux vector and the gradient vector, they can be expressed as, V X = - D. V;~,

(4.13)

where D is an eddy diffusivity tensor and is written as D = ~3s + D~,

I O)au2 where

D, =

\

60

- ~ a~b~

,o -~ayb~, f(a~ + b~)

(o) 0

D~ =

(4.14)

O)

-~-

1 x qb~(ojr),

(4.15)

~a~ x q)2(o~r).

(4.16)

a~,a~

Evidently the eddy diffusivity tensor consists of both symmetric and antisymmetric components. Since a, and b~ correspond to the first and second terms of (4.2), we see that the symmetric part arises both from the line-shaped component of a parcel motion and from the elliptic component, while the antisymmetric part comes only from the elliptic component of the trajectory. It is important to note that the symmetric part has a common factor qbl, and the antisymmetric part has ~2- As is evident from their expressions (4.7) and (4.8), q51 first increases with the increae of oJ, until it attains a maximum value 89at o~, = 1 and then decreases to approach 0, while qb2 is a monotonically increasing function and approaches 1 asymptotically for a large o r as depicted in Fig. 6. For a small ~or (<< 1), the diffusivity tensor is dominated by the symmetric part, because in this case *~ - oJr and qb2 - (co~-)2. On the contrary

0.1

/

/ 0.01

10

100- c ~

Figure 6 ~1 and q~2 as functions of oJr, showing relative magnitudes of symmetric (qbl) and anti-symmetric (q~2) components of the ' diffusivity'.

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for a large ~or, we have O1 - ( o r ) - 1 and qb2 "=. 1 - (~or)- 2 so that for a conservative tracer the diffusivity tensor becomes precisely anti-symmetric. In order to estimate components of the diffusivity tensor applicable to the real stratosphere we need to estimate a value for o~-. However, estimation of r is very difficult because in our problem an air parcel moves together with a large volume o f the surrounding air by the influence o f a planetary wave, and the usual concept of mixing by eddy motion does not apply. I f we regard the whole mass of air moving in one direction as an ' a i r parcel', a measure o f its size should be either a half of the wavelength or the latitudinal extent o f the wave region and then it m a y be around 106s m. If smaller-scale disturbances exist and cause mixing of these giant air parcels, the time constant m a y be calculated as ~- = (106.5 m)2/(106 m sec -2) = 107 sec. In the above, diffusivity due to smaller-scale eddies is assumed to be 106m sec -1, which may be the upper limit. This value would not be too large, if spectral components other than that corresponding to the wave under consideration work as a diffusing agent. If we identify ~- with the photochemical relaxation time of ozone, we have r - I0 days at 30 km and r - 1000 days at 20 km following BLAKE and LINDZEN (1973). F r o m these crude arguments we shall consider that r is of the order of l07 sec. N o w considering a planetary wave of zonal wave number one embedded in a westerly flow o f 30 m sec-1, we obtain oJ =

kuo

-

10- 5 sec- 1.

Consequently we have o2r = 100, qbl -- 10 -2 and q)2 - 1 - 10 -4. Thus we see that the antisymmetric c o m p o n e n t is predominant. Further, if we assume ay = 106m a~ = b~ = 10a m, the symmetric and the anti-symmetric parts of • become as follows (unit: m 2 sec- 1). ( 03~ =

-5 (

[D~ =

5 • 106 • 103

0 5 x 103

-5•

10~) 101

-5•

x q~l(wT),

(4.17)

) 0

• *2(w~-).

(4.18)

A p a r t from the factor ~1, each member of the symmetric part is rather close to the corresponding one obtained by REED and GERMAN (1965). But in the present treatment we need to multiply each element by qbl(oj,), which was estimated to be about 10 -2, so that the symmetric part becomes far smaller. In contrast to this, the anti-symmetric part remain as large as the off diagonal elements o f the Reed-German diffusivity and should play a significant role. Here it should be noted that an anti-symmetric diffusivity brings about a transverse-gradient eddy flux and it does not contribute to true 'diffusion'. To showing this let us consider a diffusion equation 6) 6) In the subsequent part discussion is confined to an incompressible fluid.

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8-7 = - V. Vx = V. (D- V~).

(4.19)

Multiplying both sides by ~ and integrating over the whole volume (denoted by < >), we have d 3~ <89163 = _ .

(4.20)

Since <9> is conserved, an increase of <~2> means that the distribution of )7 become more concentrated and a decrease of <~> corresponds to diffusion of s Note that the right-hand side of (4.20) is an inner product of the gradient and the flux and that diffusion occurs if the flux is down-gradient. The right-hand side of (4.20) can be written in terms of components as -

D y y - 8~ ~ 2 + D z ~[~__~'~2 S z ] + (Dvz + D~v)vX F-yy-~z

"

(4.21)

The above expression is non-positive for any distribution of ~, provided that the following conditions hold, D~, D~ > 0

and

4 D ~ D ~ > (Du~ + D ~ ) 2,

(4.22)

where equal signs correspond to the case where the quantity (4.21) vanishes. Now we notice that the anti-symmetric part does not enter (4.21) and (4.22); that is to say it does not cause concentration nor diffusion. It leaves (~2> unchanged. This is because an anti-symmetric 'diffusivity' causes a transverse-gradient eddy flux. Letting the yz component be - D , the flux is expressed as

-

Evidently the above flux is orthogonal to V~. Thus we see that, since for a conservative tracer (cot = oo), our eddy diffusivity reduces to an anti-symmetric tensor, the eddy flux becomes perpendicular to the gradient. This is quite reasonable because the anti-symmetric part comes from the elliptic trajectory. JONES (1969) has already shown that for such a trajectory the eddy flux should occur in the transverse-gradient direction, as mentioned previously. CLARK and ROGERS (1978) also showed that eddy transports of conservative tracers by planetary waves are perpendicular to the gradient of the tracers. Their expression for the flux is identical with (4.23). We arrived at the same conclusion via a somewhat different line. The above mentioned works, however, did not deal with spatial variation of diffusivity. As long as the diffusivity is constant, the transverse-gradient flux remains idle without causing any changes of T-field as is evident from inserting (4.23) into

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(4.19). Note that even in this case, the flux itself is well defined and observable (JONES, 1969; TmEBAUX, 1975). In the present problem, D is variable because it depends on the amplitude of planetary waves as indicated by (4.16). As can be understood from the arguments in Section 2, this latitudinal variation of eddy diffusivity is of primary importance for causing divergences and convergences of eddy fluxes. These may cause changes of tracer distributions unless they are counter-balanced by the effect of mean circulations. If D is variable we have c~

c~)~

-

cqD c3~

c3D ~

(4.24)

where ~7and 9 are Eulerian-mean meridional and vertical velocities, respectively. The above equation indicates that i is advected by an additional flow which is derived from a stream function D. The if-field can be changed by the effect of the eddy diffusion; but it is not a 'diffusive' process. This is exactly what we wanted for incorporating as an eddy transport into two-dimensional models, in order to compensate the transport by a mean meridional circulation. In fact it can be shown that the flow derived from the stream function D coincides with the Stokes drift in our case, so that the change of i given by the right hand side of (4.24) just cancel with the change caused by the mean vertical velocity, the last two terms on the left. As shown above, following the line taken by REED and GERMAN (1965) but by modifying their formula on the basis of new and correct information about parcel trajectories we obtained an identical result with the one deduced from the consideration of the Lagrangian-mean motion. The method to express transport effects by an Eulerian-mean meridional circulation plus an eddy diffusion, which is currently used in two-dimensional modeling of minor constituents in the stratosphere, could be justified if the eddy diffusion is expressed by an eddy diffusivity which includes a large anti-symmetric component.

5. Summary In the present article we discussed motion of individual air parcels caused by a steady upward propagating planetary wave. It was shown that trajectories of air parcels are elliptical when they are projected onto the meridional plane and they make a cyclic motion in a definite sense along the trajectories. Mean motion following an air parcel is zero both in the meridional and vertical directions. This result is not inconsistent with the presence of Eulerian-mean vertical motion (which is upward on the poleward side and downward on the equatorward side), because mean motion following an individual air parcel differs from mean motion at a fixed latitude and height and the difference, usually called the Stokes drift, is just in the opposite to the mean vertical motion. A mean following an individual air parcel can be replaced by a suitably weighted mean along the stream line in the case of a steady flow. The latter procedure is

214

Taroh Matsuno

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equivalent to calculating a mean for a material tube; in the latter form it can be applied to more general cases. This idea was developed by ANDREWSand MCINTYRE (1978a) for the treatment of the wave-mean flow interaction problems, in the first place, but it now appears to be a useful tool for describing mean meridional circulations. It may be applicable to two-dimensional models of minor constituents in the stratosphere. The theoretical result that the meridional projection of the trajectory of an air parcel in the stratosphere induced by propagating planetary waves is an ellipse rather than an inclined line requires us to reexamine the Reed-German eddy diffusivity which is currently used for two-dimensional models of the stratospheric chemistry. Then we have derived a new eddy diffusivity corresponding to the elliptic parcel motion. The diffusivity tensor is shown to be dominated by an anti-symmetric component in the case of a nearly conservative tracer. The eddy transport derived from this diffusivity is advective rather than diffusive in nature and in effect it approximately represents transports due to the Stokes drift. Thus the two new schemes (Lagrangian and Eulerian) for two-dimensional modeling are approximately equivalent.

Acknowledgements

I am grateful to Dr. M. E. McIntyre who read the original manuscript and offered me a number of valuable comments. For the reference to Plumb (1979) I am indebted to Dr. D. G. Andrews. I also wish to express my appreciation to Mr. T. Dunkerton, Drs. J. R. Holton, J. D. Mahlman, K. Nakamura, M. Uryu and J. M. Wallace for helpful discussions on the present topic. Some part of the work reported in this article was performed while I was visiting U.C.L.A. in the summer of 1972.1 would express my gratitude to Drs. A. Arakawa, Y. Mintz, S. V. Venkateswaran and M. Yanai for their hospitality. I am also grateful to Mrs. K. Kudo for her assistance in preparation of the manuscript.

REFERENCES ANDREWS,D. G. and MCINTYRE,M. E. (1978a), An exact theory o f nonlinear waves on a Lagrangian-mean flow, J. Fluid. Mech. 89, 609-646. ANDREWS,D. G. and MCtNTYRE,M. E. (1978b), On wave action andits relatives, ibid. 89, 647-664. BLAKE, D. and LINDZEN, R. S. (1973), The effect o f photochemical models on calculated equilibria and cooling rates in the stratosphere, Mon. Wea. Rev. 101, 783-802. BREWER, A. W. (1949), Evidence for a worm circulation provided by measurements o f helium and water vapor distribution in the stratosphere, Quart. J. Roy. Meteor. Soc. 75, 351-363. CHARNEY, J. G. and DRAZIN,P. G. (1961), Propagation o f planetary scale disturbances .from the lower into the upper atmosphere, J. Geophys. Res. 66, 83-109. CLARK, J. H. E. (1970), A quasi-geostrophic model o f the winter stratospheric circulation. Mon. Wea. Rev. 98, 443-461. CLARK, J. H. E. and ROGERS,T. G. (1978), The transport o f trace gases by planetary waves, J. Atmos. Sci. 35, 2232-2235.

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MOREL, P. and BANDEEN, W. (1973), The EOLE experiment: early results and current objectives, Bull. Amer. Meteor. Soc. 54, 298-306. MURGATROYD, R. J. and GOODY, R. M. (1958), Sources and sinks of radiative energy from 30 to 90 kin, Quart. J. Roy. Meteor. Soc. 84, 225-234. MURGATROYD, R. J. and SINGLETON, F. (1961), Possible meridional circulations in the stratosphere and mesosphere, Quart. J. Roy. Meteor. Soc. 87, 125-135. NAKAMURA, K. (1979), A generalization of 'Eliassen-Palm Relation', J. Meteor. Soc. Japan 57, 215-226. NEWELL, R. E. 0963), Transfer through the tropopause and within the stratosphere, Quart. J. Roy. Meteor. Soc. 89, 167-204. PERRY, J. S. (1967), Long wave energy processes in the 1963 sudden stratospheric warming, J. Atmos. Sci. 24, 537-550. PLUMB, R. A. (1979), Eddy fluxes of conservative quantities by small-amplitude waves, J. Atmos. Sci. (in press). PRABHAKARA,C. (1963), Effects of non-photochemical processes on the meridional distribution and total amount of ozone in the atmosphere, Mon. Wea. Rev. 91, 411-431. REED, R. J. and GERMAN, K. E. (1965), A contribution to the problem of statospheric diffusion by large-scale mixing, Mon. Wea. Rev. 93, 313-321. REED, R. J., WOLFE, J. and NISHIMOTO,H. (1963), A special analysis of the energetics of the stratospheric sadden warming of early 1957, J. Atmos. Sci. 20, 256-275. RHINES, P. B. (1977), The dynamics of unsteady currents. The Sea, Vot. 6, ed. E. D. Goldberg, Wiley, New York, 189-318. SCHLESINGER,M. E. (1976), A numerical simulation of the general circulation of atmospheric ozone. Ph.D. Dissertation, Department of Atmospheric Sciences, University of California, Los Angeles, 376 pp. SIMMONS, A. J. (1974), Planetary scale disturbances in the polar winter stratosphere, Quart. J. Roy. Meteor. Soc. 100, 76-108. THIEBAUX, M. L. (1975), Determination of one-particle effective eddy diffusivity tensor in linearly inhomogeneous turbulent flows, J. Atmos. Sci. 32, 2136-2143. TRENBERTH, K. E. (1973a), Global model of the general circulation of the atmosphere below 75 km with an annual heating cycle, Mon. Wea. Rev. 101, 287-305. TRENBERTH, K. E. (1973b), Dynamical coupling of the stratosphere with the troposphere and sudden stratospheric warmings, Mon. Wea. Rev. 101, 306-322. URYU, M. (1979), Lagrangian-mean motion induced by growing baroclinic wave, J. Meteor. Soc. Japan 57, 1-20. VINCENT, D. G. (1968), Mean meridional circulation in the northern hemisphere lower stratosphere during 1964 and 1965, Quart. J. Roy. Meteor. Soc. 94, 333-349. WALLACE, J. M. (1978), Trajectory slopes, counter-gradient heat fluxes and mixing by lower stratospheric waves, J. Atmos. Sci. 35, 554-558. WEBSTER,P. J. and CURTIN, D. G. (1974), Interpretation of the EOLE experiment 1. Temporal variation of Eulerian quantities, J. Atmos. Sci. 31, 1860-1875. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh~user Verlag, Basel

Observational Evidence of the Semiannual Oscillation in the Tropical Middle Atmosphere-A Review By ISAMU HIROTA 1)

Abstract-Observational studies on the semiannual oscillation in the tropical stratosphere and mesosphere are reviewed. Results of many statistics based on rocket and satellite observations reveal that the long-term behavior of the mean zonal wind exhibits two semiannual cycles which have their maximum amplitudes centered at the stratopause level and the mesopause level, each one being associated with the semiannual temperature variations predominating at levels about 10 km lower. Observational evidence obtained from recent studies of the dynamical properties of upper stratospheric waves strongly supports the theoretical consideration that the stratospheric semiannual oscillation is the manifestation of the wave-zonal flow interaction with alternating accelerations of the westerly flow by Kelvin waves and the easterly flow by planetary Rossby waves. Regarding the semiannual variation in the upper mesosphere, however, very little is known about the possible momentum source. Therefore, emphasis is placed on the need for further observations of the structure and behavior of the tropical middle atmosphere. Key words: Semiannual cycles; Kelvin waves; Rossby waves; Wave-zonal flow interaction.

1. Introduction The semiannual oscillation o f the m e a n zonal wind a n d t e m p e r a t u r e in the t r o p i c a l m i d d l e a t m o s p h e r e is certainly one o f the most interesting p r o b l e m s to be solved for the u p p e r a t m o s p h e r i c dynamics. In c o n t r a s t to the studies on the quasibiennial oscillation (QBO) in the tropical lower stratosphere, there seems as yet to be neither a satisfactory mechanistic m o d e l n o r a c o m p e l l i n g t h e o r y for the detailed m e c h a n i s m o f the s e m i a n n u a l oscillation. In the last two decades, however, a great deal o f u p p e r a t m o s p h e r i c s o u n d i n g d a t a have been a c c u m u l a t e d because o f progress in i n s t r u m e n t a t i o n such as m e t e o r o logical rockets a n d satellites, a n d significant d e v e l o p m e n t s in the study on the structure a n d b e h a v i o r o f the s e m i a n n u a l cycle have resulted f r o m these observations. Therefore, at this stage p r i o r to the beginning o f the p e r i o d o f the M i d d l e A t m o sphere P r o g r a m ( M A P ) , it is timely to s u m m a r i z e o u r present knowledge o f the observed features o f the s e m i a n n u a l oscillation in the zonal wind and t e m p e r a t u r e a n d some characteristics o f wave disturbances related to the m e a n zonal wind variation in the e q u a t o r i a l m i d d l e a t m o s p h e r e . ~) Geophysical Institute, Kyoto University, Kyoto 606, Japan.

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Isamu Hirota

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In this review paper, we will be mainly concerned with observations of wind and temperature in the tropical stratosphere and mesosphere extending from 20 to 80 km, while some other important phenomena such as the semiannual cycle in the middle and high latitudes and in the thermospheric ionized atmosphere will be excluded from our discussion. Results of theoretical studies and numerical modelling will of course be referred to interpreting the observational evidence: among them the implications of the theory of the QBO will be very useful for consideration of the semiannual zonal wind oscillation. Preceded by a brief historical review of the upper atmospheric sounding, the climatology of the semiannual oscillation is documented based on the results of many statistics, and some problems to be solved from a dynamical point of view are presented. Next, in order to give an answer to these questions, the characteristic features of large-scale wave disturbances in the tropical middle atmosphere are described on the basis of recent observations and analyses. Finally an attempt will be made to suggest future observational studies needed in order to gain a thorough understanding of the mechanism of the semiannual oscillation.

2. Discovery of the semiannual oscillation Since the period of the International Geophysical Year (1957-58), a considerable amount of wind and temperature data of the stratosphere and mesosphere have been obtained from newly developed rocket observations. By using these data, in the first half of the 1960s, many attempts were made to construct zonal cross sections of mean wind and temperature and to describe their seasonal variations on the basis of the monthly mean statistics (BATTEN, 1961; KOCHANSKI, 1963; KANTOR and COLE, 1964, 1965). However, although these climatological studies represented an improvement over earlier ones (e.g., MURGATROYD, 1957), the reliability of the statistics for the tropical regions was still inadequate, primarily because of the sparsity of data in low latitudes, hence most of their discussions were concerned with the seasonal variation in middle and high latitudes where the annual cycle is predominant with a strong contrast between summer and winter circulations. It should also be noted that, in these climatological studies, the Southern Hemispheric data were incorporated into the Northern Hemispheric data with a tinqe-lag of six months, by assuming hemispheric symmetry. Accordingly, there is no distinction between January and July at the equator. Because of this method of analysis, as was pointed out by REED (1966), such an equatorial time-section must inevitably exhibit a six-month cycle, whether real or not. On the other hand, concerning the long-term variation of zonal wind in the tropical lower stratosphere, the so-called 26-month or quasi-biennial oscillation was found by REED (1960) and EBDON (1960) independently, from balloon observations over several

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stations in the tropics. Following the discovery of this remarkable phenomenon, numerous investigations were carried out in the following decade from various points of view: as a result, studies on the structure and dynamics of the mean zonal wind and large-scale equatorial waves have now made it clear that the QBO can be accounted for in the framework of 'wave-zonal flow interaction' (see the text of I-IOLTON (1975), and PLUMB (I977) and PLUMB and McEwAy (1978), for instance). In 1962, while making observational studies on the tropical stratosphere following the discovery of the QBO, Reed found evidence of the existence of a semiannual component in the temperature variation above the 30-rob level (24 kin) at some stations near the equator: the oscillation had its maximum amplitude over the equator and at the highest levels observed, and showed downward phase propagation. However, at that time, he considered the semiannual temperature variation simply as a consequence of the direct absorption of solar ultraviolet radiation by ozone in a region where the heating cycle is semiannual due to the twice-yearly passage of the Sun across the equator. The semiannual oscillation of the zonal wind in the equatorial stratosphere and

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mesosphere was also discovered by REED (1965). Using the rocket observations of wind at Ascension Island (8~ in the region between 28 and 52 km, he found evidence of a six-month cycle which becomes increasingly dominant above 40 km (Fig. 1). In a subsequent study of these topics, REED (1966) confirmed the existence of the semiannual zonal wind oscillation by using the rocket data at Ascension Island and Barking Sands (22~ for two years which was long enough to eliminate the influence of the quasi-biennial cycle. Results of harmonic analysis at the two stations indicate, as in the case of the semiannual temperature variation, that the semiannual wind oscillation is strongest at the equator, with a maximum amplitude of about 30 m/sec near 50 km, and the phase propagates downward. From the foregoing description of the zonal wind behavior, REED (1966) pointed out some interesting problems such as the generation and maintenance of the equatorial westerly flow, the effect of solar radiation in the tropical middle atmosphere, and the dynamical interaction with winter hemispheric circulations. These problems will be discussed later in more detail.

3. Climatology of the semiannual oscillation After the pioneering work on the semiannual oscillation in the equatorial stratosphere by REED (1965, 1966), there have been a large number of statistical studies on the structure and behavior of the mean zonal wind and temperature based on highaltitude observations which were obtained from the Meteorological Rocket Network (QUIROZ and MILLER, 1967; COLE, 1968; ANGELLand KORSHOVER, 1970; BELMONT and DARTT, 1973; BELMONT et al., 1974, 1975; NASTROM and BELMONT, 1975; HOPKINS, 1975; etc.). Despite the variety of years and stations of rocket data used in these studies, results from them all indicate that the semiannual variation of the zonal wind and temperature is global in extent, and now we have the following overall picture of the climatology of the semiannual oscillation in the middle atmosphere: (a) Mean zonal wind Harmonic analyses for each latitude and height level reveal that the semiannual zonal wind oscillation has its maximum amplitude near the stratopause level (45-50 kin) with a value of 25-30 m/sec. In the middle stratosphere (~ 35 kin), the amplitude is almost the same in magnitude (~ 10 m/sec) as that of the QBO at that level. It is interesting to note, however, that the maximum amplitude appears not to be at the equator but in the Southern Hemisphere subtropics (~ 10~ showing equatorial asymmetry (BELMONTand DARTT,1973; HOPKINS, 1975). Regarding the phase of the oscillation, the maximum in the westerlies first appears in the lower mesosphere just after the equinoxes and propagates downward. It is

Vol. 118, 1980) Evidence of Semiannual Oscillation in Tropical Middle Atmosphere

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60 km level is the average of the various estimates, since there seems to be no large difference between them. The amplitude of CIRA (COSPAR International Reference Atmosphere) model (1972), evaluated from the monthly mean values for 0 ~ latitude, is somewhat large below the 60 km level compared with others, while in the upper mesosphere the CIRA model is primarily based on the results of GROVES (1972). In this regard, the CIRA model should be revised in the near future, at least for the tropical middle atmosphere.

(b) Mean temperature The mean temperature also exhibits a substantial semiannual cycle in the equatorial stratosphere (COLE, 1968; ANGELL and KORSHOVER,1970; NASTROM and BELMONT, 1975). Almost all of these statistics reveal that the semiannual temperature component has its maximum at 35-40 km in the tropics, the amplitude being 3-4~ The phase propagates downward from the lower mesosphere to the middle stratosphere. The appearance of this cycle in the equatorial stratosphere with an amplitude of several degrees has also been observed in the Nimbus 3 Satellite Infrared Spectrometer (SIRS) data for 1969-70 (FRITZ, 1974), in the Nimbus 4 Selective Chopper Radiometer (SCR) data for 1970-71 (BARNETT,1974) and in the Nimbus 5 SCR data for 1973-74 (MCGREGORand CHAPMAN,1978). On the other hand, regarding the tropical upper mesosphere, only a little is known about the semiannual temperature variation. In Fig. 3 is presented a rough estimate 100

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Vol. 118, 1980) Evidence of Semianlaual Oscillation in Tropical Middle Atmosphere

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(c) The semiannual cycle in the extratropical region Global analysis of rocketsonde data indicates another interesting aspect of the semiannual variation appearing in the extratropical middle atmosphere, as was first pointed out by AN6ELL and KORSHOVErt(1970). Further studies by BELMONTand DARTT (1973) and BELMONT et al. (1975) demonstrated that there is maximum amplitude of the semiannual zonal wind oscillation near 60~ in the mesosphere (Fig. 4a), as an extension of the 'half-yearly wave' in the stratosphere shown by van Loon et al. (1972). A similar analysis for temperature (NASTROMand BELMONT,1975) revealed that the maximum amplitude appears at polar latitudes in the middle stratosphere in agreement with van Loon's result. One of the most remarkable differences between the tropical and extratropical semiannual oscillations is the manner of the phase progression: as is clearly seen in Fig. 4b, the phase change occurs almost simultaneously in a deep layer of the polar atmosphere, in contrast to the phase propagation from higher levels to lower levels observed in the tropical region. This fact, together with the separation of amplitude maxima into tropical a n d polar latitudes, strongly suggests that the mechanisms of the two oscillations are quite different from each other. The semiannual cycle observed in the polar region is probably a consequence of mid-winter breakdown of the polar vortex associated with the stratospheric-mesospheric sudden warming. Therefore in this paper we hereafter confine ourselves to the tropical atmosphere.

4. Some theoretical considerations The inspection of observed features of the semiannual oscillation summarized in the previous section gives rise to some interesting problems concerning the driving mechanism of this phenomenon which require plausible theoretical explanations. As was pointed out earlier by REED (1966), there are two classes of forcing mechanisms: one which acts through the heat balance and the other through the momentum budget. Since the zonal wind and temperature fields are considered to be in thermal wind equilibrium for the long-term variation such as the semiannual cycle, the temperature fluctuation due to the seasonal change of heating might be responsible for the production of mean zonal wind variation through mean meridional circulations which maintain the wind and temperature fields in thermal wind equilibrium. In fact, the absorption of solar ultraviolet radiation by ozone in the tropical upper stratosphere must have a considerable semiannual component because of the double passage of the Sun over the equator. However, this possibility seems to have been ruled out as a consequence of a theoretical study of MEYER (1970). By using a diagnostic numerical model for the zonally symmetric flow similar to that of LEOVY (1964), Meyer has demonstrated

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that the response of mean zonal wind to the semiannually varying heat source by solar radiation is negligibly small. As a result, he concluded that a semiannually oscillating momentum flux divergence is required to explain the observed zonal wind variation. Generally speaking; problems of the generation of mean zonal westerlies and easterlies at the equator should be dealt with separately. As regards the equatorial zonal westerlies, we have to explain the mechanism for the production of angular momentum which is greater than the absolute angular momentum of the Earth. Note that the problem of accounting for observed 'equatorial westerly accelerations' arises not only for the Earth's atmosphere but also for other fluids on rotating spheres such as the Jovian atmosphere and the solar photosphere. Since the Coriolis torque due to the mean meridional circulation cannot generate the westerly flow at the equator, an eddy momentum flux convergence must be required, in agreement with Meyer's conclusion. Then an important question arises as to what is the nature of the 'eddies' responsible for the westerly acceleration. In his numerical model, Meyer assumed that the horizontal eddy momentum flux was due to solar diurnal tides. However, HOLTON (1975) pointed out that the possibility of zonal wind acceleration by the tidal wave is doubtful because of the rapid and irregular change of the phase of the flux with height, which is incompatible with the observed uniform acceleration over a deep layer. Instead, Holton hypothesized that vertically propagating Kelvin waves may provide the westerly momentum source for the semiannual oscillation. In view of the fact that the westerly phase of the semiannual oscillation propagates downward as in the case of the quasi-biennial oscillation in the lower stratosphere, it seems reasonable to suppose that the mechanism responsible for the mean zonal westerly acceleration might be similar to that for the QBO. In this connection, let us briefly recall here the QBO theory, especially the role of Kelvin waves as a westerly momentum source, as proposed by LINDZEN and HOLTON (1968) and HOLTON and LINDZEN (1972): Kelvin waves propagate upward more readily when the mean zonal wind is easterly. An upward flux of westerly momentum is associated with the waves. When Kelvin waves reach a westerly shear zone, the Doppler-shifted phase velocity becomes small. Since the damping rate of Newtonian cooling increases with decreasing Doppler-shifted frequency, the waves tend to be absorbed by the mean flow rather rapidly due to radiative damping. As a result, the convergence of westerly momentum occurs there, which in turn gives rise to the downward propagation of the westerly shear zone. On the basis of the consideration for the dynamical properly of Kelvin waves mentioned above, HOLTON (1975) conjectured that only short-period Kelvin waves can penetrate into the upper stratosphere and lower mesosphere with weak absorption, to supply momentum for the westerly phase of the semiannual oscillation. As will be shown later, the existence of such a Kelvin wave at mesospheric levels has been confirmed observationally by HIROTA (1978, 1979).

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Isamu Hirota

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On the other hand, as for the zonal easterly acceleration, it is difficult to trace an analogy between the QBO and the semiannual oscillation: the easterly phase of the QBO is considered to be due mainly to the absorption of mixed Rossby-gravity waves and induced mean meridional motions. However, since mixed Rossby-gravity waves are highly susceptible to radiative damping, it is unlikely that they can propagate vertically up to mesospheric levels. Indeed there has been no indication of the existence of mixed Rossby-gravity waves in the equatorial middle atmosphere, either theoretically or observationally. Therefore a different mechanism should be considered. As mentioned earlier, the semiannual easterlies appear simultaneously throughout a deep layer without showing downward phase propagation. Morphologically speaking, the appearance of the easterlies at the equator seems to be merely a consequence of penetration of the summer rnesospheric easterlies into the winter hemisphere. This suggests the possibility of an interhemispheric coupling. In view of the predominance of planetary Rossby waves with long vertical wavelengths in the middle atmosphere of the winter hemisphere and the effect of 'critical line absorption' of the planetary waves shown by the theoretical studies of DmKINSON

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(1968a,b) and others, it is likely that the horizontal momentum flux divergence due to the planetary waves is responsible for the easterly acceleration in the tropics. Some observational evidence of the hemispheric coupling relevant to the easterly phase of the semiannual oscillation is also shown in the following section.

5. Wave disturbances

During the course of studying the QBO, many efforts have been made to describe the characteristic features of large-scale wave disturbances in the lower stratosphere, with the aid of time-height section analysis and power spectrum analysis of balloon observations at several stations in the tropics. Results of these studies and their significance in relation to the QBO are summarized in a review by WALLACE (1973). However, regarding the equatorial upper stratosphere and mesosphere where daily balloon observations are not available, no attempt was made in those early studies to investigate wave disturbances, primarily because of the sparsity of data. Since the time-scale of the waves under consideration is of the order of a week or so, it is not adequate to apply conventional time-series analysis techniques to rocket data which have a coarse time resolution. More recently, significant evidence has been obtained observationally for the existence of large-scale waves in the tropical middle atmosphere, by using new techniques for analysing rocket and satellite data. Thus in the following we discuss the observed features of these waves in some detail.

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Isamu Hirota

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(a) Kelvin waves

In order to test the hypothesis that the vertically propagating Kelvin wave is responsible for the semiannual westerly acceleration, HIROTA (1978) tried to find evidence of Kelvin waves in the equatorial upper stratosphere and lower mesosphere by using rocket data at Ascension Island. Since the Doppler-shifted frequency of Kelvin waves is proportional to the vertical wavelength for a given zonal wavenumber, the short-period Kelvin waves, if they exist, must have a characteristic vertical scale longer than that of lower stratospheric Kelvin waves (6-10 km). On the basis of this consideration, Hirota applied a power spectral analysis, with respect to altitude, to the two-day difference values of wind and temperature for the height region between 25 and 60 km. The making of two-day differences removes the mean field, the long-term trend and the tidal components. An example of the result of such an analysis is shown in Fig. 5, in which a concentration of power spectral density of the zonal wind component and temperature can be seen at vertical wavelengths of 15-20 km. Long-term statistics for the four-year period (1969-72) indicate that the wave has a characteristic vertical scale of about 20 km and is associated with a strong power spectral density in the zonal wind component, with somewhat weaker power in temperature, but with little power in the meridional wind component. Therefore this wave is very likely to be identified as a Kelvin wave. Moreover, it is quite interesting to note that the power Spectral density of this wave shows a significant semiannual variation; as is seen in Fig. 6, the wave activity is stronger in January-February and July-August, corresponding to the easterly phase and the subsequent westerly acceleration in the upper stratosphere. However, it is difficult to obtain direct information about the phase velocity and zonal wavelength, and hence the period, of t h e Kelvin wave from an analysis based on single-station observations. Thus HIROTA (1979) made a further effort to determine the dominant zonal wavenumber and phase velocity of Kelvin waves in the equatorial middle atmosphere directly from global satellite observations by the Nimbus 5 SCR. For the purpose of detecting Kelvin waves from the SCR observations with coarse vertical resolution, a combination of radiances from the upper three channels of the SCR was made to fit a wave with a vertical wavelength of about 20 kin. The height region covered by these data extends from 20 to 60 km. By applying harmonic analysis and power spectral analysis to these data for the two years from 1973 to 1974, it was found that a Kelvin wave with zonal wavenumber one is prominent and moves eastward with a period of 4-9 days (Fig. 7). Note that this period is about a half of that ( ~ 15 days) observed in the lower stratosphere. It is also worth noting that the dominant period of Kelvin waves shows a semiannual cycle with the longest period occurring in January and July so that, because of the semiannual zonal wind variation, the Doppler-shifted phase velocity is almost constant from season to season. Regarding the Kelvin wave amplitude at the stratopause level, an estimate by

Vol. 118, 1980)

Evidence of Semiannual Oscillation in Tropical Middle Atmosphere westward 3 4

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HIROTA (1978, 1979) gives values of about 10 m/sec for the zonal wind component and about 5~ for temperature, which are large enough to produce the observed mean zonal wind variation. Quite recently, using the parameters of the Kelvin wave found by Hirota, DUNKERTON (1979) made a numerical model of the westerly accelerations associated with the semiannual zonal wind oscillation and demonstrated that such a Kelvin wave could indeed give rise to the observed accelerations.

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Isamu Hirota

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Apart from the detailed mechanism of the excitation of Kelvin waves, the fact that the short-period Kelvin waves have not been observed yet in the lower stratosphere by the conventional time-series analysis of balloon data can be explained by their vertical propagation: as such waves propagate upward with weak absorption, they only need to have a small amplitude in the lower levels. A rough estimate based on kinetic energy conservation between the tropopause (~ 100 mb) and stratopause (~, lmb) yields amplitudes of the order of 1 m/sec for the zonal wind component at the tropopause, which may be masked by longer period Kelvin waves at that level. In conclusion, although there still remain some questions concerning the quantitative reliability of rocket and satellite observations, it can be said without doubt that the Kelvin waves play an essential role in producing the semiannual westerly flow in the upper stratosphere and lower mesosphere.

(b) Planetary Rossby waves The tropical semiannual zonal wind oscillation is not always regular but shows a significant year-to-year variation in strength. Based on the long-term statistics of global rocket data for about 10 years, HOPKINS(1975) found that the variance of the monthly mean zonal wind at the tropical stratopause is a function of season with maximum occurring just after the solstices in the easterly regime of the semiannual cycle. By computing correlation coefficients of zonal wind anomalies between the tropical and other regions, Hopkins further demonstrated that the deviations of the individual monthly mean zonal wind from the mean monthly zonal wind in the easterly regimes of the tropical semiannual cycle are positively correlated with those in the higher latitude winter hemisphere. This evidence suggests coupling between the equatorial stratospheric easterlies and the winter hemispheric circulation. Thus, by taking account of the predominance of planetary Rossby waves in the winter stratosphere and their dynamical properties, Hopkins hypothesized that the tropical semiannual easterlies are a result of the zero-wind line absorption of planetary waves. The observed equatorial asymmetry in the semiannual cycle as denoted earlier also seems to support this hypothesis, because the wave activity in the Northern Hemisphere winter is apparently stronger than that in the Southern Hemisphere winter. Planetary wave propagation from the winter hemisphere into the tropical stratosphere, which was not directly detected in the data from the sparse rocketsonde network, has been convincingly substantiated by the analysis of global satellite observations (BARNETT, 1975; HIROTA, 1976). Using infrared radiation measurements by the Nimbus 5 SCR during the 16-month period from December 1972 to May 1974, BARNETT(1975) studied the structure and behavior of quasi-stationary planetary-scale temperature waves in the upper stratosphere, and found that the zonal wavenumber-one component shows a 6-month cycle

Vol. I 18, 1980) Evidence of Semiannual Oscillation in Tropical Middle Atmosphere - -

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232

Isamu Hirota

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The deviation of Nimbus 5 SCR Ch.B12 equivalent temperature from the zonal mean for (a) 9-23 March 1973, (b) 23 April-7 May 1973 (BARN~T'r,1975).

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Evidence of Semiannual Oscillation in Tropical Middle Atmosphere

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to a momentum flux divergence, which in turn causes the mean zonal easterly acceleration. Therefore, in agreement with Hopkins' argument, we can conclude that the planetary Rossby waves in the winter hemisphere are the most likely source of easterly momentum for the tropical semiannual oscillation.

(c) Upper mesospheric waves Above rocketsonde levels, very little is known about the waves that might be responsible for the semiannual zonal wind oscillation near the equatorial mesopause level, neither has there been any theoretical prediction of the mechanism. However, recent progress in satellite observations makes it possible to investigate the upper mesospheric waves in a global context. From infrared radiation measurements of the Nimbus 6 PMR for a one-month period during the Northern Hemisphere winter, HIROTA and BARNETT (1977) found that planetary waves with zonal wavenumber one and two have significant amplitudes in the mesosphere. HIROTA (1978) made a further analysis of the seasonal variation of planetary wave amplitudes at mesospheric levels. Figure 10 shows a latitude-time section o f zonal wavenumber one in the temperature field based on the 10-day average for the P M R channel 3000 which gives the mean temperature of a layer near the mesopause. It is found that planetary waves at the mesopause level show an apparent semiannual variation in the

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tropics, with maxima occurring after the equinoxes, in a similar m a n n e r to those at the stratopause level. It should be noted, however, that the relationship between the wave m a x i m a and the zonal wind variation is quite different at these two levels, because the semiannual cycles o f the mean flow at the mesopause and at the stratopause are out o f phase with a time-lag o f about 3 months (see Fig. 2), Therefore, this fact suggests that some other

Vol. 118, 1980) Evidence of Semiannual Oscillation in Tropical Middle Atmosphere

235

effects should be considered to account for the momentum source in the upper mesosphere and lower thermosphere. Quite recently, evidence of the day-to-day fluctuations in tropical mesospheric winds has been obtained from VHF radar observations at Jicamarca (12~ Figure 11 was derived from fragmentary measurements of zonal wind at heights between 70 and 90 km for three days during the period of Jicamarca Experiment by Japanese Group (FUKAO et al., 1979). There seems to be an indication of disturbances with a time-scale longer than 24 hours. There is also an indication of a phase difference with height in the tendency of the wind variations. Further observations in the future for longer time period will provide us with more detailed information about the behavior of these disturbances.

6. Concluding remarks Since the earlier discovery of the semiannual oscillation in the equatorial upper stratosphere by Reed, there have been many observational studies on the structure and behavior of the mean zonal flow and wave disturbances at these levels based on rocket and satellite soundings, and the climatological aspects of this phenomenon are now well documented. The mean zonal wind in the tropical middle atmosphere exhibits two distinguishable semiannual cycles; one is predominant around the stratopause level and the other has its maximum amplitude at the mesopause. Concerning the lower one, there is, at least qualitatively, good agreement between observations and theory with respect to the role of large-scale wave disturbances in producing the mean zonal wind fluctuations. Observational evidence of the dynamical properties of the upper stratospheric waves strongly supports our present view that the semiannual oscillation is the manifestation of the wave-zonal flow interaction with alternating accelerations of the westerly phase due to vertically propagating Kelvin waves and the easterly phase due to equatorward propagating planetary Rossby waves. The driving mechanism for the westerly acceleration by the Kelvin wave is considered to be almost the same in principle as that of the quasi-biennial oscillation in the lower stratosphere. The semiannual heating cycle due to the twice-yearly passage of the Sun across the equator cannot produce by itself the observed zonal wind variation. Nevertheless, since the 6-month periodicity in the easterly acceleration by the planetary wave is due to the alternately enhanced winter circulation of the Northern and Southern Hemispheres, it can be said that the tropical semiannual cycle is essentially a kind of 'forced' oscillation, while the QBO is considered as a 'free' nonlinear oscillation, the period of which is mainly controlled by internal parameters of the circulation system. For thorough understanding of the dynamics of this phenomenon, rather simplified mechanistic models are required, as is suggested by the success of the Lindzen-Holton

236

Isamu Hirota

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model for the QBO and of Dunkerton's model in reproducing the westerly flow in the equatorial upper stratosphere. However, in view of both the lateral forcing by planetary waves and the vertical transport of momentum by Kelvin waves, we cannot avoid using a two-dimensional model including the extratropical region. There will be, of course, a need for further observational studies on the coupling between the zonal wind and waves. For instance, quantitative estimates of the magnitude of the momentum fluxes associated with the waves are required for the verification of numerical modelling. The presently available rocket and satellite data are inadequate for this purpose because of their coarse resolution in space and time. Moreover, the result of 4-year statistics on the upper stratospheric Kelvin waves is suggestive of a significant modulation due to the QBO (HIROTA, 1978). Thus there is need for longer series of observations with higher reliability. As regards the semiannual oscillation around the mesopause level, on the other hand, very little is known about the wave disturbances in this region, except for fragmentary evidence of the penetration of planetary Rossby waves from the winter hemisphere into the tropical mesosphere, as observed by the Nimbus 6 PMR, and of day-to-day wind variations depicted by VHF radar. Thus the momentum source responsible for the zonal flow production is still open to question. Therefore, finally, it is emphasized that a well-coordinated observing program comprising satellites, rockets and other ground-based instruments should make a major contribution to our understanding of the dynamics of the semiannual oscillation in the tropical middle atmosphere.

Acknowledgements

The present author wishes to thank Professor J. M. Wallace for improving the original manuscript. Thanks are also due to Mrs. S. Fukuyama for typing. REFERENCES ANGELL,J. K. and KORSHOVER,J. (1970), Quasi-biennial, and semiannual zonal windand temperature harmonic amplitudes and phases in the stratosphere and tow mesosphere o f the northern hemisphere, J. Geophys. Res. 75, 543-550. BARNETT,J. J. (1974), The mean meridional temperature behavior o f the stratosphere from November 1970 to November 1971 derived from measurements by the Selective Chopper Radiometer on Nimbus 4, Quart. J. Roy. Meteor. Soc. 100, 505-530. BARNETT,J. J. (1975), Hemispheric coupling - evidence o f a cross-equatorial planetary wave-guide in the stratosphere, Quart. J. Roy. Meteor. Soc. 101, 835-845. BATTEN,E. S. (1961), Wind systems in the mesosphere and lower ionosphere, J. Meteor. 18, 283-291. BELMONT, A. D. and DARTT, D. G. (1973), Semiannual variation in zonal wind from 20 to 65 kilometers at 80~176 J. Geophys. Res. 78, 6373-6376. BELMONT,A. D., DARTT, D. G. and NASTROM,G. D. (1974), Periodic variations in stratospheric zonal wind from 20 to 65 km, at 80~ to 70~ Quart. J, Roy. Meteor. Soc. 100, 203-211. BELMONT, A. D., DARTT, D. G. and NASTROM,G. D. (1975), Variations o f stratospheric zonal winds, 20-65 kin, 1961-1971, J. Appl. Meteor. 14, 585-594.

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C I R A 1972, COSPAR International Reference Atmosphere, Akademie-Verlag, Berlin, 1972, 450 pp. COLE, A. E. (1968), Periodic oscillations in the tropical and subtropical atmosphere at levels between 25 and 80 km, Space Research VIII, 823-834. CRANE, A. J. (1979), Annual and semiannual waves in the temperature of the mesosphere as deduced from Nimbus 6 P M R measurements. Quart. J. Roy. Meteor. Soc. 105, 509-520. DICKINSON, R. E. (1968a), Planetary Rossby waves propagating vertically through weak westerly wind wave guides. J. Atmos. Sci. 25, 984-1002. DICKINSON, R. E. (1968b), On the exact and approximately linear theory of vertically propagating planetary Rossby waves forced at a spherical lower boundary, Mon. Wea. Rev. 96, 405-415. DUNKERTON, T. (1979), On the role of the Kelvin wave in the westerly phase of the semiannual zonal wind oscillation, J. Atmos. Sci. 36, 32-41. EBDON, R. A. (1960), Notes on the wind flow at 50 mb in tropical and sub-tropical regions in January 1957 and January 1958, Quart. J. Roy. Meteor. Soc. 86, 540-543. FRITZ, S. (I 974), On the causes of the annual and semi-annual variations of radiance (or temperature) from the tropical stratosphere, J. Atmos. Sci. 31, 813-822. FUKAO, S., SATO, T., HIROTA, I. and KATO, S. (1979), A long-period wave in the tropical mesosphere observed by the Jicamarca radar (submitted to J. Geophys. Res.). GROVES, G. V. (1972), Annual and semiannual zonal wind components and corresponding temperature and density variations, 60-130 km, Planet. Space Sci. 20, 2099-2112. HIROTA, I. (1976), Seasonal variation of planetary waves in the stratosphere observed by the Nimbus 5 SCR, Quart. J. Roy. Meteor. Soc. 102, 757-770. H1ROTA, I. (1978), Equatorial waves in the upper stratosphere and mesosphere in relation to the semiannual oscillation of the zonal wind, J. Atmos. Sci. 35, 714-722. H1ROTA, I. (1979), Kelvin waves in the equatorial middle atmosphere observed by the Nimbus 5 SCR, J. Atmos. Sci. 36, 217-222. HIROTA, I. and SATO, Y. (1969), Periodic variation of the winter stratospheric circulation and intermittent vertical propagation of planetary waves, J. Meteor. Soc. Japan 47, 390-402. HIROTA, I. and BARNETT, J. J. (1977), Planetary waves in the winter mesosphere-preliminary analysis of Nimbus 6 P M R results, Quart. J. Roy. Meteor. Soc. 103, 487-498. HOLTON, J. R. (1975), The dynamic meteorology of the stratosphere and mesosphere, Meteor. Monogr. 37, Amer. Meteor. Soc. 216 pp. HOLTON, J. R. and DNDZEN, R. S. (1972), An updated theory for the quasi-biennial cycle of the tropical stratosphere, J. Atrnos. Sci. 29, 1076-1080. HOPKINS, R. H. (1975), Evidence of polar-tropical coupling in upper stratospheric zonal wind anomalies, J. Atmos. Sci. 32, 712-719. KANTOR, A. J. and COLE, A. E. (1964), Zonal and meridional winds to 120 kilometers, J. Geophys. Res. 69, 5131-5140. KANTOR, A. J. and CoLz, A. E. (1965), Monthly atmospheric structure, surface to 80 km, J. Appl. Meteor. 4, 228-237. KOe~ANSKI, A. (1963), Circulation and temperatures at 70- to lO0-kilometer height, J. Geophys. Res. 68, 213-226. LEovv, C. B. (1964), Simple models of thermally driven mesospheric circulation, J. Atmos. Sci. 21, 327-341. LINDZEN, R. S. and HOLTON, J. R. (1968), A theory of the quasi-biennial oscillation, J. Atmos. Sci. 25, 1095-1107. McGgEGOR, J. and CHAPMAN, W. A. (1978), Observations of the annual and semiannual wave in the stratosphere using Nimbus 5 S C R data, J. Atmos. Terres. Phys. 40, 677-684. MEYER, W. D. (1970), A diagnostic numerical study of the semiannual variation of the zonal wind in the tropical stratosphere and mesosphere, J. Atmos. Sci. 27, 820-830. MURGATROVD, R. J. (1957), Winds and temperatures between 20 km and 100 km - a review, Quart. J. Roy. Meteor. Soc. 83, 417-458. NASTROM, G. D. and BELMONT, A. D. (1975), Periodic variations in stratospheric-mesospheric temperature from 20-65 km at 80~ to 30~ J. Atmos. Sci. 32, 1715-1722.

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PLUMB, R. A. (1977), The interaction of two internal waves with the mean flow: implications for the theory of the quasi-biennial oscillation, J. Atmos. Sci. 34, 1847-1858. PLUMB, R. A. and MCEWAN, A. D. (1978), The instability of a forced standing wave in a viscous stratified fluid: a laboratory analogue of the quasi-biennial oscillation, J. Atmos. Sci. 35, 18271839. QuIRoz, R. S. and MILLER, A. J. (1967), Note on the semiannual wind variation in the equatorial stratosphere, Mon. Wea. Rev. 95, 635-641. REED, R. J. (1960), The circulation of the stratosphere, Paper presented at 40th anniversary meeting of the American Meteorological Society, Boston, January 1960. 12 pp. REED, R. J. (1962), Some features of the annual temperature regime in the tropical stratosphere, Mort. Wea. Rev. 90, 211-215. REED, R. J. (1965), The quasi-biennial oscillation of the atmosphere between 30 and 50 km over Ascension Island, J. Atmos. Sci. 22, 331-333. REED, R. J. (1966), Zonal wind behavior in the equatorial stratosphere and lower mesosphere, J. Geophys. Res. 71, 4223-4233. VAN LooN, H., LABITZKE,K. and JENNE, R. J. (1972), Half-yearly waves in the stratosphere, J. Geophys. Res. 77, 3846-3855. WALLACE, J. M. (t973), General circulation of the tropical lower stratosphere, Rev. Geophys. Space Phys. 11, 191-222. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh~iuser Verlag, Basel

Traveling Planetary Waves in the Stratosphere By R. L. WALTERSCHEID1) A b s t r a c t - This paper reviews the theory and observations of some traveling planetary waves in the stratosphere. Two categories of waves which appear prominently in the literature are discussed: westward propagating waves of periods in the range 3-7 days (the '5-day wave') and in the range 10-20 days (the' 16-day wave'). Although the observations seem to indicate that these waves are waves of the Rossby type (planetary waves), the evidence is less clear regarding (1) the question of whether these waves are forced internal waves or free (resonant) external waves, and (2) the identification of the observed waves with specific theoretical waves of the Rossby type. When recent observations are compared with theory, the evidence seems to favor the notion that the 5-day and 16-day waves of longitudinal wave number 1 may be identified, respectively, with the gravest and next gravest symmetric free Rossby modes. However, the observational evidence seems to be less clear regarding the nature of the 16-day wave than the 5-day wave.

Key words: Traveling planetary waves; Forced internal waves; Free external modes.

1. I n t r o d u c t i o n

In this review we discuss westward traveling p l a n e t a r y waves o f the largest longitudinal scales, longitudinal wave n u m b e r s 1 and 2, with p r i m a r y emphasis on wave n u m b e r 1. These waves seem to be coherent in the vertical (DELAND and JOHNSON, 1968; MADDEN, 1978) SO that i n f o r m a t i o n a b o u t the waves in the t r o p o s p h e r e is also useful in inferring characteristics o f the waves in the stratosphere. Thus we dwell to some extent on the waves in the troposphere. These relatively weak disturbances were identified in middle t r o p o s p h e r e d a t a by KUBOTA and IIDA (1954) who found evidence o f a 16-day oscillation for longitudinal wave n u m b e r s 1 and 2 (hereafter referred to as s = I a n d s = 2) in the 500 m b height d a t a for a winter p e r i o d at 50~ DELAND (1964) p e r f o r m e d a cross-spectrum analysis o f the sine and cosine coefficients o f the 500 m b height field zonal h a r m o n i c s for a six-month winter-centered series at 40, 50 and 60~ The q u a d r a t u r e spectrum showed evidence o f westward p r o p a g a t i n g s = 1 and 2 waves with p e r i o d s in the range 289 to 6 days. ELIASEN and MACHENHAUER (1965) resolved 100 m b hemispheric 24-hour height t e n d e n c y d a t a for a winter p e r i o d into spherical h a r m o n i c c o m p o n e n t s and followed their motion. They found persistent westward p r o p a g a t i n g s = 1 and 2 c o m p o n e n t s with periods near 5 and 15 days. They c o m p a r e d observed phase speeds with theoretical phase speeds for a nondivergent b a r o t r o p i c fluid a n d found 'essential a g r e e m e n t ' between observations and theory, 1) Space Sciences Laboratory, The Ivan A. Getting Laboratories, The Aerospace Corporation, P.O. Box 92957, Los Angeles, California 90009, USA.

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although the components of largest meridional scale were somewhat slower than predicted. This discrepancy between observed and predicted phase speeds was resolved by DIKY and GOLITSYN(1968) who applied atmospheric tidal theory to account for the effects of stratification and compressibility and obtained good agreement between their predicted phase speeds and those observed by Eliasen and Machenhauer. These results established the tikelihood that the westward propagating disturbances were waves of the Rossby type. Eliasen and Machenhauer also studied the vertical structure of the various components by analyzing the deviation from 5- and 15-day time means at 1000 and 500 rob. They found the difference in phase from 1000 and 500 mb to be quite small in the mean, suggesting that the waves are external waves. Later studies (HIROTA, 1968; DELAND and JOHNSON,1968; ELIASEN and MACHENHAUER,1969), however, indicated that these waves exhibited westward tilt in height (internal wave structure). HIROTA and SATO (1969) noted an oscillation of about 15 ms-1 in the amplitude of the polar night westerlies with a period near two weeks which was apparently a manifestation of a vacillation cycle. This led HIROTA (1971) to seek an explanation for traveling waves with periods near two weeks in terms of a coupling at low levels between stationary planetary waves forced by topography and the oscillating zonal current. Using a time-dependent two-dimensional model with an idealized wind profile he produced westward traveling waves. The maximum response periods were in the range l0 to 20 days for typical conditions. The waves bore a resemblance in their vertical phase variation to the observed disturbances. Although DELAND (1973) did find westward tilt of westward moving components seen in Nimbus 3 radiance data, he noted that this tilt was not consistent with the close agreement in phase of fluctuations in the ionosphere with planetary wave fluctuations in the stratosphere (KAWAHIRA, 1970; DELAND and FRIEDMAN,1972; DELAND and CAVALIERt, 1973). The recent study of MADDEN (1978), moreover, indicates that these waves do not exhibit the vertical tilt indicative of forced internal waves. In addition, contrary to HIROTA and SATO (1969), MADDEN (1975) found no strong tendency for two-week periods in polar night westerlies. In fact, averaged winter spectra of the mean zonal wind at 60~ at several levels show no marked tendency for increased variance in the 1-3 week range. (WEBSTER and KELLER (1975) found evidence of a vacillation cycle with an 18-23-day variation in the Southern Hemisphere upper troposphere. The variation in the mean wind was not evident at high latitudes.) Although the theory of HIROTA (1971) remains an attractive possibility, the more recent observations seem to favor the notion that the waves with periods near two weeks are free external waves. The evidence that waves with periods near 5 days are external free waves appears to be stronger than the evidence for waves with periods near two weeks. Recent studies (e.g., MISRA, 1975; MADDEN, 1978) indicate that the former waves do not exhibit significant tilt in height. In addition there is no known periodic forcing near this frequency with longitudinal scales comparable t o s = 1 o r s = 2. In this review we shall present a brief discussion of the theory of free planetary

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oscillations o f the atmosphere (the reference theory). We will then review observational evidence pertaining to the existence and structure o f traveling planetary waves, and examine the correspondence between the structure o f the observed waves and the predictions o f the reference theory. We shall, henceforward, limit our discussion of observations to the two categories of waves which appear prominently in the literature: Waves with periods o f roughly 5 and 16 days. We shall for convenience refer to the waves having periods in the range from about 3 to 7 days as ' 5 - d a y ' waves and to the waves having periods in the range f r o m about 10-20 days as "16-day' waves.

2. Theory In this section we discuss the dynamical theory of free oscillations o f a quasistatic atmosphere. 2) The quantitative theory o f oscillations on a mean state o f no motion is presented as a reference model. A brief qualitative discussion of the validity o f this model when mean winds are important is also presented. We seek a unified explanation for both wave categories and we shall not specifically discuss the theory o f the 16-day wave as a forced oscillation in detail. F o r a model o f a forced 16-day wave the reader is referred to HmOTA (1971). Before we proceed, we note that it is possible that 5- and 16-day waves are forced external waves. However, such waves cannot effectively transfer energy vertically and would seem to require a yet unspecified upper stratospheric forcing in order for them to be seen there (DELAND and JOHNSON, 1968 ; HIROTA, 1975 ; RODGERS, 1976). N o w we describe the mathematical treatment o f quasi-static oscillations of an atmospheric which is in a mean state of no mean motion (LAPLACE, 1825; PEKERIS, 1937; W~LI(ES, 1949; CHAPMAN and LINDZEN, 1970). We assume an exp i(et - sA) dependence in time (t) and longitude (,~) where e is the angular frequency o f the wave and s is its longitudinal wave number. We then reduce the governing equations to a single partial differential equation describing the height and latitude dependence of the ' vertical velocity' w. (We use log-pressure coordinates where the vertical coordinate is given by z = log (1000/p) where p is pressure in millibars.) The vertical velocity in this system is w = dz/dt). This equation has the form ~2w 0z 2

Ow So ~. Oz + (2-Uff~a)~~ [w] = 0

(1)

where f2 is the Earth's angular speed, a the Earth's mean radius, So = RTo(~ log To/gz + K) is a measure of the static stability of the basic state, R is the gas constant for dry 2) In the atmosphere waves are always subject to some dissipation so that permanent oscillations cannot exist without some forcing. For this reason when we refer to observed waves as 'free waves' we mean waves which are preferred in the sense that they may have sensible amplitudes without commensurably sensible forcing. We shall also use the term 'free' with this meaning when we discuss the effects of therma/damping in this section.

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air, To(z) the basic state temperature, K the value R/C v and C v is the specific heat at constant pressure. The operator ~" is a complicated differential operator given by

"~ = -O'-y \ f 2 - ~ ~-y

f 2 - y2 \ f f 2 _ y2

1 --y2

where f = e/2f2, y = sin q~ and where ~o is latitude. Equation (1) is separable in its latitude and height dependence so that a product separation of the form w =

W(z)O(qO

gives two equations which govern separately the height dependence W(z) and the latitude dependence O@) dW

d 2W

So

~s + ~ W = 0

dz 2

~-[@] = (2~a)2 @ gh

(2) (3)

where g is the acceleration due to gravity and h is a separation constant?) The separation constant is determined as an eigenvalue of the vertical structure equation (equation (2)). The operator ~ depends parametrically upon f, the normalized frequency. When h replaces the depth of the ideal ocean in Laplace's dynamical theory of tides, the determination of the normal modes of oscillation for the atmosphere is formally identical to the problem of finding the free modes of oscillation (called Hough functions) of the 'equivalent' ocean (HouGH, 1897, 1898 ; LONGUET-HIGGENS,1968). For this reason the separation constant h is often referred to as the (atmospheric) equivalent depth. The eigenfunctions W(z) and @(~) corresponding respectively to the eigenvalues h and fspecify (to multiplicative constants) the structure of the free oscillations. The vertical structure equation may be put into the canonical form d2 dz 2 --

Y -

m 2 Y =

0

(4)

by means of the transformation Y ~

We - z/2

In equation (4), m 2 = 88- So/gh. By analogy with equations governing the propagation of electromagnetic waves the quantity - m 2 may be interpreted as a refractive index squared (WILKES, 1949). The appropriate lower boundary condition is that there be no parcel displacement at the lower boundary (z -- 0). The upper boundary condition depends upon whether the wave is evanescent (m 2 > 0) or propagating (m z < O) for all heights above some level. In the former case the upper boundary condition is obtained from the constraint that the vertically integrated kinetic energy be finite, for the latter case it is obtained from the constraint that there by no energy propagation into the domain of integration from above. Although a permanent free oscillation 3) The temperature and geopotential oscillations also have the latitude dependence |

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Traveling Planetary Waves in the Stratosphere

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cannot exist in the latter case, a strong response to weak forcing can be realized provided m 2 is sufficiently large and positive over a sufficiently deep layer. In mathematical form the lower boundary condition is d Y / d z + (no/h -

89 = 0

(5)

where H0 = RTo/g is the local basic state scale height. In the special case when m 2 is constant (and positive) the general solution to equation (4) may be written y = Aem~ + Be -m~.

The condition of finite integrability gives A = 0. Applying the lower boundary condition then gives h = 11/(1 - So/gH).

(6)

LAPLACZ (1825) assumed isothermal expansion in an isothermal atmosphere (which is equivalent to setting So = 0 in equation (6)) and obtained h = H0. (Ironically in the same paper he obtained the correct formula for the speed of sound by correcting Newton's assumption of isothermal expansion for sound waves.) LAMB (1910) treated adiabatic motion of an atmosphere in convective equilibrium (So = 0) and found h = H0(0). If we assume Laplace's isothermal atmosphere and Lamb's adiabatic expansion (So = •gH) we obtain h = 7'H0, where ~, = Cp/Cv and Cv is the specific heat at constant volume. For typical values h = 10 kin. This value is close to those obtained by detailed calculations (DIZZY, 1965) and empirically by considering the speed of propagation of the long waves produced by the Krakatoa volcanic eruption of 1883 (TAYLOR, 1932). Furthermore there is a resemblance to the case for the actual atmosphere in that the atmosphere seems to possess only one equivalent depth. The vertical eigenstructure corresponding to h = 7'Ho is W oc e ~.

(7)

When, in contrast to the free case just discussed, the waves are excited by a periodic forcing (e.g., atmospheric thermal tides) the forcing fixes the possible values of the normalized frequency f For each f there is a set of equivalent depths {h,} which are determined as eigenvalues of the operator ~ (which as we recall depends upon f ) . If a value of h, is such that m~ < 0 then above the sources the solution satisfying the upper boundary condition is Y,~ = Ae-*lm,dz.

This solution represents an internal wave which has westward tilt in height and for the westward propagating waves we are considering transfers energy upward from the source region. If the value o f h , is such that m~ > 0, then above the sources the solution satisfying the upper boundary condition is Y, = Ae-,~,z.

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R.L. Walterscheid

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This solution represents an external wave which has no phase variation or tilt with height and cannot transfer energy vertically. Thus it is 'trapped' near the source region. Returning to the case of free oscillations, as mentioned earlier, the eigenfrequencies f and the corresponding latitudinal eigenstructures | are obtained from the theory of free oscillations of an ideal ocean of depth D = h (LONGUET-HIGGENS,1968). In this theory, the latitudinal dependence of the deviation of the free surface geopotential from its equilibrium value corresponds to | The eigenfrequencies and eigenfunctions depend upon D or for the atmospheric oscillations upon h. For large h the solutions separate into two distinct classes of motion: One class comprises high frequency irrotational gravity wave oscillations, the other low frequency nondivergent Rossby (or planetary) wave oscillations. The gravity wave oscillations may propagate eastward or westward, the planetary wave oscillations may propagate westward only. The planetary wave solutions depend for their existence on the latitudinal variation of the coriolis force (the ~-effect). The solutions are continuous functions of h. For general values of h those solutions that are continuations of the Rossby wave solutions depend crucially upon the fl-effect and generally are also referred to as planetary or Rossby wave solutions. For a given value of h the solutions corresponding to Rossby waves for a given s form a sequence {f~, 0~}~=~+1 such that n - s - I is the number of nodes in the interval - ~ / 2 < ~o < ~r/2 andf~ is a decreasing sequence (in modulus). The function 19~ is symmetric when n - s is odd and anti-symmetric when n - s is even. In the nondivergent hmlt | $ -+ P,,8 where Pn is the associated Legendre function of order s and degree n. The earlier mentioned improved agreement between observed and predicted phase speeds obtained when full tidal rather than nondivergent theory was used indicates that the atmospheric value of h is not sufficiently large for nondivergent theory to apply. Thus in seeking a correspondence with observations it appears that we must apply the 'exact' solutions f o r f a n d 19 obtained from tidal theory. In the stratosphere cooling due to infrared emission (principally in the 15/z band of CO2) results in a reduction of the perturbation in temperature of the wave. The perturbation pressure gradient is also reduced since it is related hydrostatically to the perturbation temperature, thus the kinetic energy of the wave is reduced and hence the process of damping by thermal emission is dissipative. It is customary to model the effects of thermal damping by setting the resulting heating (or cooling) proportional to the perturbation temperature T so that (OT/ ~'t)a,mpi~g = - a T (LEOVV, 1964). The quantity a- ~ defines a thermal relaxation time. Typical values range from about 20 days in the lower stratosphere ( ~ 10 rob) to about 5 days near the stratopause (BLAKE and LINOZEN, 1973; DICKINSON, 1973). For a = a ( z ) equation 1 remains separable in its latitude and height dependence (LINDZEN and McKENzIE, 1967). The effect of thermal damping is to make the 'refractive index' complex : 9

"

s

m = m r q- im~

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Traveling Planetary Waves in the Stratosphere

245

where mr = M cos (89 mi = M sin (89 and M = [(88 - fi)2 + (a/3)211/4 r =-- a / a

KHo/h /3-

1 +a2

0 = t a n - 1 [ _ (a/3)/(88 - / 3 ) ] . A s before we have a s s u m e d that To is i n d e p e n d e n t o f height. I f we further assume that a is also i n d e p e n d e n t o f height then W oc exp [ - ( m r - {)z -

im~z]

where mr, m, > O. The ' m , ' term represents westward tilt o f the wave. W i t h dissipation there is no value o f h which will p e r m i t p e r m a n e n t free oscillations. However, since we only wish to o b t a i n a feeling for the i m p o r t a n c e o f t h e r m a l d a m p i n g on the vertical structure o f the waves we are discussing, we will assume that when h = ~'H0 we have a free wave in the sense m e n t i o n e d in the beginning o f this section. W e shall limit our discussions to the lower s t r a t o s p h e r e where we have observations o f vertical structure. I f P is the p e r i o d o f the wave then (1/2~)P (a-l) . F o r the 5-day wave c~ ~ 10 -2 so t h a t M - m, cos 89 -

1 and sin 89 << 1, t h e r e b y

giving m - mr. Hence, in the lower s t r a t o s p h e r e we m a y assume that t h e r m a l d a m p i n g is only o f s e c o n d a r y i m p o r t a n c e insofar as the vertical variation o f a m p l i t u d e and phase are concerned. F o r the 16-day wave cz ~ 10-1 and M "-. m. However, the factor /3/(88 - /3) ,-~ 4 so that 0 m a y be significantly different from zero. Since when 89 is not t o o large the d e p e n d e n c e o f sin(89 on 0 is stronger t h a n the d e p e n d e n c e o f cos (89 on 0, rn~ m a y b e c o m e a p p r e c i a b l y different from zero before rnr becomes a p p r e c i a b l y different from M. This means that in the lower stratosphere it is more likely that the effects o f thermal d a m p i n g would be seen in the phase variation with height (tilt) than in the a m p l i t u d e variation. It also means that some slight observed westward tilt is not inconsistent with the notion that the 16-day wave is a free wave. T h e effect o f mean motion on oscillations d e p e n d s largely upon the relative m a g n i t u d e s o f changes due to advection and to local tendencies associated with wave p r o p a g a t i o n . F o r the relatively f a s t - 5 - d a y wave, advective tendencies in the stratosphere are typically a b o u t an o r d e r o f m a g n i t u d e smaller than local tendencies; thus we do not expect the mean wind to induce great changes in the oscillation. GEVSLERand DICKJNSON (1976) p e r f o r m e d calculations which included the effects o f realistic mean zonal winds on the s = I 5-day wave. Their calculations showed that the changes

246

R.L. Walterscheid

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induced in the stratosphere, though by no means insignificant, do not seem to obviate the utility of the no-mean-wind model in identifying the observed wave. On the other hand, for the 16-day wave, advective tendencies in the stratosphere may approach local tendencies in magnitude. Thus mean-wind-related effects may produce profound changes in the frequency and structure of the oscillation. Moreover, these changes are very difficult to assess due to the variety and complexity of the processes possible when mean winds are important. This means that although the evidence seems to favor the notion that the 16-day wave is a free wave of the Rossby type, we have no strong expectation that the observed wave will agree in all essential respects with the predictions of the reference theory, and furthermore, that lack of agreement may not be readily explained in terms of specific mean-wind-related mechanisms. To see whether the properties of the observed waves are consistent with the notion that these waves are free waves of the type described by the reference theory, we seek a correspondence as follows. First, given the value of the atmospheric equivalent depth and the value of the longitudinal wave number of the observed wave we identify theoretical wave modes whose frequency (with possible allowance for Doppler shifting of the frequency due to mean winds) lies within the range of frequencies observed for the disturbance. Then we check for correspondence between the structure of the observed wave and the structure of the possible theoretical waves. We seek correspondence with respect to properties of both the latitudinal structure (e.g., symmetry, location of extrema, location of nodes) and vertical structure (e.g., vertical variation of amplitude and phase). For concreteness, we consider the waves for s = 1. Allowing for Doppler shifting of the wave due to advection by mean zonal winds, we may identify three theoretical waves which could correspond to the observed westward propagating waves. These are the waves for which the pair (s, n) designating wave number and wave mode has the values (1, 2), ( 1, 3) and (1, 4). The ground based periods of these waves are, respectively, 5.5, 10 and 17 days. These values were obtained by (1) calculating an effective rotation rate ~ + ~o-where ~ is the angular rotation rate of the atmosphere as a whole relative to the earth - and then determining the frequencies corresponding to h = 10 km from Fig. 2 of LONGUE'r-HIGGENS(1968), and (2) applying a Doppler correction soJ to the frequencies thus determined. The procedure is equivalent to that outlined in DIKY and GOLITSYN (1968). A value of ~o = 0.0225 g) obtained from ELIASEN and MACHENHAUER (1965) was used. The periods obtained from step (1) were 4.9, 8.1 and 12 days. The latitudinal structures of these waves, @~, | and | are shown in Fig. 1. (This figure was adapted from LONGUET-HIGGENS(1968). He plotted the eigenfunctions for h = 9.2 km. MADDEN (1978) noted that the eigenfunctions for h = 10 km would be close to those for values of h like 9.2 kin.) We note that | is a symmetric function with no nodal latitudes (we do not include the poles) and broad relative maxima near 40 ~ latitude, | is an anti-symmetric function with a node at the equator and relative amplitude maxima near 55 ~ latitude, and @~ is a symmetric function with a node near 35 ~ latitude and peak amplitude maxima near 65 ~ latitude. The theoretical vertical

Vol. 118, 1980)

247

Traveling Planetary Waves in the Stratosphere

--1

_

ff

C'M

|

| ~

t-m z

C3 ur

l_l.J r'm --m

-'J

F__J

13_

,,-"///:

",,\.

LA-CZ) L.IJ E:)

b-m

....J

/ 9

0

10

~

~176176

20

30

40 50 LATITUDE

60

70

80

90

Figure I Latitudinal structure of lowest three Rossby waves for (2f2a)2]gh = 10 when s = 1. Adapted from LONGUET-HmGENS (1968), Fig. 10.

structure for all three waves is the same. The amplitude varies as exp (~z) and the phase is independent of height. 3. Observations

In this section we present in some detail the results of studies of traveling planetaryscale waves. As stated earlier, observations indicate the existence of two dominant wave categories, namely the 5-day and 16-day waves. We shall discuss the observations relating to the existence, structure and seasonal behavior of these two wave categories. The discussion is limited to observations which show distinct, prominent wave motions revealed, say, by statistically significant peaks in a power spectrum, or by propagation of identifiable features in a time section. (We mention that prominent waves in this sense are not always noted, e.g., DWLAND (1973).) We shall also examine the correspondence between the properties of the observed and predicted waves for s = 1. A synopsis of the data, analysis methods, and key findings of the studies referred to are presented in Table A1 of the appendix. (a) 5-Day wave The existence of westward propagating planetary waves with periods near five days was established first in studies of tropospheric data, and is further better documented in this region than in the stratosphere. Moreover, as mentioned, the 5-day wave seems

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R.L. Walterscheid

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to be coherent in height so that information about the wave in the troposphere is also useful in deducing characteristics of the wave in the stratosphere. Thus we dwell to some extent on the wave in the troposphere. DELAND (1964) computed quadrature spectra for the sine and cosine coefficients of zonal harmonics s -- 1 and 2 for 40, 50, and 60~ at 500 mb for a six-month period approximately centered on the winter solstice and found evidence of westward propagation with periods in the middle of the range 21 to 6 days. ELIASEN and MACHENrtAUER (1965) performed a spherical harmonic analysis of the Northern Hemisphere 24-hour stream function tendency at 500 mb for a winter period. The data were extended evenly (symmetrically) about the equator so that only even harmonics were employed. The components for s = 1 and s = 2 with the greatest meridional scale were observed to travel westward with periods of about 5 and 4.5 days respectively. DELAND and LIN (1967) performed a similar analysis of 500 mb height data (using odd harmonics) for a winter and summer period and observed disturbances with periods near 5.5 days for the s = 1 and s = 2 components of greatest meridional scale (gravest components) in winter, and near 4.5 days for these components in summer. Global 1000 and 500 mb heights were analyzed by ELIASEN and MACHENHAUER (1969) for a full winter period. They observed westward propagation with about a 5-day period at 500 mb in the quadrature spectrum of the three gravest s = 1 spherical harmonic components. MADDEN and JULIAN (1972) examined a 5-10-year time series of surface pressure data from twenty-eight stations and 500 mb height data from five stations. Cross-spectrum analyses between Canton Island surface pressure and surface pressure at the remaining twenty-seven stations gave marked peaks in the coherence squares corresponding to 4-6-day periods in nearly all spectra. The average period was 4.9 days. The longitudinal variation of phase was consistent with westward propagating s = I disturbance. Cross-spectrum analyses between Canton surface pressure and 500 mb heights at the five stations similarly gave evidence of a westward propagating 5-day wave with s = 1. MISRA (1972) investigated sea-level pressure data from 76 tropical stations for the I G Y period (1 July 1957 to 31 December 1958) by means of cross-spectrum analysis. The spectra showed peaks corresponding to 4-5-day periods. Phases indicated a westward moving s ~- l wave in both hemispheres. MADDEN and SXOKES(1975) cross spectrally analyzed the pressure record for 73 years at three points in longitude at 25~ Seasonally averaged coherence squares showed a 5-day wave in summer data; the evidence for the 5-day wave in winter was not strong, but this may have been due to larger variance in the pressure record during winter. MISRA (1975) performed a cross-spectral analysis of the 24-hour tendency field of 850, 750, 500, 300 and 200 mb heights at forty-three tropical sites more or less evenly distributed in longitude for a two-month (January and December) series. He obtained spectral peaks at 4.6 days corresponding to a westward moving wave with s = 1. This behavior was most clearly seen at lower levels; at higher levels the spectral peak was not very prominent, nor was the phase progression clearly seen - most likely due to the poor signal to noise ratio.

Vol. 118, 1980)

Traveling Planetary Waves in the Stratosphere

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MONTH 5 LATITUDE 44 CHANNELB!2 8,0

v

!

I

I

I

n

~

~

#

I

I

v

I

l

r

i

i

w

I

I

i

v

!

I

r~

i

~

i

i

w

r

I

7.0

6.0

f.o 2.0

1.0

o.o 0.0

,,~ ~-, .5

i.o

~ 1.5 .

2.0

~ A ~3.0 ~,

2.5

3.5

FREQUENCYCYCLES/IIqY Figure 2 Power spe~ctrumfor May 1973 at 44~ The main peak is a traveling wave with a period of 6.2 + 0.5 days (adjusted for the westward progression of latitude crossings). The subsidiary peak has a period of 9.2 + 1 days. The units of spectral power are (deg)2/(cycles per day). RODGERS(1976).

Data for stratospheric levels were included in a study by DELAND and JOHNSON (1968). They performed a spherical harmonic analysis of two one-year series of Northern Hemisphere height data at various pressure levels up to I0 rob. One series comprised basically tropospheric data, the other stratospheric data, with overlap at 500 and 100 mb. They chose to extend the data anti-symmetrically about the equator so that the analysis involved only odd harmonics. Furthermore, they used only the two harmonics with greatest meridional scale for both s -- 1 and s = 2. Using vector regression techniques they found westward propagation for all four components. The gravest s = 1 component exhibited a dominant period in the range from about 5 to 6 days. MADDEN 0975) analyzed temperature and height data at 30 mb for 9 years. The record was broken up into eight 160-day 'winter' seasons beginning on 1 November. The 160-day mean was removed and a cross spectrum analysis was performed on the deviations. For s = 1, westward propagation with a spectral peak near 7 days was observed. Satellite (Nimbus 5) infrared radiance data representative of a layer 20 km thick centered near 45 km were studied by RODGERS (1976). He produced Fourier

250

R.L. Walterscheid

(Pageoph,

squared amplitude spectra for s = 1 at 41 latitudes from 80~ to 80~ for each month of a two-year series. A peak near 589 days is clearly seen in most of the spectra for s = 1 (Fig. 2). The frequency is slightly variable with month and latitude, usually remaining in the range 4.5-6.2 days. MADDEN (1978) cross spectrally analyzed height data for several tropospheric and stratospheric pressure levels from a nine-year period broken up into nine spring, summer and fall segments, and eight winter segments. The coherence squares and phase angles between the sine and cosine coefficients show significant evidence of westward propagating disturbances with periods near 5 days at all levels and in all seasons at both 30 and 40~ at all levels (except 850 mb at 40~ in winter). The studies mentioned above strongly indicate the existence of s = 1 westward propagating disturbances with periods near 5 days. In addition there is some indication of a similar s = 2 disturbance. Typical periods for the 5-day s = 1 wave are very near the theoretically predicted

gn (a) 2 |

~

9

j/./n

3

o.

4 I

3 I (o) 9 0 . 0 9 / n

(Po/P)

+ 1.6 5O

t~

9

o/

I00

I //q~'ln (a) 9 Kin (Po/P) + 1.6

e-

,/o

- 200

I -

/

300

I o ,,'~ I -4

I

- 500

I 6

I 8

I I0

I 20

I 40

850

a(m) Figure 3 Amplitudes (a) of 5-day composite summer season wave at 30~ Regression line determined from amplitudes is solid line. Dashed line is the theoretical expectation (constant is arbitrary). The distinction between open and solid circles is based on compositing procedure. MADDEN(1978).

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period for the gravest symmetric Rossby mode. Both the predicted and theoretical waves are westward propagating. (1) Vertical structure. DELAND and JOHNSON (1968) found almost monotonically increasing westward tilt up to the I0 mb level for the four spherical harmonics they studied. Westward tilt was also seen in the analysis of global data by ELIASEYand MACHENHAUER (1969). 4) More recent studies do not support the earlier findings of vertical tilt. MADDENand JULIAN(1972) concluded that the phase difference in height did not differ significantly from zero. As noted by DELAND(1973), phase variations in the stratosphere are not consistent with the close agreement in phase of the fluctuations in the ionosphere with planetary wave fluctuations in the stratosphere (KAwAmRA, 1970; DELAND and FRIEDMAN, 1972; DELAND and CAVALIERI, 1973). MISRA (1975) reported strong barotropy of the wave. MADDEN(1978) in his excellent and exhaustive analysis of the s = 1 zonal harmonic found that the 5-day wave is coherent in the vertical with very little slope in height. The variation of amplitude with height was also studied by Madden. He formed a composite summer season 5-day wave for 30~ and compared the amplitude increase in height with the increase predicted for oscillations on an isothermal basic state at rest (Fig. 3). He concluded that below 100 mb the amplitude of the 5-day wave increases with height consistent with theoretical predictions of equation 7. The amplitude of the oscillation in geopotential height increased from near 5 m at 850 mb to near 7 m at 100 rob. The more recent studies indicate that the 5-day wave does not exhibit a significant phase variation in height and grows in amplitude in a manner consistent with an exp 0cz) dependence in height. This dependence of phase and amplitude in height is characteristic of the predicted dependence for free oscillations. (2) Latitudinal structure. Similarities between the latitudinal structure of the observed s = 1 5-day wave and the gravest symmetric Rossby mode were noted by MADDEN and JULIAN (1972). They formed a global composite wave based on filtered IGY sea-level pressure data. The composite wave exhibited maximum amplitude at middle latitudes (40-60 ~) and did not show any large phase shifts with latitude. Moreover a cross-spectrum analysis (MADDEN and JULIAN, 1973) showed coherence and near zero phase difference between the 30-50~ zone and that at 30-50~ These observations indicate that there are no phase shifts associated with nodal latitudes. 4) The connection between the vertical structure of spherical harmonics (ELIASENand MACHENHAUER, 1965; DELANDand L[N, 1967; DELANDand JOHNSON, 1968) and the vertical structure of atmospheric waves is not clear. Since a spherical harmonic may not represent the horizontal structure of a mode of oscillation of the atmosphere, a single harmonic may include significant contributions from several waves, or it may simply fail to resolve adequately a single dominant wave. So, for example, horizontal structure variations with height unrelated to tilt (possibly associated with background winds) may produce appreciable vertical variation in the phase of a spherical harmonic.

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40N 0 40S 80S LATITUDE (Degrees) Figure 4 Amplitude of the 5-day wave as a function of latitude for November 1973. RODGERS(1976). RODGERS (1976) found similar amplitude structure in the temperature wave near 45 km (Fig. 4). He observed that maximum amplitudes (about 0.5 K) occur at around 50~ and 50~ MADDEN (1978) calculated the cross spectra between the sine coefficient of the s = 1 zonal harmonic at 30~ and the cosine coefficient at other latitudes in the Northern Hemisphere. The calculations indicated that the wave is coherent to 70~ and in phase at all latitudes, in agreement with the earlier finding of MADDEN and JULIAN (1972). We may conclude that the observed 5-day wave exhibits variations in latitude which are consistent with the variations predicted by the reference model. (3) Seasonal dependence. DELAND and JOHNSON (1968) found that the amplitude at 500 mb of the gravest s = 1 spherical harmonic of the height field was seen to be approximately constant at 10-15 m throughout the year. Ratios of the amplitudes in the stratosphere to the 500 mb amplitudes, on the other hand, show a strong seasonal dependence with the ratio increasing in winter. They found the wave to be well defined at 30 nab in January but not in July. However, RODGERS (1976) observed a slight tendency for greater temperature amplitudes in the summer hemisphere. This tendency is in agreement with the theoretical predictions of GEISLER and DICKENSON (1976).

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Also, in contrast to the earlier findings of DELAND and JOHNSON (1968), Madden found the wave to be best defined (highest coherence) in the summer season.

(b) 16-Day wave As in the case of the 5-day wave we begin by considering the 16-day wave in the troposphere. KUBOTA and IrDA (1954) performed a zonal harmonic analysis of the deviation from the mean of 500 mb heights at 50~ for a 36-day winter period and discovered westward propagating s = 1 and s = 2 disturbances with periods of about 16 days. ELIASEN and MACHENHAUER (1965, 1969) found evidence of westward traveling s = 1 disturbances with periods of about 15 days. Westward propagation for s = 2 harmonics was noted in their 1965 paper. More than 20 years of 500 mb height data at 50, 60 and 70~ were analyzed by A ~ I (1970). He Fourier analyzed 5-day means with respect to longitude for the entire year, and found westward propagation on the average for s = 1 and s = 2 at 70 and 60~ with a mean period of about 20 days. HIROTA (1968) constructed time sections along 60~ at 100, 30 and 5 mb for the s = 1 and s = 2 zonal harmonics by analyzing the 24-hour temperature tendency obtained from rocket observations and daily synoptic charts for a winter season. He found periods near 13 days associated with westward propagating s = 1 and s = 2 disturbances. Later HIROTA (1975) analyzed stratospheric data from a variety of sources. He constructed height-time sections for 25-60 km from meteorological rocket data for two three-month summer series and found evidence of a quasi-periodic oscillation with a period of about 15 days above 30 kin. A power spectrum analysis applied to the time-height sections revealed evidence o f ' 1 6 - d a y ' period oscillations in temperature and wind in the upper stratosphere at several rocket stations. A cross spectrum analysis suggested that the oscillations contained contributions from several waves. Hirota also analyzed satellite (ITOS-D) infrared measurements of temperature near 10 mb for the Southern Hemisphere for a one-month summer period and corresponding charts of 10 mb heights. He constructed time sections of zonal harmonics of the deviation from one-month means for latitudes from 30-60~ The analysis showed a westward traveling s = 1 wave with period in the range 13-15 days. The wave exhibited nearly constant phase propagation. An analysis of Nimbus 5 radiance data for the 40-45 km layer revealed behavior similar to that revealed by ITOS-D data. MADDEY (1978) in his cross-spectrum analysis of a nine-year series of height data at tropospheric and stratospheric pressure levels found evidence of a westward propagating s = 1 wave associated with significant coherence squares in about the one- to two-week period range. The cross-spectrum analysis indicated westward propagation for latitudes north of about 50~ (but see subsection (2) below). The observations mentioned above indicate the existence of s = 1 and s = 2 westward propagating disturbances with periods in the range 10-20 days. The propagation characteristics of the s = 1 disturbances with periods in the middle of this range

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resemble those of the (1, 4) Rossby wave mode which has a period near 15 days and propagates westward. However, we cannot altogether discount the (1, 3) Rossby wave which has a period of about 10 days. (1) Vertical structure. ELIASEN and MACHENHAUER (1965) found little tilt in the troposphere for both s = 1 and s = 2 waves. However HmOTA (1968) noted significant westward tilt in the stratosphere for both s = 1 and s = 2. To the contrary, Madden found that the s = 1 16-day wave is coherent in the vertical with very little (but possibly real) westward tilt. In his spectral analysis of rocket data HmOTA (1968) found that in general power density increased with height to a maximum near the stratopause. His analysis of satellite radiance data indicated a maximum amplitude near 10 mb for s =- 1 of about 1 K for the temperature wave and about 100 m for the height wave. The amplitude for s = 2 was comparatively weak. Based on the behavior of a composite wave for 60~ MADDEN (1978) concluded that the amplitude of the 16-day wave increased with height in agreement with predictions (Fig. 5). The amplitude increased from about 50 m at 850 mb to about 80 m at 100 nab. Taken together, the observations of phase variation do not represent persuasive evidence in favor of the notion that the 16-day wave is an external wave. Considerable weight however must be given to the study of MADDEN (1978) who found that the

Vol.

] I8,

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Traveling Planetary Waves in the Stratosphere

255

observed 10-day wave resembled the theoretical free waves with respect to both phase and amplitude variation. If the observed wave were a forced internal wave then according to theory (ignoring dissipation and possible complications due to mean winds) we would expect the amplitude to grow in height about as exp (z/2), that is, much faster than observed. Thus, although the observed exp (~z) growth could result from a fortuitous combination of effects, it seems reasonable to favor the supposition that the 16-day wave is a free external wave. (2) Latitudinalstructure. ARM (1970) found that the 16-day wave was more prominent at 60 and 70~ than at lower latitudes. This behavior is compatible with the structure of O~. MADDEN (1978) also found features of the latitudinal structure in common with the symmetric O~ wave mode (Fig. 6). At 100 mb the cross spectra could be interpreted to indicate a westward propagating wave at 30~ being out of phase with a similar wave at 60~ with a phase shift in between. In addition, a composite wave showed structure indicative of | including, in particular, a relative maximum near 60~ In an effort to detect inter-hemisphere coherence associated with a global oscillation, Madden performed a cross-spectral analysis between spectra at 60~ and 60~ for several years when Southern Hemisphere data were available. No significant coherence was found for periods near 16 days. A theoretical explanation for the lack of

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256

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coherence depends upon the fact that waves incident on a region where their phase velocity becomes westerly with respect to the mean zonal wind may be unable to propagate through the region. (This effect was studied theoretically by CHARNEV and DRAZIN (1961) and MATStJNO(1970) for forced planetary waves.) In addition, when the mean wind is weak westerly relative to the phase sPeed of the wave, dissipative effects due to infrared transfer may be greatly enhanced (DICKINSON, 1969). For the s = 1 16-day wave, moderately strong easterly winds in the equatorial stratosphere could effectively inhibit coupling between the two hemispheres. Lacking evidence that the observed 16-day wave is global in extent we cannot say with confidence that it corresponds to the theoretical (1, 4) Rossby wave despite the similarities in their latitudinal structures. It may be that the observed wave is the hemispheric counterpar t to the global (1, 4) Rossby wave. (3) Seasonal dependence. ARAI (1970) found that in the long-term averages of the 16-day wave height amplitudes are larger in winter than in summer (about 60 m compared to about 30 m). MADDEN (1978) found the largest coherence in winter and spring.

4. Conclusions The observations presented in this review do not present an entirely consistent view of the nature of the 5-day and 16-day waves, especially with respect to vertical structure. This is likely due to the different analysis techniques employed, and to the fact that the data sets used to refer to different geographic areas, altitude regimes, epochs and record lengths. Recent evidence, on balance, seems to favor the notion that the 5-day and 16-day waves are free waves of the Rossby type. The s = I 5-day wave seems to be consistent in frequency and structure with the gravest s = 1 symmetric Rossby mode. The identification of the s = 1 16-day wave is made highly uncertain by the finding (MADDEN, 1978) that it does not seem to be global. It may possibly be the next gravest symmetric or gravest anti-symmetric Rossby mode. The evidence seems to favor somewhat the former choice. Conclusive identification of the 5-day and 16-day wave will probably have to await an understanding of how these waves are excited. MADDEN (1978) has surmised that these waves are excited by random forcing. In order to show this it must be demonstrated that the atmosphere is capable of exhibiting some sort of phase selection, otherwise random fluctuations, though they have energy in the proper frequencies will tend to cancel in their effects. In addition an explanation of the forcing will have to account for the persistence of these waves against thermal damping. ELIASEN and MACHENHAUER (1965) observed waves with nearly continuous phase progression which completed 16 circuits of the earth, persisting for about 80 days. The thermal relaxation time however is much less than this duration. Thermal damping can have, in fact, a

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significant effect even on the relatively fast 5-day wave (GEISLER and DICKINSON, 1976). Thus it would appear that the excitation must be appreciable and, at least on occasion, continuous over a relatively long period of time. We close with the suggestion that the observed waves with periods near 16 days may be maintained against dissipation by energy derived from a topographic wave instability. In this view traveling waves are seen as integral components of flows which oscillate about equilibrium configurations. The oscillation results from the presence of topographically forced waves which are unstable with respect to wave perturbations of different horizontal scale. If the vertical scale of the instability is large the resulting traveling waves could exhibit more or less barotropic (external wave) behavior. There is some observational evidence of oscillating configurations which involve planetaryscale waves, and some theoretical support for the notion the oscillations may result from instabilities of the type mentioned. WEBSTERand KELLER(1975) examined an 18- to 23-day variation in zonal indices, momentum flux and mean and perturbation kinetic energies of the Southern Hemisphere upper troposphere and found indications that the variation results from a barotropic interaction between middle latitude mean westerlies and planetary-scale perturbations. An analysis of ozone and satellite radiance data indicated that the variation was not restricted to the troposphere or to the Southern Hemisphere. MADDEN (1975) studied 1- to 3-week oscillations in the mean zonal temperature in the high latitude winter stratosphere. Interactions between quasi-stationary and traveling planetary-scale waves were found to produce a large fraction of the horizontal eddy heat transports influencing the Oscillation. The evidence that these wave-mean flow variations may involve topography is found in recent theoretical investigations. Using a middle latitude beta-plane, barotropic channel model with both dissipation and mean flow driving, CHARNEY and DEVORE (1979) found that vacillation cycles could result from the instability of forced topographic waves. A simple analysis of their results indicated that traveling as well as standing waves were produced as components of the vacillation process involving topography (DEVORE, 1979). The traveling waves are maintained against dissipation by the instability. This barotropic model was recently extended to a baroclinic 2-level model by Professor Jule Charney of the Massachusetts Institute of Technology and Dr. David Straus of the NASA Goddard Space Flight Center (Greenbelt, M D). They found westward propagating waves with periods around 16 days which were integral components of a vacillation cycle involving baroclinic as well as barotropic processes (CHARNEY,1979). As in the earlier barotropic model the vacillation cycle involved an instability of tropographically forced waves. Thus the maintenance of the observed waves against dissipation through an instability process 5) provides a possible alternative to the two processes mentioned earlier, namely, forcing by stochastic processes (MADDEN, 1978) and forcing through ~) The possibility that these ultra-long waves were unstable perturbations with respect to a baroclinic zonal current was Considered by HIROTA(1968). He pointed out however that for such waves the phase speed must be greater (westerly) than the wind speed at the ground.

258

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periodic variation of the amplitude of the mean zonal wind (HIROTA, 1971). The hypothesis that the traveling waves are forced by stochastic processes lacks the support of a demonstrated phase selectivity. The hypothesis that the traveling waves in the stratosphere are forced from below by periodic variations in the amplitude of the zonal wind (viewed as given) lacks support from recent observations which indicate that these waves are not distinctly forced internal waves. It should be mentioned finally, that comprehensive support for the hypothesis that the observed waves with ' 16-day' periods are maintained by an instability is also lacking. The theoretical studies referred to did not deal specifically with wave numbers 1 and 2 and did not reveal the possible vertical extent of the instability. Obviously more theoretical and observational work must be done before any one of the hypotheses mentioned may be clearly preferred over the others.

Acknowledgements The author wishes to thank Mr. John DeVore and Dr. Carlos R. Mechoso of the University of California for their valuable discussions and criticism. This work was supported by the Aerospace-Sponsored Research Program.

REFERENCES ARAI, Y. (1970), A statistical study of ultra-long waves, J. Meteor. Soc. Japan 48, 469-478. BLAKE, D., and LINDZEN, R. S. (1973), The effect of photochemical models on calculated equilibria and cooling rates in the stratosphere, Mon. Wea. Rev. 101, 783-802. CHAPMAN, S., and LXNDZEN, R. S. (1970), Atmospheric Tides, D. Reidel, 200 pp. CHARNEV, J. G. (1979), Department of Meteorology, Massachusetts Institute of Technology, Cambridge, Mass., Private Communication. CHARNEY, J. G., and DRAZIN, P. G. (1961), Propagation of planetary scale disturbances from the lower into the upper atmosphere, J. Geophys. Res. 66, 83-109. CHARNEu J. G., and DEVORE, J. G. (1979), Multiple flow equilibria in the atmosphere and blocking, J. Atmos. Sci. 36, 1205-1216. DELAND, R. J. (1964), Traveling planetary scale waves, Tellus 16, 271-273. DELAND. R. J. (1973), Analysis of Nimbus 3 SIRS radiance data: Traveling Planetary-scale waves in the stratospheric temperature field, Mon. Wea. Rev. I01, 132-140. DELAND. K. J. and LIN, Y-J. (1967), On the movement and prediction of traveling planetary-scale waves, Mort. Wea. Rev. 95, 21-31. DELAND. R. J. and JOHNSON, K. W. (1968), A statistical study of the vertical structure of traveling planetary-scale waves, Mon. Wea. Rev. 95, 12-22. DELAND. R. J., and FRIEDMAN, R. M. (1972), Correlation of fluctuations of ionospheric absorption and atmospheric planetary scale waves, J. Atmos. and Terr. Phys. 34, 295-304. DELAND. R. J., and CAVALIERI, D. J. (1973), Planetary-sealefluetuations of pressure in the E-layer, f-min, and pressure in the stratosphere, J. Atmos. Terr. Phys. 35, 125-132. DEVORE J. G. (1979), Department of Atmospheric Sciences, University of California, Los Angeles, Private Communication. DICKINSON, R. E. (1969), Vertical propagation of planetary Rossby waves through an atmosphere with Newtonian cooling, J. Geophys. Res. 74, 929-938. DICKINSON, R. E. (1973), Method of parameterization for infrared cooling between altitudes of 30 and 70 kilometers, J. Geophys. Res. 78, 4451-4457.

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DIKV, L. A. (1965), The terrestrial atmosphereas an oscillating system, Izvestija Akademii Nauk SSR, Atmospheric and Oceanic Physics 1, 469-489. DIKe, L. A., and GouwsYN, G. S. (1968), Calculations of the Rossby wave velocities in the Earth's atmosphere, Tellus 20, 314-317. ELIASEN, E., and MACHENHAUER,B. (1965), A study of thefluctuations of atmospheric planetary flow patterns represented by spherical harmonics, Tellus 17, 220-238. ELIASEN, E., and MACHENHAUER,B. (1969), On the observed large scale atmospheric wave motions, Tellus 21, 149-165. GEISLER, J. E., and DICKENSON,R. E. (1976), The five-day wave on a sphere with realistic zonal winds, J. Atmos. Sci. 33, 632-641. HIROTA, 1. (1968), Planetary waves in the upper stratosphere in early 1966, J. Meteor. Soc. Japan 46, 418-430. HIROTA, I. (1971), Excitation of planetary Rossby waves in the winter stratosphere by periodic forcing, J. Meteor. Soc. Japan 49, 439-449. HIROTA, I. (1975), Spectral analysis of planetary waves in the summer stratosphere, J. Meteor. Soc. Japan 53, 33-44. HIROTA, [., and SATO, Y. (1968), Periodic variation of the winter stratosphere circulation and intermittent vertical propagation of planetary waves, J. Meteor. Soc. Japan 47~ 390--402. HOUGH, S. S. (1897), On the application of harmonic analysis to the dynamical theory of tides, Part I. On Laplace's' Oscillations of the First Species ', and on the dynamics of ocean currents, Phil. Trans. Roy. Soc. A189, 201-257. HOUGH, S. S. (1898), The application of harmonic analysis to the dynamical theory of the tides, Part H. On the general integration of Laplace' s dynamical equations, Phil. Trans. Roy. Soc. London A191, 139-185. KAWAHIRA, K. (1970), The winter anomaly of radio wave absorption in the D-region and the planetary waves in the stratosphere, Special contributions of the Geophysical Institute 10 (10), Kyoto University, Japan, 35-47. KUBOTA, S., and hDA, S. (1954), Statistical characteristics of the atmospheric disturbances, Pap. Meteor. Geophys. 5, 22-34. LAMB, H. (1910), On atmospheric oscillations, Proc. Roy. Soc. A84, 551-572. LAPLACE, P. S. (1825), Mecanique Celeste 5, Paris, 145-169. LEovY, C. B. (1964), Simple models of thermally driven mesosphere circulations, J. Atmos. 21, 327341. LINDZEN, R. S., and MCKENZIE, D. J. (1967), Tidal theory with Newtonian cooling, Pageoph 66, 90-96. LONGUET-HIGGENS, M. S. (1968), The eigenfunctions of Laplace's tidal equations over a sphere, Phil. Trans. Roy. Soc. London A262, 511-607. MADDEN, R. A. (1975), Oscillations in the winter stratosphere: Part 2. The role of horizontal eddy heat transport and the interaction of transient and stationary planetary-scale waves, Mon. Wea. Rev. 103, 717-729. MADDEN, R. A. (1978), Further evidence of planetary waves, J. Atmos. Sci. 35, 1605-1618. MADDEN, R. A., and JVLIAN, P. (1972), Further evidence of global-scale 5-day pressure waves, J. Atmos. Sci. 29, 1464-1469. MADDEN, R. A., and JULLAN, P. (1973), Reply to comments by R. J. Deland, J. Atmos. Sci. 30, 935-940. MADDEN, R. A., and STOKES, J. (1975), Evidence of global scale 5-day waves in a 73-year pressure record, J. Atmos. Sci. 32, 831-836. MATSUNO, T. (1970), Vertical propagation of stationary planetary waves in the winter Northern Hemisphere, J. Atmos. Sci. 27, 871-883. MISRA, B. M. (1972), Planetary pressure wave of 4 to 5 day period in the tropics, Mon. Wea. Rev. 100, 313-316. MISRA, B. M. (1975), Evidence of the 5-day period oscillation in the geopotentiat field, Tellus 27, 469-483. PEKERrS, C. L. (1937), Atmospheric oscillations, Proc. Roy. Soc. A158, 650-561.

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RODGERS, C. D. (1976), Evidence for the 5-day wave in the upper stratosphere, J. Atmos. Sci. 33, 710--711. TAYLOR, G. I. (1932), The resonance theory of semidiurnal atmospheric oscillations, Mem. Roy. Meteor. Soc. 4, 41-52. WEBSTER,P. J., and KELLER,J. L. (1975), Atmospheric variations and index cycles, J. Atmos. Sci, 32, 1283-1300. WILKES, M. V. (1949), Oscillations of the Earth's atmosphere, Cambridge University Press, 75 pp. (Received 15th June 1979)

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On the Interaction Between a Radiatively Damped Planetary Wave and the Zonally Averaged Circulation in the Middle Atmosphere By J. R. BATES1)

Abstract-The interaction between a planetary wave damped by cooling to space and the zonally averaged circulation in the middle atmosphere is examined for a steady-state situation in middle latitudes. Quasi-geostrophic scaling of Type 2 is assumed (i.e. the space scales are planetary and the superrotation is small). A set of mean equations is derived for this scaling which is complementary to the set of perturbation equations previously studied. The mean equations show that a planetary wave induces a mean meridional circulation which is balanced by an eddy momentum forcing function and a mean diabatic heating which is balanced by an eddy heat flux forcing function. The vertical eddy fluxes enter the forcing at the same order as the horizontal eddy fluxes. An analytical wave solution is found for the case of an atmosphere in constant superrotation. The eddy fluxes and forcing functions are evaluated for this special case. It is found that they are very sensitive to the values of the radiative damping coefficient and the superrotation. Since the damping coefficient depends on the ozone concentration and the intensity of the solar ultraviolet flux, the results suggest that changes in these quantities can strongly modify the wave-mean flow interaction in the middle atmosphere. Possible implications for climate change are discussed. Key words: Planetary wave; Radioactive damping; Wave-mean flow interaction.

I. Introduction The circulation of the middle atmosphere in the winter hemisphere is d o m i n a t e d by a westerly circumpolar vortex on which are superimposed quasi-stationary planetary waves generated by the thermal and topographic asymmetries of the earth's surface. The planetary waves are responsible for large transfers of heat and m o m e n t u m , particularly in the n o r t h e r n hemisphere, and thereby interact in a significant m a n n e r with the mean zonal circulation. The waves in t u r n are strongly influenced by the m e a n flow, thus leading to an interactive system of great complexity. Observational studies (e.g. NEWELL et al., 1972, 1974) show that in middle latitudes the planetary wave heat and m o m e n t u m transports in the winter stratosphere are directed poleward. The transports increase with height up to the limit of regular observations (approx. 30 kin) and are in m a n y regions directed u p the gradients of 1 Irish Meteorological Service, Dublin.

Vol. 118, 1980) Interaction Between a Planetary Wave and Averaged Circulation

267

mean temperature and angular velocity. Above a height of 30 km our observational knowledge of the eddy heat and momentum transports is meagre, though high altitude satellite investigations such as those of HARTMAnn (1976a, 1976b) have made a beginning on extending our knowledge of planetary waves upward. In the upper stratosphere and mesosphere planetary waves are subject to radiative and photochemical processes which strongly influence their dynamics. As shown by DICKINSON (1973), the infrared cooling at these levels can be parameterized by a Newtonian taw with the maximum cooling rate occurring in the neighbourhood of the stratopause, where the characteristic radiative relaxation time for temperature perturbations is about 5 days. It has been shown by BLAKE and LINDZEN (1973) that the effect of temperature-dependent ozone photochemistry is such as to produce a photochemical acceleration of the radiative damping in sunlit regions which reduces the relaxation time to as little as 1.5 days (though SCHOEBERLand STROBEL(1978) have questioned the importance of the photochemical acceleration for waves of vertical scale greater than the atmospheric scale height). A number of numerical models have been constructed which attempt to incorporate these radiative and photochemical processes in simulating the circulation of the stratosphere and mesosphere (a recent review is given by PRINN et al. (1978); see also SCHOEBERL and STROBEL (1978); RAMANATHAN and GROSE (1978); CHEN and RAMANATHAN (1978)). While successfully simulating the known circulation in many respects, these models still await sufficient observations to validate their findings for the higher levels. The dynamics of radiatively damped planetary waves were first studied analytically by DICKINSON (1969). In that paper the effect of the mean flow on the waves was investigated, but no attempt was made to estimate the effect of the waves on the mean flow. HOLTONand LINDZEN (1972) have studied the latter effect for equatorial waves, showing that the acceleration of the mean flow by radiatively induced wave momentum convergence in the lower stratosphere provides a mechanism for explaining the quasibiennial oscillation. HOLTON and DUNKERTON (1978) have studied the interaction between a damped transient wave and the zonal mean flow in the stratosphere using a quasi-geostrophic /3-plane model, and have emphasized the importance of wave transience in generating mean flow oscillations. The aim of the present paper is to study analytically the interaction between a radiatively damped planetary wave and the zonally averaged circulation in the middle atmosphere for a steady-state situation in middle latitudes. The waves are regarded as planetary in scale, so that they are governed by the quasi-geostrophic equations of Type 2 (BURGER, 1958; PHILLIPS, 1963; BATES, 1977: the lastnamed paper is hereafter referred to as B77). A set of mean equations is derived under the same assumptions as were used in B77 to derive the Type 2 perturbation equations. The wave forcing of the mean flow is evaluated for an idealized situation in which the perturbation equations can be solved analytically, and the dependence of the forcing on the superrotation and the radiative damping is investigated.

268

J.R. Bates

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2. The scaled perturbation and mean flow equations

The conditions under which the linearized primitive equations for small, steady perturbations about a zonal flow reduce to the quasi-geostrophic equation of Type 2 are given in B77. They are ~-~ = 0(1)

(1)

e--O = o 0 )

(2)

OZ - 0(1)

(3)

eu* =- s

17 cos~ << 1

(4)

~/Br = 0(1)

k,l~2

(5)

Br = 0(1)

(6)

sin 0 ~ cos 0.

(7)

(A list of symbols is given in Appendix 1 ; the notation is consistent with that of B77.) In the above, u* is chosen to be of order one, so that e is a measure of the superrotation of the atmosphere. Under the above conditions, it is shown in B77 that the perturbation equations, to zero order in e, are fv'=

e4'

(8)

.-=-1 ~4' a aO

fu' ~,,bl l

~---~ + Lo(v') + L~(W') = 0

--

~ tJ

U~

v a~

__

_

_

_

+ a i:)O~)z + F

w =

(9)

(10)

e4

- k, ~

(11)

where the only diabatic influence on the perturbations considered here is Newtonian cooling The primitive equations for the mean flow, where steady conditions are again assumed, are ~/~o(ti) + w t i = .fo - F

(l 2)

f+

(13)

titan 0 ) i / = I ~0 a -a

L0(o) + LAW) = 0 ~ 40~+r~=K0 a

04) ~7

05)

269

Vol. 118, 1980) Interaction Between a Planetary Wave and Averaged Circulation

where

ff = L'o(U'V') + L~(u' W') = Lo(v'qV) + L~(W'4,',) + K W'qV~. In the above we have used BOYD'S (1976) notation 1

~

1

Lo( ) -- a cos 0 ~0 [( ) cos 0],

a

1 0

L0( ) - a cos 2 0 a0 [( ) c~

0],

L~( ) = P ~-~ [( )p].

