Topics on System Analysis and Integrated Water Resources Management

Topics on System Analysis and Integrated Water Resource Management

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Topics on System Analysis and Integrated Water Resource Management

Edited by Andrea Castelletti and Rodolfo Soncini Sessa

A MSTERDAM • B OSTON • H EIDELBERG • L ONDON • N EW YORK • OXFORD PARIS • S AN D IEGO • S AN F RANCISCO • S INGAPORE • S YDNEY • T OKYO

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA First edition 2007 Copyright © 2007, Elsevier Ltd. All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: [email protected]. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication Data A catalogue record for this book is available from the Library of Congress ISBN–13: 978-0-0080-44967-8 ISBN–10: 0-080-44967-0 For information on all Elsevier publications visit our web site at http://books.elsevier.com Printed and bound in Great Britain 07 08 09 10

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Contents

Preface

vii

I.

Introduction

1

1.

A Participatory and Integrated Planning Procedure for Decision Making in Water Resource Systems A. Castelletti and R. Soncini-Sessa

3

II.

Modelling

25

2.

The Data-Based Mechanistic Approach in Hydrological Modelling P.C. Young, A. Castelletti and F. Pianosi

27

Bayesian Networks as a Participatory Modelling Tool for Groundwater Protection H.J. Henriksen, P. Rasmussen, G. Brandt, D. von Bulow and F.V. Jensen

49

Exploring Water Conservation Behaviour through Participatory Agent-Based Modelling A. Rixon, M. Moglia and S. Burn

73

Managing and MODSS

97

Decision Support Systems for Integrated Water Resources Management with an Application to the Nile Basin A.P. Georgakakos

99

3.

4.

III. 5.

v

vi 6.

Water Reservoirs Management under Uncertainty by Approximating Networks and Learning from Data M. Baglietto, C. Cervellera, M. Sanguineti and R. Zoppoli 117

7.

Optimising Irrigation Management at the Plot Scale to Participate at the Regional Scale Water Resource Management J.-E. Bergez, F. Garcia, D. Leenhardt and L. Maton 141

8.

Multi-Objective Optimization of Water Distribution System Design under Uncertain Demand and Pipe Roughness A.V. Babayan, D.A. Savic and G.A. Walters 161

IV.

Planning and MODSS

173

9.

Sustainable Floodplain Management and Participatory Planning in the Red River Basin, Canada S.P. Simonovic 175

10.

Negotiation Support System for Resolution of Disputes over International Water Resources L. Kronaveter and U. Shamir 189

11.

Workflow Oriented Participatory Decision Support for Integrated River Basin Planning J. Dietrich, A.H. Schumann and A.V. Lotov 207

12.

Comprehensive Testing and Application of the PIP Procedure: the Verbano Project Case Study A. Castelletti, F. Cellina, R. Soncini-Sessa and E. Weber 223

13.

Social Science Contributions to the Participatory Planning of Water Systems – Results from Swiss Case Studies B. Junker and M. Buchecker 243

14.

Multi-Criterion Decision Making Approach to Assess the Performance of Reconstructed Watersheds A. Elshorbagy, S.L. Barbour and C. Qualizza 257

V. Future Directions 15.

271

Outstanding Research Issues in Integration and Participation for Water Resource Planning and Management A.J. Jakeman, R.A. Letcher, J.P. Norton et al. 273 Subject Index

291

Preface

The Integrated Water Resources Management (IWRM) paradigm has entered the lexicon of water managers and stakeholders as the mainstream approach to the planning and management of water resource systems. It is the central pillar of the EU Water Framework Directive, which is widely accepted as the most significant piece of water legislation produced in the past 20 years, as well as the inspiring principle of all the water related activities sponsored by UNESCO in developing countries. However, despite huge inputs of financial resources, implementation of full IWRM remains elusive in most of the cases, we argue, owing to the lack of a systematic approach and the inadequacy of tools and techniques to address the intrinsically complex nature of water resource systems. With the purpose of dealing with the recent progress made in overcoming the operational difficulties posed by the IWRM paradigm, a Workshop on Modelling and Control for Planning and Managing Water Systems sponsored by the IFAC Technical Committee 8.3 on the Modelling and Control of Environmental Systems, was held at the Istituto Veneto di Scienze Lettere ed Arti, Venice, Italy from September 29th – October 1st, 2004. The aim of the Workshop was twofold: first, to present the state of the art of modelling and control techniques applied to water resource systems; and, second, to foster an integrated and participatory approach. In order to emphasize the role of System Analysis and Control Theory methodologies as different stages of an integrated, multi-objective approach to planning and management, within a participatory decision-making prospective, the themes of the three days were: 1st day: Modelling: participatory modelling techniques. 2nd day: Managing: Decision Support Systems and algorithms for policy design. 3rd day: Planning: Decision Support Systems and tools for participatory decision-making and negotiations. The unifying idea of the Workshop has been clarified since the call for papers in a position paper made available on the Workshop web-site. Each day/theme was introduced by an invited paper, presented over approximately 90 minutes, and was organized into two vii

viii sessions, involving two papers each, with a total duration of approximately 120 minutes. The other accepted papers were presented through an afternoon poster session followed by a 90-minute discussion, chaired by the invited speaker, which concluded the day. The unusual scheduling of the Workshop was conceived with the aim of reconciling the need, recognized in all conferences, to have a greater time dedicated to each paper, in order to understand and discuss it effectively, with the equally important objective of being able to take advantage of many contributions in order to form a meaningful picture of the variety of research in progress. This volume is an outgrowth of the Workshop and contains selected papers among those orally presented. All the contributions to the Workshop were carefully reviewed by a board of international experts and those collected in this volume have been further revised and improved on the basis of the fruitful discussion that followed the presentation. We believe that the contributors have done invaluable work which have resulted in something more than a mere collection of papers: a monograph with many authors that will facilitate the increased appropriate application of the IWRM template by practitioners, decisionmakers and scientists. Reflecting the framework of the Workshop, the book is composed of three parts, Modelling, Managing and MODSS and Planning and MODSS, plus an opening and a closing chapter. The introductory chapter is a post-Workshop revision of the position paper that enunciates the principles which drove the Workshop. It formalizes the IWRM paradigm in a nine-step decision-making procedure that provides the reader with a conceptual map of the book and shows the value of its subject matter. Each part is opened by an invited contribution from an outstanding scientist in the field: Prof. Peter Young from Lancaster University, UK, Prof. Aris Georgakakos from GeorgiaTech, USA, and Prof. Slobodan Simonovic from Western Ontario University, Canada. Present and future research directions on the border between System Analysis and IWRM are surveyed in the chapter that closes the volume, where a pool of scientists and experts, coordinated by Prof. Anthony Jakeman from the Australian National University, suggests a research agenda to achieve sustainable (environmental, economic and social) outcomes in the implementation of the IWRM paradigm. We acknowledge with much gratitude the support of the International Federation of Automatic Control and the Istituto Veneto di Scienze Lettere ed Arti, of all the contributors to this volume as well as of all the conference participants, and last but not least, of our colleagues Daniele de Rigo and Enrico Weber for their essential role in the organization of the Workshop. Milano, April 30th 2006 Andrea Castelletti & Rodolfo Soncini-Sessa

Part I

Introduction

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CHAPTER 1

A Participatory and Integrated Planning Procedure for Decision Making in Water Resource Systems Andrea Castelletti and Rodolfo Soncini-Sessa Dipartimento di Elettronica e Informazione Politecnico di Milano, Milano, Italy

1.1 Introduction In many parts of the world, water demand is increasing, while at the same time availability and quality of water resources are decreasing, mainly due to human activities, in connection with the growing world population, ongoing urbanization, industrialization and the intensification of agriculture. This development is often associated with general reductions in environmental quality and endangers sustainable development. An integrated approach is required to identify and analyse such unfavourable and undesired developments and to allow sustainable systems to be designed that integrate human society with its natural environment for the benefit of both. It is generally agreed (Bonell and Askew, 2000) that Integrated Water Resources Management (IWRM, see GWP, 2000 and 2003) plays a crucial role in this context and that a participatory approach would help to better control and accelerate the integration, to make the decision-making process more transparent and comparable across various river basins and scales, and to increase confidence in an integrated model-based planning process. Notwithstanding the popularity raised by the IWRM concept in the last decade, the applications to real world cases of the paradigm mentioned in the literature are still a few (see for instance Tortajada et al., 2004), thus feeding a growing scepticism (Biswas, 2004) towards the real potential of this attractive approach. The development of proper legislation and policy is a key-issue to disseminate integration and participation into the water management practice (Wolf, 2002). At the European level the IWRM paradigm has been adopted by the Water Framework Directive (WFD – Directive/2000/60/EC (European Commission, 2000)) that came into force in December 2000. The directive introduces a set of requirements to be fulfilled in order to reach inland and coastal water ‘good status’ by 2015, and sets out a detailed framework for the 3