In arriving at (13) the assumption has been made that the mean meridional velocity components (0, W) are of the order of the perturbation amplitude squared and can thus be neglected in comparison to ~. The quantities F and G will be referred to as the momentum and thermal forcing functions, respectively. In quasi-geostrophic theory of Type 1 (where the length scale is assumed to be of the order of the Rossby number times the earth's radius)the vertical flux terms in ff and (~ are negligible by comparison with the horizontal flux terms (HoLTON, 1975, p. 51). Under the assumptions of quasi-geostrophic theory of Type 2, however, this is not the case, as can be seen by considering the ratios of the magnitudes of the perturbation quantities. It is shown in B77 (equation 12) that these are given by

(u':v':W':d?') ~

(')

l : l : -a: a f ~

.

(16)

Using assumptions (2) and (3), we then see that the vertical flux terms in F and (7 can, in general, be expected to be of the same order as the horizontal flux divergence terms. (This question will be examined in more detail below for a case where the perturbation equations allow an exact solution.) In addition we see from (16) that

F

1

t~

af2

(17)

In order to scale the mean equations we first rewrite (12) and (13) in the form

~f[g(~

u* - u*) + a w ,~Tcot0 . ] -u-.~ 1 =f~fff(l + 89

F

(18)

= - a ~0.

(19)

1

On the basis of (14) and the assumptions (2) and (3) we take

-~ ~ w-.

a

(20)

We then see that all terms on the left of (18) are 0(e) compared with fo, so that to zero order in e (18) becomes

f g = F,

(21)

270

J.R. Bates

(Pageoph,

Similarly (19) gives, to zero order in e I f ~ = - a ~b~ _

(22)

Using (22), (15) can be written a20 2Br -sin(20)u* ~

a + W =~Q-

(7.

(23)

Using (20) and the assumptions (3), (5) and (7) we see that the first term on the left is, at most, of the same order as the second term. But using (20), (21), (17) and (5) we see that aZ~2eBrW

a~Br P 2 sin 0 67

G r~J

Br 2 sin 0

-

-

= 0(~)

(24)

= G.

(25)

so that (23) becomes, to zero order in e,

~0

The set (21), (22) and (25) are the mean flow equations for quasi-geostrophic motion of Type 2. They show that for motions of planetary scale, the mean zonal flow is geostrophically balanced, the mean meridional flow is directly determined by the eddy momentum forcing function and the mean heating is directly determined by the eddy thermal forcing function. For small deviations from radiative equilibrium the mean heating can be parameterized as Q_ = - k r c p ( T -

T*)

(26)

where T* is the radiative equilibrium temperature. Thus, (25) shows that the deviation of the zonal mean temperature from radiative equilibrium is determined by the thermal forcing function (7. Comparing (21), (22) and (25) with the corresponding equations for quasigeostrophic motion of Type I (HOLTON, 1975, pp. 42 and 51) we see that they differ in that the vertical eddy flux terms are here retained while the vertical advection term in the thermodynamic equation is scaled out.

3. Eddy fluxes - qualitative considerations The scaled perturbation equations (8)-(11) in conjunction with the condition of geostrophic balance for the mean flow (22) allow us to derive simple expressions for the horizontal and vertical fluxes of heat and momentum, viz.,

Vol. 118, 1980) Interaction Between a Planetary Wave and Averaged Circulation

271 (27)

I

W ' 4 " = p [fifty'4'. - k~(4'~)2] 1

t

u'v' =- -f--~a 4~~

= p

(28)

t

(29)

f ~ u ' v ' + ~ 4o4~,, + ~ 4o~ 9

(30/

T o what extent are the fluxes dependent on radiative d a m p i n g ? We examine this question qualitatively for a region in which it is assumed that ~ > 0 and c~F/OZ = O. |t is profitable first to consider the following flux relationships derived in B77: p oz (pw'~') = u

V

4 ' 4 ; - (~;)~

~v -4z ~ = f ~1 [F W ' 4 ' + k~4 ' 4~]. '

(30

(32)

In the case where kr = O, (31) gives pW'4' = c~

(33)

where C is independent of Z. In particular, for a trapped wave C is zero. Referring to (32) we then see that, in the absence of radiative damping, the existence of a horizontal heat flux depends on the wind field being such as to allow a vertically p r o p a g a t i n g wave. Similar considerations apply to the vertical heat flux, as can be seen by referring to (28). When kT r 0, however, (31) shows that the d a m p i n g induces a convergence (or divergence) of vertical wave energy flux, so that the wave energy flux cannot be zero t h r o u g h o u t the region, whatever the wind field. Consequently, from (32) and (28), the horizontal or vertical heat fluxes cannot be zero either. Thus, in the case of a trapping wind field, any heat fluxes which occur are entirely radiatively induced. In the simple case where ~: = 0, the influence of d a m p i n g on the vertical heat flux is immediately apparent: the flux is downward and it goes to zero as k~-+ 0, whether the wave be trapped or propagating. Thus we conclude that the mean forcing function (7 resulting from eddy heat fluxes is in general partly induced by radiative d a m p i n g and partly a result of the vertical wave energy propagation, but in the case of a trapping wind field t~ is entirely radiatively induced. Considering the m o m e n t u m fluxes (29) and (30), we see that no information about these fluxes can be obtained without a' knowledge of ~b~.To examine how this quantity is determined we assume perturbation solutions of the form (u', v', W', ~b') = (~, ~, ~, q) e ~/2) e i ~ .

(34)

272

J.R. Bates

(Pageoph,

The perturbation equations (8)--(11) then reduce to a single equation in 0: 0~

-

~20

=

(35)

0

where 1[

tO~ : . 4(tO~ - - tO~)]

n~ = ~, 1 -

,,,(l

-

i~)

1

with tO

--

a cos 0

2Brf~ toe - sin 2 0 ~=

kr mto

From B77 we know that toc is the critical angular velocity for trapping. The 0dependence of this quantity can be expected to play an important role in determining the 0-dependence of ~2, and hence in determining q~0.The damping coefficient enters the governing equation only through the parameter ~. If this parameter approaches unity, the damping can be expected to have a strong influence on the dynamics of the perturbations. For a wind field of 50 m/sec, representative of mean conditions in the upper stratosphere in winter, with kr = (1.5 day) -1 (the maximum value which has been suggested for the radiative damping augmented by the photochemical acceleration) we find that :~ = 0.69/m. In spring and autumn, when the mean circumpolar vortex is weaker, ~ may attain even larger values than this. Thus it is to be expected that radiative damping will indeed play an important role in the dynamics of the perturbations and the consequent interactions with the mean flow.

4. An exact solution for the case o f constant superrotation

In this section we consider an idealized situation where above a given base level (Z = 0) the atmosphere is in constant westerly superrotation (to = const > 0), and kT and I" are constant. The governing equation for the perturbations is then given by (35) with

,[,

t*2 = 5, where

__;,,] ~c

(I

36,

Vol. 118, 1980) Interaction Between a Planetary Wave and Averaged Circulation

273

In addition we assume that the geopotential perturbation at Z = 0 is independent of latitude. U n d e r these conditions the solution for Z > 0 will vary with latitude only through 0-dependence of o)c. Setting

and choosing the positive real part we have

~, = 2-~J~[~ + 012 + ~ ) ~ 1 ~ ~, = - v d ( 2 l z . )

where

<_ 0

'[

"~ = ~,

>-- o

('/~c

(1 oa

Requiring upward wave energy flux and/or finite energy density at Z ---o% the only permissible solution of (35) is r

= oh(O) e - " z

whence we have 4'(A, O, Z ) = ~ ( 0 ) e-(", -1/2)z cos (mA - mZ).

(37)

The eddy fluxes (27)-(30) then become, with e = eo/.q: v'4~ = W'4'~ = -

~-~

2 sin'(20)]

[ ~m ] [ l ( ~~ ) ~

I m

(38)

,N] [(/xT _~)~ - + ~],l~(O)~e_~(._~,~, ~

-II zcos01 - ,,,

= [a--7~2] [2 g n ~ 2 - 0 i J ~

(I)(0)2 e - 2(.. - 1/2,z

+

(39)

(40)

~.'~-gO + (~ - 89 ao ]1

(41) We can also evaluate the resulting forcing functions (7 and F. Separating them into horizontal and vertical parts, i.e.

~=G+G

F=f.+Fv

274

(Pageoph,

J. R. Bates

where

G = t.o(v'4-G~) G = G ( w ' 4 ; ) + . w'4" r

= L;(u'v--')

F~ = L~(,' W') we find

G=

2 sin (20) t~ cot 0 - ~

(42)

+ 2z/x, 80 ]

(43)

G = G =

2si~(20)

cos_no 2 -

sinO

~-2ZcosO~

x t~(0) 2 e- ~(",- ~i2)z

=

~

Brr) [ I - 2 t , ~ Z ]

(44.) (Izr-

89 e - 2 ( a t - 112)Z.

~

(.'U

(45) From (36) we find

@, _ o~ cot 0

~

+ ~]

8tx~ _ o5~ cot 0 ~)0 4 I +,~z

I / x r2 +/x~ 2 ] > 0

/',~tzr - /~i~

The following features of the fluxes and forcing functions are apparent: (i) The horizontal eddy fluxes of heat and momentum are directed poleward. (ii) The vertical eddy flux of heat is directed downward. (ii) The horizontal and vertical momentum fluxes are zero at Z = 0, and for small Z the forcing function f is dominated by the component Fv. (iv) The magnitudes of the fluxes and forcing functions tend to infinity at large Z unless m > 89 (46) i.e. unless o5c > 4 (47)

Vol. 118, 1980) Interaction Between a Planetary Wave and Averaged Circulation

275

and > 2/(0% - 4) I/~.

(48)

(v) As N --> 0 the behaviour of the fluxes depends on the nature of the wind field. F o r a ' p r o p a g a t i n g ' wave (~c > 1), W'~', and 6;v tend to zero, but all the other fluxes and forcing functions tend to non-zero values. F o r a ' t r a p p e d ' wave (~c < 1), all the fluxes and forcing functions tend to zero. (vi) As N --->oo all the fluxes and forcing functions tend to zero. In Figs. 1-6, the fluxes and forcing functions are shown as functions of ~ for various values of ~c, taking m = 1, Z = I, 0 = 7r/4. F r o m these figures it is clearly seen that all the fluxes are strongly dependent on ~ , particularly in the region 0 < ~ < 1. In the case of a ' p r o p a g a t i n g ' wave, the effect of increasing ~ is generally to decrease the magnitudes of the heat and m o m e n t u m fluxes, except in the case of the vertical heat flux, whose magnitude increases with ~ for small ~ . In the case of a ' t r a p p e d ' wave, the magnitudes of all the fluxes increase from zero to attain m a x i m u m values for ~ < 1. The forcing functions G and F are likewise strongly dependent on ~ . In the cases shown Ga outweighs Gv, but this need not be so for all values of the parameters. F r o m Fig. 4 it is seen that ffH and -Fv are c o m p a r a b l e in magnitude for small ~ . An interesting feature shown in Fig. 6 is that for certain wind fields, the forcing function F can increase with ~ for small ~ even in the case of a ' p r o p a g a t i n g ' wave. We note that in all cases shown the sign of G is negative, implying by equation (25) a m e a n diabatic cooling. The eddy heat flux divergences thus force a positive

1-0 Solid curves: ~-~0~' v'---Tz Do,shed curves: ~-~T a2~2 w-~'z ,C

~_c x.

=75 _ _g

-.L,~

I

I

o

I

2

3

Figure 1 The horizontal and vertical eddy heat fluxes.

276

J . R . Bates

(Pageoph,

1"0

0

,. . . . _ _ - ~ z _ - ~ = = ~ - = = = ~ : ~ - - - - 2 2 = = - - = = - =

-'S /

/ I

-1~0 -1"5

t I I I

a2~' u~

Solid curves: ~-~2

/

o3~ z

Dashed curveS: - ~

u-~"

-2"0 I 2

1

I 3

Figure 2 The horizontal and vertical eddy momentum fluxes.

0"6

.L~c=t~ __...~-.-__~:~

- - - -

~t= 1'2 = -____-~.

~c = .75 . . . . . .

0

-1-0 So lid curves: r02~ g.

Ooshed curves: ~-~2 o2~ ~,

-2.0

-3.0

I 1

I 2

I 3

Figure 3 The components of the thermal forcing function.

Vol. 118, 1980) Interaction Between a Planetary Wave and Averaged Circulation 0

-2 -3

- 5 ~F-/ /

1

.Solid . . . . . .curves: . . . . . . ~a3f22 T g .~

-6

Doshed urves:

_7'I 0

I I

I 2

I 3

Figure 4 The components of the momentum forcing function.

0

It..~

-2

-3

I 1

I 2

Figure 5 The thermal forcing function.

I 4

277

278

J. R. Bates

(Pageoph,

-7 -8

I

2 Figure 6 The momentum forcing function.

deviation of the mean zonal temperature from its radiative equilibrium value. With observed values of the perturbation amplitudes in the stratosphere and with a representative value of the thermal forcing function taken from Fig. 5, the eddy-induced cooling rate can be of appreciable magnitude (e.g. taking a geopotential perturbation of amplitude 500 m, implying q~(0) = 4.9 x 103 m2/se@, with a forcing function given by [a2f2/O(0)2]G = - 1 we obtain from (25) a cooling rate of 2.5 K/day for wavenumber one alone). Similarly from Fig. 6 we see that for all cases considered the sign of _Pis negative, implying by equation (21) an equatorward meridional velocity. Again taking q~(0) = 4.9 x 103 m~/sec 2 and with a representative momentum forcing function (from Fig. 6) of [a3f~2/qb(O)2]ff= --3 we find for 0 = ~r/4 that g = - 0 . 5 m/sec.

5. Conclusions

The steady-state forcing of the mean flow in the middle atmosphere by planetary waves has been investigated under the assumptions of quasi-geostrophic motion of Type 2. It has been shown by scaling arguments that under these assumptions the mean zonal flow is geostrophically balanced, a mean meridional circulation is directly forced by the eddy momentum flux divergences and a mean diabatic heating is forced by the thermal forcing function resulting from eddy heat fluxes. The scaling arguments (and some explicit calculations with the scaled equations) indicate that the contribution

Vol. 118, 1980) Interaction Between a Planetary Wave and Averaged Circulation

279

of the vertical eddy fluxes to the forcing of the mean flow can be of the same order as that of the horizontal eddy fluxes. This leads one to question the neglect of vertical eddy fluxes in the numerical models of the middle atmosphere which have been referred to in the Introduction. To gain insight into the fluxes and the resulting forcing functions, an idealized situation has been considered where the atmosphere above a given level is in a state of constant westerly superrotation and has a constant static stability and radiative damping coefficient. W i t h a geopotential perturbation independent of latitude prescribed at the base level, an analytical solution has been obtained which allows all the fluxes and forcing functions to be evaluated. For a given wave amplitude at the base, it has been shown that the eddy fluxes and forcing functions depend critically on the strength of the mean flow - in particular, on whether it is greater or less than the critical value for wave t r a p p i n g - and on the strength of the radiative damping. The influence of the damping is measured by a parameter ~ which is the Newtonian cooling coefficient divided by the product of the wavenumber and the mean superrotation. For a wind field such as to give wave trapping, no eddy fluxes of heat or momentum, and consequently no forcing of the mean flow, occur in the absence of radiative damping. As ~ increases from zero, however, eddy fluxes and forcing functions are generated which reach maximum absolute values for ~ in the interval (0, 1) and decay to zero for large ~ . For a wind field such as to allow wave propagation, eddy fluxes of heat and momentum (though not a vertical eddy heat flux) occur even in the absence of radiative damping; the horizontal eddy heat flux (directed poleward) is a consequence of the upward flux of wave energy, in accordance with the well-known result of ELIASSEN and PALM (1960), while the horizontal and vertical momentum fluxes (the former always directed poleward) are a consequence of the variation with latitude of the critical superrotation for trapping. The consequent (undamped) forcing functions induce a mean meridional circulation and a mean diabatic heating. [The fact that an undamped standing wave propagating through a steady mean flow should force a mean diabatic heating may at first sight appear to contradict the Charney-Drazin Theorem (CHARNEV and DRAZIN, 1961; BOYD, 1976; ANDREWS and MClNTYRE, 1976). That this is not so, however, is shown in Appendix 2.] Radiative damping has been shown to have a very strong influence on the magnitudes of the eddy fluxes and forcing functions for a propagating wave, particularly for .~ in the region (0, I). In general, for small values o f , ~ the effect of the damping is to cause a rapid decrease in the magnitude of the forcing. Under certain circumstances, however, the damping may actually increase the magnitude of the forcing for small values of .N, just as in the case of a trapped wave. This sensitivity of the eddy forcing of the mean flow to the value of.N, considered in conjunction with the balance of terms in the mean thermodynamic equation indicated by the planetary scaling, suggests that the radiative damping coefficient

280

J.R. Bates

(Pageoph,

for the waves is a crucial parameter in determining the mean circulation of the middle atmosphere. Any influence that leads to changes in the ozone concentration in the middle atmosphere will necessarily result in changes in the radiative damping coefficient, both directly through changing the mean temperature and indirectly through modifying the photochemical acceleration. For similar reasons the damping coefficient will be influenced by any changes in the intensity of solarultraviolet radiation, whether due to solar fluctuations or to seasonal changes in the zenith angle. Obviously, to study the full dynamical effects of any such changes it is necessary to consider the total circulation, i.e. the mean flow, the waves and the wave-mean flow interaction. Model calculations described in B77 have suggested that the tropospheric climate may change as a result of changes in the mean wind field in the stratosphere. This suggestion has been corroborated by the more comprehensive model calculations of AVERY (1978) and by calculations referring to the stratosphere alone by SCHOE~ERL and GELLER(1977). In these studies it was found that the sensitivity of the tropospheric planetary waves to changes in the radiative damping coefficient at high levels was of a lesser order than that associated with changes in the mean wind field. The mean wind fields, however, were prescribed independently of the radiative damping, whereas the results of the present paper suggest that the mean wind fields may to a large extent be determined by the wave-mean flow interaction, which in turn, is sensitively dependent on the radiative damping. It is possible, therefore, that the overall climatic sensitivity to changes in the radiative damping rate in the middle atmosphere may be greater than has previously been suggested. All dynamical reasoning about the middle atmosphere and its possible role in the general circulation, whether based on numerical or analytical studies, must remain tentative in the absence of more thorough observational knowledge. There is an urgent need for accurate estimates of the wave fluxes of heat and momentum and the consequent wave interactions with the mean flow.

Appendix I List of Symbols a Earth's radius Burger number (F/a2f22) Br Specific heat of dry air at constant pressure Cp Coriolis parameter (2~2 sin 0) f Radiative damping coefficient k~ 1

L~( )

p c:IZ [P( )]

Lo( )

a cos 0 70 [( ) cos 0]

Vol. 118, 1980) Interaction Between a Planetary Wave and Averaged Circulation L~( ) m

P Po

Q' 0 R

t

T T* U

t

V'

W' W Z P

8/8x

a c o s 2 0 00 [( ) c ~

0]

Zonal wavenumber Pressure Pressure at base of region of interest (constant) Perturbation heating per unit mass Zonally averaged heating per unit mass Gas constant for dry air Radiative damping parameter (kr/m~o) Time Zonally averaged temperature Radiative equilibrium temperature Perturbation westerly wind component Zonally averaged westerly wind component Dimensionless value of Complex amplitude of u' Perturbation southerly wind component Zonally averaged southerly wind component Complex amplitude of v' Perturbation component of W, dZ/dt Zonally averaged value of W, dZ/dt Complex amplitude of W' - In (P/Po) Static stability parameter [R(?;T'/~Z + KT)] I /~ a cos 0 Oh

0

Dimensionless parameter measuring superrotation Latitude

K

R/C~

h

Longitude Index of refraction divided by i Imaginary part of/z Real part of Perturbation geopotential Zonally averaged geopotential Complex amplitude of r e -z~2 Streamfunction for mean meridional flow Superrotation (9/a cos 0) Critical superrotation for trapping (2Brf2/sin 2 0)

8

F F~ FT

~p x

ose

O)c/r

Earth's rotation rate

281

282

I . R . Bates

(Pageoph,

Appendix 2 The C h a r n e y - D r a z i n theorem states that a simple harmonic wave propagating through a mean flow does not interact with the mean flow in the absence of dissipation, critical levels and thermal forcing. In the present context, where we are considering the particular case of a standing wave in a mean flow which has no critical levels, this theorem implies that setting Q' = ~) = 0 necessarily gives fit = 0, ~zt = 0. If we begin, as here, requiring that in a certain region fit = ~ t = 0 does it not follow that if Q' -- 0 (i.e. ~ = 0) in that region, we must also have Q = 07 Though such a conclusion would certainly be consistent with the C h a r n e y - D r a z i n theorem, we shall show that in general it does not hold. We argue from the primitive equations, using Boyd's (1976) paper. Setting u~ = ~ t = Q' = 0, and also taking ~ = 0 for simplicity, Boyd's equations (2.32) and (2.34) give L~(X) = L~(v'~f'z/r)

(A.1)

Lo(x) = Lo(v'~',/F) - KQ/P.

(A.2)

(Here we have replaced N ~ by I~ and have included Q; it can easily be shown that Boyd's equations will tolerate this degree of generalization.) Integrating (A. 1) gives - -

v'd~'~/r

-

P0

X = 7

[v'C'~/r

-

X]0

(A.3)

where the subscript 0 denotes values at Z = 0. Substituting (A.3) in (A.2) gives = (e~/K)[Lo(v'd?---~'~) -

rLo(X)]o

= (e~'/,<)[(~n + F W]0.

(A.4)

Thus it is indeed possible to have a non-zero Q, but it must satisfy the characteristic of having an exponential Z-dependence in the region under consideration. The mean heating calculated from our explicit wave solution and given by eqn. (25) does have this characteristic. For letting . # - + 0, we see that #~--> 0 for o3C > I (only the case I is of concern here, since only then do we find a non-zero with .# = 0) and thus (25) gives Q = dHl~.

(A.5)

This is consistent with (A.4) if Wo = 0 and GH = e:Gn(0).

(A.6)

We see that (A.6) is indeed satisfied by (42) in the limit ,# -+ 0. We therefore conclude that obtaining a non-zero Q from the scaled equations for steady planetary flow when Q' = 0 is consistent with the properties of the primitive equations and involves no violation of the Charney-Drazin theorem.

Vol. 118, 1980) Interaction Between a Planetary Wave and Averaged Circulation

283

REFERENCES ANDREWS, D. G. and MCINTYRE, M. E. (1976), Planetary waves in horizontal and vertical shear: The generalized Eliassen-Palm relation and the mean zonal acceleration, J. Atmos. Sci. 33, 2031-2048. AVERY, SUSAN K. (1978), The tropospheric forcing and vertical propagation of stationary planetary waves in the atmosphere, Ph.D. Thesis, University of Illinois at Urbana-Champaign, 145 pp. BATES, J. R. 0977), Dynamics of stationary ultra-long waves in middle latitudes, Quart. J. R. Met. Soc. 103, 397-430. BLAKE, D. and LINDZEN, R. S. (1973), Effect of photochemical models on calculated equilibria and cooling rates in the stratosphere, Mort. Weather Rev. 101, 783-802. BOYD, J. P. (1976), The noninteraction of waves with the zonally averaged flow on a spherical earth and the interrelationships of eddy fluxes of energy, heat and momentum, J. Atmos. Sci. 33, 2285-2291. BURGER, A. P. (1958), Scale considerations of planetary motions in the atmosphere, Tellus 10,

195-205.

CHARNEY,J. G. and DRAZIN,P. G. (1961), Propagation of planetary scale disturbances from the lower into the upper atmosphere, J. Geophys. Res. 66, 83-109. CHEN, T-C. and RAMANATHAN, V. (1978), A numeircal simulation of seasonal stratospheric climate. Part H. Energetics, J. Atmos. Sci. 35, 615-633. DICKINSON, R. E. (1969), Vertical propagation of planetary Rossby waves through an atmosphere with Newtonian cooling, J. Geophys. Res. 74, 929-938. DICKINSON, R. E. (1973), Method of parameterization for infrared cooling between altitudes of 30 and 70 kilometres, J. Geophys. Res. 78, 4451-4457. ELIASSEN, A. and PALM, E. (1960), On the transfer of energy in stationary mountain waves, Geofys. Publ. 22, No. 3, 22 pp. HARTMANN~ D. L. (1976a), The structure of the stratosphere in the southern hemisphere during late winter 1973 as observed by satellite, J. Atmos. Sci. 33, 1141-1154. HARTMANN, D. L. (1976b), The dynamieal climatology of the stratosphere in the southern hemisphere during late winter 1973, J. Atmos. Sci. 33, 1789-1802. HOLTON, J. R. (1975), The dynamic meteorology of the stratosphere and mesosphere, Met. Monographs 15, No. 37, American Met. Soc., 218 pp. HOLTON, J. R. and DUNKERTON, T. (1978), On the role of wave transience and dissipation in stratospheric mean flow vacillations, J. Atmos. Sci. 35, 740-744. HOLTON, J. R. and LINDZEN, R. S. (1972), An updated theory for the quasi-biennial cycle of the tropical stratosphere, J. Atmos. Sci. 29, 1076-1080. NEWELL, R. E., KIDSON, J. W., VINCENT, D. G. and BOER, G. J. (1972), The generalcirculation of the tropical atmosphere and interactions with extratropical latitudes, VoI. I, M1T Press, Cambridge, Massachusetts and London, England, 258 pp. NEWELL, R. E., KIDSON, J. W., VINCENT, D. G. and BOER, G. J. (1974), The general circulation of the tropical atmosphere and interaction with extratropical latitudes, Vo[. 2, MIT Press, Cambridge, Massachusetts and London, England, 371 pp. PHILLIPS, N. A. (1963), Geostrophic Motion, Revs. of Geophys. 1, 123-176. PRINN, R. G., ALYEA, F. N. and CONNOLD, D. M. (1978), Photochemistry and dynamics of the ozone layer, Ann. Rev. Earth Planet. Sci. 6, 43-74. RAMANATHAN, V. and GROSE, W. L. (1978), A numerical simulation of seasonal stratospheric climate, Part 1. Zonal temperatures and winds, J. Atmos. Sci. 35, 600-614. SCHOEBERL, M. R. and GELLER, M. A. (1977), A calculation of the structure of stationary planetary waves in winter, J. Atmos. Sci. 34, 1235-1255. SCHOEBERL, M. R. and STROBEL, D. F. (1978), The zonally averaged circulation of the middle atmosphere, J. Atmos. Sci. 35, 577-591. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkhhuser Verlag, Basel

A Numerical Model of the Zonal Mean Circulation of the Middle Atmosphere t) By JAMES R. HOLTON a n d WILLIAM M. WEHRBEIN2)

Abstract- The annual cycle of the zonally averaged circulation in the middle atmosphere (16-96 kin) is simulated using a numerical model based on the primitive equations in log pressure coordinates. The circulation is driven radiatively by heating due to solar ultraviolet absorption by ozone and infrared cooling due to carbon dioxide and ozone (parameterized as a Newtonian cooling). Since eddy fluxes due to planetary waves are neglected in the model, the computed mean meridional circulation must be interpreted as the diabatic circulation, not as the total eulerian mean. Rayleigh friction with a short (2-4 day) time constant above 70 km is included to simulate the strong mechanical dissipation which is hypothesized to exist in the vicinity of the mesopause due to turbulence associated with gravity waves and tides near the mesopause. Computed mean winds and temperatures are in general agreement with observations for both equinox and solstice conditions. In particular, the strong mechanical damping specified near the mesopause makes it possible to simulate the cold summer and warm winter mesopause temperatures without generating excessive mean zonal winds. In addition, the model exhibits a strong semiannual cycle in the mean zonal wind at the equator, with both amplitude and vertical structure in agreement with the easterly phase of the observed equatorial semiannual oscillation. Key words: Zonal mean circulation; Diabatic circulation; Rayleigh friction; Equatorial semiannual oscillation.

1. Introduction The general circulation of the middle atmosphere (here taken to be the region of the atmosphere between a b o u t 30-90 km) differs dramatically from that of the lower atmospheric layers. The overall mean circulation of the middle atmosphere is thermally driven by the absorption of solar ultraviolet radiation in the ozone layer. The net radiative heating which arises from the difference between this solar heating and the emission of infrared radiation by water vapor, c a r b o n dioxide, and ozone has strong meridional and seasonal variations. At the solstices there is a m a x i m u m net heating near the s u m m e r pole and a m a x i m u m net cooling near the winter pole. This differential radiative drive has a m a x i m u m amplitude of several degrees per day centered near the stratopause at a b o u t 50 km. The mean meridional circulation driven by this 1) Contribution No. 497, Department of Atmospheric Sciences, University of Washington, Seattle. 2) Department of Atmospheric Sciences, University of Washington, Seattle, Washington 98195, USA.

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A Numerical Model of the Zonal Mean Circulation

285

8O

80 4

o

*6

3

70

70 l

I

60.

b6o

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Figure 1 Latitude-height sections of the observed solstice season mean zonal wind distribution (m s-z, upper frame) and zonally averaged temperature distribution (K, lower frame). After C I R A (1965).

286

James R. Holton and William M. Wehrbein

(Pageoph,

heating distribution consists of a single thermally direct cell with rising motion in the summer hemisphere, sinking in the winter hemisphere, and a compensating meridional flow directed from the summer to the winter hemisphere?) The Coriolis torque associated with this meridional flow generates mean zonal easterlies in the summer hemisphere and mean zonal westerlies in the winter hemisphere as illustrated in Fig. l. The corresponding temperature field, which to a good approximation is in thermal wind balance with the mean zonal winds, is also shown in Fig. 1. Most observational and theoretical studies of the general circulation of the middle atmosphere have emphasized solstice conditions. However, because of the seasonal reversal of both the mean zonal and mean meridional wind fields it is clear that the equinoctial circulation regime must differ substantially from solstice conditions. In fact, the radiatively driven mean meridional circulation at the equinoxes is qualitatively similar to the diabatic mean meridional circulation in the troposphere. That is, there is rising motion in the equatorial zone, poleward meridional drift in both hemispheres, and subsidence near the poles. Thus, the Coriolis torque generates mean westerlies in both hemispheres during this season, as illustrated in Fig. 2. The corresponding mean temperature profile, also shown in Fig. 2, features temperatures decreasing from the equator toward both poles throughout most of the middle atmosphere, as required for thermal wind balance. The first attempt to partially model the general circulation of the middle atmosphere was due to MURGATROYD and S~NGLETON(1961). They used the net radiative heating fields computed earlier by MURGATROYDand GOODY (1958) to diagnostically compute the mean meridional circulation subject to the assumption that adiabatic heating (cooling) by the mean vertical motion exactly balanced the imposed radiative cooling (heating). Their computed mean meridional circulations for solstice and equinox conditions were qualitatively similar to those described above. Their model, however, was based entirely on heat balance considerations. They did not determine whether their derived mean meridional circulations were consistent with the observed zonal momentum field. The momentum budget of the mean zonal flow in the middle atmosphere was first studied theoretically in the classic paper of LEOVV 0964). Leovy divided the radiative heating into two parts: an 'external' heating which was a specified function of location and season, and an 'internal' heating which he assumed was proportional to the deviation of the zonal mean temperature from the standard atmosphere value. Thus, the n e t radiative heating in his model depended indirectly on the computed zonal mean circulation (through the temperature dependent cooling term). Leovy's model employed a linearized version of the zonally averaged dynamical equations. The annual cycle was included by specifying a sinusoidal time dependence with a period of one year. He found that even in the presence of this imposed annual :3) Superposed on this diabatic circulation in the winter hemisphere there may be an oppositely directed eddy driven mean meridional motion. Thus, the total eulerian mean meridiona[ flow may differ from the diabatic circulation described here.

Vol. 118, 1980)

287

A Numerical Model of the Zonal Mean Circulation

\ 60.

1

/

~ 50-

80

t

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Figure 2 Latitude-height section of the observed equinox season mean zonal wind distribution (m s-1, upper frame) and zonally averaged temperature distribution (K, lower frame). After C I R A (1965).

288

James R. Holton and William M. Wehrbein

(Pageoph,

cycle, substantial mechanical dissipation was required to prevent the Coriolis torque of the radiatively driven mean meridional circulation from generating excessively strong mean zonal flows. He recognized that at least part of this required damping might be due to eddy momentum fluxes associated with large scale motion systems, and that the same motions would also produce substantial eddy heat fluxes. However, since insufficient data were available to determine the magnitudes and distributions of these fluxes, Leovy parameterized their effects in the simplest possible fashion by including a Rayleigh friction damping term in the zonal momentum equation, and by combining the effects of the eddy heat flux divergence and the temperature dependent radiative cooling into a single Newtonian cooling term in the thermodynamic energy equation. In order to obtain analytic solutions with his linearized model, he specified constant values for the mechanical and thermal damping coefficients. For simplicity, he also assumed that these Rayleigh friction and Newtonian cooling coefficients were equal. He found that in order to produce realistic solstice season mean zonal flow profiles with this model a rather large damping rate (0.743 x 10 -6 s-1) was required. Even with this very short damping time ( ~ 15 days)the computed winter solstice mean zonal flow exceeded 120 m s -1 at 72 km, which is substantially larger than the observed 80 m s -1 given in CIRA (1965). Despite the many simplifications inherent in Leovy's linearized model, he did succeed in qualitatively simulating the essential features of the observed solstice circulation described above. This qualitative agreement between the model and observations suggests that Leovy's simple parameterization of the eddy flux divergences in terms of linear damping may be adequate for simulating the zonally averaged circulation in the upper stratosphere and the mesosphere. Indeed, SCHOEBERL and ST~OBEL(I 978) have shown that with an improved radiative heating formulation and height dependent damping the Leovy model can produce quite realistic mean wind fields. However, simulation of important features of the mean circulation in the lower stratosphere, such as the polar night jet and the quasi-biennial oscillation, probably requires a three-dimensional model in which large scale eddies are computed explicitly. There have been a number of attempts to model various aspects of the general circulation of the middle atmosphere using three-dimensional numerical models. The most sophisticated such models (ile., general circulation models based on the primitive equations) have been limited in vertical extent to the troposphere and lower stratosphere (at least in works published to date). For example, MANABEand MAHLMAN (1976) have used the G F D L model to study the seasonal cycle in the stratosphere below the 10 mb (-~32 kin) level. KASAHARAet al. (1973) have used the NCAR model to simulate the lower stratospheric circulation, but only for perpetual January conditions. The three-dimensional model of most relevance to the present work is the model of CUNNOLD et al. (1975). Their model domain covers the entire globe and extends vertically from the surface to about 72 km. The model is based on the balance equations,

Vol. 118, 1980)

A Numerical Model of the Zonal Mean Circulation

289

and has a highly simplified representation of tropospheric processes. Nevertheless, they obtain a fairly realistic annual cycle in the mean zonal winds and temperatures. Their mean meridional circulation does, however, differ from the thermally direct pole to pole circulation found by Leovy for solstice conditions. CU~q~OLDet al. found that in high latitudes during winter the eulerian mean meridional circulation is indirect, with rising motion near the pole and sinking equatorward of 60 ~ latitude. Although CUNNOLD et al., did not attempt to diagnose the cause of this indirect mean meridional flow; there can be little doubt that it is an eddy driven mean flow generated by vertically propagating planetary waves in the winter hemisphere. Since the work of ELlASSEN(1950) it has been known that eddy heat and momentum flux divergences tend to force a compensating mean meridional circulation. Such a compensating mean cell must exist because the eddy fluxes themselves tend to destroy the thermal wind balance in the mean flow (HOLTON, 1972, pages 228-234). The essential consequences of this eddy-mean flow compensation are expressed in the 'noninteraction' theorem (ANDREWS and MCINTYRE 1976; BOYD 1976; and refs.). Specifically, this theorem shows that under suitable conditions nondissipative waves of steady amplitude will induce a mean meridional circulation which exactly cancels the eddy fluxes of the waves. Thus, the waves produce no net mean flow acceleration. The relevance of these theoretical notions to the overall dynamics of the middle atmosphere has been discussed by DUNKERTON(I 978). He has elucidated the difference between the eulerian mean meridional circulation which arises from the combination of adiabaticalIy driven portion and an eddy driven portion, and the [agrangian mean meridional circulation which in the middle atmosphere is nearly identical to the diabatic (i.e., radiatively driven) circulation. As pointed out by Dunkerton, it is the latter flow which is more directly related to the net meridionat mass (tracer) transport in the middle atmosphere. Exact cancellation between the eddy fluxes and the induced mean meridional circulation does not occur when the eddies are transient (varying in amplitude) or subject to dissipation. Nevertheless, for normal stratospheric conditions it is clear from the general circulation model results of MANABE and MAHLMAN (1976) that the net acceleration of the mean zonal flow in the winter stratosphere is due to a small difference between the eddy forcing and the forcing by the mean meridional circulation. Furthermore, this small difference is primarily due to forcing by the diabatic circulation rather than forcing due to eddy transience or dissipation. In summary, it should be permissible in a first approximation to neglect the eddy heat fluxes and the eddy momentum fluxes due to planetary waves provided that the resulting mean meridional circulation is interpreted as the diabatic circulation and not as the total eulerian mean. 2. The dynamical model The model is based on the primitive equations in the log pressure coordinate system as given by HOLTON(1975). In order to avoid the problems inherent in simulat-

290

James R. Holton and William M. Wehrbein

(Pageoph,

ing tropospheric meteorological processes, the lower boundary of the model domain is set at the 100 mb level (i.e., near the tropopause) and the effects of forcing by the zonally symmetric tropospheric flow are included in the lower boundary condition. The upper boundary is at approximately 96 kin, and the latitudinal extent is global. 2.1. Basic equations In setting down the basic equations we will make use of the following symbols: 2, 0 z H R T~ g p Ps u v w To q~o T (1) f~ a J cp dx dy

longitude latitude a measure o f ' h e i g h t ' [-= - H l n (p/p~)] scale height [=RT~/g] gas constant for dry air a constant stratospheric mean temperature gravitational acceleration pressure a constant reference pressure eastward velocity northward velocity a measure of 'vertical velocity' [=dz/dt] a basic state temperature [-= To(z)] a basic state geopotential [~ q)o(z)] departure of local temperature from To(z) departure of local geopotential from q~o(z) angular velocity of earth radius of earth diabatic heating rate per unit mass specific heat at constant pressure ratio of gas constant to specific heat at constant pressure [= R/%] eastward distance increment [=-a cos 0 dA] northward distance increment [ = a dO].

The horizontal momentum equations can then be written in flux form as -

8u 8u 2 1 8 g-y (uv cos 2 0) ~:t + ~ + cos 2 0 -

+--

I ~z ( p o W U ) -

P0

-

8<1) + D1(u)

2~-v sin O -- - - -

/~x

(2.])

8v 8 1 0 -~ ( ~ cos 0) ~t + -~x (uv) + cos 0 -

1 8

u2 tan 0

+ -- =- (povw) + - Po cz a

+ 2f~u sin O = - - -

8r

8y

+ D2(v).

(2.2)

Vol. 118, 1980)

A Numerical Model of the Zonal Mean Circulation

291

Here, po = p~ exp ( - z / H ) , where ps is the mean density at z = 0. Dl(u) and D2(v) represent subgrid scale m o m e n t u m diffusion. Explicit forms for these terms will be given in Section 2.4. Using the above notation the hydrostatic approximation and continuity equation become

dCbo RTo dz = H '

Odp R T a---z-= - i f '

(2.3)

and c~u 1 ~z c~ (poW) = 0. . . 1 . 0 ( .v c o s 0 ) + p0 0x + cos 0 ~3y

(2.4)

The variables To and r 0 define a horizontally averaged hydrostatically balanced basic state which is specified to be the U.S. standard atmosphere. Using (2.3) we can write the thermodynamic equation for the departure from the basic state as follows 4)

~t

+ 7 x (u~l~) + - -

- ( v ~ cos 0) cos 0 -~?y

+ --

(poO)~w) + w N 2

KJ/H + D2(CI)~) (2.5)

P o -~Z

where N2 - ~ \--~z +

is the buoyancy frequency squared, and we have let D2((I)~) denote the subgrid scale diffusion. The basic state temperature profile is assumed to be in radiative equilibrium (see Section 2.5) so that the horizontal average of the diabatic heating will vanish provided that the horizontally averaged temperature equals the basic state temperature To(z). Because of the nonlinearity of (2.5) the horizontally averaged temperature need not remain equal to To(z) as the flow evolves in time. However, in practice we find that departures of the horizontally averaged total temperature from To(z) are at most a few degrees so that for practical purposes the horizontally averaged diabatic heating remains very small, and J can be regarded as the differential heating.

4) Following HOLTON(1975) we here neglect the snmll term w•T/H compared to wKTo/H. This approximation is necessary if we wish to define available potential energy in terms of the temperature variance.

292

James R. Holton and William M. Wehrbein

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2.2. The zonal mean equations We now define density weighted zonally averaged variables by letting

{i} I1 = -~-~-j_ ~ ~

da

(2.6)

I,KJ/HJ

Zonally averaging (2.1), (2.2), (2.4), and (2.5) we obtain

OU

f V = _e~12u [ 1

a (UFcos z 0) + a (UW) ] + FM + DI(U)

[cos 2 0 ~-y

aV__+ f U = ___aWF_ e~/2HU2 tan 0 + D2(V) (3t

c~y

c9 (~W a-t -~z +

(2.8)

a

1 a (VcosO)+ (a cos 0ay ~z

(2.7)

1 )~-~ W = 0

(2.9)

+ N2W =

e~/2.f

1

a [Vcos0

a + D2 ~

+

+ Q

(2.10)

where f = 2f2 sin 0 is the Coriolis parameter. Here FM denotes the convergence of the momentum flux due to zonally asymmetric motions (e.g., planetary waves) while FT denotes the convergence of the eddy heat flux. : We have neglected the advection by the mean meridional circulation and the eddy momentum flux terms in (2.8) since the mean zonal wind is nearly in gradient wind balance. The terms ~V/(lt and D2(V) are also very small but must be retained for our method of numerical solution. With the aid of (Z9) we can define a mean meridional streamfunction )(, by letting

Wcos 0 = i/y' -?)(

Vcos 0 = _ (c~_z

2-/41)-X.

(2.11)

The .~ field proves useful in specifying boundary conditions and solving the zonal mean component equations.

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A Numerical Model of the Zonal Mean Circulation

293

2.3. Boundary conditions F o r global integrations the meridional b o u n d a r y conditions are as follows:

,Y

=

G =

V =

OW/Oy = 0

at 0 = +~r/2.

(2.12)

B o u n d a r y conditions at the horizontal boundaries are specified as follows: U - O8(y, t)

at z = 0

(2.13a)

where z = 0 designates the lower b o u n d a r y (i.e., the tropopause level) and U~ is an externally specified mean zonal wind. The b o u n d a r y mean zonal flow is assumed to be in gradient wind balance. Thus from (2.8) we see that at z = 0 = 0

(2.13b)

and a~F

Oy = f U + ~2

tan 0

a

e~/SH"

(2.13C) m

Using the condition (2.13a) we can integrate (2.13c) to obtain tF(y, t) at z = 0. The constant of integration is determined by letting the horizontal average of ~'(y, 0, t) vanish. At the upper b o u n d a r y (z = zr) we assume that the vertical shear of the mean zonal wind, the mean meridional wind, and the mean geopotential all vanish. Thus, g)z

=

~ + 2-H U = 0

(2.14a)

c9 l)cTzz + 2-H V = 0

(2.14b)

(~ 1)-Fzz + ~ T = 0.

(2.14c)

and

Condition (2.14c) of course implies that the zonal mean temperature must equal the basic state To(zr) at z = zr. In addition to these conditions it is clear from (2.7) and (2.10) that b o u n d a r y conditions are also required for the vertical m o m e n t u m and heat fluxes associated with the mean meridional circulation. We wish to avoid specifying W or the fluxes themselves at z = O. Instead we assume that the flux divergences vanish at the lower boundary:

~Jz

Uzz[ \ ~ +

9

=0.

(2.15)

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James R. Holton and William M. Wehrbein

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However, for simplicity we assume that the fluxes themselves vanish at the upper boundary. If in addition we let Q = FT = 0 at the upper boundary, then from (3.10) we have W = 0

at z = zr.

(2.16)

2.4. Subgrid scale diffusion In order to suppress nonlinear instability in the course of the numerical calculations it proved necessary to apply a weak meridional smoothing to the U, V, and W fields. To prevent this smoothing from damping the large scale motions we have chosen a highly scale dependent biharmonic diffusion. Thus the operator D2( ) in (2.2) and (2.5) is defined by the differential relationship

D2() =-

K c~4( ) c o s 0 c~y4

(2.17)

where K is a constant with units of m 4 s- 1. The diffusion operator DI( ) in (2.1) must be specified so that the subgrid scale horizontal diffusion conserves relative angular momentum on an isobaric surface and also acts as a net energy sink. This requires that angular velocity be diffused:

D1(r

K ~4 ( I~ )

cos 2 0 c3y4 ~

"

(2.18)

In the solutions reported here where Ay = 10~ lat. we have set K/(Ay) 4 = 10 -a s -a which implies a decay time about 40 days for two grid length waves, while longer waves are practically unaffected by the damping.

2.5. Diabatic heating computation The net zonal mean radiative heating in the middle atmosphere arises from the difference between the solar heating Os and the infrared cooling Ore. In this model these two diabatic processes are included as follows. (a) Solar heating. Below 96 km ozone is the only significant absorber of solar radiation. The diurnally averaged solar heating Q~ is calculated by fixing the sun angle at its average value between sunrise and sunset (approximation 1 of COGLEV and BORVCKI, 1976), which is a known function of latitude and time depending on the phase of the annual cycle. The parameterization of LAClS and HANSEN (1974) is used to compute the solar heating. (b) Infi'ared cooling. This study has utilized DICKINSON'S (1973) parameterization of infrared cooling which consists of the sum of the cooling for a reference atmosphere

Vol. 118, 1980)

A Numerical Model of the Zonal Mean Circulation

295

of temperature To(z) and a Newtonian cooling approximation for temperature departures from the reference profile. Thus, the IR cooling can be expressed as

where Qn is the cooling for the reference state, a is the Newtonian cooling coefficient (QR and c~are functions of height alone), and T is the local deviation of the zonal mean temperature from To(z). The values of the Newtonian cooling coefficients have been calculated for levels between 30 and 80 km by DICKINSON (1973). Below 30 km TRENBERTH'S (1973) values are adopted. Although the accuracy of the Newtonian cooling representation breaks down above about 70 km, it shall be retained at this time for lack of a better representation. Following SCHOEBERLand STROBEL(1978), the value of a between 80 and 96 km was taken to be the CO2 cooling rate in the fundamental band at 15/~ (see Fig. 3). DICKINSON'S (1973) careful computations of a and QR were made for atmospheric temperature profiles that differ little from the reference temperature profile. Because the actual temperatures may vary considerably from this reference profile, especially in the winter polar region, his values of Qn could not be used. We have, instead, computed Qn in the following manner: at a given level the globally averaged net diabatic heating 0 is given by

(2.t9)

O = Q, - (OR + aT=")

where the tilde in all cases designates a horizontal average over the entire globe. Since the observed globally averaged temperature profile is reasonably well known, we here specify 0R so that global radiative equilibrium (Q = 0) is achieved when the globally averaged temperature profile is equal to the standard atmosphere value To (i.e., ~ = 0). Thus, from (2.19) we see that 0R = 0~ so that OR is determined from the global average of our computed solar heating field. This scheme insures that 0 is close to zero during the entire annual cycle because f remains close to zero.

90

/ /

80

50 4o

3O 20

....... ""

/"

i

91

j......... .2

DAMPING

.

[3

RATE

.

14

-5

.6

( d a y s -I )

Figure 3 Vertical profiles of the Newtonian cooling coefficient (solid line) and Rayleigh friction coefficient (dashed line) in units of d-1.

296

James R. Holton and William M. Wehrbein

(Pageoph,

2.6. Rayleigh friction parameterization

Perhaps the primary barrier to dynamical modeling of the observed circulation of the middle atmosphere is in understanding the momentum budget of the upper mesosphere. Observations (Fig. l) show that during the solstice season the meridional temperature gradient reverses sign at around 70 km. Thus, near the mesopause the warmest temperatures occur near the winter pole and the coldest temperatures occur near the summer pole. This temperature distribution is very far from radiative equilibrium and clearly must be dynamically maintained by subsidence in the winter hemisphere and rising motion in the summer hemisphere, as first suggested by KELLOGG and SCHILLING (1951). This pattern of mean vertical motion implies a strong thermally indirect mean meridional circulation directed from the summer to the winter hemisphere, which is forced by the thermally direct circulation which exists in the 30-70 km region. As described in the introduction such a meridional circulation will in turn, through action of the Coriolis torque, produce westerly accelerations in the winter hemisphere and easterly accelerations in the summer hemisphere. However, despite the strong zonal accelerations produced by the meridional circulation the mean zonal winds (Fig. l) decrease with height above about 70 km, as is required to maintain thermal wind balance: Hence, the heat and momentum budgets in this region can be satisfied simultaneously only if there is very strong eddy frictional damping of the mean zonal winds. The nature of the motions responsible for this damping is not yet certain. It appears, however, that planetary waves, although they may play a role in the winter hemisphere, cannot be entirely responsible for the eddy damping because there is very little planetary wave activity in the summer hemisphere. Moreover, satellite observations (Barnett, personal communication) show that in the winter hemisphere the mean geopotential amplitude of planetary wavenumber 1 decays rapidly with height above 60 km. Limited experiments with a version of our model which explicitly incorporated a forced stationary planetary wavenumber I have indicated, however, that in the absence of strong small scale dissipation both the zonal winds and the wave continue to increase in amplitude with height up to the upper boundary at 96 km. The most plausible explanation for the strong damping of the mean flow above 70 km is turbulent mixing due to the breakdown of atmospheric tides and vertically propagating gravity waves. EUASSEN and PALM (1961) showed that in the absence of damping or critical levels (where the mean wind speed equals the wave phase speed) the vertical momentum flux due to internal gravity waves, (pu'w'), will be constant with height. Now since density decreases exponentially with height it is clear that the wave amplitude must increase as p 112 ~ e~/2n if the momentum flux is to remain constant. The observational data base is as yet inadequate to provide a global morphology of the distribution of tides and gravity waves in the upper atmosphere. However, radar and radiowave reflection studies (GELLER et al., 1977; MAnSON and MEEK, 1976; and others) indicate that above 70 km the tidal and gravity wave motions

Vol. 118, 1980)

A Numerical Model of the Zonal Mean Circulation

297

are as energetic as the large scale winds. Furthermore, considerable turbulence appears to be present at these altitudes (WOODMAN and GUILLE~, 1974). It is therefore quite plausible that the exponential growth in the wave amplitude with height leads to breaking of tides and gravity waves above about 70 km so that further amplitude growth in height is inhibited. In that case the wave amplitudes would vary little with height and there would be a momentum flux convergence. Assuming that the waves have an average phase speed of zero the net effect would be to decelerate the mean flow. We have parameterized this process by letting l ~ z ( u'w') = k U P where k is a strongly height dependent Rayleigh friction coefficient as shown in Fig. 3. 2.7. The numerical model

The finite difference equations are described elsewhere (HoLTONand WEHRBEIN, 1979) and will not be repeated here. The model is based on a staggered grid domain with latitudinal grid increments of t0 ~ and vertical grid increments of 5 kin. A semiimplicit time differing scheme is employed which allows time steps of 1 hr in this zonally averaged model. The mean zonal wind at the lower boundary is determined geostrophically from the climatological average geopotential heights of the 100 mb surface given by LABITZKE and collaborators (1972) for the northern hemisphere and by TALJAARD et al. (1969) for the southern hemisphere. Time dependence of the lower boundary forcing is included by fitting the first two harmonics of the annual cycle to the climatological data. The model is initialized by assuming a barotropic mean zonal flow distribution, U(y, z, O ) = UB(y, 0), corresponding to the conditions for the northern hemisphere vernal equinox. For convenience the year is taken to be 360 days. It was found that transients introduced by the initial conditions decayed to negligible amplitudes in about 60 days. Thus the model run was extended for a total period of 420 days and the annual cycle study was based on the 60-420 period.

3. The annual cycle of the zonal mean circulation

Profiles of the computed mean zonal winds for the northern hemisphere vernal equinox, summer solstice, autumnal equinox, and winter solstice are shown in Figs. 4-7. When reflected about the equator, the mean circulation for the vernal equinox is nearly identical to the autumnal equinox and the winter solstice is nearly identical to the summer solstice, although there are minor differences because the mean wind at the lower boundary is stronger in the southern hemisphere than in the northern

298

James R. Holton and William M. Wehrbein

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MEAN ZONRL N[ND

~ 7o ~ 6O I -~ 50

:~ 4o 30

~\ ~. V

2o

90 7S 60 45 30

15

,

/,

2o.

,

~\ /

0 -15-30-45-60-'75-g0

LATITUDE

Figure 4 Latitude-height section of the computed mean zonal winds (m s- 1) for the northern hemisphere vernal equinox.

MEAN ZONAL NINO 9[ 8C 70

so so I

40

20

'oo

so 4,

-15 -30 -45 -60 -'75 -90

LATITUDE

Figure 5 Same as Fig. 4, but for the northern hemisphere summer solstice.

MERN ZONRL WIND

~ 7o ~ SO ~

50

I

40 3O 2O

90 75 60 45 30

t5

-15-30-45-60-'75-90

LATITUDE

Figure 6 Same as Fig. 4, but for the northern hemisphere autumnal equinox.

Vol. 118, 1980)

A Numerical Model of the Zonal Mean Circulation

299

MEAN ~8NflL NIND

60 4O 30 20

L

90

75

gO 45

30

15

- 1 5 - 3 0 - 4 5 -SO -TS -913

LATITUDE

Figure 7 Same as Fig. 4, but for the northern hemisphere winter solstice.

hemisphere for each corresponding season. This mirror symmetry is even more striking in the temperature, meridional velocity, vertical velocity, and net diabatic heating fields. Therefore, in the remainder of the discussion we will focus exclusively on times corresponding to summer solstice and autumnal equinox in the northern hemisphere. Comparing Figs. 1 and 7, we see that the computed mean zonal flow agrees very well with observations in the winter hemisphere and is qualitatively correct in the summer hemisphere although the observed easterly maximum is ~ 20 m s- 1 larger than the model value. Not surprisingly, in view of the validity of the thermal wind balance, the computed temperature profile (Fig. 8) is also in g o o d . agreement with the observations (Fig. 1). In particular, the winter to summer temperature gradient in the stratopause region is well simulated, as is the cold summer mesopause. The largest error occurs in the lower stratosphere where the model fails to simulate the observed temperature minimum in the equatorial region. This deficiency may be due in part to our very simple radiation model, but is probably primarily due to the inability of the model to simulate the various tropospheric dynamical processes which influence the lowest part of the stratosphere. Comparing Figs. 2 and 4, we see that the computed mean zonal wind field at the equinox is also in reasonable agreement with observations, although the model fails MEAN TEMPERATURE 90 ~

160

80-

180 ,80--

~

~

3C 22O i

9 90

'75

i

i

SD 4S

i

i

I

30

15

0

I

I

I

I

I

-15 -30 -45 -60 -75

913

LATITUDE

Figure 8 Latitude-height section of the zonal mean temperature (K) for the northern hemisphere summer solstice.

300

James R. Holton and William M. Wehrbein

(Pageoph,

MERN TEMPERFITURE

~ 80 -

~ ~

z4o

I~t 6 0 - - " ~ - - ~ - ~ _

260

~ 50 "i-

40

60

30 20 ~ ~ 2 2 0 90

715 6[0 415 310 t15 0I

I

I

t

I

I

-15 - 3 0 -45 -60 -75 - 9 0 LATITUDE

Figure 9 Same as Fig. 8, but for the northern hemisphere autumn equinox.

to reproduce the high level equatorial westerlies and the small region of easterlies near the springtime pole. The computed temperature field (Fig. 9) is in reasonable accord with the observed field of Fig. 2. The equinoctial temperature field is very fiat with only weak pole to equator gradients in both hemispheres. The computed net radiative heating profiles for the solstice and equinox are shown in Figs. 10 and 1 I, respectively. At the solstice there is strong net radiative cooling in the high latitude region of the winter hemisphere due to the absence of solar RRDIIqT IVE HERTINO

/)

80 -

i~

705O

c5

~40-

(

aO20-

t

90 75

I 60

k 45

I 30

i 15 0 - 1 5 - 3 0 - 4 5 - 6 0 - 7 5 - 9 0 LATITUDE

Figure 10 Latitude-height section of the zonal mean net radiative heating rate (K d-1) for the northern hemisphere summer solstice.

RflD II::IT I VE HEIqT [ NC9C I

.........

..................

f

8C

E

7o

~ 60 I --~ 5O

~

4o

J, ,),,: . . .

20 90

,'/',"7-" '75 60

45

30

I5

0 - I 5 -30 -45

60 -75 -90

LATITUDE

Figure 11 Same as Fig. 10, but for the northern hemisphere autumnal equinox.

Vol. 118, 1980)

A Numerical Model of the Zonal Mean Circulation

301

VERTI2RL VELDC[TY 8O

7o

v ~- 6Q

5o 40

O

'~

20 90 "715

415

310

L

I I I r F 1t5 0 -IS -30 -45 -60 -75 -90 LATITU DE

Figure 12 Latitude-height sections of the zonal mean vertical velocity (mm s - 1) for the northern hemisphere summer solstice.

VERTICAL VELOCITY r

gOF-~Z~~ --.,, )

7o

.........i",05 ~

!

,/ 3O

f i i 6tO 45 30 II5 0 -15 -30 LATITUDE

20

90

i

~

-45-B0

i -75

-90

Figure 13 Same as Fig. 12, but for the northern hemisphere autumnal equinox.

heating. In the summer hemisphere there is a rather uniform and weak net heating. At the equinoxes, on the other hand, there is weak heating in the equatorial region and strong cooling in high latitudes in both hemispheres. The vertical motion fields corresponding to these radiative heating profiles are shown in Figs. 12 and 13, and the corresponding mean meridional winds are shown in Figs. 14 and 15. As indicated in the introduction, the meridional circulation is a MEAN MERIDIONRL HIND 90 80

7o

v F- 6 0 I 5O

(

4o 3O 2O 90

i 75

80 45 30

i15

i

i

i

I

0 15-30-45 LATITUDE

i

L _

60 75-90

Figure 14 Latitude-height sections of the mean meridional wind (m s - 1) for the northern hemisphere summer solstice.

302

James R. Holton and William M. Wehrbein MERN

(Pageoph,

MERID[ONAL NIN0

80

~ 7o 60

---"

~ 50 w

I

40 +~

20

.

90

.

.

75 60

.

.

45 30

. t5

.

//

0

.

0

{O"

-15 -30 -45 -60 -75 -90

LATITUDE

Figure 15 Same as Fig. 14, but for the northern hemisphere autumnal equinox.

thermally direct circulation which consists of a single cell during the solstice season with rising motion in the summer hemisphere, and sinking in the winter hemisphere, together with a compensating meridional drift directed from the summer pole toward the winter pole. At the equinoxes, on the other hand, there is a two cell meridional circulation with rising in the equatorial zone, poleward motion in both hemispheres, and sinking in high latitudes. These circulations are just the patterns required so that the adiabatic temperature changes approximately balance the radiative sources and sinks. The reader is reminded that this circulation is the diabatic mean meridional motion and should not be confused with the total eulerian mean. Examination of Figs. 14 and 15 clearly indicates why very strong damping is required to satisfy the momentum budget above 70 kin. For example, at 45~ and 80 km height the winter solstice mean meridional wind is about 3 m s-i. Through the Coriolis torque this yields a zonal wind acceleration of about 30 m s- ~ per day ! Clearly, a damping time of the order of only 2-3 days is required to maintain the observed ,-~60 m s- ~ mean zonal wind in the presence of this strong Coriolis acceleration. Since it is very difficult to see how the heat budget could be satisfied without a substantial mean meridional flow near the mesopause, we must conclude that there

EOUFITOR

ZONFIL N[NO FIT 90 +

-~ ~o 7c :-io ..... 5C

:-20

........ / , l~

_5S'+ .........+..+

/-lo"-~'~<,.,

""--.

/"'

-20

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/

-2(

40 30 2O

f

I

F

I

M

F

A

+

M

I

d

I

d

I

A

I

S

I

O

I

N

MONTH

Figure 16 Time-height section of the mean zonal wind at the equator (m s -1) showing the semiannual oscillation.

Vol. 118, 1980)

A Numerical Model of the Zonal Mean Circulation

303

does in fact exist very strong damping due to the interaction of the mean flow with small scale motions in this height range. An additional aspect of our annual cycle simulation which can be seen by careful inspection of the mean zonal wind profiles (Figs. 4-7) is a strong semiannual oscillation at the equator. Advection of the mean zonal flow by the mean meridional wind causes a substantial easterly acceleration at the equator during the solstice seasons. The amplitude and vertical extent of this oscillation are illustrated in Fig. 16 which shows a time-height section of the mean zonal flow at the equator. The temporal dependence is characterized by a strong semiannual oscillation with an amplitude of nearly 12 m s - 1 at the stratopause level. The amplitude and phase of this oscillation are in remarkable agreement with the easterly portion of the observed equatorial semiannual oscillation (REED, 1966; HOPKINS,1975). Although the computed amplitude maximum occurs several kilometers higher than the observed maximum, the computed oscillation decays with height in the mesosphere in accordance with observations. This decay provides strong evidence for the reality of the strong mechanical dissipation which we have assumed to exist near the mesopause. In the absence of such dissipation the advection of the zonal wind by the mean meridional flow (which is a maximum near 80 km) would produce a peak amplitude in the semiannual oscillation near the mesopause. However, the presence of strong Rayleigh friction allows the meridional advection to be balanced by damping rather than by inertia. Thus, the semiannual oscillation in the mean flow is damped in the upper mesosphere?) The westerly phase of the observed oscillation is not simulated in the model. In fact there is no mechanism in the model which can produce mean westerlies at the equator. The observed westerly phase of the semiannual oscillation is believed to be generated by vertically propagating Kelvin waves (HIROTA, 1978; DUNKERTON, 1979). The equatorial semiannual oscillation calculated in the model has an amplitude which decays away from the equator more rapidly than the observed oscillation. In fact HOPKINS (1975) observational analysis showed that the oscillation has almost constant amplitude between 20~ and 20~ latitude. Hopkins attributed the easterly phase of the oscillation to the absorption of meridionally propagating winter hemispheric planetary waves at the zero mean zonal wind critical line in the equatorial region. Our model indicates that this wave-mean flow interaction mechanism is not required to account for the easterly phase of the oscillation at the equator. However, limited experiments with a version of our model which explicitly includes a forced planetary wavenumber one in the winter hemisphere, indicate that the critical line interaction process does in fact extend the easterly accelerations well into the winter hemisphere, and thus broadens the latitudinal extent of the semiannual oscillation. ~) HIROTA (1978) has shown, however, that there is a secondary peak in the semiannual oscillation above the mesopause (~ 85 km). Thus, the strong damping which we have postulated apparently must decrease with height above the mesopause.

304

James R. Holton and William M. Wehrbein

-50

J

-50~~

0 50I

r

i

J

I

J

i

i

i

i

f

i

i

p

i

i

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i

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i

.,

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,.

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Figure 17 The annual variation of the computed mean zonal winds (m s-1) at the 56 km level at latitude 60~ (top frame), 0~ (middle frame), and 60~ (bottom frame). This is one example of a phenomenon which cannot be accurately modelled with zonally symmetric dynamics. Finally, it is worth pointing out that there is also a semiannual component of the model computed mean zonal wind even in high latitudes. Figure 17 compares the time evolution of the mean zonal winds at 56 km for 60~ 0 ~ and. 60~ latitudes. The equatorial curve clearly is a close fit to a semiannual harmonic cycle. However the high latitude curves show significant flattening of the profiles during the winter months, indicating that a semiannual component is superposed on the annual cycle. This high latitude semiannual component may be attributed to the substantial semiannual component in the net radiative heating, which in turn is caused by the cutoff in the solar heating which occurs in the polar night. In conclusion, we believe that this work has demonstrated that a zonally symmetric model can reproduce many of the observed features of the circulation in the middle atmosphere. The results presented here provide evidence for strong momentum damping above 70 kin, and thus indirectly indicate the presence of gravity waves and turbulence. Much further work is, of course, required to provide a detailed description of such small scale features and their interactions with the mean flow. Acknowledgements

We wish to thank Professor Conway Leovy for many helpfu ! discussions during the course of this work. This research was supported by the National Aeronautics and Space Administration, N A S A G r a n t NSG-2228. REFERENCES

ANDREWS,D. G. and MCINTYRE,M. E. (1976), Planetary waves in horizontal and vertical shear: the generalized Eliassen-Palm relation and the zonal mean acceleration, J. Atmos. Sci. 33, 20312048. BOYD, J. (1976), The noninteraction of waves with the zonally averaged flow on a spherical earth and the interrelationships of eddy fluxes of energy, heat, and momentum, J. Atmos. Sci. 33, 22852291.

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A Numerical Model of the Zonal Mean Circulation

305

C I R A (1965), COSPAR International Reference Atmosphere, North-Holland, Amsterdam, 313 pp. COGLEY, A. C. and BORUCKI, W. J. (1976), Exponential approximation for daily average solar heating or photolysis, J. Atmos. Sci. 33, 1347-1356. CUNNOLD, D. M., ALYEA, F., PmLLIPS, N. and PR!tNN, R. (1975), A three-dimensional dynamicalchemical model of atmospheric ozone, J. Atmos. Sci. 32, 170-194. DICKINSON, R. E. (1973), Method of parameterization for infrared cooling between altitudes of 30 and 70 kms, J. Geophys. Res. 78, 4451-4457. DUNKERTON, T. (1978), On the mean meridional mass motions of the stratosphere and mesosphere, J. Atmos. Sci. 35, 2325-2333. DUNKERTON, T. (1979), On the role of the Kelvin wave in the westerly phase of the semiannual zonal wind oscillation, J. Atmos. Sci. 36, 32-41. ELIASSEN, A. (1950), Slow thermally or frictionally controlled meridional circulation in a circular vortex, Astrophys. Norv. 5, 19-60. ELIASSEN,A. and PALM, E. (1961), On the transfer of energy in stationary mountain waves, Geophys. Publ. 22, No. 3, 1-23. GELLER, M. A., BOWHILL, S. A. and HESS, G. C. (1977), A description of the University oflllinois meteor radar system and some first results, J. Atmos. Terr. Phys. 39, 15-24. HIROTA, I. (I978), Equatorial waves in the upper stratosphere and mesosphere in relation to the semi-annual oscillation of the zonal wind, J. Atmos. Sci. 35, 714-722. HOLTON, J. R. (1972), An Introduction to Dynamic Meteorology, Academic Press, New York, 319 pages. HOLTON, J. R. (1975), The Dynamic Meteorology of the Stratosphere and Mesosphere. American Meteor. Soc., Boston, 218 pp. HOLTON, J. R. and WEHRBEIN, W. M. (1979), A semi-spectral numerical model for the large scale stratospheric circulation. Report No. 1, Middle Atmosphere Project, Dept. of Atmospheric Sciences, University of Washington, Seattle. HOPKINS, R. H. (1975), Evidence of polar-tropical coupling in upper stratospheric zonal wind anomalies, J. Atmos. Sci. 32, 712-719. KASAHARA,A., SASAMORI,T. and WASHINGTON,W. (1973), Simulation experiments with a 12-layer stratospheric global circulation model. L Dynamical effect of the earth's orography and thermal influence of continentality. J. Atmos, Sci. 30, 1229-1251. KELLOGG, W. W. and SCHILLING, G. F. (1951), A proposed model of the circulation of the upper stratosphere, J. Meteor. 13, 561-568. LABITZKE, K., and collaborators (1972), Climatology of the stratosphere in the northern hemisphere Part I, Meteorol. Abhandl. 100, No. 4. LACIS, A. A. and HANSEN, J. E. (1974), A parameterization for the absorption of solar radiation in the earth's atmosphere, J. Atmos. Sci. 31, 118-133. LEOVY, C. B. (1964), Simple models of thermally driven mesospheric circulation, J. Atmos. Sci. 21, 327-341. MANABE, S. and MAHLMAN, J. D. (1976), Simulation of seasonal and interhemispheric variations in the stratospheric circulation, J. Atmos. Sci. 33, 2185-2217. MANSON, A. H. and MEEK, C. E. (1976), Internal gravity waves in the mesosphere and lower thermosphere at mid-latitudes, J. Atmos. Sci. 33, 1650-1655. MURGATROYD, R. J. and GOODY, R. M. (1958), Sources and sinks of radiative energy fi'om 30 to 90 kin, Quart. J. Roy. Meteor. Soc. 84, 225-234. MURGATROYD, R. J. and SINGLETON, F. (1961), Possible meridional circulations in the stratosphere and mesosphere, Quart. J. Roy. Meteor. Soc. 87, 125-135. REED, R. J. (1966), Zonal wind behavior in the equatorial stratosphere and lower mesosphere, J. Geophys. Res. 71, 4223-4233. SCHOEBERL, M. R. and STROBEL, D. F. (1978), The zonally averaged circulation of the middle atmosphere, J. Atmos. Sci. 35, 577-591. TALJAARD, J. J., VAN LOON, H., CRUTCHEN, H. L. and JENNE, R. L. (1969), Climate of the upper air, part 1 - Southern Hemisphere, N A V A I R 50-IC-55.

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TRENBERTH,K. E. (1973), Global model of the general circulation of the atmosphere below 75 km with annual heating cycle, Mon. Wea, Rev. 101, 306-322. WOODMAN, R. F. and GUILLEN, A. (1974), Radar observations of winds and turbulence in the stratosphere and mesosphere, J. Atmos. Sci. 31, 493-503. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkhhuser Verlag, Base/

Mean Meridional Circulations of the Stratosphere and Mesosphere By A. J. CRANE, J. D. HAIGH, J. A. PYLE a n d C. F. ROGERS 1)

Abstract-Observations from the Nimbus 6 pressure modulator radiometer (PMR) have been used to estimate monthly mean planetary wave fluxes of heat and momentum in the stratosphere and mesosphere, While the eddy heat fluxes play an important rote in the mean meridional circulation of the winter stratosphere they are shown to be less important in the upper mesosphere. Incorporation of the observed momentum fluxes into the Oxford two-dimensional circulation model has shown that they are incapable of providing the momentum transport necessary to balance the zonal flow accelerations induced by the mean meridional motion. Other unspecified transfer processes represented by Rayleigh frictional damping of the zonal flow are shown to dominate. In contrast the observed fluxes in the stratosphere achieve the necessary redistribution of momentum. Moreover their interannual variability profoundly influences the stratospheric circulation, as demonstrated in the model by the use of two different annual sets of observed momentum fluxes. The desirability of calculating the planetary wave behaviour within the model is indicated. Key words: Two-dimensional model; Planetary waves; Heat flux; Momentum flux; Rayleigh friction damping.

1. Introduction In the absence o f a t m o s p h e r i c m o t i o n s the t e m p e r a t u r e structure o f the s t r a t o s p h e r e and mesosphere, u n d e r the radiative equilibrium conditions that would prevail, would show a very cold winter pole from the low s t r a t o s p h e r e to the m e s o p a u s e with increasing t e m p e r a t u r e t o w a r d s the s u m m e r pole at all levels (see MUROATROYD, 1970, Fig. la). O b s e r v a t i o n s by rockets and satellites have shown that the existing t e m p e r a ture structure d e p a r t s substantially from radiative equilibrium, especially in the mesosphere which is characterized by high t e m p e r a t u r e s over the winter pole and low t e m p e r a t u r e s over the s u m m e r pole (MUROA'rROYD op cit., Fig. 4). The existence at the m e s o p a u s e o f lower t e m p e r a t u r e s in s u m m e r than in winter was suspected as early as the 1930s following the observations o f noctilucent clouds in s u m m e r but not in winter. MURGAXROYD and SINGLETOY (1961) calculated the mean meridional circulation which would be required to maintain the observed t e m p e r a t u r e structure against the effects o f radiative heating and cooling. T h e resulting circulation was a global cell with ascent at the s u m m e r pole and descent over the winter pole with strong flow from 1) Department of Atmospheric Physics, Clarendon Laboratory, Oxford, U.K.

308

A.J. Crane, J. D. Haigh, J. A. Pyle and C. F. Rogers

(Pageoph,

the summer to the winter hemisphere in the upper mesosphere. One problem with the circulation was that it gave rise to zonal flow accelerations of several tens of m s- 1 per day. They concluded that eddy momentum transports would be required to offset these accelerations and that such transports would presumably be accompanied by heat transports which would, of course, influence the thermal balance. LEOVY (1964) carried out similar calculations and, in the absence of observations, parameterized the eddy heat and momentum flux divergences in terms of damping coefficients multiplied by the perturbations from the basic temperature state and the zonal mean flow respectively. Sufficient data for the lower and middle stratosphere enabled VINCENT (1968) to include observed eddy heat and momentum fluxes in his calculations of the mean meridional circulations of the 100-30 mb region. He managed to derive circulations which balanced reasonably well both the heat and momentum budgets, suggesting that the observed eddy fluxes, i.e. those associated with the planetary scales of motion, accounted for much, if not all, of the transport required to achieve momentum and heat balances. In the light of Vincent's results it would not be unreasonable to suppose that the planetary wave heat and momentum fluxes play a role, similar to that in the stratosphere, in determining the circulation of the winter mesosphere. A problem arises, however, in explaining the momentum balance in the summer mesosphere since it is known from both theoretical evidence (CHARNEY and DRAZlY, 1961 and others) and observations that the large scale quasi-stationary planetary waves generated in the troposphere cannot penetrate easterly stratospheric flow which occurs in summer. Whilst travelling waves may occur in summer (HIROTA, 1975) it is unlikely that alone they would achieve the necessary momentum transport. One process which may be capable of substantial redistribution of momentum in the mesosphere is the breaking of gravity waves which have propagated upwards from the troposphere (BRETHERTON, 1969; HOUGHTON, 1978). The vertical and time scales of such waves are too short to be observed by the PM R and quantitative estimates of eddy transports associated with these waves have yet to be determined. The object of this paper is not to seek an explanation for the summer circulation in the mesosphere, however, but rather to investigate the role of planetary wave fluxes in influencing the mesospheric circulation, more particularly in winter, using both PMR data and the Oxford two-dimensional general circulation model. Knowledge of their importance relative to other processes contributing to the heat and momentum budgets should clarify our understanding of the mesospheric circulation. 2. Retrieval of P M R data Daily values of the height fields at 3, 0.3 and 0.03 mb have been retrieved from PMR data using 30 mb height analyses of the Free University of Berlin as base fields. The PMR measures thermal emission from atmospheric carbon dioxide in the

Vol. 118, 1980)

Meridional Circulations of Stratosphere and Mesosphere

309

Table 1 Regressions of thickness against Planek equivalent temperature

Layer (mb)

PMR channel

Scan angle (~

Correlation coefficient

Standard error (m)

Standard error Standard deviation of thickness

30 - 0.3 3 - 0.3 3 - 0.03

2 2 2

i4.5 7.5 1.0

0.999 0.998 0.993

52 42 62

0.04 0.07 0.12

15 ffm band employing the principle of selective chopping (see HOUGHTON and TAYLOR, 1973). Observations span the 35-85 km region. By scanning forwards and backwards along the line of flight radiation from different levels in the atmosphere is detected. The Planck equivalent temperature of a radiance measurement is a weighted mean temperature of a broad atmospheric layer defined by the weighting function appropriate to the particular scan angle at which the measurement is made. It should correlate well with the thickness of a substantial part of the weighting function spread (QUIROZand GELMAN,1972). Regressing layer thickness against Planck equivalent temperature is particularly suitable for P M R data on account of the very large number of weighting functions obtainable through scanning. A simple regression of the form where a, b are constants,

H = aTR + b,

has been used to determine H, the thickness between specified pressure surfaces, from the Planck equivalent temperature, TR. The 30-0.3, 3-0.3 and 3-0.03 mb thicknesses from a set of 108 standard temperature profiles (9 latitudes 0-80~ for 12 months) were regressed against the Planck equivalent temperatures of the radiances implied by these profiles for a variety of scan angles. Table 1 shows the scan angles which gave the best correlations between H and T~, together with other details of the regressions, and Fig. 1 shows the weighting

0003 t

145~

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?

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~

, i

0

01

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i

01

,

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p

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Figure 1 PMR channel 2 weighting functions for scan angles of 14.5~ 7.5 ~ and 1~ The Planck equivalent temperatures of the radiances observed at these scan angles give the best correlations with the thicknesses of the pressure intervals delineated.

310

A.J. Crane, J. D. Haigh, J. A. Pyle and C. F. Rogers

(Pageoph,

functions for these scan angles. The very high correlations are somewhat misleading in that instrumental noise has not been represented in the regression. A further shortcoming of this relatively crude retrieval method is that no account is taken of the temperature dependence of the weighting functions. This dependence is discussed briefly by CRANE (1979), and more fully by AUSTEN (1979) and HEASMAN (1979). The method, however, is considered adequate for the type of analysis undertaken. The regressions detailed in Table 1 were used to derive zonal Fourier components of the 3, 0.3 and 0.03 mb height fields, using the 30 mb base field, for each day of 1976 from the zonal Fourier components of observed radiance (converted to Planck equivalent temperature). For each day, values of the zonal mean (-) zonal wind, if, and the first four zonal wavenumber contributions to the eddy momentum flux, u ' v ' , where u' and v' are eddy zonal and meridional velocities, were calculated from the height fields for latitudes 12-76~ at 4 ~ latitude intervals, using the geostrophic approximation and centred finite differences in latitude. Monthly mean values were derived from the raw daily values. Daily values more than two standard deviations away from t h e monthly means were discarded and new means calculated. This process was repeated in order to remove all bad data points. A five-point triangular running mean, with weightings of 1/9, 2/9, 3/9, 2/9, 1/9, was used to smooth monthly means across the latitude grid. In the case of momentum fluxes, values at 24~ were extrapolated to zero at the equator, prior to smoothing, to remove unrealistically large values in the tropics. Figures 2 and 3 show latitude-time sections of monthly mean ff and u ' v ' for 0.03, 0.3, 3 and 30 nab, the 30 mb values being calculated directly from the Berlin analyses. A reliable assessment of likely error in the eddy momentum fluxes is difficult to make. Their calculation involves the evaluation of an expression of the form b,~(a,~.a -

a,~-l) -

a,~(b,~+l -- b,~_~)

where a, b are the cosine and sine Fourier coefficients of height and n - 1, n, n + 1 are successive latitude grid points. Generally the terms in parentheses are much smaller than b. and an, so the expression is very sensitive to errors in these components. Thus while it is possible to evaluate likely error in the height fields on the basis of known errors in the regression method (Table 1) and likely random errors in the observations, it is difficult to predict the likely error in the eddy fluxes. However, the reasonably consistent variations in space and time evident in the daily values leads us to suppose that the monthly mean values are good estimates. In order to calculate corresponding eddy heat flux v ' T ' associated with the planetary waves, estimates of the harmonic components of temperature at these levels are required. While radiance equivalent temperatures are good measures of the thickness of a layer within the weighting function spread, they may be used directly, albeit with less accuracy, as estimates of the temperature at the level of the peak of the weighting function. Thus the zonal harmonics of the radiance equivalent temperatures given by PMR weighting functions 2115, 2100 and 3000 (see Fig. 4), which have

Vol. 118, 1980)

311

MeridionalCirculations of Stratosphere and Mesosphere

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A.J. Crane, J. D. Haigh, J. A. Pyle and C. F. Rogers

(Pageoph,

oO

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Vol. 118, 1980)

Meridional Circulations of Stratosphere and Mesosphere

313

IO0

0.0003

0003 8O 0.03

60

E

--03

cn

3

40

o_

c~ I

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01

02

03

WEIGHTING FUNCTION Figm'e 4

P M R weighting functions 2115, 2100 and 3000 (i.e. channel 2, scan 14.5~ channel 2, scan 0~ (1.67 x channel 1, scan 0 ~ 0.67 x channel 2, scan 0~ The solid lines are weighting functions calculated for a mean J a n u a r y 70~ temperature profile, while the dashed lines are those for a mean July 70~ profile.

maximum weightings close to 3, 0.3 and 0.03 rob, were used in this way. The radiance harmonic components were first multiplied by a given factor to allow for the fact that the observed radiance amplitude is usually less than that at the levels of high weighting due to the slope with height of the planetary waves (HIROTA and BARNETT, 1977). Ideally the factor should be calculated daily according to the slope of each wave at each latitude. However, in this study fixed values were used: 1.3, 1.4 and 1.4 for weighting functions 2115, 2100 and 3000 for wavenumber one, and 1.7, 2.0, 2.0 respectively for higher wavenumbers, these values being based on the ranges of values used by Hirota and Barnett. It is recognized that this is a rather gross assumption as is the use of radiance equivalent temperatures to represent temperatures at specific levels. As an alternative the retrieved eddy components of thickness could have been used to give mean eddy components of temperature over each layer. In this case vertical interpolation of either temperature or meridional velocity would have been necessary to derive the eddy heat fluxes and again a considerable measure of uncertainty would be introduced. Thus, while the method of calculation of the eddy heat fluxes is less sensitive to errors in the height components than in the case of eddy momentum fluxes, the assumptions made therein suggest that we should regard the heat fluxes as representative values rather than accurate observations. Monthly mean values of v'T' were calculated using the same procedures as for ~ and u'v', and latitude-time sections of the monthly means obtained are shown in Fig. 5.

314

A . J . Crane, J. D. Haigh, J. A. Pyle and C. F. Rogers

(Pageoph,

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Vol. 118, 1980)

Meridional Circulations of Stratosphere and Mesosphere

315

3. Mean meridional circulation calculations from data From the derived data the Eulerian monthly mean meridional circulations can in principle be evaluated using any pair of the zonally averaged zonal momentum, thermodynamic and continuity equations: 8t

v f

a c o s C 8 r ( ~ c ~ 1 6 2 + ~-Zz 1

8

(u'v'c o s 2 r

= a cos 2 r 0-r (u'v'

-

8 IAtW p +

lltW ,

(0

e sT w(RT sT) -7

+ - \ __+

7z

0 %

1 8 (v'T' cos r a cos r 8r 1

8

a cos r 0r (g cos r

8 w'T' + w'T; ( 1 - ~ ) R - ~zz

8u~ + -~z - ~ = 0

(2)

(3)

where z = In (Po/P), P0 = 1000 mb; w = dz/dt; r = latitude; a -- Earth radius; Q = diabatic h e a t i n g ; f = Coriolis parameter; R = gas constant and cp = specific heat of air at constant pressure. A number of studies have shown that, for the observable wave motions, the terms involving eddy vertical motions are usually much smaller than those involving eddy meridional motions and can be neglected without much loss of accuracy. Since the retrievals have yielded ~ and u'v' at specified levels the best choice would appear to be an iterative solution of the momentum and continuity equations (1) and (3) to obtain g and ~, Theoretical calculations of the mean meridional circulation show that ~ changes from typically a few mm s -x in the middle stratosphere to a few cm s-X in the mesosphere. Since the depth of motion is typically several scale heights, H say, then

8if/ _

,--~_/w ~ 1/H << 1.

UZ/

Upwards integration of the continuity equation from the 30 mb boundary values of to obtain 9 at higher levels is not, therefore, possible since not only is the vertical velocity gradient a small residual in the equation but errors introduced increase exponentially with height due to the form of the equation. Downward integration would be better conditioned but the choice of upper boundary condition is not obvious, and furthermore it is the high-level circulation which is of most interest. It should be noted, however, that the mid-latitude values of g deduced from momentum balance were of order a few tenths of m s-1 in the mesosphere in contrast with a few m s -1 required by continuity to satisfy vertical motions of a few cm s -1. It may

316

A.J. Crane, J. D. Haigh, J. A. Pyle and C. F. Rogers

(Pageoph,

o i

9

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Vol. 118, 1980)

Meridional Circulations of Stratosphere and Mesosphere

317

September

March L

L /---'\,

i

0

_.--.f

o

\,

= ? < . . ~

'"""'---."/"":- ....

-4

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.... 0.3 mb June

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0

20

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60

80

0

20

40

60

80

Latitude ~

Figure 7 Zonal mean vertical velocity (mm s- 1) at 0.03, 0.3 and 30 mb plotted against latitude for March, June, September and December 1976. Positive values denote upward motion. The bold, unjoined points shown for June are values calculated when v'T' assumed zero everywhere. be supposed that the eddy momentum flux divergence due to the large scale planetary waves observable by the P M R accounts for only part of the momentum transfer required to balance the strength of meridional circulation predicted theoretically for the mesosphere. The contribution to the mesospheric circulation made by the calculated momentum fluxes has been investigated further using the Oxford twodimensional circulation model and this work is described in Section 4 of this paper. Since the obvious choice of equations (1) and (3) for a solution of the mean meridional circulation proved to be unsuccessful, an alternative method of obtaining this circulation was adopted in which the thermodynamic equation (2) was used to estimate v7 at the four levels. Values of 8~/~z were estimated from ~ so that the continuity equation (3) could be integrated horizontally to obtain ~. The term in equation (2) involving ~ is usually small and was neglected. An iterative method of solution in which the first estimate of ~ is used in equation (2) to determine a better estimate of avoids the need for this approximation. However, in view of the low accuracy of the eddy heat fluxes this refinement was considered inappropriate. The net radiative heating rates required for solution of equation (2) were calculated for a set of standard temperature profiles corresponding to each month and latitude interval by the method currently in use in the Oxford model (HAIGH and PYLE, 1979). This radiation scheme takes into account the radiative transfer between different layers of the atmosphere

318

A . J . Crane, J. D. Haigh, J. A. Pyle and C. F. Rogers March

September

,--'"'- ........ ""-..

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Figure 8 Zonal mean meridional velocity, t7 (m s-l), at 0.03, 0.3 and 30 mb plotted against latitude for March, June, September and December 1976. Positive values denote northward motion.

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plotted

V o l . 118,

1980)

319

Meridional Circulations of Stratosphere and Mesosphere

4

003rob

0"3 mb

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/

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20 '

40 '

50 '

8"0

.

0.

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. 40 .

60

80

L a t i t u d e ON

Figure 10 Comparison between zonal mean vertical velocities (mm s-1) for December as calculated from the zonally averaged thermodynamic equation (a) using observed eddy heat fluxes (solid lines) and (b) assuming zero eddy heat flux (dashed lines), plotted against latitude for 0.03, 0.3, 3 and 30 mb. Positive values denote upward motion. and includes the breakdown of local thermodynamic equilibrium at high levels. The calculated net heating rates for March, June, September and December are shown in Fig. 6. Temporal and spatial rates of temperature change were estimated from appropriate standard temperature profiles for the 3, 0.3 and 0.03 mb levels and from Berlin analyses at 30 rob. As a boundary condition for equation (3), ~ was set to zero at 90~ Figure 7 shows the calculated vertical velocities, obtained by multiplication of and the local scale height, RT/g, at the four levels for March, June, September and December. The high latitude cell with ascent over the pole and descent in midlatitudes during winter and spring in the middle stratosphere is evident in the 30 mb values. The existence in the mesosphere of a global scale meridional circulation at the solstices is confirmed with ascent in summer and descent in winter. In spring and autumn ascent occurs in the tropics and descent in extratropical latitudes in the upper mesosphere. The corresponding meridional velocities (Fig. 8) indicate that the upper branch of the global cell in the mesosphere extends sufficiently low to include the 0.3 mb level during winter and spring but during summer and autumn the 0.03 mb and 0.3 mb levels exhibit oppositely directed meridional motion. The vertical velocities for each level and month at 76~ and 52~ are plotted in Fig. 9. It is interesting to note that two factors largely account for the difference between summer and winter in the magnitude, as opposed to the sign, of the vertical velocities at 76~ and 0.03 rob. In winter, high values of the static stability (i.e. the coefficient of ~ in equation (2)) and convergence of eddy heat flux ensure that relatively small rates of descent are

320

A.J. Crane; J. D. Haigh, J. A. Pyle and C. F. Rogers

(Pageoph,

sufficient to maintain a balance against radiative cooling. In summer, however, the effect of eddy heat fluxes is negligible and the steep temperature lapse between the stratopause and mesopause necessitates vigorous ascent to offset net radiative heating. In mid-latitudes divergent eddy heat flux and somewhat larger radiative cooling in the upper mesosphere in winter, and a less steep lapse rate in summer, lead to an annual variation in vertical velocity with a mean much closer to zero. To compare the effects of eddy heat flux divergence and diabatic heating on the mean meridional circulation, the calculations were repeated with eddy heat fluxes set to zero, giving the circulations required to offset diabatic heating alone. In summer eddy heat fluxes are small and the circulations are almost identical apart from minor differences in high latitudes in the upper mesosphere. The comparison for June is illustrated in Fig. 7. In winter, however (Fig. 10), the eddy heat fluxes make a qualitative difference to the meridional circulation in the stratosphere and lower mesosphere, forcing ascent at the pole. In the upper mesosphere the eddy heat fluxes are considerably weaker (see Fig. 5) and the two circulations are qualitatively similar. The radiatively driven circulations calculated here compare well with those of MURGATROVD and SINGLETON(1961) although the radiation scheme which they used (MURGATROYD and GOODY, 1958) gave larger cooling rates at the winter pole and led to a stronger winter circulation than in our case. We are now able to update the reservations which Murgatroyd and Singleton expressed about their radiatively driven circulations and which are noted in the introduction to this paper. Firstly, the eddy heat fluxes which accompany the eddy momentum fluxes do not make a qualitative difference to the upper mesospheric mean circulation although they have a profound influence at lower levels in winter and spring. Secondly, it appears that the planetary wave eddy momentum transports are not sufficient to bring about a balanced momentum budget in the mesosphere.

4. Mean meridional Circulations in the Oxford two-dimensional model To assess more fully the role of the observed planetary wave momentum fluxes in the mesosphere the circulations developed in the Oxford two-dimensional model have been analysed. A full description of the dynamical framework of the model has been given elsewhere (HARWOOD and PYLE, 1975). It is sufficient here to note that forward integration in time is achieved by evaluating the meridional stream function, ~b, from an equation of the form ~r

= Q + M + H

(4)

where ~q~ is a linear, second-order, elliptic, differential operator, Q is a term which involves only the horizontal gradients of diabatic heating, M involves only vertical gradients of the eddy momentum flux convergence and H involves only horizontal

Vol. 118, 1980)

90S

MeridionalCirculations of Stratosphere and Mesosphere

50

30

0 LATITUDE

30

321

60

90N

Figure 11 Height-latitude distribution of zonally averaged zonal wind, 12 (m s-1), at northern hemisphere mid-winter as developed in a model run using eddy momentum fluxes for 1973.

gradients of the eddy flux of potential temperature. The meridional circulation developed is that which maintains thermal wind balance against the perturbing effects of radiative heating and the eddy heat and momentum flaxes. The values of 0 and ~ obtained from ~ are substituted into the zonal mean thermodynamic and zonal momentum equations to yield the tendencies of zonal mean temperature and zonal wind, from which their values at the next time step are determined. Eddy heat

0003

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Figure 12 As Fig. 11 but showing zonally averaged meridional velocities, ~ (m s - 1).

90N

322

A . J . Crane, J. D. Haigh, J. A. Pyle and C. F. Rogers

0"003

(Pageoph,

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Figure 13 Height-latitude distribution of zonally averaged meridional velocities, b (m s-l), at northern hemisphere mid-winter as developed in a model run using eddy m o m e n t u m fluxes for 1976. % difference in total o z o n e with ~

f r o m 1973 a n d 1976

R511,522

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<

2 ~ 30

60'

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A MONTH

S

0

N

D

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Figure 14 Latitude-time section of percentage difference in total ozone between model runs using eddy m o m e n t u m fluxes for the years 1973 and 1976. M o m e n t u m fluxes in the southern hemisphere were the same for each run. Values plotted are those for the second model year.

Vol. 118, t980)

323

Meridional Circulations of Stratosphere and Mesosphere

~z

~ t

0 003 ~

'

X)e~\ /

/

r

003 Q: ~m or) LIJ ~: ck

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03 / / 3

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Figure

15

Vertical profiles of Rayleigh frictional damping coefficient used in this study and by Schoeberl and Strobel (1978).

transport is represented by eddy diffusion coefficients and momentum transports are monthly mean values derived from satellite observations. Two sets of momentum fluxes have been calculated: those shown in Fig. 2 and a set calculated from Nimbus 5 selective chopper radiometer data for 1973. In the latter set mesospheric values are extrapolations from the top level of calculation at about

~

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60

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Figure 16 Height-latitude distribution of zonally averaged zonal wind, g (m s - 1), at northern hemisphere mid-winter as developed in a model run including Rayleigh frictional damping of the zonal flow in the mesosphere.

324

A.J. Crane, J. D. Haigh, J. A. Pyle and C. F. Rogers

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230 300 905

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60

90N

Figure 17 As Fig. 16 but showing the zonally averaged temperature field, T, (K).

50 km. Figures 11 and 12 show the height-latitude distributions of ~ and ~ for northern mid-winter using the 1973 momentum fluxes. It is immediately obvious that there are insufficient sources and sinks of mean zonal flow momentum to close the polar night westerly jet and the summer easterly jet in the mesosphere. However, the gross features of the stratospheric circulation resemble closely the real atmosphere although some differences in detail occur due partly to the use of a simplified photochemical

TI3

90S

60

30

0 30 60 90N LATITUDE Figure i8 As Fig. 16 but showing the zonally averaged meridional velocity, ~ (m s- 1).

Vol. 118, 1980)

0003

325

Meridional Circulations of Stratosphere and Mesosphere

0

0

--

-012

-

~

\

4

<----o2/o.2t

IIIIf,;'A\

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o-OO3o.o3 25/ 0-5--0.3

< 90 S

60

< I

I

I

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30

0

30

60

90N

LATITUDE

Figure 19 Height-latitude distributions in the mesosphere of the contributions made to the total meridional velocity field (shown in Fig. 18) by (a) eddy flux of potential temperature, (b) eddy flux of angular momentum, (c) net radiative heating and (d) Rayleigh frictional damping. Units are m s-1.

326

A.J. Crane, J. D. Haigh, J. A. Pyle and C. F. Rogers

(Pageoph,

scheme in this run (see HAIGH and PYLE, 1979). This confirms that planetary scale momentum fluxes carry out the bulk of the eddy momentum transport in the stratosphere. In an equivalent run in which the 1976 momentum fluxes were used in the northern hemisphere the distribution of ff at the northern winter solstice was very similar to that shown in Fig. 11. The mean meridional circulation derived was substantially different however (Fig. 13) as were the simulated total ozone amounts. Figure 14 shows the percentage difference in ozone between the two runs during the second model year. These results demonstrate that while the planetary wave momentum fluxes are incapable of producing the necessary momentum redistribution in the mesosphere they play a profound role in determining the stratospheric circulation and the distributions of minor constituents. It would, therefore, be very desirable to calculate planetary wave behaviour within the model rather than use externally specified momentum fluxes. This has been attempted with limited success by SCHOEBERL and STROBEL(1978). In view of the changes in total ozone shown in Fig. 14 the inclusion of model-dependent momentum fluxes could be particularly important in studies of possible perturbations to the ozone layer. The model has been used further to determine the momentum convergences necessary to close the mesospheric jets and thus to find the relative contribution of the planetary wave fluxes. To this end Rayleigh frictional damping of the zonal flow was introduced into the model mesosphere with a damping coefficient whose profile is shown in Fig. 15. For comparison the values used by Schoeberl and Strobel are also shown. We make no claims for the physical processes represented by the Rayleigh friction. This is a mathematical device to represent the momentum convergence by processes other than planetary wave fluxes. However, it would appear that these other processes are of small spatial scale since no evidence is found for them from Nimbus 6 PMR data. As noted in the introduction, gravity wave breaking or tidal effects near the mesopause could be important. The damping coefficient was chosen such that a realistic zonal wind structure was obtained in the model mesosphere. Figure 16 shows the zonal wind field during northern mid-winter. The jet maxima are perhaps a little too strong, consistent with the somewhat exaggerated pole-to-equator temperature gradients at the stratopause. However, the gross features of the observed zonal wind field are reproduced. Similarly the mesospheric temperature field is modelled well (Fig. 17) with a cold summer mesopause and higher temperatures (although less than observed (COSPAR, 1972)) at the winter pole. The meridional velocity field is presented in Fig. 18. The main feature is the single cell, thermally direct circulation with flow of a few metres per second from the summer to the winter hemisphere. It is possible to gain some insight into the processes which drive this circulation in the model. Since ~ in equation (4) is linear, it is meaningful to talk of that part of ~b due to Q or M or H, where M now includes the Rayleigh friction term. (The partitioning of~b in this way is not quite absolute, however, as the coefficients of co~~involve the zonal mean temperatures and zonal winds which have evolved in a non-linear manner from Q, M and H). In Fig. 19 are presented the

Vol. 118, 1980)

Meridional Circulations of Stratosphere and Mesosphere

327

contributions to the mesospheric meridional velocity field from (a) the eddy flux of potential temperature, (b) the eddy flux of angular momentum, (c) the net radiative heating and (d) the Rayleigh friction. The eddy fluxes make only a relatively small contribution to the total meridional circulation in the upper mesosphere. Moreover in much of the winter hemisphere they tend to set up a circulation in opposition to that generated by the other processes. The Rayleigh friction term dominates at the mesopause with a lesser contribution from the diabatic heating. Indeed, in an experiment in which net radiative heating was set to zero in the mesosphere, the meridional and zonal velocities retained the same structure although temperatures in the upper mesosphere were considerably reduced. The circulations driven are such as to restore thermal wind balance. There is for example, equatorward motion in regions where the friction increases the westerly flow. Likewise it can easily be inferred that the circulation driven by the diabatic heating has heated air tending to rise and cooled air tending to sink, in the correct sense to restore thermal wind balance. It is desirable, of course, to ascertain the degree to which the model accurately reproduces the detailed behaviour of the atmosphere and thus with what confidence the relative roles played by the Rayleigh friction and the diabatic heating can be determined. The model temperature structure agrees well with observation although, as stated above, the winter pole at about 80 km should be warmer by approximately 20~ Thus, throughout most of the mesosphere the radiative heating and the subsequent circulation should be modelled well. The meridional velocities calculated by MURGATROYD and SINGLETON(1961) are greater than the radiatively driven velocities shown in Fig. 19(c) owing to their use of more intense heating rates, as discussed earlier. If Murgatroyd and Singleton's radiatively driven circulation is correct, it would appear that even larger values of the Rayleigh friction coefficient would be required to balance the zonal flow acceleration by the Coriolis torque. It is clear that the processes represented here by Rayleigh friction play a very important role in the maintenance of the mesospheric circulation and a clearer understanding of what these processes are is desirable. 5. Conclusion

It has been shown that eddy momentum fluxes due to planetary scale waves play only a minor role in transferring momentum in the mesosphere. An understanding of the physicat processes represented by the Rayleigh frictional damping of the zonal flow necessary to close the mesospheric zonal flow jets is needed. In contrast the planetary wave fluxes are sufficient to balance the momentum budget of the stratosphere, their interannua[ variability having important influences on the stratospheric circulation and the distributions of minor constituents, Methods of modelling wave momentum transports are desirable. Eddy heat fluxes have been shown to be Jess important in the heat balance of the upper mesosphere than at lower levels. Whereas in the winter stratosphere a thermally indirect circulation is required to offset eddy heat transport, qualitative agreement is

328

A . J . Crane, J. D. Haigh, J. A. Pyle and C. F. Rogers

found between a purely radiatively-driven mean meridional circulation and one including the effects of eddy heat transport in the upper mesosphere in winter. During summer, eddy heat fluxes play a negligible part in the heat balance of the stratosphere and mesosphere.

Acknowledgements Financial support from the Natural Environment and Science Research Councils is gratefully acknowledged. The Nimbus project of NASA provided the spacecraft and data-handling facilities. The authors wish to thank Professor S. V. Venkateswaran for some stimulating discussions. REFERENCES ArdSTEN, M. D. (1979), D.Phil. Thesis (unpublished), University of Oxford. BRETHERTON, F. P. (1969), Momentum transport by gravity waves, Quart. J.R. Met. Soc. 95, 213 243. CHARNEV, J. G. and DRAZIN, P. G. (1961), Propagation of planetary-scale disturbances from the lower to the upper atmosphere, J. Geophys. Res. 66, 83-109. COSPAR, COSPAR International Reference Atmosphere, (Akademia-Verlag, Berlin, 1972), 450 p. CRANE, A. J. (1979), Annual and semiannual waves in the temperature of the mesosphere as deduced from Nimbus 6 PMR measurements, Quart. J.R. Met. Soc. 105, 509-520. HMGH, J. D. and PYLE, J. A. (1979), Atmospheric carbon dioxide and stratospheric ozone - a twodimensional calculation, accepted for publication in Nature. HARWOOD, R. S. and PVLE, J. A. (1975), A two-dimensional mean circulation model for the atmosphere below 80 km, Quart. J.R. Met. Soc. 101, 723-747. HEASMAN, C. C. (1979), D.Phil. Thesis (unpublished), University of Oxford. HIROa'A, I. (1975), Spectral analysis of planetary waves in the summer stratosphere and mesosphere, J. Met. Soc. Japan, 53, 33-44. H~ROTA, I. and BARNETT, J. J. (1977), Planetary waves in the winter mesosphere-preliminary analysis of Nimbus 6 P M R results, Quart. J.R. Met. Soc. 103, 487-498. HOUGHTON, J. T. (1978), The stratosphere and mesosphere, Quart. J. R. Met. Soc. 104, 1-28. HOUGHTON, J. T. and TAYLOR, F. W. (1973), Remote sounding from artificial satellites and space probes of the atmospheres of the earth and the planets, Rep. Prog. Phys. 36, 827-919. LEOVV, C. (1964), Simple models of thermally driven mesospheric circulation, J. Atmos. Sci. 21, 238-248. MURGATROYD, R. J. (1970), The structure and dynamics of the stratosphere, in The Global Circulation of the Atmosphere (ed. G. A. Corby), 159-195, (Royal Meteorological Society, London). MURGA'rRovD, R. J. and Gooov, R. M. (1958), Sources and sinks of radiative energy from 30 to 90 kin, Quart. J.R. Met. Soc. 84, 225-234. MURGATROVD, R. J. and SINGLETON, F. (1961), Possible meridional circulations in the stratosphere and mesosphere, Quart. J.R. Met. Soc. 87, 125-135. QuiRoz, R. S. and GELMAN, M. E. (1972), Direct determination of the thickness of stratospheric layers fi'om single-channel satellite radiance measurements, Mon. Weath, Rev. 100, 788-795. SCHOEBERL, M. R. and STROBEL, D. F. (1978), The zonally averaged circulation of the middle atmosphere, J. Atmos. Sci. 35, 577-591. VINCENT, D. G. (1968), Mean meridional circulations in the northern hemisphere lower stratosphere during 1964 and 1965, Quart. J.R. Met. Soc. 94, 333-349. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh/iuser Verlag, Basel

Preliminary Calculations Concerning the Maintenance of the Zonal Mean Ozone Distribution in the Northern Hemisphere By D. M. CUNNOLDI'2), F. N. ALYEAI'2), R. G. PRINN 1)

Abstract-Results from a three-dimensional photochemical-dynamical model of ozone are presented and a qualitative description of the maintenance of the ozone distribution and its seasonal variations below 1 mb is given. The .transition between photochemical and transport control of the ozone distribution is emphasized. Between 1 and 10 rob, transport by the eddies seems to play only a minor role at mid-latitudes in producing the observed ozone distribution despite the zero correlation between ozone and temperature which occurs in that region. In the lower stratosphere, mean and eddy contributions to ozone change generally strongly offset one another. The buildup and decay of the springtime ozone maximum is discussed. Emphasis is given to the mechanism of ozone transport by the mid-latitude eddies, which play an important role in the springtime accumulation of ozone. Key words: Three-dimensional model; Zonal mean ozone; Photochemical control; Transport control; Springtime ozone maximum.

1. Background O z o n e has intrigued a t m o s p h e r i c scientists for a long time, not only because o f its c o n t r i b u t i o n to the heating o f the a t m o s p h e r e , but also because, a l t h o u g h it is p h o t o chemically p r o d u c e d , its m a x i m u m c o l u m n a b u n d a n c i e s are found at high latitudes in spring. The global n e t w o r k o f D o b s o n stations has p r o v i d e d a substantial d a t a base on this latitudinal distribution o f c o l u m n a r ozone a n d its seasonal variations (see Fig. 1). Satellite observations, m o r e o v e r , provide a d d i t i o n a l evidence that the D o b s o n n e t w o r k captures the principal features o f the zonal mean distribution o f c o l u m n a r ozone (e.g. HILSENRATH et al., 1979). M o s t studies o f the ozone distribution to date have c o n c e n t r a t e d on explaining how a t m o s p h e r i c t r a n s p o r t accounts for this welld o c u m e n t e d b e h a v i o r o f c o l u m n a r ozone. However, the r e p o r t e d observations are, unfortunately, i n a d e q u a t e to provide a detailed budget o f a t m o s p h e r i c ozone. T h e p u r p o s e o f this p a p e r is to present a b u d g e t a r y b r e a k d o w n o f the zonal mean ozone distribution a n d its seasonal variations in the N o r t h e r n Hemisphere based upon calculations with a t h r e e - d i m e n s i o n a l m o d e l (CuNNOLD et al., 1975; ALVFa et al., 1975) which has p r o v i d e d an excellent simulation o f the ozone distribution there. 1) Department of Meteorology, M.I.T., Cambridge, Mass. 02139, USA. 2) Current Address: Department of Geophysical Sciences, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.

330

D.M. Cunnold, F. N. Alyea and R. G. Prinn

(Pageoph,

FEB MAR APRMAY JUN JUL AUG SEP OCT NOV DEC

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331

Vol. 118, 1980) Zonal Mean Ozone Distribution in the Northern Hemisphere

based on a calculated one-dimensional distribution. Current chemistry would suggest that C10 is important to the ozone balance between t0 and 1 mb, that NOx is somewhat less important that previously assumed because of the fast rate constant for the NO + HO2 reaction (HOWARD and EWNSON, 1977), and that hydroxyl is more important to the ozone balance than was thought at that time. The chemical differences FEB MAR

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332

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(Pageoph,

DECEMBER 17, 1970 80N 0.05.