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improved planning and management of water, including the development of River Basin Management Plans (RBMP) within 2009 (Art. 13). The Guidance Document for the Planning Process (GD11, issued by the European Commission, 2003a) explains (pag. 5) how the term ‘integration’ should be intended in the implementation of such plans. Integration must concern many aspects, among which are particularly relevant: - Integration of environmental objectives. - Integration of all water uses, functions and values into a common policy framework. - Integration of all significant management and ecological aspects [. . .] including those which are beyond the scope of WFD, such as flood protection and prevention. - Integration of stakeholders in decision making, by promoting transparency and information to the public and by [. . .] involving stakeholders in the development of RBMP. The Guidance Document recognizes that planning is a process and requires to provide procedural guidance on the production and development of River Basin Management Plans supported by appropriate toolboxes, that should help to identify the possible tradeoffs among quantifiable objectives so that further debates and analysis can be more informed. Moreover the toolboxes must support planning as a systematic, integrative and iterative process. According to these requirements a general procedure for the Participatory and Integrated Planning (PIP) has been developed (Soncini-Sessa et al., 2007a) and will be here presented. The procedure has been conceived and implemented by formalizing the methodologies developed and experienced in the Verbano Project1 (Soncini-Sessa et al., 2007b and Ch. 12 of this book) and farther tested, completed and validated on other projects (see for instance Castelletti and Soncini-Sessa, 2006b). A Multi Objective Decision Support System (MODSS) has been developed to support each phase of the procedure (Soncini-Sessa et al., 1999). The IWRM paradigm was selected as the conceptual basis for the development of the PIP procedure, but the procedure complies also the rules of the DPSIR scheme adopted by the European Environment Agency (EEA, 1999, see also OECD, 1994 and UNCSD, 1996). Therefore this scheme will be briefly introduced in the following paragraph. Then Section 3 will be devoted to the description of the PIP procedure phase by phase. For each phase, the methodology to be followed in that phase is presented. Finally, some considerations are devoted to the development of ICT tools for supporting the implementation of the procedure. The decision-making process at the management level is considered in the last section. 1.2 Framing the decision-making problem The evolution of a natural system subject to anthropic pressure is well described by the framework DPSIR (Driving forces – Pressures – State – Impact – Responses), which is depicted in Fig. 1.1: the Drivers generate a Pressure upon the system, thus altering its 1 UE - INTERREG II.

A Participatory and Integrated Planning Procedure

5

1 Responses

Drivers

2

3 Pressures

4

State Impacts

Fig. 1.1. The DPSIR framework.

State. This variation produces Impacts on society, which reacts by devising and implementing Responses, which can be directed at the Drivers, as well as the Pressures, the State or the Impacts themselves. An example can be useful to clarify the framework: consider an enchanting lake, surrounded by fields, forests, a fishing village and a few small hotels. Among the Drivers are the agricultural, industrial and domestic practices that produce a flow (Pressure) of nitrogenous substances that reach the lake, after scouring the agricultural land, or through direct or indirect discharge from the sewerage system. It follows that there is an increase in the trophic level of the lake, which induces algal blooms, anoxic conditions and fish pestilence, and so, a variation in the State of the lake. In this way two Impacts are produced: a reduction in fishing activity and a loss of the lake’s appeal to tourists. In order to respond to the fishermen’s and hotel-keeper’s discontent, the Environmental Agency (EA) must design an intervention (Response). It can choose among different forms: issue a regulation for the use of nitrogenous fertilizers in agriculture (arrow 1 in Fig. 1.1), create a stage for the removal of phosphorous in the treatment plant that purifies the sewage prior to discharge (2), collect the algae when necessary or inject oxygen at a certain depth to prevent lake waters from becoming anoxic (3), or simply introduce a monetary compensation (4) for the damages. Generally, the EA is not limited to choosing only one of these interventions, each of which can be realized in different forms and degrees: it can also select a combination of them, in an integrated and coordinated package, that we will call alternative2 . 2 In the literature (see for example, Raiffa et al., 2002) there is a distinction between the alternatives that a party (stakeholder(s) and/or decision-maker(s)) can pursue alone (i.e. without reaching a negotiated agreement), and those that are subject to negotiations, because they contain actions that can be carried out only after an

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The choice of an alternative requires a decision-making procedure, which should be integrated (i.e., it should consider the system as a whole) and participatory (i.e., stakeholders take part in the decision-making process). 1.2.1 Participation The top down approach of the standard planning approach needs to be reversed, proposing and launching a participatory process (Renn et al., 1993; Renn, 1995; Budge, 1996; Delli Priscoli, 2004), that is ‘bottom up’ and based on the management of participation: a process of participation that begins from the proposal of the planning project and continues with the choice of the alternative to be implemented, right through to the monitoring of the effects after the implementation. This process should not be limited to providing the stakeholders with information (Informative Participation), nor to just asking them for information (Consultation), it should also involve the Stakeholders in the design and evaluation of the alternatives (Co-designing) and, ideally, even in the final choice (Co-deciding)3 (Mostert, 2003 and Hare et al., 2003). Such a kind of involvement is of crucial importance, not only when there is more than one decision-maker (DM) – as would be the case if the lake from the example and its inlet were to define the border between two countries – but also in presence of a single DM that is due to make the final decision. Even in that case, involving stakeholders in the negotiations of the Response might result in more public acceptance of the decisions, less litigation, fewer delays and generally better implementation. Indeed, in this way, a process of social learning is created, in which the stakeholders become aware of the problem, of the alternatives, and of the viewpoints of others; they take responsibility and together they develop the alternative to be carried out (Renn, 1995). The goal of the decision-making process is to reach an agreement that is acceptable to all the stakeholders, to which they remain committed, and which is actually implemented. Only the last, decisive phase of the procedure, the choice of the alternative that is to be implemented, is in most cases the reserved responsibility of the DM (or DMs) that has (have) the institutional power to make the choice. 1.3 The PIP procedure In Fig. 1.2, the flow diagram of the PIP procedure4 that we are going to describe is shown. However, before detailing the phases that compose it, a couple of comments is mandatory. agreement has been reached. The term ‘alternative’ is reserved for the first, while the term ‘option’ is used for the second. However in this chapter and in Ch. 12 we will use the term ‘alternative’ to designate both of them. In some contexts instead of ‘alternative’ the term ‘program of measures’ is used. 3 With surprising speed legislation has already adapted to this need: the Århus Convention, signed in 1998 and in force since 2001, recognises citizens’ rights to “have access to information and be enabled to participate in the decision-making process with regard to the environment”, based on the principle that only participation can make sustainable development possible. In escort to that convention, the Directive 2003/35/EC (European Commission, 2003b) was issued by the European Parliament which establishes that “the public concerned shall be given early and effective opportunities to participate in the environmental decision making procedures” right from the initial phases, so that they have an effective possibility to influence the choices. The WFD anticipated this position. 4 Even though it was devised autonomously, it can be interpreted as a variation of the PROACT scheme proposed by Hammond et al. (1999), that has been suitably modified to take into account that in the case we

A Participatory and Integrated Planning Procedure

0. Reconnaissance

1. Defining Actions

2. Defining Criteria and Indicators

3. Identifying the Model CONCEPTUALIZATION

4. Designing Alternatives

8. Mitigation and Compensation

5. Estimating Effects

6. Evaluation

7. Comparison NO

Consent? YES

9. Final decision

Best compromise alternative

Fig. 1.2. The phases of the PIP procedure.

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We are talking about a procedure, not an algorithm. This means the human beings are deeply involved in it and decisions are taken at each phase on the basis of subjective judgments and compromises among the possible, often mutually exclusive, course of actions (e.g. what data are trustable, which model to adopt, what are the relevant interests to consider in designing the alternatives). The PIP procedure is a recursive procedure, in the sense that often in the development of a phase the improved understanding of the system makes apparent that something in a previous phase has to be modified. Recursions may happen in many points, however only one case will be explicitly described in this paper (see Phase 8). The PIP procedure is a methodological approach, and as such it must mainly establish and explain what has to be done in each phase, not how to do it. Many methods and techniques are often available to fulfil the goal of each phase, and a choice has to be done among them on the basis of the specific features of the problem at hand. 1.3.1 Phase 0 – Reconnaissance A conscious and participatory choice ought to begin from the acknowledgement of the problem to be tackled. For this reason the activities within this phase concentrate on defining the Goal of the planning project, the (spatial and temporal) boundaries of the system being considered5 , the normative and planning context in which the procedure operates, the data available, and the information that needs to be collected. One must start off from the identification of the stakeholders involved and their needs, expectations, fears and perceptions, in a word, their interests6 . Then the PIP procedure has to be explained to and accepted by, or, if necessary, negotiated among all the parties (stakeholders and DM(s)). At this point it becomes possible to define the Goal that the planning project must pursue. It is derived from the DM’s strategic goals, from the stakeholders’ interests and from the regulatory and planning context. It must always include the environmental objectives, e.g. good water status and sustainable uses, as required by the WFD (art. 4, see European Commission, 2000). Sometimes, it could be useful to translate the goal for each stakeholder into a vision that visualizes, with words, or better still, with a picture, the condition that the project aims for. The choice of a good vision is important when the stakeholders are not very motivated to take part in the decision-making process or resistant, or unable to express their own goals. An example of vision for a river water quality restoration project is shown in Fig. 1.3. An extensive knowledge of the system is the fundamental support to all these activities and it is acquired by: analysing the regulatory and planning context of the planning project; collecting information and data available; identifying the missing information; and finally, filling the information gaps by conducting hydrological, economic and social surveys. The actors should share all the available information, agree upon its validity (this is crucial!) and the potential need for further investigations. In other words, when necessary, even the validity and availability of the information must be negotiated. examine here the decision-making process is targeted at consensus building and actions include management, i.e. recursive decisions. 5 These two points are often referred to as scoping. 6 “It is crucial for the legitimacy of a planning process to start dialogue as early as possible in the phase of problem definition” (European Commission, 2003a).