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VoI. 118, 1980) Zonal Mean Ozone Distribution in the Northern Hemisphere

333

between the calculations reported here and those of CUNNOLD et aL 0975), while non-negligible, are probably small compared with the differences between the simulated chemistry and our current understanding of stratospheric chemistry. Because of this limitation of the model chemistry, the results reported in this paper may be qualitatively but not necessarily quantitatively appropriate for the real atmosphere. The most obvious justification for the relevance of these calculations is, however, that the seasonal variations of columnar ozone in the Northern Hemisphere have been exceptionally well-simulated without any significant role being played by any ad-hoc parameterization of atmospheric transport. (ii) The vertical diffusion coefficient for ozone and momentum was reduced so as to assume a value of 102 cm2/sec consistent with observations of small scale turbulence in the vicinity of the tropopause (HECK, 1977). At higher altitudes it was reduced by an order of magnitude, compared with CUNNOLD et aL (1975) assuming a value of 9.4 • 104 cm2/sec at approximately 71 km altitude. The principal reason

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334

D.M. Cunnold, F. N. Alyea and R. G. Prinn

(Pageoph,

for this reduction in diffusion coefficients was to reduce the role played by 'nonphysical' diffusion in transporting ozone through the tropopause. It was our hope that the motions resolved in the model might produce a compensating increase in vertical transport. The effects of this change will be discussed shortly. (iii) The static stability presented in the model troposphere was increased by approximately 25~ below 6 km altitude (levels 24, 25, and 26). The intent of this change was to see whether changes in the static stability in the model troposphere would result in a more realistic tropospheric jet stream. This change, however, produced no noticeable changes in the zonal mean dynamical fields (probably because of the limited resolution of the model) and should have insignificant consequences for the ozone distribution. Figure 2 shows the excellent simulation of the seasonal variation in total ozone as a function of latitude achieved in this Northern Hemisphere calculation. (It should be recalled that although this is a global model, the 'Southern Hemisphere' contains a Northern Hemisphere orography and a tropospheric heating distribution which lags that in the Northern Hemisphere by 6 months.) Figure 3 shows a comparison between the calculated zonal mean distribution of ozone mixing ratio at high altitudes and BUV observations represented (by KRUEGERet al., 1973) to be typical of solsticial seasons. Figure 4 compares the calculated distribution in the lower stratosphere with the balloon-determined climatological distribution. In the latter figure, we note that although the calculations result in sufficient ozone in the polar regions, ozone concentration isolines do not slope sufficiently steeply towards the pole below 50 rob. This is the only obvious deficiency in these ozone calculations. The resulting ozone deficit below 15 km (which is counterbalanced in the model by a slight excess of ozone between 20 and 25 kin) is, however, only a small proportion of ozone in the atmosphere and should have minimal consequences as far as the ozone budget is concerned.

2. The model ozone equation The ozone prediction equation in the model is

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time, pressure/1000 mb, loge P, horizontal Jacobian, streamfunction for horizontal velocity, dZ W = --dT,

Vol. 118, 1980)

Zonal Mean Ozone Distribution in the Northern Hemisphere

335

Xo3 = ozone mixing ratio, H0 = average scale height of the atmosphere, Kd = ozone diffusion coefficient and 8t ] c = the contribution of chemistry to ozone change. is also updated in the model through the equation:

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It should be recalled that this model is a quasi-geostrophic model which contains dynamical approximations additional to those of a primitive equation model such as that utilized in tracer studies by MAHLMAN and MOXIM (1978). The model uses a rhomboidal truncation in the spectral domain with a cutoff at planetary wavenumber six. Moreover, as indicated in equation (1), the divergent part of the wind advects horizontal mean, not local, ozone. This approximation is used in order to eliminate two non-linear terms and thus save a substantial fraction of the model computation time. As we shall see, the reduction in diffusion coefficient, compared with that used in the previously reported computations (CuNNOLD et al., 1975; see Fig. 5) has

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336

D.M. Cunnold, F. N. Alyea and R. G. Prinn

(Pageoph,

substantially reduced the role of 'diffusion' in vertical transport in the model. However, this reduction in dissipation had an unintended effect on the short-term variability of ozone in a narrow range in the lower stratosphere. Figure 6 compares the standard deviation of modelled ozone concentrations over the course of a season with observations. We note that this version of the model overpredicts the ozone variations between 15 and 20 km (model levels 20 and 21), particularly in the tropics. The explanation of this effect is associated with the non-linear covariance between ozone perturbations and vertical motions in the prediction of horizontal mean ozone given by equation (2). This term is evaluated by finite differences at all dynamically active model levels (i.e., below 45 km). Since it is a non-linear term, it produces vertical ' m o d e s ' which exceed the resolution of the model. These higher order modes will, as a result of aliasing, appear as perturbations in the vertical modes which the model is capable of representing. In subsequent calculations, this non-linear term has been evaluated spectrally in the same manner that all horizontal non-linear terms are computed, so that the vertical aliased modes are not formed. However, other continuing modifications to the model (e.g. the representation of stratospheric chemistry) and the development of a new, higher resolution, model have resulted in no subsequent three-year simulation of the unperturbed atmosphere having yet been made. In the calculations reported here, the retention of these higher order terms results in considerable short-term and small vertical wavelength variability of horizontal mean ozone in the region where dissipative processes are weak. That is, below the region where chemistry is active and above the troposphere, where the diffusion coefficient is large. This variability in horizontal mean ozone produces smaller scale ozone perturbations through the W(#~/~Z) term in equation (1). The overprediction of ozone variability between 15 and 20 km will have no effect on the model dynamics, however, since it occurs in a region in which ozone acts as an inert tracer. Moreover, it should have no important consequences for the qualitative discussion of ozone transport and budget, since it occurs over a considerably narrower altitude range than does ozone transport.

3. The ozone budget The photodissociation of molecular oxygen, which is responsible for the production of odd oxygen (which is 99~o or more 03 below approximately 45 kin) is dependent upon the ozone distribution (which, as we have seen, is well simulated in the model at most altitudes) and has been calculated to yield the production rate given in Fig. 7. The chemical destruction rate of odd oxygen, however, is more uncertain because it depends upon details of the odd hydrogen, odd nitrogen, and odd chlorine cycles in the atmosphere. At this time, more observations are needed to fully define these cycles. For the present, we must appeal to our ability to simulate the observed ozone distribution as evidence that the model transports and the relative contributions of chemistry and transport in determining the ozone distribution are realistic.

Vol. 118, 1980)

Zonal Mean Ozone Distribution in the Northern Hemisphere

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338

D.M. Cunnold, F. N. Alyea and R. G. Prinn

(Pageoph,

Figures 8, 9, and 10 depict the contributions that horizontal advection (E), mean circulation (M), and chemistry (C) make to the calculated ozone change during the summer and winter seasons. Results are expressed as integrals over a volume, 10~ latitude by 360 ~ longitude by approximately 2.8 km (the spacing between model levels defined by AZ = 0.40574). These three contributions are approximately in balance at e a c h ' grid point' except in the lower stratosphere, where vertical advection is responsible for downward transport of ~. Based on these calculations we see (Fig. 10) that there is a net chemical production of ozone in the lower stratosphere between approximately 20 and 35 km altitude, which is centered in tropical regions of the summer hemisphere. At these heights ozone is chemically destroyed at middle and high latitudes, particularly in the winter hemisphere. Figure 10 also exhibits a secondary chemical source of ozone at midlatitudes in winter in the middle and upper stratosphere. Between 24 and 45 km we see from Fig. 8 that horizontal advection is primarily responsible for counterbalancing the net chemical production and loss of ozone, transporting ozone away from the source region in tropical latitudes and toward the weakly illuminated destruction region at high latitudes. We note, however, from a comparison of Figs. 7 and 10 that at these altitudes advection is much smaller than the photochemical source of ozone (except at high latitudes in winter). Thus, throughout most of this region, ozone is essentially in photochemical equilibrium. The transition between the region where the zonal-mean ozone distribution is photochemically controlled to the region where the ozone distribution is dynamically controlled is illustrated by the two dashed lines on Fig. 7. The upper line represents the surface on which the smaller of chemical production and loss equals 10 tons/sec. Since we see from Fig. 8 that advection between 25 and 35 km is of order 1 ton/sec, this line represents where (the absolute value of) advection roughly equals 0.1 times the smaller of chemical production and loss. Similarly, the lower dashed line on Fig. 7 represents where (the absolute value of) advection roughly equals 10 times the smaller of chemical production and loss. Because of the steep gradients exhibited in Fig. 1, the boundaries of the regions of dynamical and chemical control of the ozone distribution and the transition region between them are unlikely to be significantly altered by any improvements in the representation of chemistry in the model. This transition from a region of chemical control to one of dynamical control can be vividly illustrated by studying the seasonal variation of ozone as a function of altitude at a particular latitude. In Fig. 11 we depict the model results for zonal mean ozone at 50~ and show that the seasonal changes are remarkably similar to the observed variations over Arosa (47~ We see that below approximately 30 mb (approximately 50 mb in the observations) ozone exhibits a springtime maximum, suggesting strong dynamical control. Between 25 and approximately 4 mb (approximately 20 and 4 mb in the observations), ozone possesses a summertime maximum providing evidence of solar, and hence chemical, control. Above 4 rob, both the observations and the model results show a maximum in winter which can also be qualitatively understood from a chemical viewpoint as we shall now discuss.

VoI. 118, 1980)

Winter 80 0.05 -

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Turning now to the observed ozone distribution between 10 and 1 mb shown in Fig. 3, we note that both the observed and the calculated distributions exhibit an increase of ozone with latitude up to approximately 60 ~ latitude in the winter hemisphere between 1 and 2 rob. Umkehr observations also show a seasonal variation of ozone at this level with a maximum in winter (DELuIsI et al., 1978). We can see from Figs. 7, 8, and 10 that this gradient is apparently defined by chemistry. In the model, the maximum at 60 ~ latitude is produced by the reduction in chemical destruction related to the cold polar temperatures in this region as well as by the uncharacteristic dependence of photodissociation rates on latitude at this level (see CUNNOLD et al., 1976). However, the unrealistically cold model temperatures in this region (see CUNNOLD et al., 1975) tend to amplify this peak. The calculations by LONDON et al. (1976) show a tendency toward an increase of ozone with latitude at these levels in

342

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the winter hemisphere but no marked peak. Calculations of the covariance between ozone and temperature in the model at this level indicate a strong negative correlation (see Fig. 12). Had the model dynamics been able to simulate the observed distribution of temperature in the upper stratosphere and mesosphere, it would appear that a significantly weaker gradient of ozone with latitude than calculated here would have been produced. However, since NOx, HOx, Ox, and C1Ox (which was omitted from these calculations) all contribute to the ozone balance at this level. Also, species which sequester radicals and whose chemistry in the stratosphere requires verification (e.g. C1NO3 and N20.~) are likely to have their maximum effect at high latitudes in winter. It does not therefore seem profitable to pursue the explanation of this feature of the observations here. Suffice it to say that a tendency toward a wintertime ozone maximum between 1 and 2 mb and an increase of ozone with latitude in winter is produced by chemistry as a result of the cold polar temperatures at that time and by the particular dependence of photodissociation rates on latitude at that level. Between 30 and 40 kin, the BUV observations show a remarkably weak gradient of ozone with latitude in winter. From Fig. 7 it would appear that the explanation of this weak gradient will probably be contained in the chemistry. NOx, which is the principal ozone destruction agent in this region, may be sequestered in an inactive form, such as N2Os and C1NOa. Evidence of this is provided by Noxon's observations of NO2 (NoxoN, 1975, 1979) which show a remarkable decrease in NO2 column abundance with increasing latitude in winter. However, it is not yet clear how this reduction in NOx varies as a function of height, nor into what chemical products NOx is being converted. In particular, it has not yet been possible to simulate this latitudinal gradient of NO2 in a multi-dimensional model. We have, however, demonstrated in a previously reported model calculation (CuNNOLD et al., 1976) that a reduction of NO2 at all altitudes in proportion to the observed latitudinal gradient in columnar NO2 leads to a substantially weaker gradient of ozone with latitude between 30 and 40 km in winter. The eddy transport of ozone in the middle stratosphere, as shown by Fig. 8, indicates that transport by the waves is much larger than transport by the mean circulation. In particular, since the contribution of the mean circulation to ozone change is proportional to the vertical gradient in horizontal-mean ozone mixing ratio in this model, the contribution of the mean circulation is particularly small in the vicinity of the ozone maximum at approximately 10 mb. In the middle stratosphere, ozone undergoes a transition with height from being controlled by dynamics to being controlled by chemistry; as a result of this transition it is not surprising that the correlation of ozone with temperature changes from negative to positive with increasing altitude (see Fig. 12). As shown in Fig. 12, there exists a surface at which, on the average, ozone and temperature variations are uncorrelated. This surface occurs in a region in which, according to Fig. 7, chemistry is dominant (except poleward of 50 ~ latitude in winter). At first glance, it is surprising that this surface does not map the transition between dynamical and chemical control of the ozone distribution. A possible explana-

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344

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(1965) for larger scale features over North America and by DANmLSON (1968) and DANmLSON et al. (1970) in their studies of tropopause folding events. It has been demonstrated by FJORTOFF (1951), BOYD (1976) and ANDREWS and MCIr~TYRE (1976a,b) that waves propagating into the stratosphere under idealistic conditions do not affect the zonal flow, and that in fact a wave induces a meridional circulatioq which just cancels its effect. It is only as a result of dissipative processes and wave transience that an effect is produced. These conclusions also apply to an almost inert tracer (MAt-ILMAN et al., 1979). The cancellation betwen the contribution of eddies and mean circulation to ozone change, noted in Figs. 8 and 9, is thus not surprising, and has been noted in previous three-dimensional model studies of ozone (HUNT and MANABE, 1968; MAHLMAN, 1973). The budget of ozone below 10 mb may be summarized by Figs. 13, 14, and 15. If we integrate horizontally to obtain the budget of horizontal mean ozone, ~, we

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345

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find that a net production of ozone exists between 20 and 25 km, amounting to approximately 12 tons/sec. This chemically-produced ozone is transported vertically downwards by the large scale eddies (note that vertical diffusion plays a negligible role in this transport). Observations (e.g. FABIAN and PRUCHNIEWICZ, 1977) indicate that in fact approximately 25 tons/sec is transported through the tropopause to be destroyed at the ground. Both observations (e.g. DANIELSONet al., 1970) and model calculations (e.g. MAHLMAN and MOXIN, 1978; KIDA, 1977a,b) indicate that much of this transfer occurs at mid-latitudes in association with the jet stream, particularly in spring. Stratospheric air may be injected into the troposphere (in a partially irreversible process) to the north of the jet stream by an induced direct circulation and to the west of extra-tropical cyclones in the upper troposphere (MAHLMANand MOXIM,1978). Additional evidence for these ideas is provided by the observed distribution of ozone in the upper troposphere (FABIAN and PRUCHNIEWICZ, 1977), which exhibits a substantial maximum at mid-latitudes in the spring. This transfer is incompletely resolved in the model of MANABEand MOXIM (1978) and it is not surprising that it is inadequately accomplished in our model, which only extends to planetary wavenumber 6. The zonal mean distribution of vertical advection of ozone by the eddies has been examined in our model and exhibits no clearly defined variation with latitude or season. Since, however, horizontal variations in this term are not used to update ozone in the model, it does not seem appropriate to discuss this. In the figures which follow, the

346

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Vol. 118, 1980) Zonal Mean Ozone Distribution in the Northern Hemisphere

347

atitudinal distribution of the contribution of vertical ozone advection by the eddies to ozone change is given as an area weighted proportion of the horizontal mean advection. The budget of total ozone is obtained by performing a vertical integration of Figs. 8, 9, and 10. Figure 14 shows that columnar ozone is chemically produced at tropical latitudes of the winter hemisphere and at both tropical and mid-latitudes of the summer hemisphere. It is chemically destroyed at high latitudes, with much of the destruction occurring in the winter hemisphere. Ozone is transported across the equator from the summer to the winter hemisphere by the mean circulation, and thence poleward by the mid-latitude eddies. There is a small poleward transport by the mid-latitude eddies in the summer hemisphere. From Fig. 11, it is seen that the spring maximum in columnar ozone results from ozone variations below 40 mb. At lower altitudes, ozone production in the tropics is offset by only a small chemical loss, while at high latitudes the chemical loss of ozone is counterbalanced by little chemical production. This suggests that at latitudes above 60 ~, the decay of ozone from the spring maximum which occurs over the course of the summer results from chemical and surface destruction of ozone, but is substantially offset by transport of ozone from the lower latitudes. At latitudes below 40 ~, the decay of ozone from the spring maximum is apparently produced by a transport of ozone into the winter hemisphere. The seasonal variations of ozone in the Northern Hemisphere are summarized in Fig. 15. The buildup of ozone occurs over the course of the winter (December, January, and February) and is dissipated over the course of the summer. We note from Fig. 2 that this accumulation of ozone is relatively uniform from month to month in the model. Transient variations having a two to three week period, probably similar to those simulated by HOLTON and MASS (1976), are a prominent feature of the model. However, a substantial breakdown of the polar vortex such as occurs in a sudden stratospheric warming has not been obtained. We suspect it is necessary to more realistically reproduce the observed zonal mean stratospheric temperature gradient, i.e., to increase temperatures in the upper stratosphere in the polar night in order that these transient events may occasionally lead to a breakdown of the polar vortex. The wintertime accumulation of ozone at mid- and high-latitudes occurs through the interhemispheric transfer of ozone from the tropics of the summer hemisphere. During the spring there is also a large transfer of ozone from the spring to the fall hemisphere. However, there is no substantial net gain in spring or loss in fall of ozone in either hemisphere, and this hemispheric interchange of ozone seems to be of importance only for the tropical ozone budget and to be the result of the definition of the model spring being March, April, and May, as opposed to a definition based on the solar declination angle. Returning to Fig. 14, we note that there appears to be a tendency for the maximum contribution of transport to columnar ozone change to occur at approximately 50 ~

348

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latitude in the winter hemisphere. It is to be noted that at that location circulation and horizontal eddies are each contributing to the convergence of ozone. It may be significant that this convergence occurs just poleward of the crossover point between mean and eddy contributions to ozone change; this result has previously been noted in the tracer studies of MAHLMANand MOXIM (1978).

4. Mid-latitude transport

Horizontal eddies are responsible for transporting ozone poleward at mid-latitudes. Two pictures of the variation of this horizontal eddy flux of ozone with altitude are shown in Fig. 16. Observations of the transient eddy flux at several mid-latitude sites in the Northern and Southern Hemispheres have been averaged to produce the 'mean-observed' profile. It should, however, be noted that there are an inadequate number of observations to attach great confidence to this mean profile. We believe that the vertical structure given by the model results, which contain both transient and standing eddies, may be more representative of total eddy transport above 50 mb while the observations are likely to be more realistic below 100 mb (where the model contains too little ozone). The observed transient eddy flux above 50 mb is very close to the minimum flux necessary to produce the observed ozone distribution, which has its maximum concentrations at high latitudes. Since the horizontal flux by the mean circulation tends to be equatorward and chemistry is indicated to play a role in the ozone balance above 50 mb with production in the tropics and destruction at high latitudes (cf. Fig. 8), it would appear that planetary waves may be responsible for creating 'a greater than minimum' poleward eddy flux above 50 mb. A schematic picture of the phase relationships responsible for this poleward eddy transport of ozone in the model above 100 mb is given in Fig. 17. In this region, poleward and downward motions are positively correlated and the ozone and temperature perturbations maximize to the east of troughs and the maximum downward motion. Under these phase relationships, air parcels traveling on trajectory $1 tend to sink (due to Stoke's drift) while parcels on trajectory $3 will rise. Since planetary waves also tend to tilt westward with height, air parcels to the north of the trough will also tend to move northward as they sink across the downward sloping isentropes. In the ozone flux balance equation, it is the positive correlation between northward and downward motion which tends to maintain the countergradient northward flux of ozone. The justification for this picture of ozone transport is given in PRINN, CUNNOLD and ALYEA (manuscript in preparation, 1979). We note, however, that analysis of observations by many researchers tend to support this picture. For example, MARTIN and BREWER (1959) found significant correlations between vertical motions, temperature, and vorticity at 100 mb and total ozone. Since ozone mixing ratio and potential temperature increase with height in the lower stratosphere and motions are apparently adiabatic, downward moving air parcels should be rich in ozone and

349

Vol. 118, 1980) Zonal Mean Ozone Distribution in the Northern Hemisphere

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potential temperature. Thus, a poleward transport of heat and ozone is expected when northward-moving air parcels tend to descend. GREEN (1960) demonstrated that this is indeed a feature of baroclinic waves in the lower stratosphere. NEWELL (196i) has provided observational evidence for a strong positive correlation between meridional velocity, temperature in the lower stratosphere, and columnar ozone. HUNT and MANABE (1968) also analyzed the synoptic structure of ozone at 65 mb in their model calculations. They also noted that the local maxima of tracer seemed to be located eastward of planetary wave troughs. It should be noted, however, that in the troposphere poleward motion tends to be correlated with upward motion (rather than downward motion, as in the lower stratosphere). The transition between these two correlations seems to occur somewhere between 100 and 200 rob. According to Fig. 16, a significant proportion of the horizontal transport of ozone occurs below this region. Thus, two pictures appear to be necessary to completely describe ozone transport; at the lower elevations, a second picture has been proposed by WALLACE (1978). In that picture, downward motions,

Vol. 118, 1980) Zonal Mean Ozone Distribution in the Northern Hemisphere

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warm temperatures, and high ozone concentrations are depicted as being shifted westward by approximately rr/2 radians, compared with those given in Fig. 17. These schematic pictures of ozone transport, while providing a Lagrangian mechanism for transport, are really appropriate only when the strong counterbalancing effect of the meridional circulation does not occur. Although model results suggest that this is not true on the average, net transport may actually be the result of a whole series of transient events. For example, MAHLMAN et al. (1979) have found that wave transience is particularly important for transport at mid-latitudes in winter. MAHLMAN and MOXIM (1978) found in their tracer studies that the mean and eddy cancellation for tracer change in the lower stratosphere is incomplete, particularly during the spring as planetary scale disturbances weaken and when the zonal mean flow in the stratosphere is weak. They attribute the latter effect to the absorption of planetary waves (and hence, alteration of the mean flow) at singular lines on which the speed of the mean flow equals the phase speed of a planetary wave. We note from Figs. 8 and 9 (and more clearly in Fig. 14) that the cancellation in the lower stratosphere in our model is weaker in summer (when planetary waves are weaker because of stronger absorption) than in winter. It is important to continue to investigate the extent to which transient events, as opposed to dissipative processes, are responsible for net ozone transport in the lower stratosphere.

5. Conclusions

Results from a three-dimensional photochemical-dynamical model which includes an approximate chemistry and dynamics of ozone suggest that the transition from chemical control of the ozone distribution to transport control of the ozone distribution occurs at approximately 30 mb in the tropics and between 10 and 20 mb at the summer pole, and at 45 ~latitude in winter. Beyond 60 ~latitude in winter transport plays a significant role in determining the ozone distribution at all heights. Therefore, the observed weak gradient of ozone with latitude at middle and high latitudes in winter at approximately 5 mb and the simultaneous ozone increase with latitude between 1 and 2 mb probably require a chemical explanation. In the latter case, it is likely that the reduction in ozone loss rate associated with the cold temperatures in the polar night play a significant role. Between 1 and 10 mb, the contribution of horizontal eddies to the seasonal change of ozone is much larger than the effect of the mean circulation. The eddies tend to transport ozone polewards, particularly in winter, from the net production region in the tropics. There does not, however, seem to be any significant tendency for a large eddy transport of ozone where the correlation between ozone and temperature is zero. Moreover, this surface of zero correlation appears to lie somewhat above the transition from dynamical to chemical control of the ozone distribution. There is a net excess chemical production of ozone in the region between 15 and

352

D.M. Cunnold, F. N. Alyea and R. G. Prinn

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50 mb which is transported downwards through the tropopause to be destroyed at the ground. In this region there is, moreover, net production in the tropics and net destruction at high latitudes. The spring maximum in ozone at 50~ is found at all heights below approximately 40 mb. The model results indicate that ozone accumulates over the course of the winter as a result of production in the tropics of both the summer and winter hemispheres, the transport from the summer to the winter hemisphere, and the mid-latitude transport by the eddy motions. The decay of the springtime ozone maximum over the course of the summer at latitudes beyond 60 ~ appears to be the result of chemical destruction as well as loss through the tropopause and destruction at the surface. At latitudes below 40 ~ however, ozone loss is associated with transport into the winter hemisphere. In agreement with other studies, we note a strong cancellation between mean and eddy contributions to ozone (or equivalently tracer) change in the lower stratosphere. We note in agreement with MAHL~AN and MoxI~ (1978) a tendency for the maximum contribution of transport to ozone change to occur in winter slightly poleward of the crossover point between mean and eddy contributions. A schematic picture of the mechanism of ozone transport by eddies at mid-latitudes in the lower stratosphere has been suggested. Additi6nal description and justification of this picture will be given in a subsequent paper. This picture differs from that proposed by WALLACE (1978), and is expected to apply above 100 mb. Such pictures implicitly envision ozone transport being the result of transient as opposed to dissipative processes. Further investigations of this assumption are indicated.

Acknowledgements

This work was supported by the National Aeronautics and Space Administration under NASA Grant NSG-2010 to the Massachusetts Institute of Technology. Computer time was provided by Goddard Institute for Space Studies under grant NGR-22-009-729.

REFERENCES

ALYEA,F., CUNNOLD,D. and PRINN,R. (1975), Stratospheric ozone destruction by aircraft-induced nitrogen oxides, Science, 188, 117-119. ANDREWS,O. G. and MCINTYRE,M. E. (1976a), Planetary waves in horizontal and vertical shear: The generalized Eliassen-Palm relation and the mean zonal acceleration, J. Atmos. Sci. 33, 2031-2048. ANDREWS,D. G. and MCINTYRE,M. E. (1976b), Planetary waves in horizontal and vertical shear: An asymptotic theory for equatorial waves in weak shears, J. Atmos. Sci. 33, 2049-2053. BOYD,J. P. (1976), The noninteraction of waves with the zonally-averaged flow on a spherical earth and the interrelationships of eddy fluxes of energy, heat, and momentum, J. Atmos. Sci. 33, 2285-2291.

VoL 118, 1980) Zonal Mean Ozone Distribution in the Northern Hemisphere

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CUNNOLD, D., ALYEA,F., PHILLIPS, N. and PRINN, R. (1974), First results of a general circulation model applied to the SST-NOx problem. 2nd International Conference on the Environmental Impact of Aerospace Operations in the High Atmosphere. July 8-10, 1974, San Diego. Published by the American Meteorological Society, Boston, Mass., pp. 187-193. CUNNOLD, n., ALYEA, F., PHILLIPS, N. and PRINN, R. (1975), A three-dimensional dynamicalchemical model of atmospheric ozone, J. Atmos. Sci. 32, 170-194. CUNNOLD, D., ALYEA, F. and PRINN, R. (1976), The ozone distribution above 10 mb in winter, Proc. Joint Symposium on Atmospheric Ozone, Dresden; 9-17 August, 1976. Published by the Nat. Com. Geodesy Geophys. GDR, Berlin, pp. 333-355. CUNNOLD, D., ALYEA, F. and PRINN, R. (1977), Relative effects on atmospheric ozone of latitude and altitude of supersonic flight, AIAA Journal 15, 337-345. DANIELSON, E. (1968), Stratospheric-tropospheric exchange based on radioactivity, ozone, and potential vorticity, J. Atmos. Sci. 25, 502-518. DANIELSON, E., BLACK, R., SHEDLOWSKY,J., WESTBURG,A., HAGENSON,P. and POLLACK,W. (1970), Observed distribution of radioactivity, ozone, and potential vorticity associated with tropopause folding, J. Geophys. Res. 75, 2353-2361. DELUISI, J., MATEER,C. and HEATH,D. (1978), Comparison of seasonal variations of upper stratospheric ozone concentrations revealed by Umkehr and Nimbus-4 BUY observations, J. Geophys. Res. 84, 3728-3732. DfbTSCH, H. (1971), Photochemistry of atmospheric ozone, Advances in Geophysics I5, Academic Press, 219-322. DUTSCH, H. (1974), The ozone distribution in the atmosphere, Can. J. Chem. 52, 1491-1504. FABIAN, P. and PRUCHNIEWlCZ,P. (1977), Meridional distribution of ozone in the troposphere and its seasonal variations, J. Geophys. Res. 82, 2063-2073. FJORTOrF, R. (1951), Stability properties of large-scale atmospheric disturbances, in Compendium of Meteorology, T. Malone, ed., p. 454. Boston, Amer. Met. Soc., 1334 pp. GREEN, J. (1960), .4 problem in baroclinic stability, Quart. J. Roy. Met. Soc. 86, 237-251. HARTMANN,D. and GARCIA,R. (1979), A mechanistic model of ozone transport by planetary waves in the stratosphere, J. Atmos. Sci. 36, 350-364. HECK, W. (t977), A comparison of estimated and directly measured turbulent heat fluxes in the lower stratosphere, Mon. Wea. Rev. 105, 1337-1340. HERING, W. (1965), Ozone and atmospheric transport processes, Tellus 18, 329-336. HESSTVEDT, E. (1974), Reduction of stratospheric ozone from high-flying aircraft, studied in a twodimensional photochemical model with transport, Can. J. Chem. 52, 1592-1598. HILSENRATH, E., HEATH, D. and SCHLESINGER,B. (1979), Seasonal and interannual variations in total ozone revealed by the Nimbus-4 back-scattered ultraviolet experiment, Submitted to J. Geophys. Res. HOWARD, C. and EVENSON, K. (1977), Kinetics of the reaction of HO2 with NO, Geophys. Res. Lett. 4, 437-440. HUNT, B. and MANABE,S. (1968), Experiments with a stratospheric general circulation model, 2: Large scale diffusion of tracers in the stratosphere, Mon. Wea. Rev. 96, 503-539. HUTCHINGS, J. and FARKAS,E. (1971), The vertical distribution of atmospheric ozone over Christchurch, New Zealand, Quart. J. Roy. Met. Soc. 97, 249-258. KIDA, H. (1977a), A numerical investigation of the stratospheric general circulation and stratospheric tropospheric mass exchange. L Long-term integration of a simplified general circulation model, J. Meteor. Soc. Japan 55, 52-70. KID#, H. (1977b), .,4 numerical investigation of the stratospheric general circulation and stratospheric tropospheric mass exchange. II. Lagrangian motion of the atmosphere, J. Meteor. Soc. Japan 55, 71-88. KRUEGER,A., HEATH,D. and MATEER,C. (1973), Variations in the stratospheric ozone field inferred from Nimbus satellite observations, Pure Appl. Geophys. 106-108, 1254-1263. LONDON, J., FREDERICK,J. and ANDERSON,G. (1976), Satellite observations of the global distribution of stratospheric ozone, J. Geophys. Res. 82, 2543-2556.

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D.M. Cunnold, F. N. Alyea and R. G. Prinn

MAHLMAN,J. D. (1973), Preliminary results from a three-dimensional general circulation~tracer model, Proc. Second Conf. Climatic Impact Assessment Program. A. J. Broderick, ed., 321377 (DOT-TSC-OST-73-4). MAHLMAN, J. D. and MOXIM, W. J. (1978), Tracer simulation using a global general circulation model: Results from a mid-latitude instantaneous source experiment, J. Atmos. Sci. 35, 13401374. MAHLMAN, J. D., LEVY, I-I. ]I and MOXlM, W. J. (1979), Three-dimensional tracer structure and behavior as simulated in two ozone precursor experiments, Submitted to J. Atmos. Sci. May 1979. MARTIN, D. and BREWER,A. (1959), A synoptic study of day-to-day changes of ozone over the British Isles, Quart. J. Roy. Met. Soc. 85, 393-403. NEWELL, R. (1961), The transport of trace substances in the atmosphere and their implications for the general circulation of the stratosphere, Geofs. Pura e Appl. 49, 131. NoxoN, J. (1975), Nitrogen dioxide in the stratosphere and troposphere measured by ground-based absorption spectroscopy, Science 189, 547-549. NoxoN, J. (1979), Stratospheric NO2. IL Global behavior, Preprint, 1979. WALLACE, J. (1978), Trajectory slopes, countergradient heat fluxes, and mixing by lower stratospheric waves, J. Atmos. Sci. 35, 554-560. Wtr, M.-F. (1973), Observations and analysis of trace constituents in the stratosphere, Annual report, Contract DOT-05-20217, Env. Res. Tech., Lexington, Mass. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkhfiuser Verlag, Basel

A Calculation of the Possible Depletion of Ozone by Chlorofluorocarbons Using a Two-Dimensional Model By J. A. PYLE 1)

Abstract-Results are presented from a two-dimensional, time-dependent model of the atmosphere which has been used to investigate perturbations to the ozone layer due to chlorofluorocarbons. The unperturbed stratosphere is modelled well with the observed features of the ozone distribution reproduced. The main features of the perturbation calculations are the large latitudinal and seasonal variations found in the modelled ozone reductions with greatest reductions where the total ozone amounts are largest. The importance of at least a two-dimensional study in problems of this kind is stressed and the important role of dynamical and radiative processes, as well as chemical, is indicated.

Key words: Ozone depletion; Chlorofluorocarbons.

1. Introduction

Although ozone has only a small concentration in the stratosphere, with a maximum mixing ratio of about 10 parts per million, it is an extremely important atmospheric constituent since it plays a vital role in determining the temperature structure of the stratosphere and mesosphere. Furthermore, it shields the earth's surface from the potentially harmful ultraviolet radiation at wavelengths less than about 3100 ~.. During recent years there have been suggestions that the release of a number of species into the atmosphere might adversely affect the ozone layer. These gases include the oxides of nitrogen from supersonic aircraft (JOHNSTON, 1971; CRUTZZN, 1971) or following the increased use of nitrogen fertilizers (CRuTZEN, 1974a) and the growing industrial use of certain chlorine compounds (MoLINA and ROWLAND, 1974). Because of the importance of stratospheric ozone, calculations of any possible depletion are of serious concern. Such calculations are made complicated by the number of feedback processes operating. F o r example, the stratospheric wind fields depend on the solar heating which is a function of the ozone concentration. The ozone concentration itself is determined in part by transport processes, and these depend on the wind fields, and in part by photochemical and chemical processes, many of which are temperature dependent. There are thus important couplings in the stratosphere between dynamics, 1) Department of Atmospheric Physics, Clarendon Laboratory, University of Oxford, U.K.

356

J.A. Pyle

(Pageoph,

radiation and photochemistry, which should be taken into account in calculations of the perturbation of the ozone layer. Since the proposal by MOLINA and ROWLAND(1974) that chlorofluorocarbons (CFCs) might have a deleterious effect on the ozone layer there have been a number of theoretical investigations of the problem using one-dimensional numerical models (e.g. CRUTZEN, 1974b; DERWENTet al., 1976, among many). These models have the merit that they are relatively inexpensive tools and thus very sophisticated chemical schemes can be employed. They suffer, however, from a number of drawbacks. They contain an extremely crude representation of transport processes. Moreover, they do not allow the feedback between radiation and dynamics and most do not contain the feedback between the ozone field and temperature. Furthermore, since they are global (or hemispheric) mean models their interpretation is not straightforward. Ideally, a three-dimensional model, in which the meteorological fields are calculated in a self-consistent manner, would be used to investigate perturbations to the ozone layer. However, the cost of such an operation is prohibitive to most research groups. To avoid this expense, while at the same time including some of the important feedback processes, two-dimensional zonal mean models can be used. This report describes the use of such a model in the investigation of the ozone layer perturbed by chlorofluorocarbons. A two-dimensional model is still an expensive computational tool and hence a number of approximations have been introduced. For instance, the chemical scheme described here is simpler than used in some studies in that it does not attempt to describe either the natural chlorine cycle of the atmosphere or the diurnal cycle of the various species. However, the most important of the known catalytic cycles for ozone destruction are included. The model can be used, moreover, to investigate the importance of dynamical processes and of latitudinal and seasonal effects which cannot be studied with a one-dimensional model. Although the model has also been used to investigate some of the other feedback processes mentioned above, description of these experiments will be the subject of a later paper.

2. The model 2.1. Dynamical representation The time-dependent, two-dimensional zonal mean model of the atmosphere developed by HARWOODand PYLE (1975) has been used to investigate some features of the problem of the ozone layer perturbed by CFCs. The model has reproduced many features of the ozone budget of the natural stratosphere (HARWOODand PYLE, 1977) and thus perturbation studies can be performed with some confidence, assuming that the state of the perturbed stratosphere does not deviate too far from that found naturally. The model extends from pole to pole and from the ground to approximately 80 kin, although in the calculations described here the top level for the chemical scheme is

Vol. 118, 1980) Calculation of Possible Depletion of Ozone by Chlorofluorocarbons

357

taken to be 60 km. The dependent variables are the zonal means of the chemical constituent mixing ratios, held as functions of time, latitude and height with a resolution of ~r/19 in latitude and approximately 4 km in height (0.5 in pressure scale height). In previous versions of the model (HARWOODand PYLE, 1975) the zonally averaged fields of wind and temperature were calculated each time-step. When combined with the solution of the continuity equations for the chemical species, the computational expense becomes high. The problem can be simplified by using precomputed fields of temperatures and the meridional winds, although at the expense of omitting the complete coupling between the chemical species and the meteorological fields. Thus, the feedback between the ozone concentration and the temperature and wind structure, via the absorption of solar radiation, is omitted. Such an approach has been followed in this work, the temperature and wind fields from a previous version of the model being used (see HARWOOD and PYLE (1975, 1979) for descriptions of the dynamical fields). The problem is then reduced to the solution of the continuity equations for the chemical species. Consider a (y, ~:) co-ordinate system with y = distance northwards and ~: = loge (Po/P), with p ---=pressure and P0 = 1000 mb, and with velocity components v and w. Let a bar (-) denote the zonal mean (e.g. g = da, a = longitude) and a prime ( )' denote the departure therefrom (i.e. s' = s - g). Then the zonally averaged continuity equation for a species of volume mixing ratio X is written

1/2~f~s

8~(~e-r

+ 7y(V~) + --(WE) = P e - r

+ F

(1)

where q~ = latitude and .P is the zonal mean net rate of production of constituent x, per unit volume of air, and the following definitions have been made: V= ve-r162 W = w e-~ cos and F = -~

( V X ) - ~ (W'x')

F arises from the divergence of the eddy flux of the species, X. The treatment of these eddy terms is one of the major problems in two-dimensional modelling. The method used here follows a diffusion coefficient approach which allows the eddies to be written in terms of the mean quantities. Thus, the northward and vertical fluxes of X are written: -v'x' 8~ - Ky~ a-~ O~ = - K . -Uy

(2)

O~ a)? w'x' = -K~y @ - K~r ~--~.

(3)

358

J.A. Pyle

(Pageoph,

The coefficients can be determined from the variance of the meridional wind (e.g. Ku~ a v'2) and typical slopes of the particle tracks. This does not allow for the calculation to be completely interactive in that the Ks should probably vary with the model state. However, we assume the largest factor of the flux variations is accounted for and a single set of Ks can be used to model both the natural and the perturbed stratosphere, assuming that the two dynamical regimes are not too dissimilar. The Ks used in these calculations are the monthly averaged values of LU3:IJER (t973). These coefficients were used in the previous runs of the model and hence there will be some consistency between the fields of V, W and T and the Ks. It should be noted that there is an eddy contribution to the net photochemical sources and sinks which has been ignored in this calculation. T u c k (1979) has shown that in some circumstances, particularly in the winter hemisphere, this term can be important.

2.2. The chemical scheme The chemical scheme used is presented in Table 1. The reaction rate constants and photochemical data used will not be discussed in detail; they are, in general, the values agreed upon by the U.K. modelling groups involved in research on the possible impact of CFCs on the ozone layer. The rate constants for the reactions of HO2 with both NO and Oa have been found to be larger than those listed (BURROWS et al., 1977; HOWARD, 1978). The importance of these changes is discussed below: our conclusions regarding ozone reductions remain valid. The scheme has been kept as simple as possible in line with the aim of a twodimensional calculation with a good representation of the dynamical processes. Nevertheless, most of the important stratospheric cycles are included. No attempt has been made, however, to model the natural chlorine cycle, the assumption being made that the influence of the chlorine compounds on the ozone layer will be a linear function of their concentration. Within the range of chlorine concentrations considered here, this approximation is valid. The computational method has been to write continuity equations, in the form of equation 1, for families of species. The families are chosen such that their lifetime is longer than 8 hours (twice the time step). The individual constituents within the family are assumed to be in photochemical steady state. Thus those reactions with very short time scales do not occur in equation 1 but only in the steady state expressions, and the stiffness of the equations can be avoided. Much longer time-steps are possible than when a continuity equation is written for each constituent. TURCO and WHITTEN (1974) have discussed generally the use of families of species. A similar method has been used by VUPPUTURI (1979) in a two-dimensional calculation. Within the constraints outlined above the choice of families is somewhat arbitrary. The particular sets of families used here are given below. Considering, for instance,

Vol. 118, 1980)

Calculation of Possible Depletion of Ozone by Chlorofluorocarbons

359

Table 1 The photochemical scheme 02 + hv--+O + 0 O + 02 + M---> O3 + M Oa + h v ~ O + 02 03 + hv--+ O('D) + 02 0 + 03 -'+ 202 O('D) + N 2 ~ O + N2 O('D) + O2--~ 0 + 02 O('D) + H20 ~ 2 0 H O('D) + CH4 ~ CH3* + OH O ( ' D ) + H 2 - + H + OH OH+ O-+H+O~ H + 02 + M--> H02 + M HO2 + O--> O i l + O2 H + O s ' - + O H + O2 OH + Oa--> HO2 + 02 H02 + O3--+ OH + 202 CO+ OH-+C02+ H H02 + HOz ~ H202 + 02 H202 + OH--+ H20 + HO2 H20~ + hv-+ 2 0 H O H + HO2--,-H20 + 02 OH + CH4--> H20 + CH3 O i l + OH---> H20 + 0 O('D) + N20 -+ 2NO O('D) + N20--~ N2 + 02 NO + O3--+ NO2 + 02 NO2 + O ~ N O + 02 NO2 + h v ' - > N O + O NO2 + O3---" NO3~ + 02 HO2 + NO--+ NO2 + OH NO2 + OH + M---" HNO3 + M HNO8 + hv--> NO2 + OH HNO3 + OH--+ H20 + NO3 NO + h v - - * N + O N + NO---> N2 + O N + O2-+ N O + O N + O 3 - ' + N O + O2 CFC13 + hv --+ 3C1 CF2C12 + hv -+ 2C1 CFCI, + O('D)--+ C10 + 2CI CF2Clz + O('D) --> C10 + C1 C1 + O3-'+ CIO + O2 C10 + O ~ C 1 + O2 C10 + N O - + C1 + NO2 C10 + NO2 + M--+ C1ONO2 + M C1ONO2 + hv--.'. CIO + NO2 C1ONO2 + O--~ C10 + NOa CH~ + C1--~ CH3 + HCI Ha + C I - + H + HC1 O H + IlC1--+ H20 + C1 HO2 + C1--~ O2 + I-ICI

1.05E(-34) exp (510/T) )t > 3077 A A < 3077 A 1.9E(- 11) exp ( - 2 3 0 0 / T ) 2.0E(-11) exp (108/T) 2.9E(-11) exp (67/T) 2.3E( - 10) 1 . 3 E ( - 10) 1.3E(- 10) 4 . 2 E ( - 11) 2 . 1 E ( - 32) exp (290/T) 3 . 5 E ( - 11) 2 . 6 E ( - 1 I) 1.5E(- 12) exp ( - 1000/T) 3 . 7 E ( - 14) exp ( - 1025/T) (1 + 4.18E(-20)-[M]).2AE(--13) exp ( - - l I 5 / T ) 6.4E(-13) exp (500IT) 1.0E( - 11) exp ( - 750[T) 5 . 1 E ( - 11) 2.36E(-12) exp ( - 1 7 1 0 / T ) 1.0E(-11) exp ( - 5 5 0 / T ) 7 . 0 E ( - 11) 7 . 0 E ( - 11) 9 . 0 E ( - 13) exp ( - 1200/T) 9 . 1 E ( - 12) 1.2E(- 13) exp ( - 2450/T) 1.2E(- 12) ANASTASIet al. (1976) 8 . 0 E ( - 14) Based on CIESLIK and NICOL~T (1973) 8 . 2 E ( - 11) exp (--410/T) 5.5E(-12) exp ( - 3 2 2 0 / T ) 5.0E(-12) exp ( - 6 5 0 [ T ) 2 . 3 E ( - 10) 2 . 0 E ( - 10) 2 . 7 E ( - 11) exp ( - 2 5 7 / T ) 1.07(-- 10) exp ( - 224/T) 8 . 0 E ( - 12) exp (250/T) Based on ZELLNER(1977) and ZAHNISERet aL (1977) 4.5E(-12) exp 7.3E(-- 12) exp 3.5E(-- 11) exp 2.8E(-12) exp 2 . 5 E ( - 11)

(--840/T) ( - 1260/T) (-- 2290/T) (-400/T)

HNO3, H202 and HC1 are removed from the model troposphere with a time constant of 20 days. *) CH3 --->3HO2, instantaneous. t) NO3 --~ (a) NO2 + O and ~ (b) NO + O2 with (a):(b) = 10:4, instantaneous. N . B . 1.0E(-10) =- 1.0 x 10 -1~.

360

J.A. Pyle

(Pageoph,

the odd oxygen family (Oa, O and O('D)), the total rate of change due to photochemical processes, P, is calculated and equation 1 is solved for the family, using the Adams-Bashforth integration scheme. The photochemical steady-state relationships between 03, O and O('D) then determine the relative concentrations of each species within the family. In using a four hour time-step the model does not resolve diurnal variations and the calculated concentrations of the various constituents represent a daily average value. Night time chemistry is not included but the reaction rates are weighted by the fractional number of sunlight hours per day. Consistent with this temporal averaging the photodissociation rates are re-calculated every ten days, finding a daytime average value by Gaussian integration over a number of solar zenith angles. Continuity equations are written for the following species or groups of species: O('D), O and 03; N, NO, NOz and C1ONO2; HNO3; H202; H, OH and HO2; C1, C10, C1ONOa and HC1; CFCla; CF2CIz. The lifetime of the HOx family (H, OH and HO2) is short and transport is ignored in this case. In the upper stratosphere the lifetimes of HNOa and H~O2 become short and these are included in the odd nitrogen and odd hydrogen families respectively, care being taken to ensure conservation. The other species, H20, CH4, Ha, N20 and CO, are assumed to be invariant. Profiles, based on a limited number of measurements, are specified, independent of latitude. The boundary conditions used are presented in Table 2. The model results are not particularly sensitive to the bottom boundary conditions of those species which are rained out in the troposphere. The upper boundary condition for the CFCs ensures that no chlorine is transported through the top level of the model and the calculated ozone depletion will be an upper limit, with the particular chemical scheme used.

Table 2

Boundary conditions

Lower

Upper

03

Constant volume mixing ratio of 3 x 10-8

NO + NO2 Ha02

Constant volume mixing ratio of 7 x 10-10 Constant volume mixing ratio of 3.2 x 10 -11

HNOa

Constant volume mixing ratio of 8.0 • 10-l~

CFCI,

Zero flux into ground

CFC12

Zero flux into ground

CIO~

Constant volume mixing ratio of 0.0

Calculated photochemical equilibrium Constant mixing ratio profile Calculated photochemical equilibrium Calculated photochemical equilibrium Zero flux through upper boundary Zero flux through upper boundary Zero flux through upper boundary

Vol. 118, 1980) Calculation of Possible Depletion of Ozone by Chlorofluorocarbons

361

3. The natural stratosphere While the stratosphere does contain chlorine of natural origin, the discussion in this section is limited to the behaviour of compounds of oxygen, nitrogen and hydrogen. In the following section the behaviour of anthropogenic chlorine compounds is discussed while their effect on the ozone layer is considered in Section 5. Two long integrations have been performed. In R1, the chlorine chemistry was suppressed. Thus R1 represents a control run against which the effects of the chlorine chemistry, included in R2, can be assessed. A comparison of the results of R1 with observational data on atmospheric minor constituents helps to ascertain the degree of confidence which can be placed in the subsequent perturbation studies. Such a comparison is the purpose of this section. Figure 1 shows the latitude-time section of the total ozone from R1. There is a gross resemblance to the behaviour of the atmosphere, although there are differences in detail. There is a maximum in total ozone in the northern hemisphere polar regions in spring with a maximum in the southern hemisphere in mid to high latitudes just over six months later, as observed. Minimum values are found in equatorial latitudes. There is, however, a little too much ozone in low latitudes due, in part, to too great a concentration in the lower stratosphere. PYLE (1976) and H ~ w o o n (1977) have stressed the sensitivity of the ozone distribution to the radiative heating, and hence

J

F

~,t

A

M

3 J A $ 0 N D MONIH Figure 1 Latitude-time section of the total amount of ozone, in Dobson units (m atm cm), for one model year from R1.

362

J.A. Pyle 50-

MODEL DAY 3680

(Pageoph,

R348

21 MAR

40-

2

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-

-

-

~

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~

~

~

~

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LATITUDE 03 (rib)

Figure 2

Cross-section of the ozone partial pressure (nb) from March of run R1. the induced vertical velocities, in the equatorial lower stratosphere. The reason for the low latitude discrepancy could, therefore, be dynamical. The maximum in the northern hemisphere should perhaps be somewhat higher. This, again, could be due to an underestimation in the model of the eddy transport of ozone to high latitudes in late winter. The distribution of total ozone is not, however, sensitive just to changes in the dynamical representation. With the newer rate constants for the reactions of HO2 with both 03 and NO, the ozone column is decreased by up to about 570 in high latitudes. It is interesting that with these rate constants important changes in the ozone profile were found at altitudes below 30 km where ozone is often assumed to be dominated by transport processes. 50- __ MODEL 22 Sept 36~ "E

+

.

A(

Anderson 0975) 32~ 25 Nov

2~

~;7

,,,

R348 / .

,;8 ' O(3p)

A

/

,;~ '

~o

(atoms cm-3)

Figure 3 comparison of modelled and observed O(aP) profiles.

Vol. 118, 1980) Calculation of Possible Depletion of Ozone by Chlorofluorocarbons

363

Figure 2 shows a cross-section of the ozone partial pressure during the northern hemisphere spring. The agreement with observations is good (see, e.g. DOTSCr~, 1971) although the maximum at the north pole is slightly too small, as expected, since the total column amount of ozone is too small there (Fig. 1). The maxima in the subtropical troposphere are real features associated with transport through the tropopause at about the latitude of the tropopause breaks (HARWOODand PYLE,1977). Above 40 km the observed summer minimum and winter maximum of the ozone mixing ratio in middle and high latitudes are well reproduced. The variation is attributed in part to the seasonal variation in the temperature structure in the upper stratosphere, the ozone mixing ratio being inversely correlated with temperature at these altitudes (BARNETTet al., 1975). Figure 3 shows the measured vertical profile of O(3P) by ANDERSON (1975) compared with a model profile for approximately the same solar zenith angle. The model reproduces the observed increase of the concentration with height with, however, somewhat smaller values. This case exemplifies some of the problems in comparing calculations with observations. For instance, the model does not attempt to reproduce diurnal behaviour while O(3P) should exhibit a strong diurnal variation (KURZEJA, 1975). Moreover, a constituent with a short time constant like O(3P) is evidently sensitive to short period variations in the temperature structure or the concentration of other trace species. Thus, a comparison of a single profile with a model which cannot reproduce these short period, or diurnal, changes can be misleading. The odd oxygen family is a good example to consider when attempting to assess the degree of confidence to be placed in perturbation calculations or any predictive MODEL DAY 3680

21 MAR

R348

50. 40. v

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~:30o

~ ~

LLI -j-

------

~

0.4-_____ 0.2

W rr D u~ u~ Ld rY O-

~ 20400

10-

%0%

I~0

30 NOx vmr

6~ LATITUDE (+10-8)

3'0

6'0

,qooo 90~

Figure 4 Cross-section of the NOx (NO + NO2) volume mixing ratio for March from R1.

364

J.A. Pyle

(Pageoph,

MODEL DAY 8500

50

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-

'

'

R348 '

'

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DRUMMOND & JARNOT (1978)

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.

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i

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i

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,

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]0-8 Volume Mixing Retio

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Figure 5 A comparison of the modelled NO= profile with observations.

MODEL DAY 3950

16 DEC

R 348

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40-

-lo

v

F: 30-

IJJ

LIJ "r ~2013_

400

rr t/3 t.t3 Ld 127 (2.

10-

~

~o

~o

6~

LATITUDE

3b

6b

9o~

HNO3 vmr (/10-9)

Figure 6 Cross-section of the HNO3 volume mixing ratio for December from R1.

Vol. 118, 1980) Calculation of Possible Depletion of Ozone by Chlorofluorocarbons 60-

MODEL DAY 3950

16 DEC

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50/

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---..., 30

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Figure 7 Cross-section of the OH number density for December from RI. studies. While the gross features of the observed distribution in time and space are reproduced there are important differences in detail. Furthermore, it is impossible to assign these discrepancies uniquely to limitations in either the dynamical or photochemical representation. Perturbation studies should be considered in this light, with the main emphasis placed on the gross, features of the calculation. Since NO and NO2 vary diurnally a comparison of single profiles with the model behaviour is not satisfactory and a better comparison is made between measured and modelled NOx (i.e. NO and N Q ) . Figure 4 shows a cross-section of the NOx vmr, with maximum values found around 40 km. Figure 5 shows the observed values of DRUMMOND and JARNOT(1978) at 43~ with a mid-latitude model profile for the same month. The agreement is good although the modelled maximum at around 40 km is a little low. Figure 6 presents the cross-section of the HNO3 volume mixing ratio. The values are at the upper limit of the range of observations in the middle stratosphere (see ACKERMAN, 1975). The broad features agree well with observations (LAZRUSand GANDRUD, 1974; MURCRAY et al., 1975). The tropospheric mixing ratios are low. Maximum values are found at about 25 kin, increasing towards high latitudes and the mixing ratio decreases rapidly with height in the upper stratosphere. Similar to ozone, the lowest column amounts are found in equatorial latitudes. A cross-section of OH is given in Fig. 7. The shape of the stratospheric profile agrees well with the observed profile of ANDERSON (1976). The model profile peaks

366

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calculation of the dashed line. above 40 km with a maximum concentration, which varies with latitude, of greater than 107 mol cm -3. The calculated values are a little lower than Anderson's observations in the stratosphere but higher than his mesospheric values (ANDERSON, 1971). The agreement between the model and the very limited number of observations is less satisfactory for HO2 (Fig. 8). The modelled values are somewhat larger than the measurements of EHHALT (1978) but less than those of ANDERSON et aL (1978). Use of the newer rate constants for the reactions of HO2 with 03 and NO is more nearly consistent with Ehhalt's observations. Agreement with one observation does not represent a particularly convincing exercise in model validation and more observations of the vertical profile are necessary to resolve what could be a serious discrepancy between model and observation.

4. The chlorine species

The run, R2, including a source of chlorine from the CFCs will be discussed in this section. The CFCs are released from mid-latitudes of the model, the release being spread equally at the bottom model level between the three latitude belts from 30~

Vol. 118, 1980) Calculation of Possible Depletion of Ozone by Chlorofluorocarbons

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Since the only source of chlorine in the model is from the CFCs, with the natural sources of chlorine ignored, the profiles of the other chlorine species should not be expected to agree in magnitude with the observations. Figure 12 shows profiles of the species at 35~ from R2 and from a run, R3, in which C1ONO~ was excluded from the photochemical scheme. HCI is the most abundant of the gases throughout the range shown but C1ONO2 is an important species in the lower stratosphere, reducing the values of HCI and C10 when it is included in the photochemical scheme.

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Figure 14 shows the variation of calculated C10 with time of year at 67~ at which latitude the modelled seasonal variation was found to be large and certainly larger than at the lower latitudes typical of the observations. The seasonal variation is much smaller than the variations in Anderson's measurements in the lower stratosphere, and, indeed, little systematic agreement can be found. An interesting feature of the model results is that the profiles intersect at about 40 km. Above this height the mixing ratios of C10 are smallest in summer, with opposite behaviour for HCI, while below about 40 km the summer mixing ratios are greatest. If a regular seasonal variation is to be invoked to explain the observations then again it must be concluded that the photochemical model used here is inadequate to explain it. The cross-section of C10 concentration is given in Fig. 15. An interesting feature is the increase in the concentration with latitude in the lower stratosphere. Maximum concentrations occur in the middle stratosphere at about 35 km. Although there is a concentration minimum at about 25 km in northern polar latitudes, the mixing ratio profile of C10 shows little variation with height in this region. In Fig. 16 the cross-section of the HC1 mixing ratio is given for model day 8050 corresponding, with the release histories used, to the late 1980s (remembering that the CFCs are the only source of chlorine). The largest values in the lower stratosphere are found in high latitudes. This is consistent with the behaviour of other long-lived species, such as ozone and nitric acid, in this region. It is interesting to note that the profiles in extratropical latitudes go through minima at about 40 km. Such minima are not inconsistent with the measurements of EYRE and ROSCOE (1977), LAZRUS et al. (1977) and EVANS et al. (1978). Dynamical processes produce the maximum at

372

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lower altitudes. At around 40 km the OH concentration is a maximum and destruction of HC1 is correspondingly enhanced. Thus photochemical processes produce a minimum in the ratio of HCI to the other chlorine species there (see Fig. 12). This feature does not appear to have been produced in one-dimensional calculations.

5. Perturbations to the ozone layer

In this section the influence of the chlorine species on atmospheric ozone will be discussed. In R1 the model reproduced many of the observed features of the natural stratosphere and thus perturbation studies can be undertaken with some confidence. However, there are areas of uncertainty which should be remembered when considering these calculations. Furthermore, the modelled chlorine species revealed additional uncertainties. It is, therefore, in the qualitative, rather than the quantitative, features of the calculations that greatest confidence can be placed. For instance, improvement in our knowledge of the chemical processes operating in the stratosphere should not change the conclusions reached below regarding latitudinal and seasonal effects, although the magnitude of the calculated reductions would probably be altered. Figure 17 is a latitude-time section of the percentage difference in total ozone 90~

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Cross-section of the percentage reduction in ozone concentration between runs R1 and R2 corresponding, with the release histories used, to March 1992. Areas where the ozone concentration has increased in R2 are shaded. between R I and R2, during one model year, corresponding roughly to the year 1992. The most obvious features are significant variations in the depletion with latitude and time, confirming the results of a previous calculation with simplified chemistry (PYLE, 1978). The minimum in the depletion occurs in low latitudes where the total ozone is a minimum; maximum depletions occur in high latitudes in spring when the total ozone is a maximum. Since the maximum depletions occur in high latitudes near to the polar night it is clear that atmospheric dynamics, as well as photochemistry, plays a role in determining the calculated pattern of ozone reduction. Some indication of the reasons for the particular pattern of ozone depletion can be gained by considering Fig. 18, a cross-section of the percentage reduction in ozone concentration during March of the year shown in Fig. t7. Maximum percentage reductions in ozone are found at about 40 kin. Since absorption of solar radiation by ozone is a dominant feature of the radiation budget at this height, the inclusion of the coupling between the ozone concentration, radiative heating and the circulation would appear to be important. A particularly interesting feature is the increase in the ozone concentration found in the equatorial lower stratosphere. This is due to the so-called 'self-healing' effect. The ozone depletion in the upper stratosphere allows increased penetration of solar ultraviolet radiation into the lower stratosphere. This leads to increased photolysis of molecular oxygen and hence enhanced production of ozone. In equatorial latitudes this actually leads to an increase in ozone below about 30 km and helps account for the fact that the reduction in total ozone is a minimum in low latitudes.

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The rate of photolysis of molecular oxygen is increased below about 30 km at all latitudes in R2. However, the effect is much smaller in high latitudes and the selfhealing effect is more than cancelled by the destruction of ozone by the chlorine compounds. Below about 20 km the catalytic destruction by the chlorine reactions actually increases towards higher latitudes due to the increase in C10 there (Fig. 15) but, of course, at these altitudes the net destruction is small. In a somewhat similar two-dimensional calculation VUP~UTURI (1978) has also found that the ozone depletion varies with latitude, although much less strongly than shown here. In Vupputuri's model the lower boundary is at 10 km and it seems possible that the difference between the two calculations is associated with the

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Vol. 118, 1980) Calculationof Possible Depletion of Ozone by Chlorottuorocarbons

375

differences in the temperature structure and the wind fields in the upper troposphere and lower stratosphere. A further example of the coupled nature of the ozone problem is illustrated in Figs. 19 and 20. These show the percentage changes in the photochemical production terms and the total transport of ozone between runs R 1 and R2. Regions of relatively increased production are unshaded. These regions could, of course, still be net dynamical or photochemical sinks. Shading indicates that the photochemical or dynamical term is more negative or less positive in the perturbed run. The area of self-healing is evident in the equatorial lower stratosphere (Fig. 19), but there is, as mentioned above, increased destruction in high latitudes in R2. An interesting feature, though, is the close balance between the photochemical and dynamical terms, with, for instance, a greater transport in the perturbed run away from the region of self healing into high latitudes. This transport will cancel to some extent the increased photochemical destruction.

6. Conclusions The two-dimensional, time-dependent model of the atmosphere presented here has successfully reproduced many of the observed features of the unperturbed stratosphere. The field of total ozone, for example, has an equatorial minimum with maxima in high latitudes in spring. There are, however, differences in detail between the model and observations and it is in the light of these differences that the perturbation calculations should be assessed. A more serious discrepancy appears to exist between the measured and calculated C10 concentrations. The main feature of the perturbation calculations is the significant latitudinal and temporal variation of the ozone depletion. Largest depletions are found in high latitudes in early spring, at a time when the ozone amount itself is a maximum. Minimum depletions occur in low latitudes throughout the year. The variation with latitude approaches a factor of four at its maximum while in mid-latitudes the depletion varies with season by almost a factor of two. The variation with latitude and time is not produced merely by photochemical processes. Dynamical and radiative processes also play important roles. For example, the increased penetration of ultra-violet radiation into the equatorial lower stratosphere gives rise to an increased ozone concentration there. There is a subsequent increase in the transport of ozone to higher latitudes. The self-healing effect is not so pronounced in high latitudes, and is countered by the catalytic destruction due to chlorine species. It is clear that the calculation of possible perturbations to stratospheric ozone is made more complicated by the interaction between photochemistry, radiation and dynamics. Only some of these complex interactions have been considered here but their importance has been demonstrated.

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Acknowledgements This work was supported by the Department of the Environment, U.K. Modelling work at Oxford University is also supported by N.E.R.C. The author is indebted to R. J. Wells for his computing work. REFERENCES

ACKERMAN, M. (1975), NO, NO2 and HNOa below 35 km in the atmosphere, J. Atmos. Sci. 32, 1649-1657.

ANDERSON, J. G. (1971), Rocket measurement of OH in the mesosphere, J. Geophys. Res. 76, 7820-7824. ANDERSON, J. G. (1975), The absolute concentration of O(aP) in the Earth's stratosphere. Geophys. Res. Lett. 2, 231-234. ANDERSON, J. G. (1976), The absolute concentration of OH(X2II) in the Earth's stratosphere. Geophys. Res. Lett. 3, 165-168. ANDERSON, J. G., MARGITAN,J. J. and STEDMAN,D. FI. (1977), Atomic chlorine and the chlorine monoxide radical in the stratosphere: three in situ observations, Science 198, 501-503. ANDERSON, J. G., MARGITAN, J. J., GRASSL, H. J., SHETTER, R. E. and MAURER, J. C. (1978), Report to the Congress and to the Administrator of the Environmental Protection Agency on The National Aeronautics and Space Administration's Upper Atmosphere Research Program, pp. 26. BARNETT, J. J., HOUGHTON,J. T. and PYLE, J. A. (1975), The temperature dependence of the ozone concentration near the stratopause, Quart. J. R. Met. Soc. 101, 245-257. BURROWS, J. P., HARRIS, J. W. and THRUSH, B. A. (1977), Rates of reaction of riO2 with HO and 0 studied by laser magnetic resonance, Nature 267, 233-234. CIESLIK, S. and NICOLET, M. (1973), The aeronomic dissociation of nitric oxide. Aeronomica Acta No. 112. CRUTZEN, P. J. (1971), Ozone production rates in an oxygen-hydrogen-nitrogen-oxide atmosphere. J. Geophys. Res. 76, 7311-7327. CRUTZEN, P. J. (1974a), Estimates of possible variations in total ozone due to natural causes and human activities. Ambio 3, 201-210. CRUTZEN P. J., (1974b), Estimates of possible future ozone reductions for continued use of chlorofluoromethanes, Geophys. Res. Letts. 1, 205-208. DERWENT, R. G., EGGLETON,A. E. J. and CURTIS, A. R. (1976), A computer model of the photochemistry of halogen-containing trace gases in the troposphere and stratosphere, A E R E Report R-8325, HMSO, London. DRUMMOND, J. R. and JARNOT, R. F. (1978), Infrared measurements of stratospheric composition II. Simultaneous NO and NO2 measurements. Proc. R. Soc. Lond. A364, 237-254. DOTSCH, H. U. (1971), Photochemistry of Atmospheric Ozone, Advances in Geophysics, Vol. 15, Academic Press, New York. EHHALT, D. (1978), Cryogenic sampling measurements of stratospheric gases. W MO Publication No. 511, 71-78, WMO, Geneva, Switzerland. EVANS, W. F. J., FAST, I-L, KERR, J. B., MCELROY, C. T., O'BRIEN, R. S., WARDLE,D. I., MCCONNELL, J. C. and RIDLEY, B. A. (1978), Stratospheric constituent measurements from project stratoprobe. WMO Publication No. 511, 58-59, WMO, Geneva, Switzerland. EYRE, J. and ROSCOE, I-L (1977), Radiometric measurements of stratospheric HCI, Nature 266, 243-244. I-IARWOOD,R. S. (1977), Dynamical feedback and stratospheric models, Proceedings of the scientific seminar on stratospheric monitoring, Paris, 21-23 March 1977, Secretariat d'Etat aupres du Ministre de l'equipment (Transports), Paris, France. HARWOOD, R. S. and PYLE, J. A. (1975), A two-dimensional mean circulation model for the atmosphere below 80 km, Quart. J. R. Met. Soc. 101, 723-747.

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HARWOOD,R. S. and PYLE, J. A. (1977), Studies of the ozone budget using a zonal mean circulation model and linearizedphotochemistry, Quart. J. R. Met. Soc. 103, 319-344. HARWOOD, R. S. and PYLE, J. A. (1979), On the response of a two-dimensional ozone model to the dynamical formulation. In preparation. HEIDT, L. E., LUEB, R., POLLOCK, W. and EHHALT,D. H. (1975), Stratospheric profiles of CClaF and CCl2F~. Geophys. Res. Letts. 2, 445-447. HOWARD, C. J. (1978), Recent developments in HO2 chemistry. Paper presented at the WMO conference, Toronto, June 1978. WMO Publication No. 511, 11, WMO, Geneva, Switzerland. JOHNSTON,H. S. (1971), Reduction of stratospheric ozone by nitrogen oxide catalysts from supersonic transport exhaust, Science 173, 517-522. KURZEJA, R. J. (1975), The diurnal variation of minor constituents in the stratosphere and its effects on the ozone concentration, J. Atrnos. Sci. 32, 899-909. LAZRUS, A. L. and GANDRUD,B. W. (1974), Progress report on distribution of stratospheric nitric oxide. Proceedings of the third CIAP conference, 161-167. U.S. Department of Transportation, Washington, D.C. LAZRUS, A. L., GANDRUD,B. W., GREENBERG,J., BONELLI, J., MROZ, E. and SEDLACEK,W. A. (1977), Mid-latitude seasonal measurements of stratospheric acidic chloride vapor, Geophys. Res. Letts. 4, 587-589. LUTHER, F. M. (1973), Monthly mean values of eddy diffusion coefficients in the lower stratosphere. AIAA paper 73-498, AIAA/AMS conference, Denver, Colorado. MCCARTHY, R. L., BOWER, F. A. and JESSON, J. P. (1977), The fluorocarbonozone theory- L Production and release. World production and release of CC13F and CC12F2 through 1975, Atmos. Environ. 11, 491-497. MOLINA, M. J. and ROWLAND,F. S. (1974), Stratospheric sinks for chlorofluoromethanes: chlorine a tom-catalysed destruction of ozone, Nature 249, 810-812. MURCRAY, D. G., BARKER,D. B., BROOKS,J. N., GOLDMAN,A., KOSTERS,J. J., MURCRAY,F. H. and WILLIAMS,W. J. (1975), Variation of HNO~ total column density with latitude and season and a measurement of stratospheric CF2Cl2. Proceedings of the fourth CIAP conference, 432-437, U.S. Department of Transportation, Washington, D.C. PYLE, J. A. (1976), D.Phil. Thesis, University of Oxford. PYLE, J. A. (1978), A simple calculation of ozone depletion by chlorofluoromethanes using a twodimensional model, Nature 271, 42-43. RASMUSSEN,R. A. (1975), Data published in National Academy of Sciences report, Halocarbons: Effect on Stratospheric Ozone, Chapter 6, Washington D.C. SCHMELTEKOPF,A. L. (1976), Data published in National Academy of Sciences report, Halocarbons: Effect on Stratospheric Ozone, Chapter 6, Washington D.C. SCHMELTEKOPF, A. L., GOLDAN, P. O., HENDERSON, W. R., HARROP, W. J., THOMSON, T. L., FEHSENFELD, F. C., SCHIrF, H. I., CRUTZEN, P. J., ISAKSEN,I. S. A. and FERGUSON,E. E. (1978), Measurements of stratospheric CFCI3, CF2CI~ and N20. Geophys. Res. Letts. 2, 393-396. TUCK, A. F. (1979), A comparison of one-, two- and three-dimensional model representations of stratospheric gases. Phil. Trans. R. Soc. Lond. A290, 477-494. VUPPUTURI,R. K. R. (1978), The possible impact of past and projected future atmospheric release of CFM's on stratospheric ozone and its climate investigated in a 2-D time dependent model. WMO Publication No. 511,263-267, WMO, Geneva, Switzerland. VUPPUTURI, R. K. R. (1979), The structure of the natural stratosphere and the impact of chlorofluoromethanes on the ozone layer investigated in a 2-D time dependent model. Pure Appl. Geophys. 117, 448-485. ZAHNISER, M. S., CHANG,J. S. and KAUEMAN,F. (1977), Chlorine nitrate: kinetics of formation by C10 + NO2 + M and of reaction with OH, J. Chem. Phys. 67, 997-1003. ZELLNER,R. (1977), Fall-off curves for the reaction CIO + NO2( + N2)--~ CIONO2(+ N2). Z. Naturforsch. 32a, 648-651. (Received 15th June 1979)

Pageoph, Vol. I 18 (1980), Birkh~user Verlag, Basel

Temperature and Ozone Variations in the Stratosphere By J. K. ANGELL 1)

Abstract- Examined are temperature and ozone variations in the Northern Hemisphere stratosphere during the period 1958-77, as estimated from radiosondes, rocketsondes, ozonesondes, and Umkehr measurements. The temperature variation in the low tropical stratosphere is a combination of the variation associated with the quasi-biennial oscillation, and a variation nearly out of phase with the pronounced 3-yearly temperature oscillation (Southern Oscillation) present in the tropical troposphere since 1963. Based on radiosonde and rocketsonde data, the quasibiennial temperature oscillation can be traced as high as the stratopause, the phase varying with both height and latitude. However, the rocketsonde-derived temperature decrease of several degrees Celsius in the 25-55 km layer of the Western Hemisphere between 1969 (sunspot maximum) and 1976 (sunspot minimum) is not apparent in high-level radiosonde data, so that caution is advised with respect to a possible solar-terrestrial relation. There has been a strong quasi-biennial oscillation in ozone in the 8-16 km layer of the north polar region, with ozone minimum near the time of quasi-biennial west wind maximum at a height of 20 km in the tropics. A quasi-biennial oscillation in ozone (of similar phase) is also apparent from both ozonesonde data and Umkehr measurements in 8-16 and 16-24 km layers of north temperate latitudes, but not higher up. Both measurement techniques also suggest a slight overall ozone decrease in the same layers between 1969 and 1976, but no overall ozone change in the 24-32 km layer. Umkehr measurements indicate a significant 6-8~ increase in ozone amount in all stratospheric layers between 1964 and 1970, and in 1977 the ozone amount in the 32-46 km layer was still 4 ~ above average despite the predicted depletion due to fluorocarbon emissions. The decrease in ozone in the 32-46 km layer of mid latitudes following the volcanic eruptions of Agung and Fuego is believed to be mostly fictitious and due to the bias introduced into the Umkehr technique by stratospheric aerosols of volcanic origin. Above-average water vapor amounts in the low stratosphere at Washington, DC, appear closely related to warm tropospheric temperatures in the tropics, presumably reflecting variations in strength of the Hadley circulation. Key words: Stratospheric temperature; Stratospheric ozone.

1. Introduction As an aid to our u n d e r s t a n d i n g of stratospheric processes, this p a p e r presents temperature a n d ozone variations within the N o r t h e r n Hemisphere stratosphere (tropopause to stratopause) based u p o n a b o u t 20 years of r a d i o s o n d e a n d U m k e h r measurements and a b o u t 10 years of rocketsonde a n d ozonesonde measurements. M e n t i o n is also made of stratospheric water vapor variations in mid latitudes. The rationale for this paper is the belief, nay certainty, that knowledge of past ' n a t u r a l ' 1) Air Resources Laboratories, ERL, NOAA, Silver Spring, Maryland 20910, USA.

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variations is a prerequisite to detection and comprehension of possible future anthropogenic effects. In the following, the data are presented at seasonal intervals (winter is December, January, February, etc.) but the annual variation has been eliminated by determining deviations from long-term seasonal means. The data have then been placed back in calendar order and a 1-2-1 weighting (divided by 4) applied twice to successive seasonal values (this is equivalent to the binomial 1-4-6-4-1 weighting). Such a smoothing reduces the amplitude of any quasi-biennial oscillation by about one-third. In the diagrams the tick marks along the abscissa refer to the summer season, the temperature data are presented as deviations from the mean in degrees Celsius, and the ozone data are presented as percentage deviations from the mean. Confidence limits have been evaluated based on the standard deviation of individual station values (though not shown in the diagrams for the sake of clarity), and reference is made in the text to temperature and ozone variations significant at the 95~ level.

2. Temperature variations Figure 1 illustrates the temperature variations from about 1958 through the spring of 1.978 in the 16-24 km layer (low stratosphere) of tropics and north temperate and polar latitudes, based on radiosonde observations at 30, t 2, and 8 stations, respectively. As a basis for discussion, the bottom trace represents the temperature variation in the 0.16 km layer (troposphere) of the tropics. The temperature variations in 0-16 and 16-24 km layers have been derived from changes in 'thickness' (height difference of constant-pressure surfaces) between the surface and 100 rob, and between 100 and 30 mb. Within the tropical troposphere there have been significant temperature variations of approximately 3-year period since 1963, with some decrease in amplitude and period during recent years. Between 1958 and 1963 there was little evidence of such a variation. It has been shown by ANGELL and KORSHOVER(1978a, 1978b) that the warm phase of these temperature oscillations has been closely related to the E1 Nino phenomenon (and hence to warm sea-surface temperatures in the equatorial Pacific, and the Southern Oscillation in general), and to intervals of unusually rapid increase in atmospheric carbon dioxide at Mauna Loa, Hawaii. The vertical arrows (representing time of the west wind maximum) in Fig. 1 show that in the low tropical stratosphere the temperatures have tended to be warm near the time of quasi-biennial west wind maximum at a height of 20 km (50 mb pressure) in the tropics, a well-known relation. However, there is also the impression of a nearly out-of-phase relation between tropospheric and low-stratospheric tropical temperatures, with the minimum temperature in the 16-24 km layer occurring 1-2 seasons before the maximum temperature in the 0-16 km layer. This is perhaps most striking in 1970-71 when, based on data around the whole tropical belt, there was a

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time of the vertical arrows. Thus, in the low stratosphere there is little lag between quasi-biennial temperature oscillations in temperate latitudes and in tropics. There has been little evidence of a quasi-biennial temperature oscillation in the 16-24 km layer of north polar latitudes, although a long-term variation is apparent with relatively warm temperatures around 1960 and again after 1970. An argument can be made for a nearly in-phase relation between tropical tropospheric temperature and temperature in the low stratosphere of polar latitudes, and this will be monitored closely as the data record is extended. Figure 2 illustrates the temperature variation in middle and high stratosphere (26-55 km) of the Western Hemisphere, as deduced from rocketsonde observations at 2 stations in north polar latitudes, 5 stations in north temperate latitudes, and 3 stations in the tropics (representative results can hardly be obtained from the small number of Eastern-Hemisphere rocketsonde stations). The temperature changes in

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26-35, 36-45, and 46-55 km layers were obtained from an averaging of rocketsonde temperatures at 1 km height intervals. These data only extend through 1976. A quasi-biennial oscillation in temperature is most apparent in the 36-45 km layer of north temperate latitudes, with a temperature minimum at, or 1-2 seasons after, the time of quasi-biennial west wind maximum at 20 km in the tropics. The oscillation occurs about two seasons later in the 26-35 km layer of temperate latitudes, and about one year later in the 16-24 km layer of temperate latitudes (Fig. 1). The quasi-biennial temperature oscillation is barely detectable in the 46-55 km layer. In both tropics and north polar latitudes, to the contrary, there is evidence of a temperature maximum in the 36-45 km layer near the time of the vertical arrows. As shown by AYaELL and KORSHOVER (1978c), the difference in phase with latitude results from an increase in descent rate of the quasi-biennial oscillation with increase in latitude. The rocket soundings in all three regions of the Western Hemisphere indicate a significant temperature decrease of several degrees Celsius between sunspot maximum in 1969 and sunspot minimum in 1976, and this decrease has been associated with a presumed decrease in solar ultraviolet irradiance between sunspot maximum and sunspot minimum by CALLIS nad NEALY (1978) and PENNER and CHANG (1978). While it will certainly be of great interest to see if stratospheric temperatures increase again with the increase in sunspot number beginning in 1977, the observation of different temperature trends based on rocketsonde data and radiosonde data (to be emphasized in Fig. 4) suggests caution with respect to any solar-terrestrial relationship. 3. Ozone variations

Figure 3 illustrates the ozone variation in 8-16, 16-24 and 24-32 km layers of the north polar region as derived from ozonesonde releases at Resolute, Canada, and in north temperate latitudes as derived from a 2, 2, 1 weighting of ozonesonde observations in North America (4 stations), Europe (4 stations) and Japan (3 stations), and a 2, 1, 1 weighting of Umkehr observations in Europe (4 stations), Japan (3 stations), and India (3 stations). The Umkehr observations also permit an assessment of the ozone variations in the 32-46 km layer, or the layer sensitive to variations in ultraviolet irradiance and fluorocarbon pollution. The ozone changes in the respective layers have been estimated from an averaging of ozonesonde observations at the mandatory pressure surfaces of 300, 200 and 150 mb, 100, 70 and 50 mb, 30, 20 and 10 mb, and the averaging of Umkehr observations in layers l and 2, 3 and 4, 5 and 6, and 7, 8 and 9. Both sets of data extend through 1977. Information concerning the Umkehr technique may be obtained from MATEER(1965). At the north polar station of Resolute (close to the north magnetic pole) the quasibiennial variation in ozone is most apparent in the 8-16 km layer bracketing the tropopause, with the ozone amount nearly 20~ less at the time of quasi-biennial

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west wind maximum at 20 km in the tropics (vertical arrows) than at east wind maximum. The variation is not nearly so evident in the 16-24 and 24-32 km layers. Based on rather infrequent soundings, the intense solar proton event in the summer of 1972 (arrow labeled S) did not have an obvious effect on ozone amount in the 24-32 km layer, although evidence for an effect above 35 km has been found from satellite data by HEATH et al. (1977). There is little evidence of a long-term trend in ozone in the 8-16 km layer, but in the two higher layers the ozone tended to peak in early 1972, or about two years after sunspot maximum.

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As pointed out by WILCOXet al. (1977), ozonesonde observations in north temperate latitudes clearly define a quasi-biennial oscillation in ozone in 8-16 and 16-24 km layers (phase shift with height of about 2 seasons in 8 kin), but not in the 24-32 km layer despite the rocketsonde evidence for quasi-biennial temperature oscillations in this layer. The phase of the quasi-biennial ozone oscillation is essentially the same in polar and temperate latitudes. The ozonesonde data suggest an overall decrease in ozone between 1969 (sunspot maximum) and 1976 (sunspot minimum) in 8-16 and, particularly, 16-24 km layers, but no appreciable change in the 24-32 km layer. The Umkehr observations in north temperate latitudes indicate, for all stratospheric layers, a significant 6-8~o increase in ozone between 1964 and 1970, and relatively little change thereafter, although in the 16-24 km layer there was a slight decrease between 1969 and 1976 in agreement with ozonesonde observations. The two sets of observations also agree in showing little ozone change after 1969 in the 24-32 km layer, but in the 8-16 km layer the Umkehr-derived evidence for some continued ozone increase is not reflected in the ozonesonde data. Of course, the ozone

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amount in the 8-16 km layer is strongly controlled by dynamical processes, so that station representativeness becomes most important. The quasi-biennial oscillation in ozone is not so well delineated by the Umkehr observations as by the ozonesonde observations, but especially in the 16--24 km layer the derived variations are similar in phase if not in amplitude (see also Fig. 4). Within the 32-46 km layer of north temperate latitudes, the Umkehr observations indicate an abrupt decrease in ozone following the volcanic eruptions of Agung and Fuego (Guatemala). ANGELLand KORSHOVER(1978d) suggested that this decrease is mostly, if not entirely, fictitious, and due to the influence on the Umkehr measurements of aerosols introduced into the stratosphere by the two eruptions. DELUIS~ (1979) shows that what is still controversial at this time is the extent to which the ozone increase after 1964 is real and not just a 'return to normal' from the Agung effect. In any event, as of 1977, the ozone amount in the 32-46 km layer is still 47o above average, and this should be compared with the nearly 470 ozone reduction in this layer which the photochemical model of LUTHERet al. (1977) and PENNERand CHANG (1978) suggests should have occurred due to fluorocarbon emission. 4. Comparisons

In summary, Fig. 4 presents a comparison of derived temperature variation and ozone variation (from both ozonesonde and Umkehr measurements) in the 16-24 km layer of north temperate latitudes; this stratospheric layer and region being chosen because it is believed the temperature and ozone data are most representative there. Also shown is the water vapor variation in the same layer at Washington, DC, based on the data of MASTENBROOK (1974), as well as the temperature variation in the tropical troposphere and in the 26-35 km layer of north temperate latitudes. There has been an intriguing in-phase relation between the tropospheric temperature variation in the tropics (Southern Oscillation) and the variation in water vapor amount in the low stratosphere at Washington, DC. It is hypothesized that warm tropospheric temperatures in the tropics are associated with an enhanced Hadley circulation transporting above-average amounts of water vapor poleward. The ozone (and temperature) variations in mid latitudes, however, are dominated by the quasibiennial oscillation rather than the Southern Oscillation, perhaps reflecting the very different source regions of ozone and water vapor. In mid latitudes the quasi-biennial oscillations of ozone and temperature have been generally in phase (warm temperatures associated with high ozone amounts), but this was not the case in 1968 and 1976. As mentioned earlier, there is a striking discrepancy between the north-temperate temperature trend determined for the 16-24 km layer from radiosonde data, and for the 26-35 km layer from Western Hemisphere rocketsonde data, even though the quasi-biennial oscillations derived from the two sets of data are compatible. One should bear in mind, however, that the middle stratosphere tends to behave independentIy of the lower stratosphere on many scales, as shown for example by

386

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BOVILLE a n d HARE (1961) a n d KULKARNI (1968), a n d that it is thus possible that different temperature trends could occur at heights 10 k m apart. This question should be resolved before a n y claims are made regarding a relation between sunspot n u m b e r (solar ultraviolet irradiance) a n d stratospheric temperature.

REFERENCES ANGELL,J. K. and KORSHOVER,J. (1978a), Global temperature variation, surface-lO0 mb : An update into 1977, Mon. Wea. Rev. 106, 755-770. ANGELL, J. K. and KORSHOVER,J. (1978b), Estimate o f global temperature variations in the 100-30 mb layer between 1958 and 1977, Mon. Wea. Rev. 106, 1422-1432. ANGELL, J. K. and KORSHOVER,J. (1978c), Recent rocketsonde-derived temperature variations in the Western Hemisphere, J. Atmos. Sci. 35, 1758-1764. ANGELL,J. K. and KORSHOVER,J. (1978d), Global ozone variations: an update in to 1976, Mon. Wea. Rev. 106, 725-737. BOVILLE,B. W. and HARE,F. K. (1961), Total ozone and perturbations in the middle stratosphere, Quart. J. Roy. Meteor. Soc. 87, 490-501. CALLIS,L. B. and NEALY,J. E. (1978), Solar U V variability and its effect on stratospheric thermal structure and trace constituents, Geophys. Res. Letters, 5, 249-252. DELuIsI, J. J. (1979), Umkehr vertical ozone profile errors caused by the presence o f stratospheric aerosols, J. Geophys. Res. 84, 1766-1770. I-~EATH,D. F., KRUEGER,A. J. and CRUTZEN,P. J. (1977), Solar proton event: influence on stratospheric ozone, Science 197, 886--889. KULKARNI, R. N. (1968), Ozone fluctuations in relation to upper air perturbations in the middle latitudes o f the Southern Hemisphere, Tellus 20, 305-313. LUTHER, F. M., WEUBBLES,D. J. and CHANG,J. S. (1977), Temperature feedback in a stratospheric model, J. Geophys. Res. 82, 4935-4942. MASTENBgOOr~,H. J. (1974), Water vapor measurements in the lower stratosphere, Can. J. Chem. 52, 1527-1531. MATEER, C. L. (1965), On the information content o f Umkehr observations, J. Atmos. Sci. 22, 370-381. NEWELL, R. E. (1970), Stratospheric temperature change from the Mr. Agung eruption, J. Atmos. Sci. 27, 977-978. PENNER, J. E. and CHANG, J. S. (1978), Possible variations in atmospheric ozone related to the eleven-year cycle, Geophys. Res. Letters 5, 817-820. WILCOX, R. W., NASTROM,G. D. and BELMONT,A. D. (1977), Periodic variations o f total ozone and its vertical distribution. J. Appl. Meteor. 16, 290-298. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh/iuser Verlag, Basel

Atmospheric Ozone over Australia- A Review By R. N. KULKARNI1)

Key words: Australia; Ozone as tracer; Anthropogenic influences. Atmospheric ozone, owing to its property of absorbing solar ultraviolet radiation and the resulting heating effect, is of intrinsic importance in stratospheric meteorology and radiation research. The main interest in atmospheric ozone remained for many years in its use as a tracer in the study of the transport processes in the stratosphere. Considerable advances in the understanding of the complex transport processes have been made in the last two to three decades from observations made on ozone at a network of stations. In recent years, interest in atmospheric ozone has been given a boost due to predictions of possible ozone depletion from anthropogenic influences and its biological and economical consequences. In the following few pages, a brief review of the increasing knowledge of the natural and global (with emphasis on the Southern Hemispheric) variability of this important trace constituent and its interaction with the circulation of the atmosphere, will be made. The usefulness of ozone studies rests heavily on the density of observational network and on the reliability of observations. The Australian network of the present six ozone observing stations is the biggest in the Southern Hemisphere and monitors daily total ozone values in addition to twice-weekly Umkehr observations using Dobson spectrophotometers at all stations, weather permitting. From one station (Aspendale), fortnightly balloon soundings for the vertical distribution of ozone are made using Mast-Brewer ozone sensors. The constant check kept on the calibration and intercomparisons of the instrument in the region makes the network one of the most reliable in the world. The long series of observations made at Aspendale since 1956 and Brisbane since 1957 have become yardsticks in the understanding of the future behaviour of ozone due to changing practices of human activities. Distribution o f ozone and circulation

Ozone is formed principally above 25 km by photochemical processes and is carried to the lower atmosphere and troposphere by circulation processes. In the lower stratosphere, where ozone is effectively shielded from photochemical destruction 1) CS1RO Division of Atmospheric Physics, P.O. Box 77, Mordialloc, Victoria 3195, Australia.

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once it is transported there, it assumes great meteorological significance as a tracer to indicate atmospheric circulation. In the late 1920s, amongst a few places in the world (about five) where first observations on ozone were made, Mr. Stromlo in Australia was one. These observations at Mt. Stromlo, which lasted only for about a year, were used along with data from other stations to establish the general behaviour of ozone in the atmosphere. In the 1950s ozone was really put to use in understanding the large circulation processes in the stratosphere on a global scale. About 80 observing stations were established in the world to report on ozone values on a daily basis. It was soon discovered that quite a lot o f information regarding the stratosphere could be obtained from the observations on total ozone and its vertical distribution. This was the time when observations at Aspendale commenced (1956) and by the early 1960s the network in the Australian region expanded to include about six stations. This became the biggest network in the Southern Hemisphere, providing valuable reliable data for stratospheric research. Quite early in the history of ozone research, a number of authors (DoBsON and HARRISON, 1926; RAMANATHAN, 1954, etc.) produced the global pictures of the meridional distribution of ozone. The main features of these early findings were similar to the more accurate later diagrams produced by DUTSCH (1971), LONDON et al. (1976), etc. For the Southern Hemisphere, using the I G Y data, KULKARN1 (1962) produced a similar diagram. Also from these diagrams the principal hemispherical differences were shown. Basically, the distribution of ozone in the Southern Hemisphere is similar to the Northern Hemisphere, showing an equatorial minimum and an increase towards higher latitudes up to about 60~ * Variations in total ozone depended on season and latitude. Polewards of 40 ~ there is more ozone in the Northern Hemisphere and in Autumn in low and middle latitudes there appears to be slightly more ozone in the Southern Hemisphere. Mean meridional distributions of ozone with height in the Southern Hemisphere were constructed for the first time (KULKARNI, 1966) for summer and spring seasons using Umkehr observations. The vertical distribution in the Southern Hemisphere was similar to the Northern Hemisphere in that the greatest concentration occurred between 15-25 km and in winter-spring seasons and above 30 km a decreasing ozone with increasing latitude (up to 60~ was noticed. Significant differences between ozone distributions with height over Antarctic and the Arctic were noted. These results could be interpreted as implying circulation in the stratosphere on the Dobson-Brewer model and could best be explained by large-scale eddy mixing processes with a flow polewards and downwards from the equatorial regions (DOBSON t956; BREWER, 1949; RAMANATHAN,1954). As this circulation accelerated as in

*) However, there were some differences, for example in the Southern Hemisphere, in spring there was a greater amount of ozone in the 50-60~ region than on either side of it, whereas in the Northern Hemisphere the maximum ozone occurred slightly farther polewards.

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winter and spring, the ozone increased in the lower stratosphere and whenever it weakened, as in summer and autumn, ozone either remained steady or decreased, depending on its rate of leakage into the troposphere. From the observed differences in the hemispherical distributions of ozone, it was interpreted that in the stratosphere, the mid-latitude eddy transport is stronger in the Northern Hemisphere than in the Southern Hemisphere (KULrCARNI, 1962). The differences observed over the Antarctic and the Arctic were necessarily associated with the differences in the temperature structures of the Antarctic and Arctic stratospheres. It is well known that there is a relationship between total ozone and the pressure pattern in the upper troposphere and lower stratosphere. High ozone is associated with pressure troughs and low ozone is associated with pressure ridges. One should, therefore, expect longitudinal variation in ozone depending on the planetary stationary waves. A comparison of station data by KtJLKARNI and GARNHAM (1970) between Brisbane in Australia and Pretoria in South Africa showed the existence of a difference in the ozone values, thus the longitudinal difference in the Southern Hemisphere. Because of the sparseness of comparable data in the Southern Hemisphere, it was difficult to arrive at any definite conclusions. LONDON (1974), earlier BOJKOV (1968), has noted that there appear to exist high ozone areas at about 140~ 40~ and 60~ and that the longitude pattern is relatively fixed in position but more pronounced in winter-spring period.

Biennial oscillation The early 1960s saw an important discovery in meteorology, of a biennial cycle in stratospheric winds in the equatorial region (E~DON, 1961 ; BELMONTet al., 1974). Since then a large number of articles have appeared on the phenomenon - trying to interpret physically and mathematically the observed 26 month oscillation. FUNI~ and GARNHAMreported in 1962, for the first time, the existence of such a cycle in the spring maximum ozone in Aspendale and Brisbane which they vaguely attributed to the equatorial stratospheric wind oscillation. The study of the vertical distribution of ozone using Umkehr method (KULKARN~, 1966, 1968) provided further insight into the oscillation in ozone at various heights. This showed that the biennial cycle was noticeable above 24 km in the middle stratosphere, but below 24 km the ozone oscillation was mainly seasonal. The interactions between the equatorial region and the middle and high latitudes and between the middle stratosphere and the lower stratosphere, were obviously influencing the ozone in the vertical column in the middle latitudes of the Southern Hemisphere. Although photochemistry was the main factor for the ozone variation in the middle stratosphere, circulation and the dynamics of that region play an important role in the behaviour of ozone. The downward motion in the polar regions at about 25 mb was thought to be at least partly responsible for the biennial cycle in the middle latitudes of the Southern Hemisphere. Figure 1

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gives the monthly mean ozone values for all available even and odd years at DarwinCairns, Brisbane, Aspendale and Macquarie Island. It is interesting to note that the difference in ozone between even and odd years began in March at Darwin, April in Brisbane, June in Aspendale and August at Macquarie Island. It appears that the biennial ozone oscillation moves polewards, the difference between even and odd years occurring later in higher latitudes. Since the middle stratospheric circulation was closely linked with the observed behaviour of ozone regarding its biennial oscillation, there was more likelihood of finding a relation between solar activity and ozone oscillation through the photochemistry and middle stratospheric dynamics. Interestingly, there was a breakdown (or a longer periodicity) in the biennial cycle of ozone during 1963-64, a period of minimum sunspot activity. This corresponded to the anomaly in the equatorial stratospheric wind (KULKARNI, 1966; PITTOCK, 1973). BERSON and KULKARNI (1968) argued that variations in solar emission associated with the double sunspot cycle (22 years) provide a possible mechanism by which period of the biennial cycle can be 24 months. A solar minimum period, thus, could have produced the observed anomaly

Vol. 118, 1 9 8 0 )

Atmospheric Ozone over Australia - A Review

391

in ozone oscillation in 1963-64. There was some evidence that similar breakdowns occurred at other places during other sunspot minimum periods. It was also realized that the volcanic eruption at Mt. Agung, which took place at about the same time, could have created an anomalous temperature structure in the lower stratosphere and the upper troposphere which in turn could have produced an ozone anomaly through changing circulation. Also, it was possible the scattering problems involved by the introduction of the volcanic debris into the upper atmosphere could have produced errors in the calculations and measurements of ozone and thus the anomaly (DE LuIsI, 1978; PtTTOCK, 1974a). This brings us to investigating and discussing the problems of the errors involved in the calculation of ozone when one considers the changing character of haze and dust in the atmosphere.

Ozone and aerosol scattering

The usual and the standard method of calculating total ozone in the atmosphere using direct Sun observations from a Dobson spectrophotometer is a differential method called the ' A D ' method, the observations for which involve the intensity ratios of two wavelength pairs. The equation used for this purpose consists of an ozone absorption term, a Rayleigh scattering term due to air molecules and a term for large particle scattering (for particles larger than air molecules). In the ' A D ' method it is assumed that the scattering by large particles is the same for the two pairs of wavelengths and these terms are considered cancelled. This may be true when the atmosphere is reasonably clear. In hazy conditions, however, when the distribution of number and size of the particles differs considerably from a clear sky distribution, the differential equation may not represent a true picture and thus may not give a correct value of ozone. The importance of being able to assess the magnitude of errors involved in the assumption that the ozone value obtained by ' A D ' method represents the true ozone in all conditions, is obvious in the light of recent efforts to find the long-term trends in global ozone data, coupled with the possibility that such trends may be influenced by long-term variations in aerosol scattering, maybe because of increased industrial output of large particles in the atmosphere. The problem involved is a difficult one and attempts have been made to get an approximate estimate of the errors involved in seasonal variation depending on the seasonal variation of the character of haze, and in the long-term trend in ozone (DOBSON, 1957; RAMANATHANand KARANDIKAR,1949; DIERMENDIJIAN,1969). A closer look at this problem was taken in 1973 (KULKARNI,1973) to estimate the errors involved in the ozone calculations and in the long-term trends of ozone, by using XAD -- XA trends which involve only large particle scattering terms. In Fig. 2 monthly values of x~o - XA (scattering) are plotted along with monthly XAD (ozone)

392

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(Pageoph,

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Figure 2 values for Darwin. One can see a clear inverse correlation demonstrating, as before for Brisbane and Aspendale (see KULKARN~, 1973), that the observed trend in XAO (ozone) is influenced by the secular change in scattering as evidenced by its trend. An approximate method, explained in the earlier paper, could be used to estimate the effect of this changing haze character on observed ozone (Xav) trend. It wilt be stressed here that the method employed in the estimation of scattering effect on the trend of ozone (xao) is approximate, which made reasonable assumptions but certainly is not rigorous mathematically. The estimate of the effect of changing aerosol scattering on the ozone trend using the approximate method was about 50~. The error was not significant in the seasonal variation of ozone. Kenneth Moe, in a recent paper (MoE, 1978/79), has reviewed the recent attempts to solve the problem of the effect of aerosol extinction on ozone measurements. His conclusion, 'The picture which emerges from the studies is that aerosol extinction is a significant source of error in ground based ozone measurements and that no definitive method of eliminating it has yet been devised', basically sums up the situation. It will be repeated that the method used above is, without doubt, only approximate, which gives a reasonable approximate estimate of the aerosol effect. Other more rigorous methods (BASHER, 1976; FARKAS, 1976) confirmed that there exists such a problem in the ozone trend analysis but did not yield any convincing results. A further study on the changing aerosol scattering problems using three pairs

Vol. 118, 1980)

Atmospheric Ozone over A u s t r a l i a - A Review

393

of wavelengths is in progress. It is important to bear in mind the possible errors involved, because of changing haze in the atmosphere, in the trend analysis of ozone.

Ozone trend and the circulation

It is well known that, because of the complexities involved in photochemistry and transport effects, the uncertainties regarding the magnitude of possible damage or change to the ozone layer by stratospheric pollution, man-made or otherwise, are considerable. Until the twin problems of photochemistry and transport are solved satisfactorily the only sure way of recognizing the behaviour of ozone lies in its measurement vertically and horizontally. In Fig. 3, twelve-monthly running means of all the available total ozone data for Brisbane and Aspendale have been plotted along with the linear regression lines. The earlier figure (KULKARNI, 1976) has been extended to include the recent data. It can be seen that ozone at Aspendale and Brisbane was decreasing since 1956 and 1957 respectively. At Aspendale ozone has decreased by 4Yo until 1977 and since then has " increased sharply. Macquarie Island also showed a decreasing trend since 1963 but was not statistically significant. These observed trends in ozone were not due to any changes in the calibration of the instrument, as monthly checks for the calibration of the spectrophotometers were clone regularly using mercury and standard lamps and corrections made whenever

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necessary. Since March 1978, Instrument Number 105, which is the standard for this region and which was modified at Boulder, U.S.A. in September 1977, is used for regular observations at Aspendale. In addition to these checks, quite frequently complete calibration of the optical wedges were carried out using the gauze method and L0 (the extra-terrestrial constant) valued determined. Thus, one can say that the 4% decrease in ozone up to the end of 1977 at Aspendale was genuine. The sharp increase of ozone at Aspendale after March 1978 (a vertical line is drawn at this point in the diagram) is probably due to the new level of ozone brought in line with the world standard. The Aspendale instrument (No. 105) was re-adjusted and recalibrated to the world standard kept at Boulder, Colorado, and the ozone values after March 1978 are, on the average, 2.5% greater than the earlier values obtained with the pevious calibrations. The next obvious step was to investigate at what level the ozone was decreasing and to find out whether there was any corresponding change in any other parameters like temperature, wind strength, etc. in the lower stratosphere. Pn'TOCK (1974b) looked at the trend in ozone in various layers using eight years of ozonesonde data obtained at Aspendale since June 1965. Soundings of the vertical distribution of ozone have been made on a regular weekly basis at Aspendale until September 1974 and thereafter on a fortnightly basis. His results clearly showed that there was a decreasing trend in ozone below 20 rob, averaging about 6% per decade, and an increasing trend above 20 mb. My recent analysis of all the ozonesonde data confirms the decreasing trend in the lower stratosphere between 20-100 mb level. Figure 4 gives the seasonal means of ozone from ozonesonde observations (Mast-Brewer type) in various layers at Aspendale from 1965 to 1977. In the diagram are also given the regression lines for these observations. It can be seen that between 100 and 20 mb Seosono[ Neons 140 120 I 100 80

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Vol. 118, 1 9 8 0 )

Atmospheric Ozone over Australia- A Review

395

Table 1 The decrease o f ozone in the lower stratosphere is consistent with the decrease o f total ozone observed at Aspendale using Dobson spectrophotometer

Average ozone in

Percentage change

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levels, ozone was decreasing. Percentage decrease in each of the layers from 1965 to 1977 is given in Table 1. A similar analysis using the Umkehr observations showed a decreasing trend in the lower stratosphere over Aspendale and to a lesser extent at Brisbane. Further, when analysed seasonally a noticeable decreasing trend in winter as opposed to an increasing trend in summer at Aspendale was observed. As the dynamical processes are of primary importance in the production and maintenance of the tropopause and also of the temperature variation in the lower stratosphere, the radiative processes being only secondary in importance, one would expect a close relationship between total ozone and lower stratospheric parameters like the tropopause height, 100 mb temperatures etc., since the same dynamical processes are mainly responsible for most of the ozone changes which are known to occur in the lower stratosphere as seen from the ozone vertical distribution data discussed above. Thus, when the deviations of 100 mb temperatures from their monthly means were investigated at Darwin, Brisbane, Aspendale and Macquarie Is/and, it was obvious that during 1963-74 the lower stratosphere had cooled on the average by 1.4~ which was statistically significant. Accepting the idea that the changes in ozone and in 100 mb temperatures are caused by the same dynamical processes, even on a long-term basis, and there is ample evidence to support this, one should be able to see whether the observed changes in ozone over Australian stations are consistent with the observed changes in 100 mb temperatures. Qualitatively, it appears that a gradual weakening of the lower stratospheric circulation, poleward circulation of subsiding air from the equator by large scale eddy mixing processes, discussed extensively in the literature, would produce a cooling of the stratosphere and a decrease in ozone. Quantitatively, one could estimate the reduction in ozone for the cooling of the stratosphere using the correspondence between ozone and 100 mb temperatures in their seasonal variations at these places. When this was done, it was found that the expected ozone changes were similar to observed ozone changes for the observed cooling of the stratosphere.

396

R.N. Kulkarni

(Pageoph,

It was therefore obvious that the reason for the observed changes in ozone was the change in the strength of the stratospheric circulation. It was not necessary to invoke processes of chemicals being put into the stratosphere and destroying ozone. The weakening of the stratospheric circulation is also supported by the evidence of changing distribution of ozone in the stratosphere as noted from Umkehr and ozonesonde observations. The discussion above is based on the assumption that there is no secular change in the aerosol scattering, which is one of the important factors in calculating total ozone using the spectrophotometer. It was pointed out earlier that a gradual change in the character of haze and dust in the atmosphere introduced a gradual change in the calculated amount of ozone. A rough estimate gave that about 50~o of the decrease of ozone at Brisbane and Aspendale can be attributed to the changing character of haze and dust. This adjustment above cannot account for all the observed trends, but in conjunction with 100mb temperature evidence shown above, it is more than sufficient to explain the observed reduction of ozone. From the above discussion, one may conclude that the decrease in ozone is explainable by the weakening of the stratospheric circulation and there is no need to involve chemical destruction which may or may not have taken place. Considering the uncertainties involved in the WMO statement on the modification of the ozone layer due to man's activities - 'the long-term steady state effect of a continual release of chlorofluoromethane at the 1977 world rate of release could be 15~o average ozone depletion with an uncertainty range of about 4 to 30~. This is on the assumption that there are no other major sinks for chlorofluoromethanes' - it is obvious that the only way of knowing the behaviour of ozone is through reliable sets of observations at a number of places.

Conclusion Only two to three decades ago, ozone was one of the important tools in understanding the main circulation processes in the stratosphere and, even today, many times it becomes necessary to use ozone for a detailed complete study of dynamical processes involved in the stratosphere, stratosphere-troposphere exchange etc. where other conventional methods have failed. Nevertheless, the usefulness of ozone as a tracer for such studies has diminished, and the emphasis on the study of ozone itself, production and maintenance of its present level in the atmosphere and complicated mechanisms involved in attaining this level, has increased manyfold. As has been said before, reliable and accurate observations on ozone on a longterm basis are the only sure way of understanding the behaviour of ozone in the absence of a complete solution to the complex photochemical and transport problems. It is worthwhile at this stage to examine briefly the possible errors involved in the ozone observations.

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Atmospheric Ozone over Australia- A Review

397

Firstly, the determination of log loa/Iox, the extra terrestrial constant is made from observations at different heights of the Sun, i.e. for various t~ values usually between 1.2 and 3.5 and the extrapolating the value when/~ = 0. This assumes that the ozone during the time of observations is unaltered. This assumption is not always correct. To avoid the errors involved due to the assumption, efforts are made to transfer calibration from the world standard at Mauna Loa, where regular observations for the extra-terrestrial constants are made, to regional standards and then to other instruments in the region. This needs the instruments to be strictly comparable. An elaborate set up for intercomparisons between regional instruments and the world standard and between regional instruments and other local instruments, is very much necessary. It involves considerable expense in transportation of instruments from place to place and the use of manpower. This may present difficulties, especially in organizations which are not committed to routine observations and intercomparisons etc. Secondly, there could be error in the calculated value of ozone because of possible errors in the determination of absorption coefficients. The presently accepted values of absorption coefficients for wavelengths used in the Dobson spectrophotometer are based on the determination by VIGROUX (1953) and INN and TANAKA (1953). Their determinations are made in the laboratory and extrapolated to temperatures of -44~ For the day to day determination of ozone to be strictly correct, one has to use the coefficients corresponding to the existing temperature in the atmosphere. HOLLAND et al. (1975), from their study at NASA Flight Centre regarding the dependence of absorption coefficients on temperature, have concluded that it was important to use appropriate average absorption coefficients (c~) evaluated for every standard temperature model and possible ozone profiles. DOBSON (1963) and KULKARNI (1968) have determined the absorption coefficients for various wavelength pairs used in the Dobson spectrophotometer assuming the laboratory absorption coefficients for one pair. Thirdly, there is the possibility that there may be other gases in the atmosphere, in addition to ozone, which absorb in the U.V. region. DOBSON(1963), on examination of this problem, found that SO2 is the only gas which can be troublesome but as it is in extremely small quantities it is unlikely it will cause any error. However, when observations are made on different wavelengths they give different ozone values when laboratory absorption coefficients are used. This implies that either the absorption coefficients are not accurate or one may be measuring some other gas or gases at these wavelengths. Fourthly, one of the important problems which could produce appreciable error in the calculation of ozone is because of the uncertainty of scattering by large particles in the atmosphere. This has already been discussed at length in another section. Various methods have been developed to make approximate corrections for this large particle scattering. Almost all of these methods make some reasonable assumptions. KULKARNI (1973), making a reasonable assumption, developed a method of

398

R . N . Kulkarni

(Pageoph,

correcting for a changing large particle scattering in the atmosphere possibly due to increasing industrial activity at stations in Australia. Further improvement of the method is necessary, perhaps by using observations on three wavelengh pairs. Use of satellites or other methods in the measurement of ozone: Satellite experiments done so far for the determination of total ozone using infrared (Lawrence Livermore Laboratory) and U.V. techniques (NASA) have been successful but the ground truth observations made by Dobson spectrophotometers remain the basis of all accurate observations. No doubt, satellite measurements have a good deal more to offer in understanding the behaviour of ozone in regard to the dynamics on a global scale. But ground based methods are useful in the studies involving long-term t r e n d s or secular changes in the scattering properties etc. and they are well known for their cheapness, ease of operation and accuracy. About 70~o of the ozone stations in the world use the Dobson spectrophotometers and the remaining 30~o use filter techniques. The filter instruments use selective transmission filters and photomultipliers and use equations similar to the ones used for observations from Dobson Spectrophotometers. Because of large bandwidths of the filters and the use of smoother absorption and scattering values over a large bandwidth, the errors involved in the calculated values of ozone are expected to be larger. Lastly, careful consideration should be given to the establishment of the network. The present network stems from research projects of individuals in various countries. In recent years, the WMO and the International Ozone Commission have taken leading parts in establishing a co-ordinated global network of stations. In the Southern Hemisphere the network is very poor and a few more well-kept ozone stations are essential. Although the main factors of the general circulation of the stratosphere are reasonably adequately understood, there are a number of problems, such as longitudinal variation etc., which are not yet clear. The effects of such circulation in the vertical and horizontal directions, their feedbacks and their chemical implications on ozone, are yet to be understood. It would perhaps require a very high density network of stations where ozone, along with other meteorological parameters, is measured. For such a study satellite observations are most useful. Other aspects of ozone research such as the behaviour of ozone with changing solar activity and other consequences etc. also require high density reliable observations. Scientists with similar objectives, initially from countries in the same region, need to get together for co-operative studies.