A Participatory and Integrated Planning Procedure

9

Fig. 1.3. The vision for a river water quality restoration project (from Nardini, 2005).

1.3.2 Phase 1 – Defining Actions In this phase, the options for intervention that are supposed to achieve the project Goal must be identified, bearing in mind the interests of the different stakeholders. This is no simple operation because the opinions can be very discordant. For example, for some the obvious solution for the well-known flooding (‘high water’) problem in Venice would be the construction of the MOSE7 at the mouths of the lagoon, for others it is the construction of gate-ships8 , which are less complicated to construct and which would be more adaptable to the bradyseism of the lagoon bottom, while still others say that the only sensible option would be the reduction in the green house gas emissions that are responsible for the eustatic sea in front of the lagoon that are held to be the cause of the continuing worsening of the phenomenon. From this initial, decidedly disorganized, collection of ideas, which are in part silly, in part gifted with incredible wisdom, good ones always emerge. It may seem strange to begin with brain storming, however it is essential to promote creative decision-making that considers more than just a set of interventions given a priori, and is able to open new perspectives and discover unexpected alternatives. If an intervention is really useful it will emerge in the following phases, and if all the stakeholders’ suggestions are considered and processed they are more prone to collaborate since they feel they are being “taken 7 A system of submerged hollow steel gates, hinged at the bottom of the lagoon and installed at each of the lagoon’s three openings to the Adriatic sea. When ‘high water’ is foreseen, they can be raised by pumping compressed air into them and creating a sea barrier. 8 Two ships, whose length is about half the width of the mouth of the lagoon, which are hinged to the two offshore piers that mark the mouth’s boundaries. The free end of each ship is equipped with a propeller that allows them to position themselves across the mouth opening. When the ships are in this position they flood their hulls that make up their bottom so that they sink, creating an insurmountable barrier for the sea. When the high water event is over, the mouth of the lagoon is reopened by reversing the operation. The major advantage with respect to the MOSE is that the construction and the maintenance are done on dry land and the mouth of the lagoon would need to be modified only slightly.

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seriously” (WFD, Annex VII point A9, see European Commission, 2000). Moreover, how can there be a participatory process if one does not stop to listen carefully to the ideas and proposals of the parties? This first, creative phase must necessarily be followed by a phase of ‘decanting’, in which the distinction is made between what can be decided and what cannot, and thus, the effective decision space becomes apparent. It is in fact useless to debate passionately about aspects that cannot be decided in the Project. But note carefully that this is not the time to discriminate the useful interventions from the useless ones, or the sensible ones from the less sensible. This will be a task for the next phases. In this way, one obtains a list of the interventions ‘that can be decided upon’ in the context of the planning project. Each intervention is finally broken down into one or more (meta)-actions, i.e. into elementary interventions that can be fully and easily defined by specifying the values of their attributes, that is by specifying who is doing what, how and when. In this way a meta-action is transformed in an instantiated action. Technically, this transformation is carried out by assigning values to the parameters and/or the functions that describe the attributes of the meta-action. The specification of these values is a matter for a future phase (Phase 4: Designing Alternative), but their feasibility sets have to be defined in this phase, thus fixing the meta-actions to be considered. The instantiated actions are the ‘building blocks’ from which the alternatives will be constructed later. In the following, as we have done so far, we will use the term ‘action’ to denote both the meta-actions and the instantiated actions. The actual meaning will be clear from the context.

1.3.3 Phase 2 – Defining Criteria and Indicators To evaluate and compare the effects of the alternatives upon the system, it is necessary to define, by interacting with the stakeholders, a set of evaluation criteria that reflect the features of the problem and the values underlaying the judgments expressed by the stakeholders. The criteria do not have to pertain only to the project Goal, but to all the positive and negative effects the stakeholders hope for or fear: in other words they must express their interests9 . In particular, the criteria for sustainable development will be proposed by the Agencies and by the Environmental Associations which must always be included in the stakeholder group. Not every evaluation criterion is necessarily expressed in an operative way, i.e., it may not spontaneously define a procedure that allows ascertaining how much a given alternative satisfies that criterion. This is why an index is associated to each criterion, that is a procedure with which to associate the criteria with a value that expresses the degree to which it is satisfied (see Soncini-Sessa et al., 2003). This is done through the identification of relationships between the evaluation criterion and the variables (e.g. lake level, etc.) that describe the system condition. In practice, one proceeds by first splitting the evaluation criterion into lower level criteria and in turn, splitting those into even lower level criteria, until it is possible to associate each one of the criteria at the 9 Objectives are the same as interest: unfortunately the negotiation theorists and the decision-making theorists have not agreed on a common term. The first talk about ‘interests’ and the second about ‘criteria and objectives’; but they mean the same thing. We will adopt the jargon of the second group.

A Participatory and Integrated Planning Procedure

11

lowest level (leaf criteria) with an indicator, i.e. a function of the trajectories of the variables describing the system condition. In this way a hierarchy of criteria (evaluation hierarchy) is obtained for each evaluation criterion. The definition of a criterion and of its hierarchy ought to encompass either thresholds or a stakeholder’s wish (leitbild, see Egger et al., 2003), which is often related to the performance level (s)he demands. It is necessary to dedicate a great deal of time and attention to interactions with the stakeholders and to studying their points of view, because it is essential that each stakeholder sees that his/her interests are expressed in at least one of the indicators. If this does not happen, negotiations in Phase 7 will inevitably fail. In the next phase we will see that very often the system is affected by random inputs (either stochastic or uncertain). It follows that also the values assumed by the indicators are not generally deterministic. When this occurs, it is necessary to take account of the riskaversion that the DMs and stakeholders may have. This can be expressed through the classical approach of utility functions, proposed by Keeney and Raiffa (1976), but more often it is translated through criteria10 from which the most frequently adopted are the Laplace criteria (expected value) and the Wald criteria (worst case) (French, 1988). Like all the phases of the PIP procedure this one must also be participatory: the evaluation criteria should be forthcoming from the stakeholders and the definition of the indicators must have their contribution and approval. This last phase is however often very technical and so, as for the technical phases in the following phases, the stakeholders can be supported by experts.

1.3.4 Phase 3 – Identifying the Model In order to quantify the effects that the different alternatives would produce on the different indicators if they were to be implemented, it is necessary to provide a model that describes the cause–effect relationships within the system. The choice of the type of model and of the degree of detail with which to describe the phenomena, is tightly dependents upon both the indicators defined in Phase 2 and the actions considered. In our example, the regulation could be devised by describing the system through a set of algebraic equations, while the project of the artificial ventilation might require a description of the lake through partial differential equations. However, it is not mandatory that the model must be mathematical, it could be for instance an expert, who is able to describe the effects that will be induced by a given alternative on the basis of his experience (see for instance the MÖLL Project (Muhar et al., 2000 and Jungwirth et al., 2000). It may also occur that the physical and/or socio-economical relations that underly some of the components of the considered system are poorly known (i.e., the knowledge on the system is unstructured or limited) or it is comparatively expensive to obtain raw data to characterize them better. In such cases a Bayesian Network (Castelletti and Soncini-Sessa, 2006a, and references therein), i.e. a probabilistic description of the cause–effect relationship linking the variables within the system can be a well-suited solution (Castelletti 10 Take care not to confuse this meaning of the term criteria (stakeholders’ attitude towards risk), with the one previously introduced (judgement category).

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and Soncini-Sessa, 2006b). However in the majority of cases the model is more or less mathematically formalized and therefore it has to be identified, i.e. its structure has to be fixed (conceptualisation) and the values of the parameters that appear in it estimated (calibration). Sometimes more than one model may be adopted, due to the constraints posed by the power of the computer at hand, i.e., a more simple model for designing the alternatives (screening model, see Phase 4) and one for estimating the effects (evaluation model, see Phase 5). When this is the case a good practice would be that the first is a parsimonious version of the second (for an example see Chappell et al., 2001). Alternatively, complexity reduction techniques can be adopted to derive a easily computable version of the evaluation model (Hooijmeijer et al., 1998). The model’s input variables must include the parameters that quantify the attributes of the actions (e.g. the maximum nitrogen supply allowed in agricultural practices and the nitrogen removal efficiency of the treatment plant) as well as all the variables that allow the future conditions of the system to be described (e.g. the precipitation in the catchment area and the users’ water demand). The choice of values to attribute to the former constitutes the matter of the planning, while the values assigned to the latter describe the context within which the alternatives are evaluated and so collectively they are called a scenario11 . Both alternatives and scenarios have to be quantitatively specified before the model can be run. Note that there can be more than one scenario: in the lake example we might be interested in evaluating what would occur in a ‘high’ or in a ‘low’ rainfall scenario. Moreover, the scenario is not compulsory deterministic: very often it can be random. The scenario(s) may be chosen by experts or it (they) can be obtained by running models, if they are available, that describe the processes that produce the driving forces. In the lake example the future scenario of rainfall can be generated by a climate change model, while the future scenario of agricultural practices can be suggested by an expert. When all the processes are stationary, the historic scenario, i.e. the trajectories registered in the past, is often adopted for the reasons that will become apparent in Phase 5. In any case the time horizon of the scenario should be sufficiently long to capture all the types of the significant events the system may face. It is a common practice to adopt different scenarios for designing the alternatives (design scenario) and for estimating the effects (evaluation scenario, sometimes also called baseline scenario), which are generally fixed in the corresponding phases. To facilitate a social learning process it is important that the stakeholders ideally go through the same thinking process and be exposed to the same information and arguments as the analyst even during the modelling phase. For this reason, the implicit assumptions of the models should be made explicit and the modelling activity supported by a MODSS that must be flexible enough to identify models through a participatory process (Loucks, 1989). Only in that way can the stakeholders share a common interpretation of the system behaviour (model), which is necessary for them to be able to trust the effects that are estimated with the model. Agreeing on the same model does not prevent them from 11 Dictionaries give the term scenario the following definition: ‘a possible set of future events’. Brought into our context the term lends itself to three different possible meanings: 1. synonymous to alternative (e.g. businessas-usual scenario means Zero Alternative); 2. the set of effects that an alternative produces; 3. the time series of input variables that are not controlled by the DM. We will strictly adhere to this last meaning.

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having different perceptions (indicators) of these effects. The set of phases 1–3 constitutes the conceptualization of the planning problem.

1.3.5 Phase 4 – Designing the Alternatives It is very often the case that the alternatives considered during a real design process are only those suggested by the stakeholders and the manager’s experience. It is suitable to start off from those, but we think that limiting to them could be a mistake. More correctly, remembering that an alternative is an integrated package of actions, all the alternatives that can be obtained by combining the actions identified in Phase 1 in all possible ways should be considered. Often the number of alternatives that follows is so high that it would be impossible to examine them all in the following phases and so it is necessary to select only the ‘most interesting’ ones. However, these must be chosen still following the stakeholders’ criteria, that were identified in Phase 2, rather than the analyst’s preferences. In more complicated projects, where a higher level of mathematical formalization is required, the identification of the ‘most interesting’ alternatives has to be made according to the principle of Pareto optimality: all the dominated alternatives are removed. These latter are those alternatives that improve the satisfaction of a (group of) stakeholder(s), without worsening the satisfaction of the others; these alternatives would never be chosen by any stakeholder, indeed. The remaining alternatives are the efficient alternatives constituting the Pareto frontier. Figure 1.4 gives a qualitative description of it in the event that, as in our example, the indicators considered are the average annual catch and the costs for a new stage in the wastewater treatment plant. The identification of the Pareto frontier is carried out by defining and solving a Design Problem, which can either be regarded as a Mathematical Programming Problem cost

performances of dominated alternatives

average annual catch Fig. 1.4. A qualitative representation of the Pareto frontier in the event that, as in our example, the indicators considered are the average annual catch and the wastewater treatment plant cost.

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(for an example see Whittington and Guariso, 1983) or an Optimal Control Problem (see for instance Georgakakos and Yao, 1993; Kelman et al., 1990 and Soncini-Sessa et al., 2001) depending on whether the actions making up the alternative are taken una tantum (like the decision of building the wastewater treatment plant) or are recursive (like the algae removal or the air insufflation). The alternatives obtained by solving the Design Problem are efficient with respect to objectives, accordingly called design objectives, that are defined on a design horizon, given the design scenario and taking into account only a subset of the evaluation indicators: the design indicators. This simplification is introduced when considering all the evaluation indicators would make the Design Problem unsolvable in acceptable computation times; it does not excessively polarize the result if the design indicators were carefully chosen, since in Phases 5 and 6 the alternatives will be evaluated with respect to the complete set of indicators. The characteristics of the system appear in the Design Problem as constraints, while other elements that define the design scenario (e.g. user demands, foodstuff prices) contribute, along with the structural and normative actions, to determine the value of parameters that appear in the constraints and in the objectives of the Problem. Solving the Problem through an appropriate algorithm provides the set of alternatives that will be examined in successive phases. To these the Zero Alternative (A0) is always added, that is, the alternative that assumes that nothing is done and everything remains the way it is (business-asusual).

1.3.6 Phase 5 – Estimating Effects Once the alternatives are identified, the effects that each of them produces must be evaluated: in other words, it is necessary to compute the values that the indicators takes on as a result of each of the alternatives being implemented. When the system is not dynamical, the evaluation is straightforward. When the system is dynamical this estimation requires that each alternative be simulated over a time horizon (evaluation horizon) long enough to make extreme events (droughts or floods) likely to occur, in order to avoid the risk of estimating the effects in ‘average conditions’ only. In both cases it is necessary to feed the model with an appropriate input: the actions of the alternative considered and one or more evaluation scenarios. The alternatives will be compared to single out the ‘best’ one on the basis of the effects estimated in correspondence to one of these scenarios, the most probable for example; the effects estimated with the others will be useful for evaluating what would happen if the scenario that was considered didn’t occur and develop a precautionary viewpoint. The choice of the scenario(s) to adopt can be critical, and the parties must agree, otherwise, the following phases would fail. The adoption of a historic scenario (i.e. of a situation that was historically recorded) has an advantage in that it allows the comparison between what happened and what would have happened if the alternative had been implemented at the beginning of the historic horizon being considered. This information has a heightened significance for the parties because it provides a more immediate perception of the effects when they have, as they often do, a direct memory of those events. If the historic horizon is too short, artificially generated scenarios can be used, provided that they are as probable as the historic one.

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By doing so the estimate of the effects is statistically more reliable, but the psychological significance is lost. Both of these ways to proceed are meaningful only when one can reasonably assume that the processes that generate the scenario (e.g. the meteorological system and land use) remain unchanged into the future. If not, the scenarios have to be generated with models that describe the expected changes. At the end of this phase the values that have been obtained for the indicators are organized in a matrix – called Matrix of the effects – whose columns correspond to the alternatives and the rows to the indicators. This matrix is the base for the cost effectiveness analysis required by WFD.

1.3.7 Phase 6 – Evaluation An indicator measures the effect produced by an alternative on a particular leaf criterion in physical units. Nevertheless, the ‘value’ that the stakeholders attribute to an alternative, in other words the satisfaction that they get from it, is not always directly proportional to the value assumed by the indicator. In the lake example, the ‘value’ that the fishermen attribute to the catch grows very rapidly for low catch yield, but very slowly at high catch yield, i.e. it ‘saturates’ when the fishermen feel satisfied. To account for this effect, it is necessary to translate each indicator (sometimes group of indicators) into the ‘value’ assigned by the stakeholders. This can be done by means of a partial value function that has to be identified through interviews to the stakeholders. Once all the indicators are transformed into ‘values’, a stakeholder (or a DM) can express the overall satisfaction that (s)he assigns to an alternative through a dimensionless index, whose value can be computed from the attained ‘values’. Therefore, it is possible to sort the alternatives for decreasing values of the index, thus identifying the alternatives that the stakeholder (or the DM) prefers (the first alternative in the ranking). This methodology is known under the acronym MAVT (Multi-Attribute Value Theory), it is due to Keeney and Raiffa (1976) and is the one most often employed. Nevertheless, it is not the only approach that can be applied: others can be also effectively adopted, like the Analytic Hierarchy Process (Saaty, 1980) or the ELECTRE (Roy, 1993) methods; however, all of them share the following severe disadvantage: in the event that one wish to evaluate a new alternative, it would be necessary to carry out new interviews with all stakeholders, while this almost never happens when the MAVT is adopted. If there is only one stakeholder (or DM), the optimal alternative is found and the decision-making process is concluded. When instead, as it is almost always the case, there is more than one stakeholder (or DM ), working in the aforesaid manner a different ranking is obtained for each one of them. The choice of an alternative then requires the expression of a judgement about the relative importance between the involved parties (stakeholders or DMs), i.e. requires that the parties negotiate between themselves or that a DM (or a Super-DM) expresses her preferences among the parties (stakeholders or DMs). Since, however, preferences and negotiations concern subjective aspects, dealing with them is postponed in the successive phases to maintain the distinction between facts and value judgements.