REFERENCES BASHER, R. E. (1976), The approximation ov particulate scattering coefficients in the determination o f total ozone, Q. J. Roy. Met. Soc. London 102, 611-617. BELMONT, A. O., DARTT, D. G. and NASTROM,G. D. (1974), Periodic variations in stratospheric zonal winds from 20-65 k m at 80~ to 70~ Q. J. Roy. Met. Soc. 100, 203-211.

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Atmospheric Ozone over Australia- A Review

399

BERSON, F. A. and KULKARNI, R. N. (1968), Sunspot cycle and the quasibiennial stratospheric oscillation, Nature 217, 5134, 1133-1134. BOJKOV, R. D. (1968), Planetary features of total and vertical ozone distribution during I Q S Y . IDOJARAS, Budapest 72, 140-152. BREWER, A. W. (1949), Evidence for a world circulation provided by the measurements of Helium and Water vapour distribution in the stratosphere, Q. J. Roy. Met. Soc. London 75, 351-363. DE LuISI, J. (1978), Umkehr vertical ozone profile errors caused by the presence of stratospheric aerosols, Journ. Geophy. Res. 84, 1766-1770. DIERMENDJIAN, D. (1969), Electromagnetic Scattering on Spherical Polydispersion. Elsevier, New York, London. DOBSON, G. M. B. (1963), Note on the measurement of ozone in the atmosphere, Quart. J. Roy. Met. Soc. 89, 409-411. DOBSON, G. M. B. and HARRISON,D. N. (1926), Measurement of the amount of ozone in the Earth's atmosphere and its relation to other geophysical conditions. Proc. Roy. Soc. London 110, 660-693. DOBSON, G. M. B. (1956), Origin and distribution of the polyatomic molecules in the atmosphere, Proc. Roy. Soc. London A 236, 187-193. DOBSON, G. M. B. (1957), Handbook on Dobson spectrophotometer. DOTSCH, H. U. (1971), Photochemistry of atmospheric ozone, Advanc. in Geophys. 15, 219-322. EBDON, R. A. (1961), Some notes on the stratospheric winds at Canton Island and Christmas Island, Q. J. Roy. Met. Soc. London 87, 322-331. FARKAS, E. (1976), Lond period variations of total ozone and of atmospheric scattering by haze, Proc. joint, symp. on atm. ozone, Dresden, August 1976, 211-223. FUNK, J. P. and GARNHAM,G. L. (1962), Australian ozone observations and a suggested 24 month cycle, Tellus 14, 4, 378-382. HOLLAND, A. C. and THOMAS, R. W. L. (1975), Error analysis of Dobson Spectrophotometer measurements of the total atmospheric ozone content. NASA Technical Note TN D-7877. INN, E. C. Y. and TANAKA,Y. (1953), Absorption coefficient of ozone in the u.v. at visible regions. Optical Society of America, 43, 870-873. KtrL~:ARNI, R. N. (1962), Comparison of ozone variations and of its distribution with height over middle latitudes of the two hemispheres, Q. J. Roy. Met. Soc. London 88, 378, 522-534. KULKARNI, R. N. (1966), The vertical distribution of atmospheric ozone and possible transport mechanisms in the stratosphere in the Southern Hemisphere, Q. J. Roy. Met. Soc. London 92, 393, 363-373. KULKARNI, R. N. (1968), Ozone fluctuations in relation to upper air perturbations in the middle latitudes of the Southern Hemisphere, Tellus XX 2, 305-313. KULKARNI, R. N. and GARNHAM,G. L. (1970), Longitudinal variation of ozone in the lower middle latitudes of the Southern Hemisphere, Journ. Geophys. Res. 75, 21, 4174-4178. KULKARNI, R. N. (1973), Ozone trend and haze scattering, Q. J. Roy. Met. Soc. London 99, 421, 480-489. KULKARNI, R. N. (1976), Ozone trend and the stratospheric circulation over Australia, Q. J. Roy. Met. Soc. London 102,433, 697-704. LONDON, J., BOJKOV, R. D., OLTMANS,S. and KELLY, J. I. (1976), Atlas o.fthe global distribution of ozone July 1957-June 1967. NCAR Tech. Note.; A joint production of Univ. of Colorado at NCAR, p. 276. MoE, K. (1978/79), Aerosol Extinction and Ozone Measurements, Pageoph 117, 361-366. PITTOCK, A. B. (1973), Global meridional interactions in stratosphere and troposphere. Q. J. Roy. Met. Soc. London 99, 424-437. PITTOCK, A. B. (1974a), Stratospheric temperature anomalies in 1963 and 1966, Q. J. Roy. Met. Soc. London 100, 39-45. PITTOCK, A. B. (1974b), Trends in the vertical distribution of ozone over Australia, Nature 249, 641-642. RAMANATHAN, K. R. (1954), Atmospheric ozone and the general circulation of the atmosphere, Sci. Proc. Int. Ass. Met. Rome, 3-24.

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RAMANATHAN,K. R. and KARANDIKAR,R. V. (1949), Effect of dust and haze on measurement of atmospheric ozone made with Dobson spectrophotometer, Q. J. Roy. Met. Soc. 75, 257-267. VIGROUX,E, (1953), Contribution a l' etude experimentale de l'absorption de l'ozone, Ann. Phys. Ser. 12, VS, 709. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh~iuser Verlag, Basel

The Observed Ozone Flux by Transient Eddies, 0-30 km By R. W. WILCOX 1)

Abstract-Ozonesonde data are matched with concomitant rawinsonde data to provide a direct determination of horizontal, meridional, flux of ozone by the transient eddies. Data are from 27 stations in 4 regions: Eastern and western North America, western Europe, and Japan. Results confirm the existence of significant northward flux near 40~ 10-18 km, in winter and spring, as shown by previous investigators. However, areas of significant equatorward flux are found at high mid-latitudes, 10-16 kin, over North America in winter and spring, and at all 3 Japanese stations, 10-18 km, in spring. Transient eddy fluxes are typically small in summer, and are also small throughout the troposphere and most of the middle stratosphere.

Key words: Ozone flux; Transient eddies. L Introduction

A l t h o u g h constituting less than one-millionth part o f the atmosphere by volume, ozone is o f vital importance to the biosphere t h r o u g h its absorption o f certain harmful ultraviolet wavelengths and its regulation o f the thermal structure o f the stratosphere. Ever since it was discovered that more ozone existed over high latitudes than could be p r o d u c e d and maintained there photochemically, a major concern has been to describe how ozone is transported to high latitudes from its source region, the tropical stratosphere. In approaching the problem, it is helpful to separate the mean total horizontal ozone transport past a station into a flux by a mean northward wind plus a flux due to the transient eddies. Symbolically, vx = ~

(1)

+ v'x'.

Here, X and v are instantaneous ozone and northward wind, an overbar denotes the time average, and a prime denotes the deviation f r o m the time average. One would further wish to k n o w the zonally averaged fluxes, i.e.

[vx]

= [~1[~1 + [~*~*] +

[v'x'],

(2)

wherein brackets represent the zonal average and an asterisk the deviation therefrom. It is seen that, upon zonal averaging, the first term on the right o f (1) gives rise to two terms, representing a flux due to the mean meridional circulation and a flux due 1) Research and Advanced Design Laboratory, Control Data Corporation, Minneapolis, Minnesota 55420, USA.

402

R.W. Wilcox

(Pageoph,

to the standing eddies. In practice, the smallness of [~] with respect to ~*, and the lack of extensive horizontal coverage of v and X observations, precludes evaluation of (2). We must therefore fall back on (1), and in particular just the transient eddy term, at stations where both v and X are observed. Such calculations are helpful not only in efforts to qualitatively understand stratospheric dynamics, but also in validating the results of various ozone-including models of the atmosphere. Several investigators have carried out the transient eddy flux computation for ozonesondes at individual stations: HERIN6 (1966) for Seattle, Fort Collins, and Bedford; PITTOCK (1968) for Aspendale, Australia; Di]TSCH and FAVARGER (1969) for Boulder; HUTCHINGS and FARKAS (197!) for Christchurch, New Zealand; and DEMUER (1976) for Uccle. Although these results varied from station to station, they generally showed a large poleward transient eddy flux of ozone at about 12-16 km over mid-latitudes in winter and spring, with small, or even equatorward, flux in other seasons and at other heightsl All thege studies were for mid-latitude stations. The present study uses similar methods as the previous studies, but encompasses more stations and regions. Specifically, these regions are Japan (3 stations), western North America (6 stations), eastern North America (12 stations), and western Europe (6 stations). Presented are seasonal height-latitude cross sections for each region; tabular results are contained in WILCOX (1978b). Vertical fluxes are not treated.

II. Data and computational method A. Data

The data used in this study are described in Table 1. The North American ozone data were primarily from the Air Force Cambridge Research Laboratories' 1963-65 sounding network (and the extension until 1969 at a few stations). These data were obtained from World Data Center-A (Asheville). Most of the remaining data were obtained through the World Data Center for Ozone, Downsview, Ontario, Canada. Data for Boulder and Thalwil were extracted from D/ATSCH (1966) and DI]TSCH et al. (1970). NASTROM (1979), among others, has shown that ozone and northward wind are nearly 90 ~ out of phase in the extratropical lower stratosphere, with the v maximum lying to the east of the ozone maximum. Typical X, v correlations are small (absolute value in the neighborhood of 0.2 or less), and sensitive to space and time lags of the individual observations. It is therefore unfortunate that, for several stations, concomitant wind data were not available. In these cases, wind data within + 8 hours from a nearby rawin station were used. For the few ozone stations which did not report temperature (needed for determination of concentration), temperature was also taken from this rawinsonde report. All wind and temperature data were required to pass certain vertical consistency checks. The choosing of a rawin station to pair with an ozone station was usually based

Vol. 118, 1980)

The Observed Ozone Flux by Transient Eddies, 0-30 km

403

simply on separation distance, but consideration was also given to the fact that v is about twice as highly autocorrelated in the north-south direction as in the eastwest direction in the upper troposphere (BUELL, 1973), and probably in the lower stratosphere as well. Therefore, Seattle is paired with Salem (283 km south) rather than with Tatoosh Is. (210 km west). There have been occasional periods at a few ozone stations when ascents were made only a few hours apart. This often led to the pairing of two or even three ozonesondes with a single rawinsonde. When this happened, the ozone data were averaged and henceforth treated as one observation.

B. Flux computation In computing seasonal mean fluxes, care was taken not to give undue weight to observation series whose temporal density indicated the individual observations were not independent in the statistical sense. WILCOX (1978a) determined that total ozone observations (at middle latitudes) may be considered independent if they are four days apart, and it seems likely that local ozone is even more highly variable. Here we have arbitrarily set 42 hours as the threshold beyond which independence is assumed, and averages are taken over any group of observations which are less than 42 hours apart. This average is used, but weighted by the square root of the number of such observations in the group, in the computation of mean flux over a single season. ffj, the flux for individual season j (j = 1. . . . . J, where J is the number of years used) is

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with transient eddies and it would be better to exclude it; however, the effect is not thought to be serious over the three-month averaging periods, and efforts to account for the variability would, in any case, be inaccurate due to dearth of data. C. Standard errors

Standard errors, o;, of the long-term seasonal mean fluxes, were estimated by ~

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IIL Analysis and results

Fluxes are statistically insignificant, typically, over most of the altitude range considered. Usually, it is only just above the tropopause that the magnitudes of individual fluxes surpass twice the standard error. These regions, usually in midlatitudes, from 10 to 18 km, show significant winter and spring fluxes which are generally poleward, except equatorward over Japan and at high mid-latitudes over North America. Above and below these regions, and at all altitudes of low latitudes, the fluxes are generally small, but usually, through consideration of fluxes at several levels and/or stations, a good guess at the proper sign can be made. A. Eastern North America

During winter and spring, there is a region of very significant northward (positive) flux near 40~ from about 10 to 16 km over eastern North America (Fig. 1). This is in qualitative and reasonable quantitative agreement with the countergradient fluxes found in previous studies (HERING, 1966; DOXSCH and FAVAR6ER, 1969). However, the present analysis shows negative (downgradient) fluxes at Goose Bay in winter and at Churchill and Goose Bay in spring above 8 km. Such negative fluxes have been found in individual seasons, at other locations, by NEWELL (1964), PITTOCK (1968) and NASa'ROM(1977). During summer, computed fluxes tend to have modest negative values in the mid-latitude low stratosphere, returning to positive values by autumn. In the tropics, as well as throughout the troposphere and the subpolar middle stratosphere, the computed ozone flux is small in magnitude and uncertain in sign. At high latitudes over eastern North America (shown mainly by Resolute), the flux is fairly large southward in all seasons but summer. However, a longitudinally

Vol. 118, 1980)

DECEMBER - FEBRUARY TR

407

The Observed Ozone Flux by Transient Eddies, 0-30 k m

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uniform southward flux of such a magnitude would imply an unreasonably large compensating downward flux through the 30 km level in polar regions. Such downward flux would have to be at least an order of magnitude larger than what is predicted by K-theory (CIAP, 1975). We conclude that there is either a large longitudinal variability in the transient eddy flux at high latitudes, or else standing eddy fluxes

408

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compensate. In this connection, it should also be mentioned that observations were not sorted according to whether there was a ' sudden stratospheric warming' occurring or not. Such warming periods are thought to be a primary mechanism through which ozone is advected from middle to polar latitudes (GODSON, 1960; CLARK, 1970). Since the flux would therefore be of different character during these periods, a statistically unrepresentative sampling of the arctic winter stratosphere would have a profound affect on computed fluxes. Extreme caution should accompany any use of these high latitude results. B. Western NorthAmerica

Western North America (Fig. 2) again shows significant northward flux near 40~ 8-16 km, except in summer. There is a tendency, as over eastern North America, for high mid-latitude stations to evidence equatorward flux. This is particularly true at Seattle, which has relatively few observations and whose 'concomitant' winds came from a fairly distant station, but the more reliable Edmonton data suggest negative fluxes also. North of 60~ an area represented solely by the Scanty data of Fairbanks, large positive fluxes above 16 km in the winter are replaced by negative fluxes in the spring, while very large positive fluxes are seen in spring just above the tropopause, 8-11 km. Fairbanks values should be taken as suggestive only. South of 60~ and above 18 km, fluxes are small throughout the year, as they also are in the troposphere. DEC-FEB ,F

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Vol. 118, 1980)

409

The Observed Ozone Flux by Transient Eddies, 0-30 km

C. Western Europe Sizeable northward fluxes exist over western Europe (Fig. 3) in winter between 40 and 50~ 10-14 km. In spring the main center of northward flux seems to have moved farther northward. Interestingly, although the farthest north station, Berlin/ Lindenberg, approaches the latitudes of Goose Bay and Edmonton, it does not show the negative winter and spring fluxes that exist at the latter stations. Flux remains positive at 10-14 km for most stations in summer but is only less than half as large as during winter. During autumn, small positive fluxes exist at almost all levels above the tropopause.

D. Japan In winter, the Japanese data (Fig. 4) paint a picture of negative fluxes 16-22 km over Kagoshima (32~ and below 14 km over Sapporo (43~ and generally positive fluxes elsewhere. At their largest values ( ~ 1 . 5 x 1018 molecules m -2 sec -1, hereafter called 'units') at around 14-16 kin, these positive fluxes are significantly smaller than the positive wintertime fluxes seen in the other regions. In spring, significant negative fluxes occur at all three stations from about 10-16 km, especially at Sapporo where the 150 mb flux is 5.8 + 2.5 units ( 9 5 ~ confidence

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IV. Discussion A. Comparison with previous observational results

It is worthwhile to compare the present results with previous investigations of the transient eddy ozone flux made at individual stations, or at groups of a few stations (as in the case of HERINO, 1966). However, although the present study includes the stations used in several of these previous investigations, differences in period of record, availability of wind data and computational technique make differences in results inevitable. All previous investigations of the ozone flux which used ozonesondes have been for mid-latitude stations. They have all shown positive winter and spring fluxes from about 10-18 kin, with maxima at about 12 km. DOTSCH and FAVAR6ER (1969) have computed this maximum to be 3.8 units in winter and 2.7 units in spring for two years at Boulder, while Hering puts it at 5.0 units for an average of two years' December-

Vol. 118, 1980)

The Observed Ozone Flux by Transient Eddies, 0-30 km

411

May fluxes at Seattle, Fort Collins and Bedford. (It is not clear whether or not Hering removed the flux due to the correlations between the annual waves of v and X. While we did not remove this correlation either (Section II-B), Hering's longer averaging period (six months) would have more serious consequences.) At Aspendale, PITTOCK (1968) found 200 mb poleward fluxes of 2.6 units in some winters or springs, but equatorward fluxes (of up to 4.0 units) in others. HUTCmNGS and FARKAS (1971), from a very small data sample at Christchurch, determined an annual average poleward flux of about 3.1 units at 12 kin. Not included in the present analysis are several recent years of soundings at Uccle, from which DEMETER(1976) has computed fluxes. His annual mean value at 200 mb is 1.5 units, which compares well with the 1.4 unit annual mean found in this paper at Berlin near the same latitude. NASTROM (1977) has computed fluxes between 11 and I2 km, 10-60~ from one year of simultaneous wind and ozone measurements aboard commercial aircraft. Again, his fluxes are in reasonable agreement with the present values, especially considering the very different sampling characteristics. Of course, comparisons of results could be made for every level and season, but the main point can now be stated very simply: The present results are consistent, in the main, with previous results, despite differences in data and computational method. This fact should lend confidence to the new results presented here, most notably the negative fluxes over Japan and North America, and, in general, the large latitudinal variability of the fluxes. It is also clear from the regional differences in the present results that there is a large longitudinal and/or interannual variability in the transient eddy flux of ozone. This comes as no surprise, as NASTROM(1977), from aircraft data, has also provided such a picture at 11-12 km, 40-50~ In particular, for one March in the longitude sector 120~ (i.e., mostly north and east of Japan), Nastrom found a negative flux of 6 units, while most other longitude sectors showed positive fluxes of varying magnitudes. The negative spring Japan flux agrees well with the values deduced from ozonesondes. It is also evident from the aircraft data that equatorward fluxes occur in other longitude sectors, sometimes at latitudes as far south as 40~ but that there is considerable interannuat variability in this latitude, as can also be inferred from the results of NEWELL (1964) and PITTOCK (1968). Interestingly, spring is the only season in which NEWELL (1964), in his correlations of v with total ozone, did not infer a negative transient eddy flux in the lower stratosphere over Japan. It is for these reasons of significant longitudinal and interannual variability that we have chosen not to try to combine our regional fluxes.

B. Qualitative remarks on the ozone flux budget

Similarities between patterns of the zonal mean observed isentropes and ozone concentrations imply that the countergradient ozone flux is effected by the same process that effects the countergradient heat flux. The spatial relationship of temperature

412

R.W. Wilcox

(Pageoph,

and height fields in the mid-latitude lower stratosphere indicates the subsidence of air in the troughs and the ascent of air in the ridges. WALLACE(1978) has explained that air must move through a lower stratospheric trough at a subgeostrophic speed and that, conversely, air moving through a ridge must do so at a supergeostrophic speed; that is, there is a poleward acceleration in the troughs and an equatorward acceleration in the ridges. Combined with the fact that potential temperature increases with height, this procees leads to the observed downward, poleward (countergradient) heat flux. Ozone, since its concentration also increases with height, is transported downward and poleward by the same process. This explanation predicts only poleward flux throughout mid-latitudes, as is observed in the case of both standing and transient eddy heat flux (OORT and RASMUSSON, 1971, pp. 286-289). However, the present results for ozone indicate an equatorward transient eddy flux in winter and especially spring at high mid-latitudes. NEWELL (1964) has suggested that the negative fluxes he found over Japan may be associated with stratosphere-troposphere exchange processes. This association is appealing, since the large convergence of ozone between the positive and negative fluxes would have to be in large part balanced by downward removal into the troposphere. What may be involved is a sort of tropopause-folding process (DANIELSEN, 1968) in which lower stratospheric air north of the jet moves southward toward eventual injection into the troposphere. More detailed observations are needed to examine this possibility further. Indeed, we are at present unable to offer a lucid explanation of these high mid-latitude equatorward fluxes. We can, however, also note their strong association with certain features of the mean potential temperature field : Climatology (LABITZKE, 1972; U.S. WEATHERBUREAU, 1970) shows that areas near Japan and eastern North America have 200 mb potential temperature maxima which are both relatively stronger and located more equatorward than those over western North America and, especially, Europe. The latitudinal positions and strengths of the high mid-latitude equatorward flux in our four regions correlate well with these mean temperature distributions. It is desirable to make some qualitative assessment of the relative importance of standing and transient eddy ozone fluxes, and we do this via comparison of the transient eddy results with a three-dimensional model's predictions of total eddy fluxes (steady plus transient). PRINN et al. (1978), have shown total eddy fluxes, integrated throughout the depth of the model atmosphere, for an annual cycle of their three-dimensional dynamical-chemical model. To compare our results, we have also integrated from the surface to 30 km for the eastern North America sector only (Fig. 5). The model's total eddy flux at its wintertime maximum (50~ is one and a half times as large as our transient eddy flux at our maximum location of 37~ The model's winter eddy flux decreases rapidly toward pole and equator, but does not become negative, as ours does from 45-55~ and again poleward of 65~ However, even if its transient and standing eddy fluxes were shown separately, it is likely that the model would fail to portray the southward transient eddy flux in winter

Vol. 118, 1980)

413

The Observed Ozone Flux by Transient Eddies, 0-30 km EASTERN NORTH AMERICAN TOTAL TRANSIENT EDDY NORTHWARD FLUX

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north of 50~ As indicated previously, this feature can be associated with the existence of a potential temperature maximum at mid-latitudes, which this model fails to predict (CtJNNOLD et al., 1975; PRINN et al., 1978). There are clearly large differences between this model's results and the present observational results. A major contributor to these differences must be in the model's inclusion of standing eddies, which must therefore be an important transport mechanism in mid and high latitudes in all seasons except possibly summer, when our results agree with the model's results fairly well. Since transient eddies are damped in the stratosphere, only the ultra-long, quasi-stationary waves are evident in the middle stratosphere, and those only in non-summer months. It is therefore reasonable to surmise, as have DOTSCH and FAVARGER (1969), that the standing eddy ozone flux is much larger than the transient eddy ozone flux above 18 km or so, and that it is basically the standing eddy flux which accounts for the rapid buildup of ozone near the level of the maximum concentration (about 20 kin) at high latitudes in winter and early spring (see WILCOX et ai., 1977; WILCOX and BELMONT, 1977; BELMONT et al., 1978 for recent ozone climatologies). For these levels KLEIN (1974) also found a much larger poleward ozone eddy flux for disturbances of wavelengths of 8000 km (corresponding closely to a standing wavenumber three pattern) than for shorter wavelengths. It might also be noted that the standing eddy heat flux (OORT and RASMUSSON, 1971, pp. 288-289) is comparable to the transient eddy heat flux (pp. 286-287) in the mid-latitude lower stratosphere. This infers that the standing eddy and transient eddy

414

R.W. Wilcox

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ozone fluxes are probably of comparable magnitude even in the lower stratosphere (i.e. tropopause to about 18 kin).

V. S u m m a r y

Concomitant ozonesonde and wind observations have been processed to yield estimates of the horizontal, meridional flux of ozone over certain regions of the Northern Hemisphere. Both the direct computations reported here and the results of other investigations imply that the transient eddy flux of ozone appears to be of about equal importance to the standing eddy flux in the mid- and high-latitude lower stratosphere. Above about 18 km, the standing eddy flux is probably more important. Direct quantitative estimates of these horizontal fluxes, as well as indirect estimates of vertical fluxes, must necessarily await more spatially extensive observations.

Acknowledgements

The author wishes to thank D. Hovland for valuable computational assistance and A. Belmont and G. Nastrom for many helpful suggestions during the course of this work. Financial support was provided by NASA-Ames Research Center and by Air Force Geophysics Laboratory under Contract NAS2-9578.

REFERENCES BELMONT, A., WILCOX, R., NASTROM, G., HOVLAND,D. and DARTT, D. (1978), Guidelines for flight planning during periods of high ozone occurrence, Report No. FAA-EQ-78-03 for Dept. of Transportation, Federal Aviation Administration, Contract DOT FA77WA-4074, 161 pp. BUELL, C. E. (1973), Correlation functions for wind and geopotential on isobaric surfaces, J. Appl. Meteor. 11, 51-59. CIAP (1975), The natural stratosphere of 1974, CIAP Monograph l, DOT-TST-75-51. CLARK,J. H. E. (1970), A quasi-geostrophic model of the winter stratospheric circulation, Mon. Wea. Rev. 98, 443-461. CUNNOLD, D., ALYEA,F., PHILLIPS,N. and PRINN, R. (1975), A three-dimensional dynamicalchemical model of atmospheric ozone, J. Atmos. Sci. 32, 170-194. DANIELSEN, E. F. (1968), Stratospheric-tropospheric exchange based on radioactivity, ozone, and potential vorticity, J. Atmos. Sci. 25, 502-518. DEMUER, D. (1976), The vertical ozone distribution over Uccle (Belgium) in relation to simultaneous observations of wind and temperature, Proceedings of the Joint Symposium on Atmospheric Ozone, Dresden, 9-17 August 1976, Volume I, 261-276. DOTSCH, H. U. (1966), Two years of regular ozone soundings over Boulder, Colorado, NCAR Technical Note 10, Boulder, 441 pp. D/,JTSCH,H. U. and FAyARGER,D. (1969), Meridional ozone transport by transient eddies over Boulder, Colorado, Ann. Geophys. 25, 279-281. D~TSCH, H. U., ZUELIG,W. and LING,C. H. (1970), Regular ozone observation at Thalwil, Switzerland, and at Boulder, Colorado, LAPETH-1, Zurich, 279 pp.

Vol. 118, 1980)

The Observed Ozone Flux by Transient Eddies, 0-30 km

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GODSON, W. L. (1960), Total ozone and the middle stratosphere over arctic and subarctic areas in winter and spring, Quart. J. Roy. Met. Soc. 86, 301-317. HERING, W. S. (1966), Ozone and atmospheric transport processes, Tellus 18, 329-336. HUTCHINGS,J. W. and FARKAS,E. (1971), The vertical distribution of atmospheric ozone over Christchurch, New Zealand, Quart. J. Roy. Met. Soc. 97, 249-254. KLEIN, W. D. (1974), Ozone kinematics and transports in unstable waves, Ph.D. Thesis, Mass. Inst. of Tech., 129 pp. LABITZKE,K. and collaborators (1972), Climatology of the stratosphere in the Northern Hemisphere, Part I, Meteorologische Abhandlungen 100, 4. Institute for Meteorology, Free University of Berlin. NASTROM,G. D. (1977), Vertical and horizontal fluxes of ozone at the tropopause from the first year of GASP data, J. Appl. Meteor. 16, 740-744. NASTROra, G. D. (1979), Ozone in the upper troposphere from GASP measurements, J. Geophys. Res. 84,3683-3688. NEWELL, R. E. (1964), Further ozone transport calculations and the spring maximum in ozone amount, Pure and Appl. Geophys. 59, 191-206. Ooa'r, A. H. and RASMUSSON,E. M. (1971), Atmospheric Circulation Statistics, NOAA Prof. Paper No. 5, U.S. Department of Commerce. PANOVSKY, H. and BRIER, G. (1958), Some Applications of Statistics to Meteorology, University Park: Mineral Industries Extension Services, The Pennsylvania State University, 224 pp. PRINN, R. G., ALVEA, G. N. and CtrNNOLO, D. M. (1978), Photochemistry and dynamics of the ozone layer, Ann. Rev. Earth and Planetary Sci. 1978.6, 43-74. PITTOCK, A. B. (1968), Seasonal and year-to-year ozone variations from soundings over south eastern Australia, Quart. J. Roy. Met. Soc. 94, 563-575. U.S. WEATHERBUREAU (1970), Selected Level Heights Temperatures and Dew Points for the Northern Hemisphere, NAVAIR 50-1C-52, U.S. Government Printing Office. WALLACE, J. M. (1978), Trajectory slopes, countergradient heat fluxes and mixing by lower stratospheric waves, J. Atmos. Sci. 35, 554-558. WILCOX, R. W. (1978a), Total ozone trend significance from space and time variability of daily Dobson data, J. Appl Meteor. 17, 405-409. WILCOX, R. W. (1978b), Studies of stratospheric eddy transport. L The observed ozone flux by transient eddies, surface to 30kin, Report No. AFGL-TR-78-0311, for NASA-Ames Res. Ctr. and A. F. Geophys. Lab. Contract, NAS2-9578, 29 pp. WILCOX, R. W., NASTROM,G. D. and BELMONT,A. D. (1977), Periodic analysis of total ozone and of its vertical distribution, J. Appl. Meteor. 16, 290-298. WILCOX, R. W. and BELMONT,A. D. (1977), Ozone concentration by latitude, altitude and month, near 80 ~W, Report No. FAA-AEQ-77-13 for Department of Transportation, Federal Aviation Administration, Contract DOT FA77WA-3999, 41 pp. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh~iuser Verlag, Basel

Variations in Zonal Mean and Planetary Wave Properties of the Stratosphere and Links with the Troposphere By R. S. QUIROZ 1)

A b s t r a c t - Zonal mean data and amplitudes and phases of planetary zonal waves were derived from daily hemispheric maps for tropospheric and stratospheric levels, for the four winters 197576 to 1978-79. Important year-to-year fluctuations in zonal means and wave activity are described, most notable of which are the changes from 1975-76 to 1976-77. Comparison of the relative strengths of the stratospheric and tropospheric jet streams shows a strong negative correlation (-0.8) between monthly mean zonal stratospheric winds (at 10 rob, 65~ and zonal tropospheric winds (at 200 mb, 32.5~ in the jet core) and a positive correlation (+0.7) between the stratospheric 10 mb winds and the tropospheric 200 mb winds at 65~ Parameters correlated were the departures from the climatological mean zonal winds. The structure of correlation between wave amplitudes in the same wave number (1, 2) at different altitudes and between wave numbers 1 and 2 is investigated. We find a high correlation (+0.93) between wave 1 in the stratosphere (10 mb height) and wave 2 (height) in the troposphere at 65~ but only a weak correlation (+0.2) between wave 1 amplitudes in the stratosphere and troposphere. These results suggest the possible importance of wave-wave interactions in processes linking the stratosphere and troposphere. The wave correlations presented here are based on comparisons of monthly means of daily amplitudes; the correlation structure in individual wave developments may differ, in view of the likelihood of altitudinal lags in wave amplification.

Key words: Planetary wave variations; Wave-wave interactions.

1. I n t r o d u c t i o n

Recent interest in the variable climate o f the s t r a t o s p h e r e is based, in part, on the possibility that large changes in the flow and t e m p e r a t u r e o f the s t r a t o s p h e r e m a y influence the state o f the t r o p o s p h e r e , p e r h a p s on climatic time-scales. Influence m e c h a n i s m s p r o p o s e d include (1) infrared r a d i a t i o n f r o m a h o t stratosphere (RAMAtqATHAN, 1977), (2) ultraviolet and visible fluxes associated with a stronglyaltered s t r a t o s p h e r i c ozone content (NAT. ACADEMY OF SOENCES, 1976), a n d (3) m o d u l a t i o n o f t r o p o s p h e r i c e d d y heat fluxes considered by BATES (1977) to a c c o m p a n y changes in u p p e r a t m o s p h e r e mean flow and t h e r m a l stability. The d e t e r m i n a t i o n o f climatic states is c o m p l i c a t e d by the occurrence o f large y e a r - t o - y e a r variations in the stratosphere. These m a y be quasi-systematic, as in the case o f the tropical ' q u a s i - b i e n n i a l ' oscillation, illustrated in Fig. 1 by m e a n zonal wind d a t a for a location near the e q u a t o r ; or they may a p p e a r irregular and at times 1) National Meteorological Center, NWS, NOAA, Washington, DC 20233, USA.

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Figure 1 Quasi-biennial oscillation in mean zonal wind, as defined by 12-month running averages of mean zonal wind for near-equatorial station at Kwajalein (based on rocket soundings). of substantial magnitude, in extra-tropical latitudes, as will be shown subsequently. Year-to-year changes in long-wave activity are of particular interest, since strong wave activity can lead to important changes in the mean circulation (insofar as there is significant wave-mean flow interaction) and moreover may alter the meridional distribution of ozone (HARTMANNand GARCIA, 1979). The purpose of this report is to describe important fluctuations, over the course of four consecutive winters (1975-76 to 1978-79), in monthly zonal mean winds and in planetary wave activity (height and temperature). Attention will be called to important variations in zonal wave 2 activity, and it will be shown that the development of wave 1 in the stratosphere was associated with the development of wave 2 in the troposphere. This finding suggests wave-wave interaction and is moreover significant because of the observed role of wave 1 in stratospheric sudden warming events (LABITZKE, 1978; QUZROZ, 1978). In the review of zonal mean data it will be shown statistically that large changes in the strength of the stratospheric polar night jet stream are associated with changes of opposite sign in the strength of the tropospheric jet stream. This finding suggests the need for including the troposphere in model simulations of stratospheric behavior. Whereas large strides have been made in theoretical studies of the vertical propagation of planetary waves and their interaction with the mean flow (e.g., BOYD, 1976; ANDREWS and MCINTYRE, 1978), little has been done in the way of comprehensive

418

R.S. Quiroz

(Pageoph,

observational studies of both the stratosphere and troposphere, over extended periods not purely concentrated on stratospheric warming events. VAN LOON et al. (1973) showed data for both the troposphere and stratosphere (based on monthly mean maps) but these are for a single month, January, which may or may not be representative of a given winter. VAN LOON et al. (1975) presented interesting data on out-of-phase relationships between stratospheric temperatures at different latitudes connected with wave 1 and 2 amplifications, but their analysis is confined mainly to the 30 mb level. LAmTZI(E'S (1977, 1978) comparisons of wave activity during 12 winters at the 30 mb level and during two winters at tropospheric levels as well are also a valuable contribution. The approach followed in this study is broad, aimed at discerning important year-to-year differences and basic links between the stratosphere and troposphere. More detailed results taking into account the space and time evolution of the planetary waves are in preparation.

2. Data used

We have derived zonal means and amplitudes of zonal harmonic waves from constant-pressure maps of the National Meteorological Center (height and temperature) and from analyzed maps of radiances measured by stratospheric channels of the NOAA satellite Vertical Temperature Profile Radiometers (VTPR). The harmonic results have been obtained since the winter of 1975-76. For compactness, data will be presented mainly for selected levels from 500 to 10 mb. Data on the thermal behavior of the stratosphere determined from the satellite radiances have been assembled, but will not be presented here. Most of the data were generated daily and for each latitude, 0, 5 . . . . . 80 ~ For this report, the bulk of our results on planetary wave amplitudes will be for two selected latitudes, 45 and 65~ near the 'preferred' latitudes of maximum amplitudes in the troposphere and stratosphere, respectively. 2) Some subjectivity enters in the choice of latitudes, since amplifying height and thermal systems at times undergo significant shifts in latitude. In an earlier stage of this work, we have derived statistics based on data along the axis of daily maximum amplitude at each pressure level, but for this report the simpler choice of two latitudes was made. Figure 2 shows, for a selected month (December 1976), the average daily amplitude of waves 1 and 2 as a function of latitude and pressure. There is clearly a height maximum near 65~ at 10 rob, in the stratosphere; in the upper troposphere, at 300 rob, wave 2 has a maximum at 60-65~ while wave 1 has a flat maximum pattern from middle to high latitudes. These patterns are qualitatively similar to the standing wave patterns given by VAN LOON et al. (1973), based on mean constantpressure maps for January, owing to the large standing component in waves 1 and 2. 2) Preferred latitude refers to period under study, during winter, as well as to earlier winters (1964-70) (VAN LOONet aL, 1973).

Vol. 118, 1980)

Zonal Mean and Planetary Wave Properties of the Stratosphere

p,m6

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419

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Figure 2 Average daily amplitude in December 1976, as a function of latitude and pressure, for zonal waves 1 and 2 (height, 500-10 mb, top; temperature 100-10mb, bottom); height in meters, temperature in deg C.

In the temperature diagrams (Fig. 2), note the numerical dominance of wave 1, with maximum amplitude at or above the 10 mb level, in contrast to a mid-stratosphere maximum for wave 2. Subjectivity enters also in the choice of statistic for describing wave activity. HIROTA (1976) used the root mean square (rms) amplitude to describe stratospheric thermal wave activity, using Nimbus 5 Selective Chopper Radiometer measurements for the combined years 1973-74. We have derived such data for the stratosphere (from VTPR measurements) to monitor differences in thermal wave activity in recent winters. In this report, however, we present wave data for 500-10 mb in the form of monthly mean values of daily amplitudes, incorporating the contribution of traveling, transient, and standing components. It is well known that conditions within a winter season are ordinarily more variable than those in summer. This applies to the interannual fluctuations as well, as shown in Table 1, giving mean zonal wind statistics at latitudes within 5-10 ~ of the latitude of maximum wind at 50 mb (stratosphere) and 200 mb (troposphere). The standard deviation of the winter and summer mean zonal winds in individual years is about four times as great in winter as in summer, both in the troposphere and stratosphere. (Note from Table 1 that this determination is based on a longer period of data than the basic 4-year data set used for this study.) Accordingly, our results will focus on the interannual changes from winter to winter, based on data from 1975-76, 1976-77, 1977-78, and 1978-79. Sections 3 and 4 concern changes in zonal means and planetary wave activity, respectively.

420

R.S. Quiroz

(Pageoph,

Table 1 Standard deviation (m s - z) o f winter and summer mean zonal wind in individual years from long-period means*)

Winter (Dec-Feb) 200 mb, 32.5~ 200 mb, 40~ 50 rob, 65~ 50 mb, 25~

Summer (Jun-Aug)

4.3 1.2 8.7 1.9

*)Based on years 1968-78 for troposphere (200 mb) and 1974--78 for stratosphere (50 rob). The summer stratospheric data refer to easterly winds. Data source: computer tabulations based on daily constantpressure maps of the National Meteorological Center.

3. Z o n a l m e a n s

Perhaps the most dramatic interannual changes in many years were those from 1975-76 to 1976-77, depicted in Figs. 3 and 4. Note in Fig. 3 the changeover from anomalously strong flow in the stratospheric polar night jet in January 1976 (nearly twice as strong at 10 mb, near 65~ as the climatological mean zonal wind) to weak flow in January 1977; and in the tropospheric jet stream core, at about 200 mb, 30--35~ a changeover from weak flow to anomalously strong flow. In the tropics,

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Vol. I18, 1980) ZonalMean and Planetary Wave Properties of the Stratosphere

421

p, mb 10

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300

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Figure 4 Change in zonal mean temperature from January t976 to January 1977.

the change from stratospheric westerlies to strong easterlies reflects the tropical biennial oscillation, seen earlier in Fig. 1. The temperature changes giving rise to this overall change in wind structure are shown in Fig. 4. Most notable are the warming in high latitudes, cooling in midlatitudes; and in tropical latitudes, warming (1-2~ in the troposphere and strong cooling in the lower stratosphere. The meridional gradients from low to middle latitudes can largely account for both the anomalously strong tropospheric jet stream and the strong biennial-oscillation easterlies at 25-30 km. Although there may be some connection between the tropical biennial oscillation and changes in extra-tropical latitudes, the discussion henceforth will concern only the behavior in sub-tropical to high latitudes. The indication in Fig. 3 of an inverse relationship between the strength of the stratospheric polar night jet and the tropospheric jet stream flow was examined further. Figure 5 depicts the monthly mean zonal wind, November-March, for the

422

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Monthly mean zonal wind in 4 winters at levels and latitudes representative of the stratospheric (10 rob, 65~ and tropospheric (200 rob, 32.5~ jet flows. Dashed curves gives climatological values. See text.

last four winters, in the stratosphere (10 rob, 65~ and troposphere (200 rob, 32.5~ The dashed lines give climatological values from VAN Loon et al. (1972, based on data for 1958-63) for 10 mb, and from OORT and RASMUSSEN(1971, from 1958-63 data) for 200 rob. The strongest fluctuation in this 4-year data set (Fig. 5) is obviously the change from 1975-76 to 1976-77. Numerical evaluation of the correlation between the strength of the stratospheric and tropospheric flow (after minimizing any seasonal effect in the correlations by subtracting the climatological value in each month from the observed monthly mean wind) yielded the correlation coefficients shown in Table 2. These results indicate that a high negative correlation (~ -0.8) prevails in winter between the strengths of the stratospheric and tropospheric jet flows. A moderate positive correlation (,-~0.7) prevails between the stratospheric and tropospheric mean zonal winds at 65~ suggesting that there is not sufficient thermal 'compensation' in the stratosphere to negate the hydrostatic contribution of tropospheric pressure gradients in sub-polar latitudes. This finding is further borne out by a comparison of monthly mean values of the gradient of mean stratospheric temperature (based on VTPR channel 1 radiance measurements), between 60 and 70~ with U(65~ 10 rob), which showed a correlation of only +0.54. In other words, a substantial part of the variations in stratospheric wind at 65~ is due to contributions from the troposphere.

Vol. 118, 1980) Zonal Mean and Planetary Wave Properties of the Stratosphere

423

Table 2 Correlation between stratospheric and tropospheric mean zonal wind Months included (1975-79)

Variables*) /7(65~

10 mb), U(32.5~

0(65~

10 mb), U(65~

200 mb) 200 mb)

Nov-Mar Dec-Jan Nov-Mar Dec-Jan

Correlation - 0.73 - 0.86 + 0.61 + 0.77

N 19t) 8 197) 8

*) Computation based on comparison of winds after subtracting climatological portion; i.e., wind anomaly in each of 5 months (November-March) of each of 4 winters at 10 mb was compared with anomaly at 200 mb. Correlation is higher if only December and January are included in the sample. t) Data for March 1979 were not available for inclusion in sample; N is number of months in the sample.

The explanation of the high negative correlation between the stratospheric and tropospheric jet flow at 65 and 32.5~ respectively, is probably more complex and may involve consideration of wave activity, to be examined in Section 4. In any case these results show that the stratospheric and tropospheric flows are strongly linked in diverse ways. It should be stressed that the interannual fluctuations described here are large at specific latitudes; net hemispheric changes have not been examined in this study. It should also be emphasized that these results refer to monthly means at fixed latitudes. The correlations between daily winds at l0 and 200 rob, either at fixed latitude or following the precise latitude of maximum wind, was not investigated.

4. Long-wave activity

Figure 6 depicts traces of the average daily amplitude of zonal waves 1 and 2 in height, at 45 and 65~ in December and January of each of the four winters. The height data are for selected pressure levels in the stratosphere (10 mb) and upper troposphere (300 mb), and the temperatures are for the 10 mb level. Standing wave height amplitudes in January from VAN LOON et ak (1973) are also shown for comparison. Evident are several features: (a) The higher amplitudes in the stratosphere at 65~ versus 45~ (b) Large year-to-year changes. Note, e.g., the strong wave 2 height increase (decrease) at 10 mb and 65~ from 75-76 to 76-77 in December (January). (c) The numerical predominance of wave I, at 65~ in the stratosphere. (d) The greater similarity, at 65~ of the stratospheric wave 1 traces to those for wave 2 in both the stratosphere and troposphere. Wave 1 traces at 10 mb bear scarcely any resemblance to the wave 1 traces at 300 rob.

424

R.S. Quiroz 1000

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1976-77.

Feature (c) is of particular interest because warming of the polar stratosphere, as seen in zonal mean temperature data, is commonly directly linked to wave 1 activity within the stratosphere. This has been emphasized by LAB['rZKE (1978), who has argued that major stratospheric warmings occur if height wave 1 'reaches a pronounced maximum in the middle stratosphere with a marked minimum of height wave 2.' Q u m o z (1978) also noted that stratospheric warming activity in recent winters was exhibited primarily in temperature wave 1. (Notable exceptions include the major warming events of January 1963 and February 1979, in which thermal wave 2 appears to be of overriding importance.) Evidence of significant interactions

Vol. 118, 1980)

Zonal Mean and Planetary Wave Properties of the Stratosphere

425

between waves 1 and 2 in specific warming events (QUIROZ and NAGATANI, 1976; QU]ROZ, 1977), however, suggests that wave 2 may have unsuspected importance. This is also suggested in Fig. 6 (feature d, above) and in profiles of the monthly average amplitude of wave I and 2 at altitudes 700-10 mb (not shown). These considerations led to a determination of the structure of correlation between wave l and 2 amplitudes based on the monthly average amplitudes in December and January of the four winters. Some of the chief results are shown in Fig. 7. Figure 7a reveals, indeed, that the amplitude of wave 1 (height) in the stratosphere is closely related to the amplitude of wave 2 (height) in the troposphere, at 65~ The correlation between the wave 1 amplitude at 10 mb and wave 2 at 300 mb is 0.93, whereas the correlation of wave 1 at 10 and 300 mb is only 0.20. It is emphasized that these results are based on monthly average statistics from daily amplitudes.

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426

R.S. Quiroz

(Pageoph,

Individual situations are possible in which a wave 1 feature in the troposphere may be structured coherently into the stratosphere, as in a minor warming event observed in early January 1976 (QuiRoz and NAGATANI, 1976). Moreover, lags of several days are often observed between wave developments in the troposphere and in the stratosphere (QuIROZ, 1978), so that a high correlation is not expected if stratospheric and tropospheric wave amplitudes are compared at zero-days lag. Figure 7b, comparing temperature wave 1 amplitude at 10 mb with wave 1 and 2 height amplitudes at various levels can be seen to be consistent with Fig. 7a, as would be expected from hydrostatic considerations. A correlation less than 1.0 for T, H T (N = 1, 10 mb) is expected from the non-uniform thermal structure of pressure height systems. The work of VAN LOON et al. (1975) and QUIROZ (1978) has shown significant interlatitudinal coupling of stratospheric zonal mean temperatures. It is therefore of interest to compare wave results at 65~ with those at 45~ Figure 7c does not appear to show a well-defined correlation of 10 mb height amplitude (N = 1) (65~ with amplitudes at 45~ The comparison of amplitudes at the same pressure level, however (Fig. 7d), indicates a positive correlation between latitudes in the stratosphere, and a negative correlation in the troposphere. The former is probably due to the fact that high-amplitude systems in the stratosphere may have substantial latitudinal extent (as often can be seen in the latitudinal time-sections mentioned in Section 2). The tropospheric negative correlation suggests that amplitudes in high latitudes may grow at the expense of mid-latitude systems. It is planned to examine these inferences further from detailed sequences of daily data.

Acknowledgments

I am very grateful for programming assistance received from R. Nagatani, K. Johnson, and J. Laver, of the Upper Air Branch, National Meteorological Center.

REFERENCES ANDREWS,D. G. and MCINTYRE,M. E. (1976), Generalized Eliassen-Palm and Charney-Drazin theorems for waves on axisymmetric mean flows in compressible atmospheres, J. Atmos. Sci. 35, 175-185. BATES,J. R. (1977), Dynamics of stationary ultra-long waves in middle latitudes, Quart. J. R. Met. Soc. 103, 397-430. BOYD, J. P. (1976), The noninteraction of waves with the zonally averaged flow on a spherical earth and interrelationships of eddy fluxes of energy, heat, and momentum, J. Atmos. Sci. 33, 2285-

2291. HARTMANN,D. L. and GARCIA, R. (1979), A mechanistic model of ozone transport by planetary waves in the stratosphere, J. Atmos. Sci. 36, 350-364. HIROTA,I. (1976), Seasonal variation of planetary waves in the stratosphere observed by the Nimbus 5 SCR, Quart. J. R. Met. Soc. 102, 757-770.

Vol. 118, 1980)

Zonal Mean and Planetary Wave Properties of the Stratosphere

427

LABITZKE,K. (1977), Interannual variability of the winter stratosphere in the Northern Hemisphere, Mon. Wea. Rev. 105, 762-770. LABITZKE, K. (1978), On the different behavior of the zonal harmonic height waves 1 and 2 during the winters 1970171 and 1971172, Mon. Wea. Rev. 106, 1704-1713. NATIONAL ACADEMY OF SCIENCES (1976), Halocarbons: environmental effects of chlorofluoromethane release, Report, Washington, DC 125 pp. OORT, A. H. and RASMUSSEN,E. M. (1971), Atmospheric circulation statistics, NOAA Professional Paper No. 5, 323 pp. QtJiROZ, R. S. (1977), The tropospheric-stratospheric polar vortex breakdown of January 1977, Geophys. Res. Lett. 4, 151-154. Qurgoz, R. S. (1978), Precursors of stratospheric warmings and constraints on their development, Paper presented at Amer. Met. Soc. Conf. on Met. of Upper Atmos. (Boston, October 24-27). QuIRoz, R. S. and NAGATANI,R. M. (1976), A study of tropospheric-stratospheric interaction "based on combined satellite and rawinsonde data, Proc. Syrup. on Met. Obs. from Space (COSPAR XIX meeting, Philadelphia, June 8-10), 368-373. RAMANATI~AN,V. (1977), Troposphere-stratosphere feedback mechanism: stratospheric warming and its effect on the polar energy budget and the tropospheric circulation, J. Atrnos. Sci. 34, 439-447. VAN LOON,H., JENNE,R. L. and LABITZKE,K. (1972), Climatology of the stratosphere in the Northern Hemisphere, Part 2, Berlin Free Univ., Met. Abh., 100, Heft 5, 160 pp. VAN LOON, H., JENNE, R. L. and LABITZKE,K. (1973), Zonal harmonic standing waves, J. Geophys. Res. 78, 4463-4471. VAN LOON, H., MADDEN, R. A. and JENNE, R. L. (1975), Oscillations in the winter stratosphere Part 1, Description, Mon. Wea. Rev. 103, 154--162. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh/iuser Verlag, Basel

Major and Minor Stratospheric Warmings and their Interactions on the Troposphere By J. P. KOERMER1'2) and S. K. gAD 2)

Abstract - Analyses of evolutions of the kinetic and thermal energy associated with the major and minor stratospheric warmings in the winters of 1976-77 and 1975-76 respectively indicate that the predominant ultra-long waves in the stratosphere oscillated at periods of 10-20 days, whereas in the troposphere the predominant long waves oscillated at periods of 8 to 12 days. These tropospheric long waves are almost out-of-phase with the stratospheric ultra-long waves for the minor warming, but in-phase for the major warming. The kinetic energy of the zonal mean flow in the stratosphere for the minor warming is much greater than that for the major warming, indicating that the occurrence of a major warming depends on the magnitude of the kinetic energy of the zonal mean flow relative to that of the meridional convergence of the poleward flux of sensible heat. In both the major and minor warmings, most of the stratospheric eddy kinetic energy is contained in waves of wavenumbers 1 and 2, whereas the stratospheric available potential energy is primarily contained in waves of wavenumber 1. The kinetic energy associated with waves of wavenumber 1 appeared to be 180o out-of-phase with those of wavenumber 2, indicating that nonlinear transfer of kinetic energy occurred between waves of wavenumbers 1 and 2. The occurrences of wind reversals were accompanied by decouplings of the stratospheric and tropospheric motions, and blockings in the troposphere.

Key words: Stratospheric warmings; Ultra-long waves; Blocking; Energy conversions.

1. I n t r o d u c t i o n

M u c h effort has been expended in the study o f the remarkable p h e n o m e n a o f sudden stratospheric warmings since its discovery by SCHERHAG (1952). M a n y individual major warmings have been investigated in great detail (e.g., REED et al., 1957; JULIAN and LABITZKE, 1965; PERRY, 1967; QU1ROZ, 1969, 1977; MILLER and JOHNSON, 1970; LAB1TZKE, 1977). In recent years, stratospheric models have shown steady progress in producing warmings (e.g., MATSUNO, 1971; HOLTON, 1976), A n e n o r m o u s a m o u n t o f literature on stratospheric warming has accumulated. A n excellent review o f these previous research efforts has recently been made by MCINTURFF (1978). A stratospheric warming is characterized by a destruction o f the circumpolar stratospheric westerly jet by a vertical propagation o f energy from the troposphere, 1) Present affiliation: U.S. Air Force. 2) Department of Meteorology, University of Utah, Salt Lake City, Utah 84112, USA.

Vol. 118, 1980)

Major and Minor Stratospheric Warmings

429

accompanied by an anomalous heating in the stratosphere and the high latitude troposphere but by a decrease in thermal energy in the mid-latitude troposphere. On many occasions stratospheric warmings are accompanied by poleward movements of high pressure cells in the troposphere, causing blockings of storms developed upstream. In every winter the stratosphere experiences several warmings of various intensities. Whether such warmings can be classified as major, minor, or a combination of these depends on the degree of destruction of the stratospheric westerly jet and overall extent of the warming. Certain conditions appear to favor the outset of warmings, as will be discussed later in this paper. The purpose of this paper is to analyze and compare the evolution of major and minor stratospheric warming processes and relate them to changes in the stratosphere and troposphere. Thus, analyses will be made of the distribution and changes of mean temperature and zonal wind velocity, and fluxes of kinetic and thermal energy, before and during stratospheric warmings. Eddy kinetic and available potential energy development and interactions during stratospheric warmings will also be discussed and related to dynamic theories.

2. D a t a s o u r c e

The 00Z and 12Z National Meteorological Center (NMC) gridded analyses of meteorological data were used in this study. Initial grids consisted of data at 5~ latitudinal and longitudinal increments for the Northern Hemisphere between 20~ and 85~ at the 1000, 850, 700, 500, 300, 200, 100, 50, and l0 mb levels. Isolated missing fields of height and temperature were constructed by linear interpolation and missing wind fields were constructed geostrophically from observed height data. Vertical velocities were computed by the quasi-geostrophic vorticity method used by PERRY (1967). First, we computed the right-hand side of the following vorticity equation: + a

+

O)

where ~7 = ~ + f f = 2g~ sin ~, ~ is the Earth's angular velocity, and 1 c~v = a cos----~8A

1 c~u a 0~

u tan q~ a

(2)

is the relative vorticity. Equation (1) was then solved for ca. Hence, the twelve hourly data sets consisted of w, T, u, v and z at each of the 1008 grid ,points at the nine levels specified above. These data were then transformed in wavenumber domain at each level using the standard fast Fourier transform program. The entire winter seasons for 1973-74, 1975-76, and 1976-77 were analyzed in the same manner. However, only the latter two seasons will be discussed in detail in

430

J.' P. Koermer and S. K. Kao

(Pageoph,

the paper for the sake of brevity. It may be noted that although all warmings are in a sense unique, the differences and similaries between the major and minor warmings described in this paper are in many aspects common to other warming events.

3. Evolution of zonal mean temperature

To examine the evolution and relationship of meteorological variables before and during the major and minor stratospheric warmings, we have computed the zonal mean temperature for the winters of 1975-76 and 1976-77 as shown in Figs. 1 and 2 respectively. Figures la and 2a show the meridional cross-sections of zonal mean temperatures which were characteristic of the mean atmospheric conditions prior to more significant warming activity for the minor and major warming seasons respectively. The overall temperature patterns are similar for both seasons with only a very slight difference in the high latitude stratospheric regions due to a very minor warming pulse in progress on 18 January 1976 during the minor warming seasons. This pulse, primarily affecting the highest levels shown, tended to shift the -60~ isotherm northward and to push the = 70~ isotherm northward and downward. All three seasons studied showed similar responses during any kind of warming process, and support the downward propagation of warm layer into the lower stratosphere (SCOTT, 1972; QtJIROZ, 1969, 1971). Figures 1b and 2b show the mean conditions during the final stages of the warmings. During the minor warming, there are few changes evident, except for the northward shift of the -50~ isotherm. This is in startling contrast to the remarkable changes during the major warming. During earlier stages of the warming process (not shown), the region of temperatures below -60~ began shrinking, as noted above, but it continued to concentrate around the 80 to 100 mb levels in the polar regions, until completely displaced with warmer air, as shown in Fig. 2b. There is also a temperature gradient reversal evident at the 10 mb level at this stage of the warming. For the minor warming, there is only a slight temperature reversal near the surface high latitude regions. At the peak of the warming activity in the lower stratospheric regions, represented by Figs. lc and 2c, there appears to be few changes for both seasons from their ~ previous respective cross-sections. However, for the minor warming, the coldest air has been displaced poleward and downward. In both cases, slight cooling has started in the uppermost levels at the middle latitudes. Both seasons also show N-S temperature reversals in the polar latitude troposphere with the downward bulge in the isotherms at around 70~ This bulge is more pronounced in Fig. 2c, indicating that the strong warming in January 1977 penetrated to the surface in the polar regions, and eventually led to the complete wind reversal in the troposphere as shown in Fig. 4c.

Vol. 118, 1980)

Major and Minor Stratospheric Warmings

431

~,18 JAN 76

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432

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Vo1.118,1980)

Major and Minor Stratospheric Warmings

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434

J.P. Koermer and S. K. Kao

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Vol. 118, 1980)

Major and Minor Stratospheric Warmings

435

4. Evolution of the mean zonal velocity Figures 3 and 4 show the cross sections of the mean zonal wind corresponding to Figs. 1 and 2. Prior to significant warming activity (Figs. 3a and 4a), the major features are the tropospheric jet and the lower extension of the polar night jet in the lower stratosphere. The major difference between the two seasons lies in the larger magnitude of this extension during the minor warming case. It had a pre-warming magnitude on the order of 60 m/sec for the 1975-76 winter season. Another difference is the weak easterly region in the lower polar troposphere during the 1976-77 season. Although they are nearly nonexistent for this particular minor warming cross-section, they appear on others not shown and tend to be transitory in nature. During the latter stages of the warmings, there are only slight changes in the mean zonal wind for the minor warming but tremendous change for the major warming. Figure 3b shows that there is a slight decrease in magnitude of the polar night jet extension to around 50 m s- 1 and a slight decrease in tropospheric mid-latitude mean zonal wind. However, in Fig. 4b the extension of the polar night jet is nonexistent due to the incipient wind reversal. Easterlies appear to spread downward and southward from higher level polar regions. The tropospheric jet remains nearly unchanged during the minor warming but has intensified strongly for the major warming. Perhaps this is a result of compensation for the loss in stratospheric westerly momentum. At the peak of its warmings, tropospheric easterlies due to N-S temperature gradient reversals are present for both seasons, as shown in Figs. 3c and 4c. There is little other significant change in the 1975-76 season. Figure 4c shows the full wind reversal of this remarkable warming. The easterfies continued from 8 January 1977 to push downward and southward, eventually joining with the enhanced tropospheric low-level easterlies to cause a complete wind reversal at all levels and as far south as 60~ The formation of easterlies down to the lower troposphere in January 1977 has previously been reported by Qumoz (1977) and O'NEILL and TAYLOR(1979).

5. Mean fluxes of geopotential, westerly momentum and sensible heat Observational evidence (PERRY,1967; MILLERand JOHNSON, 1970) indicates that stratospheric warmings result from an increase of the vertical wave energy flux usually in the form of a strong eddy flux of geopotential from the troposphere to the stratosphere. O'NErLL and TAYLOR (1979) indicate the importance of horizontal momentum and heat fluxes in the warming process. Daily meridional cross-sections of the vertical eddy geopotential flux (now shown) reveal a quasi-permanent feature consisting of an upward flux maximum located around 200-300 mb and 35-45~ Prior to warming pulses, the upward flux was primarily confined to the troposphere. However, as the warming trend began, the region of maximum upward flux typically amplified and shifted to higher latitudes

436

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Vol. 118, 1980)

Major and Minor Stratospheric Warmings 10

5 ~

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438

J.P. Koermerand S. K. Kao

(Pageoph,

while extending upwards in the stratosphere. The stratosphere reponded at even higher polar latitudes with a strong downward flux of geopotential, which might assist the warming process in these regions because of adiabatic compression. The two main differences noted between the seasons under investigation were the more northern shift of the area of maximum upward flux of geopotential during the strong warming pulses of the 1976-77 winter and the parodoxically larger upward and downward flux maxima during the minor warming of the 1975-76 winter, especially in the stratosphere. This follows from the ELIASSEN-PALM(1960) approximation which shows that vertical flux of geopotential is essentially proportional to mean zonal velocity. Recall that the relative strength of the polar night jet was weaker during the winter of 1976-77. Some of these features can be seen in the meridional cross-sections of the vertical geopotential flux (Figs. 5a and 6a) which represent early stages of warming pulse for the two seasons. The arrangements of the fluxes are similar for both cases. However, these cross-sections do show the larger magnitude of the vertical geopotential flux in the higher latitude stratospheric regions (Fig. 5a) typical of the 1975-76 winter and more northern extent of the upward flux region (Fig. 6a) characteristic of the 1976-77 winter. Meridional cross-sections of meridional flux of momentum are shown in Figs. 5b and 6b for the early stages of the final warming pulses associated with each season. There is strong negative flux in the higher latitude stratospheric regions for the major warming season. Convergence of westerly momentum in the stratosphere is confined to the higher latitudes for the minor warming, but extends into mid-latitudes for the major warming. As expected, tropospheric momentum fluxes are strongest near the jet. Meridional fluxes of sensible heat (Figs. 5c and 6c) show a somewhat reversed situation. Here, the strongest positive convergence of meridional heat flux at higher latitudes (north of 70~ is associated with the major warming. Meridional convergence of heat flux occurs north of 60~ for the minor warming season. The magnitude of the flux for this season is almost half that of the major warming season which also has correspondingly stronger fluxes in the troposphere. More will be discussed on contributions of meridional momentum and heat fluxes in Section 9.

6. Evolution o f mean zonal winds at 60~

Figures 7 and 8 show the evolution of the mean zonal wind at 60~ and the dramatic differences between the two types of warmings. The latitude of 60~ was chosen as the basis for these and subsequent time height sections of energy because (1) 60~ is in the general vicinity of the maximum of the extension of the polar night jet; (2) the data showed the important features noted at higher latitudes and is probably more reliable than extreme polar data; (3) this is the region of maximum eddy available potential energy in the lower stratosphere; and (4) maximum meridional momentum and heat fluxes are generally located in this region. Hence, we

Vol. 118, 1980)

Major and Minor Stratospheric Warmings

5C ~

439

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Figure 7 Pressure-time sections at 60~ of the mean zonal velocity (m s-1) for the 1975-76 season. Easterlies are stippled. felt that 60~ would adequately represent higher latitudes and best reflect the often tremendous changes associated with warming processes. Activities at more southerly latitudes were not presented since vertical wave propogation is less pronounced than at higher latitudes as noted by DiC~ZINSON (1968). Our time-height energy sections (not shown) clearly show a greater decoupling between the troposphere and stratosphere at these lower latitudes. Returning to the changes in the mean zonal wind, we can see that there are only minor oscillations in the stratospheric mean zonal wind (Fig. 7) for the minor warming and much more extensive oscillations and ultimate wind reversal for the major warming (Fig. 8). Oscillations with periodicities on the order of 8-12 days are present in the troposphere and 10-20 days in the stratosphere for both seasons. As noted before, the strength of the polar night jet was much more pronounced during the minor warming season. The strength of the extension also to some degree determines the corresponding strength of tropospheric mean zonal winds. Perhaps the lack of

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25

440

J.P. Koermerand S. K. Kao

(Pageoph,

strong mean zonal winds in the troposphere, which is more prevalent during more significant warmings because of the breakdown of this polar night jet, may be in part responsible for the tropospheric blocking that is often associated with major warmings (LABITZKE, 1965). Certainly strong tropospheric blocking was prevalent during the 1976-77 season (TAUBENSEE,1977; WAGNER, 1977). The stroiag thermal wind relationship is manifested by the variations of the zonal wind in the lower stratosphere. Reflecting the strength of each warming pulse, there is a correspondingly lagging decrease in the zonal winds in these regions. As soon as the warming pulse subsides, ~ eventually begins to increase. This can be highlighted by examining Fig. 8 towards the end of December and early January. The wind reversal extended even for several days into the troposphere as far south as 60~ Finally, the strong zonal winds in our minor warming case may in themselves inhibit a major warming for two reasons. First, the large zonal index tends to reduce eddy effects. Secondly, more work has to be done on the stronger and correspondingly larger N-S temperature gradient to cause a reversal.

7. Evolution of eddy kinetic energy (EK) at 60~ Since eddy fluxes play such an important role in the warming processes, we felt that it was logical to examine the kinetic and available potential energies associated with these eddies. In actuality, we examined the total eddy energies and the energies for individual wavenumbers 1 through 4. However, contributions from waves 3 and 4 were relatively small in the stratosphere compared to the longer waves, and their results are not included. This is similar to MILLERand JOHNSON(1970) who found that eddy kinetic and available potemial energies decrease rapidly with increasing wavenumber in the stratosphere with the latter decreasing even more rapidly than the former. Total eddy kinetic energy is much greater in the stratosphere during the minor warming season (Fig. 9a) than during the major warming (Fig. 10a). The stronger mean flow of the minor warming season probably provides a greater mean kinetic energy source for the waves to draw upon through interaction and transfer. Comparing these time-sections of eddy kinetic energy with those for the mean zonal flow, it appears that the amplitudes of the two are out of phase in the stratosphere, indicating energy transfer between the mean flow and the waves. Perhaps the most significant important difference between the major and minor warmings is the behavior of the eddy kinetic energy near 100 rob. Except for early in January 1976, the eddy kinetic energy is fairly steady throughout the remainder of the period in the case of minor warming as shown in Fig. 9a. On the other hand, Fig. 10a shows frequent periods of minimal wave energy at these levels. The most pronounced period with almost negligible eddy kinetic energy in this region follows the

Vol. 118, 1980)

Major and Minor Stratospheric Warmings

EK ( k ~ O)

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Vol. 118, 1980)

Major and Minor Stratospheric Warmings

443

wind reversal of the major warming. We believe that these periods of minimal wave activity at or above the tropopause reflect a general decoupling of the troposphere and stratosphere that may aid in establishing tropospheric blocking regimes. For example, the only significant blocking reported during the corresponding period of 1975-76 season was during the week of 5-11 January (WAGNER, 1976; DICKSON, 1976), corresponding to the minimum in eddy kinetic energy above the tropopause as shown in Fig. 9a. Similarly, the blocking regimes mentioned by TAUBENSEE(1977) and WAGNER(1977) seem to be closely related to minima in Fig. fla. Conversely, it appears that tropospheric and stratospheric eddy kinetic energy couplings appear to be a major driving force of moving tropospheric systems. The extent of the coupling is proportional to the strength of the eddy kinetic energy present at higher levels in the stratosphere. Figures 9b-c and 10b-c show that the wave kinetic energy for wavenumbers 1 and 2, which do not account for as much of the tropospheric kinetic energy as short waves, but which do account for practically all of that in the stratosphere. Examining the phase relationships between wave 1 and 2 from these figures, we can see that wave 1 increases at the expense of wave 2, reported by LABITZKE(1977 and 1978). It also appears that there were transfers of kinetic energy between wave 1 and wave 2 during the minor warming, since the amplitudes of waves 1 and 2 are almost 180~ out of phase. These energy exchanges between waves 1 and 2 occur with periodicities of the order of 10-20 days. The winter of 1975-76 had strong wavenumber 2 activities in the stratosphere in November and from mid-January on as shown by QUIROZand NAGATANI(1976). This latter period is quite evident from Fig. 9c. However, the three warming pulses of this season (late December-early January, early February, and late February) are almost exclusively wavenumber 1 phenomena, with minimal wave 2 activity. The strongest warming pulses in the stratosphere during the winter of 1976-77 occurred from 12-21 December and 27 December-10 January (QuIROZ, 1977). Somewhat conversely, the former period started with strong wavenumber 2 activity as shown in Fig. 10c, but then turned into an almost entirely wavenumber I phenomena (Fig. I0b). The 1973-74 major warming (not shown) was primarily a Wavenumber I warming except for some slight wavenumber 2 activity in agreement with LABITZKE(1978). In all cases, the ultra-long wave kinetic energy tends to increase first at higher levels of the stratosphere and then spread downward through time. After peaking, the wave kinetic energy decreases first at the lower tropospheric levels and then often abruptly at higher levels.

8. Evolution of eddy available potential energy (EA) Eddy available potential energy is weaker for the minor warming than for the major warming case as shown in Figs. 1la and 12a. EA appears to be completely

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Vol. 118, 1980)

Major and Minor Stratospheric Warmings

EA

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J.P. Koermer and S. K. Kao

(Pageoph,

decoupled for the case of the minor warming in the vicinity of the tropopause from 50 to 300 rob. This decoupling is not as pronounced and is sometimes nonexistent during the major warming. The 1973-74 major warming (not shown) also displays similar EA features. During the minor warming, EA was also relatively steady in comparison with the other season. For the major warmings of 1973-74 and 1976-77, we noted a dramatic decrease in EA in both the upper troposphere and lower stratosphere regions following the wind reversals. There also appears to be a compensation effect between EA and EK which could be a consequence of the conversion between the two types of energies. In analyzing EA for wavenumber 1 (Figs. 1 lb and 12b) and comparing these figures with those for the mean zonal wind and EK, the major Warming seems to follow the baroclinic energy transfer process as outlined by MclNTURFF (1978), whereas the minor warming case for wavenumber 1 does not show the same clear-cut relationship. It, along with the EA for wavenumber 2 (Figs. 1 lc and 12c), seems to be more barotropic in nature. For both seasons, most stratospheric EA is contained in wavenumber 1. As opposed to EK, longer waves account for much of the EA in the lower troposphere. Compensation effects in time between wavenumbers 1 and 2 are again present, which could be a consequence of energy transfers between these wavenumbers. Significant warming pulses seem to result in increases in EA for wavenumber 1 and decreases in EA for wavenumber 2.

9. Effects o f linear and nonlinear interactions on the rate o f change o f ~ and T

Recent work by O'NEILL and TAYLOR (1979) has stressed the importance of considering horizontal eddy fluxes in studying the warming and reversal processes. In this section, we will look at these effects and hence the influence of transient motion on the rates of change in ~ and T. Consider the zonal mean of the zonal component of the momentum equation, 8ff 8-'t = f~

1 0 a cos 2 r 8r (b-~cos 2 r

+ R

(3)

where the overbar represents zonal averages, /v represents the frictional effects, vu = ~ + v'u', where the primed quantities are deviations from the zonal means. Taking the time-mean, represented by ( ) of (3), we obtain: a cos 2 r 8r (b~ cos ~ 4,) + /v

(4)

which shows the noninteraction effect of (b--~). Subtracting (3)-(4) yields: 8~

-~ = fgt

1

0

a cos z r 8~ (V~ cos 2 r

where ( )~ = ( ) - ( ) , representing the transient motion.

(5)

Vol. 118, 1980)

Major and Minor Stratospheric Warmings

447

Similarly, we can reduce the thermodynamic equation: 8-7 =

a c o s r 8r (vTcos r

- ~o(Fa - F) + ~

(6)

r)t.

(8)

by taking the time-mean, we have

o =

a cSs r

and (6)-(7) yields 8~ a--7 =

1 8 a cos r 8r ( v T cos r -

-

-

~

-

Figures 13a and 14a show the graphical results for equation (5) averaged over 60 ~ to 80~ at l0 mb. The m i n o r w a r m i n g is characterized by m a n y wild fluctuations in ,

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Figure 14 Same as Fig. 13 except for the 1976-77 major warming season.

the terms of the equation. The net result is that periods of accelerations and decelerations are too brief to allow for significant changes in ft. In examining Fig. 13a, neither the convergence of horizontal momentum flux term - ( 1 / a cos r 0/~r cos 2 r nor the coriolis term f~t predominate for any extended periods during this season. However, this is not the case during the major warming season. Accelerations and decelerations continue for much longer periods, reflecting the changes in fi noted in Fig. 8. The terms change much more smoothly, especially after the reversal and continuing through most of January. For this case, we can also see from Fig. 14a that the convergence of momentum flux influences Off/St to a much greater and constant degree than it did for the minor warming. The equatorial flux of zonal momentum during much of January 1977 is essential in affecting the zonal wind reversal. However, strong southward momentum flux does not always insure decelerations as can be noted in the later half of January 1976 (Fig. 13a), where the negative momentum flux convergence is nearly balanced by the f~t term. During this season, the Coriolis

Vol. 118, 1980)

Major and Minor Stratospheric Warmings

449

term sometimes is dominant, which supports the theory of MATSUNO(1971), but at other times the convergence of momentum flux seems to dominate. This strongly suggests the delicate balance between these two effects and the need for their inclusion in future modeling efforts. Looking at the heat budget, temperature increases and decreases appear small and unsteady for the minor warming (Fig. 13b) than for the major warming (Fig. 14b). Temperature increases for the minor warming tend to be a result of vertical motions (i.e., subsidence). However, the major warming seems to be influenced to a much greater degree by the convergence of meridional heat flux term -(1/acosff)8/b~ (vT cos ~b)t, especially during the two significant warming surges (mid-December and early January). After the warming ends, the terms become negative and small, resulting in steady slow cooling for most of the second half of January. The relationship between the stratospheric momentum and heat budgets for the 1976-77 winter season seems quite clear. As periods of warming occur primarily as a response to poleward heat flux convergence, decelerations result in the mean zonal flow in agreement with the thermal wind relationship. Conversely, cooling periods produce accelerations in the mean zonal velocity. This is depicted in Figs. 14a and 14b. Ultimately, the N-S temperature gradient reversed and was later followed by a zonal wind reversal. This was accompanied by an extended period of equatorward momentum transport that aided directly in the maintenance of the reversal. Indirectly, it assisted the warming by reducing the effects of adiabatic cooling because of the weakened and reversed meridional circulation due to conflicts between the induced meridional flow of poleward heat transport and equatorward momentum transport as discussed by O'NEILL and TAYLOR(1979). During the 1975-76 season the smaller magnitude and period of poleward heat transport resulted in small temperature changes not significantly affecting the N-S temperature gradient and hence there was no wind reversal. Although the thermal wind relationship still holds, the relative contributions of poleward heat transport versus equatorward momentum transport is questionable. Possibly, this is due to the small extent of the heat transport characteristic of this season. Perhaps the reason that meridional momentum and heat fluxes play a much smaller role during minor warmings is due to the strength of the polar night jet that serves as a barrier to damp effects of the fluxes before they become too great. This causes a greater variability in the flux contributions and other terms and hence little change in the mean zonal motion and temperature.

10. Summary and conclusions Analyses of evolutions of the kinetic and thermal energy associated with the major and minor stratospheric warmings in the winters of 1976-77 and 1975-76 respectively indicate that during the major warming both the temperature and zonal

450

J.P. Koermer and S. K. Kao

(Pageoph,

wind reversals occurred first in the upper stratosphere then extended downward, and appeared nearly simultaneously in the lower stratosphere and troposphere; in the meantime the tropospheric jet intensified, and high pressure cells moved poleward blocking the storms developed upstream. During the minor warming, however, no reversals of temperature and zonal wind occurred in the stratosphere, and the amplitude of the mean tropospheric westerly jet remained almost unchanged. During both the major and minor warmings, upward flux of geopotential appeared in the mid-latitude stratosphere and troposphere with its maximum located near the tropopause, whereas the downward flux of geopotential occurred mainly in the high latitude stratosphere. However, the upward flux of geopotential for the major warming extended about 10~ latitude further north than for the minor warming. Meridional convergence of poleward flux of westerly momentum in the stratosphere is confined to the high latitudes for the minor warming, but extended into mid-latitudes for the major warming. The magnitude of the meridional convergence of poleward flux of sensible heat in the high latitude stratosphere for the major warming is twice that for the minor warming. Analyses of evolutions of the eddy kinetic and available potential energy associated with the major and minor stratospheric warming at 60~ where maxima of eddy kinetic energy, available potential energy, meridional fluxes of westerly momentum and sensible heat were located in the stratosphere, indicate that the predominant ultra-long waves in the stratosphere oscillated at periods of 10-20 days, whereas in the troposphere the predominant long waves oscillated at periods of 8-12 days. The kinetic energy of the zonal mean flow in the stratosphere for the minor warming is much greater than that for the major warming, indicating that the occurrence of a major warming depends on the magnitude of the kinetic energy of the zonal mean flow relative to that of the meridional convergence of the poleward flux of sensible heat. In both the major and minor warmings, most of the stratospheric eddy kinetic energy is contained in waves of wavenumbers 1 and 2, whereas the stratospheric available potential energy is primarily contained in waves of wavenumber 1. The kinetic energy associated with waves of wavenumber 1 appeared to be 180~ out of phase of those of wavenumber 2, indicating that nonlinear transfer of kinetic energy occurred between waves of wavenumbers 1 and 2. The occurrences of wind reversals were accompanied by decouplings of the stratospheric and tropospheric motion, and blockings in the troposphere.

Acknowledgments This research was partly supported by the National Aeronautics and Space Administration, Contract NAS 5-26373. We wish to thank R. S. Quiroz for his review and comments on this paper.

Vol. 118, 1980)

Major and Minor Stratospheric Warmings

451

REFERENCES

DICKINSON, R. E. (1968), Planetary Rossby waves propagating vertically through weak westerly wind wave guides, J. Atmos. Sci. 25, 984-1002. DICKSON, R. R. (1976), Weather and cireulation of February 1976- Extreme warmth over the eastern two-thirds of the United States, Mon. Wea. Rev. 104, 660-665. ELIASSEN,A. and PALM, E. (1960), On the transfer of energy in stationary mountain waves, Geofys. Publ. 17, No. 3, 44 pp. HOLTON, J. R. (1976), A semi-spectral numerical model for wave-mean flow interactions in the stratosphere: Application to sudden stratospheric warmings, J. Atmos. Sci. 33, 1639-1649. JULIAN, P. R. and LABITZKE, K. (1965), A study of atmospheric energeties during January and February 1963 stratospheric warming, J. Atmos. Sci. 22, 59%610. LABITZKE, K. (1965), On the mutual relation between stratosphere and troposphere during periods of stratospheric warmings in winter, J. Appl. Meteorol. 4, 91-99. LABITZKE, K. (1977), Interannual variability of the winter stratosphere in northern hemisphere, Mon. Wea. Rev. 105, 762-770. LABITZKE, K. (1978), On the different behavior of the zonal harmonic height waves 1 and 2 during the winters 1970/71 and 1971/72, Mon. Wea. Rev. 106, 1704-1713 MATSUNO, T. (1971), A dynamical model of the stratospheric sudden warming, J. Atmos. Sci. 28, 1479-1494. MCINTtrRFE, R. (1978), Stratospheric warmings: Synoptic, dynamic and general circulation aspects, NASA Ref. Publ. 1017, 166 pp. MILLER, A. J., BROWN, J. A. and CAMVANA,K. A. (1972), A study of the energetics of an upper stratospheric warming (1969-1970), Quart. J. Roy. Meteorol. Soc. 98, 730-744. O'NEILL, A. and TAYLOR, ]3. F. (1979), A study of the major stratospheric warming of 1976/77, Quart. J. Roy. Meteorol. Soc. 105, 71-92. PERRY, J. S. (1967), Long wave energy processes in the 1963 sudden stratospheric warming, J. Atmos. Sci. 24, 537-550. QrJIROZ, R. S. (1969), The warming of the upper stratosphere in February 1966 and the associated strueture of the mesosphere, Mon. Wea. Rev. 97, 541-552. QtJtROZ, R. S. (1971), The determination of the amplitude and altitude of stratospheric warmings from satellite-measured radiance changes, J. Appl. Meteorol. 10, 555-574. QutROZ, R. S. (1977), The tropospheric-stratospheric polar vortex breakdown of January 1977, Geophys. Res. Lett. 4, 151-154. QuJROZ, R. S. and NAGATANI,R. M. (1976), A study of tropospheric-stratospherie interaction based on combined satellite and rawinsonde data, Proc. Syrup. on Meteor. Obs. from Space (Philadelphia, June 8-10), 368-373. REED, R. J., WOLF, J. and NISrnMOTO, H. (1963), A special analysis of the energeties of the stratospheric sudden warming of early 1957, J. Atmos. Sci. 20, 256-275. SCHERHAG, R. (1952), Die explosionsartige Stratosphdrenerwarmung des Spdtwinters 1951/52, Ber. Deut. Wetterdieustes 6, 51-63. Sco-r'r, A. F. D. (1972), Mesospherie temperatures and winds during a stratospheric warming, Phil. Trans. Roy. Soc. London 271, 547-557. TAUBENSEE, R. E. (1977), Weather and circulation of December 1976 - Extremes of dryness in the west and mid-west, Mon. Wea. Rev. 105, 368-373. WAGNER, A. J. (1976), Weather and eirculation of January 1976 - Increasing drought in California and the southern Great Plains, Mon. Wea. Rev. 104, 491-498. WAGNER, A. J. (1977), Weather and circulation of January 1977- The coldest month on record in the Ohio valley, Mon. Wea. Rev. 105, 553-560. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh~iuser Verlag, Basel

The MST Radar Technique: Potential for Middle Atmospheric Studies By B. B. BALSLEy1) and K. S. GAGE1)

Abstract- We examine the potential of the MST (mesosphere-stratosphere-troposphere) radar technique for obtaining detailed information on the middle atmosphere. This techniquewhich uses very sensitive coherent VHF and UHF radars - is capable of detecting signal returns arising from weak fluctuations in the atmospheric refractive index. With certain limitations the MST technique is capable of continually observing winds, waves, turbulence and atmospheric stability over the height range 1-100 km with good-to-excellent time and space resolution. We examine the relatively large body of literature that has been written over the past few years and outline some aspects of a promising future. Key words: MST radar; Wind observation; Wave observation.

1. Introduction It has become apparent in the last few years that a complete understanding of long-term climatic changes, including possible Sun-weather effects and the effects of anthropogenic contamination, requires an understanding of the dynamic processes occurring in the region between the tropopause and 100 km - i.e., the middle atmosphere. A coordinated study of this region using a variety of experimental techniques will take place during the next few years under the auspices of the Middle Atmosphere Program (MAP). The MST (mesosphere-stratosphere-troposphere) radar technique is a recent development that offers a great deal of promise in advancing our understanding of the middle atmosphere. This technique uses ultrasensitive V H F (30300 MHz) and U H F (300-3000 MHz) radars to study the weak backscattering arising from refractive index fluctuations in the neutral atmosphere and lower ionosphere. Analysis of these scattered signals enables measurement of the dynamic properties of the atmosphere - winds, waves, turbulence and atmospheric stability - throughout the middle atmosphere. While we will refer to the MST radar technique in subsequent sections, specific systems have been subdivided into either MST or ST (stratospheretroposphere) systems by their operating frequency and/or average power-aperture products.

1) Aeronomy Laboratory, National Oceanic and Atmospheric Administration, Boulder, Colorado 80303, USA.

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453

The MST technique is capable of obtaining useful returns over the height range 1-100 kin. Echoes coming from heights below approximately the stratopause (_~ 50 kin) arise primarily from refractive index fluctuations due to small-scale (one-half the transmitted wavelength) inertial range turbulence. Echoes returned from above the stratopause, which are normally observed only during daylight hours, arise primarily from free electrons that enhance the scattering cross-section of the neutral turbulence fluctuations at these heights. The most difficult region to observe by the MST technique is the region near the stratopause because of the combined effect of the exponentially decreasing atmospheric density and the lack of sufficient free electrons. The temporal and spatial resolution provided by the MST technique varies with radar sensitivity and with height. A resolution of a few tens of meters and a few seconds is possible when the effective signal-to-noise ratio of the scattered signal is well above unity. Resolution degrades to a few km and tens of minutes when the signal is weakest, for example, near the stratopause. The advantage of the MST technique over other techniques lies in the continuity of the data in both time and height. The time resolution is orders of magnitude better than rocket or balloon data. Other ground-based techniques (meteor winds, airglow, laser radar, etc.) have poorer time continuity or are sensitive only to specific heights. Thus the advent of the MST technique offers an unparalleled opportunity to study not only gross features of the total wind field, but also small-scale, time-varying structures such as gravity waves and turbulence throughout the middle atmosphere. Development of the MST technique has its historical roots in decades of radio propagation experiments, radar probing of the optically clear neutral atmosphere and radar investigations of the ionosphere by the thermal (also known as incoherent or Thomson) scatter technique. As far as the authors can determine, the first observations of true atmospheric echoes were reported by COLWELLand FRIEND (1936) and WATSON-WATTet al. (1937), who used a pulsed HF system to observe a series of scattering layers ranging between 2-60 kin. A review of the history of radar probing of the clear atmosphere appears in GAGEand BALSLEY(I 978), and a review of the history of thermal (incoherent) scatter has been given by EVANS(1969). Specific references are given in the following sections when appropriate. 2. General considerations of the M S T radar technique a. MST/ST systems defined

Conceptually, the MST technique involves radar backscattering from nonthermal fluctuations in the atmospheric refractive index (for additional discussions of MST/ST concepts, see GORDON, 1978). The pertinent scale size for backscattering is one-half the transmitted wavelength. The non-thermal fluctuations considered here arise primarily from turbulence, although a number of additional processes contribute to the scattering under special conditions. Among these are the stratification of the stable atmosphere into thin layers and the generation of ionized trails by incoming

454

B.B. Ba!sleyand K. S. Gage

(Pageoph,

meteor particles. The first is discussed below in terms of a Fresnel or partial reflection process; the second, which can also be considered in terms of Fresnel reflection, holds the promise of extending MST studies to the nighttime upper mesosphere. Many of the radars involved in MST studies are also capable of obtaining echoes from thermal fluctuations (i.e., the statistical fluctuations of a medium in thermodynamic equilibrium), provided that the radar is sufficiently sensitive and that the medium contains a sufficient number of free electrons. Scattering from thermal fluctuations in an ionized medium has been variously termed thermal, incoherent, or Thomson scattering (see WOODMAN and GUILLt~N (1974) and RASTOGI and BOWHILL (1976a) for a discussion of thermal versus non-thermal scattering). In this paper, we will adopt the term thermal scattering for incoherent or Thomson scattering while recognizing that the other terms are at least as commonly used in the current literature. The various types of non-thermal scattering will be discussed in terms of their specific mechanisms. Determination of atmospheric motions by the MST radar technique requires that the radar system be frequency coherent- i.e., that the received signal is mixed with the transmitted frequency to retain both the amplitude and phase of the returned signals. Typical analysis procedures entail obtaining the echo power spectrum of the coherently demodulated returns. Moments of the resulting spectrum yield the echo power, mean Doppler shift, and spectral width. These parameters, in turn, describe respectively the fluctuation intensity, the radial velocity of the scattering medium, and the distribution of random velocities within the scattering volume (WOODMAN and GUILL~N, 1974). Radar systems capable of observing non-thermal scattering throughout the entire atmospheric system must be exceedingly sensitive. The rapid decrease of received power with height from the lowest heights to about the stratopause as shown in Fig. 1 (BALSLEY, 1978) is in excess of ten orders of magnitude. The requisite average power-aperture product (average transmitter power capability multiplied by the effective antenna area), which is useful in determining the ultimate sensitivity of an MST system, must be at least 109 W mL (GORDON (1978) suggests a roughly equivalent value for peak power aperture product of 1011 W mL) An equally important requirement is that the transmitted frequency be sufficiently low so that the scattering scale size normally lies within the inertial subrange of turbulence at all heights (cf. Section 3c), since turbulence on scales smaller than this will be strongly damped by viscous dissipation. This limits the operating frequency of an MST radar to values below at least 100 MHz and preferably below 50 MHz (GORDON, 1978).2) Radars operating at higher frequencies or having smaller average power-aperture products that are

2) A 30 MHz lower limit for MST radars has been suggested (GORDON, 1978) to preclude the undesirable effects of ionospheric reflection, round-the-world echoes, and HF spectrum pollution. However, the possibility of sounding the middle atmosphere at lower frequencies has been anticipated by WATSON-WATTet al. (1937) and may provide a fruitful field for further investigation.

Vol. 118, 1980)

The MST Radar Technique

455

JICAMARCA, PERU 10 JANUARY f977 1710-1724/1852

~

- 1 9 2 7 ( 7 5 ~ W)

4o

7- 3c

._~ I

2C

2

3

4

5

6

7 8

9

10 11 12 13

Log Received Power (Reletive) ---,Figure 1 A 49 minute average of received power vs. height obtained from the Jicamarca Radar Observatory in Peru with the antenna directed - 1 . 5 ~ south of vertical (on-axis position). Error bars below 20 k m arise from matching different profiles. Data points between about 42 k m and 52 k m are approximate and indicate the maximum possible echo power. The increased echo power above 50 k m is due to the presence of free electrons. (After BALSLEY, 1978.)

capable of observing non-thermal scattering at some, but not all, heights have been termed ST (stratosphere-troposphere) radars. It should be emphasized that the practical delineation between MST and ST radars is not precise. The 109 W m 2 average power-aperture product suggested by GORDON (1978) as a minimum value for an MST system enables a radar operating at about 50 MHz to obtain useful data over the complete height range, particularly in the region 45 km __+ 15 km where the signal returns are weakest. Systems with smaller power-aperture products are clearly capable of obtaining high-quality mesospheric data above about 60 kin, as we will discuss in Section 5. It is only the region near the stratospause that is typically inaccessible to an ST radar operating in the lower VHF.

b. MST/ST facilities A list of existing and proposed MST/ST radar systems throughout the world is given in Table l, and their locations are noted on the world map in Fig. 2. Pertinent parameters for each system have been included for reference. The average poweraperture product has been obtained from published literature. For the phased dipole arrays, the antenna aperture is assumed to be comparable to the physical area. For other antenna configurations, the aperture is computed from the published antenna beamwidths. Antenna and transmission line losses are thereby neglected. A number of the more sensitive systems-Jicamarca, Arecibo, Chatanika, Millstone, and EISCAT - have been designed as thermal (incoherent) scatter radars

456

B . B . Balsley and K. S. Gage

(Pageoph,

0

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Vol. 118, 1980)

The MST R a d a r Technique

457

50~

50*

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Figure 2 Location of various radar facilities with MST/ST capability listed in Table 1.

Figure 3 The 50 M H z Jicamarca radar located near Lima, Peru.

458

B.B. Balsley and K. S. Gage

(Pageoph,

Figure 4 The 40 MHz Sunset radar located near Boulder, Colorado. for ionospheric investigations. A similar n u m b e r - S O U S Y , Sunset, Platteville, Poker Flat, Urbana, Defford and the Japanese (MU) radar - have been or are being designed specifically as MST or ST radars. The wide range of possible operating frequencies of MST/ST radars, particularly of the ST radars, allows for a variety of different antenna configurations. At the lower VHF frequencies it is possible to construct inexpensive dipole arrays having moderate steerability and large apertures. The Jicamarca array shown in Fig. 3 and the Sunset array shown in Fig. 4 are examples of this type of construction. A basic difference between these two systems is that, while the Jicamarca array consists of dipoles constructed of coaxial aluminum tubing, the Sunset array (and Platteville and Poker Flat) comprises collinear dipole arrays constructed from ordinary coaxial-cable (BALSLEYand ECKLUND,1972). Antennas at higher frequencies range from the small but completely steerable dish at Chatanika (Fig. 5) to the large fixed dish at Arecibo (Fig. 6). Although a dish configuration is much more expensive than the dipole array, this disadvantage is largely offset by its inherent versatility. c. Pertinent radar equations

The radar equation relates the received signal strength P~ to the radar parameters appropriate to any particular system and the volume reflectivity '7, or reflection coefficient IPl, for any particular atmospheric process being studied. Although radar equations differ slightly for dishes and arrays, they can be treated in a unified manner. The pertinent radar equation for Fresnel reflection takes a somewhat different form.

Vol. 118, 1980)

The MST Radar Technique

459

Figure 5

The 1290 MHz Chatanika radar located near Fairbanks, Alaska. For scattering from distributed (beam-filling) targets the radar equation for dish antennas has been derived by PROBERT-JONES(1962). The radar equation for an array is given by VANZANBT et al. (1978). These equations can be expressed in the common form Pr = a2PtA*Ar

9~r2

~/

(1)

where a takes into account the efficiency of the antenna and waveguides, Pt is the peak transmitter power, Ar ( - c-r~2, where ~-is the pulse width) is the range resolution, r is the range and ,j is the volume reflectivity. For a dish Ae (_~2/3A) is the equivalent area of the antenna aperture having a physical area A. For an array Ae = A cos X where A is the physical area of the horizontal array and X is the zenith angle. The

460

B.B. Balsley and K. S. Gage

(Pageoph,

Figure 6 The 430 MHz Arecibo radar located near Arecibo, Puerto Rico. cos X factor accounts for the apparent reduction in antenna area when the antenna is directed off-zenith. For Fresnel reflection at vertical incidence from a horizontal layer assumed to extend over a Fresnel zone the appropriate radar equation has been derived by FRIEND (1949)

a2PtA2e

er = ~

Ipl 2

(2)

where IPl z is the power reflection coefficient and k is radar wavelength.

d. Detectability and signal processing The small radar scattering cross-section of the turbulent fluctuations, especially in the upper stratosphere and lower mesosphere, requires that MST systems have large power aperture products and employ relatively sophisticated signal detection and processing techniques. Most of the analysis procedures involve the power spectrum of the signal returns. A typical power spectrum is shown in Fig. 7, where spectral power density is

Vol. 118, 1980)

The MST Radar Technique

461

co c I1) C)

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+Afmox

Doppler Shift Figure 7 Example of a typical echo power spectrum from GAOEand BALSLEY(1978). See text for details. -.,,,--

plotted against A f t h e Doppler shift of the transmitted frequency. The signal is indicated by the enhanced peak in the region near the vertical arrow marked S~(Af) + Su(Af). (St and SN refer to the power spectral densities of the signal and noise, respectively.) The noise power spectral density in the absence of a signal is shown as SN(Af). The mean power spectral density SN of the noise is indicated by the horizontal dashed line, and the r.m.s, of the statistical fluctuation around the mean level, ASN, is also shown. The + Afm~x limits are determined by the transmitted pulse rate and the number of coherent integrations. (Coherent integration involves the coherent summing of a number of samples obtained from a specific echoing volume after sequential transmitter pulses and prior to performing a spectral analysis. Within limits, this process reduces the number of subsequent computer operations necessary to obtain the average echo power spectrum for a given period.) GAGE and BALSLEY(1978) define the detectability of the received signal in terms of ST (the expected amplitude of the spectral peak of the received signal density after averaging) relative to ASN (the noise fluctuation level after averaging). Then, in terms of the radar equation for distributed targets (i.e., when the sampled volume is filled with scatterers), the detectability criterion may be written as:

ASN

8,,~/~-r2k(Ts+ ~ro)~f

where Pt = average transmitter power, Ae = effective antenna area, F1 = fractional received power passing through the receiver filter, F2 = fractional received power passing through the coherent integration process, n~ = number of power spectra averaged together to reduce the noise fluctuation, k = Boltzmann's constant ( = 1.38 x 10 -23 Joules/~ Ts = system noise temperature, To = cosmic noise temperature at the antenna terminals, and Sf = signal bandwidth (the halfwidth of the signal in Fig. 7). A discussion of the frequency dependent terms in (3) appears in GAGE and BALSLEY (1978). Typical MST radar operation requires observations of the 1-100 km region with

462

B.B. Balsley and K. S. Gage

(Pageoph,

a height resolution equal to or better than 1-2 km. This requirement limits the useful transmitter duty factor (on time/off time) to a few percent. Considerably better height resolution with no reduction in the average transmitted power can be achieved by phase coding the transmitter pulse (i.e., switching the phase of the transmitted signal at prescribed intervals within the transmitted pulse) and by appropriately decoding the received signal. Since the average power is not reduced, the resulting loss in detectability for distributed targets is only proportional to the effective pulse width decrease, and not to the square of the decrease that would result from the additional decrease in average transmitted power from a non-coded pulse. For layered targets, where the layer thickness is < the pulse width, there will be no loss. Of the number of phase-coding schemes in current use, the best choice appears to be the so-called complementary code (see, for example, CZECHOWSKYet aL, 1979). In this scheme alternate transmitter pulses are phase coded so that the sum of the autocorrelation functions of the two pulses (and the resulting echoes) for a single target produces a non-zero result at zero lag and a zero result at all other lags. This feature strongly reduces the effect of unwanted signal returns in nearby range gates, an important factor when the echo strength in nearby range gates can vary by more than an order of magnitude.

3. Scattering and reflection mechanisms The echoing mechanisms (turbulent scatter, Fresnel reflection, and thermal scatter) which give rise to the signals observed on MST radars are somewhat diverse. Until recently these mechanisms have been studied in isolation. Indeed, radar studies of the clear neutral lower atmosphere and radar studies of the ionosphere have been quite separate disciplines. With the advent of the MST technique both disciplines are being brought together. In order to foster a better appreciation for the theoretical unity underlying these fields, we briefly survey in this section some of the theoretical foundations common to the study of radar echoes from the neutralkK0d ionized atmosphere. Basically, all radar echoes arise from scattering or reflection from inhomogeneities in the atmospheric dielectric constant ~ or index of refraction n (FRIEND, 1949; BOOKER and GORDON, 1950; WOODMANand GUmL~N, 1974). The dielectric constant of free space is % ( = 10-9/367r farads m -1) and a relative dielectric constant can be defined by E

Er = --"

(4)

C0

The refractive index n is related to the dielectric constant by n = v'm,,

(5)

Vol. 118, 1980)

The MST Radar Technique

463

where the relative permeability/zr of air is approximately unity (BEANand DUTTON, 1968). The radio index of refraction is given approximately by n-

1=

3.73 x 10-1e 77.6 x IO-~P T2 + T

Ne 2Ne

(6)

where P is atmospheric pressure in mb, e is the partial pressure of water vapor in rob, T is absolute temperature, Ne is the number density of electrons and, for a critical frequency f, Arc = 1.24 • 10-2f 2 is the critical plasma density in MKS units (see, for example, YEH and Lift, 1972). Contributions to the atmospheric refractive index due to both bound and free electrons are contained on the r.h.s, of equation (6). The first two terms express the contributions due to bound electrons inherent in density fluctuations of water vapor and dry air, respectively, whereas the third term expresses the contribution due to the presence of free electrons. The first term is usually more important in the lower troposphere because of the high humidity. The second term, the dry contribution, is most important from mid-troposphere up to the stratopause (,,~ 50 kin). The Ne/Nc ratio in the third term, which is usually negligible below 50 kin, becomes the major contributing factor above this level where the electron density increases rapidly with height. a. Turbulent scatter The mechanism of turbulent scatter was invoked by BOOKERand GORDON(1950) to explain over-the-horizon tropospheric radio propagation. Since then the theory has been developed extensively (TATARSKII, 1971) and its relevance to tropospheric radio propagation has been established experimentally (CHISHOLMet al., 1955; GJESSING, 1964; LANE and SOLLUM,1965). With the advent of radar studies of the clear neutral atmosphere the theory has been tested more extensively and it has been established (HARDY et al., 1966; KROPFLIet al., 1968; LANE, 1969) that scattering from turbulent irregularities is the primary cause of clear air echoes observed at microwave frequencies (wavelengths ~ 10 cm). The turbulent scattering theory has also been applied to lower-ionospheric radio propagation mechanisms (WHEELON, 1960). Several MST radar experiments in recent years (WOODMAN and GUILL~N, 1974; RASTOGIand WOODMAN,1974; RASTOGIand BOWHILL, 1976a,b,c; MILLERet al., 1978; VANZANDT et al., 1978; FUKAO et al., 1978, 1979; and ECKLUNDet al., 1979) have established the relevance of turbulent scatter to explain some of the stronger echoes received at VHF throughout the middle atmosphere. In evaluating the relevance of turbulent scattering for a particular radar frequency and for a specific atmospheric region, there are several parameters that must be considered. These parameters include the eddy dissipation rate (per unit mass) ca, which is proportional to the intensity of turbulence, and the outer scale Lo and inner scale lo (=(vs/Ea) 114, where v is kinematic viscosity) of turbulence (see, for example,

464

B.B. Bals!ey and K. S. Gage

(Pageoph,

TATARSKII, 1971). According to theory the radar backscattered signal arises from irregularities in the refractive index of length scale equal to one-half the radar wavelength. Therefore, for turbulent backscatter h/2 should fall in the range hmin < ?,/2 < A=, x where A~ln and A ~ are related to lo and Lo, respectively. Although some authors state this relationship rather loosely as lo << ?,/2 << Lo, it is more precise to specify C12~rlo < A/2 < C227rLo where C1 and C2 are constants of order unity. MEGAW (1957) has determined (71 ~ 0.94 and (72 ~ 0.75. Note that L0 is significantly smaller than the thickness scale of a turbulent layer. Using values of v from the standard atmosphere and typical values of ~a expected for different altitudes we have constructed Fig. 8. The solid curve gives a rough variation with altitude of the minimum scale of turbulence ?,~l, ( - 5.92/o). Since ?,mi, oc c~ 114, it is insensitive to changes in ~d- The shaded region in Fig. 8 illustrates the variation in Am~, due to an order of magnitude increase or decrease of ca. It should be noted that an increase in Ea leads to a decrease in ?,m~n-Since the values of ca used in Fig. 8 are typical values and since ~a can be expected to be several orders of magnitude larger in a region of locally intense turbulence, the maximum altitude to which a given radar can observe turbulence is likely to change from time to time. The outer scale of turbulence is also dependent upon the intensity of turbulence. In the free atmosphere the outer scale is thought to be on the order of 10 m (VANZANDT et al., 1978). In the lower ionosphere, WOODMAN and GUILLt~N (1974) and CUNNOLD (1975) argue that a thickness scale is about 100 m.

I00

I

I

Mesopause Viscous ""~/ Subrange

80

Inertial

E 60

Subrange

v

Strato[

"m

O dicarnarca

.~ 40 <

0 =~ =

10"z

I

I

I

I

10q 10~ 101 102 Minimum Scole of Turbulence Figure 8

Height distribution of the minimum scale of turbulence (solid circles) (m/2~rradians) based on data from RASTOGIand BOWmLL(1967C); CUNNOLO(1975); ROF~R(1977); and GAGEet al. (1979). The open squares denote the maximum height of observed atmospheric echoes (non-ionized region) for sensitive radars operating at three different frequencies.

Vol. 118, 1980)

The MST Radar Technique

465

The general expression for reflectivity for backscattering due to turbulence scattering is given by (TATARSKn, 1971) ~2

Vturb = -~- K4a)m(K)

(7)

where K is the wavenumber (=4rr/~) of disturbances to which the radar is sensitive and q~,(K) is the three-dimensional wavenumber spectral density for refractive index fluctuations. For locally homogeneous and isotropic inertial range turbulence qb~(k) = 0.033C,Zk- 11t3

(8)

where k = 2~r/L The refractivity structure constant Cg is related to the mean-square fluctuations (An) ~ of radio index of refraction by Cg = 5.45( An)2Lo 213.

(9)

By substitution of equation (8) into equation (7) we find Vturb = 0.38CgA- 1/3

(I0)

~turb = 2.07(An)2Lo 21ah- lt3.

(11)

and using equation (9)

For a detailed derivation of these results see HARDY et al. (1966). It is instructive to examine the above relationship in terms of the mean square electron density fluctuation (ANe) 2 for mesospheric applications. WOODMAN and GUILL~N (1974) show [f~ ANal 2 (An) 2 = [ 2 f 2 N e ]

(12)

wherefp is related to the local electron density byfp = (80.65Ne) lj2, and the transmitter frequency f = c/A where c is the velocity of light in vacuo. Combining equations (11) and (12), r]tur b =

3.25 x 103(AN~)2c-~L~213)d 1/3

(13)

where a strong wavelength dependence of the volume reflectivity is indicated. b. Fresnel (partial) reflection Fresnel reflections (also termed partial or specular reflections) from coherent structure and sharp gradients have long been thought to play an important role in long distance radio propagation. As with turbulent scatter, this mechanism appears to contribute to radar echoes both from the lower neutral atmosphere and the ionosphere, especially at vertical incidence for long wavelength radars. In the

466

B.B. Balsley and K. S. Gage

(Pageoph,

ionosphere partial reflection sounding has a long history starting in the early 1950s. Most experiments have been made in the frequency range 1-5 MHz. This work has been reviewed by BELROSE(1970) and more recent developments are surveyed by EVANS (1974). Recent work in the lower neutral atmosphere with VHF radars has offered considerable evidence for the importance of Fresnel reflections from stable, horizontally-layered structure in the troposphere and stratosphere (GAGE and GREEN, 1978; R{)TTGERand LID, 1978; FUKAO et al., 1978; ROTTGERand VINCENT,1978) and in the mesosphere (FUKAO et al., 1979). The general form of the power reflection coefficient ]p[2 for an electromagnetic wave at vertical incidence upon an infinite horizontal layer is (e.g., WAIT, 1962) lPl2 = 4

-/2 ~ e x p

---

(14)

dz

IAnl2 w (-t'/2 d(n/An_____~)exp [-47riz*] dz* 2 4

. , +~.12

dz*

(15)

where z is altitude, 1 is the thickness of the layer, An is the total change of n across the layer, l* = l/A and, z* = z/l. For some simple layer shapes the integral can be expressed in closed form. For a step of magnitude An Ipl2= IAnl2/4.