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1.3.8 Phase 7 – Comparison The aim of this phase is the identification of an alternative that is judged to be an acceptable compromise by all the parties and so does not encounter opposition from anyone. Obviously a win–win alternative, i.e. an alternative that improves all the parties’ indices with respect to the Zero Alternative, would be the ideal solution for the decision-making process. Unfortunately, such an alternative does not always exist. In the case of irresolvable conflict between the interests of different parties, the phase concludes with the identification of the alternatives that gathers a large consent from them and listing the supporting and opposing parties for each of them. We call these alternatives reasonable alternatives12 (or compromise alternatives13 as they are also called). Thus, with this term we refer to the alternatives that are supported by at least one party, are admissible (because they fit physical, technical and legal constraints), are economically feasible, and Paretian, i.e., they are such that it is impossible to improve the satisfaction of one party without worsening that of another. To achieve this result, first of all a series of activities are promoted, which help each of the parties to know and understand the others’ points of view, and, if they exist, the negative effects that the alternative (s)he prefers produce for the others. Once this information has been shared, the heart of the phase is the search for a compromise through negotiations among the parties. Negotiations can be carried out with different methods that can be gathered in two main groups. The methods in the first group are based on negotiations of the weights that each stakeholder assigns to different evaluation criteria; the ones of the second operate in a dual manner upon the thresholds. Leader of this latter family is the method named Pareto-Race (Korhonen and Laakso, 1986 and Soncini-Sessa et al., 2007a). Sometimes it is necessary to suspend negotiations and move back to Phase 4 to design other alternatives, in view of what has been understood of the needs, aspirations, and requests of the Parties; the effects of the new alternatives should be then estimated (Phase 5), evaluated (6) and brought to negotiations (7). In this way and iteration between the Phases 4-5-6-7 is established. 1.3.9 Phase 8 – Mitigation and Compensation If an alternative enjoys the consent of the majority of the parties, but not all them, it is important to explore whether or not it is possible to increase the consent and satisfy some of the unsatisfied parties through measures (meta-actions) of mitigation or compensation. To do this it is necessary to identify new (meta-)actions to include in the alternative, that act specifically on the criteria of unsatisfied parties. Once these (meta-)actions have been identified, they must be instantiated into actions (Phase 4), their effects estimated (5), then they must be evaluated (6) and compared (7) with the reasonable alternatives previously identified, in order to see if they actually produce an enlargement of the consent. In this 12 This term is taken from art. 5 of the Directive 2001/42/ EC (European Commission, 2001) about strategic Environmental Evaluation (VAS). 13 They are given this name because they emerge from a negotiation process in which an attempt is made to find a compromise among different points of view. However, it is not necessarily possible to achieve this, so the term seems equivocal to us and we prefer the first.

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way one obtains a new set of reasonable alternatives, that could be examined in their turn to find new mitigation measures, until no more mitigation measures broadening the consent can be identified. If opponents still exist at this point the possibility of compensating the disadvantage they perceive must be explored, in our example the economic losses of the fisherman can be reimbursed. Here a recursion is established between the Phases 4-5-6-7-8 (Fig. 1.2), which sometimes also includes Phases 1-2-3, during which the whole set of alternatives is ‘sifted’ in order to single out the reasonable alternatives. Sifting ends when a reasonable alternative is identified, which is accepted by all parties; or when it is no longer possible to identify mitigation measures or new measures that make it possible to enlarge the consent; or simply when the time available for the decision-making process has run out. By construction, each alternative obtained in this way has the support of at least one of the parties. The whole of them are presented in the summary document of the study (see for example Ch. 16 in Soncini-Sessa et al., 2007b), that sums up the entire development of the planning project and its results. This document is the material needed to begin the next and last phase. 1.3.10 Phase 9 – Final decision This phase is put into practice only when there are one or more DMs, who are at a higher level than the parties who sifted the alternatives, and are responsible for the final decision about which alternative will be implemented. It is therefore up to these DMs to choose the best compromise alternative from the reasonable alternatives, where ‘best compromise’ means the alternative that best reconciles the different interests, or simply the one upon which they manage to agree. In many cases, this phase is simply a comparison (if there is only one DM) or negotiations (if there is more than one) of the reasonable alternatives, which is often carried out with less formalized methods than those used in Phase 7, being mindful of the customs and local culture. Sometimes however the DM(s) feels the need to explore new alternatives or introduce new criteria. In that case the phase transforms into a new cycle of the Phases 1-8. 1.3.11 Comments and remarks Often the importance of phases that have an engineering or modelling character (in particular Identifying the Model (Phase 3) or Designing Alternatives (Phase 4)) is emphasized, at the expense of more ‘sociological’ phases, like Defining Criteria and Indicators, Evaluation and Comparison. This is a mistake, since a correct decision can be taken only when the expectations, desires, images, knowledge, problems and fears of the stakeholders are as well described and understood as the physical, technical, and economic aspects of the system. Therefore, not only are Phases 3 and 4 of equal importance to the others, and must be considered as such, but the participation of stakeholders should be full and continuous in all the phases, because only in this way will negotiations in Phase 7 be successful. We will never tire of repeating that if the stakeholders do not believe in the index values that are shown to them in that phase, they will never be willing to negotiate. Actually, they will probably not decline to participate in negotiations, but it will develop

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painstakingly, with stakeholders that listen passively or react aggressively and the result, even if formally it can be achieved, will not really change anything in the existing conflict. Not all the phases are always necessary. If, for example, in Phase 2 only one criterion is identified the decision-making process concludes with Phase 4 (or at most with Phase 5). If instead there is only one DM and she does not intend to activate a participatory decisionmaking procedure, the process concludes with Phase 6. If there is no DM above the parties that participated in negotiations, it makes no sense to go through Phase 9. It is important to underline that the real development of the decision-making process is not serial as Fig. 1.2 might lead one to think. Besides the recursion between the Phases 4-5-6-7-8, which is explicitly highlighted in the figure, many others can appear. For example, the criteria cannot actually be correctly identified if one does not take note of the actions being considered, since these latter produce the effects that the stakeholders endure. On the other hand, it is not possible to identify the actions without knowing the interests at stake, and therefore the criteria. The presence of recursions is essentially due to the fact that in carrying out the decision-making process new information is produced, because it is a process of social learning. In view of the new information that are acquired, it is then necessary to re-examine the conclusions of the phases that were considered to be already finished and, when necessary, modify them. In one sense the aim of the decisionmaking process is to increase the parties’ understanding about the planning project, so that they can formulate more and more precise requests and motivated opinions. 1.3.12 The FOTE paradigm Negotiations and relations among the parties are easy or difficult in relation to the degree to which they share and exchange information about the problem, the system and their own personal interests; that is the degree to which they adopt a paradigm of FOTE (Full Open Truthful Exchange (Raiffa et al., 2002). This is why the PIP procedure does not begin with negotiating the alternatives, but instead with an information exchange (Phase 0). It goes on with a participatory definition of the actions (Phase 1), the enunciation of the interests (Phase 2), the identification of a shared model of the system (Phase 3). 1.3.13 The data Do not underestimate the essential role that the data, and the methodologies for their acquisition play in the decision-making process. The data are used, in a qualitative way, in the phases of Recognition and Defining Actions, and in a quantitative form in Phases 2, 3, 4, 5 and 8. Their quantity, availability and accuracy are essential to the success of the decision-making process, but even more important is that all the parties believe that the data is valid and meaningful. The credibility of the model, which is the basis for the credibility of the evaluation of the alternatives, is founded upon this belief, without which the negotiation process is a fruitless exercise. In simple terms: the entire decision-making process depends on the social acceptability of the data. 1.3.14 The uncertainty Ignorance is being unaware that our awareness is imperfect. An imperfect awareness implies uncertainty and uncertainty generates apprehension. For this reason, DMs often

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have the tendency to remove the problem of uncertainty: they want scenarios to be deterministic and models to provide exact estimates, so that their evaluations will be perfect. However, hiding uncertainty is none other than a form of ignorance. Thus, in many phases of the PIP procedure the problem of treating uncertainty arises. Uncertainty, is produced by corrupt, insufficient or scarce information, and by the errors that are committed unknowingly. We will see in the following that all these causes are represented as the effects of disturbances, which can assume different forms: disturbances are stochastic when we know or we can estimate their probability distributions; they are uncertain when we know only the set of values that we guess they might assume. The form of a disturbance depends upon the source that generates it, for example data collection generates the most common uncertainty: measurement errors, which are always described as stochastic and that afflict all the phases in which the data are used. In Phase 1 uncertainty appears also in the description of the actions, since the way in which they will actually be implemented is not always certain (implementation uncertainty); this uncertainty is not only due to implementation aspects, but also to institutional inertia. In Phases 3 and 6 one must account for the disturbances that can make the design and evaluation of scenarios uncertain: it is when confronted with this type of uncertainty about the future that DMs and stakeholders reveal their aversion to risk, which we discussed in the description of Phase 2. In Phase 3 it is necessary to take into account the so-called process errors, i.e. the eventuality that the model does not perfectly describe reality. The effects produced by all these disturbances combine to generate the uncertainty that afflicts the indicator values that make up the Matrix of effects.