(16)

For the constant gradient, Ipl 2 = ~

~

9

(17)

For a smoothly varying layer of the form exp 4z*

]

n = no + An 1 ; e - - ~ z * ) J

(18)

the reflection coefficient is given by (FRIEND, 1949) IPI~=

[An[2[ 9l* ] 2 4 [sinh~l*)J

(19)

The oscillations in equation (17) are the result of interference caused by the discontinuities in dn/dz. Variation of IPl 2 as an inverse power of I* is typical. The approximate expressions used by SAXTON et al. (1964) and GAGE and GREEN (1978) are intended for estimation of [p[2 to an order of magnitude in the absence of detailed knowledge of the shape of layers of refractive index. c. Thermal (incoherent) scatter

Several of the large radars listed in Table 1 have been used for the past two decades to observe the weak scattering from random thermal motion of electrons. The subject

Vol. 118, 1980)

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467

of thermal scattering has been reviewed by EVANS(1969, 1974). Most of the research in this field has been limited to altitudes above 80 km and will not be considered here. Recently, however, thermal scatter has been observed down to 65 km at Arecibo (HARPER, 1978), and to even lower heights at Chatanika (HuNSUCKER, 1974; REAGAN and WATT, 1976) under disturbed conditions. The volume reflectivity for thermal scattering is, with some simplification, ~7<.~. = Need2

(20)

where Are is the number density of electrons and oe (~10 -2a m 2) is the backscattering cross-section of an electron. The received power is proportional to the electron density, and the altitude profile of received power can be used to obtain the altitude profile of electron density. Thermal scatter can be a useful technique for probing the ionized portion of the middle atmosphere, especially for radars operating at wavelengths less than one meter. At these wavelengths the turbulent echoes at mid stratospheric heights and higher will be suppressed, since the pertinent fluctuations are viscously damped. This allows measurement of the background electron density, a necessary parameter in assessing the relative contributions of the turbulent fluctuations. Also, since the electron and neutral particles are strongly coupled below about 90 kin, the Doppler shifted echoes provide a measurement of the neutral wind.

d. General comments on M S T scattering and reflection mechanisms

In the above discussion we have considered a number of scattering and reflection mechanisms appropriate to MST radar studies. The relative importance of each mechanism is assessed in the following paragraphs. It is clear that turbulent scatter (including turbulent scatter enhanced by free electrons) holds the dominant role for continuously measuring winds, waves, and turbulence at all heights. The major limitations of turbulent scatter at VHF and UHF are that (1) typically the electron-density-enhanced scatter from the mesosphere is possible only during the daytime, and (2) in the upper stratosphere and mesosphere, turbulent echoes may not be continuous on spatial scales less than a few hundred meters. However, except for determining the diurnal variations of mesospheric turbulence and winds or for the examination of fine scale vertical structure of atmospheric parameters, these limitations do not appear to be of major importance. Comparison between Fresnel reflection echo amplitudes and turbulent scatter echo amplitudes appears to offer an excellent means of studying atmospheric stability at all heights and of possibly extending the maximum height range of VHF ST systems. It is worthwhile pointing out that the possibility of Fresnel-like reflections at off-vertical angles from large refractive index structures has been considered (METCALFand ATLAS, 1973). This may be the cause of the strongly varying off-vertical

468

B.B. Balsleyand K. S. Gage

(Pageoph,

echo amplitudes obtained on MST/ST radars. This particular idea, however, is embrionic, and much remains to be done. Thermal scatter is an additional useful adjunct that can be used to measure the background electron densities and the mesospheric winds during daytime without depending on the presence of neutral turbulence. Therefore, it enables sensitive radars operating at wavelengths smaller than the local minimum scale of turbulence to monitor the mesospheric wind field. However, studies of turbulence parameters are precluded at heights where the scattering scale size is smaller than the minimum scale of turbulence. Scattering from meteor trails has the potential of extending mesospheric wind (and possibly turbulence) studies to nighttime periods. This mechanism which may be considered as a Fresnel reflection process (GRoSSI et al., 1972) yields useable data during daytime and nighttime from about 75 km to 100 km on radar systems with MST capability. Preliminary results at Poker Flat indicate that two orthogonal antenna directions can be used to determine the average mesospheric winds with good resolution (BALSLEYet al., 1979). 4. Stratospheric observations

Enormous progress has been made during the past five years in observing the lower (neutral) atmosphere below 20 km using Doppler radar. In recent years many observations and experiments have documented the capabilities of Doppler radar for observing wind, waves, turbulence and even atmospheric stability. Many of the recent developments have been surveyed by GAGE and BALSLEY(1978). Here, we summarize the Doppler radar capabilities for observing the clear neutral atmosphere, focusing attention on those developments which are of special interest in studying the middle atmosphere. Two types of radar echoes will be considered in this section. The first type is the echo received via turbulent scatter. These echoes provide a measurement of the radial component of the wind and the intensity of refractivity turbulence as a function of height. A time sequence of such measurements enables the observation of at~ospheric motions over a wide range of periods and heights. The second type of echo arises from Fresnel reflections when the radar antenna is directed vertically. The intensity of these reflections has been shown to be well correlated with atmospheric stability. Experiments to date indicate that these echoes are much stronger at longer wavelengths; their presence constitutes a new dimension in radar probing for VHF radars. a. Winds

Figure 9 shows a typical set of normalized Doppler spectra vs. height for the Platteville radar produced from observations taken on the north antenna on 7 February 1979 in the presence of a moderate jet stream. The radial velocity scale is

Vol. 118, 1980)

The MST Radar Technique

Platteville MST Radar (North Antenna)

469 7 February 1979 16,'20 MST

S/N (dB) _~

-7

~

km (MSL) 23.3

-

~

14.6

12.5 10.3 8.1 5.9 3.8 1.6

-20

-15

-10

-5 0 5 Radial Velocity (m/s)

l0

15

20

Figure 9 Normalized echo power spectra versus height at 725 m intervals obtained from the prototype MST radar at Platteville, Colorado. Signal-to-noise ratios shown on the left for every third height. The X's denote the computer-estimated mean spectral shift (scaled here in radial velocity). For S I N <_ - 17 dB, the X's represent the mean spectral shift of the noise level in the absence of signal and should be ignored. proportional to the Doppler frequency shift and the mean shift of each spectrum is approximately the mean radial wind velocity in the radar-observed volume. For the 15~ antenna zenith angle the horizontal wind velocity is about a factor of four larger than its projection along the antenna beam. This example shows the profile of the southward wind with a maximum southward velocity close to 30 m/s. Vertical profiles of the radar-observed horizontal winds have been compared with vertical profiles of horizontal winds deduced from balloon sounding techniques for several of the radars considered here. As might be expected, the quality of the agreement is best for nearly simultaneous, nearby observations. The agreement deteriorates somewhat over rough terrain where temporal and spatial variability of the wind is large. A profile of wind speed and direction observed by the Arecibo radar (FARLEY e t a l . , 1979) is presented in Fig. 10. This profile, extending in altitude to above 20 km, was obtained from analyzing VAD (Velocity Azimuth Display) data as a function of height. Also shown is the wind profile obtained nearly simultaneously by the NWS (National Weather Service) rawinsonde launched from San Juan, PR (about 70 km east of Arecibo). Taking this separation into account, the agreement is excellent.

470

B.B. Balsley and K. S. Gage

(Pageoph,

Puerto Rico 6 April 1977 ....... Rodar Derived Winds(Arecibo) Igh 39rn - 2Oh 13 m(60*W) --

Rowinsonde Winds (Son Juon) 19h O O m - 2 O h 51 m

25

I

I

I

v

~o

I I0

20

Wind Speed (m/s)

50

t 0

100

200

500

400

Wind Direction (Degrees)

Figure 10 Comparison of vertical profiles of wind speed and direction observed by Arecibo radar on 6 April 1977 with nearly simultaneous NWS rawinsonde observation from San Juan, Puerto Rico. (After FARLEYet al., t979.)

Additional profiles from Chatanika and Arecibo (which both use relatively expensive dish antennas) show excellent agreement when compared with routine balloon wind observations. Although not included herein, similar comparisons made with the Sunset radar (GREENet al., 1979), the temporary Poker Flat radar (ECKLtJND et aL, 1977), and the Platteville radar (ECKLUNO et al., 1979) demonstrate that at longer wavelengths the less expensive radars employing phased arrays can obtain equally accurate wind profiles. Continuous - or essentially continuous - radar wind observations are very useful for the study of mesoscale variations in the atmospheric wind field. Figure 11 (from ECKLUND et al., 1979) shows a sequence of hourly averaged wind profiles observed over a 48-hour period using the prototype MST radar at Platteville. Times of synoptic rawinsonde observations are indicated by darkened profiles. Clearly, much of the variability in the wind field was missed by the twice daily synoptic soundings. Similarly, a set of observations by the Sunset radar of a jet stream passage on 15-16 April 1976, has been analyzed (GREEN et al., 1978) to yield a time height cross-section of vertical and horizontal winds over the radar site. The variability of the mesoscale wind can be determined simultaneously at many altitudes using the time series of wind observations available from long observing periods. GAGEand CLARK(1978) have analyzed the variability of the jet stream winds

Vol. 118, 1980)

The MST Radar Technique

471

RADAR-DERIVED WIND VELOCITY Plotteville, Colorado

2~ 5

_ 210m/s 0 ]

+210 '!

EASTWARD

Of " r ~"4~'"" '8a"i"~''.',:'T. : ~: 1 ",:16 V"2Z"L: :,":: 20:,:,.'",: ol": : :,'.:,'.";" " , '2"". : " 4"7 8 '""''12"" '"/"16": "" '" ":20"': " "O[ k 7 FEB. 1978 + 8 FEB. 1978

co E 10

5

-20rn/s 0 +20 i ,i

:ii:,iiii 0 4

p,

ili;'ii i v ' , " / , " J / . " . ' : , " : , L , , : i :, ,,,::::, ii i,","",.".';';'].",'i."",,I 8 12 16 20 0 4 8 12 16 20 0 7 FEB. 1978 "4 8 FEB 1978 --

SOUTHWARD

Figure 1l Hourly averaged wind profiles observed by the Platteville, Colorado radar. The darkened profiles at 05 hr and 17 hr correspond to times of synoptic rawinsonde observations at Denver. (After ECKLUNDet al., 1979.) observed by the Sunset radar over a 14-hour period on 15-16 April 1976. Although a systematic height variation was found in the power law for lag variability (cr~ = [v(t) - v(t + r)] 2, where v is velocity and r is time lag) over lags r ranging from a few minutes to several hours, the average variability for all heights combined, satisfies a r ua power law. If the temporal variability follows the 1/3 power law out to lag times of several hours during such large winds, spatial variabilities on scales of several hundred kilometers must also be consistent with the same power law. Since a 1/3 power law for lag variability is consistent with k -5/3 inertial range (GAGE, 1979), these observations provide evidence for a mesoscale inertial range. Because turbulence cannot be three-dimensionally isotropic on these scales, this is probably a two-dimensional k -513 inertial range (KRAICHNAN,1967; GAGE, 1979). The vertical wind component can be determined from the Doppler shift of the echoes from turbulent irregularities. Vertical velocities can be inferred from a VAD (Velocity Azimuth Display) or from a vertical scan at one azimuth. Vertical velocities derived from these methods are subject to errors arising from horizontal gradients of the wind, etc. (BALSLEY et aL, 1977). A more direct method is to measure the vertical velocity using a vertically-directed radar beam. This latter method suffers from the problem of differentiating the spectrum of the slow vertical motions from that of stationary terrain echoes arriving via the antenna sidelobes. Vertical profiles of the vertical velocity obtained sequentially during a two-hour period by all three methods at Chatanika (PETERSON and BALSLEY, 1980) are reproduced in Fig. 12. With some exceptions, these measurements show the same approximate magnitude

472

B.B. Balsley and K. S. Gage I

I

I

[

(km) 20

4

(Pageoph,

r

Chatanika, Alaska 21 October 1976

10

e"~" o I -i,o

1

I

I

I

I

1,0

Vertical Velocity (m/s)

Figure 12 Vertical profiles of the vertical wind inferred from Chatanika radar data (PETERSONand BALSLEY, 1980). The dashed lines refer to azimuth-scan data (VAD), dashed-dotted lines to elevation-scan data, and the solid line to data obtained with the antenna directed vertically.

of the vertical velocity. Of the three methods, the most accurate is to directly measure the vertical velocity with a vertically directed beam. It is important to realize that these results provide local measurements of the vertical v e l o c i t y - in this case the vertical velocity was probably associated with a lee w a v e - and it is not surprising that the magnitude of the velocities so obtained are considerably greater than the ' m e a n ' synoptic scale vertical velocities derived indirectly from routine rawinsonde data. b. Waves Any technique that can be used to continuously measure wind or other atmospheric variables at many heights is ideal for observing atmospheric waves. Atmospheric waves of periods ranging from seconds to days have been observed using MST/ST radars. Here we illustrate the kinds of observations that can be made by selecting examples of each type of wave motion that has been observed to date. On the shortest time scale, the microbarom is a very short period infrasonic wave of period close to 5 seconds (DoNN and R~NI~, 1972). Microbaroms are thought to be generated by ocean waves and travel to great distances in the atmosphere. They are associated with pressure amplitude variations of a few microbars and have been studied primarily by sensitive ground-based pressure sensing devices. Preliminary data showing relatively continuous short period (_~ 4 s) intensity fluctuations in backscattered power have been observed using the Jicamarca radar (LAGoS, private communication). These fluctuations are seen at tropospheric-stratospheric heights,

Vol. 118, 1980)

473

The MST Radar Technique Gravity Wave Observations Sunset Radar April 15,1976

[~

I

I

,

[--

I

t,..

~

I

~,

I

N---

"Yr%'4

~

~D"

~

k.x-W

--V

~__.~ ,t ~ - " -

,-'-, "~

Lt~"w It_ ._

V

x/v ~

[_~ ~

,'~

~

..... ~ .~

~

~v-

~-J

~

,oK,

..., _...~ ___I ~~/-LI ~K"

.y ......

~

".' V J

"-4 V

...._ .,'-, _..-.__ ~,f v w--'r

.~A

V ~

-v

v',,,'~"

L ....

-I

-'-" k /

V - w

I__AS

k~_.l

v-,,~y~---~/\ ....

wv-.

_ k - ~ v

_

.,.~.

~j~K~

.,,-,

.

,

.-1

~.~ . . . . --~.~_13K~

L

I

I

I

I

I

1600

1610

1620

1630

1640

1650

IO5 ~ W Time

Figure 13 Fluctuations in the detrended radial velocity due to gravity waves observed on the north-directed antenna of the Sunset radar on 15 April 1976. (GREEN and VANZANDT, private communication, 1978; see also VANZANDT e t aL, 1979.)

are coherent over a few km in height, and the fluctuation intensity appears to be quite anisotropic with respect to antenna azimuth. It has not been possible to isolate the mechanism whereby microbaroms would modulate the normal echoes and clearly much more research will be required to understand this phenomenon. Internal gravity waves of a few minutes period have been observed in the troposphere by the Sunset radar (VANZANDT et al., 1979) and in the lower stratosphere by the Jicamarca radar (R/3sTER et al., 1978). Figure 13 shows gravity waves observed during the passage of a jet stream over Sunset radar on 15 April 1976. The observed

474

B.B. Balsley and K. S. Gage

(Pageoph,

wave properties are in good agreement with theoretical calculations (GRANT, 1979; VANZANDT et al., 1979) which show that the waves are generated in a region of high shear near 7 kin. Gravity waves of longer periods (a few hours) are also evident in the jet stream observations but have not yet been studied extensively. Waves of tidal period have been observed recently (FUKAO et al., 1978) at stratospheric altitudes at Jicamarca. The quasi-vertical wind (obtained from a 1.06 ~ wide antenna beam at a zenith angle of 0.36 ~ observed at Jicamarca during a 24 h period spanning 23-24 May is shown for several stratospheric altitudes in Fig. 14. Although these data are contaminated by horizontal winds (causing the non-zero mean), they show evidence of tidal oscillations in the true vertical velocity on the order of 1-2 cm/s. Zonal winds observed in the same experiment showed a very large diurnal component of amplitude of 1-5 m/s. Planetary waves are easily observed as they propagate past an MST radar. Figure 15 shows the oscillations in the meridional component of the wind due to travelling Rossby waves observed by the Platteville radar (ECKLUND et al., 1979) during the seven day period 7-14 February 1978. These waves are most evident in the large synoptic-scale structure of jet stream winds. Their maximum amplitude is of the order of 50 m/s and their observed periods range from about a day to many days. In accordance with the Rossby wave dispersion relation, the short wavelength Rossby waves propagate most rapidly from west to east while the largest scale waves may be stationary or even propagate westward. c. Turbulence

There are several ways in which quantitative measurements of turbulence can be deduced from clear air radar observations. These include estimates from (1) the mean refractivity turbulence structure constant C~ observed in the radar volume, (2) the width of the observed Doppler spectrum, and (3) time series analysis of observed mean winds. According to theory, the volume reflectivity from clear air echoes is proportional to the refractivity turbulence structure constant C~, provided the radar half-wavelength lies within the inertial subrange. For stationary turbulence C~ is deft'ned by [n(r0 + r) - n(ro)] 2 = C~r 2t~

(21)

where n is the radio refractive index. It provides a measure of the intensity of refractivity turbulence in a manner anaIogous to the way in which r provides a measure of the intensity of velocity turbulence. The gross structure of turbulence in the free atmosphere is intermittent in time and inhomogeneous in space with active turbulence confined to thin horizontal layers. Within the turbulent layers the small-scale structure of turbulence approaches a locally homogeneous and isotropic condition and approximately conforms to inertial range turbulence theory. In view of the inhomogeneity of the gross structure it is

Vol. 118, 1980)

The MST Radar Technique

475

qUASI-VERTICAL WINO

q

' '

~

" ~.J~*'~t;

'iJ

0.2

',',r ~, .~" 4 0 . ,

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useful to distinguish between local and volume measures of turbulence. For example, the radar measures a volume-averaged C~ which is related to the local (C.)tu~b by C~ = F. (C~)tu~b

(22)

where F is the fraction of the observed volume which is turbulent (VANZANDT et al., 1978). A radar measurement of C~ can be obtained from the amplitude distribution of the Doppler spectra such as are shown in Fig. 9. Note that the peak amplitudes of the spectra in Fig. 9 are normalized. The actual integrated signal-to-noise ratio, S/N, is given at the left of each spectrum. Note, also, that the S / N values decrease by more than a factor of 104 from 3 to 17 kin. The observed S / N c a n be expressed in terms of the volume reflectivity. Since the volume reflectivity is directly proportional to C~, the vertical profile of received power with height can be converted to a vertical profile of C~. Radar observations of C~ sometimes show more than an order of magnitude

476

B.B. Balsley and K. S. Gage

(Pageoph,

P L A T T E V i L L E . COLORADO R A D A R - D E R I V E D WIND PROFILES SOUTHWARD COMPONENT

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Figure 15 Hourly values of the meridional wind between 6-19 km during 7-14 February 1978 obtained with the Platteville radar. Southward values are plotted above the horizontal dashed line at each height and northward values are plotted below. Magnitude scale is on left. (After ECKLUNDet aL, 1979.)

v a r i a t i o n w i t h i n m i n u t e s as s h o w n i n Fig. 16, over a few k m a l t i t u d e as s h o w n in Fig. 17, a n d h o r i z o n t a l l y with spatial d i m e n s i o n s o f a few k m as s h o w n in Fig. 18. Vertical profiles o f o b s e r v e d C~ h a v e p r o v e d especially useful i n d e t e r m i n i n g ~the

meteorological factors responsible for the observed C~. VAnZANDT et al. (1978) have h a d c o n s i d e r a b l e success i n p a r a m e t e r i z i n g m e a n C~ profiles u s i n g r o u t i n e r a w i n s o n d e o b s e r v a t i o n s o f w i n d , t e m p e r a t u r e a n d h u m i d i t y . T h i s has b e e n a c c o m p l i s h e d despite i

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Vol. 118, 1980)

477

The MST Radar Technique 16

1

I

I

14--

(~

19 March 1976

12

" ~ /,~

on Denver Rawinsonde 25101~

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Figure 17 Comparison of the vertical profile of C~ observed by the Sunset radar on 19 March 1976 with calculated values using a new theoretical model. T and J indicate the altitude of the tropopause and jet stream maximum velocity, respectively. (After VANZANDTet aL, 1978.)

Figure 18 Spatial variation of relative echo power (oc C~) observed at a height of 12 km by the Chatanika radar. These data were obtained by observing the echo power at one range as the antenna rotated 360~. Shaded regions indicate antenna azimuths where the radial velocity is near zero, precluding accurate determination of echo power. (Similar to BALSLEYet al., 1977.)

478

B.B. Balsleyand K. S. Gage

(Pageoph,

several assumptions and approximations in the analysis, the most severe of which is the use of a constant value of 10 m for Lo, the outer scale of turbulence. The theoretical model used by VanZandt et al. has been calibrated against radar observed mean C~ profiles and comparisons have been presented for several MST/ST radars (GA~E et al., 1978). A sample comparison of observed and calculated vertical profiles of C~ is shown in Fig. 17. This model, although still under development, shows considerable promise for the development of a climatology of C~ from archival meteorological data. Such a climatology would have several applications, including guidance for designing new MST radars for different parts of the world. The rate of dissipation per unit mass of turbulent kinetic energy Ea is an important turbulence parameter. The relationship between C~ and Ea is discussed in some detail by GAGE and BALSLEY(1978) and GAGE et al. (1979). Recent developments have raised the possibility that under certain circumstances ga can be determined from radar observations of C~ alone. The width of the Doppler spectrum may provide an independent measure of Ed under suitable circumstances. The technique has been developed for use with microwave Doppler radars that are sensitive to hydrometeors. For such radars the observed Doppler spectral width is partly due to the variance of precipitation fall speeds so that special techniques have had to be developed to infer the spectral width of the turbulent component alone (GORELICKand MEL'NICHUK,1938; FRISCHand CLIFFORD, 1974). The determination of ea from clear air Doppler radars is inherently simpler, but still involves practical measurement difficulties. This aspect of the subject has also been considered in more detail by GAGEand BALSLEY(1978). The remaining technique for obtaining estimates of ea employs the familiar spectral, or time series, analysis of a sequence of wind observations. To obtain ca, the velocity spectrum of the velocity structure function is determined first. After demonstrating the inertial range dependence of the spectrum or structure function, known relationships between these quantities and ea can be used to deduce ca. For small-scale turbulence this technique has been used by KROPFLI(1971) and LILLY et al. (1974) to determine Ea from aircraft observations. FRISCHand STRAUCH0976) used this technique to determine ea from microwave Doppler radar observations during a convective storm. ELLSAESSER0969) also used this method to estimate Ea for largerscale motions, but there is still some controversy concerning the applicability of the theory to these larger scales of atmospheric motion. d. Stability

Hydrostatic atmospheric stability is proportional to the potential temperature gradient. The potential temperature gradient is related to the gradient in absolute temperature T by 1~0 08z-

I(~T ) T ~-z + p

(23)

Vol. 118, 1980)

479

The MST Radar Technique

where 0 is the potential temperature and F is the adiabatic lapse rate of 9.8~ Hydrostatic stability plays a very important role in determining the dynamics of the atmosphere. Very stable atmospheric regions suppress vertical motion and microscale turbulence and permit the development of large vertical gradients of wind, humidity, pollutants, ozone, etc. In Section 3b the theory for Fresnel reflection from stable atmospheric layers was presented. Below, we review some of the recent observations by VHF radars that demonstrate the existence of Fresne! reflection echoes from the troposphere and stratosphere, reveal the close relationship between these echoes and atmospheric stability, and show how the presence of these echoes can be used to determine the height of the tropopause. With the Sunset radar, it is often observed that the signal received on the vertical antenna is considerably enhanced compared to the signal received on antennas pointed 30 ~ off the zenith (GAoE and GREEN, 1978). This enhancement has been attributed to Fresnel reflection from stable regions of the atmosphere. The enhanced intensity and the narrowed spectral width of the vertical returns appear to be directly related to the stability of the atmosphere. Similar observations have been made using a bi-static radar (GAGE et al., 1973) and more recently using the monostatic SOUSY radar (RGTTGER and LIU, 1978) and the Jicamarca radar (FuKAO et al., 1979; see Fig. 19). A comparison of the vertical and oblique power profiles using the Sunset radar

MEAN SIGNAL POWER PROFILES 23 MAY 12-18 LT 24 MAY 8-12 LT 90~ / ~

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Figure 19 Mean signal power versus height in quasi-vertical ( - 0 . 4 ~ to southwest) and off-vertical ( = 3.5 ~ to west) antennas observed at Jicamarca on 23-24 May 1974. (After Fu~Ao et al., 1979.)

480

B. B. Balsley and K. S. Gage f8

)elec~

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Vertical profiles of the normalized received signal observed by the Sunset radar near 0000 UT, 26 March 1977. Also shown are the vertical profile of potential temperature gradient and the vertical temperature profile from 0000 UT, 26 March 1977, Denver NWS sounding. (After GAGE and GRgEN, 1978.) on 26 March 1977 appears in Fig. 20. The vertical profile of the measured temperature and the inferred potential temperature gradient obtained from the nearly simultaneous Denver radiosonde are also shown in this figure. The radar power profiles have been normalized and range corrected to compensate for the r - 2 range dependence, Note that the power profile at vertical incidence is correlated with the vertical profile of the potential temperature gradient (at least up to 14 km where the radar signal becomes very weak). Note in particular the increase in radar signal just above the tropopause at 10 km. Also, the strongest signal received on the vertical antenna is from the height of a very stable region near 13 km. Even though the details of the reflection mechanism are quite complex, the technique holds promise of a quantitative measure of atmospheric stability. A very practical application of the enhanced Fresnel reflection echoes is the determination of the height of the tropopause. GAGE and GREEN(1979) have presented a comparison of tropopause heights in the vicinity of Denver, CO, as determined by the routine NWS Denver soundings and by the Sunset radar. The comparison reproduced in Fig. 21 covers the three month period March-May 1977. The tropopause during this period varied between 7 and 14 km and in almost all cases the radar tropopause was found to agree within the altitude increment of the one kilometer range gates. The ability of VHF radars to observe Fresnel reflection echoes in stable regions of the atmosphere enables the longer wavelength ST radars to observe considerably higher into the stratosphere than would be possible using turbulent scatter alone. Although it may be possible to extract vertical velocities from the narrow specular

Vol. 118, 1980) 16r-- !

The MST Radar Technique [

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Figure 21 Sampled time series of the tropopause height determined from Denver radiosonde data for March 1977 and concurrent estimates of the tropopause height determined using the Sunset radar. (After GAGEand GREEN,1979.)

echoes, echoes obtained from turbulent scattering at oblique incidence will still be needed for the measurement of horizontal velocities.

5. Mesospheric observations

a. Thermal scatter

As discussed earlier, although the MST technique presumes a non-thermal scattering process involving turbulence-generated refractive index fluctuations, radar returns via thermal (incoherent) scattering also yield useful data on the background electron density and the neutral wind field9 Mesospheric thermal scattering experiments at Arecibo have been reported by MATTHEWS (1976) and HARPER (1978). At the 430 MHz Arecibo operating frequency, mesospheric returns must arise from thermal scatter, since the equivalent 37 cm backscattering wavelength is much smaller than the minimum scale of turbulence (see Fig. 8 and RASTOGI and BOWHILL, 1976a). Harper's results, which go down to about 65 km, yield an estimate of the electron density profile as well as series of spectra showing the inferred horizontal velocity of the ion-neutral background. Figure 22 is a profile of the zonal wind between 65-87 km obtained by scaling the mean spectral shift shown in Fig. 1 of HARPER (1978).

482

B.B. Balsleyand K. S. Gage

90

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Arecibo, RR 25 September 1977 IlO0-

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65

b. Non-thermal scattering Earliest evidence of enhanced VHF backscattering from mesospheric heights was reported by BOWLES(1961) using a high powered 41 MHz radar in Illinois. He found enhanced echoing strata at a number of heights between 55-85 kin, and inferred horizontal velocities of about 20 m/s from the signal fading rate. Similar strata between 70-80 km at equatorial latitudes (Jicamarca) were reported by FLOCK and BALSLEY(1967) who attributed the echoes to turbulent scattering in the presence of an electron density gradient. The potential of using sensitive VHF radars to study both the total wind field and turbulent processes in the mesosphere was first appreciated by WOODMANand GUILL~N (1974) in their pioneering work at Jicamarca. Excellent time resolution records of the wind field showed not only mean and tidal components but also revealed the presence of strong velocity perturbations arising from gravity waves. An example of these perturbations taken from their paper is given in Fig. 23. Woodman

Vol. 118, 1980)

The MST Radar Technique

483

and Guill6n were able to explain their results in the mesosphere as well as the stratosphere in terms of a scattering mechanism based on neutral atmospheric turbulence (produced by wind shear) working on the height gradient of the refractive index. Further studies of the intermittent nature of the mesospheric echoes at Jicamarca, and the relationship of the velocity fluctuations to gravity waves were reported by RASTOO~and WOODMAN(1974) for a single mesospheric height. RASTOOIand BOWHILL (1976b) studied the gravity-wave oscillations, showing the dominant wave period to be 10-20 minutes, and inferring the horizontal wavelength to be 200-300 km. In a subsequent study RASTOGIand BOWmLL(1976C) showed that horizontally stratified regions of intermittent turbulence (with vertical dimensions of a few tens of meters) have horizontal dimensions roughly an order of magnitude less than the dominant internal gravity wave scale.

I

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Figure 23 Example of gravity-wave velocity fluctuations obtained by the Jicamarca radar on 24 September 1970. V= is zonal component and V~ is quasi-vertical. Height resolution is about 5 kin. (After WOODMANand GUILL~N, 1974.)

484

B.B. Balsley and K. S. Gage

(Pageoph,

Following the installation of a more versatile data processing system at Jicamarca that allowed for simultaneous multiheight analysis, HARPER and WOODMAN(1977) described the stratified nature of the mesospheric echoes and discussed their discontinuous spatial structure. The multiheight capability also produced zonal wind profiles between 65-85 km which supported the earlier conclusion (RAsTOGI and WOODMAN, 1974) that the semidiurnal tide over Jicamarca is small. Increased interest in mesospheric processes during the past few years has led to a series of VHF radar studies at a number of facilities. Essentially continuous measurements of scattered power and radial velocity between 60-90 km for many daytime hours using the Urbana radar have been reported by MILLERet al. (1978). An example of strong gravity wave activity is shown in Fig. 24 (Fig. 1 in MILLER et aL, 1978). Periods on the order of minutes are apparent in this example. FUKAO et al. (1979) have recently compared mesospheric zonal wind profiles between 62-85 km measured by the Jicamarca radar (12~ latitude) with profiles between 40-65 km measured by meteorological rockets at Ascension Island (8~ latitude) during the same season. This comparison appears in Fig. 25. The good agreement in the region of overlap has been taken by FUKAOet aL (1979) as confirmation that the radar indeed measures neutral wind. Figure 19 (also from FUKAOet al., 1979) shows that mesospheric echoes below 70 km (or sometimes somewhat higher) are stronger when observed with a vertically directed antenna- a feature noted previously in troposphere-stratosphere returns by GAGE and GREEN (1978) and R6TTGEV, and Lru (I978) and ascribed to Fresnel reflection.

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485

The MST Radar Technique

Vol. l18, 1980) 90

80

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Comparison of zonal wind velocities by the Jicamarca radar (9-12 UT, 24 May 1974) and rockets at Ascension Island (April-June 1974). (After FUKAOet al., 1979.)

High resolution (~ 150 m) VHF radar studies of turbulent mesospheric structure using the SOUSY radar have recently been reported by R6TTGER et al. (1979). Their results show three separate types of turbulent structure: blobs and sheets, which are sporadic in nature, only a few hundred meters thick, and which occur preferentially between 60-70 km; and layers, which are thicker (___2km) and which occur above 70 km. ROTTG~Ret al. (I 979) also discuss the possibility of Fresnel reflection contributions below 70 km. Recent mesospheric results from the prototype MST radar at Platteville have been reported by ECKI~UNDet aL (1979). In addition to the strong day-to-day and hour-to-hour variability of the scattered power reported by many investigators, occasional measurements of the zonal wind component were obtained with relatively good time resolution. Figure 26 (from ECKLUNDet aL, 1979), shows an example of the mesospheric zonal wind. A major feature of the Platteville radar is that it is run on a virtually unattended basis: it was only necessary to visit the site every few days to change data tapes.

486

B . B . Balsley a n d K. S. G a g e

(Pageoph,

PLATTEVILLE,COLORADO RADAR-DERIVED WIND PROFILES EASTWARDCOMPONEN

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MST

M e s o s p h e r i c Winds Radar, Poker Flat, A l a s k a 24 February 1979

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Vol. 118, 1980)

The MST Radar Technique

487

\

W

S

Transmitter Module

Poker Flat MST Radar

Figure 28 Artist's conception of the complete Poker Flat MST radar.

A seasonal variability in the height of the predominant mesospheric echoing region has been reported by CZECHOWSKYet al. (1979) using the SOUSY radar. These authors report that the region of maximum echoes in winter is 70-80 km, and although echoes from this region are occasionally observable in summer, there is an additional stronger region of echoes between 80-90 km during summer. Finally, a continuous eight hour record of high-latitude mesospheric winds in the height range 62-71 km obtained by the MST radar under construction at Poker Flat, Alaska, is shown in Fig. 27 (BALSLEYet al., 1979). The general trend of southerly to westerly flow, from noon to sunset seen in Fig. 27 was observed during a period of moderate ionospheric absorption (2-3 db at 30 MHz), so that the mesospheric ionization density was somewhat enhanced (PARTHARSARTHYe t al., 1963). The antenna configuration for the Poker Flat MST system, shown in Fig. 28, consists of two superimposed but independent dipole arrays that are phased to produce two orthogonal beams fifteen degrees from vertical. The system is being designed to operate on a nearly continuous, relatively unattended basis. Although these data were obtained with the system operating at greatly reduced sensitivity (three orders of magnitude less than the eventual system), they demonstrate the potential of MST systems for making continuous observations.

488

B.B. Balsley and K. S. Gage

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6. Concluding remarks This paper was intended to examine the potential of the MST radar technique for studies of the middle atmosphere. Toward this end we have attempted to review the large body of literature that has already been written. It appears that there is an unparalleled opportunity to study atmospheric dynamics between the ground and an altitude of about 100 km using the MST technique.

Figure 29 Artist's conception of a small ST radar mounted on an ocean buoy. Currently, radars of this size are capable of continuously measuring winds, waves and turbulence up to at least 15 km with 2 km resolution (cf. Fig. 11).

Vol. 118, 1980)

The MST Radar Technique

489

Topics ranging from the general circulation of the atmosphere to the dynamic coupling between the troposphere, stratosphere and mesosphere, and the morphology of atmospheric waves and turbulence are all amenable to study by MST/ST radars. While the future for MST studies looks bright, there are a number of problems that need to be addressed: (1) except for particle precipitation events and for meteoric scatter above about 75 km, mesospheric echoes occur only during the daytime; (2) although high resolution ( ~ 100 m) sounding is possible in the lower atmosphere and at some mesospheric heights, such resolution over the complete height range would require extremely sensitive radars if the echoing regions are distributed and not stratified; (3) while the cost of an ST radar is moderate (~$100K), the cost of an MST facility is in the vicinity of $1000K; (4) MST observations of winds and turbulence parameters have yet to be sufficiently corroborated by other techniques (i.e., balloons, rockets, satellites, partial reflection drift facilities, etc.). This problem is specially acute in the mesosphere. As of this writing, troposphere-stratosphere research using MST and ST radars is more active than mesospheric research. This is due in part to the proliferation of the less expensive ST radars. Research activities in the higher heights should increase with the completion of a number of proposed MST systems (i.e., Poker Flat, MU, and Urbana). Should the problems listed above be satisfactorily resolved, then a nested network of operational MST/ST radar systems (similar to the current configuration of the NWS radiosonde and M R N rocket sites) becomes attractive. In this configuration, the MST radars would provide information on winds, waves and turbulence between 1-100 km on a coarse grid and the ST radars would serve as intermediate monitors of the troposphere and lower stratosphere on a smaller spatial grid. Clearly this is an ambitious concept and one that will require a large investment in time and money to achieve. On the other hand, estimates of the costs of individual MST or ST systems, when amortized over many years, are not excessive, particularly when one considers the relatively unattended operation and the continuous data taking capability. A future MST/ST network could nicely complement the existing meteorological monitoring network by providing continuous measurements of winds, waves and turbulence. In this connection it should be recognized that the radar technique by itself is incapable of providing temperature, and humidity by conventional sounding techniques. 3) It is reasonable to expect that future ST radar systems will be more-or-less portable and will be capable of observing to greater heights. Calculations based on existing data show that portable systems capable of producing averaged profiles similar to those shown in Fig. 11 up to at least 15 km can be designed in the lower U H F range 3) A hybrid ground-based system (consisting of an ST radar to measure wind profiles and a microwave radiometer (DECKERet al., 1978) to measure temperature and humidity profiles) could operate to measure winds, temperature, and humidity on a relatively continuous basis (LITTLE, private communication).

490

B.B. Balsley and K, S. Gage

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using an array of four yagi-uda antennas and a total physical area of less than 150 mL An example of such a system is shown in Fig. 29. While this figure shows a system installed on an ocean buoy, similar systems could operate equally well on land. A number of such systems might operate temporarily, for example, in a tight grid to obtain data for mesoscale studies (e.g., orographic effects, sea-land interface, severe storms). Operation at frequencies < 40 MHz has yet to be fully examined. While there are a number of inherent problems (ionospheric reflections, radio-frequency spectrum contamination, less spatial resolution and higher background noise) in operating at lower frequencies, the early experiments of Watson-Watt and extrapolations from current VHF studies indicate that scattering and Fresnel reflections may be considerably stronger at lower frequencies. The capability of measuring vertical velocities on a continuous basis should also be emphasized. For example, proposed solutions for a number of unanswered mesospheric problems (e.g., the generation of noctilucent clouds, and the occurrence of a cold summertime mesosphere) require relatively large vertical velocities. Similarly, measurements of vertical velocities in the troposphere-lower stratosphere can yield important information on a variety of dynamical phenomena. Finally, it is worthwhile mentioning the idea of examining possible Sun-weather relationships. It is reasonable to expect that a correlation between solar variability and weather - if indeed a correlation exists - will be manifested in middle atmosphere patterns of winds and waves. Continuous observations of these parameters by MST radars, particularly in the auroral zone where ionospheric effects of solar variability are most pronounced, will provide an ideal data base for such studies.

7. Acknowledgements We are happy to acknowledge many useful and interesting discussions with T. E. VanZandt, J. L. Green, W. L. Ecklund and D. A. Carter of the Aeronomy Laboratory, NOAA, and with R. F. Woodman (Arecibo Observatory) and R. M. Harper (Rice University). We are also indebted to Mrs. H. Axtell for her prompt and efficient typing of the manuscript. This research was partially supported by the Atmospheric Research Section of the National Science Foundation. REFERENCES BALSLEY, B. B. and ECKLUND, W. L. (1972), A portable coaxial collinear antenna, IEEE Transaactions on Antennas and Propagation, AP-20, 513-516. BALSLEY, B. B., CIANOS, N., FARLEY, D. T. and BARON, M. J. (1977), Winds derived from radar measurements in the Arctic troposphere and stratosphere, J. Appl. Meteor. 16, 1235-1239. BALSLEY, B. B. (1978), The use of sensitive coherent radars to examine atmospheric parameters in the height range 1-100 kin, Preprints, 18th Conf. on Radar Meteorology (Atlanta) AMS, Boston, pp. 190-193. BALSLEY, B. B., ECKLUND, W. L., CARTER, D. A. and JOHNSTON, P. E. (1979), The Poker Flat M S T radar: First results, Geophys. Res. Letters, in press.

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BEAN, B. R. and DUTTON, E. J. (1968), Radio Meteorology (Dover, New York) 435 pp. BELROSE, J. S. (1970), Radio wave probing of the ionosphere by the partial reflection of radio waves (from heights below 100 km), J. Atmos. Terr. Phys. 32, 567-596. BOOKER, H. G. and GORDON, W. E. (1950), Theory of radio scattering in the troposphere, Proc. IEEE 38, 401-412. BOWLES, K. L. (1961), Incoherent scattering by free electrons as a technique for studying the ionosphere and exosphere: Some observations and theoretical considerations, J. Res. Natl. Bur. Standards 65D, 1-14. CHISHOLM, J. H., PORTMANN,P. A., DEBETTENCOURT,J. T. and ROCHE, J. F. (1955), Investigations of angular scattering and multipath properties of tropospheric propagation of short radio waves beyond the horizon, Proc. IEEE 43, 1317-1335. COLWELL, R. C. and FRIEND, A. W. (1936), The D-region of the ionosphere, Nature 137, 782. CUNNOLD, D. M. (1975), Vertical transport coefficients in the mesosphere obtained from radar observations, J. Atrnos. Sci. 32, 2191-2200. CZECHOWSKY, P., RfDSTER, R. and SCHMIDT, G. (1979), Variations of mesospherie structures of different seasons, Geophys. Res. Lett. 6, 459-462. DECKER, M. T., WESTWATER,E. R. and GUIRAUD, F. O. (1978), Experimentalevaluation of groundbased microwave radiometrie sensing of atmospheric temperature and water vapor profiles, J. Appl. Meteor. 17, 1788-1795. DONN, W. L. and RIND, D. (1972), Microbaroms and the temperature and wind of the upper atmosphere, J. Atmos. Sci. 29, 156-172. ECKLUND, W. L., CARTER,D. A. and GAGE, K. S. (1977), Sounding of the lower atmosphere with a portable 50 MHz coherent radar, J. Geophys. Res. 82, 4969-4971. ECKLUND, W. L., CARTER, n . A. and BALSLEY,B. B. (1979), Continuous measurement of upper atmospheric winds and turbulence using a VHF Doppler radar: Preliminary results, J. Atmos. Terr. Phys., in press. ELLSAESSER,H. W. (1969), A climatology ofepsilon (atmospheric dissipation), Mon. Wea. Rev. 97, 415-423. EVANS, J. V. (1969), Theory and practice of ionosphere study by Thomson scatter radar, Proc. IEEE 57, 496-500. EVANS, J. V. (1974), Some post-war developments in ground-based radiowave sounding of the ionosphere, J. Atmos. Terr. Phys. 36, 2183-2234. FARLEY, D. T., BALSLEY,B. B., SWARTZ, W.E. and LA Hoz, C. (1979), Winds aloft in the tropics measured by the Arecibo radar, J. Appl. Meteor. 18, 227-230. FLOCK, W. L. and BALSLEY, B. B. (1967), VHF radar returns from the D region of the equatorial ionosphere, J. Geophys. Res. 72, 5537-5541. FRIEND, A. W. (1949), Theory and practice of tropospheric sounding by radar, Proc. IEEE 37, 116-138. FRISCH, A. S. and CLIFFORD, S. F. (1974), A Study of convection capped by a stable layer using Doppler radar and acoustic echoes sounders, J. Atmos. Sci. 31, 1622-1627. FRmCH, A. S. and STRAUCH, R. G. (1976), Doppler radar measurements of turbulent kinetic energy dissipation rates in a Northeastern Colorado convective storm, J. Appl. Meteor. 15, 1012-1017. FUKAO, S., KATO, S., YOKOI, S., HARPER, R. M., WOODMAN, R. F. and GORDON, W. E. (1978), One full-day radar measurement of lower stratosphere winds over Jicamarca, J. Atmos. and Terr. Phys. 40, 1331-1337. FUKAO, S., SATO, T., KATO, S., HARPER, R. M., WOODMAN, R. F. and GORDON, W. E. (1979), Mesospheric winds and waves over Jicamarca on 23-24 May 1974, submitted to J. Geophys. Res. GAGE, K. S., BIRKEMEIER,W. P. and JASPERSON,W. H. (1973), Atmospheric stability measurements at tropopause altitudes using forward-scatter C W radar, J. Appl. Meteor. 12, 1205-1212. GAOE, K. S. and BALSLEY,B. B. (1978), Doppler radar probing of the clear atmosphere, Bull. Am. Meteor. Soc. 59, 1074-1093. GAGE, K. S. and CLARK, W. L. (1978), Mesoscale variability of jet stream winds observed by the Sunset VHF Doppler radar, J. Appl. Meteor. 17, 1412-1416.

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GAGE, K. S. and GREEN,J. L. (1978), Evidence for specular reflection from monostatic VHF radar observations of the stratosphere, Radio Sci. 13, 991-1001. GAGE, K. S., GREEN, J. L. and VANZANDT,T. E. (1978), Verticalprofiles of C~ in the free atmosphere, Preprints, 18th Conf. on Radar Meteorology (Atlanta) AMS, Boston, pp. 80-87. GAGE, K. S. and GREEN, J. L. (1979), Tropopause detection by partial specular reflection using VHF radar, Science 203, 1238-1240. GAGE, K. S. (1979), Evidence for a k-518 law inertial range in mesoscale two-dimensional turbulence, J. Atmos. Sci. (in press). GAGE,K. S., GREEN,J. L., CLARK,W. L. and VANZANDT,T. E. (1979), Doppler radar measurement of turbulence in the clear atmosphere, Proc. Conf. Fourth Symp. on Turbulence, Diffusion, and Air Pollution (RenD) AMS, Boston, pp. 522-529. GJESSlNG, D. T. (1964), Determination of isotropy properties of the tropospheric permittivity and wind velocity fields by radio-propagation methods, J. Geophys. Res. 69, 569-581. GORDON, W. E. (1978), Atmospheric dynamics in the 1980's, Position paper for the 1978 Summer Study Programs of the National Academy of Science Committee on Solar-Terrestrial Research, Rice University, Houston. GORELICK,A. G. and MEL'NICHUK,YLr. V. (1968), A new method for measuring dissipation rate of turbulence in clouds and precipitation using conventional radar, Proc. ThirdAll-Union U.S.S.R. Radar Meteorology Conf., Israel Program for Scientific Translation, Jerusalem, pp. 150-156. GRANT, J. R. (1979), Generation and characteristics of jet-stream associated gravity waves, Ph.D. Thesis, Univ. of Colo., Boulder. GREEN, .L L., GAGE, K. S. and VANZANDT, T. E. (1978), Three-dimensional wind observations of a jet stream using a VHF Doppler radar, Preprints, 18th Conf. on Radar Meteorology (Atlanta), AMS, Boston, pp. 184-189. GREEN, J. L., GAGE, K. S. and VANZANDT, T. E. (1979), Atmospheric measurements by VHF pulsed Doppler radar, to be published in the Nov. issue of IEEE Transactions on Geoscience Electronics. GROSSI, M. D., SOUTHWORTH, R. B. and ROSENTHAL, S. K. (1972), Radar observations of meteor winds above Illinois, in Thermospheric Circulation (Willis L. Webb, ed., Mass. Institute of Technology), pp. 205-248. HARDY, K. R., ATLAS, D. and GLOVER, K. M. (1966), Multiwavelength backscatterfrom the clear atmosphere, J. Geophys. Res. 71, 1537-1552. HARPER, R. M. and WOODMAN, R. F. (1977), Preliminary multiheight radar observations of waves and winds in the mesosphere over Jicamarca, J. Atmos. Terr. Phys. 39, 959-963. HARPER, R. M. (1978), Preliminary measurements of the ion component of the incoherent scatter spectrum in the 70-90 km region over Arecibo, Geophys. Res. Lett. 5, 784-786. HUNStlCKER, R. D. (1974), Simultaneous Riometer and incoherent scatter radar observations of the auroral D region, Radio Sci. 9, 335-340. KRAICHNAN, R. H. (1967), lnertial ranges in two-dimensional turbulence, Phys. Fluids 10, 14171423. KROPFLI,R. A., KATZ, I., KONRAD,T. G. and DOBSON,E. B. (1968), Simultaneous radar reflectivity measurements and refractive index spectra in the clear atmosphere, Radio Sci. 3, 991-994. KROPFLI, R. A. (1971), Simultaneous radar and instrumented aircraft observations in a clear air turbulent layer, J. Appl. Meteor. 10, 796-802. LANE,J. A. and SOLLUM,P. W. (1965), VHFtransmission over distances of 140 and 300 km, Proc. IEEE, London, 112, 254-258. LANE, J. A. (1969), Radar echoes from clear air in relation to refractive-index variations in the troposphere, Proc. IEEE, London 116, 1656-1660. LILLY, D. K., WACO, D. E. and ADELFANG,S. I. (1974), Stratospheric mixing estimated from highaltitude turbulence measurements, J. Appl. Meteor. 13, 488-493. MATHEWS,J. D. (1976), Measurements of diurnal tides in the 80- to 100-km altitude range at Arecibo, J. Geophys. Res. 81, 4671-4677. MEGAW, E. C. S. (1957), Fundamental radio scatter propagation theory, Institute of Elec. Eng. Proc., 104, Part C6, 441-456 (Monograph No. 236R).

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METCALF, J. I. and ATLAS, D. (1973), Microscale ordered motions and atmospheric structure associated with thin echo layers in stably stratified zones, Boundary Layer Meteor. 4, 7-35. MILLER, K. L., BOWHILL, S. A., GIBBS, K. P. and COUNTRYMAN,I. D. (1978), First measurements of mesospheric vertical velocities by VHF radar at temperate latitudes, Geophys. Res. Lett. 5, 939-942. PARTHASARATHY,R., LERFALD, G. M. and LITTLE, C. G. (1963), Derivation of electron-density profiles in the lower ionosphere using radio absorption measurements at multiple frequencies, J. Geophys. Res. 68, 3581-3588. PETERSON, V. L. and BALSLEY,B. B. (1980), Clear air Doppler radar measurements of the vertical component of wind velocity in the troposphere and stratosphere, Geophys. Res. Lett., in press. PROBERT-JONES, J. R. (1962), The radar equation in meteorology, Quart. J. Roy. Met. Soc. 88, 485-495. RASTOGI,P. K. and WOODMAN,R. F. (1974), Mesospheric studies using the Jicamarca incoherentscatter radar, J. Atmos, Terr. Phys. 36, 1217-1231. RASTOGI, P. K. and BOWHILL, S. A. (1976a), Scattering of radio waves from the mesosphere1. Theory and observations, J. Atmos. Terr. Phys. 38, 399-411. RASTOGI,P. K. and BOWHILL,S. A. (1976b), Gravity waves in the equatorial mesosphere, J. Atmos. Terr. Phys. 38, 51-60. RASTOGI, P. K. and BOWHILL, S. A. (1976c), Scattering of radio waves from the mesosphere- 2. Evidence for intermittent mesospheric turbulence, J. Atmos. Terr. Phys. 38, 449-462. REAGAN, J. B. and WATT,T. M. (1976), Simultaneous satellite and radar studies of the D region ionosphere during the intense solar particle events of August 1972, J. Geophys. Res. 81, 45794596. ROPER, R. G. (1977), Turbulence in the lower thermosphere, in The Upper Atmosphere and Magnetosphere, National Academy of Sciences, Washington, D.C. ROTTGER,J. and LIU, C. H. (1978), Partial reflection and scattering of VHF radar signals from the clear atmosphere, Geophys. Res. Lett. 5, 357-360. R~)TTGER,J. and VINCENT,R. A. (1978), VHF radar studies of tropospheric velocities and irregularities using spaced antenna techniques, Geophys. Res. Lett. 5, 917-920. ROTTGER,J., RASTOGI,P. K. and WOODMAN,R. F. (1979), High-resolution VHFradar observations of turbulence structures in the mesosphere, Geophys. Res. Lett. 6, 617-620. ROSTER, R., ROTTGER,J. and WOODMAN,R. F. (1978), Radar measurements of waves in the lower stratosphere, Geophys. Res. Lett. 5, 555-558. SAXTON, J. A., LANE, J. A., MEADOWS,R. W. and MATTHEWS,P. A. (1964), Layer structure of the troposphere- Simultaneous radar and microwave refractometer investigations, Proc. IEE 111, 275-283. TATARSKn,V. I. (1971), The effects of the turbulent atmosphere on wave propagation, U.S. Dept. of Commerce, pp. 74--76. VANZANDT,T. E., GREEN,J. L., GAGE, K. S. and CLARK,W. L. (1978), Verticalprofiles of refractivity turbulence structure constant: Comparison of observations by the sunset radar with a new theoretical model Radio Sci. 13, 819-829. VANZANDT, T. E., GREEN, J. L. and CLARK, W. L. (1979), Buoyancy waves in the troposphere: Doppler radar observations and a theoretical model, Geophys. Res. Lett. 6, 429-432. WAIT,J. R. (1962), Electromagnetic Waves in Stratified Media (Pergamon Press, London) Chapter IV. WATSON-WATT,R. A., WILKINS,A. F. and BOWEN, E. G. (1937), The return of radio waves from the middle atmosphere - 1, Proc. Roy. Soc. A 161, 181-196. WHEELON, A. D. (1960), Relation of turbulence theory to ionospheric forward scatter propagation experiments, J. Res. NBS 64D (Radio Prop.), 301-309. WOODMAN, R. F. and GUILL~N, A. (1974), Radar observations of winds and turbulence in the stratosphere and mesosphere, J. Atmos. Sci. 31, 493-505. YEH, K. C. and LIu, C. H. (1972), Theory of Ionospheric Waves, Academic Press, New York, 464 pages. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh~iuser Verlag, Basel

Structure and Dynamics of the Stratosphere and Mesosphere Revealed by VHF Radar Investigations By J. ROTTGER 1)

Abstract-Powerful VHF radars are capable of almost continuously monitoring the threedimensional velocity vector and the distribution of turbulence in the middle atmosphere, i.e. the stratosphere and mesosphere. Methods of radar investigations of the middle atmosphere are outlined and the basic parameters, mean and fluctuating velocities as well as reflectivity and persistency of atmospheric structures, are defined. Results of radar investigations are described which show that the tropopause level as well as a criterion on the stability of the lower stratosphere can be deduced. Besides mean wind velocities, VHF radars can measure instantaneous velocities due to acoustic gravity waves. The interaction of gravity waves with the background wind is discussed, and it is shown that cumulus convection is an effective source of gravity waves in the lower stratosphere. The vertical microstructure of the stratosphere, manifesting itself in thin stratified sheets in which temperature steps occur, is investigated by applying knowledge from investigations of the oceanic thermocline. Possible origins, like shear generation and lateral convection of the microstructure of the stratosphere, are discussed. Observations of gravity waves in the mesosphere are reviewed and their connection with turbulence structures is pointed out. Finally, some open questions which could be answered by further VHF radar investigations are summarized. Key words: MST radar; Gravity waves; Turbulence; Stratospheric structure.

1. Introduction D u r i n g recent years w i d e s p r e a d interest has developed in investigating the middle a t m o s p h e r e , which is the height region between the t r o p o p a u s e ( ~ 10 kin) a n d the t u r b o p a u s e (_~ 100 km). Intensified scientific activities p l a n n e d for the M i d d l e A t m o s phere P r o g r a m , M A P , elucidate this interest (BowHILL, 1976). T h e p u r p o s e of this p a p e r is to outline h o w m e s o s p h e r e - s t r a t o s p h e r e - t r 0 p o s p h e r e (MST) r a d a r s can contribute to study the structure and d y n a m i c s o f the middle a t m o s p h e r e (GORDON et al., 1978). These r a d a r s o p e r a t e in the very high frequency ( V H F ) b a n d at frequencies a r o u n d 50 M H z and therefore are also called V H F radars. T h e m a i n d y n a m i c a l and structural p a r a m e t e r s which can be m e a s u r e d with V H F r a d a r s are the t h r e e - d i m e n s i o n a l velocity vector and the distribution o f turbulence in the middle a t m o s p h e r e . It is obvious that V H F r a d a r observations have several a d v a n t a g e s over o t h e r techniques, viz. g o o d time and height resolution a n d rather c o n t i n u o u s determ i n a t i o n o f height profiles t h r o u g h o u t the t r o p o s p h e r e , s t r a t o s p h e r e and mesosphere. a) Max-Planck-Institut for Aeronomie, 3411 Katlenburg-Lindau 3, Fed. Rep. Germany.

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In Section 2, the experimental methods and a description of the general radar signal characteristics observed with the SOUSY-VHF-Radar (R6xmER et al., 1978) are outlined. Examples of radar observations of the stratosphere are presented in Section 3, and of the mesosphere in Section 4. Tropospheric phenomena are treated only if they have an impact on the regions above. Sections 3 and 4 are subdivided in terms of the scale sizes of the observed phenomena. Synoptic-scale phenomena, such as the variation of the tropopause as well as stability and mean wind velocities in the lower stratosphere, are discussed in Section 3.1. Mesoscale phenomena, such as jet stream and convection processes and their connection with atmospheric gravity waves, are described in Section 3.2. Turbulence as a small-scale phenomenon is treated in Section 3.3. In Section 4.1 mesoscale phenomena in the mesosphere down to the scale of gravity waves are reviewed, and in Section 4.2 turbulence structures in the mesosphere are presented and interpreted. Open questions are summarized in Section 5. The application of VHF radars to investigating the lower and middle atmosphere is a newly developing research field (WOODMAN and GUILLEN, 1974; RASTOGI and BOWHILL, 1975; BALSLEYand GREEN, 1978; GAGE and BALSLEY, 1978; GORDON et al., 1978; ROTTGER et al., 1978; BALSLEYand GAGE, 1980). Some of the preliminary results and interpretations outlined in this paper, therefore, may be tentative and hopefully will stimulate further investigations. Much research work must still be done in the future to deduce quantitative indications from the qualitative evidence of the first results. This task could be appropriately solved during special research programs of MAP. 2. Radar measurements o f the atmosphere 2.1. Methods and basic parameters

Radar probing of the atmosphere makes use of scattering and reflection from refractive index variations. The refractive index of the atmosphere in the height region up to 100 km for VHF is t 1 +nl+ n2+t

n=

with the wet term 3.7.10 -1 e

t

n1 ~

T 2

the dry term , 77.6.10-6p n2 = T ' and the ionospheric term , 1/3

-40.3Ne f2

n t

3

(1)

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In these equations, T is the absolute temperature in K, e the partial pressure of water vapor (humidity) in rob, p the pressure in mb, Are the number density of free electrons per m a, a n d f t h e frequency in Hz. Using reasonable values of T, e, p and Are, we find In[I, In, I, ]n~] << 1~ Both n[ and n~ determine the refractive index of the troposphere and stratosphere, where the wet term n[ is most essential in the lower troposphere. The ionospheric term n~ is dispersive and determines the refractive index in the mesosphere and lower thermosphere between about 50 and 100 kin. This is the D-region of the ionosphere. Depending on the height region, any discontinuity of pressure, humidity, temperature or electron density corresponds to a change An in the refractive index, which causes electromagnetic waves to be scattered or reflected. In the context of this paper, precipitation scatter in the troposphere and thermal scatter in the mesosphere are neglected. The power which a monostatic radar receives from a backscattering or reflecting region at a radial distance z is Pth 2 Pr -'= ~ ( Cs2 "q- Cr2)

(2)

where Pt is the average transmitted power, G the antenna gain, and ~ the radar wavelength. The term C~ = Az.~.G

(2a)

is the contribution due to volume scattering from turbulent refractive index variations. The scattering volume is given by the radar beam width 4, oo G-l/~ and the pulse length Az. A measure of turbulent fluctuations is the turbulence refractive index structure constant Cg which determines the radar reflectivity ~ = 0.38CgA -ls3. C~ is proportional to the mean square variations An2 of the refractive index. The backscattering process is sensitive to turbulent, i.e. random changes of n with scales of half the radar wavelength (radar wavelength filtering). The term c~ = G ~. ]pl 2

(2b)

is the contribution due to (partial or Fresnel) reflections from coherent discontinuities of refractive index perpendicular to the propagation direction of the radar signal. The reflection coefficient p is determined by the structure of the discontinuity. Reflection is simply given by the coherent superposition of wavelets reflected from structure components at half the radar wavelength. [p[Z increases for increasing changes of refractive index and decreasing thickness of smooth structures. Details on the mechanisms of scattering and reflection of VHF radar signals can be found in GAGE and GREEN (1978), RI3TTGERand LIu (1978) and BALSLEYand GAGE (1980). Radar measurements of the atmosphere, taking advantage of scattering and reflection from refractive index variations, have been in use for about half a century. This remark presumes that ionosondes, which are applied to investigate the upper atmosphere, can be regarded as radars operating in the MF (medium frequency) and

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HF (high frequency) bands. Special versions of MF radars are still being used. These are known as partial reflection drift facilities (PRD) for studying the dynamics of the mesosphere (e.g. BRIGGS, 1977). Also, scattering of VHF signals from meteor trail ionization can be used to investigate dynamic processes in the mesosphere (e.g. reviews in WEBB, 1972). Experimental evidence has existed for a long time that VHF signals can also be scattered from ionospheric turbulence structures (e.g. DAVIES, 1965). Because of strong collisional coupling between ionized and neutral particles, the refractive index variations due to ionization fluctuations in the D-region can result from fluctuations in the neutral atmosphere. VHF radar signals scattered back from these ionospheric structures therefore can be evaluated to study neutral atmosphere dynamics in the mesosphere (e.g. FLOCKand BALSLEY,1967; WOODMAN and GUmLEN, 1974). Refractive index variations in the stratosphere and troposphere have been studied for the purpose of over-the-horizon radio communication by means of VHF, UHF (ultra high frequency) and SHF (super high frequency) signals. A mutual influence of research for the purpose of radio communication and (radio) meteorology is obvious (BEAN and DUXTON, 1968). Radar meteorology, which is remote sensing of the atmosphere by making use of backscattering from refractive index variations (e.g. reviews in DERR, 1972), has emerged as an outgrowth of radio meteorology. Apart from those weather radars detecting echoes scattered back from precipitation, several radars in the UHF and SHF bands have been operated utilizing backscattering from turbulent refractive index fluctuations in the clear air (e.g. BATTAN, 1973). Only a very few of these powerful radars were able to detect echoes from clear air turbulence in the stratosphere (e.g. HARDY et al., 1969; Aso et al., 1977; CRANE, 1977). Since WOODMAN and GUILLEN(1974) showed that VHF radar signals from the mesosphere and stratosphere can be used to evaluate wind velocities and turbulence, a steadily growing interest in the MST VHF radar technique has developed. VHF radars are capable of measuring vertical as well as horizontal velocities. Mean velocities can be deduced from the Doppler shift of the echo signals, the instantaneous vertical velocities w by means of a vertical pointing antenna, and the horizontal velocities u and v from swinging the antenna beam in different directions about the zenith. Another possibility is to use the spaced antenna drifts technique, which can measure with a high degree of sensitivity horizontal velocities with vertically pointing antennas (e.g. ROTTGER and VINCENT, 1978). Fluctuating or turbulent velocities can be obtained from the width aw of the Doppler spectra (provided that instrumental errors like beam width broadening etc. are small). For turbulence scattering the spectral width aw is inversely proportional to the microscale correlation time ~- of the turbulence structures at half the radar wavelength. A further valuable parameter is the integral-scale correlation time TE, which is the integral over the autocorrelation function of the signal (FROSTand MOULDEN, 1977). TE is also called persistency since it is a measure of the longest deterministic connection in turbulence behavior, i.e. the temporal stability of a structure.

498

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The radar equation (2) indicates that C~ and C~ determine the amount of transmitted power which is backscattered or reflected to a radar. The quantity C ~ = C~ + C~

(3)

can be regarded as the effective reflectivity of a scattering and/or reflecting medium. If one can separate C~ and C~, the turbulence refractive index structure constant C~ and consequently the turbulence temperature structure constant Cr2 in the stratosphere (e.g. MEECHAM, 1972) can be deduced from C~. The determination of turbulence parameters, like the eddy dissipation rate, from VHF radar measurements has been attempted by GREEN et al. (1978a) and GAGE et al. (1979). The contribution from partial reflection Cr2 detected with a vertically beaming radar is regarded as an indicator of stable horizontally stratified structures (GAGE and GREEN, 1978 ; ROTTGER and LIU, 1978). These stratified structures or laminae are vertical temperature steps in the stratosphere. An indication of the strength of C~ can be obtained by measuring the degree of stratification when swinging the radar beam from the vertical to an off-vertical direction (directional filtering), or by smoothing the time series of echo power to filter out contributions from turbulence scattering. Another possibility is to investigate the shape of the Doppler spectrum. A quantitative interpretation of C~ is, however, not available at present. VHF radar echoes are coherent up to a time-scale of about a second (typical turbulence coherence time at the 3 m scale) so that an essential improvement in sensitivity can be obtained by applying coherent signal detection and pre-integration. There are a few coherent radars which use this technique (e.g. GAGE and BALSLEY, 1978). We will mention here only the VHF radars which are in operation: Jicamarca/ Peru, Platteville/U.S.A., Pokerflat/Alaska, SOUSY/Germany, Sunset/U.S.A., and Urbana/U.S.A. In the sections that follow, some results obtained with the SOUSYVHF-Radar which is run by the Max-Planck-Institut ffir Aeronomie in the Harz mountains in northern Germany will be presented. This radar operates at 53.5 MHz and a maximum pulse power of 600 kW (average power 24 kW). The minimum pulse length is 0.8 ~s, corresponding to a range resolution of 100 m. Phase coding of the radar pulse allows the detection of even very weak signals at an optimum height resolution. The antenna is a phased array of 196 Yagis yielding a gain of 31 dB. The beam can be steered to any zenith angle between 0 ~ and 12 ~ The SOUSY-VHF-Radar is part of a sounding system, including a microbarograph and HF-Doppler array, to investigate the dynamics of the troposphere, stratosphere, mesosphere and thermosphere (e.g. CZECHOWSKYet al., 1976; ROITGER et al., 1978).

2.2. General radar signal characteristics

Depending on the radar parameters, a high sensitivity radar, such as the Jicamarca VHF radar, is capable of detecting echoes from the whole altitude range from the troposphere to the upper mesosphere (e.g. BALSLEY, 1978). The vertically beaming

Vol. 118, 1980) Structureand Dynamics of the Stratosphere and Mesosphere

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SOUSY-VHF-Radar in its present configuration detects signals from a height of about 1 km in the troposphere up to about 25 km in the stratosphere, as well as signals from the mesosphere in the height range 60-90 km. Besides the variability in the appearance of radar signals at synoptic time scales, a diurnal variability manifests itself in principally day-time occurrence of mesospheric echoes due to the diurnal variation of the electron density. All day long the radar echoes from heights below 6-8 km are stronger than those from the stratosphere. The reason for this is that the refractive index is strongly controlled by the partial pressure of water vapor which decreases with height in the atmosphere. Radar signals from the mesosphere are generally much weaker than those from the troposphere and the stratosphere, except for echoes from meteor trails and the very occasional bursts due to strongly enhanced turbulence or electron density gradients (Wool)MAY, 1974; CZECHOWS~Yet al., 1979). An impression of a radar image of the troposphere and lower stratosphere can be obtained from Fig. 1. This figure shows in the lower part a modified height-time SOUSY - VHF - RADAR 16600

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500

J. ROttger

(Pageoph,

intensity (HTI) plot, obtained by subtracting an average radar power profile Po(z) from the instantaneously measured power profile P(z). The average power decreases with height by roughly 6 dB/km in the lower troposphere and changes to a decrease of about 2-3 dB/km in the lower stratosphere. Due to decreasing atmospheric density, refractive index changes in the upper stratosphere become very small and barely can be detected. A rise in power just above the height of the tropopause is usually found (zt - 10 800 m at 12 G M T on 29 June 1978); this will be treated further in Section 3.1. The modified HTI plot shown in Fig. 1 allows the laminar structure of refractive index variations in the troposphere and in the stratosphere to be clearly identified. There is appreciable day-to-day variability in these structures that is related to synoptic-scale and mesoscale phenomena (Sections 3.1 and 3.2). In general, the characteristics of the fine structure are similar in the troposphere and the stratosphere. Thin laminae of coherent echo power often remain in the same range gate (Az = 150 m) for about ten minutes. It was suggested by ROTTGER and Litr (1978) that these laminae are due to partial reflections from thin sheets of refractive index variations. These horizontally stratified sheets may have a vertical extent less than the normally applied range resolution of 150 m (R&rTGER and SCHMID~, 1979) and a horizontal extent of a few hundred meters. An example of the thickness of the sheets in the stratosphere may be obtained from the enlargement of the altitude range 15 100-16 600 m shown in the upper part of Fig. 1. This plot was recorded by means of a pulse-scanning technique at an apparent resolution of 15 m. To a first approximation the laminae are the replica of the radar pulse width of 150 m, indicating that the two sheets observed between 15 400 and 15 700 m were much thinner than 150 m. In Section 3.3 further investigations of these structures, particularly their association with stratospheric turbulence, will be described. Most of the essential characteristics of VHF radar signals from the mesosphere were described in detail by WOODMAN and GtJILLEN (1974), RASTOGI and BOWHILL (1975) and HARVER and WOODMAN (1977). There is evidence that a layered structure is also characteristic for the mesosphere. It was estimated by WOODMANand GUILLEN (1974) that even thin sheets of turbulence of 100 m thickness should occur. The high-resolution measurements with the SOUSY-VHF-Radar confirm these estimates. We will discuss the mesospheric turbulence structures in Section 4.

3. Investigations of the stratosphere A monostatic, quasi-vertically beaming VHF radar can only provide a spot glimpse of synoptic-scale and mesoscale phenomena. An extended network of VHF radars would thus have to be installed if one were to get an overview at a sufficiently small grid scale. However, since VHF radars are capable of measuring continuously the height profiles of some meteorological parameters, they appropriately supplement existing routine sounding networks (GAGE and BALSLEY, 1978). Some of the possibilities are outlined in this Section.

Vol. 118, 1980) Structure and Dynamics of the Stratosphere and Mesosphere

501

3.1. Synoptic-scale phenomena The capabilities of V H F radars to investigate the dynamics and structure during synoptic- and mesoscale disturbances have been described by GAGE and BALSLEY (1978) and ROTTGER et al. (1978). Continuous observations of wind velocities in a polar front jet were presented by GAGE and CLARK (1978), and the passage of a warm front occurring in connection with an extratropical cyclone was investigated by ROTTGER (1979a). In the following section attention is drawn to synoptic-scale features of the lower stratosphere. 3.1.1. Determination of tropopause and stratospheric stability It was reported by GAGE and GREEN (1978), ROTTGER and CZECHOWSKY (1978) and ROTTGER et aL (1978) that V H F radars find an echo power peak near or above the tropopause level. The lower stratosphere is stably stratified which can give rise to this enhanced radar signal strength because of partial reflection. In a recent paper GAGE and GREEN (1979) showed a significant correlation between the tropopause height detected by radiosonde and by V H F radar. They emphasized the importance of these capabilities of V H F radars since a knowledge of the tropopause height greatly improves the determination of temperature profiles from satellite radiance measurements (THoMPsoN and WOLSI(I, 1977). In addition to the tropopause detection the persistency of structures revealed by radar can indicate the stability of the stratosphere. In Fig. 2, the relative radar echo power Pr is plotted as a function of the height z. A power maximum around z = 12 km can be recognized which is assumed to

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502

J. R6ttger

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correspond to the tropopause level. Much stronger power was received from heights between 6 and 9 km. One would not expect this to be related to the tropopause. There are two criteria that can be applied to discriminate between these different types of power maxima: One is aspect sensitivity, and the other is the persistency of the echoes. In case of stratified, stable layers, a distinct aspect sensitivity and a large persistency, whereas for scattering from turbulent layers an isotropic response and short persistency is expected. These criteria were used by R6TTGER and LiE (1978) for evaluation of radar signals from the troposphere, and for signals from the stratosphere by GA6E and GREEN (1978). It is accepted that these indicate qualitatively the type of atmospheric structure causing the radar echoes. The power profiles (Fig. 2) show that signals from heights larger than 10-11 km are stronger with the vertically (VE) than with the off-vertically (OB = obliquely) pointing antenna. This is due to horizontal stratifications, which in the height region above the tropopause are most likely to occur due to the large gradient of potential temperature. This altitude region is more statically stable than the region below. The region below the tropopause can also be dynamically unstable due to shear in wind systems (e.g. jet streams) flowing below the tropopause level. A measure of the static stability is the square of the Brunt-V~is/il~i frequency: N2 = g ~0 0 az

(4)

where 0 is the potential temperature, g is the acceleration due to gravity, and z is the height. The larger the N 2, the greater is the static stability. A measure for dynamical stability is the gradient Richardson number: N 2

Ri =/au\---~ /

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\Tz/ where u is the horizontal component of the wind. The square of the vertical wind shear ~u/Oz strongly determines the Richardson number. A medium is regarded to be dynamically unstable if Ri < 0.25. Both quantities N 2 and Ri deduced from radiosonde data are drawn in the righthand diagram of Fig. 2. Above the tropopause, which was at 11 km, the general trend in N z adequately fits to the second radar power maximum observed with vertical antenna near 12 kin. One therefore concludes that this power maximum is due to stably stratified layers that cause the partial reflection of radar signals. The tropopause is in the altitude region where N 2 increases to its maximum value; thus, the radar power peak is a few hundred meters above the level of the tropopause. When comparing the Richardson numbers with radar data, one has to take care if the calculated Ri's are realistic since they depend on gradient of temperature and wind. Due to data smoothing, small velocity gradients may result in large Richardson numbers. Not too much importance is therefore attached to the peaks superimposed

Vol. 118, 1980) Structure and Dynamics of the Stratosphere and Mesosphere

503

on the mean profile of Ri. It is also to be expected that velocity gradients due to waveinduced shear, which cannot be resolved by normal radiosonde measurements, may cause small Ri's. The peak of Ri near 9 km, however, appears to be physically real since it occurred at the maximum of the wind velocity (centre diagram of Fig. 2). These winds very closely approached the defined value of 25 m s-1 for a jet stream. The integral-scale correlation time or the persistency TE is by definition closely related to the stability of atmospheric structures revealed by the radar. A T E profile therefore should correlate with a mean Ri profile. This is recognized in Fig. 2 for the region up to 12-14 km. Some differences are expected since the radiosonde data used to calculate the Ri values were taken at Berlin, 220 km N E of the radar site. Largest values of Ri and T~ occurred between 9 and 10 km and lowest values of Ri and TE were observed between 6 and 9 km and between 10.5 and 12 km. This is consistent with an interpretation of turbulence generated in regions of wind shear at the bottom and top of a jet stream. For all that, the calculated Richardson number never passed its critical value Ri = 0.25. However, small disturbances in wind velocities, unresolvable by radiosondes, would easily yield wind shears that in turn cause the Richardson numbers of, say, 1-10 to cross the critical value. The high radar echo power observed between 6 and 9 km therefore may be due to wind shear generated turbulence. The uniform aspect sensitivity (at both antenna directions VE and OB the same power was received from heights up to 9 kin), the small values of TE and further investigations of instabilities (Section 3.2.1) support this suggestion. In the altitude region above the jet level a significant correlation between power and persistency points to a dominance of partial reflections from stable stratifications instead of scattering from turbulence. The following conclusions can be drawn from these results: The persistency TE is a qualitative indicator of atmospheric stability. Small values of TE and scattering from rather isotropic turbulence are observed during conditions of low stability in wind shear. Large values of TE and stratified structures occur during conditions of high stability. An increase of radar power and persistency is observed above the tropopause. These radar observations can be used to indicate the tropopause height.' To enable a continuous comparison of radiosonde and radar data we examined data from radar operation during a period of high-pressure conditions from 29 May to 5 June 1978. During this time a stable anticyclone (max. surface pressure ~ 1030 mb) was located over central and western Europe. In general, clear warm weather predominated, and until 1 June only a few weak disturbances of moist air travelled westward over central Germany. Around 1-2 June convective activity increased and thunderstorms were reported in the vicinity of the radar. Around 5 June 1978, the anticyclone weather conditions were destroyed due to fronts approaching from the west. In Fig. 3 plots of the persistency T~ and the effective reflectivity C 2, which is the relative radar echo power range corrected by z 2 (eqs. (2) and (3)), are shown for this observation interval. The radar reflectivity had large values in the altitude region between 11 and 14 km. These characteristic structures are attributed to the stable

504

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Plots of persistency TE and reflectivity C = deduced from data taken with vertically beamed radar between 29 May and 5 June 1978. The prints are mean values taken from a 2 min data set recorded on the hour. The difference between the blank and dark screen points is ATE = 2 s in the TE plot and AC z = 10 dB in the C 2 plot. The arrows point to the tropopause height measured with radiosondes at Berlin (220 km NE of the radar site). region above the tropopause, which is marked by the arrows. F r o m preliminary comparisons it is deduced that the tropopause is 300-750 m lower than the steep increase in the radar reflectivity, observed above 10 km. The reflectivity structures sometimes split into two or more distinct sheets or layers (e.g. 1/2 June). This leads to the assumption of a layered temperature structure near the tropopause. There is no diurnal variation in the tropopause structure, but some mesoscale variation is discernible. In the morning hours of 31 May, the tropopause level started to lift by about 1 km and then gradually descended until the end of the observation period. The lift on 31 M a y was accompanied by an increase in reflectivity around 8 km height. This structure, which descended by 100 m/hr, may have been connected with a warm front embedded in the geostrophic flow around the anticyclone. The descent rate of 100 m/hr was considerably lower than the descent rate of 400 m/hr observed during a warm front passage occurring in connection with a cyclone (e.g. ROTTGER, 1979a). After 1 June, the radar observations showed a lot of short-term disturbances in the altitudes up to 9 km, which mainly were connected with convective activity. Further investigations, including more meteorological data, need to be made to check how the disturbances observed in the altitude region up to 9 km influence the structures near the tropopause level. It would also be of interest for the interpretation and calibration of cloud-scanning data from satellites if one could use the upper tropospheric structures revealed by radar as indicators of cloud top heights (e.g. GREEN et al., 1978c). The persistency TE of structures revealed by the radar is plotted in the upper part

Vol. 118, 1980)

Structure and Dynamics of the Stratosphere and Mesosphere

505

of Fig. 3. It also increases near the tropopause level and a course similarity in the pattern of reflectivity and persistency is found again. However, there was low persistency at the beginning of the observations which then increased to a maximum in the lower stratosphere between 1-3 June. Afterwards it again decreased until the end of the observation period. It was pointed out by RrTTGER (1979b) that this long-term variation of persistency was correlated with the mean dynamic stability of the lower stratosphere. 3.1.2. Mean wind velocities During the radar experiments carried out on 19 and 20 June 1978 a transition from anticyclone to cyclone weather conditions took place over central Europe. This can be seen in the 300 mb charts shown in Fig. 4. In the vicinity of the radar site the wind system had its maximum velocity of 25 m s- 1 at about an altitude of 9 km. In spite of the fact that this value is marginal with respect to the definition of a jet stream, the name jet is used for the purpose of our interpretations. A distinct change in wind direction and a turning over to a meander shape in the jet occurred during 20 June. It is suspected that these particular changes in the mesoscale pattern generated disturbances propagating through the stratosphere into the mesosphere (Section 4.2). In Fig. 5, vertical profiles of the wind velocity measured with radiosondes at the three locations Berlin, Hannover and Stuttgart are shown. It also was possible to measure the zonal wind component with the radar by means of the Doppler beamswinging method, like it was introduced by GREEN et aL (1975) and VANZANDT et al. (1975). The dots in Fig. 5 denote the radar winds averaged over height intervals of 750 m. Due to aliasing, zonal velocities larger than 12 m s- 1 were not reliably deduced; radar wind velocities near the maximum of the jet are therefore not available. The remaining data of radar winds up to 22.5 km are in fairly good agreement with radiosonde winds observed at the nearest location of Hannover. Radar measurements of height-time cross-sections of horizontal and vertical velocities of a jet stream have already been made with the Sunset radar by GAGEand CLARK(1978) and GREENet al.

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506

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(Pageoph,

19 JUNE 1978 24.0

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Atmospheric gravity waves which are influenced or generated by the mesoscale variability of the wind and due to cumulus convection penetrating the tropopause will be discussed in this section. It will be checked if these waves propagate up to larger heights in the stratosphere. Dynamic processes observed by VHF radar in and above a thunderstorm cloud were investigated by GAGE et al. (1978) and GREEN et al. (1978c). In this section, gravity waves observed in the stratosphere during thunderstorm activity will be described. 3.2.1. Gravity waves in critical layers Internal .gravity waves encounter critical layers when their phase-trace velocities are equal to the background wind velocity (Boo~:ER and BRETHERTON,1967). Reflection

Vol. 118, 1980) Structure and Dynamics of the Stratosphere and Mesosphere

507

o r a b s o r p t i o n at critical layers occurs a n d the waves transfer m o m e n t u m a n d energy to the wind if the R i c h a r d s o n n u m b e r o f the m e a n flow is large. A t small R i c h a r d s o n n u m b e r s (Ri < 0.25), over-reflection, i.e. amplification o f the reflected waves results a n d the waves extract energy f r o m the b a c k g r o u n d wind. A l s o shear-wave instability c a n occur a n d waves m a y be generated which o v e r t u r n a n d b r e a k up into turbulence ( K e l v i n - H e l m h o l t z instability = K H I ) . W i n d shears in j e t streams are eminent c a n d i d a t e s for e x a m i n i n g critical layer effects a n d K e l v i n - H e l m h o l t z instabiltiy. The first V H F r a d a r observations o f waves in a j e t stream were r e p o r t e d by GREEN et al. (1978b). They a r g u e d t h a t the observed waves with p e r i o d s o f a few minutes were generated in a region o f high wind shear. Waves with p e r i o d s o f a few hours also were detected. KLOSTERMEYER a n d RI~STER (1979) f o u n d by m e a n s o f V H F r a d a r experiments velocity oscillations near the B r u n t V/iis~l/i period, o c c u r r i n g in a j e t s t r e a m at 5 k m height. KLOSTERMEYER et al. (1979) s u p p o s e d that these oscillations, which showed a phase shift by 120 ~ n e a r the j e t s t r e a m m a x i m u m , were due to an instability generated in strong wind shear. A similar event was r e p o r t e d b y VANZANDT et al. (1979). W a v e s with a p e r i o d o f 4 min were detected in the lower s t r a t o s p h e r e with the J i c a m a r c a V H F r a d a r (ROSTER et aL, 1978). It was a s s u m e d t h a t an interaction between these waves a n d an observed b a c k g r o u n d w i n d shear was possible. KLOSTERMEYER a n d LIU (1978) presented a m o d e l calculation i n d i c a t i n g t h a t this event was consistent with w a v e - m e a n flow interaction in a critical layer where a large wind shear caused n e a r total reflection a n d s t r o n g transmission. R a d a r m e a s u r e m e n t s were carried o u t on 19 a n d 20 June 1978 when a m a r g i n a l jet s t r e a m was a b o v e the S O U S Y - V H F - R a d a r . Vertical velocities m e a s u r e d d u r i n g

Figure 6 Left (a): Contour plot of vertical velocity measured during jet stream conditions with the SOUSYVHF-Radar. Velocity is upward in the gray-shaded parts. The velocity difference between contour lines is 0.05 m s - 1. The velocity time series are smoothed with a Hamming filter with cut-off period 1.5 rain. Right (b): Spectrogram: Velocity power spectra (deduced from unfiltered velocity data) plotted in tile form of contour lines. The peaks in the spectrogram correspond to a velocity power density of 0.17 x 10 - ~ m 2 s - 1. The dotted curve shows the height profile of the mean Brunt-V~is/il~i period calculated from radiosonde data taken at noon on 20 June 1978. T is the period in min.

508

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a 50 rnin period around noon on 20 June 1978 are shown in the velocity contour plot of Fig. 6a. It is discernible that oscillations with periods near 5-10 min occur at levels up to about 11 km. These oscillations, with a peak-to-peak amplitude of 0.4 m s- 1, rather abruptly disappear around the tropopause level at 11 km. At this level, a discontinuity in the vertical velocity is observed throughout the entire observation period, which may be attributed to mesoscale variations. The vertical oscillations underneath do not penetrate this discontinuity. At heights larger than about 12 km, vertical velocities are generally less than + 0.1 m s- 1 and no oscillatory pattern can be recognized. Figure 6b shows the corresponding spectrogram of the velocity fluctuations (height-time contours of velocity power spectra). These are calibrated in velocity square, which corresponds to the energy contained in the vertical fluctuations. It is evident that a noise-like spectrum dominates in the altitudes up to 9.5 km. This height delineates a definite boundary in the spectrogram. Between 9.5 and 12 km, longer periods are significant. If this spectrogram is compared with the profile of the horizontal velocity and the mean Richardson number in Fig. 2, the following observations are made: (1) Lowest Ri's and random fluctuations in vertical velocity are observed at the bottomside of the jet. (2) The velocity fluctuations cease above the maximum of the jet around 9.5 km where the Ri profile has a maximum value. (3) Ri's are larger at the topside of the jet than at the bottomside. At the topside higher frequency oscillations than those close to the Brunt-V~iis/il~i frequency are not observed. (4) Ri's increase above 12 km where the jet drops to zero. Above this height significant vertical oscillations cannot be observed. It is realized that these examples are consistent with critical layer effects or KelvinHelmholtz instability: In the height region of low Richardson number at the bottomside of the jet over-reflection and transmission of waves generated somewhere below the jet may occur. Because of amplification, waves in this region may break up into turbulence manifesting itself in the higher harmonics which are evident in the spectrogram. It is also possible that waves and turbulence are locally generated by KHI. The strong turbulence cascades down to Bragg scales of 3 m, which is also evident in the vertical and oblique power profiles of Fig. 2. Since the power received from heights up to about 9 km is almost equal at the oblique and vertical direction, the radar detected rather isotropic turbulence. Similar evidence is found in the persistency TE indicating small values of only a few hundred milliseconds. These values are accepted to be in the range of the coherence time of turbulence structures at the 3 m scale. Around the level of 9.5 km, where the maximum wind velocities but minimum shear occur, TE and Ri exhibit small maxima. Above this level of 9.5 km, the vertical antenna direction shows stronger power than the oblique, and TE does not reach such small values as seen in the lower region. This indicates a greater stability and diminishing

Vol. 118, 1980) Structure and Dynamicsof the Stratosphere and Mesosphere

509

turbulence. Incidentally the spectrogram (Fig. 6b) does not show any higher harmonics at this height range. It is assumed that some transmission of the waves at longer periods than the Brunt -V/iis~il/i period from the bottomside to the topside of the jet took place or these waves were generated at the topside. The velocity oscillations of 5-10 min period were observed in all levels up to 10.5 km. The corresponding wave therefore could have penetrated into the topside of the jet. At the topside of the jet the wind velocity still may have satisfied critical level conditions but the Richardson number was large enough not to cause instability, since almost no turbulence was observed. Due to absorption at the topside of the jet, no significant wave amplitude could be detected in the altitudes higher than 11.5 km. These observations are qualitatively consistent with critical layer effects. They incidentally may display absorption, reflection and/or Kelvin-Helmholtz instability causing turbulence at the bottomside of the jet. Absorption occurring at the topside of the jet prevented the waves in the jet from propagating upwards into the stratosphere. In succeeding investigations it is intended to deduce a more quantitative picture of this process. Also the conditions shall be checked when the generated waves can propagate to larger altitudes.

3.2.2. Gravity waves generated by penetrative cumulus convection In the foregoing section wave disturbances which occurred in connection with wind shears in an upper tropospheric jet stream were discussed. Significant evidence was not found that the waves propagated into the stratosphere. This should be expected from interpretations of waves observed in the thermosphere (e.g. GOE, 1971 ; BERTEL et al., 1978). In this section another tropospheric source mechanism for gravity waves which propagate into the lower stratosphere and possibly up to the thermosphere will be examined. It was assumed by DAVIES and JONES (1972) that some thermospheric waves are connected with thunderstorm activity. A correlation between these waves in the thermosphere and convective activity in the tropics was pointed out by ROTTGER (1977). A proof of these considerations should be expected from VHF radar observations during a thunderstorm. Thunderclouds appear as a consequence of atmospheric instability and develop when warm moist air rises due to convection from the boundary layer. The convection process can extend through the entire troposphere up to at least the tropopause. Fast-rising convective air parcels can penetrate from the top of the turbulent mixed troposphere through the capping inversion layer (tropopause) into the stable lower stratosphere. This process is called 'penetrative convection'. Due to static stability, the interfacial inversion layer will start to oscillate (Kuo and SUN, 1976). Besides horizontally propagating interfacial waves, vertically propagating internal waves can be excited. It was pointed out by STULL(1976a) that, due to vertical energy flux by means of the internal waves, some energy may be lost from the Convective mixing

510

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process. STULL (1976b) also estimated that the entrainment rate of air into the mixed layer can be reduced due to internal waves generated during penetrative convection. This may have a reasonable impact on estimating parameters of convective processes. Some of the energy and m o m e n t u m is transferred by waves propagating into the stratosphere where conversion into turbulence may take place. Supplementary information that V H F radar experiments can afford to research of the dynamics in a thundercloud were intimated by GAGE et al. (1978). In this paper, an outline of the implementations to stratospheric dynamics based on the generation of gravity waves by penetrative cumulus convection is given. It seems worthwhile also to note that due to the vertical oscillations of the tropopause level, pollutants can be pumped from the troposphere into the stratosphere (e.g. KAO, 1979), which has impact on the research of turbulent diffusion by means of V H F radars. During the decaying period of the high-pressure system which was followed with the S O U S Y - V H F - R a d a r from 29 M a y to 5 June 1978, convective activity increased continuously (Section 3.1). On 2 June a severe thunderstorm was over the radar site from about 19.00 to 21.30 G M T . Figure 7 shows a velocity contour plot deduced from the radar data taken on 2 June 1978 between 22 and 23 G M T when the thunderstorm had just migrated away. F r o m the velocity contours it can be deduced that some convective updraught still existed up to a height of the tropopause of about 11-12 km. The most intriguing effects are the vertical velocity oscillations observed at the heights above the tropopause. The oscillations have peak-to-peak velocity amplitudes of 1.0 m s - 1. Generally one surmises that coherent oscillations are restricted to height intervals of not larger than 2-3 km. Except on perhaps a few occasions (e.g. 22.08 and 22.30 GMT), no vertical phase shift in the oscillations is discernible. The spectrogram shown in Fig. 7b demonstrates that a spectrum of oscillations with

Figure 7 Left (a): Contour plot of vertical velocity measured with the SOUSY-VHF-Radar after the passage of a thunderstorm. The gray-shaded and non-gray-shaded parts denote upward and downward velocity. Velocity difference between contour lines is 0.125 m s -1. The velocity time series are smoothed with a Hamming filter with cut-off period 3 min. Right (13): Spectrogram: Velocity power spectra (deduced from unfiltered velocity data) plotted in form of contour lines, The peaks in the spectrogram correspond to a velocity power density of 1.1 x 10 -5 m2 s -1. The dotted curve shows the height profile of the mean Brunt-Vfiisal~i period calculated from radiosonde data taken at noon on 2 and 3 June 1978 in Berlin.

Vol. 118, 1980) Structure and Dynamics of the Stratosphere and Mesosphere

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periods larger than the Brunt-V/iis/il/i period is observed in the entire height interval. The correspondence between the height profile of the cut-off of the velocity power spectra and the height profile of the Brunt-V/iisfil/i period deduced from radiosonde data appears convincing. It proves experimentally that no gravity wave oscillations at periods shorter than the Brunt-V/~is~ilS. period are possible. On the other hand, it appears intriguing to discuss if a mean profile of potential temperature gradient (determining the Brunt-V/iisfil/i period, see eq. (4)) can be deduced from the cut-off of the gravity wave spectra. A most pronounced oscillation near the Brunt-V/iis/il/i period of 5 min was observed just above the tropopause. This demonstrates that this region was excited by penetrative convection and started to oscillate. Even in the convective regions below the tropopause, oscillations at shorter periods than the Brunt-V/iis/il~i period were non-existent, and turbulence (expected at the shorter periods) was no more dominant. The spectrogram demonstrates that most of the spectral energy is found in the stratosphere. This leads to the assumption that not only interfacial waves travelling along the tropopause but also internal waves travelling upwards into the stratosphere existed. These radar observations confirm the theoretical expectations of STULL (1976a) that a spectrum of gravity waves is generated during the process of penetrative convection. Note that the oscillations are coherent over a height range of a few kilometers only, which will make it difficult to trace a distinct wave over a larger altitude range. A check carried out during time intervals when no cumulus convection was observed showed that significant oscillations in the upper troposphere and lower stratosphere were not present. Thus, strong cumulus convection is evidently necessary to generate the observed waves. Rather high dynamic stability and low wind velocities were observed in the lower stratosphere on 2/3 June 1978 so that the waves generated near the tropopause could propagate upwards without undergoing critical layer effects. The comparison of the spectrograms of Figs. 6 and 7 conspicuously indicates opposing behavior. These spectrograms are regarded as typical examples of two different kinds of atmospheri c gravity wave generation and propagation: (1) Under certain critical layer conditions, waves generated in a jet stream can be reflected or absorbed so that they cannot propagate into the stratosphere (Fig. 6). (2) Penetrative cumulus convection, on the other hand, appears to be an effective source of atmospheric gravity waves (Fig. 7). Without undergoing critical layer interaction, these waves may propagate upwards into the stratosphere and even into higher regions.

3.3. Small-scale phenomena In this section emphasis is placed on a description of the characteristics of reflectivity structures revealed by VHF radars in the stratosphere and their possible origins. Some similarity between atmospheric structures and the vertical microstructure of the ocean (e.g. WOODS and WILEY, 1972; THORPE, 1975; KRAUS, 1977; MONIN et al., 1977) as

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well as the fresh water thermocline (SIr,IPSON and WOODS, 1970) is found and therefore the definitions used in oceanography will be applied to describe atmospheric structures.

3.3.1. Layers, sheets and turbulence Fine-scale measurements of temperature carried out by WOODS (1968) showed that the oceanic thermocline is divided into a series of relatively uniform layers, separated by thin interfacial regions or sheets which are embedded in a laminar flow. Due to its static stability, the thermocline is the oceanic equivalent of the stratosphere. The high-resolution VHF radar measurements of the atmosphere show laminae or thin sheets (thin stratified striations in Fig. 1) which are superimposed on a mean background layer of refractive index variations (yielding a mean power Po indicated by the right-hand scale of Fig. 1). It was shown (GAGEand GREEN,1978; Rt)TTGER and LIu, 1978; ROTTGERand VINCENT, 1978) that most of these thin sheets are not due to scattering from turbulent irregularities at the 3 m scale but rather due to partial specular reflection at vertical gradients of refractive index (BOLGIANO, 1968). The observations of aspect sensitivity and persistency presented in this paper also support this evidence. In the stratosphere, the refractive index variations are due to temperature changes. This implies that the laminae revealed by VHF radar can be regarded as indicators of steps in the vertical temperature profile. WOODS (1968) introduced the name 'sheets' for the small-scale vertical temperature gradients measured in the oceanic thermocline. This definition of sheets will be used here also for the atmospheric laminae seen by VHF radars. Figure 1 indicates that these laminae in the stratosphere are mostly confined to height intervals of 100-300 m. At a radar pulse length of 150 m, one then estimates that the vertical extent of the steps or gradients of temperature is not exceeding about 100 m. On the other hand, it follows from estimates of the radar echo power due to partial reflection from these gradients that the vertical extent even can be a fraction of the radar wavelength of 6 m, From the current measurements of radar signal strength it is not possible to deduce the temperature difference in the sheets since the reflected power depends on the gradient as well as on the vertical and horizontal shape of these discontinuities. However, besides using the refractive index changes as tracers to measure atmospheric velocities, the general spatial and temporal variations of the temperature fluctuations can be inferred from the existing data. It is deduced from the evidence of partial reflection at VHF that the sheets must have a horizontal extent of the first Fresnel zone which is a few hundred meters at stratospheric heights. Assuming that the sheets which may have a persistency of some ten seconds are advected with the background wind (e.g. horizontal velocity Uo = 10 m s- 1) and do keep their statistical identity during the advection through the radar beam (Taylor frozen turbulence hypothesis), the horizontal extent of an individual sheet is then estimated to be around 1 km. This is in accordance with the estimate deduced from Fresnel-zone condition. The sheets are almost horizontally stratified

VoI. 118, 1980) Structure and Dynamics of the Stratosphere and Mesosphere

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(Section 3.1.1, and ROTTGER and VINCENT, 1978). From the evaluation of the correlation functions and the persistency, it can be shown that the sheets are faintly corrugated by superimposed 3-m-scale turbulence. Figure 1 indicates that individual sheets mostly occur in patches or ensembles (WOODS and WILEY,1972) covering a height range of a few hundred meters. The radar observed these sheet ensembles over several 10 min periods. Applying the Taylor hypothesis also to the ensembles of sheets, it is estimated that these have horizontal dimensions of some 10 km. One finds a vertical separation of 1-3 km between individual ensembles o f sheets. Usually radar echo power is even received from the gaps between individual sheets or ensembles which can be either due to partial reflection from weaker sheets or due to scattering from 3 m turbulence. These gaps filled with fluctuating structures may be regarded as the equivalent of the 'layers' observed in the oceanic thermocline (e.g. WOODS, 1968, 1973). The layers should not in general be attributed to individual sheets or ensembles at their topside and bottomside boundaries since they also may result from continuous background fluctuations or microstructure turbulence associated with mesoscale or synoptic-scale disturbances (e.g. GOSSARD, 1977). From Fig. 1 it can be inferred that individual sheets may keep their identity for at least a few seconds. The sheets often recur intermittently at the same height, and spatial intermittency is also evident in the vertical scale. Since the radar measures data time series as function of altitude, it is possible to calculate frequency power spectra of reflectivity variations observed above the fixed radar location. These reflect the temperature fluctuations per frequency band measured in Eulerian coordinates, and the reflectivity spectra represent an image of temperature fluctuations above the radar. Figure 8 shows examples of the reflectivity spectra drawn in log-log coordinates deduced from data obtained with vertically beamed radar. It is evident that the rather z=9-12km 3I:~

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fiat top at low frequencies starts to decline near a limiting frequency a,0 of about 0.4 rad/s. This is most pronounced in the spectra of the height interval 15-18 km. The spectra of 9-12 km are influenced by jet stream winds, and the spectra of 21-24 km are deteriorated by low signal-to-noise ratio. In the upper frequency range co > a,o the spectra generally follow a power law C 2 oc oJ". Series of radar data suggests that the slope of the spectra at frequencies o~ > coo is given by the exponent m which lies between - 1 . 5 and - 2 . 2 . These values are close to the exponent - 5 / 3 of the Kolmogorov spectrum (TATARSKII, 1971), respectively to the exponent defining the slope of frequency spectra of step-like fine structure superimposed on the gross vertical profile of temperature in the oceans (GARRETTand MONK, 1971). It has to be checked in further investigations if the shape of the spectra is determined by Fresnel Zone filtering of scattered and reflected components (e.g. ISmMARU, 1978), or represents the inertial and buoyancy subranges of turbulence spectra (e.g. BOLGIANO, 1968; WOODS, 1973). It has to be assumed that in the flow conditions examined in the stratosphere, fluctuating temperatures as well as fluctuating velocities are present. Under the suppositions which are summarized in Section 2.1, estimates of turbulent velocity fluctuations can be obtained from the width of the Doppler spectra of the radar returns. These, however, have to be filtered from the long-term fluctuations due to large-scale spatial variations of sheets advecting through the radar beam. Because meaningful velocities can only be obtained by integrating over time periods of at least several seconds, spectra of short-term velocity fluctuations in the time range of seconds cannot be deduced. When averaging over one minute, the rms vertical velocity fluctuations are typically less than + 0 . 5 m s -~ in the stratosphere. Spectra of vertical velocities at frequencies lower than 0.1 rad/s (T > 1 min) are depicted in the spectrograms of Figs. 6 and 7. Conspicuously, a clear cut-off at the Brunt-V/iisfil~i frequency N (corresponding period Ts) is found. Only during unstable conditions, due to strong wind shear, are higher frequency components significant (Fig. 6). The spectrum at o~ > N (T < TB) is comparable to a white noise spectrum, and does not fall off with co-r~ (m = 5/3). A spectral power slope according to o~-~j3 was not found for co < N which GAGE and CLARK(1978) reported to be existent in horizontal velocity variations. The turbulent fluctuations in vertical velocity w' and the turbulent fluctuations of the temperature T' determine essentially the turbulent transport process of energy and momentum in the atmosphere. It is shown in this section that both these basic quantities can be qualitatively monitored by means of VHF radar. However, to make these observations more quantitative, more detailed investigations of the intimated processes need to be made. 3.3.2. Possible source mechanisms of stratospheric structures In the former section attention was drawn to some similarities between the observed fine structure of the atmosphere and the fine structure of the oceans. When

Vol. 118, 1980) Structure and Dynamicsof the Stratosphere and Mesosphere

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describing the structure of the ocean, one has to take into account the temperature as well as the salinity. Obviously one cannot be allowed to apply all of these theories (e.g. 'double diffusion' (MoNIN et aL, 1977)) to the atmosphere. There are however still other mechanisms that are applicable to atmospheric structures, and these are briefly described next. The first mechanism envisages the breaking of internal waves (BRETIJERTON, 1969; ORLANS~:Iand B~YAN, 1969). For wave amplitudes larger than a critical value, the particle velocity exceeds the phase velocity, and unstable gradients occur. These unstable gradients lead to convective instability, and energy will be extracted from the wave and transferred into turbulent kinetic energy. It could be suspected that the sheets reflect these regions of turbulence. LUD•AM (I967) developed a similar theory for the characteristics of billow clouds and their relation to clear air turbulence. It was mentioned by GELLZRet al. (1975) that probably another mechanism than breaking of large amplitude waves has to be adopted to explain the thin sheets. Internal waves may also cause turbulence structures and lose energy by shear instability. For this condition to apply, the shear generated by the waves must add to a pre-existing shear so that the local Richardson number becomes less than 0.25. It remains questionable if the large Richardson numbers observed in the stratosphere (e.g. Fig. 2) can be overcome by wave-induced shear to transit into the unstable regime. WOODS and WILEY(1972) pointed out that as an internal wave propagates along a sheet, in the neighborhood of its crests and troughs, the sheet may become unstable and turbulent. Because of entrainment of air, the now turbulent medium becomes thicker. Turbulence will tend to mix the medium and there will be discontinuities in temperature at the top and bottom surfaces so that new sheets form (BOLGIANO, 1968). Repetition of this process creates a whole ensemble of sheets, which incidentally is observed with the VHF radar. We have to check in further investigations if the mechanisms of internal wave-breaking or shear instability apply to explain the stratospheric structures encountered by VHF radar. Another hypothesis for the origin of the stepped microstructure is 'lateral convection' (MoNIN et al., 1977). In this process, horizontal differences between neighboring, differently stratified air masses are equalized by quasi-horizontal displacement of individual layers or lenses of air packets embedded in a laminar flow. Such displacements, for example, may be the result of baroclinic instability and could be produced by sliding layers that are heavier than their horizontal neighbors along isentropic surfaces which lead to the formation of stable stratifications. Pronounced sheets in the tropospheric refractivity pattern during the approach of a frontal system connected with an extratropical cyclone were indeed found (ROTmER, 1979a). Since WOODS (1969) stated that most of the atmosphere is in laminar flow, the hypothesis of lateral convection by means of large, almost horizontally extending eddies or laminae should be followed up in further VHF radar investigations,

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4. Investigations of the mesosphere Since BOWLES (1958) and FLOCK and BALSLEY(1967) first reported VHF radar echoes from the ionospheric D-region, a wide-spread interest has grown up in the use of V H F radars to investigate the dynamics of the mesosphere. These echoes received with VHF radars are from fluctuations in electron density which can be very much enhanced over the thermal level in the D-region. This is a consequence of strong collisional coupling between the ionized and the neutral particles which do fluctuate due to turbulence in the neutral atmosphere. Because of this coupling, the fluctuations revealed by VHF radar can be used as tracers of the neutral background in the mesosphere. The mechanism which gives rise to the radar echoes from the mesosphere is not as yet fully understood. It is assumed that under certain conditions, besides pure scattering from turbulence structures at half the radar wavelength, diffuse partial reflection from horizontally stratified laminae of refractive index may occur (FUKAO et al., 1979; R6TTGER et al., 1979). In addition to VHF radars, other radio methods have been successfully applied to investigate mesospheric dynamics such as the partial reflections drifts technique operating at MF (e.g. BRIGGS, 1977), the meteortrail radar technique operating at H F or VHF (e.g. reviews in WEBB, 1972), and the incoherent scatter technique operating at U H F (e.g. MATHEWS,1976). The partial reflection drifts (PRD) technique turned out to be a very potent tool to rather continuously monitor the height range from about 60 to 110 km (e.g. MANSON et al., 1974; VINCENT and STUBBS, 1977). WOODMAN and GUILLEN 0974) introduced a powerful method of coherent data processing to show that non-thermal scattering at VHF is predominant in the mesosphere. In the context of this paper we extend the definition of WOODMAN and GUILLEN (1974) and include diffuse reflection into the term non-thermal scattering. The method of Woodman and Guillen was subsequently used in all VHF radar experiments to improve the sensitivity. In the following sections the results of VHF radar investigations of tides and gravity waves are briefly reviewed and some recent results on turbulence structures in the mesosphere are described.

4.1. Mesoseale phenomena Almost all of the VHF radar results dealing with tides and gravity waves in the mesosphere were obtained with the Jicamarca radar which is located near Lima/Peru in the equatorial region. This radar operates on 50 MHz at a maximum power rating of 4 MW. T h e antenna has a collecting area of 8.4 • 104 m 2, and the beam can be tilted to different zenith directions to measure horizontal as well as vertical velocities. The best height resolution is 2.5 km, which is comparable to the height resolution obtained in PRD experiments. WOODMAN (1974)and WOODMAN and GUILLEN (1974) measured mesospheric velocities with an accuracy of better than 2 m s -1 in the horizontal and better than 0.2 m s-1 in the vertical. The horizontal velocities were

Vol. 118, 1980) Structure and Dynamics of the Stratosphere and Mesosphere

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typically 20-40 m s- 1; in general the instantaneous vertical velocities were found to be less than 2 m s- 1 (RASTOGIand WOODMAN, 1974). WOODMANand GUILLEN(1974), RASTOG~ and BOWmLL (1976a) as well as HARPER and WOODMAN (1977) apparently did not measure such large amplitudes of tides which were expected from theory. Also FUKAO et aL (1979) did not clearly identify a diurnal tide. The sense and the magnitude of the winds measured by FUKAOet at. (1979) are in general agreement with annual and semiannual oscillations. Superimposed on the mean background velocities were periodic velocity fluctuations with a sharp cut-off in the spectra near the BruntV/iis~il/i period of 5-7 min (WOODMAN and GUILLEN, 1974). Further evidence for this cut-off period was given by the experiments of RASTOGI and WOODMAN (1974) and RASTO~I and BOWrIILL(1976a), They interpreted the oscillations to be a manifestation of atmospheric gravity waves in the period range of 4 min to 1 hr. The dominant waves had periods of 10-20 min. It was argued that these waves were vertically evanescent and had a horizontal wavelength of 200-300 km. Possibly also acoustic gravity waves of periods less than 4 rain were observed. There is as yet no clear evidence for possible origins of the mesospheric gravity waves. HARPER and WOODMAN (1977) evaluated vertical velocity oscillations in the period range from about 5-15 rain which were highly correlated at nearby altitudes, while velocities at altitudes separated by more than 5 km showed little or no correlation. The dominant periodicities of the oscillations were observed to change with altitude. A same sort of evidence was reported by FUKAO et al. (1979) who inferred that the velocity oscillations near the Brunt-V/iis/il/i period are largely vertical. Also ROSTER et al. (1979) found a wave with dominant period changing with height. Some similarity between the gravity waves observed in the mesosphere and the stratosphere may be discovered. In Fig. 7b a spectrum of waves with a clear cut-off near the BruntV~iis~it/i period is shown. Like the oscillations of the mesospheric waves, the oscillations of the stratospheric waves seem to be coherent over height ranges of only a few kilometers. It thus appears to be difficult to trace a distinct wave over a larger altitude range. As it was pointed out in Section 3.2, it would be very intriguing to see if a mean profile of the Brunt-V~iis~il/i period can be deduced from the gravity wave spectrum. This profile (if gravity waves are present) could give an indication of the gradient of potential temperature in the mesosphere. Scattering layers at discrete heights, oscillating in intensity with about twice the frequency of a simultaneously occurring velocity oscillation, were found by HARPER and WOODMAN (1977). They pointed out that the turbulent irregularities responsible for the scattering may be at least partially driven by energy from short-period gravity waves. Their assumption was supported by the correlation between velocity and echo power (in some cases). These results were confirmed in recent experiments with the Urbana radar (MILLER et al., 1978) indicating enhanced scattering regions which in many cases corresponded to high-amplitude waves. MILLER et al. (1978) showed waves that were coherent over altitude ranges of up to 10 km. They presented an example interpreted as a wave becoming unstable and generating high-frequency

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waves. The mechanism possibly is critical layer interaction or wave-induced shear instability and it is anticipated that gravity waves as well as tides and planetary waves play a role. An example of shear-generated layers due to a tide may be found in the intensity plots obtained with the SOUSY-VHF-Radar by CZECI-tOWSKYet al. (1979), where downward sloping ensembles of layers can be recognized over time periods of hours. It is reported by Rt3TTGERand RASTOGI(1978) and CZECHOWSKYet al. (1979) that an apparent downward motion of a layered structure can be connected with a downward Velocity component, which points to a downward progressing shear layer due to a wave. Depending on the background conditions of electron density, temperature and wind, which vary with season, shears induced by tides and gravity waves may not always be sufficiently large to cause an instability. This could be part of the reason for the seasonal variability in the mesosphere (GREGORY,1961 ; STUBBS, 1976; STENINGet al., 1978; CZECHOWSKYet al., 1979). It appears that radars operating at VHF or at MF (PRD) are appropriate instruments to observe not only mesoscale but also synoptic-scale phenomena in the mesosphere. The PRD technique incidentally seems to be more versatile for these investigations since VHF radars have to be very powerful to provide rather continuous observations of dynamic processes. VHF radars on the other hand can provide better height resolution and therefore are essential instruments to investigate small-scale processes.

4.2. Small-scale phenomena

The echo power from the mesospheric heights varies considerably during the day and from one day to the next (WOODMAN, 1974). Strong variability as function of height is also observed (e.g. HARPER and WOODMAN, 1977). The first experiments did not indicate echoes from the 35-55 km height region (e.g. WOODMANand GUILLEN, 1974), but recently BALSLEY(1978) detected signals in this gap region of the upper stratosphere and lower mesosphere. He used the powerful Jicamarca radar and applied long integration times. It was reported by WOODMAN (1974) that at certain times the echoes between 60 and 85 km in a particularly narrow height range can be 10-15 dB stronger than a mean profile. WOODMAN(1974) suggested that these echoes are caused by the coincidence of a layer of turbulence with a region of strong electron density gradient. It was estimated from the echo power and the spectral width (WOODMANand GUILLEN,1974) that the turbulence in the mesosphere may be confined to layers of the order of 100 m thickness. A first height-time intensity (HTI) diagram of VHF radar echoes from the mesosphere was published by HARPER and WOODMAN (1977). This diagram which was deduced from data taken at 12 altitudes in the height region between 62.5 and 90 km shows regions of enhanced echo power separated by regions from which little or no power was received. HARPERand WOODMAN(1977) pointed out that the appearance of scattering layers (revealed by VHF radar) at discrete heights is similar to partial

Vol. 118, 1980) Structure and Dynamics of the Stratosphere and Mesosphere

519

reflection results obtained at M F (GREGORY, 1961). Apart from the spatial (vertical) intermittency, a temporal intermittency is characteristic for the mesospheric echoes (RASTOGI and BOWmLL, 1976b; HarPER and WOODmaN, 1977). In recent high-resolution measurements carried out with the SOUSY-VHF-Radar it was possible to measure the thickness of structures in the mesosphere (CZECHOWSKY et al., 1979; RQTTGER et al., 1979). By means of these measurements, applying a best resolution of 150 m, different types of turbulence structures were identified. Figure 9 shows an example of the life-history of structures in the height range of 66-85 km observed on 20 June 1978. A layer as thick as 2 km was observed from 10.45-10.55 G M T at 70 km height. Another layer of 1.5 km thickness commenced around 11.00 G M T and lasted for more than 30 min. The thinner structure at 80 km, which can be called sheet, shows evidence of a downward progression. This layer descent was accompanied by a downward velocity deduced from the Doppler spectrum (ROTTGER and RASTOGI, 1978). A burst of a short-lived blob of turbulence is discernible at 71 km around 11.25 GMT. In addition stronger echoes due to meteors, which are spread over many contiguous range cells and confined to short time intervals, can often be seen. In Fig. 10 further selected examples of sheets and blobs are shown. The upper heighttime intensity diagram was deduced from data taken with the complementary code system applied by CZEC~OWS[~u et aL (1979), and the lower diagrams were obtained with a different coding system described by WOOD~AN et al. (1979). Both experimental configurations yield a similar impression of turbulence structures in the mesosphere. Intermittent sheets, which have a thickness of less than about 1 km, sporadically may recur at the same height intervals over several minutes. They also may shift down in height during their lifetime. Often sheets may be as thin as the minimum range resolution of 150 m. Blobs of turbulence, also confined to height ranges of

20 JUNE 1978 I---!: ::~:~.:!H~:/;" i"~:-~;--:~!:.-..-:-::."~-;i ~I-i'il'":,': =:I-"i:,'-!::.~:, ~,: ,'I "' :: '~'-:-~ " ~: ~=: ?' '~ ~i-.:'."~:':-'.--::~ :!, - :--w i~." "-:~-!; : ;~ ~ I~ ~ . i~!if:~!:,i~:~i ~ ~_Ii!~"-,:: ~{I::.?l.i:l'-!;.._!-j.w:~!! -:.-~;.: :' ,-i~ ~. ....! , ~:.. ..I:! ~ '.!i!i]:!::::,[':::i{!:.:l~::; /:. li :~,~I:

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Figure 10 Examples of sheets and blobs of turbulence observed in the mesosphere. The HTI plot 1 is deduced from data (original range resolution 300 m) taken around noon on 8 May 1978 and published by Cz~crtowsKYet al. (1979). The HTI plots 2, 3 and 4 are from data (original range resolution 150 m) taken around noon on 19 June 1978 (RrTTGERand RASTOOI,1978). The height of the structures is z0 + Az. The gray scales denote the power ratio for plot t, respectively plots 2, 3, 4.

less than about 1 km, can commence within some ten seconds and rise up to large intensity from one range gate to the neighboring. The blobs suddenly decay after living for 1-2 minutes. Assuming that all these structures are advected with the background wind, it was estimated by R6TTGEg et al. (1979) that the blobs can result from bursts of turbulence or even enhanced ionization density gradients generated locally within the radar beam. Their horizontal extent is typically about 1 km. The sheets have horizontal dimensions of several kilometers and the layers of at least 10-50 km. The horizontal size of these turbulence structures is thus much larger than their vertical size. A similar result has been reported from M F partial reflection studies by VINCENT and BELROSE (1978). Reports on aspect sensitivity of structures in the mesosphere below about 70 km (e.g. HARPER and WOODMAN, 1977; R6TTGER and RASTOGI, 1978; FUKAO et al., 1979) allow the assumption that the small-scale structure at half the radar wavelength (~_ 3 m) is also in some way anisotropic. The role of partial reflections from the lower mesosphere is discussed by RSTTGER et al. (1979), who noted the possibility of diffuse partial reflections from heights below 70 km. The velocity spectra of turbulence structures in the mesosphere indicate the typical feature that sheets and blobs, which are thin, exhibit smaller velocity fluctuations (spectral width) than thicker layers. In general, it was found by ROTTGERet al. (1979) that the velocity fluctuations are proportional to the thickness of turbulence structures, which is consistent with turbulence theory. CZECHOWSKY et al. (1979) found that thickness and lifetime are correlated.

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Based on considerations of thickness, height of occurrence, duration, and spectral width, RrTTGER and RASTOGI(1978) proposed a classification of these structures, which is summarized in Table 1. It was shown by CZECHOWSKY et al. (1979) that layers, which may occur at heights up to 90 kin, may even be as thick as 10 km so that they proposed a further subdivision into thin and thick layers. They also reported a seasonal variation with thick layers detected only during summer. The high-resolution observations indicate that a boundary altitude exists ( ~ 7 0 km during summer) below which sheets and blobs dominate and above which most of the structures are layers. The maximum duration of sheets and layers may be several hours. It cannot be verified from the current investigations if the structures observed in the mesosphere are similar to those observed in the stratosphere, in spite of the fact that some of their features are similar. A reasonable difference however is established by the diurnal variation of mesospheric echoes caused by the diurnally varying background ionization in the mesosphere. It is also possible that the mesospheric structures are more turbulent than the stratospheric structures, and that the mesospheric structures are closely connected to the background ionization conditions as well as to phenomena in the neutral atmosphere, like gravity waves and tides. The fact that mesoscale phenomena, such as planetary waves, also play a role may be deduced from the day-to-day variability. Varying features of turbulence in the mesosphere from 19 to 20 June 1978 (intermittent sheets were dominant on 19 June, but layers on 20 June) were observed for iflstance with the SOUSY-VHF-Radar when during conditions of geostrophic turbulence rather strong winds in the upper troposphere changed their direction from E over S to NW (ref. Fig. 4). During radar operation on 5 and 7 June 1978, mesospheric structures were rather weak and less obvious. The winds at 300 mb level during that period were constantly blowing from W at a moderate strength. However, much more work has to be carried out to learn about the generation mechanism of these different structures and their connection with lower atmospheric disturbances. Two important parameters inferred from high-resolution VHF radar experiments are the thickness of turbulence structures and the rms velocity fluctuations in these structures. These parameters can be used for estimating the vertical transport or eddy diffusion coefficients K and the dissipation rate e of turbulence (CUNNOLD, Table 1 Blobs

Sheets

Layers

Duration T(min)

< 1-2

Velocity fluctuations

small

60-90 dominant < 70 <0.9 preferably <0.3 >1-2 intermittent small

> 70

Thickness Az (km)

60-90 dominant < 70 < 0.9

Height z (km)

>0.9 > 5 continuous large

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1975). R6a'a'G~Ret al. (1979) found values of ~ and K which appear in fair agreement with those in use in aeronomic models (e.g. ZIM~tERMANand MtrRPtqu 1977). It should be remarked, however, that the transport coefficients inferred from the radar observations refer to transport in the region within the structures, whereas those used in aeronomic models are transport coefficients averaged over large temporal and spatial scales. Any comparisons naturally require a similar averaging of radar results, and even then it would be necessary to resolve the following objections: (1) In estimating K and ~ from radar data, only turbulence scattering is considered, whereas diffuse partial reflections can also contribute to the signals and influence their correlation time. (2) The scattering has to be from turbulence in the inertial subrange. For a large variation in turbulent energy dissipation the Kolmogorov inner scale is accepted 9 to be at a few meters in the mesosphere (RAsTOGI and BOWHILL, 1976b; GAGE and BALSL~Y,1978). Thus, the Bragg scale of VHF radars is barely marginal in the inertial subrange of mesospheric turbulence. Answering these objections will have an impact on the further understanding of turbulence and the corresponding vertical transport processes in the mesosphere.

5. Summary and conclusion

An attempt was made to summarize existing material and attach recent results to outline the capabilities of VHF radars for atmospheric research, such as the determination of the tropopause level and stratospheric stability, as well as the mutual dependence of winds, waves, laminar structures and turbulence observed in the stratosphere and mesosphere. The investigation of the stratosphere and mesosphere with VHF radars is a rapidly developing research field and innovative processing techniques are being developed. Many questions remain to be solved, which may have impact on the understanding of the structure and dynamics of the middle atmosphere. Some of them were considered in this paper and are summarized below, without laying claim to completeness or importance: (1) How reliable are the tropopause height and stratospheric stability inferred from radar observations? (2) Can gravity wave generation be studied in detail, and can the propagation of wave disturbances from the troposphere into the stratosphere and mesosphere be tracked by VHF radars ? (3) Does a possibility exist to deduce a height profile of the Brunt-V/iis/il/i frequency, i.e. profile of gradient of potential temperature, from internal wave spectra measured with radar? (4) What is the origin of the laminar and turbulence structures in the stratosphere and mesosphere? (5) Can the energy and momentum transport due to wave disturbances be

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estimated from radar observations? How reliable are estimates of eddy diffusivity due to turbulence in the stratosphere and mesosphere ? (6) What are the operational parameters of a V H F radar for continuously monitoring wind velocities and turbulence in the entire middle atmosphere ? It is expected that continuing investigations with V H F radars and supplementary experiments, which are planned to be carried out during the Middle Atmosphere Program, can give answers on some of these questions.

Acknowledgements

The author appreciates the continuous cooperation with his colleagues of the SOUSY project group of the Max-Planck-Institut fiir Aeronomie as well as the stimulating discussions with Prof. K. C. Yeh and Dr. P. K. Rastogi. The provision of meteorological data from the Deutscher Wetterdienst is kindly acknowledged.

REFERENCES Aso, T., KATO,S. and HARPER,R. M. (1977), Arecibo middle atmosphere experiment, Geophys. Res. Lett. 4, 10-12. BALSLEY,B. B. (1978), The use of sensitive coherent radars to examine atmospheric parameters in the height range 1-100 km, Preprint Vol. 18th Conf. on Radar Meteorology (to be publ., Amer. Meteor. Soc., Boston). BALSLEY,B. B. and GREEN,J. L. (1978), Coherent radar systems forprobing the troposphere, stratosphere, and mesosphere, Preprint Vol. 4th Syrup. on Meteorological Observations and Instrumentation (to be publ., Amer. Meteor. Soc., Boston). BALSLEY,B. B. and GAGE,K. S. (1980), The MSTradar technique: Potential for middle atmospheric studies, J. Pure Appl. Geophys. 118,452-493. BATTAN,L. J., Radar Observation of the Atmosphere (The University of Chicago Press, Chicago and London 1973). BEAN,B. R. and DUTTON,E. J., Radio Meteorology (Dover Publ., Inc., New York 1968). BERTEL,L., BERTIN,F'., TESTUD,J. and VIDAL-MADJAR,D. (1978), Evaluation of the verticalflux of energy into the thermosphere from medium scale gravity waves generated by the jet stream, J. Atmos. Terr. Phys. 40, 691-696. BOLGIANO,R, JR. (1968), The general theory of turbulence - Turbulence in the atmosphere, in Winds and Turbulence in Stratosphere, Mesosphere and Ionosphere, ed. K. Rawer (North-Holland

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CUNNOLD, D. M. (1975), Vertical transport coefficients in the mesosphere obtained from radar observations, J. Atmos. Sci. 32, 2191-2200. CZECHOWSKY,P., K.LOSTERMEYER,J., ROTTGER,J., ROSTER,R., SCHMIDT,G. and WOODMAN,R. F. (1976), The SO US Y- VHF-Radar for tropo-, strato- and mesospheric sounding, Preprint Vol. 17th Conf. on Radar Meteorology, 349-353 (Amer. Meteor. Soc., Boston). CZECHOWSKV, P., ROSTER,R. and SCHMIDT, G. (1979), Variations of mesospheric structures at different seasons, Geophys. Res. Lett. 6, 459-462. DAVIES, K., Ionospheric Radio Propagation, National Bureau of Standards Monograph 80 (U.S. Government Printing Office, Washington, D.C. 1965), 343-392. DAVIES, K. and JONES, J. E., Ionospheric Disturbances Produced by Severe Thunderstorms, NOAA Professional Paper 6 (U.S. Government Printing Office, Washington, D.C. 1972). DERR, V. E. (Ed.), Remote Sensing of the Troposphere (U.S. Government Printing Office, Washington, D.C. 1972). DEUTSCHER WETTERDIENST(1978), Europ~ischer Wetterbericht 3, Nos. 170, 171, 172 (Deutscher Wetterdienst, Zentralamt, Offenbach, Germany). FLOCK, W. L. and BALSLEY,B. B. (1967), VHF radar returns from the D region of the equatorial ionosphere, J. Geophys. Res. 72, 5537-5541. FROST, W. and MOULDEN,H. (Eds.), Handbook of Turbulence, Vol. 1: Fundamentals and.4pplications (Plenum Press, New York and London 1977). FUKAO, S., KATO, S., YOKOI, S., HARPER, R. M., WOODMAN,R. F. and GORDON, W. E. (1978), One full-day radar measurement of lower stratospheric winds over Jicamarca, J. Atmos. Terr. Phys. 40, 1331-1337. FUKAO, S., SATO, T., KATO, S., HARPER, R. M., WOODMAN,R. F. and GORDON, W. E. (t979), Mesospheric winds and waves over Jicamarca on 23-24 May 1974, J. Geophys. Res. 84, 43794386. GAGE, K. S. and BALSLEY,B. B. (1978), Doppler radar probing of the clear atmosphere, Bull. Amer. Meteor. Soc. 59, 1074-1093. GAGE, K. S. and CLARK, W. L. (1978), Mesoscale variability of jet stream winds observed by the Sunset VHF Doppler radar, J. Appl. Meteor. 17, 1412-1416. GAGE, K. S. and GREEN, J. L. (1978), Evidence for specular reflection from monostatic VHFradar observations of the stratosphere, Radio Sci. 13, 991-1001. GAGE, K. S., GREEN, J. L. and VANZANDT,T. E. (1978), Application of the VHFpulsed Doppler radar to cloud physics research, Proc. Vol. Conf. on Cloud Physics and Atmospheric Electricity (to be publ., Amer. Meteor. Soc., Boston). GAGE, K. S. and GREEN, J. L. (1979), Tropopause detection by partial specular reflection using VHF radar, Science 203, 1238-1240. GAGE, K. S., GREEN,J. L., CLARK,W. L. and VANZANDT,T. E. (1979), Doppler radar measurement of turbulence in the clear atmosphere, Preprint Vot. 4th Symp. on Turbulence, Diffusion, and Air Pollution (to be publ., Amer. Meteor. Soc., Boston). GARRETT,C. and MUNK, W. (1971), Internal wave spectra in the presence of fine-structure, J. Phys. Oceanography I, 196-202. GELLER, M. A., TANAKA,H. and FRITTS,n . C. (1975), Production of turbulence in the vicinity of critical levels for internal gravity waves, J. Atmos. Sci. 32, 2125-2135. GOE, G. B. (1971), Jet stream activity detected as wavelike disturbances at mid-latitude ionospheric F region heights, J. Pure Appl. Geophys. 92, 190-206. GORDON,W. E., BOWHILL,S. A., EVANS,J. W. and VANZANDT,T. E. (1978), Atmospheric dynamics in the 1980's, Position Paper for CSTR Summer Study from Radar Workshop at Logan, Utah, 12-15 Dec. 1977 (Rice Univ., Houston). GOSSARD, E. E. (1977), Refractive index variance and its height distribution in different air masses, Radio Sci. 12, 89-105. GREEN, J. L., WARNOCK,J. M., WINKLER,R. H. and VANZANDT,T. E. (1975), Studies of winds in the upper troposphere with a sensitive VHF radar, Geophys. Res. Lett. 2, 19-21. GREEN,J. L., GAGE,K. S. and VANZANDT,T. E. (1978a), VHF Doppler radar studies of CAT in the troposphere and lower stratosphere, Preprint Vol. Conf. on Atmos. Environment of Aerospace Systems and Applied Meteorology (to he publ., Amer. Meteor. Soc., Boston).

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GREEN,J. L., GAGE,K. S. and VANZANDT,T. E. (1978b), Three dimensional wind observations of a jet stream using a VHF Doppler radar, Preprint Vol. 18th Conf. on Radar Meteorology (to be puN., Amer. Meteor. Soc., Boston). GREEN,J. L., WINKLER,R. H., WARNOCK,J. M., CLARK,W. L., GAGE,K. S., and VANZANDT,T. E. (1978c), Observations of enhanced clear air reflectivity associated with convective clouds, Preprint Vol. 18th Conf. on Radar Meteorology (to be publ., Amer. Meteor. Soc., Boston). GREGORY, J. B. (1961), Radio wave reflections from the mesosphere, 1. Heights of occurrence, J. Geophys. Res. 66, 429--445. HARDY, K. R., GLOVER, K. M. and OTTERSTEN,H. (1969), Radar investigations of atmospheric structure and cat in the 3 to 20-kin region, in Clear Air Turbulence and its Detection, ed. Y.-H. Pao and A. Goldburg (Plenum Press, New York), 402--416. HARPER, R. M. and WOODMAN,R. F. (1977), Preliminary multiheight radar observations of waves and winds in the mesosphere over Jicamarca, J. Atmos. Terr. Phys. 39, 959-963. ISHIMARU, A., Wave Propagation and Scattering in Random Media (Academic Press, New York 1978). -KAO, S. K. (1979), Oscillation of inversion layer and pollution pumping, Conf. Preprints 4th Symp. on Turbulence, Diffusion, and Air Pollution, 448--449 (Amer. Meteor, Soc., Boston). KLOSTERMEYER,J. and LIU, C. H. (!978), Indication of gravity wave-meanflow interaction in upper atmospheric radar observations, Geophys. Res. Lett. 5, 507-510. KLOSTERMEYER,J. and ROSTER, R. (1979), Model computation of a jet stream-generated KelvinHelmholtz instability, (submitted to J. Geophys. Res.). KLOSTERMEYER,J., ROSTER,R., CZECHOWSKY,P., ROTTGER,J. and SCHMIDT,G. (1979), Atmospheric research by high power VHF radars, Umschau 79, 514-515. KRAUS, E. B. (Ed.), Modelling and Prediction of the Upper Layers of the Ocean (Pergamon Press, Oxford 1977). Kuo, H. L. and Stm, W. Y. (1976), Convection in the lower atmosphere andits effects, J. Atmos. Sci. 33, 21-40. LUDLAM, F. H. (1967), Characteristics of billow clouds and their relation to clear-air turbulence, Q. J. Roy. Meteor. Soc. 93, 419-435. MANSON,A. H., GREGORY,J. B. and STEI'HENSON,D. G. (1974), Winds andwave motions to 110 km at mid-latitudes, L Partial reftection radiowave soundings, 1972-73, J. Atmos. Sci. 31, 2207-2215. MATHEWS,J. D. (1976), Measurements of diurnal tides in the 80- to lO0-km altitude range at Arecibo, J. Geophys. Res. 81, 4671-4677. MEECHAM, W. C. (1972), Atmospheric turbulence, in Remote Sensing of the Troposphere, ed. V. E. Derr (U.S. Government Printing Office, Washington, D.C.), 4/1-4/22. MILLER, K. L., BOWHILL,S. A., GIBBS,K. P. and COUNTRYMAN,I. D. (1978), First measurements of mesospheric vertical velocities by VHF radar at temperature latitudes, Geophys. Res. Lett. 5, 939-942. MONIN, A. S., KAMENKOVlCH,V. M. and KORT, V. G., Variability of the Oceans (John Wiley and Sons, New York 1977), 43-98. ORLANSKI,I. and BRYAN, K. (1969), Formation of the thermocline step structure by large-amplitude internalgravity waves, J. Geophys. Res. 74, 6975-6983. RASrOGI, P. K. and WOODMAN,R. F. (1974), Mesospheric studies using the dicamarca incoherentscatter radar, J. Atmos. Terr. Phys. 36, 1217-1231. RASTOGI,P. K. and BOWrlILL,S. A. (1975), Remote Sensing of the Mesosphere Using the Jicamarca Incoherent-Scatter Radar, Aeronomy Report No. 68 (Aeronomy Lab., Univ. of Illinois, Urbana). RASTOGI,P. K. and BOWHILL,S. A. (1976a), Gravity waves in the equatorial mesosphere, J. Atmos. Terr. Phys. 38, 51-60. RASTOGI, P. K. and BOWHILL, S. A. (1976b), Scattering of radio waves from the mesosphere- H. Evidence for intermittent mesospheric turbulence, J. Atmos. Terr. Phys. 38, 449-462. R(STTGER, J. (1977), Travelling disturbances in the equatorial ionosphere and their association with penetrative cumulus convection, J. Atmos. Terr. Phys. 39, 987-998. ROTTGER,J. and CZECHOWSKY,P. (1978), VHF-radar echoesfrom the troposphere and stratosphere, Kleinheubacher Berichte 21, 279-290.

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Advances in Noctilucent Cloud Research in the Space Era By O. A. AVASTE1), A. V. FEDYNSKy2),G. M. GRECHrZOa), V. I. SEVASTYANOV 3) and CH. I. WILLMANN!)

Abstract - A summary of NLC research in the last two decades is presented. Results of NLC studies from the near-Earth space are discussed. It is shown that NLC can cover much larger territories than those estimated earlier and that there exists asymmetry in the coverage and also in the physical properties of NLC in the Northern and Southern Hemispheres. The mesopause often reveals a compelx multilayered structure. The pilot program of NLC research is discussed as a subprogram of the Middle Atmosphere Program and some vistas in NLC research are discussed. Key words: Noctilucent clouds; Mesosphere.

1. Introduction Noctilucent clouds (abbreviation NLC) have been a challenge to many investigators during the past century. These clouds resemble tenuous cirrus or cirrusstratus clouds except for their extraordinary height which is about 82 km. So they are indicators of the physical processes which take place in the mesopause: i.e. in the top layer of the mesosphere where in summertime the temperature minimum is of the order of 135-145~ Because of their small optical thickness they are visible to the observer on the Earth's surface only in twilight conditions when the Sun's depression angle ranges between 6 to 16~ The nature and origin of these clouds is still under discussion. There exist different hypotheses and contradictive theoretical concepts which try to explain the origin and evolution of N L C as well as their physical and optical parameters. The first recorded observations of N L C were made after the eruption of the volcano at Krakatoa in 1883. In June 1885 N L C were noticed by many observers in different countries. This could be explained by the occurrence of an extraordinarily bright display of NLC. The first well-documented recognition of the observed clouds as being an unusual phenomenon in respect of height was made by BACKHOUSEin 1) Institute of Astrophysics and Atmospheric Physics, Estonian Academy of Sciences, Tartu 202444, Estonia USSR. 2) Central Aerological Observatory, State Committee of Hydrometeorology and Control of Natural Resources, Moscow. a) Pilot-astronaut of the USSR.

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1885 at Kissingen, Germany, on June 8 of that year. On June 10 these clouds were recorded by Laska in Prague (according to JESSE, 1889) and on June 12, 1885 by TSERASKn (1890) in Moscow. Jesse himself observed NLC on June 23, 1885 (see JESSE, 1885). To Jesse we owe the name 'Leuchtende Nactwolken' or noctilucent clouds. The NLC occurrence on June 23, 1885, was recorded by several observers in Europe (see ASTAVOVICIJ, 1939) including Hartwig at the Tartu Observatory, Estonia (HARTWI6, 1893). The first sufficiently accurate NLC height determination (h = 75 km) was carried out by Tseraskii and Belopolskii making use of measurements on June 26, 1885 (see TSERASKII, 1890). The earliest publication of the accurate height measurement belongs to JESSE (1887). He determined the height of NLC which occurred in July 1887 and also obtained the result h = 75 km. Interest in these clouds waned during the period of 1909-24 but picked up again when Astapovich in the USSR began to study them. A summary of those observations was published by ASTAPOVICHin 1961. In the years 1932-34 STORMER (1933) and VESTINE (1934) made the first reported observation in Norway and over North America. The research of NLC intensified around 1948 when Paton in Scotland and Khvostikov in the USSR began their work on NLC. A special effort in NLC research was started during the I.G.Y. A wide network of NLC observation stations was set up over the Northern and Southern Hemispheres between the latitudes of 45-90 ~ and these data were processed and published by specie/1data centers located at College, Alaska; Edinburgh, Scotland and Tartu, Estonia. A NLC observation manual was prepared by Khvostikov, Willmann, Grishin, Fogle and Paton and was published in 1966 under the auspices of the WMO. In the years 1956-76 11 national symposia on NLC were carried out in the USSR. NLC data were discussed at international symposia in Tallinn (1966) (see KHVOSTIKOVand WITT, 1967), Tokyo (1968), Moscow (1971), Koblenz (1973), Berlin (1973), Grenoble (1975), Tallinn (1975), Seattle (1977) and Aberdeen (1978). International cooperation in NLC research is coordinated by the NLC Panel of the International Association of Meteorology and Atmospheric Physics. Bibliographies on NLC research were published in Meteorological and Geoastrophysical Abstracts (Vol. 15, No. 4, 1964) and by KOSIBOVAand PYKA (1969). In the years 1964 to 1974 the Canadian Atmospheric Environment Service published a NLC Newsletter Nos. 1-20 (Editor A. D. Christie). A catalog of NLC occurrences was published by SCHRI~DER(1968) and FAST (1972). In the years 1973-77 the Soviet Geophysical Committee published three topical collections on NLC research: by editors EERME(1973), VASILYEV0975) and AVASTE(1977). Several monographs and review articles on this topic were published (FOGLE, 1967; VASILYEV,1967; WILLMANN (ed.), 1967; WITT, 1969; KHVOSTIKOV, 1970; BRONSHTEN and GRISHIN, 1970; and SCHR()DER, 1975, 1978) where the knowledge of NLC is well documented. Following the excellent summary published by FOGLEand HAURWITZ(1966) the NLC research results from the Earth surface observations in the Northern Hemisphere can be presented as:

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Color: bluish white. Height (average): 82.7 km. Latitude of observations: 45-80 ~, best visible at about 60 ~. Season of observations: March through October, best in June through August. Times of observations: nautical and part of astronomical twilight, while the solar depression angle varies from 6 to 16~ Spatial extent: 10 000 to more than 4 000 000 kmL Duration: several minutes to more than 5 hours. Average velocity: 40 m/sec towards SW; individual bands often move in different directions and at speed differing from the speed of the display as a whole. Thickness (geometrical): 0.5 to 2 km. Vertical wave amplitude: 1.5 to 3 km. Average particle diameter: about 3 • 10 ~5 cm. Number density of particles: 10 -2 to 1 per cm 3. Temperature in the presence of NLC: about 135~ The general properties of NLC, presented in a thorough summary by FOGLE and HAURWlTZ (1966), are valid also at the present time. Nevertheless, the last ten years in NLC research brought some detailization and made several questions more precise. We shall discuss some of these advances in the years 1966 to 1978 and shall pay special attention to the NLC studies carried out from orbital stations.

2. Climatology o f N L C

The subject of NLC climatology covers latitudinal, longitudinal, seasonal and daily regularities of their occurrence and variations as well as their activity characteristics. The data on NLC occurrences prior to 1964 are based on observations of many individuals (see e.g. BRONSHTENand GRISHIN, 1970) randomly distributed (in time and geographical coordinates). Starting from 1964, NLC observations were carried out by a large network of ground stations according to a unified program (see INTERNATIONALNLC OBSERVATIONSMANUAL,1970) in many countries (e.g. Canada, Denmark, England, Federal Republic of Germany, Ireland, Poland, USA, USSR). These observations allow us to investigate some problems of NLC climatology based on statistically sounder data. All earlier observations took into account only the location of the NLC observer on the Earth. A more convenient way of calculating the probability of NLC occurrences and their analyses lies in the determination of their spatial coverage above the points of the Earth's surface where NLC can occur. For every point at an altitude of 82 km above the Earth's surface, the direction towards the point of occurrence can be calculated from many nearby stations and the possibility and probability of discovering NLC at that point can be estimated from the given observation stations. The Bayes' estimate has been suggested by Vasilyev (see WILLMANNand VASILYEV,1973; VASILYEVet al., 1975) for the above calculations.

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The first calculations were carried out on the probability of the presence of NLC at individual points of the Earth's surface and in accordance with the chosen significance level of p r o b a b i l i t y - a r e a s of NLC fields on the Earth's surface undoubtedly show the promising nature of the method suggested by Vasilyev. A probabilistic model of the seasonal and the latitudinal distribution of NLC was elaborated by VASmYEV and MELNIKOVA (1975). They demonstrated that the earliest maximum (in the first decade of June) occurs in the latitude of 45~ later this maximum shifts towards the north and in the first decade of August lies in latitudes of 67~ The problem of variations in NLC activity during the whole observation period (starting from 1885) was investigated by many authors. The summary of the number of nights with NLC is given in Fig. 1. As was pointed out by FAST and FAST (1977) this long muttiyear data set is so inhomogeneous that it is not possible to deduce a statistically sound estimate of the NLC activity in these years (see also DIETZE, 1973). Nevertheless, the number of nights in the given year when NLC occur can serve as a crude characteristic of NLC activity. Figure 2 gives the dependence of the number of nights with NLC (nt) on the number of stations that record these NLC occurrences (mr). Numbers at the circles indicate the year of occurrence. Figure 2 shows that theoretical maximum number of nights with NLC cannot exceed 160, while the maximum observed value nt was 144 (in the year 1966). Figure 3 illustrates the annual variation of NLC activity calculated on the basis of NLC occurrences in ten-day periods all over the globe. The activity is given in tenths: 10 indicates that every night somewhere over the Earth N L C were observed, 0 denotes that in the decade no NLC were observed all over the nt ! T50 ~ 730 I10 90 7O 50 JO lU 1890

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globe. Activity of NLC occurrences increases in summer and has a maximum in July. Figure 4 shows the annual mean activity deviations from the eleven-year mean value (which is taken to be a zero line). In the years 1964-67 the NLC activity was considerably higher than the mean value, in the years 1958, 1959, 1969-72 it was considerably lower. The eleven-year cycle was also clearly observable from the uniform observations carried out in 1957-72 by the observers of the All-Union Society of Astronomy and Geodesy of the USSR. All these observations were carried out in the latitude zone 54 to 59~ Figure 5 gives the number of the NLC occurrences observed in this zone: a maximum occurs in the year 1967 and a minimum in 1971. As pointed out by FAST and FAST (1977), in the year 1976 the NLC activity was rather high. FAST and FAST (1977) drew the following conclusions on the NLC climatological research from the earth surface: (1) the season of NLC occurrences begins in the Northern Hemisphere in the first half of March, the end of the season is less pronounced, ranging from late October to November; (2) 68.7700 of nights and 90.6~ of reports of NLC occurrences fall in summer months, almost a half of the reports, and 28.3700 of nights fall in July;

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533

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(3) in the same latitude belt the frequency of N L C occurrences is the same for any longitudes; (4) the belt of the N L C observation zone is in latitudes 45-71 ~ occasional N L C appearances have been recorded as far as 81-82~ the latitudes 53-57~ are optimal for N L C observations;

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HEAN NLG OCCURENCE$ PER YEAR

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(5) towards the north the period of maximum frequency is gradually shifted to a later time; (6) NLC are observed before midnight only in 37% of the observation time, though NLC occur more often before midnight; (7) NLC are observed during some minutes up to 5 hours and more, bright NLC are observed for 4 hours and more; (8) N L C tend to appear on several successive nights (forming a series of occurrences); (9) in the activity of NLC is revealed an 11-year period with a maximum occurring 2 years after the minimum solar activity. Over the Southern Hemisphere we possess only a limited number of observations from which it is not possible to draw sufficiently reliable long-term climatological conclusions. A summary of NLC observations in the Southern Hemisphere is given by FOGLE and HAURW[TZ (1966). An illustration of the NLC occurrences at 53~ at Punta Arenas, Chile, is given by Fogle in Fig. 6. It appears that the peak of the NLC activity at 53~ occurs some 20-30 days after the austral summer solstice. NLC observations from the Soviet Antarctic stations have been carried out starting from the year 1965 (see e.g. KREEM, 1967, 1968; DOLGIN and VOSKRES~NSKn, 1973), but their maximum occurrence lies in the period of a polar day and therefore only limited data on the transitional months, on autumn and spring are available (see also KILFOYLn, 1968). In the papers by McKAY and THOMAS (1978), COAKLEY and GRAMS (1976), HUMMEL and OLIVERO (1976), HUMMEL (1977) estimates were made of the effect of N L C on the global climate. The analysis of COAKLEYand GRAMS (1976) implies that for ice particles of 10 -5 cm radius in a 10 km thick layer, a density of 12 x 10 -12 g km -3 would produce a drop of 1~ in the global surface temperature. This result is consistent with regional temperature effects present in polar mesospheric ice clouds derived by HUMMEL and

Vol. I18, 1980)

Advances in Noctitucent Cloud Research in the Space Era

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80

60 lZ ILl U 40 rr hi 0-

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Percentage of clear nights with NLC at Punta Arenas, Chile, during the austral summer of 1956-66. OLIVERO (1976). MCKAY and THOMAS (1979) pointed out that the solar system in its motion through the galaxy may have suffered a number of encounters with a dense interstellar cloud for which the number density of molecular hydrogen H2 is higher than 10a cm-3 and then the Earth's atmosphere would be subjected to an interstellar H2 flux of 7 x 109 cm-2 sec-1 for periods of l0 s years. This could greatly enhance the water vapor content in the middle atmosphere, reducing the mesospheric ozone concentration and thereby lowering the average temperature and altitude of the mesopause. As a result of this, widespread mesospheric clouds would occur increasing the planetary albedo and the resulting radiative cooling at the surface may have been sufficient to 'trigger off' an ice age. Later on, HUMMEL (1977) showed that ignoring the diffuse nature of the radiation reflected from the Earth-atmosphere system below NLC, as was done in the previous simple models, can result in an overestimation of the climatological impact of aerosols in sign and magnitude by a factor of 4-6, especially when one calculated regional (polar cap) effects. This is consistent with the results of calculations by BRASLAUand DAVE (1973), that an increase of the absorbing aerosol in the atmosphere may lead to cooling or heating depending on the scattering and absorbing characteristics of the aerosol substance and upon the location of dust within the atmosphere. All these calculations include such aerosol parameters as number density, size distribution, refraction index, which have not been determined in the NLC layer with sufficient reliability, and for that reason the climatic effect of N L C needs further investigation.

3. Morphology and dynamics of NLC A specific character of N L C is their extremely diverse, often complicated and filigreed morphological structure. The study of this structure enables one to make

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several conclusions on the physical nature and genesis of NLC as well as upon the processes in the mesopause and its adjacent layers. The morphological classification of NLC was proposed by GRISHIN (1954, 1955a,b). This classification served as a basis for internationally accepted classification (e.g. GRISmN, 1957; INTERNATIONAL NLC OBSERVATIONMANUAL, 1970) and was used as an aid for observers during the I.G.Y. and the I.Q.S.Y. The above papers contained a detailed description of the NLC morphological structure using five main types and seven subtypes. We summarize in the following the description of NLC structural types as it enables one to understand the build-up and genesis of a N L C field. Type L Veils: These are very tenuous, lack well-defined structure and are often present as a background to other forms. They resemble cirrus clouds, occasionally contain faintly fibrous structure, and often exhibit a flickering luminosity. Veils are the simplest form of NLC and often precede (by about half an hour) the appearance of NLC with well-defined structure. Type II. Bands: These are long streaks, often occurring in groups arranged roughly parallel to each other or interwoven at small angles, but occasionally an isolated band is observed. Two groups of this type occur: II.a, are comprised of streaks with diffuse, blurred edges; II.b, have sharply defined edges.

Type IlL Billows: These are arrangements of closely spaced roughly parallel short streaks. The distance separating adjacent billows ranges from about 1 to 10 km. Billows sometimes lie across the long bands, giving the appearance of a comb or feather. At other times they appear alone against the veil background. The billows may change their form and arrangement, or appear and disappear within several minutes or tens of minutes, much more rapidly and frequently than the long bands. This NLC type also may be divided into two groups: III.a, are comprised of short, straight and narrow streaks; Ill.b, exhibit a wave-like structure with undulations.

Type IV. Whirls: These are partial or, on rare occasions, complete rings of cloud with dark centers, and may indicate the presence of turbulence near the mesopause. They are sometimes seen in veil, band and billow forms. Three subgroups may be observed: IV.a, are comprised of whirls of small radius of curvature (0.1 to 0.5~ and may appear as small bright crests looking somewhat like light ripples on a water surface; IV.b, have a form of a simple bend of one or several bands with the radius of curvature of 3-5 ~ IV.c, have a large-scale ring structure.

Type 1I. Amorphous: These are similar to veils in that they have no well-defined structure, bu t they are brighter and more readily visible than the veil type.

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In complex displays, two or more forms may be seen simultaneously, and it is not unusual for two intersecting groups of long bands to occur, and these give rise to bright knots where the waves cross. It is worth noting that the above classification, which was deduced from the observations carried out on the Earth's surface, is applicable also to observations from space. NLC descriptions and sketches in logbooks of the orbital stations 'Salyut-4' and 'Salyut-6' made by the Soviet astronauts V. Sevastyanov, P. Klimuk, G. Grechko and J. Romanenko indicate that the morphological structure of NLC is discernible from space (e.g. WILLMAYN et aL, 1977). The special features of NLC structural forms are evidently connected with their formation mechanism on the one hand and with the dynamic processes in the atmosphere on the other hand. To study these connections the temporal-spatial NLC field parameters and their genesis must be determined. Spatial parameters include the altitude of the NLC field and the geographical coverage, the thickness of the NLC layer and the simultaneous existence of several layers. Genesis is expressed in temporal variations of the NLC field extent as well as in variations of its morphological structure. In the period 1885 to 1967 were published data on 4166 cases of NLC height determinations (e.g. TSERASKII, 1887; JESSE, 1887, 1896; STORMER, 1933; BUROV, 1959, 1966, 1967; WITT, 1962; FOGLE, 1966; DIRIKIS et al., 1966; FRANZMAN and FRANZMAN, 1967; BRONSHTENand GRISHIN, 1970). The weighted mean value of the NLC layer height is 82.97 kin, the maximum and minimum values measured being 95 and 73 kin. It should be mentioned that this result agrees excellently with the mean value obtained from 187 photogrammetric measurements by JESSE (1896), which was 82.08 + 0.009 km. It is remarkable that in some years NLC heights vary in comparatively narrow altitude limits: e.g. in 1958 NLC height varied from 81 to 85 km (598 measurements). Moreover, height determinations by different authors in different geographical locations, made on the same night, differed less than 0.5 km. But there exist years when the height of NLC varies within broad limits: e.g. in 1964 measurements in Estonia and Latvia gave the NLC height range 74-95 kin. Very likely conditions for NLC formation at different moments and locations differ and this is expressed in a large variation of the NLC heights in some years. It was pointed out that the areal coverage of NLC fields varied in a range of 2 • 10~ to 3.6 x 106 km 2 (FOGLE, 1968). The NLC observation data from the surface network processed at the Tartu NLC Center confirmed this estimate. Figure 7 illustrates the areal coverage of NLC fields. Statistical analyses of the data derived from the global surface observations during the I.Q.S.Y. allowed W~LLMANN(1968) to conclude that NLC fields can cover considerable parts of latitudinal belts north of 45~ This was later confirmed by space observations (WILLMANN et al., 1977), and a considerably more complete picture of the coverage and of the specific features in the morphology of NLC was

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Figure 7 Distribution of NLC fields on 24-25 July 1964, deduced from surface observations. obtained. An extract from the notes made by V. Sevastyanov in the log-book of the Orbital Station 'Salyut-4' can serve as an illustration of this: ' . . . i n observations of N L C it struck me that they not only enrapture the observer, but also attract his attention with their unusual picturesqueness. ' I was struck: (1) by their appearance (lustreless, but very intensive color, I called it " m o t h e r of-pearl"-like); (2) by their extension (we observed them over Kamchatka, but on another orbit we saw them extending from the Urals to Kamchatka. Later on the same day we observed them over Canada);

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539

(3) by their fine azure structure. Their strict upper border (never higher than the "aureole") sometimes reaches its height. Then they (NLC) are visible over the sunlit horizon. Their structure is swan-feather-like, when NLC are observed full in the face; (4) not only by their lateral extension but also their extension in depth. In depth we observed them in different phases...' and further: ' . . . ( I ) are they rotating? Certainly, they are rotating. Together with the Earth's atmosphere but at a speed which is considerably less that of the Earth, i.e. observing them from the Earth surface they must move at a high speed in the direction opposite to the Earth's rotation. (2) They spread over the whole latitudinal belt'. The monitoring of NLC fields from space allows us also to specify the question of the multilayered structure of NLC. GRISmN (1952, 1955b, 1967) deduces from the observations carried out in the years 1950 and 1951 that NLC can occur in twolayered form. He pointed out that as a rule veils occur lower than the wave forms of NLC. The multilayered structure of NLC is distinctly observable from time-lapse cinematography. In some cases different layers of NLC move in different directions. Theoretically the question of the two-layered structure of NLC was discussed by NovozHirov (1962, 1967). He showed that in the mesopause it is possible for two layers to exist with a minimum temperature. Two-layered (even three-layered) NLC fields have also been described from space observations (WmLMANN et al., 1977). There exists no unique theory explaining genesis and distribution of NLC. Several observers (e.g. CHRISTIn, 1969) pointed out that the evidence for a direct relationship between synoptic distributions of NLC and the quasi-geostrophic systems in the tropospheric circulation has been shown to be ill defined. A more indirect coupling mechanism may exist in internal gravity waves originating in the tropospheric jet streams (e.g. HINES, 1959, 1968; AUFF'MORDT and BRODHtJN, 1974). CHRISTm(1969) proposed that the gravity waves, generated sporadically during periods when the mesopause temperature is less than 140~ propagate energy upward, and generate locally increased vertical eddy mixing throughout the upper mesosphere and lower thermosphere. He showed that in the summer mesosphere local supersaturation, in the steady state, could result at the mesopause with an eddy transfer coefficient of about 10 -3 km 2 sec-1. This value is one order of magnitude higher than that given by HESSXVEDr(1969). Thus, NLC may be formed in a region where a local increase in the eddy transfer coefficient has resulted from the gravity wave coupling, and may be advected out of the source region for some considerable distance before evaporating. To prove this it will be necessary to study the effect of the gravity wave source region on NLC, either directly or by means of large-scale parameters found indicative of the gravity wave source.

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HAtn~WITZ and FOGLE (1969), HAURWITZ(1971, 1972) showed also that bands and billows in NLC fields can appear on the ridges of internal gravity waves. REITER and HAtntWITZ (1974) inferred that wave formations observed in NLC regions are most likely generated in situ and not propagated upward from the troposphere. KROPOTKINAand SrIEVOV(1975) also noted that lunar tides, being manifestations of longwave gravity waves, can lead in the summer mesopause to a drop of temperature of 15-20~ and most likely cause the formation of NLC in the form of uniform veils.

4. Characteristics of the mesosphere This section reviews some physical and chemical properties of the Earth's atmosphere relevant to the understanding of the NLC phenomenon.

4.1. Temperature of the mesopause Essential additions to the U.S. Standard Atmosphere 1976 of the Arctic and Subarctic Region, where NLC occur, were prepared by COLE and KANTOR (1977, 1978). Sets of monthly reference atmospheres, which show the seasonal changes in the vertical distribution of the temperature, pressure and density for altitudes up to 90 km, are presented there. Estimates of the magnitude of the diurnal, day-to-day and spatial variability of temperature and density are included. In the lower layers the assumption of the local thermodynamic equilibrium (LTE) enabled Kirchoff's law to be applied so that the Planck black-body function could be employed as a source function in radiative transfer calculations. At high levels in the atmosphere LTE is no longer a good assumption, and the molecular processes involved need to be considered in more detail. However, at the height of the mesopause (80 km) one can yet consider that the rates of excitation and de-excitation by collisions will be sufficiently rapid so as to dominate over radiation processes. This is the situation of local thermodynamic equilibrium. As the temperature in the mesopause appears to be an important parameter for NLC formation, and since NLC seem to form in a thin layer, it would be of great interest to obtain continuous temperature measurements over the height range of 75-90 km. Curves representing the sum of the annual and semiannual cycles of temperature for altitudes between 30 and 80 km are shown in Fig. 8 for Churchill, Fort Greely, Thule and Point Barrow (COLE and KANTOR, 1977). These measurements confirm the deduction of KELLOGand SCHILLING(1951) that the mesopause at high latitudes is warmer in winter than in summer. Latitudinal temperature-height cross-sections of mean monthly temperatures for January and July are shown in Fig. 9 (COLE and KANTOR, 1978). At latitudes 60~ and 75~ the observed day-to-day variations

Vol. 118, 1980)

Advances in Noctilucent Cloud Research in the Space Era t

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the space observations of NLC on board 'Salyut-6', carried out by Soviet astronauts Yuri Romanenko and Georgii Grechko in the period from December 1977 to March 1978 (see Sections 7 and 8 of this paper), the systematic weekly launches of Soviet meteorological rockets M-100B were performed at the Soviet Antarctic Station 'Molodezhnaya' (68~ 46~ with the aim of determining temperature and wind profiles up to 80 kin. The temperature was measured by using standard rocketresistance thermometers (e.g. IZAKOVet al., 1967). The wind velocity and its direction was detected by tracking the cloud of dipole reflectors (chaff clouds) (PAHOMOV, 1969). The uniform data-set was derived from December i977 to March 1978. The apogee of rocket trajectores was at a height of 85 to 86 kin. A careful critical analysis of the data and an improved data-processing technique allowed Fedynsky to determine mean temperature profiles up to 84 km (see Fig. 10). Average deviation from the mean profile is presented in Table 1. The temporal variation of isotherms above 'Molodezhnaya' is presented in Fig. 11 for altitudes of 78-83 kin. Figure 11 indicates that at a height of 84 km (and higher) there occu r periodically regions with extremely low temperatures (100-120~ The air remains cold also after an adiabatic descent. At heights of 80-79 km these temperature contrasts are considerably smoothed out. Just these periods of a local drop in temperature at an altitude of 80 km are accompanied by the occurrence of intensive

Vol. 118, 1980)

Advances in Noctilucent Cloud Research in the Space Era

543

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NLC (see shaded areas in Fig. 11). In the intervening periods of warming NLC disappear. The existence of the general trend of warming in the period studied can be explained by the seasonal variation of the temperature in the mesosphere. The temperature of the mesosphere increases in the austral winter. The maximum decrease of the temperature is reflected in independent wind measurements. A considerable decrease in temperature is connected with the intensification of the eastward zonal flow. An increase in temperature corresponds to the periods of weakening of the eastward zonal flow and to a rise of the meridional flow. Sometimes the eastward flow changes even to a westward one. It should be emphasized that the above local temperature variations are worth more detailed further investigations.

Table 1 Average temperature profile and temperature variation according to rocket soundings at 'Molodezhnaya" (68~ 46~ from December 1977 to March 1978 H(km)

T~ AT~

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of 78 to 83 km in the period of December 1977 to March 1978. At heights of 78, 80 and 82 km, wind velocities and directions are indicated. Shaded areas show NLC existence observed from the Orbital Station 'Salyut-6'. Probably NLC continued their existence on 4 February 1978, but then astronauts did not carry out any observations.

4.2. Chemical composition The chemical composition of the atmosphere is fairly uniform up to 80 km, when we consider the main components N2 and 02. Above this altitude photodissociation produces a marked increase of atomic oxygen. A brilliant review of the neutral composition of the stratosphere and the mesosphere is given by ANDERSON and DONAHUE (1975).

4.3. Ionosphere Ionization of the upper atmosphere depends primarily on the Sun and its activity. The major part of ionization is produced by solar ultraviolet radiation, X-rays and corpuscular radiation from the Sun. As the Earth rotates with respect to the Sun, ionization increases in the sunlit atmosphere and decreases on the night-side. It is reasonable to seek a correlation between N L C parameters and the ionospheric D layer (the part below 90 kin) and the E region (90-160 km). There exists so far no general and overall theory to explain all the peculiarities of the ionization in the D

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region. According to HOUSTON (1958) the electrons in the D region arise from the ionization of NO by Lyman-alpha radiation. HUNTENand MCELRoY (1968) proposed an additional mechanism ionizing the excited molecules O2(1Ag) by the radiation of the wavelengths A = 1027-1118 A. In the night-time the main agent of ions in the D layer seems to be electrons with the energy of n x 10 KeV; GOLDBERGand WtTT (1977) determined from the rocket mass-spectrometric measurements that in the case of NLC occurrences the concentration of ion dusters H30 + • (H20)~,, m = 2-4 and NO + x (H20),, n = 2-3, is in the mesopause by one order of magnitude higher with no NLC. They also noticed that in the layer of 81-86 km are present heavy ion clusters with atomic mass 70 to 128 which contain Fe +, FeD + and FeD +. GOLDBERGand WITT (1977) drew the conclusion that these heavy clusters could act as condensation nuclei where ice crystals grow in the cold mesosphere as a result of the nucleation process. Some theoretical estimates of this kind of NLC formation were discussed by REID (1975) and BURI~E(1977). REID (1975) showed that nonspherical ice particles could fall in the mesopause sufficiently slowly to achieve optically observable sizes in the NLC layer. LAUTER (1974) pointed out that the height distribution of both NO and of the minor constituents involved in water-cluster chemistry will strongly depend on atmospheric dynamical transport processes, like turbulence and advective transport. The thermo-dynamic and circulation regime of the mesosphere has been reviewed in a monograph by RAKIPOVAand YEFIMOVA(1975) and in a recent monograph edited by PORTNYAG~Nand SI'RENGLER(1978). But it should be pointed out that while there exists reasonably good agreement between observations and theory in the mesosphere for odd hydrogen, nitrogen and oxygen systems, serious shortcomings exist in our empirical knowledge of other minor species and of the coupling between dynamics and chemistry in the upper layers. Hopefully the global measurements of the concentration of minor constituents of Nimbus 7 satellite will soon be available and will serve as a basis for a more detailed investigation of the interrelation of the parameters of the mesospheric and ionospheric structure. 4.4. Water vapor concentration

The water vapor concentration in the mesosphere is an important parameter studying the physical processes connected with NLC formation. The available experimental data are rather contradictory. Episodic and sparse measurements of water vapor in the mesosphere show a scatter of data as large as two orders of magnitude. This is partially caused by the use of different methods of measurement. Numerous photochemical models which consider formation and destruction of such minor constituents as H20, CH4, H2 etc. under the influence of solar ultraviolet radiation (HESSTVEDT, 1964; HUNT, 1963, 1973; SHIMAZAKIand LAIRD, 1970; NICOLET, 1970; ANDERSON and DONAHUE, 1975; and others) made use of basic information on the relative water vapor concentration measured in the lower stratosphere: usually the

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value of the mixing ratio equalled 2-3 x 10 -6 g/g. Considering the fact that the atmosphere must be well mixed, this value is inserted into calculations also at the height of the mesopause. However, taking into account that even at a height of 30 km there exist contradictory data on the 'dry' and 'moist' stratosphere models, such an approach needs a critical analysis, the more so as the majority of recent measurements indicate considerably higher values of the water vapor mixing ratios at a height of 30 km compared with the earlier data (e.g. BLrR~ERTet al., 1974; EVANS, 1974; CHALONERet aL, 1975; RADFORDet al., 1977). A more detailed survey of the water vapor concentration in the mesosphere up to I

I

I

I

I

I

I

I

Ht~

50 40 f0q' 30

.20

\ -~40

-f20

-tO0

-NI

-60

-40

-gO

0

*tO

.40 T('l)

Figure 12 Water vapor mixing ratio versus altitude: (1) data generalized by SONNTAG(1974); (2) measurements carried out by FEDYNSKYand YUSHKOV(1974); (3) by EVANS(1974); (4) by ABADIE(1974); (5) by MARTELLand EHHALT(1974); (6) by PEROV and FEDYNSKV(1968); (7) by CHYZHOVand KIM (1970); (8) by ARNOLD and KRANKOVSKV(1977); (9) by MARTVNKEVICH(1972); (10) by QUESSETTE(1968); (11) by MARKOVe t al. (1978); (12) by KONDRATVEVe t aL (1976). Curve T~ gives the mean temperature at 60~ in July (COLE and KANTOR,1978).

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100 km is given by SONNTAG (1974). The data generalized by him are indicated in Fig. 12 as a shaded area (1). Figure 12 illustrates more recent data on the mesospheric water vapor, which were obtained by different methods: curve 3 gives optical rocket measurements (EVANS, 1970); curve 4 shows the results when aluminum oxide sensors were used (ABADIE, 1974); curve 5 denotes the results of cryogen traps of two launchings by MARTELLand EHHALT (1974); curve 6 represents data obtained by means of Pirany gauge type heat recorders (PEROV and FEDYNSKY, 1968); curve 7 displays data derived from absorption in the Lyman-alpha band (CHYzHOVand KIN, 1970); curve 8 gives mass-spectrometric measurements by ARNOLD and KRANKOVSKY (1977); curve 9 illustrates mass-spectrometric measurements by MARTYNKEVICH (1972); curve 10 shows optical measurements by QUESSETTE(1968); curve 11 indicates optical measurements obtained by MARKOV et al. (1978) from the orbital station 'Salyut-5'; asterisk 12 shows an estimate from optical measurements performed aboard 'Salyut-4' (KONDRATYEVet al., 1976). All the data are given in curvilinear coordinates. Thin solid lines indicate isolines of water vapor mixing ratios. In the period of 1977-79 FEDYNSKYand YUSHKOV(1974) carried out measurements of the water vapor mixing ratio using Pirany gauge type heat recorders at Volgograd (46~ and at the station Tumba (8~ These results with the above uniform apparatus and data processing techniques are presented in Fig. 12 as a shaded area (2). The data received by the above method allowed Fedynsky to study the water vapor mixing ratio (in the altitude region of 30 to 80 km) dependence on the season: the results indicated a distinct annual cycle with a maximum in July-August and a minimum in January-February in the Northern Hemisphere. It should be noted that in Fig. 12 solid lines give measurements in tropical regions, and broken lines in middle latitudes. Humidity in the mesopause in middle latitudes always exceeds that in the tropical zone. All soundings indicated that the water vapor mixing ratio increases with height, but nevertheless in tropical regions the atmosphere is closer to the ' d r y ' model up to 50-60 km. In middle latitudes, especially in the summer period, the increase of the mixing ratio is observable starting from the height of 25-30 kin. The quadratic mean error is less than 4 0 ~ ; this value is considerably lower than the mixing ratio variations observed. It should be noted that the differences in the water vapor mixing ratio estimates one based on the data from the orbital station 'Salyut-4' (see KONDRATYEV et al., 1976) and the other from the orbital station 'Salyut-5' (see MARKOV et al., 1978)are explainable as the first estimate was made on the basis of the measurements over the tropical zone, the other over middle latitudes. It follows from the above discussion that the water vapor concentration in the mesosphere depends not only on the season but also on the latitude. Episodical measurements of the water vapor at 80 km using different methods must be systematized and submitted to a critical analysis, taking into account the accuracy of the measuring techniques. The cause of the increase of water vapor mixing ratio with the height and latitude is still under discussion.

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Estimates show that the observed increase of the water vapor mixing ratio could be explained by taking into account the velocity of the vertical drift in the atmosphere of 1 mm sec-1; nevertheless the scarce data on the vertical and meridional velocity components measured independently are insufficient for the construction of global models. From the standpoint of the condensation hypothesis the temperature data (given in Section 4.1) show that in the summer period in the mesopause water vapor easily reaches the supersaturation condition. This is illustrated by the curve of the mean temperature at 60~ in July according to COLE and KANTOR (1978) (curve Ts in Fig. 12). Ion clusters (e.g. MARTVNKEVICH,1973; WITT, 1974b)or aerosols of meteor origin (BRoNSHTEN, 1950) can serve as condensation nuclei in the formation of NLC.

5. Aerosols in the mesosphere

The suggestion that NLC particles may be composed of ice belongs to WEGENER (1925, 1926), JARDETSKY0926), HUMPHREYS(1933) and VEGARD (1933). This idea was reviewed and quantitatively examined by HESSTVEDT(1961). This idea has gained general acceptance, as measurements and theoretical estimates of the temperature and the water vapor content in the mesosphere have shown that supersaturation conditions might well be expected to occur in the high-latitude summer mesopause. The idea of the condensation mechanism of NLC particles was in recent years supplemented by the coagulation mechanism proposed by RosINsI~I and PIERRARD (1964), ANDREYEV et al. (1975). They pointed out that considering the lower water vapor concentration in the mesopause the condensation mechanism is insufficient in forming NLC ice particles. So they assumed that spatial-temporal changes in aerosol characteristics are mainly controlled by vertical air currents and the influence of relative humidity on the aerosol structure. In case of low absolute humidity the main mechanism of particle growth must be coagulation of particles. The nonspherical form of particles is typical for crystals formed from hydroscopic materials. The origin and chemical composition of condensation nuclei has been discussed in many papers. A theoretical estimate of the accumulation of cosmic dust in the mesopause was made by DMITRIYEV0959) (see also FOGLE and HAURWITZ, 1966). Rocket samplings by HEMENWAYet al. (1964a,b), W[~rT (1967), Flocco and GRAMS (1971), WlTT et al. (1976) gave a rather good agreement with the theory. Flocco and GRAMS (1971) concluded that in the polar summer mesopause the particles with the radius r = l0 -6 to 5 • 10 -~ cm can be trapped for a period of 1-5 days and they could turn to condensation nuclei in case of the formation of NLC. Later in 1970 (see HEMENWAYet al., 1972; HEMENWAY,1973) nickel and iron nuclei were determined from two rocket experiments carried out at Kiruna, Sweden. HEMENWAY(1973) also put forward a suggestion that particles of La, Tu, Pr, Os, Yt, Ta were present in NLC, but this has not been confirned by other investigators.

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Electron micrographs of NLC particles captured in rocket experiments (e.g. SOBERMANand HEMENWAY, 1965; WITT, 1968; S~:RWANEK, 1969; HEMENWAYet al., 1972; HEMENWAY, 1973) showed that there was usually a halo-like structure around the particles. This structure is impressive only when NLC exist and it has been interpreted as a volatile particle coating, possibly being due to the ice coating on the particles collected from the NLC layer (see Fig. 13). The existence of a permanent layer of light scattering particles in the polar mesopause during the summer months was inferred by DONAHUE et aL (1972). They carried out measurements of the vertical brightness profiles by means of a scanning two-color photometer (~ = 5893 A and 5577 A) on the OGO-6 satellite. DONA~UE and GUENTH~R (1973) showed that the probable thickness of this aerosol layer is less than 5 km and that it is located close to the mesopause having an average height of 84.3 km. They found that the concentration of scattering particles increases by a factor of between 50 and 100 between 65~ and 80~ (see Figs. 14 and 15). They also inferred that this intense scattering layer, whose average vertical optical thickness

Figure 13 Electron micrographs of noctilucent cloud particles collected in a rocket experiment.

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O . A . Avaste et al.

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2.7 x I0~

i0 3 YELLOW 786 ~ LATIIUDE 175 DAY, 1969 10:27 UT

RAYLEIGH SCATTERING

2.'/x 103

SCA11ERING'LAYER n-

0~

.E

n,,

la

.E

o

2.1x10 zn"

c

._o

E

rr"

t~

21

50

100 Altitude

150

2.1

in km

Figure 14 Slant emission rates observed by OGO-6 airglow photometer at 5890 ~ above the horizon as a function of the altitude of the closest approach of the line of sight for 78.6~

is r = 10 -4, develops over the polar region about 15 days before the solstice and is a permanent feature of the summer polar atmosphere. This scattering layer seems to be a daytime manifestation of N L C ; assuming that the particle radius is r = 10 .5 cm (WITT, 1968, 1974a,b; FARLOW et al., 1970; DONAHUE et al., 1972), the particle concentration must be 15-40 particles per cm 3. This concentration of particles is considerably higher than that estimated in the noctilucent cloud layer (e.g. WITT, 1968). Assuming that particles of the polar aerosol layer are also ice-coated nuclei, ANDERSON and DONAHUE (1975) estimated their total water content. Since each particle with a radius of 1.5 x 10 .5 cm contains 2.7 x 108 H 2 0 molecules, the water amount tied up in these clouds would be between 4 to 13 x 109 cm -3 at about 85 km. According to the model of hydrogen compounds presented by ANDERSON and DONAHUE (1975) the density of H2 at 85 km would normally be 8 x 10 a cm -a, that of H 2 0 about 7 x 107 cm -3 and that of H about 10 a cm -3, making the total 2H only 109 cm -a. This discrepancy could be explained by adding an efficient H~O transport mechanism

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551

IOQ(

H SCATTERING

YELLO| 86.9* LATITUDE 64' SOLARZ IT50AY,1969 10:29UT

,,,~'SC~TTERING"LAYER :. ~,,,o~

,~

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g

-1

g

4

~

~, z,,,o 2 - ~1,

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Figure 15 Same as Fig. 14 except for 86.9~

to the cold trap in the polar summer mesopause. The above mechanism shows a characteristic build-up time of only about 5 days. On the basis of rocket soundings (e.g. HEMENWAY e t al., 1964a,b) and of optical measurements, WITT (1968) deduces that N L C particles can exist within a large radius range of 2.5 • 10 -6 cm _< r < 10 -4 cm. As a first approximation, the particle distribution is given by the Junge law dn(r)

= c •

r -v

d o n r),

where r is the particle radius. The constant c is a measure of turbidity depending on the number ofpartic/es in a cubic centimeter. The value v occurs in the range 2 < v < 3 (e.g. HEMENWAY e t al., 1964a). As presented above, many papers give an estimate of the mean particle radius r = 10 -5 to 1.3 • 10 -5 cm (e.g. FO6LE and HAURW~TZ, 1966). Three recent papers (TOZER and BEESON, 1974; HUMMEL and OLIVEgO, 1976; HUMMEL, 1977) also suggest that a practical upper limit of particle sizes in the N L C layer can be taken to be 10 -5 to 1.3 • 10 -5 cm. GADSDEN (1978) showed that their analysis is not convincing since cloud particles are non-spherical the deduction of the particle size from measurements of the degree of polarization is rather uncertain, if not erroneous. GADSDEN (1978) also pointed out that the discrepancy in the H 2 0 content estimate (see above) in the aerosol layer over the polar cap in summer derived by ANDERSON and DONAHUE (1975) could be due to assumed unrealistically small sizes of ice particles in the clouds which leads one to postulating impossibly high amounts of the mesopause water vapor.

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FRANK et aL (1970), DE BARY and ROSSLER(1974), GADSDEN (1975) inferred that the observations of the NLC gave an indication of 3 x 10 -5 cm as a characteristic radius of cloud particles. GADSDEN (1977a) noted that this could be revised down to 2 x 10-5 cm if particles are rod-like. GADSDEN(1977a,b) pointed out that if measurements show even a small amount of elliptical polarization, this is an indicator that there exist uniformly orientated elongated crystals in NLC; the presence of elliptical polarization indicates clearly that the NLC models involving only spherical scatterers need to be modified. In recent years a number of papers have been published where the optical properties of nonspherical particles are discussed. CHYLEK (1977) proved that the extinction cross-section of a randomly orientated nonspherical particle is always larger than the extinction cross-section of a spherical particle of equal volume. JENNINGS et al. (1978) showed that absorption is generally less dependent on the size distribution than extinction and in general is not linear with the imaginary refractive index, especially in case of broad particle distributions. FAXVOG and ROESSLER(1978) demonstrated that in a highly absorbing particle set the optically most active particles are those whose diameters lie in the range of 0.15 to 0.5L LATIMERet al. (1978) showed that the shape and orientation of particles can strongly influence the measurement of the whole particle size. The effects of the refractive index are also found to be significant but smaller. Results of calculations carried out by GOTTLER(1952) and FENN and OSER (1965) indicate that for compound particles with an absorbing nucleus smaller than about one-tenth of the total diameter of the particle, the optical properties are almost completely determined by the outer shell. The idea of ice-covered particles of NLC was generally accepted; their optical properties were estimated by using data on the complex refractive index of ice (e.g. IRVINE and POLLACK,1968; RAY, 1972). NLC were considered to consist of compounds of ice particles, minerals and metal particles (e.g. HEMENWAYet al., 1964a). It should be noted that if the ice shell is smaller than nine times the absorbing nucleus radius, the optical properties of two-layered particles are essentially different (e.g. R66M, 1974) and these peculiarities must be considered in future research on NLC optical parameters, especially in the first stages of cloud development. A systematic comparison of extinction and absorption efficiencies of nonspherical and spherical particles was carried out by WELCH and Cox 0978). They found that whether the nonspherical correction has any applicability depends on the distribution of particle sizes. Small ice crystals in the solar spectrum can lead to increases in the absorption coefficients of 2 orders of magnitude compared with those resulting from a spherical approximation. No significant difference was found in the extinction coefficients between the distributions of spherical and nonspherical particles. However, the nonspherical distribution led to smaller scattering parameters. It follows from the above that the effects of nonspherical corrections are in need of further research, especially when one tries to make estimates of the radiative

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equilibrium of NLC particles. Since we do not possess such calculations, it will be instructive to estimate the radiative equilibrium for spherical NLC particles. The radiative equilibrium of the spherical particles of different materials was studied by BAmULATOV and IVANIA (1976, 1977) and GRAMS and FIocco (1977). The radiative equilibrium temperature for particles was calculated by taking into account: (1) direct solar radiation, (2) solar radiation scattered in the Earth-atmosphere system, (3) thermal radiation from the Earth, (4) heat released in recombinations of oxygen. BAmULATOV and IVANIA (1976) demonstrated that the radiative equilibrium temperature of particles formed from Cu, Fe, C, SiQ, MgO and ice at a height of 80 km was essentially different. The dependence of the equilibrium temperature on height is given in Fig. 16. This figure demonstrates the difference between strongly absorbing particles (Fe, Cu, C) and dielectric particles of moderate absorption (SiO2, MgO, ice). For the first group the equilibrium temperature increases in the height interval between 80100 km and reaches the value in vacuum. Below 60 km the particle temperature does not differ from the surrounding air temperature. The above-mentioned high temperature gradient in a layer of 80-100 km is probably partially due to the high concentration of atomic oxygen in this layer, partially to an increase in the molecular temperature of the surrounding air as well as due to a decrease in heat conductivity according as the air density decreases. For the dielectric particles in the equilibrium temperature curve there appears a deep minimum near the altitude of 80 km and a maximum is observable in the lower thermosphere. This maximum is more pronounced in case of smaller particles. BAIBULATOV and IVANIA (1976) pointed out that the above-mentioned high gradient in the temperature increase in the 80-100 km layer of strongly absorbing particles leads to intensive evaporation, although the temperature is lower than the melting temperature of these particles. As a result, small condensation nuclei can be formed. Figure 16 (for ice particles) also carries a histogram of NLC heights (see BRONSHTEN and GRISHIN, 1970). The shaded area indicates the region where particle temperatures are lower than the saturation temperature at height of 80 kin. The minimum radiative equilibrium temperature for ice particles coincides with the height of maximum NLC occurrences. Figure 16 illustrates the fact that only in this altitude region can the temperature of ice particles be lower than the water vapor saturation temperature. For particles with r _< 10 -4 cm this condition is fulfilled for a wider height interval. BAmULATOVand IVANIA(1977) also carried out radiative equilibrium calculations of two-layered particles containing an absorbing nucleus (iron) coated with an ice shell. Let the radius of the nucleus be R1 and the particle radius be R2. Figure 17 presents the results for particles with R2 = 5 • 10 -6, 10 -5, 5 • 10 -5 and 10 -4 cm. The ratio R1/R2 increased with a step of 0.1 until the equilibrium temperature exceeded the saturation temperature at a height of 80 km, i.e. calculations were carried out in the temperature interval where ice particles can exist. Figure 17 shows that in the case

554

O.A. Avaste et aL

,+_

(Pageoph,

'+'I

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~'

"~176 t........... "~

il

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F i g u r e 16

Temperature of aerosol particles versus altitude taking into account the following heat sources: (1) direct solar radiation; (2) solar radiation scattered and reflected in the system Earth-atmosphere; (3) thermal emission of the Earth's surface. Numbers at curves indicate the radius of particles in t~m (10 -+ cm).

of an absorbing nucleus the equilibrium temperature increases with the ratio Rz/R2. The stability interval of such existing two-layered particles decreases when the absorbing nucleus is larger. The region where two-layered (iron-ice) particles are stable is presented in Fig. 18. This gives the interrelation of the values R2 and R1/R2 for particles at a height of 82 kin, i.e. in the NLC layer. The above calculations were carried out for a settled regime. It is possible that the conditions for starting the sublimation process on the absorbing nucleus demand more favorable conditions in the temperature and supersaturation regimes. The above radiative equilibrium calculations were carried out for spherical particles. It seems that the radiative

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T,K a

eoo

a2

300

I

200 I

Joe

G

z

I

I

I

h

l

d

r

3oo

l

IZO 60

60

fOO

~,~

Figure 17 Temperature of two-layered iron-ice particles versus altitude for four values of the ice shell radius (i.e. particle outer radius): (a) R2 = 5 x 10-6; (b) R~ = 10-s; (c) R2 = 5 x I 0 - 5 ; and (d) R2 = 10 -4 cm. Numbers at curves indicate the ratio of the nucleus radius to the particle radius. Broken line indicates the front point temperature versus altitude.

equilibrium temperatures for cylindrical particles (ice crystals) are essentially different and this demands a more detailed further research.

6. Optical properties of NLC Optical properties of NLC are determined by the particle size distribution, the particle shape a complex index of refraction, and of the total number of particles. If

e,/ 0,6

o,e 0

~///7/. ~//7///////,//77/ t

0

I

o,e

J

1

0,,

l

I

g6

1

I

~

1

4e

Figure 18 The region of a stable presence o f two-layered iron-ice particles (shaded area) at an altitude of 82 krn in case of NLC occurrences.

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O.A. Avaste et al.

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the above parameters are well known, the brightness field of NLC can be easily calculated by means of the Mie theory. Measurements of the optical constants of natural aerosols are experimentally difficult and subject to significant errors owing to the mixed and variable nature of aerosols. The optical properties of aerosols include the single scattering albedo, the scattering phase function, scattering absorption and extinction cross-sections. The correct way to obtain average optical properties is to average the optical properties of different materials by using cross-section weighting factors (see e.g. TOON and POLLACK, 1976). The reason is that optical properties are not necessarily linear functions of the optical constants (e.g. BERGSTROM, 1973a; HANSEN and TRAVIS, 1974). Another important source of error is that different aerosol materials have a different size distribution (see e.g. TOON and POLLACK, 1976). Neglect of these differences by averaging optical constants can lead to substantial errors (e.g. BERGSTROM,1973b). Extensive tables of optical characteristics of polydispersions have been published by SHIERINand ZELMANOVICH(1971), where three-digit values ofpolydispersion coefficients of extinction, scattering and light pressure in clouds, mists and water aerosols were given within the range of the wavelengths varying from 0.6 to 40/zm. Shifrin and Zelmanovich calculated these values for 9 different Junge distributions and 79 different gamma distributions of particle sizes. The scattering phase functions and the polarization indices were calculated for 9 Junge's distributions and 35 gamma distributions. Regardless of having the above-mentioned extensive calculations at one's disposal (see also DEIRMENDJIAN,1963b, 1969), WILLMANNand SERGEYEVICH(1969) carried out calculations for a NLC model, where the physical properties of polydispersion were close to those determined from the NLC experiments. They modelled NLC as a three-component system, where the properties of the particles were given by the following complex indices of refraction ml = m ( A ) - ik(A) for water particles (KISLOVSKII, 1959); m2 = 1.55 - ik2 for SiO2; m3 =oo. The weights of different particles in the total number of concentrations were correspondingly: N1 = 0.5, N2 = 0.25, N3 = 0.25. Particles were distributed according to Junge law. The scattering phase functions were calculated for 63 wavelengths in the range of 0.22 to 6/zm (WILLMANN, 1975). It should be pointed out that increases in the absorption index greatly raise the contribution of small particles (r < 10-5 cm) but exercise little effect on large particles (r > 5 x 10 -4 cm) for A = 0.55/~m (BERGSTROM, 1973a; WILLMANN et al., 1973). Polarization properties of NLC models were analyzed in papers by VASILYEV and RADIONOV (1975), ZUEV et al. (1975). All these calculations were made assuming that particles of NLC were small compared with the radiation wavelengths, the effect of their shape was assumed to be small, too. This assumption is not very accurate as it was later shown by GADSDEN (1975, 1977a,b). Nevertheless, the calculated scattering intensities are quite correct. As pointed out by GADSDEN (1977b), the polarization properties of ice crystals are essentially different from those of spherical particles and the NLC models involving only spherical scatterers need to be modified.

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The NLC spectral brightness dependence on the wavelength in the visible and near infrared region was summarized by VESELOVet al. (1976). Figure 19 presents a comparison of the calculated (WILl.MANN and SER6EVEVICH, 1969) and measured (BRoNsnTEN and GRISnIN, 1970; FO6LE and REES, 1972) spectral brightnesses of NLC. Theoretical data show that the optical thickness of NLC can be approximated in the wavelength region of 0.2 to 4/~m by the curve r(A) = r(A0) x 5.5A~ exp (-2A~ where ro(A) is the optical depth of NLC at the wavelength ho = 0.55 tzm. The absolute spectral brightness of NLC according to the data presented in the paper by VESELOV et al. (1976) is shown in Fig. 20. In the above models NLC were assumed to form a uniform spherical layer. Some problems of the variability of NLC optical depth in this layer according to their morphological structure were discussed by AVASTE et al. (1977a). In general the optical depths of NLC can be described as a random function and the radiative

BA REI.ATJVEUNITS 70 ~

\ 10 o

r ..)~.

// ~

7

70 -7

~3

o,5

o,z

~8

7,z

/,s

Figure 19 Spectral brightness of NLC (in relative units) versus wavelength: (1) measurement (VESELOVe t al., 1976); (2) data presented by BRONSHTEN and GRISHIN (1970); (3) FOGLE and REdS (1972); (4) calculations by WILLMANNand SERGEYEVICIt(1969).

558

O.A. Avaste et

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al.

TO-)

10 -~

~~

~

Figure 20 Brightness of NLC versus wavelength in W cm -2 sr-1/~m-l: (1) by VESELOVet by FOGLEand REES(1972); (3) by HARRISON(1973).

al.

(1976); (2)

transfer can be calculated in a stochastic medium (AvASTEand WILLMANN,1973). Avaste and Willmann determined the distribution function of NLC optical depths from photometric measurements of the NLC brightness. Figure 21 illustrates the optical depths distribution function of different morphological structures. Optical depths of NLC vary within the limits of 10 -5 to 5 • 10 -5. In case of a chaotic structure (e.g. type 'whirls') in the distribution function, secondary maxima are present and the distribution function broadens. The NLC optical depth distribution could be approximated by the ZOLD function (zero order logarithmic distribution) or by the superposition of these functions. In case o f ' w h i r l s ' the distribution function changes in the evolution of clouds; in case of stable 'waves' the distribution function practically does not change.

n(r~}

10-6

5./0-6

lo-S

5./o-S

r0-o

y./O-~rz

Figure 21 Distribution of the optical thickness in different NLC fields.

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7. Observation and photography of NLC from space For the first time the task of observing and photographing mesospheric aerosol layers from space was given to the team of the Soviet spaceship 'Voskhod' in 1964. Observations were carried out in the direction of the twilight aureole as well as in the nadir direction. Observations in twilight aureole conditions were assumed to be most favorable (which was also confirmed afterwards). Observations of the mesospheric aerosol layers in the nadir direction were assumed to be possible due to their structure at a suitable distance from the terminator when the subpoint of the spaceship moved into the Earth's shadow. Unfortunately, the above-mentioned spaceflight was carried out at a time which was quite unfavorable for NLC observations (in autumn in the Northern Hemisphere) when the probability of NLC occurrences is smallest on the planetary scale. Brightness observations revealed the presence of aerosol scattering in the mesospheric layer; however, it was impossible to determine the presence of pronounced aerosol layers which might have been interpreted as NLC (FEoKTISTOV et al., 1965). Later on the possibility of observing and photographing NLC from near-Earth space was studied in several papers (FESEYKOV, 1966 ; ROZENBER6, 1966a,b; JOSEPH, 1967; EERME, 1971, 1973; HOPPE, 1974). The idea of photographing NLC from space in the ultraviolet region at 2550/k was recommended by MARMO et al. (1967). In an intensive ozone absorption band the background emission of the atmosphere from layers lower than 40 km is practically totally absorbed in the ozone layer and calculations show that NLC with the particle concentration of 107 cm -2 in the vertical column can be photographed above the horizon. In the subsequent spaceflights Soviet astronauts continued attempts to observe NLC. For the first time an atmospheric optical phenomenon, which was later identified as an NLC, was observed from space by the Soviet astronaut Aleksei Leonov aboard the spaceship 'Voskhod-2' on 18-19 March 1965, and later by the Soviet astronaut Vitaly Sevastyanov on board the spaceship 'Soyuz-9' on 9 June 1970 (e.g. KONDRATYEV et al., 1971 ; WILLMANN et aI., 1975). Unfortunately, the photographs taken were underexposed. The observed clouds had a rather extended flat filament-cellular structure parallel to the Earth's horizon. The next visual observations of NLC from space were carried out by the pilot of the second Spacelab mission Paul Weitz (see PACKER and PACKZR, 1977) in May and in the first week of July 1973 near 50~ and 10-40~ NLC were observed a total of about four times during that mission. They were always seen at dawn and in the direction of the rising Sun, although clouds and the Sun were never observed together. The clouds were bright, as conjectured, and formed a thin bright line just above the Earth's horizon when first detected. As the spacecraft approached, the thin line appeared to become broken, and finally two or four patchy, thin, stratified clouds were visible. Their lateral angular subtense was of the order of 5 ~, and as the spacecraft drew nearer, the clouds appeared to rise above the Earth's horizon, finally vanishing into the airglow.

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More systematic observations of NLC were carried out aboard the Orbital Stations 'Salyut-4' in the Northern Hemisphere and 'Salyut-6' in the Southern Hemisphere (WmLMANN et al., 1977). Occurrences of NLC were visually determined by the astronauts in several orbits in the period lasting from 1-17 July 1975. An approximate territory over which NLC occurred on 3 and 4 July as well as the subpoint tracks of the OSS are given in Fig. 21. It should be mentioned that for the case illustrated in Fig. 21 only few ground observations were possible from the routine ground network on account of an overcast sky obtaining over the major part of this territory. These few ground observations confirmed that the NLC observed by the astronauts were comparatively bright (on a 5-point scale their brightness was estimated to belong to the numbers 4 and 5, i.e. their optical thickness varied from 10 -5 to 10-~). Visual observations indicated an important fact: certain types of NLC have a multilayered structure, which allows us to judge of a complex build-up of the mesopause. In addition to the above-mentioned visual observations, NLC occurrences were photographed. Considering the fact that the first expedition on the orbital station 'Salyut-6' was carried out from December 1977 to March 1978, it was hoped to discover NLC occurrences in the Southern Hemisphere. According to sparse ground observations, their maximum occurred in January. An unexpectedly large amount of bright NLC occurrences was detected. The number of occurrences was considerably higher than the one expected on the basis of current ideas. The wide spatial-temporaldistribution of a strongly developed NLC field shows that the occurrence of these clouds in the mesopause in the summer period in the Southern or the Northern Hemisphere, respectively, is by far not a rare phenomenon, at least not in the present state of the mesosphere. NLC were observed on 'Salyut-6' in altogether 127 orbits from 23 December 1977 to 2 February 1978, i.e. during 31 days. It should be noted that in this time interval several periods were detected when NLC occurred almost continuously. Thus from 24 December 1977 to 5 January 1978 NLC were observed in all orbits when their viewing conditions were favorable. On 6 January 1978 NLC seemingly abruptly disappeared, making its appearance again on 8 January in the form of a weak veil.

Figure 22 Subpoint tracks of the Orbital Station 'Salyut-4' on 3 and 4 July 1975, when NLC were observed. The sign 9 indicates ground observations.

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Active periods of NLC occurrences were also noted from 14 to 16 January and from 27 January to 2 February. Similar periodic NLC occurrences had been previously detected in the Northern Hemisphere by ground observations (e.g. FAST and FAST, 1977). NLC were always observed at a constant height (at 2 degrees above the horizon) both in the case of a negative and a positive height of the Sun (some degrees above the horizon). Their distance from the orbital station was detected from the geometry (see Fig. 23): when the spacecraft approached NLC, the NLC field seemingly rose from the Earth's horizon and had a pronounced wave structure. On reaching the height of 2 degrees (height of the perigee about 80 km), their brightness increased as their structure seemingly disappeared since they were transformed into a bright thin line above the horizon. Cases were noted when an NLC field extended over the whole southern horizon and it was observed during 7-8 successive orbits. This shows that NLC sometimes completely cover a latitudinal zone, sometimes exceeding a half of the whole latitudinal belt. The above-mentioned fact had been earlier noted for the Northern Hemisphere (WILLMANN et aL, 1977). The observations carried out aboard 'Salyut-6' confirmed this also for the Southern Hemisphere. According to preliminary estimates, NLC in the Southern Hemisphere are situated at latitudes higher than 53-55~ As is known, the wave-like structure is the most frequently observed type of a NLC field. In space observations it is easy to detect medium (20-100 km) and long waves (100-280 kin). It is more difficult to detect short waves (3-12 km). The geometrical effect of the projection of a spherical layer on to the horizon complicates the detection of the fine structure. Therefore a space observer may mistake a projection 8

,/

o Figure 23 The geometry of NLC observations from space.

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of 3-12 km waves for the multilayered structure. This does not mean that multilayered NLC do not exist at all. Both ground observations and photography from space reliably determined the existence of a multilayered structure of some morphological forms of NLC. Altogether 40 black-and-white and 5 colored photographs of NLC were made on board 'Salyut-6' during the first mission. By way of illustration two photographs are presented in Figs. 24 and 25 (one taken when the Sun was above the horizon, another taken when the Sun was below the horizon). A color photograph of NLC from space is given on the frontispiece of this volume. Below will be discussed some preliminary results of the photometric processing of several NLC photonegatives taken on 15 January 1978. Figure 26 shows photometric profiles of the brightness of the Earth's aureole made on 15 January, 17h, 36m MT, when NLC were present. The abscissae indicate angular height above the horizon, the ordinates denote the scaled brightness of the aureole and NLC. Different curves present the change in the azimuth from the Sun. The azimuth step of these brightness profiles was 1 degree. This family of curves shows the morphological structure of this NLC field and illustrates the wave-like structure of this NLC layer, which is projected onto the horizon of the space observer. The decrease of brightness with an increasing azimuth angle is due to the effect of the scattering phase function. The contrast of NLC relative to the aureole was calculated by using the equation K

=

(B,

-

where Br is the absolute brightness of the aureole, Br~Le -- the absolute brightness

Figure 24 A photograph of the Earth's horizon when NLC occurred, taken on board 'Salyut-6'. The Sun is above the horizon. In the lower part of this Figure sunlit tropospheric clouds are visible.

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Figure 25 Same as Fig. 24, except for the Sun being below the horizon.

H

Figure 26 The family of photometric profiles measured ~om a photograph taken aboard 'Salyut-6' on 15 January 1978.

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of NLC. The brightness contrast between NLC and the aureole ranges from 0.38 to 0.78. Figure 27 shows the dependence of NLC brightness upon the azimuth from the Sun's vertical (A - A0) for the height of the perigee h = 82 km. The thick solid line gives the total brightness at the height of NLC, the thin solid line indicates the brightness of the aureole, the dashed line presents the brightness of NLC (measured) and the dot-dashed line shows the calculated brightness according to the NLC model proposed by WILLMANN and SERGEYEVICH(1969). The parts a, b, c give the profiles detected in the three successive photographs (with a time lapse approximately 1 min). From these photometric measurements one can draw the foUowing conclusions: (1) The brightness of the aureole diminishes monotonically with an increasing azimuth. (2) NLC brightness curves have usually a wave-like structure (depending on their optical thickness). (3) The measured brightness of NLC in the Sun's vertical is higher than the one calculated from the model. This points to the fact that in the observed NLC there are more large particles than adopted in the model by WmUaANN and SERGEYEVICH(1969), but these particles must be in the Southern Hemisphere smaller than those detected in the Northern Hemisphere. Summarizing this section on the observations and photography of NLC from space, the following conclusions can be drawn: 1. Photography and visual observations from space enable one to determine the NLC on a global scale. In particular, the investigations performed on board' Salyut-4' revealed that in summer in the Northern Hemisphere NLC often completely covered B

B

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~

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Figure 27 Brightness of NLC and of the Earth's aureole versus solar azimuth. Parts a, b, c give consecutive profiles with a time lapse of 1 minute.

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the latitudinal belt north of 45 ~ Similar observations aboard 'Salyut-6' ascertained that in summer in the Southern Hemisphere there also exist extensive NLC fields, but they are shifted more southward: the NLC belt is south of 53-55~ 2. Photometric investigations as well as visual observations revealed that in both hemispheres the mesopause often has a complex structure (sometimes there exist two- and three-layered NLC fields). 3. These observations allow one to make sound estimates of the spatial-temporal characteristics of NLC fields as well as the morphological features of their evolution. 4. The photometric investigations from space also confirm that in the NLC layer there exist particles whose radius exceeds 10 -5 cm. The NLC in the Southern Hemisphere probably consist of smaller particles than those in the Northern Hemisphere.

8. Radiometric measurements of NLC from space The idea of the possibility of detecting NLC from space photometrically was expressed already in 1962 (see: DEIRMENDJIAN, 1963a), which, however, remained unrealized. The task of optically detecting NLC by using radiometric and spectrometric instruments on board the spaceship was put to all teams of the Orbital Scientific Station (OSS) 'Salyut-4'. It was successfully carried out during the second expedition of 'Salyut-4' in June and July 1975. An illustration of the possible brightness of NLC in the visible region (A = 0.55 /xm) is given in Fig. 28, in case the zenith angle of the Sun equals 96 ~ and the Sun is in the vertical plane. For comparison the brightness of the horizon calculated by the DART method (GRAY et al., 1972) as well as the first-order scattered radiation (SMorcTY, 1969) are given. Figure 28 shows that when the optical thickness of the NLC layer ~ = 10 -5, the brightness of NLC at a height of 80 km is nearly by one order higher than that of the twilight aureole. Moreover, it seems to us that the DART method overestimates the effect of multiple scattering since the Monte-Carlo calculation and the method of characteristics with iterations on the order of scattering (NAZARALIEVand SUSHKEVICH,1975) show that the second-order scattering at A = 0.55/~m constitutes less than 30~ of the horizon brightness in the layer of 0-20 kin. With increasing height the contribution of second-order scattering has a tendency to diminish. The isolines of the brightness of NLC in relative units considering the first-order scattering and extinction in the atmosphere are given in Fig. 29. Compared with the Earth's radius, the vertical scale in Fig. 29 is considerably distorted. The main conclusion resulting from the above data is that in the NLC field the maximum brightness occurs in the vertical plane of the Sun. The brightness decreases rapidly with the increasing azimuth A. Optimum azimuth angles for NLC brightness measurements lie between _+15~ In a summar~y of the airglow VALLANCEJONES(1973) pointed out that the molecular emissions of OH and 02 account for the major part of the emission intensity from the

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3

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k,' #d~ .

d+r ~ '

_,o-t,.

ds

#os! i

i

I

I

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~o 2a 30 4a 50 bO to 80 90#00

H(~m) Figure 28 Brightness of N L C in the vertical plane of the Sun, when the zenith angle of the Sun ~ = 96 ~ for 7 = 10 -~ 10 -5 and 10 -5. The brightness of the horizon for different zenith angles of the Sun (0, 30, 60 and 80 ~ calculated by the D A R T method (GRAY et al., 1972), first-order scattering (SMoKTY, 1969) (dashed line).

3~ ~

\/

~'30~

Figure 29 Isolines of the relative brightness of NLC depending on the line of sight and the azimuth A.

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upper atmosphere in the infrared region. We use the term 'airglow' limited to emissions from the minor constituents which are not in thermal equilibrium (or nearly so) with the atmosphere. An essential feature of O H emissions during N L C occurrences was discovered by SHEFOV (1968). According to his estimates the intensity of O H emissions increased by a factor of 1.5 to 2 during N L C with respect to the mean value, sharply decreasing to a value 2 to 3 times lower than the average intensity of the following day when no N L C were observed. Taking this into consideration, we find that O H emissions increase the brightness of N L C by a measurable amount in the near-infrared region, e.g. Boll, zenith (2, = 2/~m) = 0.5 x 10 -7 [W cm -2 txm -1 sr-1]. The O2(1Ag) dayglow in the zenith direction 1.27/xm band yields Bo2, zenith = 4 x 10-7 [W c m - 2 sr-1] and consequently this emission essentially exceeds the N L C brightness in the direction of the line of sight with the perigee H0 = 80 km. It is concluded from the above that it is important to take into account the emissions of O H and 02 when analyzing N L C brightness measurements (AvASTE et al., 1977b). A four-channel near-infrared radiometer (VALOV et al., 1973) was installed aboard the Orbital Scientific Station (OSS) 'Salyut-4' for measuring N L C brightness. The limb scanning technique was employed by controlling the space orientation of the OSS, with the aim of obtaining the altitude information on the optically observable phenomenon occurring below the spaceship. Spectral bands of the interference filters used had a maximum at the wavelengths of 1.35, 1.9, 2.2 and 2.7 ~m. An example of scanning the twilight segment with N L C at A = 1.9/~m is presented in Fig. 30. It should be noted that all curves of the vertical brightness profile at a wavelength of A = 1.35/zm on lines of sight with a perigee of H0 = 50-70 km had a secondary maximum or a plateau. Figure 31 presents an example of the results of the measurements of the daylight atmospheric aureole in the channels of 1.35 and 1.9/zm. This figure illustrates the case when there are no N L C and the above-mentioned effect ought to be expressed in the most pronounced way. This may be explained as the influence of the wing of the O2(1Ag) emission band centered at A = 1.27 ~m. Over twenty scannings of the N L C field above the Earth's horizon were performed. Depending on the structure and the optical thickness of NLC, the brightness varied within the limits of one order of magnitude. Figure 32 presents an estimate of the spectral brightness of N L C and of the hydroxyl emission in case the line of sight has a perigee of H0 - 81 km. The results of measurements have been entered on the same graph: both average values and maximum deviations from them for channels of 1.35, 1.9 and 2.2/xm. For the channel of 1.35/~m the emission of O~(1Ag) was eliminated. The data at A = 2.7/~m turned out to be insufficiently reliable and were omitted. The N L C spectral brightness was calculated for the optical thickness ~-= 10 -5, 3 x 10 -~, 10 -4 and for a scattering angle of), = 80 ~ since measurements of the N L C brightness were carried out at angles which lay close to 80 ~. The spectral intensities of the hydroxyl emission in the direction of the line of sight with a perigee of Ho = 81 km for 60~ were calculated, taking into consideration the increase of O H when N L C occurred according to Shefov (see FEDOROVA et al., 1974). The solid line

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t98~

\ -1

.=..

-2

9-.

........,-. : 1 i

t -3

,I 2O

80

h (K~)

Figure 30 Brightness measurements of the horizon with N L C at a wavelength of 1.9 t~m.

0 7../- x

.... .....

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Figure 31 Brightness measurement o f the horizon with no N L C : dotted line indicates A = 1.9 t~m, dot-dash line denotes k = 1.35/~m.

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,

I

,

,

,

,

I

I

,

I

5\

0

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Figure 32 Spectra] distribution o f N L C brightness at a scattering angle of 7 = 80~ (1) calculated when T = 10-5; (2) calculated when -r = 3 x 10-~; (3) calculated when ~- --- 10-3; (4) O H emission (SHEFOV, 1968); (5) sum of NLC brightness when ~ = 3 x 10 -s ai~d of OH emission. 9 indicates

mean experimental values, vertical bars denote variation in NLC brightness. characterizes the total effect of both the hydroxyl emission and the radiation scattered by N L C (~- = 3 x 10-5). As can be seen from Fig. 32, the calculated and measured brightnesses have rather close values. The hydroxyl emission at A -- 2.2 t~m is comparable with the radiation scattered by NLC, while at A = 3/~m the former exceeds the latter by one order of magnitude. The following conclusions can be drawn from the above: 1. The consideration of the O2(1Ag) and O H emissions in the near-infrared spectral region shows good agreement between the calculated and measured values of the N L C hrightnesses. This confirms the fact that the model we used in the calculations for the description of the polydisperse ensemble of N L C particles satisfactorily describes the basic optical properties of NLC. 2. The results of the investigations carried out on board the OSS 'Salyut-4' confirm an increase in the O H content in the mesopause at the occurrence of N L C established by H. N. Shefov. 3. F o r the further study of the optical characteristics of N L C from space it is expedient to continue the studies of their spatial distribution and also to carry out measurements in the ultraviolet spectral region as well as in the intensive hydroxyl emission band at h = 3 tzm.

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9. N L C investigations during M A P

As NLC are good indicators of physical and photochemical processes in the mesopause, special attention is paid to this problem in the planning document of MAP (GREGORY et al., 1976). It follows from the previous section that the NLC phenomenon is related to such processes as water vapor transport in the mesopause, temperature variations in the mesopause, the variation of OH, 02 emissions, several photochemical reactions as 03 + H, H20 + M, etc. The occurrence and disappearance of NLC is also related to some problems of solar-terrestrial physics: solar activity, geomagnetic disturbances, characteristics of the Es layer, etc. The wide range of the morphological structure of NLC and its variations allows one to observe various complex dynamic processes in the mesopause (wave-like motions, jet stream, turbulence). It should be mentioned that NLC investigation for the determination of the above parameters of the processes described above has a definite advantage over the other methods as NLC fields cover vast territories (sometimes millions of square kilometers) and are visible from the Earth's surface during several hours. Considering this circumstance and also the fact that the interrelation of the neutral and ionized atmosphere in the mesopause in case of NLC formation has still been insufficiently studied, it is reasonable to start a preparatory MAP project also on NLC research. Such a project was proposed by the Soviet Geophysical Committee for the years 1979-1980. This project included the investigation of the following problems: 1. Climatology of NLC. Investigation of the spatial-temporal characteristics of NLC occurrences with the aim of obtaining uniform and reliable data from ground and space observations both in the Northern and Southern Hemispheres. Special attention must be paid to the existence of breaks in the temporal NLC series. 2. Dynamics and morphology of NLC. Investigation of the morphological and kinematic structure of NLC (different forms of waves, jet streams, whirls, multilayered NLC occurrences). Making use of simultaneous time-lapse cinematography and stereophotogrammetry from the adequately separated ground surface stations, the velocities of horizontal and vertical shifts of different structural forms will be determined as well as the drift of the cloudfield on the whole. 3. Nature of NLC. Investigation of the physical and chemical characteristics of NLC particles, as well as of the optical parameters which characterize the cloud field on the whole. Making use of the optical remote sounding technique and direct rocket soundings, the particle sizes, their physico-chemical properties and the number concentration will be determined. Also optical densities, spectral brightness, etc. will be inferred.

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4. Genesis of NLC; the relation between the meteorological conditions, heliogeophysical phenomena and NLC; the forecast of NLC occurrences. 4.1. Investigation of the conditions which are necessary and sufficient for NLC formation. 4.1.1. Investigation of the water vapor transport and of the temperature variations in the mesosphere. 4.1.2. Investigation of the interrelations between solar acitvity, ozone content in the atmosphere and forms of global atmospheric circulation (the circumpolar vortex). 4.1.3. Investigation of the global distribution of aerosols in the mesosphere. 4.1.4. Modelling physical conditions at the level of the mesopause and investigations of dynamics of the water vapor sedimentation on ice crystals. 4.2. Investigation of interrelations between helio-geophysical phenomena and NLC. 4.2.1. The complex determination of geomagnetic disturbances (index K), emissions (OH, O2), ion concentration and electron density in the mesosphere together with the wind and thermobaric regime. Investigation of the peculiarities in E~ layer in cases of appearance, occurrence and disappearance of NLC. 4.2.2. Investigation of the correlation between NLC occurrences and solar activity, meteor fluxes, ionospheric conditions in D, E and E~ layers, OH emission, 02 emission, meteorological regime in the troposphere and stratosphere. 4.3. Elaboration of methods for forecasting NLC occurrences.

10. Concluding remarks The monitoring of NLC from space demonstrated that: (1) The classification proposed in the International Noctilucent Cloud Observation Manual (1970) is applicable in case of observations from space. (2) NLC fields often cover considerable parts of latitudinal belt north of 45~ (or south of 53~ The NLC coverage in the Northern and Southern Hemispheres are asymmetric, but in both hemispheres the multilayered structure of NLC is observable, indicating the complex structure of the mesopause. (3) In the Southern Hemisphere NLC probably consist of smaller particles than NLC in the Northern Hemisphere. The characteristic radius of cloud particles in the Northern Hemisphere is 2 x 10-5 cm for rod-like crystals, while for spherical particles it is 3 x 10 .5 cm. This exceeds the previous estimates by 1.5 to 2 times. (4) NLC brightness, polarization properties and their particles equilibrium temperatures could be correctly interpreted only when one considers that NLC consist of ice crystals with absorbing nuclei. (5) Ion clusters can play an important role as condensation nuclei. The latitudinal distribution of these electrically charged particles is dependent on the Lorentz forces

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in the Earth's magnetosphere and high particle concentrations were observed over the polar cap. Measurements f r o m space indicate a scattering layer of 15 to 40 particles per c m 8 which seems to be a daytime manifestation o f N L C . (6) In all probability both condensation and coagulation mechanisms play an important role in the growth o f ice crystals in the mesopause. (7) Rocket soundings carried out at the Soviet Antarctic Station ' M o l o d e z h n a y a ' indicate that N L C occurrences are connected with advection and descent o f extremely cold air (110-120~ from the upper layers into the mesopause. The N L C formation is interrelated with m a n y fundamental parameters governing physical processes in the mesopause. Thus visual observations, p h o t o g r a p h y and remote soundings using the satellite technique allow one to monitor data on physical conditions in the mesopause over large territories.

REFERENCES

ABADIE, G. (1974), Mdsure de la teneur en eau de la haute atmosphere par sonde a alumine, La Mdtdorologie, 31/32, 225-236. ANDERSON, J. G. and DONAHUE,T. M. (1975), The neutral composition of the stratosphere and mesosphere, J. Atm. Terr. Phys. 37, 865-884. ANDREYEV,S. D., IVLEV,L. S., SPAZHAKINA,N. K. and YANCHENKO,YE. L. (1975), Space-time variations of atmosphere optical properties caused by interaction between atmospheric aerosol and humidity field (in Russian), in Trudy MGK, Fizika mezosfery i mezosfernyh oblakov. Meteorotogicheskie issledovania, No. 22, pp. 34-49. ARNOLD, F. and KRANKOVSKY,D. (1977), Water vapour concentration at the mesopause, Nature 268, 218-219. ASTAPOWCH, I. S. (1939), Noctilucent clouds (in Russian), in Akademia Nauk SSSR, Izvestia, Geografia i geofizika, No. 2, pp. 183-204. ASTAPOVICH, I. S. (1961), Summary of noctilucent cloud observation in Russia and USSR from 1885 to 1944 (in Russian), in Trudy VI sovechchania po serebristym oblakam, Riga, pp. 49-92. AUFF'M ORDT, N. and BRODHUN, D. (1974), Zur Deutung yon Wellenstrukturen aufLeuchtenden Nachtwolken, Z. Meteorol. 24, 291-298. AVASTE, O. A. (ed.) (1977), Trudy MGK. Meteorologicheskie issledovania, No. 23 (in Russian),

(Publ. House Sovetskoye Radio, Moscow), 87 pp. AVASTE,O. A., VAINIKKO,G. M. and K,~RNER,O. YU. (1977a), Some statistical characteristics of the mesospheric cloud field (in Russian), in Trudy MGK, Meteorologicheskie issledovania, No. 23, 5-11. AVASTE,O. A., VEISMANN,U. K., WILLMANN,CH. ][., GRECHKO,G. M., GUBAREV,A. A., KLIMUK, P. I., LOBANOVA,G. I., POPOV,O. I., SEVASTYANOV,V. l., FEDOROVA,E. O. and EERME,K. A. (1977b), The determination of the daytime and twilight profiles of the O2(1Ag) at 1.27 t~m from measurements aboard the orbital station 'Salyut-4' (in Russian), in Optical Investigation of the Emission of the Atmosphere, Aurorae and Noctilucent Clouds aboard the Orbital Scientific Station "Salyut-4', Tartu, pp. 79-87. AVASTE, O. and WILLMANN,CH. (1973), On the method of determination of the optical depths of noctilucent clouds, in Noctilucent clouds. Optical properties, Tallinn, pp. 80-97. BACKHOUSE,T. W. (I 885), The luminous cirrus clouds" of June and July, Met. Mag. 20, t 33. BAmULATOV,F. KH. and IVA•IVA, S. P. (t976), Numerical studies of aerosol particle temperature in the upper atmosphere (in Russian), Akademia Nauk SSSR, Izvestiia, Fizika atmosfery i okeana 12, 523-530.