1.4 ICT Tools The PIP procedure has to be supported: all the phases, except for the phase of Recognition, must be handled by an appropriate set (toolbox) of ICT (Information and Communication Technologies) tools, which its users must perceive as parts of a unique and coherent system, i.e. a Multi Objective Decision Support System (MODSS). Since these systems were first applied to water related problems (SFWMG, 1987; Simonovic and Savic, 1989; Loucks, 1990 and Soncini-Sessa et al., 1990) considerable progress was made (Jolma, 1999; Soncini-Sessa et al., 1999; Nandalal and Simonovic, 2002 and Liu and Stewart, 2004). However, relatively few of them have been actually and regularly applied in real world decision-making processes. In the authors’ opinion this is essentially due to a general lack of communication and information exchange between analysts, DM(s) and stakeholders. Models and algorithms almost always need an expert to be run and the practitioners (DMs and stakeholders) can only evaluate and believe to the assumptions made by the analyst without being able to effectively handle the tools. To reduce the gap between the academy and real world methods and algorithms developed by the scientist should be usable and accessible even by the non-scientists and shared between stakeholders and policy-makers. A promising step-head in this direction is enabled by the Internet technologies, through which WEB-based MODSS might be developed (some prototypes have been already devised, see Salewicz and Nakayama, 2004). There are three main further reasons for a MODSS to operate on the WEB:

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A prototype version of a MODSS covering Phases 3-6 of the PIP procedure is already running at DEI-Politecnico di Milano (Soncini-Sessa et al., 1999) and has been tested on the Verbano Project and MERIT-FP5 Project as well as on other national projects. 1.5 The decision-making process at the management level Once the best compromise alternative has been selected (Phase 9 of the PIP procedure), it has to be implemented: this is achieved by implementing the structural and normative actions it includes, and applying the regulation policy – if this has been designed – at the scheduled time instants. Since this policy may leave some degree of freedom to the Regulator (see Aufiero et al., 2001 and 2002), a decision-making problem must be formulated at the management level as well, though the degree of freedom that the policy allows is much less than the degree that the DM had when the problem was formulated at the planning level, i.e. at the level that we have been considering until now. The best compromise alternative is therefore at the same time the conclusion of the decision-making process at the planning level and the starting point for the decision-making process that is renewed periodically, often daily, at the management level, on the basis of the new information which are obtained as the time goes on. Acknowledgements The preparation of the chapter was carried on within the Project COFIN 2004 Sistemi di supporto alle decisioni per la pianificazione e gestione di serbatoi e laghi regolati [prot. 2004132971_004]. Bibliography Aufiero, A., R. Soncini-Sessa and E. Weber (2001). Set-valued control laws in minmax control problem. In: Proceedings of IFAC Workshop Modelling and Control in Environmental Issues, August 22–23. Elsevier. Yokohama, J. Aufiero, A., R. Soncini-Sessa and E. Weber (2002). Set-valued control laws in TEV-DC control problem. In: Proceedings of 15th IFAC World Congress on Automatic Control, July 21–26. Elsevier. Barcelona, E. 14 The Beowulf Cluster Site, http://www.beowulf.org; Apple ACG Xgrid, http://www.apple.com/acg/xgrid/; DataGrid Project, http://web.datagrid.cnr.it, visited 01/2006.

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Soncini-Sessa, R., A. Castelletti and E. Weber (2007a). Integrated and participatory water resources management. Theory. Elsevier. Amsterdam, NL. to appear. Soncini-Sessa, R., A. Nardini, C. Gandolfi and A. Kraszewski (1990). Computer aided water reservoir management: a prototype two level DSS. In: Proceedings of the NATO ARW on Computer Aided Support Systems in Water Resources Research and Management, September 23–28. Ericeira, P. Soncini-Sessa, R., A.E. Rizzoli, L. Villa and E. Weber (1999). TwoLe: a software tool for planning and management of water reservoir networks. Hydrolog. Sci. J. 44(4), 619–631. Soncini-Sessa, R., F. Cellina, F. Pianosi and E. Weber (2007b). Integrated and participatory water resources management. Practice. Elsevier. Amsterdam, NL. to appear. Tortajada, C., Varis, O. and Biswas, A.K., Eds.) (2004). Integrated Water Resources Management in South and Southest Asia. Oxford University Press. Oxford, UK. UNCSD – United Nations Commission on Sustainable Development (1996). Indicators of sustainable development framework and methodologies. Technical report. UNCSD. New York, NY. Whittington, D. and G. Guariso (1983). Water Management Models in Practice: A Case Study of the Aswan High Dam. Elsevier. San Francisco, CA. Wolf, A.T., Ed.) (2002). Conflict Prevention and Resolution in Water Systems. Edward Elgar. Cheltenham, UK.

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Part II

Modelling

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CHAPTER 2

The Data-Based Mechanistic Approach in Hydrological Modelling Peter C. Young1 , Andrea Castelletti2 and Francesca Pianosi2 1 Centre for Research on Environmental Systems and Statistics

Lancaster University, Lancaster, UK; and Centre for Resource and Environmental Studies Australian National University 2 Dipartimento di Elettronica e Informazione

Politecnico di Milano, Milano, Italy

2.1 Introduction Throughout the 20th century, the hypothetico-deductive approach to scientific research, as extolled so lucidly by the philosopher Karl Popper (1959), reigned supreme. The inductive approach, that had provided the cornerstone for scientific research in earlier centuries, became less attractive to the physicists and chemists who dominated science during the 20th century and whose well planned experimentation provided some of the stimulus for Popper’s views. Moreover, the rise of the computer, with its ability to construct and solve large mathematical simulation models, provided a magnificent engine for the implementation of the hypothetico-deductive approach. And today, such computer-based simulation modelling has become straightforward, almost simple, with the availability of iconographic software, such as Matlab/Simulink™, where a complex model can be assembled quickly from a built-in and comprehensive library of simulation objects. All this would appear to be good news for environmental scientists involved in the management and planning of environmental systems. But is it? While acknowledging the virtues of simulation modelling, particularly when it is carried out in stochastic terms, this chapter will discuss the limitations of this approach when it is used in the context of environmental systems, where planned experimentation is difficult, if not impossible, and where uncertainty about the nature of the processes involved sits uncomfortably with the deterministic models that appear to dominate simulation modelling practice. The chapter will outline a Data-Based Mechanistic (DBM) approach to modelling, forecasting and control that often starts with the construction and evaluation of a simu27

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lation model which reflects the scientists’ perception of the physical, chemical and biological mechanisms that characterise the environmental system. However, these DBM studies are not simple exercises in simulation modelling: rather they constitute a critical evaluation of the model in both stochastic and response terms; an evaluation that marks only the beginning, not the end, of the modelling process. Exploiting some of the tools of DBM modelling that are later applied to real data, this critical evaluation considers the simulation model as a natural extension of the thought processes and scientific speculation that resides in the mind of the model builder. And, by providing insight into the strengths and limitations of the simulation model, it provides a prelude to the exercises in DBM modelling from real data that becomes possible when data are available on the response of the environmental system to natural or anthropogenicallyinduced perturbations. Of course, in this environmental context, the real data required for DBM modelling is most often the result of monitoring studies, rather than planned experimentation. As a result, such data may not be available or, as is often the case, they may provide an insufficient basis for DBM modelling. Even in this data-deficient situation, however, the DBM modelling methodology can provide valuable insight into the strengths and limitations of the simulation model; insight that can radically effect the way in which the model is used as a tool in planning and management. Whatever model emerges from the DBM modelling process, it should be a model that is well suited to the objectives of the study team. These may range from ‘what-if’ simulation, where the complexity of the simulation model is a clear advantage, to exercises in forecasting and operational control, where the over-parametrization that normally characterizes the large simulation model is a definite disadvantage. This chapter will argue, therefore, that the construction of a single model that suits all purposes is normally impossible and, in any case, undesirable. Rather the objectives of the study should be clearly defined and a well integrated suite of models should be constructed, each designed to satisfy the requirements of these objectives. It is suggested that, wherever possible, the parametrically efficient (or ‘parsimonious’) DBM model should provide a description of the core mechanisms that dominate the observed behaviour of the environmental system under study. And it should also provide the basis for the final construction of a stochastic model that reflects this core behaviour but may involve other, more speculative elements that are required for ‘what-if’ simulation and planning exercises. The advantage of this DBM ‘moderation’ of the simulation model is that the relative confidence in the historically validated DBM core (when sufficient data are available) can be balanced with the reduced confidence in the more poorly validated speculative elements. Thus the results of any analysis can be better evaluated with these relative uncertainties in mind. For instance, if the model contains nonlinearities that have not been well-validated during DBM modelling over the historical period, but are thought to be of potential importance in the future, then the large level of uncertainty in this regard must be reflected clearly in any predictive application of the model. Given its generic nature, the Data-Based Mechanistic approach has wide application potential in many areas of study ranging from ecological (Young, 2000) and biological (Jarvis et al., 1999; Price et al., 2001), through engineering (Young, 1998a; Price et al., 1998) and environmental (Price et al., 2002), to business and macro-economic systems (Young and Pedregal, 1999; Pedregal and Young, 2002). Within a hydrological context, it