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TOZER, W. F. and BEESON,D. E. (1974), Optical model ofnoctilucent clouds based on polarimetric measurements from two rocket sounding campaigns, J. Geophys. Res. 79, 5607-5612. TSERASKII,V. K. (1887), Astronomicalphotometer and its applications (in Russian), Matematicheskii sbornik 13, pp. 76-81. TSERASKII,V. K. (1890), Sur les nuages lumineux, Annales de l'Observatoire de Moscou, II, Ser. 2, 176-180. STANDARDATMOSPHERE,U.S. (1976), NOAA/NASA/US AF, Washington, D.C., 227 pp. VALLANCEJONES, A. (1973), Infrared spectrum of the airglow, Space Sci. Rev. 15, 355--400. VALOV, N. I., VEISMANN,U. K., WILLMANN,CH. J., GANELIN, G. Z. and DEMIDOV, V. V. (1973), Multichannel telephotometer (in Russian), in Izobretenia, promyshlennye obraztsy, tovarnye znaky, No. 37. VASILYEV, O. B. (1967), Astrophysical investigation of noctilucent clouds (in Russian), Akademia Nauk SSSR, Astronomicheskii Sovet, Moscow, 86 pp. VASILYEV, O. B. (ed.) (1975), Trudy MGK, Fizika me2osfery i mezosfernyh oblakov, Meteorologicheskie issledovania No. 22, 149 pp.+Supplement: Materialy issledovania mezosfernyh oblakov, 111 pp. VASILYEV, O. B. and MELNIKOVA,]. N. (1975), Statistical spaeetime model of the appearance of mesospheric clouds (in Russian), in Trudy MGK, Fizika mezosfery i mezosfernyh oblakov, Meteorologicheskie issledovania, No. 22, pp. 125-136. VASILYEV, O. B. and RADIONOV,B. F. (1975), Optics ofmesospheric clouds (in Russian), in Trudy MGK, Fizika mezosfery i mezosfernyh oblakov, meteorologicheskie issledovania, No. 22, pp. 50-64. Supplement in Materialy issledovania mezosfernyh oblakov, VINITI, Moscow, 1975, pp. 5-53. VAStLYEV, O. B., W~LLMANN,CH. I., MELNmOVA,I. N. and CHUBEY, M. S. (1975), Technique of statistical analysis of observations of mesospheric clouds applied by the network of stations of the Hydrometeorological Service (in Russian), in Trudy MGK, Fizika mezosfery i mezosfernyh oblakov. Meteorologicheskie issledovania, No. 22, pp. 110-118. VEGARD, L. (1933), Investigations o f the auroral spectrum based on observations from the auroral observatory, Geophys. Publ. 10, 53 pp. VESELOV, D. P., POVOV, O. I., SEMYENOVA,V. I., SELEZNEV,G. I. and FEDOROVA,YE. O. (1976), Spectral brightness of noctilucent clouds in the visible and the near infrared region of spectrum (in Russian), Akademia Nauk SSSR, Izvestiia, Fizika atmosfery i okeana 12, 1097-1099. VESTINE,E. ILl.(1934), Noctilucent clouds, J. Roy. Astron. Soc., Canada 28, 249-272, 303-317. WEGENER, A. (1925), Die Temperatur der obersten Atmosphiirenschichten, Meteorol. Zeitschr. 42, 402-405. WEGENER,A. (1926), Zusatz zu F. A. Lindemann, G. M. B. Dobson, Die Temperatur der obersten Atmosphiirenschichten, Meteorol. Zeitschr. 43, 102-103. WELCH, R. M. and Cox, S. K. (1978), Nonspherical extinction and absorption efficiencies, Appl. Optics 13, 3159-3168. WILLMANN, CH. I. (ed.) (1967), Observations of Noctilucent Clouds (in Russian) (Publ. House Nauka, Moscow), 136 pp. WILLMANN, CH. I. (1967), Some problems of noctilucent clouds climatology, in Noctilucent Clouds (International Symposium, Tallinn, 1966) (I. A. Khvostikov and G. Witt, eds.) (Publ. House VINITI, Moscow), pp. 19-28. WILLMANN, CH. I. (1968), Statistical data on noctilucent cloud occurrence in the period of the IQS Y (1964-1965) (in Russian), Astronomicheskii Vestnik 1I, 161-170. WILLMANN,CO. I. (1975), Indicatrixes of solar radiation scattering by noctilucent clouds (in Russian), in Trudy MGK, Fizika mezosfery i mezosfernyh oblakov, Meteorologicheskie issleodvania No. 22, pp. 65-77. Supplement in Materialy issledovania mezosfernyh oblakov, (VINITI, Moscow), 1975, pp. 75-111. WILLMANN,CH. I., KLIMUK,P. I., KOKSHAROV,I. I., SEVASTYANOV,V. I., SERGEYEVICH,V. N. and EERME, K. A. (1977), Visual observations and photography of noctilucent clouds aboard orbital station 'Salyut-4" (in Russian), in Optical Investigation of the Emission of the Atmosphere, Aurorae and Noctilucent Clouds aboard the Orbital Scientific Station "Salyut-4', Tartu, pp. 79-87.

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Pageoph, Vol. 118 (1980), Birkh/iuser Verlag, Basel

The Structure of the Equatorial Mesosphere at Thumba By B. H. Subbaraya 1 and Shyam LaP

Abstract - The structure of the equatorial mesosphere is being investigated at Thumba by rocket borne ultraviolet absorption photometry as well as by the meteorological M-100 rocket launching programme. Whereas the meteorological M-100 rocket launching programme has been regular, the UV absorption studies have been few in number and sporadic in nature. In this paper an attempt is made to consolidate the results so far obtained from both these investigations.

Key words: Stratosphere; Mesosphere; Ultraviolet absorption; Gravity waves.

Introduction

In spite of the great improvement (brought about by space-borne/n situ techniques) in our understanding of the physical state of the upper atmosphere vis a v i s its structure and composition, the mesosphere and the lower thermosphere remain largely unexplored. Meteorological programmes based on balloons, rockets, and more recently satellites, have contributed a great deal towards the understanding of the structure and circulation at tropospheric and lower stratospheric levels. In the thermosphere, at altitudes above about 200 km satellite drag technique and the satellite borne massspectrometers have contributed towards an understnading of the atmospheric structure and composition as well as their variations. In recent years satellite measurements have been extended to lower heights, down to about 150 km. The intermediate regions, the mesosphere and the lower thermosphere, however, have till recently been dependent mostly on rocket borne techniques, and a significant gap in observational data exists in the upper atmosphere for the altitude range of 60 km to about 150 km. Further, geographically there is much less observational coverage for the equatorial regions than for the other latitude regions and the presently available standard atmospheric models are based to a large extent on mid-latitude data.

The Thumba observational programme

At the equatorial rocket launching station, Thumba (8 ~ 31'N, 76 ~ 52'E), the low latitude mesospheric structure has been explored by rocket borne ultraviolet absorption photometry, a technique which yields molecular oxygen concentration profiles, as well 1) Physical Research Laboratory, Ahmedabad-380009, India.

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as by the Indo-USSR collaborative meteorological rocket programme which involves weekly soundings with the M-100 rocket carrying standard meteorological payload to measure temperatures and winds. Both programmes were initiated in 1970-71. The M-100 meteorological rocket launchings are generally effected every Wednesday around 2000 h local time. Molecular oxygen concentrations in the mesosphere and lower thermosphere have been determined by solar ultraviolet absorption photometry. An ultraviolet ion chamber can be used to measure the solar radiation flux within a selected wavelength band in the extreme ultraviolet (HINTERREGGER, 1969). Molecular oxygen concentrations can be determined from the absorption profile of these radiations in the upper atmosphere since molecular oxygen is the main absorbing constituent in the Earth's atmosphere at these wavelengths (FREIDMAN, 1960). At altitudes below about 90 km the atmosphere is well mixed, and the molecular oxygen concentration measurements can be used to study the atmospheric structure. For these altitudes, a nitric oxide filled ion chamber with MgF2 or LiF window is found to be most convenient since it includes the hydrogen Lyman-Alpha line (1216/~) in its passband 1120-1340A (CARVER and MITCHELL, 1967). The Lyman-Alpha line dominates this wavelength region of the solar spectrum, contributing nearly 90~ to the flux in the total passband that penetrates these altitudes. 02 densities can be estimated by using a single effective absorption cross section at the Lyman-Alpha line and molecular oxygen concentrations can be obtained in the 65-95 km altitude region (HALL, 1972). The instrumentation used at Thumb has been described in the literature (SuBBARAVAet al., 1973). The special features of the instrument are: 1. Use of positive bias to the ion chamber to reduce effects due to photoelectric emission. 2. Use of linear amplifier with gain switching to give a large dynamic range as well as high sensitivity throughout the range. The ion chambers used by the authors at Thumba were fabricated and calibrated indigenously at the Physical Research Laboratory, Ahmedabad.

Stratospheric and mesospheric structure over Thumba

Data from the Indo-USSR collaborative M-100 rocket sounding programme at Thumba for the period 1971-74 has been used to study the behaviour of the stratosphere and mesosphere over Thumba. Data for this period is available in the form of monthly means (mean of four rocket flights) for 2000 h local time, tabulated as a function of altitude up to 80 kin. The data for representative heights in the stratosphere and mesosphere are plotted in Figs. la and lb to show the variations in stratospheric and mesospheric structure. The most striking feature of these figures is a strong semi-annual variation in density and temperature at all heights above 40 km with maxima in the equinoxial months, and minima in the winter and summer months.

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The figures also show that the winter minimum is deeper than the summer minimum. Further, the amplitude of the semi-annual feature shows an altitude dependence and there are differences from year to year (SHYAM LAL et al., 1979). Semi-annual variations in the atmospheric densities were first recognized by PAETZOLD and ZSCHORNER (1961) in the satellite drag data for the 300-400 km altitude region. Since then it has been the subject of several studies (JACCHIA, 1965; KING HELE, 1967; JACCHIA et al., 1969; JACCHIA, 1971; MAROV and ALPHEROV, 1971; GROVES, 1972; WALKER, 1978) and the existence of a semi-annual variation in atmospheric densities is well established for the entire thermosphere and exosphere. C o o k (1969) has recognized a semi-annual effect at an altitude of 90 km in phase with the variation at higher altitudes. At lower

584

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altitudes, in the stratosphere and mesosphere, seasonal effects have been known in the circulation, especially at tropical and sub-tropical latitudes where the annual oscillation becomes small (COLE, 1975). Studies based on satellite measurements (e.g. HEATH et al., 1974) have shown that the average stratospheric temperatures are lower in December-January than in June-July. However, the semi-annual feature in low latitude stratospheric and mesospheric densities does not seem to have been noticed so far. A comparison of the density behaviour with that of the temperatures shows further interesting results. While there is a semi-annual feature both in densities and temperatures, they go in phase below about 50 kin. A change of phase occurs somewhere in the 50-60 km range and in the mesosphere the temperature and density are opposite in phase. The data of Figs. la and Ib are subjected to a seven point running average and shown in Figs. 2a, b to study features with longer periods. An annual cycle is clearly evident. Further, a long term trend of temperatures decreasing and densities

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B.H. Subbaraya and Shyam Lal

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increasing with decrease in solar activity from 1971 to 1974 is clearly seen at 80 km. The trend persists down to about 75 kin, below which height the trend does not seem to exist.

Molecular oxygen concentrations

A number of Lyman-Alpha absorption profile measurements have been made at Thumba during daytime, mostly within a few hours around noon. The measurements were made sporadically over a period of time, on rockets which were flown for various ionospheric investigations. Some of these results have been reported earlier (SUBBARAYAet al., 1972, 1974). It is not possible to resolve from these occasional measurements the finer aspects of low latitude mesospheric structure such as diurnal variations, variation due to solar and magnetic activity etc. However, an attempt is made to obtain some gross features of mesospheric structure from these measurements. Molecular oxygen concentration profiles from five rocket flights are shown in Fig. 3. Table 1 gives information regarding the flight day and time. Data of Fig. 3 is restricted to the altitude region of 65-85 km even though on some of the rocket flights measurements extend beyond 85 km. It is observed that three of these five profiles shown in Fig. 3a agree within 20~ of one another, while the other two profiles shown in Fig. 3b differ markedly from these three. The O2 concentrations of the first three profiles are less than the standard atmospheric model values such as CIRA 72,

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spread in the model values for January, April and June months.

Vol. 118, 1980)

The Structure of the Equatorial Mesophero at Thumba

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below about 80 km. A second order polynomial fit to the observations of these three flights meets the CIRA model at an altitude of about 82 km. Scale heights, and hence the gas temperatures, deduced from this mean profile exceed the standard atmospheric model values by 30-50% in the altitude region of 65-80 km. The two profiles from the September 1977 and October 1978 rocket flights Show a behaviour quite different from the earlier three profiles. The observed densities on these flights are larger than the model atmospheric values by factors lying between 1.8 and 2.7 throughout the altitude region. The larger values of these two profiles would be in qualitative agreement with the semi-annual feature of Figs. 1a and lb which shows maximum values for September-October months. The excess amplitudes are, however, larger than given by Figs. la and lb. This, however, could be attributed to the fact that Figs. la and Ib refer to 2000 h local time whereas the 02 densities of Fig. 3 are for day time conditions. Diurnal variations in the tropical atmosphere are known to exist (HEATHet al., 1974) and there could be differences in the features of the day time and night time atmospheric structure even though no definitive observational evidence exists for the same. Further, the rocket flight which has yielded the largest 02 densities, flight No. 08.393 was on a large solar flux day, the 2800 MHz flux index was 171.5 and the sunspot number was high (Rz = 161). Note the increase in 02 densities by about 50~/obetween the flights 08.348 and 08.393 for an increase in 2800 MHz index from 104 to 170 for the same September-October period. These results indicate a large variability in mesopheric 02 density and hence the mesospheric structure with solar UV flux if 2800 MHz index is taken as an indicator of solar UV flux. Figure 4 shows the molecular oxygen concentration profile obtained on 28 January 1971 at 1040 h IST (Solar Zenith angle 34~ The 65-85 km portion of this profile was included in Fig. 3a. The day was characterized by a high level of solar flux, as indicated by the 2800 MHz index which was 171, and large values for the geomagnetic index (Ap = 39). This profile merits special attention because of the wave type structure in the observed concentration profile. Errors of the individual 02 concentration estimates are indicated to emphasize the fact that the wave-like perturbation is significantly above the error bars. Further, the periodicity is unrelated to the period of rocket precession and spin. Hence it is proposed that the observed perturbation is genuine. The observed wavelength is suggestive of gravity waves. Gravity wave associated features in neutral atmospheric structure at stratospheric and mesospheric altitudes have been seen earlier by several workers (THEoN and SMm-I, 1971 ; HEAT~Iet al., 1974). However, it is interesting to note that this is the only one out of the five noon time profiles obtained at Thumba that exhibits such wave-like structure. While the equatorial and the auroral electrojets have been considered as potential candidates for launching gravity waves in the upper atmosphere (cf. CHIMONAS and HINES, 1970; NAGPALand SEN GUPTA,1977), it should be noted that this particular day was marked by normal electrojet conditions. It is not clear how frequently such perturbations occur at Thumba and whether some of these are related to the flow of the electrojet currents.

Vol. 118, 1980)

The Structure o f the Equatorial Mesophere at Thumba

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Acknowledgements The ultraviolet absorption measurements were initiated under the guidance and encouragement of the late Prof. Vikram A. Sarabhai. Acknowledgements are due to Prof. Satya Prakash, who was intimately associated with the programme in the initial stages, for continued encouragement and frequent discussions. Prof. P. R. Pisharoty was the Chief Scientist for the Indo-USSR collaborative M-100 rocket launching programme. Messrs T. M. Raval and J. T. Vinchi have been helping the authors in instrumentation. Detector fabrication and calibration were facilitated by the kind cooperation of Dr. Vijay Kumar and his associates. Messrs R. I. Patel and K. S. Patel have done most of the data reading and analysis. The authors would also like to acknowledge the cooperation of the staff at TERLS during payload integration and rocket launching phases and Dr. V. Narayanan, Meteorologist, for fruitful discussions on the M-100 data. REFERENCES

(1) CARVER,J. H. and MITCHELL,P. (1967), Journal of Optical Society of America 57, 738. (2) CHIMONAS, G. E. and HINES, C. O. (1970), Planetary and Space Science 18, 565. (3) COLE, A. E. (1975), Space Research 15, 173.

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(4) COOK, G. E. (1969), Nature 222, 969. (5) FREIDMAN,H. (1960), Ch. 4 in Physics of the Upper Atmosphere, ed. J. A. Ratcliffe, Academic Press. (6) GROVES,G. V. (1972), Planteary and Space Science 20, 2099. (7) HALL, J. E. (1972), Journal of Atmospheric and Terrestrial Physics 34, 1337. (8) HEATH,D. F. HILSENRATH,E. KRUEGER,A. J. NORDBERG,W. PRABHAKARA,C. and THEON, J. S. (1974), Structure and Dynamics of the Upper Atmosphere, ed. F. Verniani, Elsevoir Pub. Co. (1) HINTEREGGERH. E. (1969), in I Q S Y Notes, ed. A. C. Stickland, Pergamon Press. (10) JACCHtA,L. G. (1967), Space Research. 5, North Holland, p. 1152. (11) JACCHIA,L. G. (1971), Jour. Geophys. Res. 76, 4602. (12) JACCHIA,L. G., SLOWLY,J. W. and CAMPBELL,I. G. (1969), Planet Space Sci. 17, 49. (13) KING HELL, D. G. (1967), Nature 216, 880. (14) MAROV, M. Ya. and ALPHERO,A. M. (1972), Space Research. (15) NAGPAL, O. P. and SEN GUPTA, A. (1977), in Proceedings of the Workshop on 'Equatorial Electrojet and Associated Phenomena' hem at Ahmedabad, Oct. 77, 1977. (16) PAETZOLD,H. K. and ZSCHORNER,H. (1961), Space Research 2, North Holland Pub. (17) SHYAMLAL, SUBBARAYA,B. H. and NARAYANAN,V. (1979), Space Research 19, 147. (18) SUBBARAYA, B. H., PAREEK, P. N. and PRAKASH S. (1972), Journal of Atmospheric and Terrestrial Physics 34, 1141. (19) SUBBARAYA,B. H., DASHB. K. and PRAKASH,S. (1973), Journal of the Institution of Electronics & Telecom. Engineers 19, 397. (20) SUBBARAYA,B. H. PRAKASH,S. KUMAR,V. and PAREEK,P. N. (1974), Space Research 14, 173. (21) THEON, J. S. and SMITHW. S. (1971), in Mesospheric Models and Related experiments, ed. G. Fiocco, D. Reidel Co., p. 131. (22) WALKER, D. M. C. (1978), Planet Space Science 26, 291. (Received 15th October 1979)

Pageoph, Vol. 118 (1980), Birkhauser Verlag, Basel

Scientific Objectives of the Solar Mesosphere Explorer Mission By GARY E. THOMAS1'2), CHARLES A. BARTHI'2), ELAINE R. HANSEN1), CHARLES W. HORD 1,2), GEORGE M. LAWRENCE1,2,3), GEORGE H. MOUNT 1.2), GARY J. ROTTMAN1,2), DAVID W. RUSCH1,2), A. IAN STEWART1,2), RONALD J. THOMAS1,2), JULIUS LONDON4), PAUL L. BAILEYS), PAUL J. CRUTZENS), ROBERT E. DICKINSONS), JOHN C. GILLES), SHAW C. LIUG), JOHN F. NOXON 6) a n d CROFTON B. FARMER7'8)

A b s t r a c t - T h e 1981-82 Solar Mesosphere Explorer (SME) mission is described. The SME experiment will provide a comprehensive study of mesospheric ozone and the processes which form and destroy it. Five instruments will be carried on the spinning spacecraft to measure the ozone density and its altitude distribution from 30 to 80 kin, monitor the incoming solar ultraviolet radiation, and measure other atmospheric constituents which affect ozone. The polar-orbiting spacecraft will be placed into a 3 PM-3 AMSun-synchronous orbit. The atmospheric measurements will scan the Earth's limb and measure: (1) the mesospheric and stratospheric ozone density distribution by inversion of Rayleigh-scattered ultraviolet limb radiance, and the thermal emission from ozone at 9.6/~m; (2) the water vapor density distribution by inversion of thermal emission at 6.3 ~m; (3) the ozone photolysis rate by inversion of the O2(1Ag) 1.27/~m limb radiance; (4) the temperature profile by a combination of narrow-band and wide-band measurements of the 15 t~m thermal emission by CO2; and, (5) the NO2 density distribution by inversion of Rayleighscattered limb radiance at 0.439/zm. The solar ultraviolet monitor will measure both the 0.2-0.31 /zm spectral region and the Lyman-alpha (0.1216/~m) contribution to the solar irradiance. This combination of measurements will provide a rigorous test of the photochemical equilibrium theory of the mesospheric oxygen-hydrogen system, will determine what changes occur in the ozone distribution as a result of changes in the incoming solar radiation, and will detect changes that may occur as a result of meteorological disturbances.

Key words: Solar Mesosphere Explorer; Ozone; Water vapor; Solar ultraviolet monitor; Limb radiance. 1) Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado 80309, USA. 2) Also Department of Astro-Geophysics, University of Colorado, Boulder, Colorado 80309, USA. 3) Also Department of Aerospace Engineering, University of Colorado, Boulder, Colorado 80309, USA. ~) Department of Astro-Geophysics, University of Colorado, Boulder, Colorado 80309, USA. 5) National Center for Atmospheric Research, Boulder, Colorado 80303, USA. 6) Aeronomy Laboratory, National Oceanic and Atmospheric Administration, Boulder, Colorado 80303, USA. 7) Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125, USA. 8) On leave from the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91103, USA.

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L Introduction

The Solar Mesosphere Explorer (SME) is a National Aeronautics and Space Administration (NASA) satellite designed to study the upper part of the Earth's ozone layer, its response to changes in solar activity and its relationship to the meteorology of the stratosphere and mesosphere. There are two primary objectives of the SME experiments. The first is to determine the changes that may occur in the mesospheric ozone distribution as a result of changes in the incoming solar radiation. The second is to measure all changes in the ozone density distribution in the altitude range 30-80 km and to determine the causes of these changes. In order to carry out this second objective, the mission will include not only measurements of the solar ultraviolet irradiance and ozone distribution, but also temperature, pressure, water vapor, nitrogen dioxide concentrations, and near-infrared airglow. The instruments will all be built at the University of Colorado's Laboratory for Atmospheric and Space Physics (LASP). University of Colorado faculty and students, and scientists from the National Center for Atmospheric Research, the National Oceanic and Atmospheric Administration, and the Jet Propulsion Laboratory will work jointly on the project. The instruments o n SME will be a solar ultraviolet spectrometer, an ozone ultraviolet spectrometer, a four-channel infrared radiometer, a near infrared spectrometer, and a nitrogen dioxide visible light spectrometer. A solar proton alarm will also be carried to signal the presence of energetic solar protons in the range 10-500 Mev. The solar ultraviolet spectrometer will continuously measure the solar irradiance in the wavelength region which dissociates molecular oxygen (A < 0.242/~m), in the primary region which dissociates ozone (A < 0.31/zm), and in the Lyman alpha line (0.1216/~m) which is primarily responsible for the photodissociation of water vapor in the mesosphere. Three different limb scanning instruments will measure the altitude distribution of ozone and related species from 30 km to 80 km. The ozone ultraviolet spectrometer will measure the combination of Rayleigh scattering and ozone absorption in the Hartley region centered at 0.255 ~m. The infrared radiometer witl measure the thermal emission from ozone in the 9.6/~m band, water vapor in the 6.3/zm band, and carbon dioxide emission in the 15 ~m band. The latter will be used to determine the temperature structure of the atmosphere. The near infrared spectrometer will measure both the 1.27/~m emission from excited molecular oxygen resulting from the photodissociation of ozone at solar wavelengths less than 0.33 t*m and the near infrared hydroxyl emissions which result primarily from a reaction between atomic hydrogen and ozone. The nitrogen dioxide visible light spectrometer will determine the nitrogen dioxide concentrations in the 20-40 km region by measuring the combination of Rayleigh scattering and absorption in the band centered at 0.439/~m. To be launched in mid-1981, the SME spacecraft will be placed into a circular Sun-synchronous orbit (inclination 97.8 ~ altitude 600 km) such that the atmosphere will be viewed at a constant local time of 3 : 00 PM on the dayside, and 3: 00 AM on the

Vol. 118, 1980) ScientificObjectives of the Solar Mesosphere Explorer Mission

593

nightside. The constant local time orbit allows investigation of seasonal effects and removes the diurnal effect from investigations of latitude, longitude, seasonal and solar variations. The spacecraft will be operated in a spin stabilized mode at a rate of 5 rpm in a 'cartwheel' configuration, so that all the instruments, except the solar UV monitor, will scan the atmospheric limb in the plane of the orbit with the fields of view subtending an atmospheric volume of height 3.5 km at the minimum ray height. Atmospheric limb radiance profiles will be measured from about 100 km down to 20 km. Figure 1 illustrates the altitude range over which each instrument will be capable of taking meaningful data. The primary region of study for the SME mission is the lower mesosphere at 50-70 km. In this region, oxygen-hydrogen photochemistry is dominant in establishing the ozone density distribution. Figure 2 shows how the characteristic time scales for ozone formation and destruction are normally much smaller than those expected for dynamical transport. Therefore, ozone should be most responsive to solar variability in this part of the atmosphere. Solar Lyman alpha at 0.1216/xm emission is variable (up to 30~) with the 27-day solar rotation (see VIDAL-MADJAR,1977 and references therein). In the ultraviolet the 27-day solar

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variability declines with increasing wavelength, from 5~ at 0.174/zm to 1~ near 0.3 ~m (HEATH and THAEKEKERA, 1977). The SME mission will occur during a period of fairly high solar activity, according to predictions of the smoothed sunspot number (Fig. 3). It should be comparable to the maximum of the previous solar cycle (1969-70). Sporadic solar output in the form of either ultraviolet enhancements or energetic proton bombardment will therefore be more likely to occur during the SME time period than during later missions, such as HALOE and UARS. Knowledge of the water-vapor density during times of ozone changes is crucial, since its dissociation products are the primary agents for ozone recombination in the mesosphere. Knowledge of the temperature is also very important, as certain key chemical reactions involving ozone are temperature sensitive. The SME complement of instruments provides essentially all the information necessary to provide a rigorous test of photochemical ozone theories. Such tests have been absent in the past, due to the fact that simultaneous measurements of all the important quantities are seldom available, particularly over a large enough time period to provide confidence that one has isolated the causative agent for the variability. It will also map the various regions where dynamical phenomena are important; for example the high-latitude winter mesosphere is often disturbed by planetary wave activity and changes in ozone density in this region are not expected to be controlled strictly by solar variability.

Vol. 118, 1980)

Scientific Objectives of the Solar Mesosphere Explorer Mission

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1I. Theoretical background The d o m i n a n t p h o t o c h e m i c a l processes between 30 a n d 80 k m involve ozone. O z o n e is p r o d u c e d as a result o f the p h o t o d i s s o c i a t i o n o f m o l e c u l a r oxygen

02 + hv(h < 0.242 t ~ m ) - + O + O

(1)

followed by the three b o d y reaction O + 02 + M ~ O 3

+ M.

(2)

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The ratio of ozone and atomic oxygen is determined primarily by a photochemical balance between reaction (2) and the following reaction: 03 + hv(,~ < 1.08/zm)--> O + 02.

(3)

It is convenient to define odd oxygen (Ox) to be the sum of ozone and atomic oxygen. Odd oxygen is destroyed by the following reactions O+O+M-~O2+M

(4)

and O + 03 --> 202.

(5)

Reactions (1)-(5) were proposed by Chapman in the 1930s and were believed adequate until the 1960s when measurements showed less ozone than predicted, necessitating modification of the theory involving catalytic ozone-destroying reactions. Odd hydrogen (HOx = H + OH + HO2 + H202) catalytic cycles were first proposed to explain the lower ozone densities observed (HUNT, 1966). The simplified reaction scheme for the mesosphere is illustrated in Fig. 4. The catalytic cycles are H + O 3 - - > O H + 02 O H + O - - > H + 02 Net:

03 + O --> 202

(6)

597

Vol. 118, 1980) Scientific Objectives of the Solar Mesosphere Explorer Mission and O + O H - ~ H + 02 H+O2 + M--~H02 + M HO2 + O - ~ O H + O 2 Net:

O + O --~ 02

(7)

In the stratosphere there is an additional important cycle O H + Oa--> HO2 + 02 HO2 + Oa--~ O H + 202 Net:

2Oa ~ 302.

(8)

In the mesosphere the source of odd hydrogen is mainly photodissociation and O(1D) oxidation of water vapor. The sinks are the reactions O H + HO2 ~ H 2 0 + 02

(9)

H+ HO2->H20 +O H + HO2--> H2 + 02.

(10)

and

Because of their short lifetimes the odd hydrogen species are in photochemical equilibrium with each other and with water vapor. So it is essential to measure the water vapor content. Mesospheric water vapor also is the major source of hydrogen escape flux.

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Figure 5 shows theoretically predicted ozone profiles and the measured midlatitude ozone profile summarized by KRLrE~ER and MINZER (1976). With only the Chapman scheme the predicted ozone is far too high, especially in the upper mesosphere. Including the odd hydrogen catalytic cycles greatly improves the agreement in the mesosphere. Below about 40 km the production of odd hydrogen by photodissociation of H20 drops off due to the increasing opacity of the atmosphere, and it is necessary to include odd-nitrogen (NO2, NO, NOa, HNO3) photochemistry (CRurZEN, 1970, 1971 ; JOHNSTON,1971). Ozone is destroyed by NO and NO2 through NO +. 03--~ NO2 + 02 NO2 + O--~ NO + 02 Net:

O + O8---~ 202

(11)

Inclusion of this catalytic destruction of ozone brings the predicted ozone density in reasonable agreement with observed values. The complete nitrogen chemistry must, however, consider reactions involving N, N2, NO, NO2, HNO3, N205, and N20 (CRuTZEN, 1970 and 1971) and chlorine photochemistry (ROWLANDand MOLINA, 1975; STOLARSKIand CICERONE,1974). The natural source of NO is provided by the oxidation of N20, which is produced by bacteria in the soil. The chlorine catalytic ozone destruction cycle is similar to the nitrogen cycle in equation (11) with NO and NO2 replaced by C1 and C10, respectively. In the lower mesosphere odd oxygen is in photochemical equilibrium, and hence simultaneous measurements of ozone density, ozone photodissociation rate, water vapor density, temperature, and solar ultraviolet irradiance will provide a rigorous test of the above photochemical theory. However there remain uncertainties in the values of several key reaction rates that determine the effectiveness of the odd-hydrogen catalytic cycle (particularly reaction (9)). Thus, if confidence in the basic theory can be established, the SME observations may also provide useful information about reaction rates. The O3-H20 model is expected to break down near the mesopause because of the effects of diffusion on odd oxygen and odd hydrogen, and below about 40 km because of the increasing importance of odd-nitrogen and odd-chlorine species. SME will detect the departures of the measurements from the O3-H20 model predictions and will, therefore, demonstrate and measure the importance of these perturbing influences. In the 30-40 km region the major loss of odd oxygen is due to catalysis by odd nitrogen. The measurement of NO2 and 03 will provide an estimate of the odd oxygen destruction rate in this region. The geographical distribution of NO2 is also of interest because it exhibits an unexpected latitude dependence, marked by a sudden drop in concentration above + 50~ geographic latitude (NOXON, 1979). This marked change is not yet fully understood but appears to be tied to profound changes in stratospheric circulation patterns with latitude. This drop or 'ledge' may be associated with the equatorial edge of the so-called winter circumpolar circulation vortex.

Vol. 118, 1980) ScientificObjectives of the Solar Mesosphere Explorer Mission

599

The SME measurements will also provide information concerning dynamical transport of ozone in regions of the atmosphere where the transport time scale is comparable to the photochemical lifetimes (Fig. 2). It is likely that vertical mixing and horizontal advection are sporadic, that is, much more rapid at some times than at others. This is particularly evident during a winter stratospheric warming event. It is safe to assume that species involving chemical reactions requiring a few days or less will be in chemical equilibrium with each other, and conversely species reacting only on time scales of a year or more will have their distribution largely controlled by transport. In the lower mesosphere, the odd oxygen species depend on fast reactions and so are all in chemical equilibrium. The same is true of the odd hydrogen species. However, molecules, such as H20, are destroyed (or generated) more slowly, and the possible role of transport in determining their distribution must be established. Water vapor has dissociation time scales in the range 10-100 days from 50-70 km. Thus its concentration in the mesosphere is probably not uniformly mixed but controlled jointly by transport and chemistry. Changes in H20 concentration as monitored by the infrared experiment will indicate the action either of transport processes or a changing solar irradiance. Monitoring the temperature field may also indicate possible unusual transport activity, since the radiative time scale (see Fig. 2) may at times be exceeded by the dynamical time scale. There will be additional opportunities to observe changes in the high-latitude mesospheric ozone distribution during solar proton precipitation events (SPE, in the earlier literature called polar cap absorption or PCA phenomena). At geomagnetic latitudes higher than about 60 ~ protons with energies greater than 5 Mev penetrate to altitudes below 75 km, and can produce ionization rates many orders of magnitude greater than quiet-time values. Recombination ultimately results in the destruction of water vapor in the lower mesosphere, with rates comparable to the natural destruction rate. This enhanced production of odd-hydrogen species leads to the greater destruction of mesospheric ozone (SwIDER and KENEASHA, 1973). At lower altitudes the ionization-produced odd-nitrogen species can cause a decreased stratospheric ozone content (HEATH et al., 1977). High-energy electrons at lower latitudes can also produce enhanced ionization in the mesosphere. These so-called REP (Relativistic Electron Precipitation) events are of shorter duration and are on a smaller spatial scale than solar proton events; however, they can cause as much ionization in the lower mesosphere as a PCE and occur more frequently (BAILEY, 1968). In addition to irregular changes in ozone due to changing solar irradiance and energetic particle precipitation, the regular seasonal changes in mesospheric ozone can be readily observed by the SME instruments. Local time variations will not be observable during the nominal mission because of the 3 : 00 AM-3: 00 PM orbit. However, the comparison of ozone data at these two local times at the same longitude will be important in determining the relaxation time scale for ozone recombination at these levels.

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IlL Instrument descriptions In this section we summarize important aspects of each of the five instruments on SME. A more detailed description of the optical and mechanical designs is given in GAUSE and STUART(1979). Three of the instruments, the ultraviolet ozone, the infrared airglow, and the visible NO2, are programmable Ebert-Fastie spectrometers. Their basic design is shown in Fig. 6. The telescope, entrance slits and Ebert mirrors will be the same but the optical coatings, gratings and detectors will be chosen specifically for the desired experiment. The instrument collecting optics will be f/5, 25 cm focal length off-axis parabolic telescopes. These systems demonstrate particularly low off-axis scattered light levels and are easily baffled. The telescope mirrors are 5.0 x 5.0 cm aluminum-coated cervit and will feed f/5, 12.5 cm focal length Ebert-Fastie spectrometers with 0.32 x 3.2 mm entrance slits resulting in a field of view of 0~ x 0~ and a height resolution on the Earth's limb of 3.5 kin. The instruments differ in choice of grating, resolution, and detectors. The main features of all the instruments are summarized in Table 1.

1. Ultraviolet ozone spectrometer. The ultraviolet ozone instrument employs a 3600 grooves/ram grating blazed at 0.24 ~m giving 1.8 nrn/mm dispersion in the focal plane. There are two EMR type 510F photomultiplier tubes behind 0.83 • 3.4 mm exit slits giving 1.5 nm resolution. The exit slits are 19.05 mm apart giving a wavelength separation between the two channels of 30 nm. The sensitivity is 1.1 • I05, 1.2 • 105 and 3.5 • 104 (counts/s)/ kiloRayleigh at 0.22 t~m, 0.26 t~m and 0.3 tzm, respectively.

2. The NO2 visible spectrometer The NO2 visible spectrometer will use a 2000 g/mm grating blazed at 0.4 t~m giving 3.2 nm/mm dispersion in the focal plane. The NO2 measurement will employ dual silicon diode detectors to handle the high photon flux expected near 0.44/zm. The sensitivity expected is 1 x 10 -11 amps/(109 ph/s) at 0.44/~m. The active diode area is 0.32 m m • 3.4 mm giving 0.97 nm resolution in each channel. This instrument will employ an EMR type 510-N photomultiplier in the airglow channel and a 0.64 mm • 3.4 mm exit slit giving 1.96 nm resolution. The airglow channel will cover the wavelength range 0.249 ~m to 0.6 tzm in 0.71 nm steps. The sensitivity at 0.3914 nm is 4 • 105 (counts/s) per kR.

3. Infrared airglow spectrometer The telescope and Ebert mirrors for the infrared airglow instrument will be coated to optimize for the near infrared. The grating will have a ruling density of 150 g/ram

Vol. 118, 1980) ScientificObjectives of the Solar Mesosphere Explorer Mission

603

blazed at 1.8 ~m. The dispersion at the exit stit is 51.4 nm/mm. The exit slits are 0.32 m m wide and give a triangular response function with a full width at half maxim u m of 16.4 nm. This will match the O2(1A~) emission at 1.27/zm. A relay lens behind the exit slit increases the effective speed from f/5 to f/1 and allows the use of small-area lead sulfide detectors. The spectrometer has two exit slits. The wavelength ranges in the two channels are 0.6 to 1.38/Lm and 1.2 to 2.0/~m. Thus there is built-in redundancy for the 1.27/~m measurement. The slit separation of 0.63/~m is chosen so the instrument can measure the 1.27/zm radiance from O2(1Ag) and the (7-5) band of OH(X2~r) at 1.9/zm simultaneously. The signal to noise ratio at 1.27 ~m is expected

SPIN AXIS

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MODULE

Figure 7 SME Observatory module. The placement of individual instruments is indicated. The spacecraft spin axis is coincident with the axis of the Winston Horn. The Solar UV spectrometer drawing does not show the diffusing screen housing.

604

Gary E. Thomas et al.

(Pageoph,

to be 7 at 90 km and to increase with decreasing altitude. The signal will be chopped with a frequency of 400 Hz at the entrance slit and synchronously demodulated. 4. Four-channel infrared radiometer Infrared Radiance measurements of thermal emission from CO2, Oa and HzO are achieved with a Mersenne telescope system. The four detectors are radiatively cooled Hg-Cd-Te photoconductors with filters covering the spectral bands 6.1-7.2, 8.6-10.6, 14.7-15.7, and 13.2-17.2/zm. The filters cover thermal emission from the u2 band of H20, the v3 band of 03, the core of the u2 band of CO2, and the entire v2 CO2 band, respectively. Inversion of the CO2 limb scans yields temperature and CO2 density profiles. Knowledge of the temperature profile and emission from H20 and Oa yields H20 and Oa densities. Such procedures have been developed on the LRIR LIMS programs (GILLEet aL, 1978; RUSSELLand GILLE,1978). The Mersenne telescope which employs off-axis confocal paraboloids has a 203 mm aperture and uses gold-nickel plated aluminum optics. The primary mirror ( f = 406 mm) forms the first images at four apertures in a tuning chopper (2400 Hz). The secondary mirror ( f = 76 ram) is followed by a Lyot stop, a third mirror ( f = 57 mm) and the detector package. The overall focal length is 305 mm yielding an f/1.5 beam into the detector. The detectors are passively cooled by radiative loss from a 10 cm diameter disc which is protected from thermal emission from the Earth by a specially shaped horn, coaxial with the roll axis. Since the Earth's limb is 20 ~ from the roll axis, the horn must exhibit ~ 10 -4 rejection of heat inputs past 18~ from the axis. A design that accomplishes this is the Winston horn, or compound parabolic concentrator (Fig. 7). Its cross section consists of parabolas tipped by 18~ and, given a highly polished (~ 2.5 nm rms) interior, exhibits a sharp cutoff of rays entering at angles greater than 18~ The horn has end-diameters of 100 and 328 mm and a length of 660 mm. The expected temperature of the detectors is 105~ With commercially available detectors, the tangent point altitudes at which the signals equal the rms detector noises will be 64, 70, 80, and 86 km for the H20, Oa, CO2 narrow and CO2 wide channels, respectively. If the detector temperature should rise to 140~ these limiting altitudes would decrease by 7 km for the CO2 channels, and 3 km for the H20 and 03 channels. 5. Solar ultraviolet spectrometer The solar ultraviolet spectral irradiance instrument will measure solar radiation in the spectral region 0.16 to 0.31/zm in addition to Lyman-~ at 0.1216/~m. The instrument will be mounted on the side of the Observatory Module with its field of view directed 45 ~ to the spacecraft spin axis (Fig. 7). Data will be taken as the instrument scans through the Sun-satellite line once per spacecraft rotation. The angle between the Sun-satellite vector and the spacecraft spin axis is nominally 45 ~ but, in

Vol. 118, 1980) Scientific Objectives of the Solar Mesosphere Explorer Mission

605

fact, it will continually vary due to seasonal effects and possibly due to irregularities in the satellite attitude and orbit. The design incorporating a diffusing screen allows the angle of incident solar radiation to vary + 15~ requiring only a small and calibrated correction. Several screens will be available and by protecting and 'duty cycling' certain calibration screens, long-term degradation of the instrument can be evaluated. The spectrometer will be an f/5 Ebert-Fastie design with a focal length of 12.5 cm. There are two spectral channels using separate exit slits, detectors, and pulse counting electronics. The short wavelength detector will be a 510 G photomultiplier tube (CsI photocathode) with a MgF2 window and will measure solar radiation in the spectral region 0.16/~m to 0.25/zm, and 0.115/zm to 0.125/zm. The long wavelength detector will be a 510 F photomultiplier tube (CsTe photocathode) with a quartz window and will be used in the spectral region 0.22/zm to 0.31 #m.

IV. Simulations In this section we present simulated radiance data for each instrument as it views the Earth's limb. The limb scanning geometry is illustrated in Fig. 8. The instrument views the Earth's limb with the center of its field of view along 1. We first consider the Ultraviolet Ozone and the NO2 instruments which measure Rayleigh scattered sunlight where scattering and/or absorption have depleted the radiance along the line of sight. The Rayleigh-scattered radiance is optically-thin above 20 km and decreases exponentially with altitude, with most of the radiation originating from

/

R

Figure 8 Illustration of limb scanning geometry. Light emitted or scattered from a small volume along the line of sight is seen by the satellite instruments. Zo is the minimum ray height.

606

Gary E. Thomas et al.

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within one scale height of the point of closest approach (or minimum ray height), Zo, of the line of sight. In the optically thin approximation, the radiance seen by the satellite instrument when the emitting species exponentially decreases with a constant scale height, H, is 4~rI(Zo) = g

S

n(Zo) e -m dl

(12)

co

where g is the emission rate per atom or molecule, n ( Z ) is the number density of Rayleigh scatterers, and the integral is taken along the path 1. Using the HUNTEN (1954) approximation for the Chapman function at 90 ~, equation (12) becomes 4=I(Z0) = gn(Zo)~V/2~--=RH

(13)

where R is the Earth radius. For pure Rayleigh scattering g = rrF. a-p(tF)

(14)

where rrF is the solar flux, e is the Rayleigh scattering cross section, and p0F) is the Rayleigh phase function for scattering angle ~ . The situation becomes more complicated if a pure absorber is present in the atmosphere. For the ultraviolet ozone experiment measuring Rayleigh scattered sunlight in the 0.2-0.3/xm region, the presence of ozone acts to deplete the incident and scattered sunlight. In this case the contribution to the signal from a small element, P (see Fig. 8), is d(4rrI) dl 9o~

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Vol. 118, 1980) ScientificObjectives of the Solar Mesosphere Explorer Mission

607

where r~ is the optical depth for ozone between point P and the Sun; and % is the optical depth between point P and the satellite. In the above formulation

r~ = ao see X

03(Z) dZ

(16)

P

where X is the solar zenith angle, eo is the absorption cross-section for ozone, 03(Z) denotes the number density of ozone, and, % = %

Oa(Z) dl

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P

where the integral is along the viewing path from point P to the satellite. The radiance seen by an observer at the satellite is the total line of sight integral 4~rI(Zo) =

f oo oo

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(18)

The calculated spectral radiance in Rayleighs/nm as a function of Z0 is plotted in Fig. 9 for three wavelengths at a solar zenith angle of 60 ~ The calculation employed the total atmospheric density and profiles from the U.S. Standard Atmosphere (1976). At each wavelength the emission increases exponentially with decreasing altitude until absorption by ozone becomes important. The maximum radiance occurs when the total optical depth along the line of sight of the ozone is ~ 2. Below this altitude no information is received from the atmosphere near the minimum ray height. For the cases presented, useful information is obtained above 60 km at 0.25/zm, above 57 km at 0.28/zm and above 52 km at 0.29/xm. Thus as the instrument scans in wavelength away from the absorption maximum, the ozone cross-section decreases, and the instrument probes deeper into the atmosphere. The NO2 instrument will monitor Rayleigh scattering at 0.439 ~m and 0.442 txm with 0.97 nm resolution. The technique adopted to determine the NO2 column content along the line of sight is essentially that of NOXON (1975). Although NO2 absorbs light throughout most of the visible region of the spectrum, the two wavelengths were chosen because a relative maximum in the NO2 absorption cross-section occurs at 0.439/xm and a relative minimum occurs at 0.442 ~m. Furthermore an intense signal is required to make the difference between the emission measured in the two wavelength regions statistically meaningful as the total optical depth of NO2 along the line of sight is not normally expected to exceed 0.2. The solar flux when integrated over the two band passes in the two channels is nearly equal and the Rayleigh scattering cross-sections differ by only 2.5%. Any additional difference in the Rayleigh scattered signal is due to absorption by NO2. For the simulation we have adopted an NO2 profile measured by KERR and MCELROY (1976). The calculated spectral radiances are shown in Table 2, where Z is the minimum ray height. In this calculation we

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In Table 2 the expected radiance in the two channels, the current generated, the difference, the noise and the signal to noise ratio are presented where the signal is the difference between the current in the two channels. The uncertainty in the difference is < 170 at 20 km, 370 at 25 kin, 870 at 30 km and 3570 at 35 km. The statistics may be improved by adding data from two or more spins together to produce one NO~ absorption profile. The excited ~Ag level of 02 results primarily from the photolytic loss of ozone in the sunlit atmosphere. The infrared airglow instrument will monitor the O2(aXAg--> X3E)) emission at 1.27/~m to determine the altitude profile of ozone photolysis between about 50 and 80 km during the daytime. The lower limit will be determined by the observations. The calculated limb radiance of the O2(~Ag) emission is shown in Fig. 10. Here we have assumed that one excited O2(XAg) molecule is formed from each Oa dissociation between 0.2 and 0.3 ~m and that O2(~Ag) molecules are lost to quenching by O2 at a rate of 2 • 10 -~8 cm* s-L The noise level of the detector is equivalent to about 3.5 x 106 R, giving a signal to noise ratio for maximum intensity at 54 ~ solar zenith angle of 330 and at 90 ~ solar zenith angle of 43. The O2(XAg) emission in the nightglow, although much less intense, may be monitored by adding data from two or more spins. The infrared instrument will simultaneously monitor the emission in the 7-5 band of OH(X2~r) at 1.9/~m. The seventh vibrational level of OH is populated directly 90

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Vol. 118, 1980) ScientificObjectives of the Solar Mesosphere Explorer Mission

611

by the reaction of H and 03 and indirectly by cascade from levels 8 and 9. Thus the interpretation of the 7-5 emission is relatively simple and will provide information on the product of H and 03 in the mesosphere. A simulation of the radiance expected during the night is given in Fig. 11. This model has been shown to be consistent with OH radiance measurements from the AE-E satellite (FREDERICKe t al., 1978). The four-channel infrared radiometer provides radiance measurements in four wavelength channels. The instrument makes temperature measurements by viewing carbon dioxide thermal emission with narrow- and wide-spectral bandwidth channels centered at 15.5 Fm. Thermal emissions from ozone and water vapor are measured at 9.6 t~m and 6.3/~m, respectively. Simulations of expected radiance from the four channels are shown in Fig. 12a-d for mid-latitude winter and for a stratospheric warming. Here NEN denotes the anticipated noise equivalent radiance. For the CO2 channels (Fig. 12a and b) a signal-to-noise ratio greater than one can be expected over the entire region of the experiment. The signal-to-noise ratio for the ozone channel (Fig. 12c) reaches one at about 75 km and occasionally to 70 kin. In most cases the lowest signals occur for cold mesopause situations. The water vapor channel (Fig. 12d) reaches the noise level at about 76 km. The fundamentals of the inversion are described in GILLEand HOUSE (1971) and HOUSE and GILLE (1979), although the implementation for rapid processing will embody the emissivity approach described by BAILEYand GILLE (1978). Accurate results have been demonstrated in the mesosphere and stratosphere (GILLEe t aS., 1979). Ozone densities at high latitudes may be perturbed in the mesosphere and stratosphere during charged particle precipitation (SPE or REP) as discussed earlier. The enhanced ionization produces odd-hydrogen and odd-nitrogen species that catalyzes ozone recombination. The solar proton alarm will signal the occurrence of an SPE above some pre-determined flux threshold. If the spacecraft data system is in the alarm mode it will automatically re-program the observing strategy to concentrate the measurements in high latitudes. Under night-time conditions, the polar particle induced airglow emission in the N + 0.3914 Fm band will be easily measured by the visible light spectrometer. A measurement of the night-time emission profile will directly provide the ionization rate profile in the same volume in which ozone, water vapor and temperature are measured. The ionization rate profile in turn yields the odd-hydrogen and odd-nitrogen production rate profiles. It is important that the SME instruments be able to respond to a particle event in real time, particularly for the mesospheric ozone. This is due to the fast photochemical response time of ozone in this region, for which there is some evidence in the data of HEATH et al. (1977). After-the-fact information on the proton and electron energy spectrum will be obtained from particle measurements on the GOES and TIROS satellites and made available by the NOAA Data Center in Boulder, Colorado. Rocket measurements of the proton spectrum for the 2 November 1969 SPE have been made by SELLERSand HANSER(1972). The ionization profile at the maximum

612

Gary E. Thomas et al.

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IONIZATION RATE (cm-a s-I) 103

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F i g u r e 13 I o n i z a t i o n rate (electrons-cm -a s -1) vs. altitude (km), a n d 0.3914/zm limb r a d i a n c e (R) vs. m i n i m u m r a y h e i g h t p r o d u c e d b y t h e solar p r o t o n event o f 2 N o v e m b e r 1969 at its m a x i m u m intensity. T h e ionization rate values are f r o m LAVERGNAT et aL (1972). T h e 0.3914/~m fluorescent efficiency o f 14.1 i o n pairs per 3914 A p h o t o n was t a k e n f r o m BORST a n d ZIPF 0 9 7 0 ) .

of the event was computed by them and by LAVERGNATet al. (1972) using Explorer 4 charged particle measurements, and were in good agreement. The 0.3914/~m production rate resulting from their ionization profile, and the predicted limb radiance of the 0.3914/zm emission is shown in Fig. 13. The fluorescent efficiency was taken to be 14.1 ion-pairs per 0.3914/zm photon (BORSTand ZU'F, 1970). Using the production efficiency of 10 O2(1Ag) molecules produced per ion pair estimated by SWIDER and GARDNER (1972), the limb radiance in the 1.27/~m band can be inferred from the figure by multiplying the 0.3914/zm profile by 140. Thus a maximum value of 1.27 /zm limb emission of 0.7 megaRayleigh would have resulted from the 2 November 1969 event. However, quenching would greatly reduce this value below about 60 kin.

V. S M E experiment operations

The SME mission has been designed to take advantage of the existing NASA satellite tracking and communications capability. Telemetry, command, and tracking coverage requirements vary from a maximum of two 30-min contacts per orbit for the first three weeks, to 14 contacts per day for the remainder of the mission. The data will be analyzed by the Science Team at LASP as it is processed during the mission.

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The SME Project Operations control center at LASP will be the central facility for the control of the SME satellite and the evaluation and analysis of its data. The commands and data links will also utilize existing facilities at the Goddard Space Flight Center. Tracking data will be linked to Goddard for orbit determination. The real-time and tape recorder playback data will be received and recorded at LASP. Real-time data will be used to monitor the health of satellite subsystems and verify the status of the observatory. Tape recorder playback data will be formatted and available for quick-look scientific evaluation, attitude determination, and scientific analysis. Data from recorded real time and tape recorder playback data will be processed and analyzed using a mini-computer system. A general purpose data reduction language, along with many data reduction programs, has been written for use on other LASP projects and will be available for SME 'quick-look' evaluation and analysis. The Interactive Display language will provide users with easy-to-use, flexible, interactive computing power with no turnaround time. It is display oriented, making use of storage and CRT displays and plots. The language is designed to manipulate and display scalars, vectors (spectral data), and matrices (image data) as any simple variable, allowing a relatively untrained user to reduce and analyze scientific data with desk calculator ease. The interactive nature of the language allows execution of stored or standard routines as well as execution of single statements from the keyboard, where the results of each operation are automatically displayed on the user terminal. Standard data reduction routines will be available for functions such as data smoothing, averaging, contouring, curve fitting and noise removal along with special purpose calibration and inversion routines.

VI. SME personnel and acknowledgements The Principal Investigator of the SME mission is Charles Barth, Director of the Laboratory for Atmospheric and Space Physics. Lowell Dorman is the University of Colorado Project Manager. The SME Project is managed by the Jet Propulsion Laboratory, with John Paulson as JPL Project Manager and James Stuart as Spacecraft Manager. D. W. Rusch has contributed to all phases of preparation of this manuscript, and has also provided the calculations for the simulated radiances for the 03, NO~, O2(1Ag) and OH signals. P. Bailey and J. Gille provided the simulated radiances for the infrared radiometer experiment. S. C. Liu contributed much of the material contained in Section II. The original proposal is described in the unpublished University of Colorado document 'Solar Mesosphere Explorer Experiment Description'. We thank G. P. Anderson for a careful reading of the manuscript and for helpful suggestions. We acknowledge the National Center for Atmospheric Research for

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c o m p u t e r services. N C A R is sponsored by the N a t i o n a l Science F o u n d a t i o n . The S M E Project is supported u n d e r JPL C o n t r a c t n u m b e r 955357.

REFERENCES BAILEY, D. K. (1968), Some quantitative aspects of electron precipitation in and near the auroral zone, Rev. Geophys. 6, 289-346. BAILEY, P. G. and GILLE, J. C. (1978), An approximate method for non-linear inversion of limb radiance observations, in Remote Sensing of the Atmosphere: Inversion Methods and Applications, A. L. Fymat and V. E. Zuev (eds.), Elsevier, Amsterdam, pp. 107-113. BORST, W. L. and ZIPF, E. C. (1970), Cross-section for e- impact excitation of the 0,0 1N N~ band from threshold to 3 Key, Phys. Rev., Sect. A 1, 834-840. CRUTZEN, P. J. (1970), The influence of nitrogen oxides on the atmospheric ozone content, Quart, J. Roy. Meteor. Soc. 96, 320-325. CRUTZEN, P. J. (1971), Ozone production rates in an oxygen-hydrogen-nitrogen oxide atmosphere, J. Geophys. Res. 76, 7311-7327. FREDERICK, J. E., RUSCH, D. W. and LIu, S. C. (1978), Nightglow emissions of OH(X%r): Comparison of theory and measurements in the (9-3) band, J. Geophys. Res. 83, 2441-2443. GAUSE, K. A. and STUART,J. R. (1979), Solar Mesosphere Explorer Optical-Mechanical Systems Engineering, IEEE Region V Annual Conference, April 3-5, E1 Paso, Texas. GILLE, J. C., BAILEY,P., HOUSE,F. B., CRAIG,R. A. and THOMAS,J. R. (1978), in Nimbus 6 Users Guide, J. E. Sissala (ed.), Greenbelt, Maryland, NASA, pp. 141-16t. GILLE, J. C., BAILEY,P. L. and RUSSELL,J. M. III (1979), Temperature and composition measurements from the LRIR and L I M S experiment on Nimbus 6 and 7, Proc. Roy. Soc. (submitted for publication). GILLE, J. C. and HOUSE,F. B. (1971), On the inversion of limb radiance measurements I: Temperature and thickness, J. Atmos. Sci. 28, 1427-1442. HEATH, D. F., KRUEGER,A. J. and CRUTZEN,P. J. (1977), Solar proton event: Influence on stratospheric ozone, Science 197, 886-889. HEATH, D. F. and THEKAEKARA,M. P. (1977), The solar spectrum between 1200 and 3000 A~, in The Solar Output and its Variation, O. R. White (ed.), (Colo. Assoc. Univ. Press, Boulder), pp. 193-212. HOUSE, F. B. and GILLE, J. C. (1979), On the inversion of limb radiance measurements II: Ozone and water vapor, J. Geophys. Res. (submitted for publication). HUNT, B. G. (1966), Photochemistry of ozone in a moist atmosphere, J. Geophys. Res. 71, 1385-1398. HUNTEN, D. M. (1954), A study of sodium twilight. I theory, J. Atmos. Terr. Phys. 5, 44-56. JOHNSTON, H. S. (1971), Reduction of stratospheric ozone by nitrogen oxide, catalysts from supersonic transport exhaust, Science 173, 517-522. KERR, J. B. and MCELROY, C. T. (1976), Measurement of stratospheric nitrogen dioxide from the AES stratospheric balloon program, Atmosphere 14, 166-171. KRUEGER, A. J. and MINZNER, R. A. (1976), A proposed standard mid-latitude ozone model, 1975, Goddard Space Flight Center, NASA, Greenbelt, Maryland. LAVERGNAT,J., BERTHELIER,J. J. and PIRRE, M. (1972), Riometers observations in Antarctica of 2 November 1969 solar proton event, in Proc. of COSPAR Symp. in Solar Particle Event of November 1969, J. C. Ulwick (ed.), AFCRL-72-0474, pp. 181-200. MIEGHAM,VAN J. (1978), Scale analysis of large atmospheric motion systems in all latitudes, Adv. in Geophysics 20, Academic Press, 87-130. MURGATROYD,R. J. (1971), Dynamical modeling of the stratosphere and mesosphere, in Mesosphere Models and Related Experiments, Fiocco, ed., Reidel Publ., 104--121. NATIONAL ACADEMY OF SCIENCES PANEL ON ATMOSPHERIC CHEMISTRY (1971), Halocarbons: Effects on Stratospheric Ozone, Nat'l. Acad. of Sciences, Washington, D.C., p. 107.

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NOXON, J. F. (1975), Nitrogen dioxide in the stratosphere and troposphere measured by ground-based absorption spectroscopy, Science 189, 547-549. NOXON, J. F. (1979), Stratospheric NO2: II. Global behaviour, J. Geophys. Res., in press. PARK, J. H. and LONDON, J. (1974), Ozone photochemistry and radiative heating of the middle atmosphere, J. Atmos. Sci. 31, 1898-1916. ROWLAND,F. S. and MOLINA,M. J. (1975), Chlorofluoromethanes in the environment, Rev. Geophys. Space Phys. 13, 1-35. RtrSSEL, J. M. II and GILLE,J. C. (1978), in Nimbus 7 Users Guide, C. R. Madrid (ed.), Greenbelt, Maryland, NASA, pp. 71-103. SELLERS, B. and HANSER, R. A. (1972), Heavy Particle Ionization Rates, in Proc. of COSPAR Symp. on Solar Particle Event of November 1969, J. C. Ulwick (ed.), AFCRL-72-0474, pp. 181-200. STOLARSKI,R. S., and CICERONE, R. J. (1974), Stratospheric chlorine: a possible sink for ozone, Can. J. Chem. 52, 1610-1615. SWIDER, W. and KENESrIEA,T. J. (1973), Decrease of ozone and atomic oxygen in the lower mesosphere during a PCA event, Planet. Space Sci. 21, 1969-1974. U.S. Standard Atmosphere (Gov. Printing Office, Washington, D.C., 1976), p. 227. VIDAL-MADJAR,A. (1977), The solar spectrum at Lyman-Alpha 1216 A, in The Solar Output and Its Variation, O. R. White (ed.), (Colo. Assoc. Univ. Press, Boulder), pp. 213-236. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh[iuser Verlag, Basel

Satellite Solar Occultation Sounding of the Middle Atmosphere By JAMESM. RUSSELLIII 1)

Abstract- This paper discusses the principles, achievements, and prospects for satellite solar occultation sounding of the middle atmosphere. Advantages, disadvantages, and spatial and temporal coverage capabilities are described. Progress over the past 15 years is reviewed, and results from a recent satellite aerosol experiment are presented. Questions with regard to Doppler shift, atmospheric refraction, instrument pointing, pressure sensing, and measurement of diurnally active species are addressed. Two experiments now orbiting on the Nimbus-7 and AEM-B satellites, and approved experiments under development for future flights on Spacelab and the Earth Radiation Budget Satellite, are also described. In some cases more than one experiment is scheduled to be flown on the same spacecraft, and the advantages and synergistic effects of these applications are discussed. Key words: Solar occultation sounding.

Introduction The middle atmosphere, extending from the tropopause to 100 kin, is an important region of our atmosphere not only from the viewpoint of scientific interest and study, but also because it serves as a buffer zone to shield the Earth surface from extreme ultraviolet rays of the Sun. In addition, it affects the Earth radiation balance, and it is dynamically coupled to the lower atmosphere. It is generally an accommodating region for remote probing since it contains no cloudiness except occasionally at the lower boundary near the tropopause, and this occurs mostly in the Tropics. Noctilucent clouds are also a consideration in this regard but they are not very important since they occur mostly at high altitudes ( ~ 80 km) and latitudes ( < 50~ On the whole, the problems of remote sensing in the middle atmosphere are tractable, and a number of satellite experiments have been conducted including both nadir and limb sounders. Both the thermal emission approach (for sensing of the more abundant gases such as 03, H20, and N20) and solar occultation (for Oa and aerosols) have been used. Early experiments were directed to the nadir and concentrated primarily on measurements of temperature and/or ozone using upwelling thermal emission measurements. These included the Infrared Interferometer Spectrometer - IRIS (PRABHAKARAet al., 1) NASA, Langley Research Center Hampton, VA 23665, USA.

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1976), the Satellite Infrared Spectrometer - SIRS (WARK,1970), the Selective Chopper Radiometer - SCR (ABELet al., 1970), and later the Pressure Modulated Radiometer PMR (CURTISand HOUGHTON, 1974). The Backscatter Ultraviolet (BUV) experiment was also developed and flown on the Nimbus-4 satellite to infer total ozone in a vertical column below the satellite using measurements of solar radiation backscattered by the atmosphere (HEATH et aL, 1973). These experiments provided a wealth of new information on the upper atmosphere. As our knowledge progressed, however, the need for increased vertical resolution became apparent. GILLE (1968) was the first to suggest limb thermal emission sounding for this purpose which he proposed as a means to study diurnal temperature changes. This idea was developed into the Limb Radiance Inversion Radiometer (LRIR) experiment which was later flown on the Nimbus-6 satellite (GILLEet al., 1979). The LRIR experiment relied on measurements of infrared thermal emission coming from the planetary horizon to infer profiles of temperature, ozone, and water vapor concentrations. It was the first satellite experiment to provide temperature and ozone data with high vertical resolution, especially in the mid to lower stratosphere. As model studies of the chemistry in the upper atmosphere became more sophisticated, a number of mechanisms were revealed that could lead to catalytic destruction of stratospheric ozone through reactions with odd-nitrogen, odd-chlorine and oddhydrogen compounds (NOx, CIOx, and HO~). Because of the potentially serious biological and climatic consequences of ozone depletion, a number of experiments were proposed and selected for flight to study the chemistry and dynamics in the upper atmosphere. The Nimbus-7 satellite, launched October 1978, carried several experiments designed to study the first of these chemical chains- the NOx compounds. These experiments included the Limb Infrared Monitor of the Stratosphere (LIMS) (RUSSELL and GILLE, 1978), the Stratosphere and Mesosphere Sounder (SAMS) (DRUMMOND et al., 1978), and the Solar Backscatter Ultraviolet/Total Ozone Mapping Spectrometer (SBUV/TOMS) (HEATH et al., 1978). Both LIMS and SAMS are thermal limb sounding experiments. The LIMS measures radiance profiles which are processed to yield the vertical distributions of temperature, 03, NO2, HNO3, and H20 as a function of pressure, while SAMS provides measurements of temperature, CO, N20, NO, CH4, and H20. The SBUV/TOMS measures 03 profiles above the main peak and total ozone in a vertical column. The measurement of chemical species in the chlorine chemistry is more difficult than is the case for NO~. Consequently, no satellite experiments currently exist, although several are under development. The concentrations of important gases are generally less than those in the NOx family by about an order of magnitude, and in some cases (e.g. HC1), the molecular absorption band occurs at a relatively short wavelength (~3/zm) where emission is very weak. These limitations suggest that another approach, namely solar occultation, be used to obtain high signal-to-noise ratios especially at the shorter wavelengths. The use of solar occultation also facilitates the measurement and study of another problem of the middle atmosphere-the

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James M. Russell III

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aerosol distribution and its effect on the Earth radiation balance. Two solar occultation experiments for this purpose were recently launched on the Nimbus-7 and AEM-B satellites. The Stratospheric Aerosol Monitor II (SAM II) on Nimbus-7 is designed to measure polar region aerosol distributions, and the Stratospheric Aerosol and Gas Experiment (SAGE) on AEM B measures aerosols, ozone, and NO2 profiles (McCoRMICK et aL, 1976). The purpose of this paper is to describe the principles, achievements, and prospects for application of satellite solar occultation sounding in the middle atmosphere. The advantages and disadvantages, geographic and temporal coverage, and past, current, and future approved experiments are described.

Principles of solar occultation sounding The general approach in the solar occultation experiment is to observe the attentuation of the Sun's rays due to absorption by atmospheric constituents (Fig. 1). The general relation for the measured signal, S, at a tangent height, Ho, can be written in terms of the solar intensity and atmospheric absorption by the equation

s=cf~

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Figure 1 Solar occultation experiment geometry.

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extent of the field of view. For a spectrometer, Av is small (e.g. _<1 cm -1) while for a radiometer, it is large (e.g. > 20 cm-1). The transmittance for a ray traveling along the instrument optical axis can be written ~-a(v, P, T) = exp

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where K~ is the absorption cross-section at wavenumber u, e~ is the scattering crosssection, n is the number density of the absorbing constituent, and L is total path length across the horizon along the ray path. The absorption cross-section cart be a function of both pressure and temperature, depending on the spectral region used. In the infrared, it depends on both parameters. Also, the rather simple Lorentizion expression used in the lower atmosphere must be replaced for the middle atmosphere by the more complicated voight line shape. Equation (1) can be approximated by the expression S ~_ CA~N~-7~F Av

(3)

where the bars denote mean quantities over Av. In this equation S is in units of volts, C is in units of volts per watt, .N~ is in watts/m 2 tLm, Au is in t~m, A in units of m 2, and ~, ~a, and F are unittess. The experiment scenario is to track the solar disk as it rises or sets on the horizon thereby obtaining a profile of signal versus time, t. The transmittance ~ ( t ) can be determined by dividing the signal, S ( t ) , by the signal for an exoatmospheric measurement, S| for which t = 0 and ~ = 1. In principle, time can be converted to tangent altitude using satellite and solar ephemeris data. In practice, effects of atmospheric refraction must be included in the calculations because of the long paths across the limb. This affects the tangent altitude as well as the apparent Sun shape as seen from the spacecraft. PEPIN et al. (1977) show a series of photographs of the setting Sun (Fig. 2) which demonstrate the apparent decreasing

Figure 2 Composite of photographs taken during Apollo-Soyuz mission showing refraction effects on the Sun image (after PEPINet al., 1977).

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James M. Russell III

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vertical extent of the Sun as it sets. For a field of view locked at a fixed angle relative to the edge of the Sun, this effect causes the center of the field of view to move to successively different points on the solar limb darkening curve at lower tangent altitudes. Thus, it must be taken into account in relating the solar intensity value at any given time, t, to the exoatmospheric value. Refraction also causes the instrument field view to cover a larger area of the Sun for the lower tangent altitudes and must be considered in calculations of spatial averaging. C n u and McCoRMICK (1979) present a method for using the Sun shape at each tangent altitude to accurately account for these factors. The value of N~ at 3 tzm wavelength varies by about 5 ~ due to these effects, and it should be possible to correct for this with little error ( ~ 0.3~o) using climatological temperature-pressure data. If the field of view has infinite spatial resolution, if the instrument pointing capability is perfect, and if other factors such as the atmospheric temperature-pressure profile and Sun spot occurrences are known exactly, it would not be necessary to define the solar limb darkening curve in an occultation experiment. Since these conditions are not met, however, the general approach is to scan the exoatmospheric limb darkening curve on each occultation event to obtain S= versus angle data (relative to one edge of the disk). This procedure will permit determination of Sun spots effects on the signal and any sensitivity the instrument may have to other solar surface features such as granularities. These effects can then be removed later in the data reduction. The scans will also allow effects due to changing field of view area on the disk to be properly considered. Once the limb darkening curve has been defined, the disk can be tracked during occultation either in a continuous scan mode or a mode where the field of view is locked at some fixed angle from one edge or at the disk center. There are advantages and disadvantages to each approach depending upon the instrument and measurement being made. The scanning approach provides more data since each tangent altitude is crossed several times during an occultation, and for certain conditions, when the Sun is not fully occulted by the Earth, a wider altitude range can be covered than in the lock mode. The lock mode, on the other hand, provides a longer measurement integration time, and therefore a given measurement can be made with smaller instrument optics. Thus, it should be possible in principle to sense more tenuous gases with this approach without resorting to data averaging. Effects due to spacecraft motion can be automatically removed with either method by designing the instrument pointing control bandwidth or scan rate to be much greater than 'the frequency of expected spacecraft motions. Sun shape data are obtained automatically in the scan mode and can also be measured with the lock mode approach by proper instrument design. Pressure sensing The use of the transmittance equation (2) at infrared wavelengths to determine number density requires that pressures be determined by some method in order to

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account for pressure effects on the absorption cross-section. Temperature also affects the cross-section but it is mostly a second order effect, particularly for those lines with a low ground state energy. One approach is to use the tangent altitude calculated from the satellite-Sun ephemeris data along with climatological data to obtain a representative temperature-pressure profile. This places stringent requirements on tracking and pointing stability, and with current systems it can result in substantial errors in number density. PARK et al. (1979) outline a broadband (~100cm -1) method for remotely sensing tangent shell pressure using the occultation technique. The method is based on measurement of limb absorption in the 2.0, 2.7, or 4.3/~m CO2 band and assumes a constant and known CO2 mixing ratio. By proper choice o f spectral regions, lines can be selected which are only weakly temperature dependent, and climatological temperature data may be used with little error. An excellent first guess pressure profile can be obtained by constructing a transmittance versus pressure plot using a climatological temperature-pressure profile. The CO2 ~(t) data can then be used to read pressure directly from the plot. These authors also describe an iterative procedure which carries the initial guess to a final solution. Pressure can be inferred with an RMS accuracy of about 3~o up to 55 km altitude using present instrument systems. A similar approach can be used with high spectral resolution data to determine temperature as well as pressure. A line with low ground state energy and therefore weak temperature dependence is selected for pressure sensing and a line with high energy is used for temperature sensing. Some iteration would be required (ToTH, 1977). Other considerations

Other effects which may need to be considered in applying the occultation approach include Doppler shift, and interpretation of measurements of diurnally active species. With regard to the Doppler shift, the maximum value for 3/zm as an example, is about 0.07 cm-1. This compares with absorption line widths in the upper atmosphere of 0.007 cm-1 or less. Thus large errors result if this is neglected. Since the spacecraft velocity can normally be determined to within a few meters per second, corrections for the Doppler shift do not present a problem in the data analysis. For events where the Sun direction is nearly perpendicular to the orbital velocity vector, the Doppler shift is very small; but the latitude skew, or the latitude range covered during the time required for the occultation to occur, is large. When the latitude skew is minimal, the Doppler shift is maximum. The measurement of diurnally active species (e.g. NO, NO2, CIO, CIONO2, Oa) also adds complexity to the data reduction and interpretation of occultation measurements. Nitric oxide for example is believed to be converted almost entirely to nitrogen dioxide (NO2) during the night. At the occultation solar zenith angle of 90~ the Sun's dissociating potential at the tangent point has been depleted relative to lower zenith angle rays due to the long path. Thus, the vertical distribution of NO with altitude is not the same as for the high noon case. This effect creates a non-spherically

622

James M. Russell III

(Pageoph,

symmetric NO distribution along the horizon path (see MURCRAY, 1978). Sunset measurements by RIDLEY et al. (1976) show that the change in NO concentration from the zenith Sun position to 90 ~ is only 207o in the mid-stratosphere. A method for correcting NO occultation measurements and relating these data to daytime values is described by KERR et al. (1977). The diurnal effect is not serious in this instance, but this may not be true for some gases. The effects and errors depend on the magnitude and speed of the diurnal change and must, therefore, be studied on a case by case basis. Advantages and disadvantages

The solar occultation approach has a number of advantages. Because of the experiment geometry and the exponential decrease of density with height, high vertical resolution is obtainable. Most of the absorption occurs in a narrow height range weighted near the tangent point. Also, the limb view provides long optical paths allowing measurements to be made of more tenuous gases than can be measured in a nadir experiment. The Sun provides a very large signal making it possible to perform the measurements using uncooled or, at worst, thermoelectrically cooled detectors. The solar background is a source of nearly constant intensity rather than a highly variable source, as is the case for the nadir experiment. All of these effects simplify data reduction and enhance measurement accuracy. The large solar signal allows use of narrow spectral intervals thereby increasing the potential for measurement of gases in regions spectrally contaminated by interfering species. Solar occultation also covers a much wider spectral range for remote sensing than is the case for emission, thereby allowing measurements of some gases, such as HC1 and HF, which are difficult or impossible to measure by infrared emission techniques. One of the most important advantages of solar occultation is that a relative measurement is made. This self-calibrating feature provides higher accuracy since the instrument is calibrated just before or just after each measurement. Other concerns, such as long term instrument drifts, are also decreased. The only requirement is that the instrument be stable over the time required for an occultation (typically 30 seconds to 3 minutes). All of these factors are important in the design of an experiment for making longterm observations. The solar occultation approach has some disadvantages in that the sampling rate around the globe is less frequent than for a thermal emission experiment which provides data night and day and in any view direction. Also, the geographic coverage is limited. This is not a serious limitation for certain types of experiments such as long-term trend studies, large-scale dynamics, hemispheric differences, or global budgets of chemical constituents. These points are discussed further in the next section of this paper. The horizontal resolution is not as good as in the nadir experiment since the weighted absorption occurs over an effective length of 200-300 km along the path. This should not be a critical factor for study of the middle atmosphere since large horizontal variability is not expected. Finally, the occultation measurements

Vol. 118, 1980)

623

Satellite Solar Occultation Sounding of the Middle Atmosphere

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are confined to the 90 ~ solar zenith angle condition which, in some cases already noted, can cause added complexity in data reduction and analysis.

Spatial and temporal coverage considerations A detailed analysis of the spatial and temporal coverage attainable with solar occultation has been presented by HARRISONet al. (1975) and BROOKS(1977). Figure 3 shows the effect of orbit inclinations and seasonal changes on latitude coverage, and Fig. 4 shows the latitude coverage for 1 full year at 56 ~ inclination (HARRISON, 1979). 2) Latitudes of + 45 ~ + 75 ~ and + 90 ~ can be observed for orbital inclinations of 28.5 ~ 56 ~ and 70 ~ respectively. A high noon Sun-synchronous orbit provides only 64-80 ~ coverage in both hemispheres. I f the equatorial crossing time is different than high noon, a different latitude range can be covered but it will still be limited in comparison to the coverage attainable with a non-Sun-synchronous inclination. Note from Fig. 4 that at several times of the year, 100 ~ of latitude is covered in under 1 week time period and that for most of the year, this range is spanned in 2 weeks or less. There are several periods where no occultation occurs due to the satellite-EarthSun geometric relationship created by the orbital precession. The percentage of the year when this condition exists, however, is small. The frequency of coverage for 56 ~ inclination is about twice a month for latitudes of + 45 ~ decreasing to about once a month, on the average, for latitudes greater than + 45 ~ These coverage frequencies will vary with orbital inclination. In a 70 ~ inclined orbit, both poles are covered 2) Private communication, NASA, Langley Research Center, Hampton, VA 23665:

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twice a year at the times of the equinoxes. The longitudinal distance between measurements varies from about 2500 km in the equatorial region to about 500 km at high latitudes, depending on the orbital period. As the orbital inclination increases, the frequency of north-south latitude traversals decrease and the time required to cover a given latitude range increases. The latitude range that can be covered, however, also increases. The maximum Doppler shift and vertical sink rate of the Sun on the horizon occurs at those times of rapid latitude coverage. The minimum values occur as the non-occulting condition is approached. A total of 15 events occur each day in each hemisphere, providing 30 vertical scans of the horizon. This data coverage is useful for studying latitudinal trends and zonal average variations. Coverage over 1 month, for March, is shown in Fig. 5. The latitude range is approximately 50~ to 80~ in this case, but it varies with month of the year as indicated by Fig. 4. For any given day, a particular latitude band is covered uniformly in longitude ( ~ 2 4 ~ separation per sounding). The study of budgets of chemical compounds requires data on about 3 km vertical by 500 km in the latitudinal direction by a zonal average spatial grid. Monthly global averages for latitudes less than or equal to about 70 ~ are sufficient for studying budgets. The coverage provided by occultation permits valuable observations and studies of the atmosphere to be performed, especially with regard to refinement of multi-dimensional models which describe the photochemistry

Vol. 118, 1980) 90

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and dynamics of the middle atmosphere, long term trend analyses, studies of hemispheric differences in concentration, and large scale circulation studies.

Achievements in satellite solar occultation sounding

Satellite measurements of atmospheric ozone using ultraviolet solar occultation were conducted as early as 1964 using 3800/~ wavelength (MILLER, 1967). This same author also noted extra attenuation which he attributed to dust or aerosols injected by a volcanic eruption at Bali in March 1963. Since that time, numerous occultation experiments have been conducted from rockets and satellites to study both of these parameters in the upper atmosphere (e.g. ROBLE et al., 1972; MmLER et al., 1973; JONCKHEEREet al., 1974; RIEGLERet al., 1976; OGAWAet al., 1976; LLEWELLYNet al., 1977; RIEGLERet aL, 1977; GUENTHERet al., 1977; and PEPIN et al., 1977). The most concentrated satellite - solar occultation study of upper atmosphere aerosol and ozone distributions has been initiated by the University of Wyoming-NASA, Langley Research Center team. The first satellite experiment, the Stratospheric Aerosol Monitor (SAM) was flown on the Apollo-Soyuz Test Project in 1975 (PEPIN et aL, 1977). A follow on experiment, the Stratospheric Aerosol Monitor II (SAM II), was launched on the Nimbus-7 satellite in October 1978 ( M C C O R M I C K et al., 1979). A

626

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(Pageoph,

third experiment, the Stratospheric Aerosol and Gas Experiment (SAGE), was launched only a few months later in February 1979 to measure aerosols, ozone, and NO2 distributions (CHU and MCCORMICK, 1979). Although published results are available only from the SAM experiment, the others are functioning well in orbit and each of these experiments will be briefly described. The SAM,experiment consisted of a single channel photometer which used a pin diode detector having a 10~ field of view (about 20 times the angular extent of the Sun). The spectral filter was centered at a wavelength of 0.84 ~m and had a 600 A bandwidth. The instrument was equipped with a projection sight system to allow the astronaut to manually lock onto the Sun. The spacecraft was then placed in an inertial mode to track the Sun during occultation. In addition to the photometer, a camera equipped with special infrared fiIm was used to photograph the setting and rising Sun (photographs are included as Fig. 2 of this paper). The experiment observed four events: two sunsets at 39~ and two sunrises at 43~ Even though a large field

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Vol. 118, 1980) Satellite Solar Occultation Sounding of the Middle Atmosphere

627

of view was used, the investigators were able to obtain finer resolution in the measured parameter (aerosol extinction coefficient) by using an onion skin inversion algorithm approach. The results (Fig. 6) were corroborated by balloon underflights and groundbased lidar measurements. The total extinction due to aerosols was greater at the peak of the aerosol layer in the Northern Hemisphere than was observed for the Southern Hemisphere by a factor of 1.5. The authors attributed the differences to injection of aerosol in the Northern Hemisphere stratosphere by the Volcan de Fuego in Guatemala, which erupted during October 1974. The SAM II experiment is based on SAM technology. It, too, is a single-channel photometer having a spectral filter centered at 1/zm, but it is a more sophisticated instrument with an automatic pointing capability so that it can be used from an unmanned spacecraft. Absorption by atmospheric gases at 1 ~m is virtually negligible, leaving only aerosol and Rayleigh scattering to cause extinction. Unlike SAM, the SAM II experiment has high vertical resolution; the instantaneous vertical field of view (IFOV) is 0.6 arc minute, providing a vertical resolution at the horizon of 0.5 kin. After acquiring the Sun in azimuth and elevation, the IFOV is scanned across the Sun surface at a rate of 15 arc minutes per second during the entire occultation. The scan reverses itself after each limb crossing. Because of this feature, the angular scan amplitude decreases and the scan frequency increases at lower tangent altitudes due to the apparent decreased Sun vertical extent caused by refraction. Coverage by SAM II is limited to the high latitudes (640-80 ~ in each hemisphere since the Nimbus-7 is in a high noon, Sun-synchronous satellite. The measured signal is used with the exoatmospheric solar scans (to obtain S~) for computation of transmission which is then inverted to obtain total extinction. The data reduction approach is to use temperature-pressure profile measurements by auxiliary methods to calculate the Rayleigh scattering extinction, leaving as the final product, aerosol extinction. The experimenters estimate that the aerosol extinction coefficient in the Junge layer can be determined to within 10~ accuracy. Orbital performance, preliminary data, and implications of the early signals are discussed in an article by McCORMICK et al. (1979). The SAGE experiment is more advanced than the previous two experiments in terms of parameters measured. It is mounted on the AEM-B satellite which is in an orbit inclined at 55 ~ having a 600 km perigee, and a 96.7 minute orbital period. Thus, wide geographic coverage is being provided to complement the data from SAM II. The latitudes covered range from 79~ to 79~ The pointing characteristics, field of view, and solar scan rate are essentially the same as those for SAM II. The SAGE instrument is different, however, in that it is a four-channel photometer. Also, the incoming energy is not spectrally filtered by an interference filter at the entrance aperture as for SAM II, but instead, a holographic diffraction grating disperses the light in different directions, depending on wavelength. Channels are centered at 0.385 /zm, 0.45 t~m, 0.63 tzm, and 1.0/zm. Figure 7, from CI~u and McCoRMICK (1979), shows the various factors contributing to extinction at these wavelengths. The primary contrib-

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utors at 1.0/~m are Rayleigh and aerosol scattering. The main factor at 0.6/~m is ozone absorption in the Chappuis band, and at 0.45/zm and 0.38/zm it is extinction due to Rayleigh scattering and NO2 absorption. The experimenters have developed an inversion scheme to determine aerosol extinction, ozone mixing ratio, neutral density, and NO2 mixing ratio. It is based on four coupled systems of linear equations corresponding to the four wavelengths. The ozone profiles will extend from the tropopause to about 45 km. The estimated inverted extinction coefficient accuracies are 10% for ozone and neutral density between 10 and 40 km, 10% for aerosol between 10 and 25 km, and 25% for NO2 between 25 and 40 kin. Absolute mixing ratio accuracy will be less due to absorption coefficients uncertainties; errors from this source are expected to be small since the absorption cross-section exhibits little pressure-temperature dependence. The SAGE results have not yet been published.

Occultation experiments under development Several satellite solar occultation experiments have been approved for flight and are under development. All provide high spectral resolution. Two experiments produce detailed spectral absorption information throughout the middle infrared from 2/zm to N 16/zm. These are the Grille Spectrometer 3) (Spacelab I) and the Atmospheric a) Co-Principal Investigators are Dr. M. Ackerman, Belgian Institute for Space Aeronomy, Brussels, Belgium; and Dr. A. Girard, Office Nationale d'Etudes et de Recherches Aerospatials, Chatillon, France.

Vol. 118, 1980) SatelliteSolar Occultation Sounding of the Middle Atmosphere

629

Trace Molecule Spectroscopy 4) (ATMOS) experiment (Spacelab I/Ill). A third experiment, the Halogen Occultation Experiment (HALOE) (RUSSELLet al., 1977) uses a gas specific instrument to make long term observations of selected key constituents in the upper atmosphere (Spacelab III and the Earth Radiation Budget Satellite - ERBS). A fourth experiment, SAGE II, 5) is a follow on to SAGE which will have more channels for better definition of aerosol size distribution and more accurate NO2 measurements (ERBS). The first three of these experiments will be briefly described. Since SAGE II is very similar to SAGE, no further discussion will be presented. The Grille Spectrometer is being designed to study atmospheric constituent distributions over the altitude range from 15 to 150 kilometers. The spectral resolution varies from 0.06 cm-1 to 0.1 cm-1, depending on wavelength. The spectral range of 2.5/~m to 13 ~m allows a number of molecules to be observed including, for example, CO2, H20, 03, CH4, N20, CO, NO, NO2, HNO3, HC1, HF, CF2Clz, and CFC13. The experiment can also operate in an emission mode over the wavelength range of 9/~m to 12/~m. The grille, which is a plate having a large area and a set of alternating reflecting and transparent zones, replaces the entrance and exit slits in a conventional spectrometer and eliminates the interdependance of luminosity and resolving power. The luminosity, which is about 100 times better than that for a conventional slit spectrometer, depends on the width of the zones. The instrument has a scanning grating with programmable grating positions so that the entire grating angle does not have to be traversed continuously in order to cover the spectral range. Instead, small spectral invervals (~ 1 cm-1) can be selected and scanned anywhere in the range, thereby decreasing the time required to measure the full complement of constituents. The programmed positions can be changed interactively either from the ground or by a payload specialist onboard Spacelab. Two detectors are used simultaneously to cover the entire spectral range. The instrument field of view is about 3 km at the horizon. The pointer has elevation and azimuth tracking capability and tracks the Sun in a lock mode as opposed to a scanning mode. The ATMOS experiment has as its objectives to determine the compositional structure and spatial variability o f the upper atmosphere from the tropopause to 150 km altitude and to collect detailed, high spectral resolution data for use in the design and application of gas specific instrumentation. The ATMOS instrument is a continuous scanning Michelson Fourier spectrometer capable of generating an interferogram each second with an unapodized spectral resolution of 0.01 cm-1. The very high spectral resolution and extended range (2/zm-16/zm) make it possible for ATMOS to measure all of the gases measured by the Grille Spectrometer plus many

4) Principal Investigator is Professor C. B. Farmer, California Institute of Technology, Pasadena, CA. 5) Experiment Scientistis Dr. M. P. McCormick,NASA, LangleyResearch Center, Hampton, VA.

630

James M. Russell III

(Pageoph,

others including such tenuous molecules as C10, C1ONO2, CH3C1, COF2, HBr, HCHO, and OCS to name a few. Cat's eye retroreflectors replace the plane mirrors used in a conventional Michelson interferometer and make the instrument insensitive to angular misalignment of the moving elements. In addition, a retroreflecting mirror double passes the radiation through the two paths of the interferometer, making the instrument insensitive to lateral motion of moving elements as well. A single, HgCdTe detector cooled to liquid nitrogen temperature is used. The instrument does not scan the entire spectral range from 2 ~m to 16/~m in each scan. Rather, it is divided up into six smaller wavelength intervals with each region carefully selected so that taken as a whole, absorption features of all of the species currently of interest are included. The ATMOS IFOV is selectable in flight to be either 2 km or 4 km at the horizon. The instrument pointer provides azimuth and elevation tracking capability and tracks the Sun in a lock mode at the Sun's center. The lock position can be varied by ground command to either avoid solar features such as sun spots for atmospheric studies or to include these features for solar physics studies. The H A L O E experiment is being designed to make long term observations of key constituents in the chlorine chemistry as well as certain other gases needed to study interactions with the NOx and HOx chemistry. In this sense, the experiment complements and extends the data base begun with experiments on the Nimbus 7 satellite which are focused on the NOx chemistry only. The H A L O E measurements include 03, HC1, HF, CH~, H20, NO, and CF~CI~. A CO2 channel is also included for pressure sensing in the manner described earlier in this paper. These measurements will be made from the tropopause to about 30 kin-65 km, depending on the channel. The IFOV is 2 km at the horizon. The measurement approach for HC1, HF, CH~, and NO is gas filter spectroscopy, and for 03, H20, CF2C12, and CO2, it is broad band spectroscopy. The effective spectral resolution for the gas filter channels is about 0.1 cm- 1. The instrument has a two axis pointing capability and operates in a hybrid scan-lock mode. The exoatmospheric Sun is scanned to define the limb darkening curve, and then the Sun is tracked in a locked position during occultation at a fixed angle down from the top edge. Since the gas filter technique is not conventional a more detailed description is presented here. The principle of gas filter radiometery is illustrated schematically in Fig. 8. Solar energy enters the instrument and is divided into two paths. The first path contains a gas cell filled with the gas to be measured (i.e. HC1, HF, CH4, or NO); the second is a vacuum path. An electronic gain adjustment is used in one detector circuit to adjust the signal output so that the two electro-optical paths are matched when there is no target gas in the intervening atmosphere (i.e., 'balanced' outside the atmosphere). When the target gas is present in the atmosphere, a spectral content is introduced to the incoming energy which is correlated with the absorption line spectrum in the gas cell. This correlation upsets the matched condition, causing a signal difference which can be related to stratospheric HC1, HF, NO, or CH4 concentration. To minimize the sensitivity of the HC1 measurement to interfering CH4 absorption, a CH4 attenuation

Vol. 118, 1980)

Satellite Solar Occultation Sounding of the Middle Atmosphere

631

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cell is included in front of both the vacuum and gas cell paths. This is an important addition to the HC1 measurement because of the significant CH4 interference in the HC1 spectral region. A single-channel, H A L O E brassboard instrument has been built and laboratory tested for HCI measurements in preparation for flight evaluation on the Convair 990 aircraft in the late summer of 1979. A full measurement complement engineering model will be flown on the 7 day Spacelab I I I mission, and a flight model will be used on the long duration ERBS. A unique gas cell construction technique has been developed to contain the reactive gases HC1 and H F for long time periods. The ceils are made of an inert gold body with sapphire windows. An HC1 cell has been filled for over one year with no measurable change in cell concentration. Testing of a filled H F cell is just beginning. A simulation study was conducted to determine expected accuracies of the various parameters measured by H A L O E by calculating synthetic signals, injecting errors as indicated by brassboard testing, and then inverting those signals to obtain constituents. Results for HC1 and N O are shown in Fig. 9. The Doppler shift in this case causes a loss of signal and a slightly degraded result. Similar studies for all channels indicate an RMS error of 10 to 15 percent for the 10 to 40 km altitude range (10 to 20 km for CF2C12). Ozone errors will be less than 5 ~ over that range.

632

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Vol. 118, 1980) SatelliteSolar Occultation Sounding of the Middle Atmosphere

633

Concluding comments This paper has described some of the principles, advantages, disadvantages, achievements, and prospects for satellite solar occultation sounding of the middle atmosphere. The primary strength of the approach is its self-calibrating feature which leads to lessened requirements on instrument stability and drift. In addition, the use of the Sun as a source allows measurements with high signal to noise and high wavelength specificity to be made using uncooled or, at worst, thermoelectrically cooled detectors. Thus, the method provides the primary features desired for a monitoring experiment: high precision and a potentially long experiment lifetime. Spatial and temporal coverage, which are sometimes held to be servere limitations of the occultation experiment, have been shown to be adequate for the study of a number of important problems of the upper atmosphere. Also, the solar occultation approach may provide the only way to obtain accurate global information on a main element of the chlorine chemistry, HC1, because of its low concentrations and the low wavelength (3/zm) of its fundamental absorption band. The pioneering efforts of Pepin and McCormick have already produced new information on the stratospheric aerosol layer from the Apollo-Soyuz project. In addition, the currently orbiting SAM II and SAGE experiments are providing for the first time, nearly continuous, global observations of the upper atmosphere dust layer. The evolution of solar occultation experiments is proceeding in a logical fashion. The application of ATMOS and the Grille Spectrometer will provide a wealth of new information on the distribution of minor species in the upper atmosphere. Also, the very high spectral resolution data from ATMOS in particular will serve as a valuable aid in the interpretation of data from gas specific experiments such as HALOE and will contribute in the design of future experiments for making long term observations. The planned simultaneous flight of ATMOS and HALOE on Spacelab III provides an unprecedented opportunity to compare results from two vastly different instrument concepts. Both will view virtually the same solar background and the same atmospheric volume at the same time. HALOE will then be applied on the ERBS mission in a free flyer mode simultaneous with SAGE II. The application of these two experiments over a long time (~ 2 years), again viewing the same atmospheric volume at the same time, will provide an extensive data set on ozone from the tropopause to the mesopause, as well as important gases in the C1Ox, NOx, and HOx chemistry, and aerosols. Several synergistic studies can be performed with the data including potential heterogenous aerosol-gas chemistry effects. The total collection of data from all these experiments on Spacelab as well as ERBS, promises to yield more information on the composition, structure, chemical interactions, and long term variability of the upper atmosphere than any previous data set.

634

James M. RusseU III

(Pageoph,

Acknowledgements

The a u t h o r wishes to acknowledge the help of Drs. M. P. M c C o r m i c k a n d J. D. Lawrence, Jr., for their review of the m a n u s c r i p t a n d for their helpful suggestions.

REFERENCES ABEL, P. G., ELLIS, P. J., HOUGHTON,J. T., PECKHAM,G., RODGERS, C. D., SMITH, S. D. and WILLIAMSON, E. J. (1970), Remote sounding of atmosphere temperature from satellites II. The Selective Chopper Radiometer for Nimbus D, Proc. R. Soc. London, Ser. A. 320, 35-55. BROOKS,DAVIDR. (1977), An Introduction to Orbit Dynamics and its Application to Satellite-Based Earth Monitoring Missions, NASA Ref. Pub., 1009. CHU, W. P. and MCCORMICK, M. P. (1979), Inversion of stratospheric aerosol and gaseous constituents from spacecraft solar extinction data in the 0.38-1.0 tzm wavelength region, Accepted for Publication in App. Opt., May. CURTIS, P. D. and HOUGHTON,J. T. (1974), Remote sounding of atmospheric temperature from satellites. V. The pressure modulator radiometer for Nimbus 17. Proc. R. Soc. London, Ser. A 377, 135-150. DRUMMOND,J. R., HOUGHTON,J. T., PESKETT,G. D., RODGERS,C. D., WALE, M. J., WHITNEY,J. and WlLLIAMSON,E. J. (1978), The Stratospheric and Mesospheric Sounder (SA MS) Experiment. Nimbus 7 User's Guide (C. R. Madrid, ed.), NASA, Goddard Space Flight Center, Greenbelt, MD., 139-174. GILLE, J. C. (1968), On the possibility of estimating diurnal temperature variation at the stratopause from horizon radiance measurements, J. Geophys. Res. 73, March 1963. GILLE, J. C., BAILEY,P. L. and RUSSELL,J. M. III (1979), Temperature and composition measurements from the LRIR and L I M S experiments on Nimbus 6 and 7, Accepted for publication in Proc. R. Soc. London. GUENTHER, B., HEATH, D. and DASGUPTA,R. B. (1977), Twilight ozone measurement by solar occultation from AF 5, Geophys. Res. Lett. 4, 434-436. HARRISON, E. F., GREEN, R. N., BROOKS,D. R., LAWRENCE,G. F. and MCCORMICK,M. P. (1975), Mission Analysis for Satellite Measurements of Stratospheric Constituents by Solar Occultation, Proc. of the 13th AIAA Aerospace Science Meeting, Pasadena, CA, January 20-22. HEATH, D., MATEER, C. L. and KRUEGER, A. J. (1973), The Nimbus 4 backscatter ultraviolet (BUV) atmospheric ozone experiment- Two year's operation, Pure Appl. Geophys., 106-108, 1238-1253. HEATH, D., KREGER,A. J. and PARK, H. (1978), The Solar Backscatter Ultraviolet (SBUV) and Total Ozone Mapping Spectrometer (TOMS) experiment. Nimbus 7 User's Guide (C. R. Madrid, ed.), NASA, Goddard Space Flight Center, Greenbelt, MD. JONCKHEERE, D. E. and MILLER, D. E. (1974), A measurement of the ozone concentration from 65 km to 75 km at night, Planet and Spc. Sci. 22, 497-499. KERR, J. B., EVANS,W. J. F. and MCCONNELL,J. C. (1977), The effects of N02 changes at twilight on tangent ray NOz measurements, Geophys. Res. Lett. 4, 13, 577-582. LLEWELLYN, E. J. and WITT, G. (1977), The measurement of ozone concentrations at high latitude during the twilight, Planet and Spc. Sci. 25, 165-172. OGAWA, T., TOHMATSU,T. and WATANABE,T. (1976), Measurements of stratospheric aerosols by the solar occultation method, J. Geornog. and Geoelec. 28, 3, 237-242. MCCORMICK, M. P., HAMILL,P., PEPIN, T. J., CHU, W. e., SWISSLER,T. J. and McMASTER, L. R. (1979), Satellite studies of the stratospheric aerosol, Bull. Am. Met. Soc. 60, 9, September. McCoRMICK, M. P., EDWARDS, H. B., MAULDIN, L. E. and McMASTER, L. R. (1976), Satellite solar occultation measurements, ' S A M H and SAGE', in Atmospheric Aerosols: Their Optical Properties and Effects, NASA CP-2004.

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MILLER, D. E. (1967), Stratospheric attenuation in the near ultraviolet, Proc. Roy. Soc. London, Set. A 301, 57-75. MILLER, D. E. and RYDER,P. B. (1973), Measurement of ozone concentration from 55 km to 95 km at Sunset via the occultation technique from rocket payloads, Planet. and Spc. Sci. 2I, 963-970. MURCRAY, DAVID G. (1978), On the Interpretation of Infrared Solar Spectra for Altitude Distribution of Atmospheric Trace Constituents, Final Report, Department of Transportation Contract FA77-WA-3949. PARK, J. H., RUSSELL,J. M. III and DRAYSON,S. R. (1979), Pressure sensing of the atmosphere by solar occultation using broad band CO2 absorption, Appl. Opt. 18, 12, June. PEPIN, T. J., MCCORMICK,M. P., CHU, W. P., SIMON,F., SWISSLER,T. J., ADAMS,R. R., CRUMBLY, K. H. and FULLER, W. H. (1977), Stratospheric Aerosol Measurements, Experiment MA-007. NASA SP-412, 127-136. PRABHAKARA,C., RODGERS,E. B., CONRATH,B. J., HANEL, R. A. and KUNDE, V. G. (1976), The Nimbus 4 infrared spectroscopy experiment 3. Observations of the lower stratosphere thermal structure and total ozone, J. Geophys. Res. 81, 4997. RIDLEY, B. A., BRUIN,J. T., SHIFF,H. I. and MCCONNELL,J. C. (1976), Altitude profile and Sunset decay measurements of stratospheric nitric oxide, Atmosphere 14, 3, 180-188. RIEGLER, G. R., LIU, S. C , CICERONE,R. J. and DRAKE,J. V. (1976), Stellar occultation measurements of atmospheric ozone and chlorine from OAO 3, J. Geoph. Res. 81, 4997-5001. RIEGLER, G. R., LIU, S. C., WASSER,B., ATREYA,S. K., DONAHUE,T. i . and DRAKE,J. F. (1977), UV stellar occultation measurements of nighttime equatorial ozone, Geophys. Res. Lett. 4, 145-148. RUBLE, R. G. and HAYS, P. B. (1972), The nighttime distribution of ozone in the low-latitude mesosphere, Pure and Appl. Geophys. 106-108, 5-7, 1281-1289. RUSSELL, J. M. III, PARK, J. H. and DRAYSON, S. R. (1977), Global monitoring of stratospheric halogen compounds from a satellite using gas filter spectroscopy in the solar occultation mode, Appl. Opt. 16, 3, 607-612. RUSSELL,J. M. III and GILLE, J. C. (1978), The limb infrared monitor of the stratosphere (LIMS) experiment, The Nimbus 7 User's Guide (C. R. Madrid, ed.), NASA, Goddard Space Flight Center, Greenbelt, MD, 71-103. TOTH, R. A. (1977), Temperature sounding from the absorption spectrum of C02 at 4.3 ~m, Appl. Opt. 16, 2661-2668. WARK, D. Q. (1970), SIRS: An experiment to measure the free air temperature from a satellite, Appl. Opt. 9, 1761-1766. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh/iuser Verlag, Basel

Threats to the Ozone Layer By H. A. PANOFSKY1) Key words: Ozone layer; Ozone changes; Ozone public policy.

1. History and overview Since ozone in the atmosphere is chemically active, its natural equilibrium can be upset if the natural chemical environment of the atmosphere is altered appropriately. Furthermore, certain gases, through their catalytic reactions with ozone and other closely related chemical species, can alter the present distribution of ozone. This can be accomplished by only a tiny change in the amount of these gases (of the order of parts per billion of natural air densities). In particular, three groups of chemicals can attack ozone (08) and oxygen atoms (O) through catalytic reactions: oxides of nitrogen (NO and NO2), oxides of chlorine and chlorine itself (C10 and C1), and oxides of hydrogen (HO and HO2). Recently, bromine species (Br, BrO) were also shown to be effective in catalytic reactions with ozone and oxygen atoms. In recent years the potential of human activities in introducing a sufficient amount of these substances into the stratosphere to affect ozone significantlyhas been clearly demonstrated. The problem was first raised around 1970 and then injected into the debate concerning the possible construction of large American SSTs (supersonic transports). All high-temperature combustion processes (such as those in the jet engines) produce NO and NO2 which, when introduced into the stratosphere, could reduce stratospheric ozone catalytically. The problem has been under intensive study by the Climatic Impact Assessment Program of the U.S. Department of Transportation and reviewed critically by a special committee of the U.S. National Academy of Sciences. Although the reports issued by these studies disagreed in some quantitative details, they agreed in their basic conclusion: that continuous development of a large fleet (several hundred airplanes) of SSTs with engines then available would be a serious threat to the ozone layer, although the small fleet of existing Anglo-French Concordes and Russian Tupolev 144s did not constitute a serious threat. This was because the existing fleet of Concordes and Tupolev 144s (~ 30 in number) constitutes only a relatively weak source of NO and NO2 in the stratosphere, and because these planes fly at relatively low levels. 1) Department of Meteorology,PennsylvaniaState University, University Park, Pennsylvania 16802, USA.

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At about the time of these reports a second problem was raised: that of the chlorofluoromethanes, CF2C12 and CFCIa, often referred to as F-12 and F-11, respectively. Chlorofluoromethanes (CFMs) were the principal propellants in aerosol spray cans and remain the principal refrigerants for refrigerators and air conditioners. They are also finding increasing use as insulating foams. CFM's are extremely stable in the troposphere and can only be destroyed by intense ultraviolet radiation found high in the stratosphere. To the accuracy of measurements, all the CFMs ever released into the atmosphere are still located in the troposphere with a small loss (about 17oo per year) to the stratosphere. The CFM problem was studied by panels of the U.S. National Academy of Sciences and by NASA. Late in 1976, the Academy released a report suggesting that, at the 1973 rate of CFM release, eventually about 77o of the ozone would be destroyed with a large uncertainty range. Measurements made 6 months later showed that a critical chemical reaction, to be discussed in detail, proceeds much faster than was previously assumed. The result was that it is now (late 1979) believed that the potential effect is twice that estimated in 1976, but still very uncertain. Although no new surprises are anticipated, the possibility still exists that some of these conclusions will be modified in the future. In any case, as a result of these estimates, the U.S. Government has phased out use of CFM's in spray cans as of January l, 1979. However, at this time, the U.S. is responsible only for about 307o of world production of CFM's; further, spray cans use only about half the CFM's produced. Hence the U.S. ban of CFM's for use in spray cans will only reduce the potentially damaging effect of the CFM's by less than 20~o. While the change in the measured reaction rate caused an increase in the computed ozone change due to the CFM's, it decreased the effect of NO, as will be seen. It now appears that low-flying SST's (e.g., the Concorde) may actually increase total ozone; the higher-flying large SST's would still destroy ozone, but not at a significant rate. Further, it now appears that the effects of CI and NO are synergistic; the more NO is added to the stratosphere, the smaller is the effect of C1 and C10 ! A further potential problem for the ozone layer was also raised about the same time as the CFM problem. Certain nitrogen fertilizers release N20. In the presence of excited oxygen, this produces NO. NO interferes with the ozone layer. Fortunately, the recalculation of the NO-ozone chemistry has made this possibility less serious; and the threat, if important, is very slow. The fertilizer problem is so complex that there is no agreement on even the sign, much less on the magnitude of the problem. Other threats to the ozone layer have been suggested. For example, other substances are produced by man which contain chlorine, e.g., methylchloroform. This chemical is used in increasing amounts for metal degreasing, because most of its rivals have been banned for other reasons. This solvent may produce serious problems in the future. Quite a different mechanism for disturbing the ozone layer is based on the sensitivity of some chemical rate constants to temperature. And it now appears likely that

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human activity will affect the temperature distribution. For example, CO and CO2 concentrations are increasing and will increase further as a result of burning of fossil fuels. The result will be that the temperature near the ground will rise, but that the temperature in the stratosphere will decrease. Preliminary estimates of this change in the next century suggest that this temperature modification will only have a relatively small impact on the ozone layer.

2. Effects of ozone changes Presumably, the most important effect of ozone change will be on the amount of ultraviolet radiation reaching the ground, in the wavelength regions called UVB, between 290 and 320 nm. In this region, ozone absorbs partially, and a change in total ozone column by X ~ will increase the UVB radiation reaching the ground by approximately 2 X ~ . For humans, the most serious direct consequence of an increase in UVB is an increase in skin cancer; the fractional increase of skin cancer occurrences is estimated to be of the same order as the fractional increase in UVB. For example, a 10~ decrease of ozone would increase skin cancer by 20~. The connection between UV and skin cancer rests on strong circumstantial evidence. 1. Skin cancer is more common at low latitudes, where the ozone amount is lowest, and the solar intensity greatest. 2. Skin cancer occurs on parts of the body which are frequently or occasionally exposed to sunlight, depending on the type of cancer. 3. Rats develop skin cancer when irradiated with UVB. 4. Some persons suffering of skin cancers can prevent future occurrence by use of PABA, a cream specially formulated to absorb UVB. Damaging effects of UV on animal and plant life also are indicated by some studies, but require more documentation. Since ozone has strong absorption bands in the infrared and ultraviolet, and weak bands in the visible, any change of ozone concentration could influence climate. Surface climate is affected in compensating ways: a reduction of ozone would cool the stratosphere, hence infrared radiation reaching the ground would be reduced, cooling the surface. At the same time, more UV and visible would reach the troposphere. But the net effect will certainly be small compared to heating caused by increasing CO2, probably even small compared to the warming caused by the CFM's themselves by absorption of infrared radiation from the ground.

3. Ozone chemistry Until the sixties, the 'classical' Chapman reactions seemed to explain most of the known properties of ozone: 02 + UV--+ 0 + O,

(1)

03 + U V - + 02 + O,

(2)

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O + O ~ + M-->O3 + M,

(3)

0 + 08 -+ 202.

(4)

We will refer to O and Os as species o f ' o d d oxygen'. O and 03 tend to be in equilibrium with each other through the 'rapid' reactions (2) and (3). The principal source of odd oxygen is reaction (1). The sink is reaction (4). It has been clear for some time that reactions 1-4 cannot account for the observed average ozone distribution, because reaction (4) is too slow. The actual O8 concentration is smaller than that expected from the Chapman reactions. There must be other reactions which remove odd oxygen. Basically, all such reactions are 'catalytic reactions' which provide efficient paths equivalent to reaction (4). Oxides of chlorine, hydrogen and nitrogen (as well as chlorine itself) can initiate such catalytic reactions; and a combination of these substances seems to be responsible for the fact that ozone concentrations are lower than expected from reactions 1-4. We will here consider only the catalytic reactions involving chlorine and nitrogen: NO + 03--> NO2 + 02,

(5)

N02 + 0 - - > NO + 02,

(6)

C1 + 03--> CIO + 02,

(7)

CIO + O ~ C I +

02.

(8)

Reaction sequence 5-6 and 7-8 each produce 202 from O and 03 while the catalysts remain intact. A single molecule of NO and C1 can destroy many ozone molecules. This is the reason why even small concentrations of the catalysts have an important impact on the ozone distributions. Eventually, the chlorine forms HCI and is transported out of the stratosphere; and NO forms HNO3, which also is transported out. The importance of reactions 5-8 in the present context is, of course, that the concentration of the catalysts is affected by human activity, as was described in Section 1. In order to study this impact, reactions 1-8 are not sufficient. Altogether, at least 50 reactions are needed which govern the concentrations of the substances in reactions 1-8, including molecules containing H, singlet oxygen, and carbon. As a result of these many equations, reactions 5-6 and 7-8 are closely coupled with each other, a fact not realized at first. Two of the important reactions neglected at first are: CIO + NO2 -+ C1NO3

(9)

and HO2 + NO--+ OH + NO2.

(10)

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Reaction (9) removes the catalysts C10 and NO2 and makes them less active. Addition of reaction (9) to the system of reactions without it, cuts the CFM threat in half. It also cuts the NO threat. Reaction (1) is important for many reasons. In particular, it introduces OH. OH has opposite effects on the C F M prolSl~m and the SST problem. O H reacts with HC1, forming C1 and H20. It thus releases more catalyst from a stable gas which could otherwise have been removed from the stratosphere. In contrast, O H also reacts with NO2 to form relatively stable HNO3. Thus, reaction (10) reduces the SST and fertilizer problems. In combination, reactions (9) and (10) almost eliminate the threat of NO but exacerbate the threat of the CFM's. Of course, this treatment of the ozone chemistry is greatly simplified. In the past, important reactions have been overlooked. The question now is whether additional 'surprises' will appear in the future. Specialists are confident that all important reactions are known. But some of the reaction rates are still sufficiently uncertain to constitute an important source of error of the estimates of man-made ozone changes.

4. Ozone transport In Section 3, ozone chemistry was treated as though transport did not exist. Actually, the two strongly interact with each other. The difficulties with evaluation of transport arise from two sources: 1. Atmospheric motions occur on all scales, from a millimeter or so to the global scale. 2. Atmospheric motions depend on four dimensions, three space dimensions plus time. These are some indications that motions on a scale smaller than those resolvable on w,eather maps are not important in the stratosphere compared to synoptic motions. Ther~efore, three-dimensional models which describe the change of large-scale motions with time, should be satisfactory for the description and prediction of ozone transport. But these models generally deal only with the meteorological equations. Only a few active chemical species have so far been included. Complete chemistry has been included only in two-dimensional and one-dimensional models. Two-dimensional models with zonal averages as function of latitude, height and time; one-dimensional models describe the behavior of global averages as functions of height and time. The main difficulty with two-dimensional models is the need to describe the meridional and vertical transports by synoptic-scale wind systems. This is usually accomplished by K-theory,* a very dubious procedure. Of course, the 2-D models have the advantage over 1-D models in that they describe N-S variations of ozone change. Thus, results from recent models suggest that the greatest ozone changes occur where there is the * K-theory assumes that transport is down-gradient and proportional to the magnitude of the gradient.

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most ozone, that is at high latitudes and in late winter. But the magnitudes of the meridional and temporal changes are completely different in the various models. Most models for ozone change are in one dimension; in that case, obviously, horizontal transport is averaged out. Vertical transport is described by diffusion coefficients K which now vary only with height'. Many different K-profiles have been tried. But the computed ozone decrease produced by C F M ' s is not very sensitive to the actual K-profile, because the source is at the surface. In contrast, the effect of N O emitted by SST's in the stratosphere depends much more on the selection of the distribution of K. Eventually, 3-D models should be developed, with complete chemistry, in order to evaluate the meridional variation of man-produced ozone reduction.

5. Ozone and public policy Up to this time, only in the U.S.A. has the production of C F M ' s been regulated by government. Other countries (except for Scandinavia) have not considered immediate action necessary. The situation is complicated. On the one hand, the ozone changes are so slow that delay of regulations by a few years is relatively unimportant. On the other hand, if release of C F M ' s should suddenly cease, the ozone would decrease for another ten years or more. This is because a fraction of the C F M ' s in the troposphere and in man-made devices now would continue to seep into the stratosphere. The reason for the reluctance of other governments to follow the U.S. lead in regulating C F M production is based on the large uncertainty in the predictions of ozone reduction. At present, the most likely eventual equilibrium reduction of ozone at 1977 C F M release rates is of order 15700, with a possible increase in skin cancer of order 30~. These estimates are quite uncertain, as are estimates of the uncertainties. The U.S. National Academy of Sciences will attempt quantitative error estimates in 1979. A frequently held view suggests that no action should be taken until significant ozone decreases have actually been noted. The difficulty with this argument is that no ozone trend or lack of ozone trend can be ascribed to the release of CFM's. Trends of total ozone can be established in a few years. But trends of the order of 5 ~ per decade have been noted in the past, before C F M ' s could have been responsible. Many reasons for such trends have been suggested, but none can be verified: atomic tests or recovery from atomic tests ; changes of large-scale atmospheric circulations; solar variations; and deterioration of measuring instruments. Since we cannot predict the natural variations of ozone we cannot identify man-made ozone changes until they are so large that they exceed natural changes significantly. Recent estimates suggest that it will take at least 10 years to isolate man-made ozone changes from other effects. If we wait up to that time before reducing emission of stable chlorine-contain-

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ing compounds, the potential damage is likely to be serious because, as pointed out, ozone will decrease for at least a decade after emission has been stopped. As for future U.S. action, the possibility exists of limiting further CFM releases into the atmosphere by conservation and recycling, or by limitation of other uses besides use in spray cans. However, it is clear that international cooperation is becoming increasingly essential. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkh~iuser Verlag, Basel

Monitoring, Causality, and Uncertainty in a Stratospheric Context By A. BARRIE PITTOCK 1)

A b s t r a c t - Our increasingly complex understanding of stratospheric chemistry and transport processes leaves us with various theoretical possibilities of appreciable and perhaps serious environmental impact due to human activities. These possibilities raise policy questions in which the economic and other costs of regulating human activities must be weighed against the possible consequences of no such regulation. The natural variability of the atmosphere, the physical and other limitations on our global sampling and monitoring abilities, and the difficulties in establishing causal connections leave us in a state of uncertainty as to the reality and magnitude of at least some of these theoretical environmental impacts. Policy-makers must make decisions in the face of these uncertainties. The proper role of scientists as such in narrowing and quantifying the uncertainties is discussed, with particular regard to the evidence that cultural and other biases often affect individual scientists' conclusions. Conscious efforts are needed to minimize bias, quantify uncertainties, and speed up the process of scientific consensus-building. A careful distinction should be drawn between scientifically determined probabilities, and cost-benefit analyses which necessarily involve value judgments.

Key words: Natural atmospheric variability; Anthropogenic trend detection.

1. I n t r o d u c t i o n

Each year our understanding o f the workings o f the stratosphere becomes more and more complex. Once it was considered to be a stably stratified, and hence dynamically inactive region where the radiative balance was dominated by atomic and molecular oxygen and ozone according to the classical photochemical theory o f CHAPMAN (1930). M e a n meridional m o t i o n was invoked by BREWER (1949) and DOBSON (1956) to account for the observed seasonal and latitudinal variation of water vapor, ozone, and other trace constituents of the stratosphere. Then in 1964 HAMPSON suggested that water vapor played an active role in ozone photochemistry, since this could account for observed ozone concentrations lower than those which simpler theories (using then recently refined rate constants) predicted. By this time, too, the dynamics o f the stratosphere was recognized to be far more complex, with eddies, long waves, and stratospheric polar vortices (NEWELL, 1961 ; MURGATROYD, 1969). The possibility that oxides o f nitrogen also play a potentially important part in the 1) CSIRO Division of Atmospheric Physics, P.O. Box 77, Mordialloc 3195, Australia.

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stratospheric ozone budget was suggested by CRUTZEN(1970) and JOHNSTON(197t). This and other environmental considerations played a major role in the controversy over the production and use of supersonic transport aircraft (SMIC, 1971 ; CRUTZEN, 1972; DOTTO and SCHIFF, 1978). Later it was suggested (MOLINA and ROWLAND, 1974; STOLARSKIand CICERONE, 1974) that chlorine compounds might also play an important role in ozone photochemistry, and this has led to the phasing out in the U.S. of the use of freon compounds in aerosol sprays. It has even been suggested that oxides of nitrogen released by fertilizers and agriculture may play an increasingly significant part in the stratospheric photochemical system (LIu et al., 1977). The latter presents a very serious dilemma since agriculture is too fundamental to human survival to be regulated like air transport or freon production. It has also been suggested (GRovEs et al., 1978) that the cooling effect of increasing CO2 on stratospheric temperatures, may lead to an increase in ozone amounts. This increasing complexity is not, of course, the result of changing physicochemical laws but rather of the increasing detail of our knowledge of the physics and chemistry of the stratosphere which no longer allows us to fit simple theories to very limited bodies of data. This has been compounded by the introduction into the atmosphere by mankind of significant quantities of hitherto rare substances such as freons, carbon tetrachloride, and many others (GALBALLY,1976; SINGH,1977). Each of these developments in our understanding of the complex photochemical/ dynamical system of the atmosphere has had major impact not only on our scientific knowledge of the atmospheric environment but also on questions of public policy. The possibility of appreciable and perhaps serious environmental effects has raised questions as to the desirability of limiting or regulating human impact on the atmospheric system. As this involves the possibility on the one hand of regulation of multi-billion dollar industries such as air transport, and on the other of perhaps multi-billion dollar climatic or other impacts, for example, on global agricultural production, the financial, political and emotional stakes involved are huge (KELLOGGand SCHNEIDER,1974; PITTOCKet ak, 1978). It is therefore understandable and indeed inevitable that pressures exist to make policy decisions before all the scientific and technological uncertainties have been resolved (ATLAS,1976). The 'art' of political and economic decision-making is largely the art of reaching decisions in a state of uncertain knowledge. My concern, and the focus of this paper, is that both scientists and economic and political decisionmakers should appreciate what uncertainties exist, and what should be the proper role of scientists in the process of making decisions before we have perfect knowledge. A clearer understanding of this role should facilitate the decision-making process. 2. Natural variability of the atmosphere A major contributor to our uncertainty is the large natural variability of the atmosphere. Most of the climatically important atmospheric variables such as temperature, precipitation, and ozone content, show day to day, seasonal, and year to year

Vol. I18, 1980)

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Monitoring, Causality, Uncertainty in Stratospheric Context

variations which are usually comparable with or larger than the variations in longerterm mean values which are generally believed to be of environmental significance. Synoptic (i.e., day to day weather-pattern-associated) and seasonal variations in surface temperature at any given point on the Earth, for example, generally exceed the differences in mean temperatures at that point between glacial and inter-glacial epochs. In the middle atmosphere the vertical distribution (and total amount in a vertical column) of ozone is highly variable particularly on the synoptic and seasonal timescales. This is illustrated in Figures 1 and 2 for ozone data based on 443 individual soundings from June 1965 through May 1973, i.e., on 8 consecutive years of more or less weekly soundings, for Aspendale, Australia (38~ 145~ which may be taken as a typical mid-latitude station. In Fig. 1 we have plots of the overall mean vertical distribution of ozone partial pressure (full line) together with a plot of the total percentage variability (dashed line), defined as the percentage ratio of the standard deviation about the mean to the mean value at each level. For the Aspendale data the variability exceeds 75% in the lowest layers of the stratosphere, with minima of about 20,5/00in the mid-troposphere VARIABILITY 0

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(%)

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646

(Pageoph,

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(nb) 30

IO

20

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and about 10~o at the 20-30 mb level. In Fig. 2 the total variance of the ozone partial pressure at each level is plotted along with its components on various time scales. As we shall see below, the small proportion of the total variance on the longer time scales, even if we neglect instrumental errors, sets serious limits on the detectability of trends or changes in ozone which might be attributed to pollution or other causes. The very high variability in the lower stratosphere, both on synoptic and seasonal time scales, will also be of vital importance in calculating photochemical effects if these are significant at these heights and non-linear with respect to the concentration of ozone or whatever other chemical species we might be considering. Variability in temperature which will affect reaction rates, may also prove to be important in this respect, especially as temperature variations are in general correlated with ozone concentrations. Indeed such correlations may introduce non-linearity into an otherwise linear reaction. The message from this example is that where it is desired to detect trends or changes in the concentration of ozone or other chemical species, or to test photochemical

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theory and apply it in atmospheric models, time variations on the synoptic and seasonal time scales will have to be adequately defined by measurements or modelling, or otherwise allowed for in our estimates of uncertainty. Spatial variations are also important both to the monitoring question and in modelling effects. Spatial variations in the concentrations of various chemical species, in atmospheric temperature, and in some radiative properties, will in general be correlated (either positively or negatively depending on the case) on the synoptic, seasonal, and longer time scales. This applies for example to the standing long-wave troughs which are important on climatic time scales of months to years in the Northern Hemisphere (see e.g., PRABHAKARAet al., 1976; VAN LOONand WILLIAMS,1976). These troughs in the lower stratosphere are warmer than the ridges and also richer in ozone. They also tend to occur over continental areas and are therefore relatively overrepresented in surface-based monitoring networks, and indeed in many sampling programs using aircraft or recoverable balloons. In attempting to understand what is happening or likely to happen in the global atmosphere we must also be conscious of the very different latitudinal and height distributions of sources and sinks of the various natural and anthropogenic chemical constituents and of the atmospheric transport and mixing processes. This applied particularly to differences between the Northern and Southern Hemispheres. For instance ozone has a predominantly mid-stratospheric low latitude source (BREWER and WILSON, 1969) with the additional possibility of significant tropospheric production in the Northern Hemisphere (FISHMANand CRUTZEN,1978). By way of contrast NOx is predominantly produced either at the surface over mid-latitude Northern Hemisphere land masses by combustion and various other natural processes or in the upper troposphere and lower stratosphere predominantly around 10 to 12 km altitude in mid-northern latitudes by aircraft. NO production from the decomposition of N20 occurs in the stratosphere with a maximum at about 26 kin. Then again chlorine from chlorofluoromethanes is produced by photo-decomposition in the stratosphere from a widely dispersed and well-mixed tropospheric reservoir which is little different in the Northern and Southern Hemispheres due to the long residence time of the chlorofluoromethanes. Differences between the Northern and Southern Hemispheres, not only in anthropogenic source strengths, but also in sink strengths due to differences in the ratio of land areas to sea areas, and in atmospheric circulation, must be taken into account. Major circulation differences extending well into the stratosphere, and affecting stratospherictropospheric exchange and meridional transports, include the greater relative importance in the Southern Hemisphere of mean zonal motion as opposed to eddy motion, and of transient eddies as compared to standing eddies (ADLER, 1975). Very significant differences between the behavior of the winter stratospheric polar vortices in the two hemispheres (GoDsoN, 1963) particularly in regard to sudden warmings (e.g., see GHAZIet al., 1976) and the final breakdown of the vortices could well lead to significant differences in stratospheric-tropospheric exchange. This may well account

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in part for observed differences in both stratospheric and tropospheric ozone content and their seasonal variations as between the hemispheres (Duxscu, 1978; PITTOCK, 1977a) and militate against the arguments of FISttMAN and CRUTZEZ~(1978). Available data suggest that short-term trends in tropospheric temperatures may well be different in the northern and southern hemispheres (ANGELL and KORSHOVER, 1975). These inter-hemispheric differences make it essential for any study claiming to be global in scope to take into account and successfully model the different seasonal and mean behaviors of the two hemispheres. Ambient temperatures, and the concentration ratios of the various active chemical constituents of the atmosphere and their correlations with temperature will in general vary with season, latitude, and between hemispheres. This will not necessarily be true of concentration ratios dominated by certain reactions having equilibrium times, over the range of possible ambient temperatures, which are fast compared to transport processes. However, if we are ultimately concerned with potential changes in ozone concentrations in the middle and lower atmosphere where fast reactions are not dominant, and in temperature distributions which will affect atmospheric dynamics and climate, these spatial differences must be taken into account.

3. Monitoring and trend detection Monitoring what is happening in the real atmosphere is of course a necessary, if not sufficient, test of our understanding of atmospheric chemistry and dynamics and of the ultimate effects of anthropogenic emissions. Ultimately monitoring will provide us with the data with which to derive significant statistical correlations and with which to quantitatively test our hypotheses as to cause and effect. Our monitoring efforts are necessarily limited in their sensitivity to real changes or trends in the monitored quantity by three basic problems. One is the existence of systematic Or random errors in individual measurements at individual stations. A second is the degree to which the global monitoring network or system (e.g., a series of satellites) falls short of the ideal in terms of spatial and[or temporal coverage. The third, and most fundamental, arises from the time and space fluctuations of the parameter being measured, which impose a background statistical variability on any change or trend we may hope to detect. Those not directly involved in the development and operation of the monitoring instruments often do not appreciate the severity of the problem of errors in individual measurements. In principle, individual random errors can be reduced in the aggregate to negligible proportions by repetition of measurements in time or space, by a factor N 1r where N is the number of individual measurements. Where the individual random errors are large and each measurement is expensive this can nevertheless be a problem, e.g., in measurements of stratospheric water vapor. Systematic, or quasi-systematic errors are more difficult. In the field of ozone measurements for instance, systematic errors in the Dobson spectrophotometer arise from calibration drifts, uncertainties in

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ozone absorption coefficients, variable and inadequately understood effects of aerosol scattering, and in some cases synoptic-weather induced biases (PITTOCK, 1970; GUSHCmN, 1972; KULKARNI, 1973; DZIEWtrLSKA-LOSIOWA and WALSHAW, 1975; BASHER, 1977; TtJOMAS and HOLLAND, 1977). Some of these errors may be correlated with total ozone amount. It is not generally appreciated that intercomparisons between regional standard total ozone measuring instruments only as recently as 1977 for the first time established an intercomparable global total ozone network (HuDsON, 1977). Data from filter photometer instruments used by some countries are even now not strictly comparable with those from the Dobson instruments. The homogeneity of long ozone data series is a particularly serious problem due to many minor changes in the assumed absorption coefficients, calibrations, and corrections applied to the data in the past. For this reason major effort is now going into reconstructing a more homogeneous series using whatever individual station histories are on file. It is arguable that anthropogenically induced trends in ozone content should be larger and natural variability smaller in certain altitude bands (notably around 40-45 km in the case of chlorofluoromethane-induced depletions) and are therefore more likely to be detected by measurements sensitive to the vertical distribution of ozone. Unfortunately systematic errors in measurements of the vertical distribution of ozone may welt be considerably more severe than the errors in the total amount and there are far less such measurements in any case. The ' Umkehr' method is particularly vulnerable to synoptic weather bias and to aerosol effects (PITTOCK, 1970; DELuIsI, i979), while balloon-borne soundings do not reach the 40 km region and are vulnerable to assumptions made in extrapolating to the top of the atmosphere (PITTOCK, 1977b). The absolute accuracy (MATEER et al., 1971) and long-term drift of satellite-borne instrumentation still leaves much to be desired and these problems may be compounded by changes in instrumentation and analysis procedures (e.g., see discussion by PRIESTLEYand PITTOCK, 1977). Some of the problems involved in obtaining a globally representative monitoring network have been touched upon in the discussion of natural variability above. Clearly we need data from both the Northern and Southern Hemispheres, from the climatically important latitudinal zones (i.e., at least from the tropics, mid-latitudes, and polar regions) in each hemisphere, and from both continental and oceanic regions. Climatological mean and anomaly patterns, including eigenvector anomaly patterns, give us a good idea as to the spatial scale of the secular variations on the time scales of interest to monitoring programs. These are available with reasonably adequate global networks (at least in the Northern Hemisphere) for temperatures, surface pressure, and pressureheight contour surfaces and to a less satisfactory degree for ozone (LONDON, 1963; LONDON et al., 1977). After allowing for the various locations of sources and sinks of the various natural or anthropogenic trace species we are considering, and the probable resulting correlations with the known climatic variables, we can obtain at least a first guess as to the likely anomaly fields of these species and thus of which regions should be sampled to obtain a representative mean quantity.

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Eigenvector analysis of climatological data fields (e.g., GRIMMER,1963; KIDSON, 1975) show that the first 8 or l0 eigenvectors usually account for 80-90% of the total variance. Allowing for some desirable redundancy in the data (which might help to reduce random errors and eliminate or substitute for faulty or missing data), in general some 30 or more ideally distributed monitoring stations would thus contribute the 10 or so possible independent pieces of information from which a representative global average might be obtained. If the Northern and Southern Hemispheres turn out to be substantially independent in their behaviour (which the climatological record and Kidson's results suggest is unlikely) there could be as many as 15 or 20 independent pieces of information. I would suggest that this represents an absolute upper limit to the independent information content of even an ideal global monitoring network (which includes a satellite-based monitoring system), and I think the more probable figure is 10. The importance of this limit to the amount of independent information which can be obtained by even an ideal monitoring system or network is that, given a background variability due to synoptic weather variations (or other causes), separating the trend or change 'signal' from the background 'noise' can only be further achieved by a longer time series of measurements. Using the Aspendale total ozone data series as an example, this limit was explored quantitatively by PITTOCK (1972 and 1974b). If we assume that Aspendale, as a mid-latitude station in the perhaps less variable Southern Hemisphere, is typical of the average total ozone station, and that at a typical station half of the total variance is due to the annual cycle, we can estimate the limit to the sensitivity of an ideal global network. This is shown in Fig. 3 where it is assumed that the ideal network will produce 10 independent pieces of information in each time interval. While the above assumptions are subject to some uncertainty this graph serves to illustrate the nature and order of magnitude of the fundamental limits to even an ideal global monitoring system. The graph shows, for instance that a real trend in global total ozone content of 2.5% per decade could not be detected at the 95% confidence level under about 6 years of observations with an ideal network (by which time the cumulative change would already be 1.5%). If a higher confidence level (say 99%) were demanded before reaching a conclusion it would take about 7 years (by which time the cumulative change would be 1.75%). Refined estimates as to the limits of trend detectability have been the subject of a number of papers (e.g., KAROL et al., 1976; HILL et al., 1977; WILCOX, 1978) and a series of meetings have considered this in relation to the real (as opposed to the ideal) monitoring network (e.g., see HUDSON, 1977; NASA, 1977). Estimates of the threshold of detectability range from a change of 1.5% to as high as 6% when conservative allowance is made for instrumental errors and possible non-representativeness of the data. Don Heath of NASA Goddard Space Flight Center (personal communication, 1978) has reported that time series of global total ozone amounts estimated by the satellite BUV method using all available data points differ non-uniformly in time by up to

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I

]

I

i

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I

0.6

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0.3~)

5

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Figure 3 Approximate limits to trend detectability, expressed as Type I error probabilities of 1X and 5 ~ (based on a two-sided Student's t-test) for estimated trend levels, b (percent per decade), of total ozone amount, versus number of years, N, of observation. The upper pair of curves refer to a typical single mid-latitude monitoring station, while the lower pair refers to an ideal global monitoring network having 10 independent pieces of information. The variance due to the mean annual cycle has been assumed to be about half of the total variance and has been removed. These curves are based on the variability at Aspendale (38~ 145~ which is considered to be a fairly typical midlatitude station.

several percent from series obtained using only satellite data for points in close proximity to the existing ground-based total ozone monitoring network. Given the further lead time which may be necessary to 'turn off' any given source of anthropogenic pollution, which may be considerable due to physical, economic and political factors, the above considerations indicate that the use of a global monitoring system as an effective 'early warning' system for anthropogenic effects is highly questionable. Effective warning would only be given after appreciable effects had already occurred, and considerably greater effects might well occur before remedial action could be expected to take effect. This suggests that it may be necessary to act on the basis of physical theory, if it is sound enough to justify action, without waiting for a monitoring system to confirm the existence of an effect. This is of course the conclusion already reached in relation to the freon problem (NATIONAL ACADEMY OF SCIENCES, 1976), where the long physical lead-time due to the large reservoir in the troposphere (SINGH,1977) makes it clear that a decision based on the monitoring of effects would be far too late to avert major impact, if the relevant theory is correct. A further consideration in relation to the relevance of monitoring relates to the

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question of multiple causality. Monitoring of a single variable such as ozone, even if it established that a trend exists, does not establish a causal connection with some specified pollutant, for example, in the face of several possible causes. Not only is a theory as to a physical linking mechanism necessary, but quantitative agreement (or at least commensurability) between hypothesized cause and effect is necessary, allowing for possible competing mechanisms due to other causal factors such as volcanism or 'natural' climatic variations. This requires therefore a quantitative understanding of the effects of these other causal mechanisms and some monitoring of their variation. Monitoring of some variable peculiar to an intermediate step or corollary of a particular mechanism would be an ideal diagnostic tool. All of this is to say that monitoring of an effect without adequate understanding and monitoring of the whole system will not provide conclusive answers as to causality, let alone a reliable and adequate early warning of anthropogenic effects.

4. Questions of causality In a rapidly changing and expanding field such as atmospheric chemistry, with big environmental pollution and regulation issues hanging on the scientific conclusions, it is at once desirable and dangerous to ascribe causality to observed variations. It is desirable because decisions whether or not to regulate emissions are in effect being made voluntarily or involuntarily right now and should be made on the basis of the best possible scientific conclusions. It is dangerous because of a multitude of statistical, technical, logical and emotional pitfalls which lie in wait. Many of these pitfalls have been described at some length and with examples in a recent review of one frequently proposed hypothetical cause of climatic variations, viz. sunspot cycles (Pn'TOCK, 1978). In a recent paper on the use of statistics in climatological research GANI (1975) concluded that: 'many of the arguments presented by climatologists are based on poor foundations: apparent similarities, parallel looking curves, and analogous trends are no proof of a scientific hypothesis. The similarities may be based on doubtful data, or be due to spurious coincidences. That is where statistical analysis can be useful, and should be more frequently relied upon . . . . There is very little statistical analysis in the climatologists' work, and some of this is either superficial or wrong.' Unfortunately in the middle atmosphere, where even the longest climatological data sets seldom exceed 30 years, and those appertaining to most trace constituents a~;e much shorter, more fragmentary, of sometimes doubtful quality, and often unrepresentative, the temptation to jump to conclusions (however tentative) in the way Gani describes is often overwhelming. Despite the known time and space variability of those parameters for which we have longer data series (e.g., total ozone amounts or lower stratospheric temperatures) we tend to decide for or against simple causal

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mechanisms on the basis of one or two observed events, such as volcanic eruptions, solar flares, or nuclear explosions, even when a number of other causal mechanisms may be operating simultaneously to modify the hypothesized effect. Simple statistical considerations, and the long and unfortunate history of the solar cycle-weather/ climate hypothesis, suggests that observations of at least 5 or 6 discrete events are necessary to establish a correlation with any useful statistical significance. Otherwise (and preferably in addition) a detailed physical mechanism leading to close quantitative agreement between theory and prediction is necessary to raise a hypothesis about cause and effect from mere speculation to a scientifically credible theory. In such a complex system as the atmosphere we are necessarily dealing with the possibility of both multiple causes of a given effect and multiple effects of a given cause. The former is exemplified by the wide discussions concerning observations and possible causes of changes or trends in total ozone content on a regional or global basis. In considering observed total ozone data series, supposed changes have been variously ascribed to nuclear bomb tests, volcanic debris, solar activity, variations in the quasi-biennial oscillation, global changes of unknown origin, statistical sampling fluctuations, and shifting or deepening of standing wave patterns (see e.g., the discussion in ANGELL and KORSHOVER, 1973 and 1976, and PITTOCK,1974a). It is of course possible that more than one of these hypothesized causes may be having simultaneous effects, and that other as yet unknown causes should also be considered. The case of multiple effects is well exemplified by the history of concern over the possible effects of aircraft emissions, notably NOx and water vapor, on the ozone content of the atmosphere. The initial, and evidently the most emotionally appealing concern, was that these emissions would lead to a reduction in the total amount of ozone in a vertical column, with a consequent increase in the intensity of solar UV in the erythemal bands reaching the Earth's surface. This, it was feared, would lead to a significant increase in skin cancer in humans and possibly to other significant biological effects. At the time of the conclusion of the Climatic Impact Assessment Program (GROBECKERet al., 1974), the scientific consensus appeared to be that such an effect, although small with then projected supersonic aircraft fleets, was indeed possible and potentially significant. As the name of the CIAP program indicates, it was also considered possible that the effect of the emissions on the vertical distribution and temperature structure of the atmosphere might lead to changes in the atmospheric circulation with accompanying climatic changes. While the very complex agricultural and economic impacts of climatic change were discussed in the CIAP report and these were recognized to be remarkably large for even small climatic changes, our ability to quantitatively model and predict the nature and extent of climatic change due to fairly small changes in the vertical distribution of ozone and temperature was (and still is) quite inadequate. This meant that little confidence could be placed in quantitative estimates of the effects on climate, and the possibility of serious climatic impact was consequently not stressed at that time.

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More recently, changes in our knowledge of atmospheric chemistry and in particular the inclusion of chlorine effects (not of aircraft origin) have led to significantly reduced estimates of the reduction in ozone concentrations in the middle stratosphere by NOx emissions from aircraft (BRODER~CK, 1978). Indeed there is now a real possibility that NO,~ emissions will lead to an increase in ozone concentrations in the upper troposphere and lower stratosphere (e.g., see TURr et al., 1978), particularly when emissions from the large number of subsonic aircraft flying at these altitudes are considered. While these developments largely discount fears about increased UV and skin cancer they again raise the possibility of significant climatic change due to the changed vertical distribution of ozone and temperature. Even with improved climatic models these effects are still very difficult to model. What is most interesting in this case, however, is that the possibility of affecting an increase in ozone concentrations in the upper troposphere now raises a new potential h a z a r d - that of creating photochemical smog conditions throughout the troposphere similar to those now evident in essentially urban smog situations. The possibility of directly detrimental health and environmental effects due to increased ozone concentrations reaching the surface air has been raised.

5. Scientific method and the decision-making process

The above discussion may be summarized as follows: 1. There are a great many gaps and uncertainties in our knowledge of the behavior of the atmospheric system and the possible effects of anthropogenic inputs upon it. 2. There is a finite probability that these effects will be both statistically and practically significant, and indeed potentially serious in terms of their impact on health, climate, and human activity generally. 3. It would appear that a global monitoring program, while desirable and necessary to obtain a fuller understanding of the atmospheric system, will probably not provide an adequate early-warning system of undesirable or dangerous effects. Decision-makers will therefore have to make their decisions in the face of uncertainty, before all the facts are in, and largely on the basis of theory. What is the proper role of the scientific community as such in this decision-making process ? Obviously its ongoing role is to seek to reduce the uncertainties, but at any given point in time it should be to define, as quantitatively as possible, the present state of knowledge including particularly the uncertainties and the relative probabilities of the various possible outcomes. This role must be clearly distinguished from the making of value judgments and the subsequent recommendation of particular courses of action such as regulation or the setting of particular emission standards. The latter are properly the responsibility of the political representatives of the people generally, as they must take into account not only the scientific probability but a weighing of the

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economic, environmental, political, and other consequences of different courses of action. Scientists as citizens may have a legitimate role to play in this area, but not as scientists. I would further submit that the proper and traditional scientific method may in fact be inappropriate to a policy-making role which should be consciously based on a value-weighted cost-benefit analysis. Traditionally science elevates a hypothesis to the status of an accepted theory when the evidence satisfies a statistical significance test that assesses the risk of asserting that the hypothesis is true when in fact it is not. Such an error is termed a 'Type I error.' The acceptable magnitude of this risk is usually set in science at 5 ~ or less depending on the rigor of the work. Such a criterion serves to safeguard the purity of that body of theory which science regards, at least for the time being, as truth. Such a criterion, however, generally allows a much higher risk of the rejection of a hypothesis as untrue (or at least unproven) when in fact it is true. The latter is known as a 'Type II error' (see e.g., DAVIES, 1957). A simple example of the application of these error types is in a decision whether or not to carry an umbrella, based on a forecast of a given probability of rain. One possible error is to carry an umbrella when it doesn't rain; the other is not to carry an umbrella when it does rain. In general these two types of errors will have quite different probabilities, and our practical decision is properly biased towards reducing the risk of the more serious error at the expense of increasing the risk of the less serious error. A value judgment is involved in weighing the relative seriousness of the two types of error, and this is expressed in the (usually unconscious) choice of probability criteria which we apply. In the case of the umbrella it may be influenced, for example, by whether we have a convenient folding umbrella and by what clothes we will be wearing, both of which are factors quite unrelated to the probability of rain. Decision-making having practical consequences thus should not automatically employ Type I error criteria which are appropriate to science. Indeed some value judgment or cost assessment must be made as to the consequences of different courses of action, appropriately weighted by the probabilities of their occurrence. These value judgments and cost assessments are necessarily often subjective and difficult or impossible to quantify; in fact they often hinge on personal preferences. They therefore fall outside the legitimate area of expertise of scientists as such, and into the areas of religion, politics, and ethics. Numerous examples can be found in the literature of seemingly scientific disputes which in my view have largely arisen from a failure to distinguish clearly between Type I and Type II error assessments and the often implicit value judgments involved in the choice of probability criteria upon which practical decisions or recommendations are made (see e.g., PITTOCK, 1972; REED, 1973; ELSSAESSER,1974, 1978; SCORER, 1977; SCHNEIDER,1977, 1978). Despite our attempts at objectivity, scientists are human and fallible in that they often allow conscious or unconscious value judgments, prejudices, biases, and hunches to influence their ostensibly scientific judgment, particularly in areas of appreciable

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statistical uncertainty. This has been rather amply demonstrated in a recent review of the literature on solar variations and weather/climate (PITTOCK, 1978), but a few other recently documented examples ranging from deliberate fraud to apparent cultural bias (HAMPRECHT and GULLIS, 1977; DORFMAN, 1978; GOULD, 1978) may serve to underline the point. Gould states 'I suspect that unconscious or dimly perceived finagling, doctoring, and massaging are rampant, endemic, and unavoidable in a profession that awards status and power for clean and unambiguous discovery.' BRUSH (1974) says that on the basis of the examples which he has studied ' I suspect that improper behavior is not peculiar to a handful of great scientists but is characteristic of a much larger group. Indeed the burden of proof would seem to be on anyone who claims that a majority of scientists habitually use the hypothetico-deductive method in the strict sense (that is, rejecting a theory if it fails to agree with all experimental facts).' The above opinions voiced by Gould and Brush would seem to hold out little hope that individual scientists can and will reach completely objective conclusions. Nevertheless Gould gives two hopes for alleviation of the problem ' . . . first, that by acknowledging the existence of such a large middle ground [of unappreciated bias and more conscious manipulation in the interest of a " t r u t h " passionately held but inadequately supported] we may examine our own activity more closely; second, that we may cultiv a t e . . , the habit of presenting candidly all our information and procedure, so that others can assess what we, in our blindness, cannot.' We might go a long way to realizing Gould's first hope if we consciously endeavor to examine our own assumptions and preferences and to apply more rigorous statistical and error calculations and criteria to our own work. Elsewhere I have attempted to formulate some such guidelines as regards the statistical analysis of data (PITTOCK, 1978), while EISENHART(1968) has done much to clarify our often fuzzy concepts about errors and uncertainty. Gould's second hope implies that the scientific community, given enough information about our individual work, will eventually reach a consensus as to which of various opposing hypotheses in the literature stands up to critical examination. In other words, the hope is that the scientific consensus will be more objective than the individual scientist. I see two problems with this answer to the lack of individual objectivity. Firstly, I suspect that the consensus on stratospheric poUution reached by 100 scientists employed by the aviation industry would be significantly different from the consensus reached on the same subject by 100 scientists employed by, say, the Sierra Club. The second problem is that in the past such a scientific consensus has only been reached on contentious issues over a relatively long time (e.g., see HULL et al., 1978), whereas the potential threats to the environment posed by anthropogenic pollution require decisions to be made soon. The problem of group bias will hopefully be overcome by the participation in the consensus building process of scientists from a wide range of backgrounds including industry, environmentalist organizations, a range of government agencies, and independent university scientists. In my view this may require special attention to

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funding non-governmental and non-industry-oriented science, and a deliberate openness to minority points of view since it is almost axiomatic that new theories and important revisions of old ones start off as minority opinions (HULL et aL, 1978; BAKER, 1978). The problem of urgency in reaching consensus demands a rapid, free, and open exchange of data, opinions, and methodologies between all participating scientists and agencies. Such a consensus will be facilitated by a clear division of the overall problem into areas of agreed data, agreed errors and uncertainties, and of areas of disagreements (which pro tern constitute further uncertainties), with conscious separate attention being given to cost-benefit analyses which involve value judgments. Government agencies and the scientific community generally are of course already rising to this challenge through meetings, working groups, scientific advisory committees, and special funding (e.g., see HUDSON, 1977; BRODERICK, 1978) as well as through the usual processes of peer review, publication, and comment. What I am suggesting is merely that we be more aware of these processes, of why they are necessary particularly in the field of middle atmospheric research, and of how we can each help the process which will ultimately lead to the best possible decisions being made in our present state of uncertainty. REFERENCES ADLER, R. F. (1975), A comparison of the general circulations of the Northern and Southern Hemispheres based on satellite, multi-channel radiance data, Mon. Weather Rev. 103, 52-60. ANGELL, J. K. and KORSHOVER,J. (1973), Quasi-biennial and long-term fluctuations in total ozone, Mon. Weather Rev. 101, 426-443. ANGELL, J. K. and KORSHOVER,J. (1975), Estimate of the global change in tropospheric temperature between 1958 and 1973, Mon. Weather Rev. 103, 1007-1012. ANGELL, J. K. and KORSHOVER,J. (1976), Global analysis of recent total ozone fluctuations, Mon. Weather Rev. 104, 63-75. ATLAS,D. (editor) (1976), Atmospheric Science andPublicPolicy, American Meteorological Society, Boston, 105 pp. BAKER, V. R. (1978), The Spokane flood controversy and the Martian outflow channels, Science 202, 1249-1256. BASHER, R. (1977), Systematic errors in Dobson measurements, in Proceedings of NASA-Sponsored Symposium on Ozone Trend Detectability, July 28-29, 1977, pp. 14-18, Boulder, Colorado, 105 pp. duplicated. BREWER,A. W. (1949), Evidence for a world circulation provided by measurements of helium and water vapour distribution in the stratosphere, Quart. J. Roy. Met. Soc. 75, 351-363. BREWER,A W. and WILSON,A. W. (1969), The regions offormation of atmospheric ozone, Quart. J. Roy. Met. Soc. 94, 249-265. BRODERICK, A. J. (1978), Stratospheric effects from aviation, J. Aircraft 15, 643-653. BRUSH, S. G. (1974), Should the history of science be rated X ?, Science 183, 1164-1172. CHAPMAN, S. (1930), A theory of upper-atmospheric ozone, Mere. Roy. Meteor. Soc. 3, 103-125. CRUTZEN P. J. (1970), The influence of nitrogen oxides on the atmospheric ozone content, Quart. J. Roy. Met. Soc. 96, 320-325 CRUTZEN, P. J. (1972), SST's - A threat to the Earth's ozone shield, Ambio, 1, 41-51. DAVIES, O. L. (1957), Statistical Methods in Research and Production (3rd edn.), Oliver and Boyd, London.

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DE LutsI, J. (1979), Umkehr vertical ozone profile errors caused by the presence of stratospheric aerosols, J. Geophys. Res. in press. DOBSON, G. M. B. (1956), Origin and distribution of the polyatomie molecules in the atmosphere, Proc. Roy. Soc. London A236, 187-193. DORFMAN, D. D. (1978), The Cyril Burr question: new findings, Science, 201, 1177-1186. DOTTO, L. and SCHIFF, H. (1978), The Ozone War, Doubleday, Garden City, N.Y., 342 pp. DUTSCH, H. U. (1978), Vertical ozone distribution on a global scale, Pageoph 116, 511-529. DZIEWULSKA-LostowA, A. and WALSHAW,C. D. (1975), The international comparison of ozone spectrophotometers, Belsk, June 24 to July 6, 1974, Publications of the Institute of Geophysics, Materialy 2, Prace 89, Polish Academy of Sciences, Panstwowe Wydawmnictwo Naukowe, Warszawa. EISENHART,C. (1968), Expression of the uncertainties of final results, Science 160, 1201-1204. ELLSAESSER,H. W. (1974), The dangers of one-way filters, Bull. Amer. Meteor. Soc. 55, 1362-1363. ELLSAESSER,I4. W. (1978), A reassessment of stratospheric ozone: credibility of the threat, Climatic Change, 1,257-266. FISHMAN,J. and CRUTZEN,P. J. (1978), The origin of ozone in the troposphere, Nature 274, 855-858. GALBALLY,I. E. (1976), Man-made carbon tetrachloride in the atmosphere, Science 193, 573-576. GANI, J. (1975), The use of statistics in climatological research, Search 6, 504-508. GHAZI, A., EBEL, A. and HEATH,D. F. (1976), A study of satellite observations of ozone andstratosphere temperatures during 1970-1971, J. Geophys. Res. 81, 5365-5373. Got)soN, W. L. (1963), A comparison of middle-stratosphere behavior in the Arctic and Antarctic, with special reference to final fvarmings, Met. Abhandlungen XXXV1, 161-206. GOULD, S. J. (1978), Morton's ranking of races by cranial capacity, Science 200, 503-509. GRIMMER, M. (1963), The space-filtering of monthly surface temperature anomaly data in terms of pattern, using empirical orthogonalfunctions, Quart. J. Roy. Met. Soc. 89, 395-408. GROBECKER, A. J., CORONITI,S. C. and CANNON, R. H. Jr. (1974), CIAP Report ofF&dings: The Effects of Stratospheric Pollution by Aircraft, U.S. Dept of Transportation, Washington, D.C., Rept. DOT-TST-75-50. GROVES,K. S., MATTINGLY,S. R. and TUCK,A. F. (1978), Increased atmospheric carbon dioxide and stratospheric ozone, Nature 273, 711-715. GUSHCHIN, G. P. (1972), Comparison of ozonometric instruments, in Actinometry, Atmospheric Optics, Ozonometry, G. P. Gushchin, ed., translated from Russian, Gidrometeozdat, Leningrad. HAMPRECHT,B. and GULLIS, R. J. (1977), Statement, Nature 265, 764. HAMPSON,J. (1964), Photochemical Behavior of the Ozone Layer, Canadian Armament Research and Development Establishment (CARDE), Valcartier, Quebec, Canada, TN 1627/64, 280 pp. HILL, W. J., SHELDON, P. N. and TILDE, J. J. (1977), Analyzing worldwide total ozone for trends, Geophys. Res. Lett. 4, 21-24. HUDSON, R. R. (editor) (1977), Chlorofluoromethanes and the Stratosphere, NASA Reference Pub. 1010 (NASA Goddard Space Flight Center, Greenbelt, Maryland), 266 pp. HULL, D. L., TESSNER,P. D. and DIAMOND,A. M. (1978), Planck'sPrinciple, Science 202, 717-723. JOHNSTON, H. S. ( 1971), Reduction of stratospheric ozone by nitrogen oxide ca talysts from supersonic transport exhausts, Science 173, 517-522. KAROL, I. L., POLYAK, I. I. and VINNIKOV, K. YA. (1976), Statistically correct determination of long-period trends in geophysical data series, Pageoph 114, 965-974. KELLOGG,W. W. and SCHNEIDER,S. H. (1974), Climate stabilization:for better orfor worse ?, Science 186, 1163-1172. KIDSON, J. W. (1975), Eigenvector analysis of monthly mean surface data, Mon. Weather Rev. 103, 177-186. KULKARNI,R. N. (1973), Ozone trend and haze scattering, Quart. J. Roy. Met. Soc. 99, 480-489. LONDON, J. (1963), The distribution of total ozone in the Northern Hemisphere, Beitr. Phys. Atmos. 36, 254-263. LONDON, J., FREDERICK,J. E. and ANDERSON,G. P. (1977), Satellite observations of the globaldistribution of stratospheric ozone, J. Geophys. Res. 82, 2543-2556.

Vol. 118, 1980)

Monitoring, Causality, Uncertainty in Stratospheric Context

659

LIU, S. C., CICERONE,R. J., DONAHUE,T. M. and CHAMEIDES,W. L. (1977), Sources andsinks of atmospheric N20 and the possible ozone reduction due to industrial fixed nitrogen fertilizers, Tellus 29, 251-263. MATEER, C. L., HEATH, D. F. and KRUEGER,A. J. (1971), Estimation of total ozone from satellite measurements of backscattered ultraviolet Earth radiance, J. Atmos. Sci. 28, 1307-1311. MOLINA, M. J. and ROWLAND,F. S. (1974), Stratospheric sink for chlorofluoromethanes: chlorine atom catalyzed destruction of ozone, Nature 249, 810-812. MURGATROYD,R. J. (1969), The structure and dynamics of the stratosphere, in The Global Circulation of the Atmosphere, ed. G. A. Corby, Roy. Meteorol. Soc. (London), pp. 159-195. NATIONAL ACADEMYOF SCIENCES (1976), Halocarbons: Effects on stratospheric ozone, National Research Council, Washington, D.C., Report, 'September 1976. NASA (1977), NASA-Sponsored symposium on ozone trend detectability, July 28-29, 1977, Boulder, Colorado, Proceedings, 105 pp. duplicated. NEWELL, R. E. (1961), The transport of trace substances in the atmosphere and their implications for the general circulation of the stratosphere, Geofys. Pura Appl. 49, 137-158. PITTOCK, A. B. (1970), On the representativeness of mean ozone distributions, Quart. J. Roy. Met. Soc. 96, 32-39. PITTOCK,A. B. (1972), Evaluating the risk to society from the SST: Some thoughts occasioned by the A A S report, Search 3, 285-289. PITTOCK, A. B. (1974a), Comments on ' Quasi-biennial and long-term fluctuations in total ozone', Mon. Weather Rev. 102, 84-86. PITTOCK, A. B. (1974b), Ozone climatology, trends and the monitoring problem, Proc. Int. Conf. on Structure, Composition and General Circulation of the Upper and Lower Atmospheres and Possible Anthropogenic Perturbations, Vol. 1, pp. 455-466, Int. Assoc. Atmos. Physics, Toronto, Ontario. PITTOCK, A. B. (1977a), Climatology of the vertical distribution of ozone over Aspendale, Quart. J. Roy. Met. Soc. 103, 575-584. PITTOCK,A. B. (1977b), Ozone sounding correction procedures and their implications, Quart. J. Roy. Met. Soc. 103, 809-810. PITTOCK,A. B. (1978), A critical look at long-term Sun-weather relationships, Rev. Geophys. Space Physics 16, 400-420. PITTOCK,A. B., FRAKES,L. A., JENSSEN,D., PETERSON,J. A. and ZILLMAN,J. W. (eds.), (1978), The effects of climatic change and variability on mankind, Chapter 7 of ' Climatic Change and Variability: A Southern Perspective', Cambridge University Press (London, New York, Melbourne), pp. 294-338. PRABHAKARA,C., RODGERS, E. B., CONRATH,B. J., HANEL, R. A. and KUNDE, V. G. (1976), The Nimbus 4 infrared spectroscopy experiment 3. Observations of the lower stratospheric thermal structure and total ozone, J. Geophys. Res. 81, 6391-6399. PRIESTLEY, C. H. B. and PITTOCK,A. B. (1977), lnhomogeneity of satellite-derived climatological data, Bull. Amer. Meteor. Soc. 58, 258. REED, J. W. (1973), Cloud seeding at Rapid City: a dissenting view, with comments by E. Bollay: M. C. Williams: R. A. Schleusener and A. S. Dennis: P. St.-Amand, R. J. Davis, and R. D. Elliott: and A. H. Murphy and S. W. Borland, Bull. Amer. Meteor. Soc. 54, 676-684. SCHNEIDER,S. H. (1977), Climate change andthe world predicament : A case study for interdisciplinary research, Climatic Change, 1, 21-43. SCHNEIDER, S. H. (1978), The Worm predicament: Author's reply to Hugh ~Ellsaesser, Climatic Change 1, 299-302. SCORZR, R. S. (I 977), Stability of stratospheric ozone and its importance, At mos. Envir. 11, 277-281. SINGH, H. B. (1977), Atmospheric halocarbons : Evidence in favor of reduced average hydroxyl radical concentration in the troposphere, Geophys. Res. Lett. 4, 101-104. SMIC (1971), Inadvertant Climate Modification, Report of the Study of Man's Impact on the Climate (SMIC), Cambridge, Mass. (M.I.T. Press). STOLARSKI, R. S. and CICERONE, R. J. (1974), Stratospheric chlorine: possible sink for ozone, Canadian J. Chem. 52, 1610-1615.

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THOMAS, R. W. L. and HOLLAND, A. C. (1977), Ozone estimates derived from Dobson direct Sun measurements: effect of atmospheric temperature variations and scattering, Applied Optics 16, 613-618. TURCO, R. P., WHITTEN,R. C., POPPOFF,I. G. and CAPONE,L. A. (1978), SSTs, nitrogenfertiliser and stratospheric ozone, Nature 276, 805-807. VAN LOON, H. and WILLIAMS,J. (1976), The connection between trends of mean temperature and circulation at the surface: Part L Winter. Mon. Weather Rev. 104, 365-380. WILCOX, R. W. (1978), Total ozone trend significance from space and time variability of daily Dobson data, J. Applied Met. 17, 405-409. (Received 15th June 1979)

Pageoph, Vol. 118 (1980), Birkhfiuser Verlag, Basel

Acceleration of Mean Zonal Flows by Planetary Waves By MICHIYAURYt?)

The mechanism of acceleration of the mean zonal flow by a planetary wave is explained intuitively by considering the wave drag which a corrugated bottom feels when it excites the wave. The explanation is justified by solving the problem of vertical propagation of a planetary wave packet and the second order mean motion induced around it. The discussion is slightly extended to the case of small damping, to illustrate in a compact form the fact that the mean zonal acceleration is determined by a forcing due to wave transience plus that due to wave dissipation. The mean flow induced by a steady, dissipating planetary wave is discussed, and it is shown that it depends largely on the dissipation scale-height of the wave whether the northern region is heated or cooled. For example, if the wave velocity-amplitude increases upward in spite of dissipation, the induced easterly flow increases with height and the temperature of the northern region increases relative to that in the southern region. A similar point has been made by DtrNKERTON (1979) in connection with westerly flows induced by Kelvin waves. The Lagrangian-mean motion indt/ced by a planetary wave is briefly discussed in connection with the mechanism of acceleration of the mean zonal flow, in the case of a slowly varying wave packet. Further, in order to elucidate the effects of wave dissipation and time dependence of wave amplitude, the results obtained for a steady, dissipating wave and for a growing baroclinic wave are mentioned. Abstract -

1. I n t r o d u c t i o n

I n recent years, m e a n m o t i o n s induced by planetary waves a n d internal gravity waves have been studied intensively by several authors (BRETHERXON, 1969a,b, 1971, 1979; DICKINSON, 1969; LTNDZEN a n d HOLTON, 1968; HOLTON a n d LINDZEN, 1972; MATSUNO, 1971; URYU, 1973, 1974a,b; HOLTON, 1974; ANDREWS a n d MCINTYRE, 1976, 1978a,b,c2); BoYD, 1976; etc.). These works are the extension a n d generalization of CHARNEY a n d DRAZIN'S (1961) work a n d ELIASSEN a n d PALM'S (1961) work. ELIASSEN a n d PALM (1961) showed that a vertically p r o p a g a t i n g stationary wave gives rise to a horizontal m o m e n t u m flux a n d a meridional heat flux, and that if neither diffusive processes n o r zero-wind line of the basic zonal flow (critical levels) exist, the vertical derivative o f the m e r i d i o n a l heat flux is identically equal to the

1) Department of Physics, Faculty of Science, Kyushu University, Fukuoka 812, Japan. z) In this paper, Andrews and McIntyre have shown how the theoretical structure that has emerged is related to certain classical concepts in theoretical physics.

662

Michiya Uryu

(Pageoph,

meridional derivative of the horizontal m o m e n t u m flux or Reynolds stress, under the quasi-geostrophic approximation. This is called an E-P relation, as is its generalization (also given by Eliassen and Palm) to nongeostrophic motion. On the basis of this relation, CHARNEYand DRAZIN (1961) showed that stationary planetary waves cannot cause any change in mean zonal flow to the second order in wave amplitude. This is the so-called Charney-Drazin or C-D theorem, sometimes called a 'nonacceleration theorem'. In other words, this theorem states that the effect of eddy fluxes due to planetary wave is cancelled out by that of the wave-induced mean meridional circulation, and thus the mean flow does not accelerate (ANDREWSand MCINTYRE,1976, 1978a,b; BOYD, 1976). I f dissipation such as Newtonian cooling and critical level absorption of wave (cf. BOOKERand BRETHERTON,1968) are incorporated, the balance between the effects of eddy fluxes and meridional circulation breaks down, and hence a change in mean zonal flow can be induced (DICKINSON, 1969). When a planetary wave is incident on a critical level from below, the associated heat flux vanishes discontinuously just above the level as a result of absorption of the wave, according to linear theory in the large-time limit. Thus, the northern atmosphere below the level is heated, and hence a meridional circulation is induced, on which the Coriolis force acts, to accelerate the mean flow in an easterly sense in the vicinity of the critical level. With this mechanism and the effect of density stratification in mind, MATSUNO (1971) has explained the main features of a channel model of the so-called stratospheric sudden warming phenomenon, a) When dissipating processes act on the wave, momentum-transport divergence occurs, inducing acceleration of the mean zonal flow. By considering this mechanism and the propagation characteristics of equatorial waves, LINDZEN and HOLTON (1968, 1972) have shown that the quasi-biennial oscillation of mean zonal flow can be caused by Kelvin waves and Rossby-gravity waves. We note here that the effect of critical level absorption of wave is not really different from that of wave transience plus dissipation, because the group velocity tends to zero near the critical level and hence the wave is absorbed by dissipation even if viscosity and radiative cooling rate are very small. On the other hand, considering a transient and conservative planetary wave packet propagating upwards into a zonal-mean state of zero flow, URYU (1974b) has shown that such a wave packet is associated with ' m o m e n t u m ' equal to E/C, 4) where E is the wave energy density and C is the horizontal phase velocity. In other words, a fluid within the extent of wave packet flows with this magnitude of momentum. An acceleration of the mean zonal flow occurs at the leading edge of the wave packet, while the reverse acceleration occurs at the trailing edge. It is noted that the

3) It is noted that in IMATSUNO'S(1971) spherical model, the easterly acceleration is associated more with the horizontal momentum flux divergence than with the Coriolis force acting on the mean meridional flow, as is seen from a northward progression of the zero-wind line in his result (see also HOLTON(1976)). 4) More correctly, this is the pseudomomentum (see ANDREWSand MCINTYRE(1978C)).

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

663

result depends on taking zonal averages and would be less simple if wave amplitude or mean flow were allowed to depend on longitude. Such problems have been discussed by BRETHERTON(1969) and MCINTYRE (1973) for the case of internal gravity waves. Most recently, ANDREWS and MClNTYRE (1976, 1978a,b) have discussed extensively the problem of mean zonal acceleration by waves, by including the effects of basic flow shear, dissipation and transience, and shown that the acceleration of the mean zonal flow can be given by wave transience term plus wave dissipation term. BoYD (1976) has also performed a similar but less general analysis. In these theoretical advances in planetary wave-zonal flow interaction, one of the most interesting products is the development of theory on mean motions of fluid particles induced by waves. That is, in order to clarify how momentum transfer is induced by waves in a material medium, theoretical interest has been directed towards the mean motions of air parcels, i.e., Lagrangian-mean motion. In this connection, URYU (1974b) has shown that in the case of a slowly varying wave packet, air parcels do not change their mean height. ANDREWS and MCINTYRE (1978b) have formulated a general theory of Lagrangian-mean motion induced by wave. BRETHERTON(1979) has studied this problem from the somewhat different angle of Hamiltonian principle. On the basis of these works, URYU (1979) has discussed the Lagrangian-mean motion induced by a growing baroclinic wave, while MATSUNO and NAKAMURA (1979) have studied the mean motion of air parcels at the time of a sudden warming in an idealized model. In this article, by means of several examples which are mathematically simple, we shall illustrate the role of wave transience and dissipation in the acceleration of a mean zonal flow by planetary waves, a statistically steady mean flow induced by a dissipating wave, and Lagrangian-mean motions due to a slowly varying wave packet, a strongly growing wave and a steady, dissipating wave. We shall not concern ourselves with the general theory as developed by ANDREWS and MCINTYRE (1978b) and BRETHERTON (1979). It is recommended for the reader to refer these works for general theoretical background.

2. Role o f wave transience and dissipation in the mean zonal acceleration

(a) Mechanism of mean zonal acceleration

As has been mentioned in the last section, according to CHARNEY and DRAZIN (1961), a stationary conservative planetary wave superposed on a westerly current dependent only on height and forced by, for example, a mountain, cannot accelerate the mean zonal flow to the second order in wave amplitude if there is no critical level in the atmosphere considered.

664

Michiya Uryu

(

F

TC'

\

(Pageoph,

I I

-

a(qE~

-

//

11

C"--

/

x /I /I

I

iI

ix

/

/

/x

1 /

/ /

I

// x

/

//

/I

/ x

x

/

///

I

/

/

I

I /x

/,, //

/ /

//

I

i/

/

//

I

/i

/

//

/

//

//

//

//

/

/

//

/

C

j

....

:: 'I

..............

Figure 1 Mechanism of acceleration of the mean zonal flow. A planetary wave packet is excited by a corrugated bottom moving westward and is propagating upward. The, latitudinally averaged force F corresponding to the wave drag which the bottom feels appears near the leading edge, and accelerates the atmosphere there in the direction of the phase velocity C.

This conclusion seems paradoxical at first sight. The wave is maintained by forcing by the mountain, and hence the mountain must feel a wave drag insofar as the wave has a propagating as opposed to a trapped character. This means that the atmosphere over the mountain must feel a force corresponding to the wave drag force. This would appear, at first sight, to imply that the mean velocity of the atmosphere should change. Nevertheless, the C-D theorem states that such a change cannot occur.

This apparent paradox can be resolved by considering a transient state of wave propagation. In order to simplify the problem without losing the physical essence, we consider a situation in which a corrugated bottom is moving westward with a constant speed C relative to an inviscid Boussinesq atmosphere, exciting a planetary wave, as shown in Fig. 1. The atmosphere is bounded by two rigid vertical walls at different latitudes. The leading edge of the wave is propagating upward with the group velocity Cg. Let D be the wave drag which the bottom feels, and E be the wave energy density (latitudinally averaged). Then, the energy supplied per unit time to the atmosphere from the bottom is given by CD. The wave is excited by this energy supply and propagating upward. In a frame of reference in which the mean flow is initially zero, the energy flux carried by the wave is CgE, and therefore the wave drag D is related to E at the bottom by CD

= CgE(O)

(2-1)

9 D = C~ 9 "

C

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

665

where E(0) is the wave energy evaluated at the bottom. Thus, D is of the second order in wave amplitude as well as E. That the bottom feels a mean resistance with this magnitude means, in turn, that the atmosphere is acted on by the corresponding mean force. The latitudinally averaged force F corresponding to wave drag D will be given by F=-~ at an arbitrary height. That is, the atmosphere near the leading edge where the amplitude change is large feels this force. Then, the following equation for the mean zonal flow (latitudinally averaged) U will hold, provided that the vertical scale of the wave packet greatly exceeds the Rossby height ( = N/fL, where f, N and L are the Coriolis parameter at a reference latitude, the Brunt-V~is/il~ frequency and the width of the channel, respectively):

Poo 7 7

= F = -

N\--F-]'

(2-3)

where po0 is the mean density. The essential mechanism of the acceleration of mean zonal flow by a vertically propagating conservative wave is expressed by this equation, though its validity remains to be proved. This will be done in the next subsection. The force F on the right of equation (2-3) is the force with which the atmosphere is acted on by the bottom when the wave is excited, and this force appears near the leading edge of the wave, to accelerate the atmosphere there in its direction, or equivalently in the direction of the phase velocity C. Further, as is seen from equation (2-3), in case of a free wave packet, the acceleration is reversed in the trailing edge because the amplitude increases in the vertical there. Thus, in such a case, as the wave packet propagates away from the point under consideration, the mean flow is restored to the initial state in which there is no wave. In this sense, a transient wave is accompanied by a mean flow. ANDREWS and MCINTYRE (1978b) discuss the circumstances under which a similar result would hold for arbitrary, finite-amplitude waves. If the wave is steady, the right-hand side of equation (2-3) vanishes, because the amplitude is independent of height. Then, changes in mean zonal momentum do not occur, up to the second order in wave amplitude. This provides a simple illustration of C-D theorem, and can be verified under a more general configuration of the basic zonal flow if a steady wave without a critical level is assumed (ANDREWSand MCINTYRE, 1976, 1978a,b; BOYD, 1976). On the basis of equation (2-3), it is seen that the apparent paradoxical conclusion of C-D theorem can be attributed to the assumption of steady state. A steady state can be attained after an infinitely long time from the excitation of the wave, and hence the wave has ' already' arrived at infinity. Thus,

666

Miehiya Uryu

(Pageoph,

we can consider that the wave accelerates the atmosphere at infinity; the force F does not appear in any finite region of the atmosphere. In the present particular problem, the mean vertical flow is independent of height, with upward motion in the northern side and downward motion in the southern side. However, the compensating meridional flow occurs only on the bottom, and thus the acceleration at infinity is completely compensated by the wave drag on the bottom. At the same time, the adiabatic cooling due to the mean vertical flow is also cancelled out by the eddy heat flux at each level. Such a steady state is a final state in which no further change Occurs.

As pointed out by DICKINSON (1969), even under a steady wave condition, however, the mean zonal flow can be accelerated if there is a critical level (which really implies transience and/or dissipation hidden in the singularity, cf. ANDREWS and MCINTYRE, 1976) and/or a dissipating mechanism such as radiative cooling or viscous dampling acting on the wave. This can be qualitatively understood on the basis of equation (2-3) which shows that the acceleration of the mean zonal flow is caused by the amplitude decrease in the vertical. When a wave is incident on a critical level, the amplitude decreases discontinuously there (cf. BOOKER and BRET~ERTON, 1968), and then the right-hand side of equation (2-3) (or a more general (elliptic differential) equation for the mean flow, cf. MATSUNO, 1971) will behave like deltafunction, while in case of a dissipating wave, the amplitude also decreases though not so extremely as in the former. Thus, in both cases, the mean zonal flow can be changed.

(b) Slowly varying wave packet with small damping In order to show more exactly that equation (2-3) holds for a conservative wave, we shall discuss the problem in more detail using the "equations of motion for planetary waves and mean flows. The discussion is extended a little from that by URYU (1974b) by including the effects of small damping and density stratification, p0 = p00 e -~m. Consider an atmospheric layer which is at rest on/3-plane and bounded by two rigid walls at two different latitudes. Then, using the conventional local Cartesian coordinate system, equations for the planetary waves and the induced second order mean flows can be written as follows:

~.~+~)-/]~ + ~ \ o z ~ / t ~ ! ] + ~

\Oz~ 14~z!=~ (2-4)

~-~ L~y~ + ~ -

~

\ez 2 ~-

B ~7 ~\dx

+ ~ [g~y~+ 7 &!

\~z2

~r ~ ! ]

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

667

here r and r are perturbation of geostrophic stream function and the zonal mean part of it, respectively, and a* is a damping coefficient. Other notations are those usually used. In equation (2-5), we assume that the coefficients of Rayleigh friction and Newtonian cooling are equal, while in equation (2-4) the damping mechanism is assumed to be only a Newtonian cooling (cf. DICKINSON, 1969). 2) The latter assumption implies that the Rossby height exceeds greatly the vertical wave length. We transform r in equation (2-4) by r

(2-6)

= e*12n. 9

to remove the density factor. Substitution of (2-6) into (2-4) gives

qo )] aVo f2a* (~29 4B ~ + ~ + - ~ \ e z ~

eq [~z~o ~29 f2 [~2r e~[ex ~+~y~+~-~\ez~

cp ) 4B ~. =0.

(2-7)

Then, we consider a slowly varying wave packet propagating upward: cp = r

T) sin[, y . e~"'

~(~x+.~+~t~,

(2-8)

where L is the width of the channel and Z and T are slow variables defined as ~t and ~z, respectively, with the small parameter ~ expressing the slowness of the wave envelope. Here, we assume that a* is of same order as E, i.e., small damping, to replace it by Ea where a is of order of unity. Substituting (2-8) into equation (2-7) and expanding r in powers of E, we obtain, to zeroth order in E, the following dispersion relation for a conservative free Rossby wave,

~k k2+

+7

n2 + 4--H-~

The equation for the amplitude change can be obtained from first order equation as follows;

1)

where suffix zero indicates 0-0rder quantity, and C~ is the vertical group velocity defined by = f2

Cg

N2 k2 +

(;;

2n f 2

(')

.

(2-11)

+ ~-2 n2 +

5) Certain problems which this assumption gives rise to in Lagrangian-mean dynamics are discussed in URYOand TAKAHASHI(1979).

668

Michiya Uryu

(Pageoph,

The third term on the left of equation (2-10) shows the damping of wave amplitude by dissipation. If c~ = 0, the wave propagates vertically with C o without changing its shape to this order (cf. URYU, 1974b). Defining wave energy density E as poo fL [[~4,'~

ia~b,~2

E=~-~.lo L\~x ] + \ a y ]

21 e -~m dy,

f z 4/~4,,~

+-~\az]

]

(2-12)

equation (2-10) implies the following energy equation; 1

aEo C OEo 2fza aT + o--~z + N z kS+

n + 4H 2 +-~-~ n2 + ~~-~

In order to determine the induced mean field ~, we calculate the heat flux on the right of equation (2-5) and obtain, to leading order in e,

e~b' e~b'

=

Ox ~z

kn e __.

2

zlH

.sm ~ y. 14012. "

(2-14)

2 ~

Transforming ~ by = e ~m- ~

(2-15)

and assuming that ~ is a function only of slow variables and expanding into e-series, we obtain that

{0 ~ ~2~o \ ~+~/ ey~--

f2 rrkn sin2~r ~[~Oo12 2N ~ t L--y" a---2--'

(2-16)

to leading order in e, where e is tacitly assumed much smaller than (vertical wave length/Rossby height). We can rewrite this equation by using the definition of wave energy density and equation (2-13) as follows: - -L- sm -L--y.

=---L sm~-y

~

+

N 2 n2+TH7 k2 +

Eo

+'-~-2 n2 + 4-~) C ' (2-16')

where C is phase velocity given by O" C

=

_ _

k

~

f2

(2-17)

Vol. 118, 1980)

669

Acceleration of Mean Zonal Flows by Planetary Waves

Then, the following equation for the mean zonal flow U is obtained: n2 + "4H2 poo ~

+ c~ U = 2 e ~m. sin Ly.

~

+ N---~ k2+

+-~

Eo ,

n2 + ~--~ (2-18)

or

(O

)

2f2~ =

[rr\

n +4.~12 f / z

~

-

.

-

~

9

(2-18') where ( ) means latitudinal average and we make use of U = dary condition F (mean meridional velocity) = - y

a~b/Oyand the boun-

~ + c~* ~-~ = 0

aty=0andL. The first term on the right of equation (2-18) or (2-18') is a forcing due to wave transience and the second is that due to wave dissipation. This equation provides a compact illustration of the statement that the acceleration of mean zonal flow is given by forcing due to wave transience plus wave dissipation (ANDREWS and MCINTYRE, 1976, 1978a; BOVD, 1976). A very similar result was obtained by HOLTON and DUNKERTON (1978). In the case of a conservative wave packet, equation (2-18) is identical with equation (2-3), which is now verified. Then, we obtain that P0o e-~m(U) = Eo

C"

(2-19)

This has been obtained by URYU (1974b) for a Boussinesq fluid (H = ~). Then, the zonal flow within the extent of wave packet has this magnitude of momentum. In Fig. 2, the propagation of planetary wave packet and the induced mean flow around it are shown schematically. As is seen from equation (2-5), the origin of the second order zonal mean flow is the eddy heat flux associated with the wave, and hence a mean meridional circulation with upward flow to the north and downward flow to the south is induced, whose Coriolis force acts to accelerate easterly flow near the leading edge region. An opposite acceleration occurs in the trailing edge region. This mechanism is summarized in equation (2-19).

670

Michiya Uryu

(Pageoph,

! t

W

7 Figure 2 Mean meridional circulation induced around a vertically propagating planetary wave packet. The circulation is caused by the southward buoyancy (equivalently, the northward heat) flux indicated by p'v'.

If frictional dissipation of mean zonal flow can be neglected, equation (2-18') integrates to 1

poo e - ~ m ( U )

Eo = ~

2f2~ + ~N

n2 + 4 H ~ k2 +

~r Eo dT

(2-20)

+ ~-~ n 2 + 4 H 2]

where we assume ( U ) = E0 = 0 at T = 0. Equation (2-20) shows that mean momentum consists of two parts, i.e., momentum accompanying the wave packet and that detached from it by dissipation. While the former is transient, the latter is left behind after the wave has propagated past. GRIMSIfAW (1975) has given explicit calculations of the corresponding effect for internal gravity waves. Recently, by including the feed-back effect of wave-induced mean zonal flow on the wave, HOLTON and DUNKERTON (1978) have shown numerically that in the change of mean zonal flow, the role of wave transience is important especially in the lower stratosphere. They have assumed that ~- ~ = 20 days near 20 km height, the wave period is 10 days or so and vertical group velocity is about 2 km/day. It is considered, then, that the effect of wave transience acts faster than that of wave dissipation, and the former can continue to dominate the latter owing to constant input

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

671

of the wave at the lower boundary. So far as the 'nonvacillating case' in Holton and Dunkerton's model is concerned, the above consideration seems to be plausible. Further, in their model, the induced mean zonal flow oscillates until the wave becomes steady. This may be attributed to the interaction between the existing wave and the boundary corrugation. In the 'vacillating case', we cannot imagine such a simple picture as mentioned above, because complicated nonlinear interaction including transient critical layers occurs. However, also in this case, Holton and Dunkerton have found the role of wave transience is important; since the assumed time-scale of dissipation is relatively long, then the zonal flow change is caused mainly by wave transience and in turn it produces continuingly transient waves, even for constant wave input at the lower boundary. Although the situation is very complicated, the essential part of the role of wave transience may be summarized in equation (2-18) or the fact that wave transience induces changes in mean zonal momentum equal to the change in E/C, provided always that the vertical scale of the changes is much larger than the Rossby height. We note finally that equation (2-18') gives a steady state solution in which the dissipation of mean zonal flow is in balance with the wave dissipation term; '

2

p00(U) = e ~m'2f~ N 2 k2 +

n 2 + - -1 4H 2 + ~ n2 +

Eo

Note that damping coefficient disappears only because of the assumption that horizontal mean-flow friction and wave Newtonian cooling have identical time constants.

3. Steady mean flows induced by dissipating planetary waves 6) In this section, we consider a steady mean flow induced by a stationary planetary wave which is forced at the bottom of the atmosphere and is damped by Newtonian cooling. This may be connected to the problem to what extent planetary waves contribute to the structure of a statistically steady state of the atmosphere, such as the higher temperature in the winter polar middle atmosphere. The present calculation may help towards a qualitative understanding to the problem. The notations are those usually used. For simplicity, we assume a channel model of the atmosphere with a constant Newtonian cooling rate (see Section 2(b)), and a planetary wave is excited by the bottom corrugation over which a constant westerly wind blows. Then, the forcing at the bottom is given by Oh w' = UoFx a t z = O, 6) This section follows URYU and TAKAHASHI(1979).

672

Michiya Uryu

(Pageoph,

where -ff

(3-1)

h = ho s i n z y ' e t k X .

Substituting the following simple sinusoidal wave form ~o = A sin Z y" e*~kx+ '*~

(3-2)

into equation (2-7) in which O/St is replaced by Uo(O/Ox), we obtain the equation for the refractive index n as follows; fl N2 Uo n~

f2

(

)

~.2 k 2 + ~2

{ a* ~2 1 + \Uok]

+ . N 2 . ~*

1 - 4H-----2

t-f~

t

/3 Uo

Uok

k2 + [~*~

1 + \Uok]

Thus, the refractive index becomes complex owing to Newtonian cooling (cf. HOLTON, 1975). We choose positive n~ (the imaginary part of n) 7) so that wave energy density is bounded as z --> oo. Then, the eddy heat flux is written as follows: e~' ~ ' ~x 8z

=

Ial2.knr

" 2 zr

9s i n

~ y . e ((~m~- 2'~0~,

(3-4) 8)

where nr is the real part of n and the amplitude A is related to the height of the bottom corrugation ho as follows: N' 1 +

1 c~,Uo/~/ o*v n~ + (n~h~-

(3-5) ~-~

Substitution of (3-4) into equation (2-5) gives -

= ~.~.

kn~n~ [A

9sin -L- y" e((1/m- 2,~,~.

(3-6) Hereafter, our concern is focused on the steady solution, i.e., O/Ot = 0. We expand

7) The sign of n, (the real part of n) is determined as follows : n, ~ 0 for Uo ~ UR(-fl/(k 2 + ~r2/L2)). Un is the speed of two-dimensional free Rossby wave. a) It follows from (3-4) that the eddy heat flux is directed southward if Uo is larger than UR (see footnote 7).

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

673

into Fourier cosine series so that the side boundary conditions (mean meridional velocity V vanishes at the walls) are satisfied automatically (cf. URYU, 1974a): ~ = e ~I2n. m:oaa ~" ~mCOS mrr --ff y"

(3-7)

Further, we use the following Fourier expansion: m~-

27r sin-ry=-

8

cos -L-" y m2-4 9

9~

(3-8)

re:odd

Then, equation (3-6) is reduced to the equation for ffm as follows: tZ2m~m=

d2~m dz 2

8 IAI ~ zrkn,n, e(ll2m_2,h,~. ~r m 2 - 4" Lo~*

(3-9)

where I~ =

N2m%r 2 1 f2L-----T - + 4H----~.

The general solution to this equation can be written as ~m = B m "e""z + Cm "e-""~ __8_ [A[ 2 IrknTn~ e((l12H)-2~')~ zr m2 _ 4 L a , ( 1 )2 ~ - B - 2n' - t 4

(3-10)

where A is given by (3-5), and Bm and Cm are determined from the boundary conditions which are assumed as follows; W = u' ~h

v' ~h

e-~ml~ t ~ 0

~y

as z - +

at z = 0, )

(3-11)

~.

We can rewrite (3-11) in terms of ~m by using the thermodynamic equations (including Newtonian cooling) for the wave and the mean flow as follows; + ~-~ = ~r rn~ -- 4 2L--Uo ~ - ~ - n ~ eZlH(am--> 0

at z = 0, t

(3-12)

as z -~> oo.

Substitution of (3-10) into (3-13) gives

B m = 0,

Cm =

s

IA12

rr m 2 - 4

1H _ 2n~ ~ [4--~o ~* + 1 La* 2H tLm

Hrrli

l

674

Michiya Uryu

(Pageoph,

Then, we o b t a i n that m~r

~b= ~

ra:odd

~'k 8

]AI 2

cos--~-y L c ~ . ~ r m ~ 4

(z*

"-

+

(

-;

l'lrn i

e ( ( l / 2 H ) _ t~ra)Z

1 - 2n~

-

1

- i~

nrn~ 2

Thus, it is seen from this solution that the sign of n~ -

. e(am~- 2~,~ 1 .

(3-13)

1/2H is a n i m p o r t a n t factor

for d e t e r m i n i n g the flow structure, a n d the sign is determined by the difference between the amplification effect of density stratification and the d a m p i n g effect of dissipation (cf. DUNKERTON, 1979). F o r inStance, if n~ < 1/2H, i.e., if the wave amplitude increases in spite of the dissipation due to N e w t o n i a n cooling, easterly flows increasing u p w a r d are induced a n d the temperature of the n o r t h e r n region increases relative to that in the southern region. I f the wave amplitude decreases u p w a r d

Uo=20 m/sec 7O

E 50

r121

'~, r

3O

10 S

( m/sec

)

N

Figure 3a Meridional cross section of the mean zonal flow induced by a stationary, dissipating planetary wave applied at 10 km level. Parameter values are as follows. Uo = 20 m/see, ~* = 1.65 x 10- 6/see (= 1/(7 days)), k = 4.42 x 10 -9 cm, L (width of the channel) = ~r/(4.42 x 10 -9) cm, N --= 2 x 10-2/sec, f = 10-4/see,/3 = 1.6 x 10-1Z/sec.cm, H = 7 km, ho = 200 m. In this case, n~ = 1.42 x 10-7[cm, and then n~ < l[2H.

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

675

Uo=20 m / s e c 70

/ \ ~50 E

10

-10

/\

7: -~, ~- 30

-1

1 v

/ -

0-1

0.1 V

10 S

? ( deg ) Figure 3b Meridional cross section of the zonal mean temperature anomaly corresponding to Fig. 3a. (n~ > 1/2H), the induced easterly flows also decreases upward and hence a lower temperature appears in the northern side. In Fig. 3a,b, the former example is shown, while the latter is in Fig. 4a,b. In both cases, we assume ~* = (7 days)-1 which m a y be close to the vertically averaged Newtonian cooling rate in the stratosphere and mesosphere (HOLTON, 1975). F r o m the former example, it is likely that dissipating, Uo = 5 m l s e c 70

-0.2 50 E v

"$ r

30

10 S

N ( rn I sec

Figure 4a Same as Fig. 3a but for Uo = 5 m/sec. In this case, n~ = 9.75 x 10-7/cm, and then nj > 1/2H.

676

Michiya Uryu

(Pageoph,

Uo= 5 m I sec

S 50

-•0.04

E

-0.04

r O~

"~, 30

10 S

T (deg)

N

Figure 4b Same as Fig. 3b but for Uo = 5 m/see. stationary planetary waves may contribute to maintaining the higher temperature in the winter polar middle atmosphere. However, to be more convincing, we should calculate the mean flow under more realistic conditions, because ~* and Uo are not constant in the actual atmosphere. In Fig. 6a,b, we show an example obtained for longitudinal wave number 1 by assuming 7O

50

E

z= 30

10 0

20 basic zonal flow

40

60

( rnlsec )

Fig. 5a Vertical distribution of the basic zonal wind.

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

20

70

i

677

damping time ( d a y s ) 10 7 5 r

,

5O E

"~ 30

1%

t

2

Newtonian cooling coefficient

( ,o' s-' ) Figure 5b Vertical distribution of the Newtonian cooling rate.

5=1 ~x : c x ( z ) 70 -30 A

5o

i

30

10;

N 0

( ml sec )

Figure 6a Meridional cross section of the mean zonal flow induced by the wave with longitudinal wave number 1 (k = 2.21 x 1 0 - 9 / c m ) when the distributions of the basic zonal wind and the Newtonian cooling are assumed as in Fig. 5a and Fig. 5b, respectively. As to the parameter values used except k, see the legend of Fig. 3a.

678

Michiya Uryu

(Pageoph,

5--1 oc=~(z)

70

"•50 -4

Zr

3O -1 0 10

E

7 (deg)

N

Figure 6b Meridional cross section of the zonal mean temperature anomaly corresponding to Fig. 6a.

the vertical distributions of Uo and c~* shown in Fig. 5a,b. It is seen that the wave reduces the basic westerly wind by about 30 m/sec near z = 70 km in the mid-latitudinal region and causes the meridional temperature difference of about 7~ near the same level. By the numerical simulation with use of the quasi-geostrophic model, MATSUNO (1976) 9) has shown that in a statistically steady state, the temperature of the polar atmosphere near 70 km height becomes higher than that in the equatorial atmosphere by about 15~ and the mean zonal wind decreases by about 20 m/sec from the initial value there. Our results are not so different from Matsuno's.

4. Wave-induced Lagrangian-mean motion As mentioned in the previous sections, a transient wave and a dissipating wave can accelerate mean zonal flow. However, the zonal mean flows obtained in the previous sections do not show the mean motion of air particles, because the averaging procedure employed does not concern any ensemble of air particles, but it is applied merely along a latitudinal line. This averaging procedure is called Eulerian mean. It is interesting, then, to ask how the mean flows obtained so far are related to the mean motion of air particles or how a wave can force air particles to move. This problem is 9) Presented at the autumn meeting of Meteor. Soc. Japan at Nagoya, 23 Oct. 1976.

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

679

important not only from the dynamical viewpoint, but also in connection with the transport of minor constituents by planetary waves in the atmosphere. There may be two methods of approaching such a transport problem. One is to evaluate the eddy fluxes and Eulerian-mean circulations due to the waves, while the other is to discuss the mass transport Velocity field. The former is involved in the framework of the Eulerian zonal mean dynamics described in the previous sections, because it concerns an average along a latitudinal line, which is defined independently of the wave disturbance. The latter approach treats an ensemble-mean velocity field of air particles, and is called a Lagrangian mean. As will be shown later, these two methods give different views of the same physical phenomena. The original idea of the Lagrangian-mean approach can be traced back to G. G. Stokes who studied the mass transport by water waves, and particularly in recent years such studies have been developed in connection with m o m e n t u m transport by waves in a material medium. A general theory of Lagrangian-mean dynamics has been formulated by ANDREWS and MClNTYRE (1978b). In what follows, we shall mention briefly the Lagrangian-mean motion associated with the examples described in the previous sections, and in addition the Lagrangianmean motion induced by a growing baroclinic wave. As for the general theory, see ANDREWS and MCINTYRE (1978b) and the article by Dr. McIntyre appearing in this issue and concurrently in Phil. Trans. Roy. Soc. L o n d o n ? ~ Further, Prof. Matsuno will elucidate a detailed mechanism of Stokes drift (see below) in this issue.

(a) Concept of Lagrangian mean Let us consider a latitudinal line (or tube) at a constant height in a fluid layer at rest or flowing in parallel in the zonal direction. In the absence of waves, this line (or tube) is regarded as a material line (or tube). In the presence of waves, however, the latitudinal line does not coincide with a material line, which is now undulating because of the wave. A familiar example similar to this is seen in case of water wave. When the water surface is calm, a line z = H, y = constant in the free surface is identical with a material line, while when a wave is present, z = H cannot specify the free material surface. The equation for the free surface is now given by z = H + ~(x, y, t). Then, in the presence of a wave, we can consider at least two different ways to take a ' m e a n ' value of a physical quantity Q. One is to average Q along a latitudinal line;

QE = Q(x, y, z, t),

(4-1)

where the usual local Cartesian coordinate system is employed and the overbar on the right means the usual zonal mean operation. This is the so-called Eulerian mean and ao) In this paper, Dr. Mclntyre discusses the nonuniqueness and also certain difficulties in using Lagrangian mean on a sphere.

680

Michiya Uryu

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is the one usually employed in meteorology. The discussions in the previous sections are also based on this Eulerian-mean. Another procedure is to average Q with respect to air particles labeled by the fact that they were located on a latitudinal line in the absence of waves. Let (x, y, z) be the'initial' position of an air particle. The particle is now displaced to (x + ~, y + r/, z + ~) because of the wave, where ~:, r/and ~ are the components of the particle displacement vector 1~and they are defined as functions of space (x, y, z) and time t in the Eulerian sense. Thus, the quantity Q belonging to this particle should now be evaluated at the displaced position (x + ~:, y + V, z + ~). We note here that motions of member particles of a material line are identical with each other apart from a phase shift. Conversely, this fact allows us to label particles on a material line by x. In this sense, x plays a dual role as Eulerian coordinate and Lagrangian label. Thus, averaging Q(x + ~, y + ~7, z + ~) with respect to x, we can obtain a different mean value from Q(x, y, z, t). In practice, if we can assume the wave is of small amplitude, we can obtain, to the second order in wave amplitude, by Taylor expansion, that

Q---L= Q(x + ~,y + ~7,z + ~ , t ) -

Q ( x , y , z , t ) + ~ . V Q ' + 89

(4-2)

where Q0 is the basic distribution of Q and Q' is the perturbation. This is the Lagrangian-mean value of Q correct to second order in the small amplitude approximation. It is clearly seen that Qc is different from QE at the second order in wave amplitude. The correction term ~-VQ' + 89 (~-V)VQo is called the Stokes correction (although the second term was first given by ANDREWSand MClNTVRE (1978b)). Particularly, if Q is velocity, the correction term is called the Stokes drift. It is further noted that ~3Ldefined above is equal to a mean value obtained by averaging Q along an undulating material tube with a weight of the cross-sectional area, and hence the Lagrangianmean velocity is the velocity of the center of mass of the tube (MATSUNO, personal communication;ANDREWS and MCINTYRE, 1978b). Since ~ is related to Eulerian perturbation velocity through the following kinematical relationship at the first order in wave amplitude

(c~ ~ 7 + U o ' V ) [ = u' + ~-VUo,

(4-3)

where Uo is the basic velocity vector, we can obtain QL from a solution of the Eulerian equations of motion.

(b) Examples of the wave-induced Lagrangian-mean flow In what follows, we shall illustrate several examples of the Lagrangian-mean flow obtained from the consideration mentioned in the last subsection.

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

68 |

(i) Case of a slowly varying wave packet In the case of a slowly varying wave packet, URYU (1974b) showed that the Lagrangian-mean meridional circulation is zero to two orders in the Small parameter E of wave-packet theory (see Section 2). This can be shown as follows without handling the wave-packet solution. For simplicity, we consider a Boussinesq fluid following URYU (ibid.). Under the quasi-geostrophic approximation, the Lagrangian-mean vertical velocity WL is written, from (4-2), as follows; --

~w'

~w'

~w'

~ ~-~

w ~ = w + ~-~x + ~-g)-y + C-Ez - W + F y ~ , -

-

(4-4)

where use has been made of the Boussinesq relation V. g = O(a2) (a is the small amplitude parameter) and the smallness of ~ in quasi-geostrophic flow. W is the Eulerian-mean vertical velocity. Using the adiabatic equation e~ \ az t + -7- w, = 0,

(4-5)

WL is rewritten as Wz = W -

N

-

-

-

v'

,

(4-6)

where v' = O~/~t has been used. Then, in the present case, the first term in square brackets is two orders smaller in the slowly-varying parameter e than the second term (meridional heat flux), because O/Ot = 0(e) and ~ and O~b'/az are in quadrature to leading order. Thus, we can write the Stokes drift W~ as Ws = ~yyr/w' ~ ~-~ ~yy v'

.

(4-7)

On the other hand, the Eulerian-mean vertical velocity W can be obtained from the zonal mean adiabatic equation as follows; W=-N4

~

Fzz +Fyy v'

.

(4-8)

Assuming ~ is a function of slow variables only, the first term on the right of (4-8) becomes two orders smaller in e than the second. That is, -N--~y

+ 0(C).

(4-9)

Then, to this order the Stokes drift W~ just cancels the Eulerian-mean vertical flow W; consequently, Wz = W + W~ = 0(e2). (4-10)

682

Michiya Uryu

(Pageoph,

This result can be obtained also from a somewhat different consideration. Since we are concerned with adiabatic motion, we transform the Eulerian-mean adiabatic equation into its Lagrangian analogue, to obtain that, to the leading order in Rossby number,

e~L d~o e--7 + --~ W~ = 0

(4-11) 1t)

where 17L = P + (O/Oy)vp', in which fi is the Eulerian-mean density anomaly and p' is the perturbation of density (cf. ANDREWS and MClNTYRE, 1978b; NAKAMURA, 1979). This means that the Lagrangian-mean density anomaly tSL is conserved along mean trajectories. Taking into account that 15 =-O~b/3z = 0(E), ~Tp'= 0(E) and 8/8t = 0(~), we can conclude that W~. = 0(42). Then, it is verified that in case of vertically propagating wave packet, the Lagrangian-mean meridional circulation vanishes to two orders in the small parameter E (the slowness of the wave envelope), while the Eulerian-mean circulation is two orders larger. A stronger result holds for a stationary wave; then, WL can be shown to vanish exactly (ANDREWS and MclNTYRE, 1978b; MATSUNO and NAKAMURA, 1979). This means that the C-D theorem is verified on the basis of Lagrangian mean dynamics (cf. ANDREWS and MClNTYRE, ibid.). Also, in case of a wave packet with small damping as discussed in Section 2, WL vanishes approximately because the wave structure in the leading order is same as that of a steady, conservative wave. Further, we note from (4-4) that Ws results from motion of air particles in the x-z plane plus that in the y-z plane; from the assumed form of r to the leading order in E, we have

Ow'

aw'

f%kn

~:-~-x = ~-b--fy = 4 ~

sin

Y'1r176

(4-12)

The Lagrangian-mean zonal flow UL can be written as --

--

8u'

~u '

8

UL = U + ~:-8--/x+ ~/-~y = 8 + ~y-qu

,

(4-13)

again using smallness of the Rossby number. Then, substituting the assumed wave form, we have U~ = ~:"b--xx+ "q ~y -

4or

c~

y1r176 + ~

4~

cos-L- y'1r176

am ~y-[r

2 (4-14)

p

11) Under steady conditions, we can deduce WL = -- Q - (O/Oy)w" where Q is the Eulerianmean heating rate and q' is the perturbation of heating. If ~q' can be neglected, we can obtain WL from a knowledge of Q only. DUNKERTON(1978) has calculated WLfrom this consideration.

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

683

It is seen that Stokes drift Us has a jet-like structure in the meridional direction as result of the superposed effects of two terms. As is seen from (2-18), U is proportional to sin2(rr/L)y, and hence a zonal mass transport occurs more strongly in mid-latitudes than in other latitudes. Further, integrating UL in the y-direction, we obtain that

Poo(UL) =

Poo(U) = Eo C"

(4-15)

Then, ' m o m e n t u m ' E/C (more correctly, the pseudomomentum) is equal to the mean momentum of air particles in this particular problem (as to a rigorous consideration on E/C, see ANDREWS and MclNTYRE, 1978C). In the situation considered in Section 2, the origin of the acceleration of the mean zonal flow is the pressure drag force acting on the corrugated bottom. Then, replacing the bottom by an arbitrary undulating material surface in the fluid and calculating the pressure drag on the surface, we obtain

"-~x"5 = C~176

- PYxx/

C "

(4-16)

Thus, we can consider that the acceleration of mean zonal flow by the wave is caused as a result that a fluid below an undulating material surface acts with a pressure drag force -p'(9~/Ox) on a fluid just above the surface. The intuitive discussion in Section 2 is verified within the approximation of wave-packet theory. We note that in the Lagrangian-mean description, the secondary meridional circulation induced by the (Eulerian) eddy heat flux does not appear. In the Eulerian-mean framework, such an effect of the eddy flux does, by contrast, play an important role. The above result can be obtained also from the general theory by ANDREWS and MCINTVRE (1978b). (ii) Case of a stationary, dissipating wave In the case of a stationary, dissipating planetary wave as treated in Section 3, the Lagrangian-mean meridional circulation is induced, as well as the Eulerian-mean one. When the Newtonian cooling rate ~* and the basic westerly wind U0 are constant, the Lagrangian-mean meridional circulation can be easily calculated from the solution mentioned in Section 3 (URYt) and TA~ASHASm, 1979). The results are shown in Figs. 7a and 8a. The former is for n~ < 1/2H, while the latter is for n~ > 1/2H. Figures 7b and 8b show the corresponding Eulerian-mean meridional circulation, respectively. In the case where the wave amplitude decreases upward (n~ > 1/2H), both the Eulerianand the Lagrangian-mean meridional circulations have the upward branch to the north and the downward branch to the south. On the other hand, in the case where the wave amplitude increases upward (n~ < 1/2H), the Lagrangian-mean meridional circulation is completely opposite to the Eulerian-mean one. According to MATSUNO and NAr:AMURA (1979) who have discussed the Lagrangian-mean meridional circulation in the situation in which a stationary planetary wave is incident on a critical level

684

Michiya Uryu

(Pageoph,

Uo= 20 m/sec

2O

/ 1 aO

so

~ 30

1

5

~L ( g cn31/sec )

N

Figure 7a Lagrangian-mean meridional circulation induced by a stationary, dissipating planetary wave applied at 10 k m level. XL is the mass stream function, defined by poVL = -a~L/gz and poWL = a~HOy. The parameter values used are same as those in Fig, 3a. Note that Uo = 20 m/see (n~ < 1/2H).

Uo=20 mlsec 70

~SO E

O~

= 30

10 $

N ~--~ ( g c n ~ l l s e c )

Figure 7b Eulerian-mean meridional circulation corresponding to Fig. 7a. is the mass stream function defined by po F = -8"~E/Sz and poW = a-~JSy.

Vol. 118, 1980)

Acceleration of Mean Zonal Flows by Planetary Waves

Oo= 5 m/sec 70

-0.1

\

E

7_

\

.c 30

S

~L ( g crfil/sec )

N

Figure 8a Same as Fig. 7a but for Uo = 5 m/sec (n~ > 1[2H).

Uo= 5 m/sec

70

A 5O E v

t-

"~ 30 r

,o\

,oS

N

~'E ( gcrfillsec

)

Figure 8b Same as Fig. 7b but for Uo = 5 m/sec.

685

686

Michiya Uryu

(Pageoph,

from below, the Lagrangian-mean meridional circulations below and above the critical level are opposite to each other; the lower one is associated with upward motion to the south, while in the upper one the upward flow appears in the northern side. Since the wave is absorbed at the critical level according to linear theory at the large-time limit, we can consider that the Lagrangian-mean meridional circulations above and below the level correspond to Fig. 8a and Fig. 7a, respectively. According to URYU and TAKAHASHI(1979), if Uo exceeds a certain value, say Urn,12) the Lagrangian-mean meridional circulation shows the so-called 3-cell structure in the meridional direction, consisting of one circulation in the central region of the channel with upward (downward) motion to the north (south) and of two opposite circulations near the side walls. In addition, the central circulation spreads in the meridional direction as U0 increases. By contrast, the Eulerian-mean meridional circulation does not change its pattern substantially so far as Uo changes between Um and URla) (the speed of two dimensional free Rossby wave; > Urn). These results seem due to the assumption that the planetary wave is damped by Newtonian cooling

7~

!

S=I

-10 / E50 -I00 E, '- 30

S

N ~,( gcrff)sec )

Figure 9a Lagrangian-mean meridional circulation induced by the wave with longitudinal wave number 1(k = 2.21 • 10-9/cm) when the distributions of the basic zonal wind and the Newtonian cooling rate are assumed as in Fig. 5a and Fig. 5b, respectively. As to the parameter values used except for k, see the legend of Fig. 3a. ~L is defined in the legend of Fig. 7a. 12) Um- 28 m/see when we adopt the numerical values listed in the legend of Fig. 3a. It is noted that at Uo = U~,, the vertical energy flux po~b'w' becomes maximum when the other parameters are fixed (URYu and TAKAHASHI,1979). 13) UR -- 41 m/sec under the same condition above.

Vol. 118, 1 9 8 0 )

Acceleration of Mean Zonal Flows by Planetary Waves

687

5=1

~=c~[z)

10!/

N ~E ( g crfi1/sec) Figure 9b

Eulerian-mean meridional circulation corresponding to Fig. 9a. ~E is defined in the legend of Fig. 7b.

only (see equation (2-4)). Further, it is noted that if Uo exceeds UR, the directions of both the Eulerian-mean and Lagrangian-mean circulations are reversed to those obtained for U0 below UR (URYu and TAKAHASm, 1979; see also footnote on page 672). When U0 and a* are dependent on height as presented in Fig. 5a,b, the Lagrangianand Eulerian-mean meridional circulations become as shown in Figs. 9a, and 9b, respectively. It is seen that the Eulerian-mean meridional circulation is not so different from that in Fig. 7b, except for the difference in the intensity due to that in the wave amplitude. However, the Lagrangian-mean meridional circulation is completely different from that in Fig. 7a. In the present case, it is split into two parts in the vertical direction; the lower circulation is associated with upward (downward) motion to the south (north), while the upper one is opposite, as a result that the central circulation in the 3-cell structure spreads over the channel (URYU and TArCArlASm, 1979). Although the present circulation pattern happens to be somewhat similar to that obtained by MATSUNO and NAKAMURA(1979), it should be emphasized that while under the present conditions (see the legend of Fig. 3a) the wave amplitude increases upward, it decreases suddenly above the critical level in Matsuno and Nakamura's case. Here, it is emphasized that as is seen from the figures, the Lagrangian-mean mass flux is solenoidal in the meridional plane. This is due to the stationarity of the wave considered (ANDREWS and MCINTYRE, 1978b). In practice, under the stationary wave

688

Michiya Uryu

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assumption, the meridional and vertical components, Vs and follows; V~ =

Fz - H

W~, are written as

~v

0-W~ = ~y ~/w'

(4-13)

(4-14)

where use has been made of v' = Uo(O~/Ox)and w' = Uo(OUOx),from which v'~ = w'~r = 0 is obtained. Then, considering that the Eulerian-mean mass flux is solenoidal in the meridional plane, i.e.,

-~y p 0 V + ~0 poW = 0, -

-

(4-15)

and that v'C + wq7 = 0 for stationary waves, we can conclude that the Lagrangianmean mass flux is solenoidal in the meridional plane for stationary waves, i.e., m

~

m

-~poV, + ~poWL = o

(4-16)

(cf. A~qDREWSand MclNTYRE, 1978b; MATSUNO and NAICAMURA, 1979). (iii) Case of a growing baroclinic wave In the previous subsections, we have treated waves of almost stationary ((i)) and stationary ((ii)) properties. It is then interesting to ask what mean motion of air particles are caused by a stronger time-dependent behavior of a wave. We shall discuss the recent results of URYU (1979), although it should be noted that one of the relevant effects (divergence of the Lagrangian-mean flow induced by wave transience) was pointed out by MclNTYRE (1973). As is well known, there exists an indirect mean meridional circulation in the troposphere, and this is interpreted as a result of heat transport by cyclone waves. However, this circulation does not show the trajectories of air particles. Figure 10 shows the Lagrangian-mean meridional motion induced by a growing baroclinic wave, which can be regarded as an idealized model of a cyclone. The calculation is done for Eady's model. At first sight, it is quite different from the usual Eulerian-mean picture with an indirect cell in mid-latitudes (cf. RIEHL and FULTZ, 1957; MATSUWO et al., 1977). Air parcels converge toward mid-latitudes almost horizontally, with slow upward motion near the southern wall and downward motion near the northern wall. These vertical motions are thermally direct, showing the process of release of available potential energy. Figure 10 agrees qualitatively well with KIDA'S (1977) numerical experiment as far as the behavior of tropospheric particles is concerned. However, we note that his result was obtained in a statistically

Vol. 118, 1980)

r

~

Acceleration of Mean Zonal Flows by Planetary Waves ,--,9

~

~

4-

~

4"-

689

'-I

I mlsec I cmlser

r

~

7

L

--~

~

,,

-~

4

S

4---

#---

4-

-J

N VL ,Wl

Figure l0 Lagrangian-mean motion in the meridional plane associated with a growing Eady wave. Arrows are drawn by (VL, WL x 500). Parameter values are as follows. Disturbance amplitude measured by maximum meridional disturbance velocity v" = 11 m/sec, growth rate = 0.7/day, wave length (= 27r/k) = 5000 km, width of the channel -- 5000 kin, height of the channel = 10 km, vertical shear of the basic zonal flow = 3 m/sec.km, N = 10-2/sec, f --- 10 -4 sec. Note that the Lagrangian-mean motion is convergent in spite of the Boussinesq assumption, because of disturbance growth (cf. ANDREWSand MCINTYRE,1978b).

steady state, while Fig. 10 is obtained for a growing wave. The reason for the similarity o f two results m a y be attributed to diffusive processes included in Kida's experiment. This point is discussed further in MCINTYRE (1979b). It is noted that the meridional m o t i o n seen in Fig. 10 is largely associated with a balance between the Coriolis force with a force p'(O~/~x) due to a systematic correlation between the disturbance pressure and the zonal gradient o f the meridional displacement of a material surface. A l t h o u g h a small departure flow f r o m such a balance can contribute to changing the Lagrangian-mean zonal flow, the direction o f the contributionfVL to the acceleration is opposite to that in the Eulerian-mean zonal flow, which is accelerated toward west (east) in the upper (lower) layer in the midlatitudinal region by the Coriolis force associated with the Eulerian indirect cell. This difference ( b e t w e e n f V andfVL) is due to the dominance of the Stokes drift U, in that region.

690

Michiya Uryu

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Finally, we note that the converging (or diverging) flow of air parcels is one of the most characteristic properties of the Lagrangian-mean motion induced by a growing wave (cf. MClNT~'RE, 1973; ANDREWS and MclNTYRE, 1978b; MClNTYRE, 1979b).

5. Conclusions In this article, we have mentioned various aspects of planetary-wave-induced mean motions including Eulerian- and Lagrangian-mean motions, which might be helpful towards understanding phenomena occurring in the middle atmosphere. First, we have shown that the acceleration of the mean zonal flow is a transmission process of force acting from the bottom (i.e., is equivalent to a mean stress), and confirmed such an intuitive discussion to be correct, at least in one particular case, by considering a vertically propagating wave packet. On the basis of the foregoing discussion on transient waves, the fact that the so-called C-D theorem concerns a final state in which no further change occurs has been illustrated. At the same time, by including the small damping due to Newtonian cooling and Rayleigh friction, we have illustrated in a compact form the fact that the acceleration of the mean zonal flow is caused by a forcing due to wave transience and one due to wave dissipation. Particularly, when the dissipation of the zonal mean flow itself can be ignored, the induced mean zonal momentum is equal to E/C plus the deposited part during the propagation through the wave dissipation (cf. GRIMSHAW, 1975). In Section 3, we have discussed a steady (Eulerian-mean) flow in the presence of a dissipating planetary wave. For the case where the Newtonian cooling rate and the basic westerly wind are both constant, it is shown that depending on whether or not the effect of density stratification dominates the damping effect, the distribution of the induced easterly flow is quite different (cf. DUNKERTON,1979). When the wave amplitude increases upward in spite of dissipation, the induced easterly wind becomes large with increasing height, and hence the northern region becomes warmer (Fig. 3a,b), while when the amplitude decreases, the northern region becomes cooler (Fig. 4a,b). Thus, the distribution of the damping coefficient and the basic zonal wind, both of which determine the transmissivity of planetary waves, are very important factors for the purpose of discussing how planetary waves can contribute to the flow structure in a statistically steady state of the atmosphere. To be more convincing, we have shown the result (Fig. 6a,b) for the case where the Newtonian cooling rate and the basic westerly wind are both dependent on height (Fig. 5a,b) and the wave with longitudinal wave number 1 is assumed. According to this result, near z = 70 km, the induced easterly wind becomes 30 m/sec in the mid-latitudinal region and the temperature in the northern region increases about 7~ relative to that in the southern region (cf. MATSUNO, 1976). This suggests that the contribution of planetary waves to the structure in a statistically steady state of the upper atmosphere such as the higher temperature observed in the winter polar region (cfl HOLTON, 1975) may be large.

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Acceleration of Mean Zonal Flows by Planetary Waves

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Finally, we have briefly discussed the Lagrangian-mean motion induced by planetary waves. In case of a stationary conservative wave or a slowly varying wave packet, the Lagrangian-mean meridional circulation does not occur, to within certain approximations. Especially, this result for a stationary wave is part of which is involved in the C-D theorem from a Lagrangian-mean dynamical viewpoint (cf. ANDREWS and Mr 1978b). As to the Lagrangian-mean zonal flow, it has been shown that UL has a jet-like structure partly because of the Stokes drift and partly because of the Eulerian-mean zonal flow. We have also shown the Lagrangian-mean meridional circulation induced by stationary, dissipating waves under the assumption that the Newtonian cooling rate and the basic westerly wind are constant. If the wave amplitude decreases upward because of the dominance of damping effect, the Lagrangian-mean meridional circulation is associated with upward motion to the north and downward motion to the south as well as the Eulerian-mean one (Fig. 8a,b). If the wave amplitude increases because of the dominant effect of density stratification, the Lagrangian-mean meridional circulation is associated with upward motion to the south and downward motion to the north, and is opposite to the Eulerian-mean one (Fig. 7a,b). In addition, from the result by URYU and TAKAHASn~(1979), we have noted that the Lagrangianmean meridionaI circulation changes remarkably, depending on the speed of the basic westerly wind: particularly, it is split into 3 cells in the meridional direction when the speed of the basic zonal wind exceeds a certain value. When the Newtonian cooling rate and the basic westerly wind are both dependent on height, the Lagrangian-mean meridional circulation induced by the wave with longitudinal wave number 1 is split into two parts in the vertical (Fig. 9a). The lower circulation is associated with upward (downward) motion to the south (north) and opposite to the Eulerian-mean one. However, the upper circulation is opposite to the lower one, and can be regarded as a result that the central circulation of the 3-cell structure spreads over the channel (URYU and TAKAHASm, 1979). In the case of a growing baroclinic wave, the Lagrangian-mean motion shows convergent flow toward the mid-latitude, with slow upward motion near the southern wall and downward motion near the northern wall (URYU, 1979). These vertical motions are thermally direct. This Lagrangian-mean motion is quite different from the Eulerian-mean picture such as the so-called 3-cell circulation in the troposphere. Further, the convergence of air parcels is one of the most interesting features of the Lagrangian-mean motion induced by a growing wave (cf. ANDREWS and MCINTYRE, 1978b).

Acknowledgements The author wishes to express his hearty thanks to Dr. M. E. Mclntyre, University of Cambridge, for his critical reading of the manuscript and for many valuable comments and suggestions. The author is deeply indebted to Prof. T. Matsuno, who always helpfully criticizes the author's work.

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MCINTYRE, M. E. (1973), Mean motions and impulse of a guided internal gravity wave packet, J. Fluid Mech. 60, 801-811. MCINTvRE, M. E. (1979a), Paper in this issue. MClNTVRE, M. E. (1979b), Towards a Lagrangian-mean description of stratospheric circulations and chemical transports, Phil. Trans. Roy. Soc. London, A (middle atmosphere issue) (to appear). NAKAMURA,K. (1979), A generalization of 'Eliassen-Palm' relation, J. Meteor. Soc. Japan 56, 215-226. RIEHL, H. and FULTZ,D. (1957), Jet stream and long waves in a steady rotating-dishpan experiment: structure of the circulation, Quart. J. Roy. Meteor. Soc. 83, 215-231. URYU, M. (1973), On the transport of energy and momentum in stationary waves in a rotating stratified fluid, J. Meteor. Soc. Japan 51, 86-92. URYU, M. (1974a), Induction and transmission of mean zonal flow by quasi-geostrophic disturbances, J. Meteor. Soc. Japan 52, 341-364. URYIJ, M. (1974b), Mean zonal flows induced by a vertically propagating Rossby wave packet, J. Meteor. Soc. Japan 52, 5481-490. URvu, M. (1979), Lagrangian mean motion induced by a growing baroclinic wave, J. Meteor. Soc. Japan 56, 1-20. URYO, M. and TAKAHASHI,M. (1979), The Eulerian- and Lagrangian-mean flows induced by stationary, dissipating planetary waves: parts L 11, J. Meteor. Soc. Japan (to be submitted). (Received 15th June 1979)