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was applied first in the early 1970s to the modelling of water quality in rivers (Beck and Young, 1975) and, in the subsequent years, to the modelling of rainfall–flow processes in river basins (e.g. see Young, 2002 and the prior references therein). However, only recently has its potential been explored to model river flow in snow-affected basins, in which the snow-melt makes a significant, and sometime dominant, contribution to the flow. This chapter will illustrate this novel application through a case study in Switzerland. 2.2 The Fundamentals of Data-Based Mechanistic modelling The term ‘data-based mechanistic modelling’ was first used in Young and Lees (1993) but the basic concepts of this approach to modelling dynamic systems have developed over many years. The evolution of the DBM philosophy and its detailed methodological underpinning are described in previous publications (e.g., Young, 2001a, 2003 and prior references therein), and so it will suffice here to merely outline the main aspects of the approach. The six major stages in the DBM modelling strategy are as follows: 1. The important first step is to define the objectives of the modelling exercise and to consider the type of model that is most appropriate to meeting these objectives. Since DBM modelling requires adequate data if it is to be completely successful, this stage also includes considerations of scale and the data availability at this scale, particularly as they relate to the defined modelling objectives. However, the prior assumptions about the form and structure of this model are kept at a minimum in order to avoid the prejudicial imposition of untested perceptions about the nature and complexity of the model needed to meet the defined objectives. 2. In the initial phases of modelling, it may well be that observational data will be scarce, so that any major modelling effort will have to be centred on simulation modelling, normally based on largely deterministic concepts, such as dynamic mass and energy conservation. In the DBM modelling approach, which is basically Bayesian in concept, these deterministic simulation equations are converted to a stochastic form by assuming that the associated parameters and inputs are inherently uncertain and can only be characterised in some suitable stochastic form, such as a probability distribution function (pdf) for the parameters and a time-series model for the inputs. The subsequent stochastic analysis uses Monte Carlo Simulation (MCS), to explore the propagation of uncertainty in the resulting stochastic model, and sensitivity analysis of the MCS results to identify the most important parameters which lead to a specified model behaviour: e.g. Parkinson and Young (1998). 3. The initial exploration of the simulation model in stochastic terms is aimed at revealing the relative importance of different parts of the model in explaining the dominant behavioural mechanisms. This understanding of the model is further enhanced by employing a novel method of model order reduction that we term Dominant Mode Analysis (DMA). This is applied to time-series data obtained from planned experimentation, not on the system itself, but on the simulation model

30

P.C. Young et al. that, in effect, becomes a surrogate for the real system. This rather unusual analysis is exploited in order to develop low-order, dominant mode approximations of the simulation model (e.g. Young et al., 1996; Young, 1999a) approximations that are often able to explain its dynamic response characteristics to a remarkably accurate degree (e.g. coefficients of determination RT2 , based on the simulated model response error, of greater than 0.999: i.e. greater than 99.9% of the large model output variance explained by the reduced order model output1 ). 4. Conveniently, the statistical methods used for DMA exercises in 3., above, are the same as those used for the DBM modelling from real time-series data that follows as the next stage in the modelling process. Here, appropriate model structures are identified by a process of objective statistical inference applied directly to the timeseries data and based initially on a given generic class of linear Transfer Function (TF) models (i.e. differential equation models or their discrete-time equivalents) whose parameters are allowed to vary over time, if this seems necessary to satisfactorily explain the data. In particular: • If the model is identified as predominantly linear, linear with slowly varying parameters or piece-wise linear, then the parameters that characterize the identified model structure in step 1 are estimated using advanced methods of statistical estimation for dynamic systems. The methods used in the present chapter are based on optimal, recursive Refined Instrumental Variable (RIV) estimation algorithms (Young, 1984) that provide a robust approach to model identification and estimation and have been well tested in practical applications over many years. Here the important identification stage means that objective statistical methods are used to determine the dynamic model order and structure, rather than assuming these a priori. In this manner, the identifiability of the model from the data is assured and the possibility of overparametrization is minimized. Full details of these time series methods are provided in the above mentioned references. • If significant parameter variation is detected over the observation interval, then the model parameters are estimated by the application of an approach to time dependent parameter estimation based on the application of recursive Fixed Interval Smoothing (FIS) algorithms (e.g. Bryson and Ho, 1969; Norton, 1986; Young, 1984, 1999). Such parameter variation will tend to reflect statistically significant nonstationary and nonlinear aspects of the observed system behaviour. In the case of nonlinear systems, the FIS algorithm provides a method of nonparametric (graphical) estimation that can often be interpreted in State-Dependent Parameter (SDP) terms (Young, 1993; Young and Beven, 1994; Young, 2000, 2001b). • If nonlinear phenomena have been detected and identified in step 2, the nonparametric, state dependent relationships are normally parameterized in a finite form and the resulting nonlinear model is estimated using some form of

1 Note that this is a much more discerning measure of the model’s adequacy than the conventional coefficient of determination R 2 based on the one-step-ahead prediction errors.

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numerical optimization, such as nonlinear least squares or Maximum Likelihood (ML) optimization. 5. Regardless of whether the model is identified and estimated in linear or nonlinear form, it is only accepted as a credible representation of the system if, in addition to explaining the data well, it also provides a description that has direct relevance to the physical reality of the system under study. This is a most important aspect of DBM modelling and differentiates it from more classical ‘black-box’ and ‘grey-box’ modelling methodologies, such as those associated with standard TF, nonlinear autoregressive moving average-exogenous variables (NARMAX), neural network and neuro-fuzzy models. 6. The final stage of model synthesis should always be an attempt at model validation: see e.g. Young (2001a). The word ‘attempt’ is important since validation is a complex process and even its definition is controversial. Some academics (e.g. Konikow and Bredehoeft, 1992 within a ground-water context; and Oreskes et al., 1994 in relation to the whole of the earth sciences) question even the possibility of validating models. However, statistical evaluation of the model by confirming that statistical diagnostics are satisfactory (e.g. no significant autocorrelation in the residuals or cross correlation between the residuals and input variables; no evidence of un-modelled nonlinearity, etc.) is always possible and can engender greater confidence in the efficacy of the model. Also, one specific, quantitative aspect of validation is widely accepted; namely ‘predictive validation’, in which the predictive potential of the model is evaluated on data other than that used in the identification and estimation stages of the analysis. When validated in this narrow sense, it can be assumed that the ‘conditionally valid’ model represents the best theory of behaviour currently available that has not yet been falsified in a Popperian sense. Of course, in any specific application, not all of these stages in the DBM modelling procedure will be required. Indeed, in the Case Study discussed in the next section, suitable time series data are available and these are entirely adequate for data-based modelling. Consequently, the simulation modelling, MCS and DMA analyses outlined in stages 2 and 3 are not required. The reader should refer to the cited publications for further information on these aspects of DBM modelling. Whatever stages in the DBM modelling procedure are utilized, however, they are not the end of the modelling process. If the model is to be applied in practice (and for what other reason should it be constructed?) then, as additional data are received, they should be used to evaluate further the model’s ability to meet its objectives. Then, if possible, both the model parameters and structure can be modified if they are inadequate in any way. This process, sometimes referred to as ‘data assimilation’, can be achieved in a variety of ways. Since most data assimilation methods attempt to mimic the Kalman Filter (KF), however, it is likely to involve recursive updating of the model parameter and state estimates in some manner, as well as the use of the model in a predictive (forecasting) sense. This process of data assimilation is made simpler in the DBM case because the favoured estimation methods used in DBM modelling are all inherently recursive in form and so can be used directly for on-line, Bayesian data assimilation (Young, 1984). Recursive estimation is, of course, the embodiment of Bayesian estimation and the KF has long been interpreted in these terms. In the case of linear stochastic systems with

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Gaussian disturbances (or linear systems having only input nonlinearities: see Young, 2002), the KF provides the ideal Bayesian data assimilation and on-line forecasting algorithm. For nonlinear systems, however, other approaches become necessary, some of which can be related directly to the KF: e.g. the Extended Kalman Filter (EKF) (Beck, 1979), the SDP version of the KF (Young, 2000) or numerical Bayesian methods (e.g. Beven and Binley, 1992; Thieman et al., 2001; Beven and Young, 2003). Finally, since most of the computational procedures used in DBM modelling have been described elsewhere in the cited references, they will not be discussed in the present chapter. Most of them are available in the CAPTAIN Toolbox2 , a suite of algorithms developed at Lancaster for use within the Matlab/Simulink™ software environment.

2.3 Case Study: the upper Ticino River basin The upper Ticino River basin (Fig. 2.1) extends for 1515 km2 from the alpine continental divide to the northern shores of Lake Maggiore. It is characterized by significant variations of the climatic and hydrologic conditions and by pronounced orographic heterogeneity. The altitudinal variation in the basin ranges from 220 to 3402 m a.s.l., with more than 80% of the area located higher than 1000 m a.s.l. and a mean slope exceeding the 27%. The dominance of a sub-alpine climate regime results in extremely variable weather conditions, which cause notable flood and drought periods. The meteorological observational data3 used in this study consist of time series covering a 19 yr period (1979–1997). These data are shown in Fig. 2.2: the flow data in the upper panel (a) are measured daily at the Bellinzona stream gauge (225 m a.s.l.); the precipitation values in the middle panel (b) are obtained through interpolation (Thiessen Polygon) of daily sum readings taken at five different rain gauges; finally, the mean daily temperature values in the lower panel (c) are recorded at the Guetsch station (2287 m a.s.l.). It is worth noting that, due to the high elevation of this last station, the snow-melt might be active even if the temperature at Guetsch is negative, because the temperature at lower altitudes might be positive. The flow series plotted in Fig. 2.2a clearly shows the distinctive profile of the subalpine flow scenario, with two seasonal peaks: the first in the late spring, when the smoothing effect of the snow-melt contribution is prevailing; and the second in autumn, when the rainfall is the dominant flow producing process, resulting in sharp and extremely intensive floods. Even in the spring, however, sharp floods are driven by storm events. The strong orography of the basin and the high frequency of precipitation has led, since the 1960’s, to the heavy exploitation of the water resources available in the basin, mainly for hydropower generation purposes. The presence of many alpine hydropower reservoirs, operated on a weekly basis, is easily interpretable from low amplitude, periodic fluctuations in the river flow during the winter periods, which are apparent in Fig. 2.2a. 2 See http://www.es.lancs.ac.uk/cres/captain/ 3 Provided by the Swiss Federal Office for Meteorology (MeteoSwiss) and by the Swiss Federal Office for Water and Geology (BWG).

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Fig. 2.1. The upper Ticino River basin (Switzerland) showing the measurement stations used in the model.

600

3

flow [m /s]

(a)

400

precipitation [mm]

200 (b) 60 40 20

A

B C

0

temperature [°C]

(c) 10 0 −10 −20 J F M A M J J A S O N D J F M A M J J A S O N D

Fig. 2.2. A sample of daily flow yk , precipitation uk and temperature Tk data over a period of 2 years from January 1979 to December 1980 for the upper River Ticino. The capital letters A, B and C are referred to in the text.

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Fig. 2.3. Upper River Ticino: plots of (a) Precipitation and (b) Temperature against Daily flow; (c) cross-correlation diagram for precipitation–flow and (d) temperature–flow.

2.3.1 Choice of the model structure The first task in DBM modelling is the definition of the objectives. In the present example, this is the first time that DBM modelling has been applied to rainfall–flow modelling in a situation where the effects of snow-melt are important. Consequently, the primary objective is that the model should serve as a vehicle for better understanding the nature of the nonlinear precipitation–flow dynamics at the catchment scale and the relative importance of the rainfall and snow melt contributions to the river flow. A secondary objective is to consider the potential of the model in adaptive flow forecasting and flood warning. As the data are plentiful in this example, there is no need for initial simulation modelling, since a dominant mode DBM model, based on the analysis of these data, should be adequate. Moreover, as we shall see, the DBM model obtained here cannot be used directly for simulation modelling purposes. With these objectives in mind, some initial ideas about the choice of a suitable model structure may be obtained by exploring the nature of the nonlinear relationships between the rainfall, flow and temperature data. One simple yet useful, initial exercise is to map the daily flow values against the rainfall and temperature data, as shown in the scatter plots of Figs. 2.3a and 2.3b. These two graphs illustrate how both precipitation and tem-

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perature appear to be highly correlated with flow. This is also illustrated in the two cross correlation plots below in Figs. 2.3(c) and 2.3(d). Within a SDP modelling context, the scatter plots suggests that the flow itself could be used to explain the nonlinear effects of both the precipitation and temperature. Initial estimates of such relationships are given by the full lines in these figures, which are obtained by nonparametric SDP estimation. As far as the precipitation input is concerned, these observations follow rather naturally from previous research on simple rainfall–flow models [Young, 2003 and previous references therein]. Of course, the flow is not actually influencing the effect of the rainfall and temperature inputs, it is simply acting as a surrogate for the catchment storage (soil moisture) which naturally has a considerable influence on how flow is affected by changes in precipitation. As for the temperature input, an interpretation of the temperature–flow relation is discussed later. In the first stage of quantitative modelling, the most parsimonious model structure is initially identified using constant parameter RIV estimation applied to a general linear model structure of the form: xk =

B1 (z−1 ) B2 (z−1 ) u Tk−δT , + k−δ u A1 (z−1 ) A2 (z−1 )

(2.1)

yk = xk + ξk , where yk , uk and Tk are the daily flow, rainfall and temperature measurements, respectively; xk is the unobserved deterministic output of the model; and ξk represents the noise in the model, which will arise from factors such as measurement noise, the effects of unmeasured stochastic inputs and model approximation. Allowance is made for the presence of pure time delays by the introduction of δu and δT . The transfer function polynomials are expressed in terms of the backward shift operator, i.e. z−r yk = yk−r , and are defined as follows: A1 (z−1 ) = 1 + a1,1 z−1 + a1,2 z−2 + · · · + a1,n1 z−n1 , B1 (z−1 ) = 1 + b1,1 z−1 + b1,2 z−2 + · · · + b1,m1 z−m1 , A2 (z−1 ) = 1 + a2,1 z−1 + a2,2 z−2 + · · · + a2,n2 z−n2 , B2 (z−1 ) = 1 + b2,1 z−1 + b2,2 z−2 + · · · + b2,m2 z−m2 . In the present case, however, initial linear identification suggests that the simpler ‘common denominator’ model, where A1 (z−1 ) = A2 (z−1 ) = A(z−1 ), provides as good an explanation of the data as the unconstrained model (2.1). Table 2.1 shows the order of the three best identified models, together with the corresponding identification criteria: namely, the YIC (Young et al., 1996), higher values of which suggest possible over-parameterization; and the coefficient of determination RT2 , which defines the fraction of the measured output variance that is explained by the simulated deterministic output of the model xˆk , where, xˆk =

Bˆ 1 (z−1 ) uk−δu + ˆ −1 ) A(z

Bˆ 2 (z−1 ) Tk−δT ˆ −1 ) A(z

(2.2)

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P.C. Young et al. Table 2.1. Linear model identification. denominator

numerator

time delay

YIC

RT2

2

2 2 2 2 2 2

0 1 0 0 0 2

2.917

0.595

3.096

0.595

3.072

0.592

2 2

and the ‘hats’ denote the estimated values of the associated polynomials. Note that xˆk here and in the later nonlinear models, is the ‘simulated’ output, driven entirely by the measured inputs uk−δu and Tk−δT , without any reference to the measured flow series yk . It is not, in other words, the one-step-ahead predicted output often mis-used in assessing the quality of ‘black-box’ models, such as those based on neural network methods. These results suggest that the best initial identification of the model structure is that presented in the first row (normally denoted by [2 2 2 0 1]). Of course, these model structures are based on linear modelling, so they only provide a preliminary indication of the likely model orders and time delays: they will not necessarily remain exactly the same in the wider nonlinear context discussed below. On the basis of this preliminary identification exercise, and in conformity with previous DBM rainfall–flow modelling exercises (see previous references), initial nonparametric SDP estimation suggests that the major nonlinearities occur at the input to each transfer function, so that the model can be written in the form: yk =

B1 (z−1 ) e B2 (z−1 ) e u + T + ξk A(z−1 ) k A(z−1 ) k

(2.3)

where uek and Tke are the ‘effective’ precipitation and temperature inputs arising from the estimated state-dependent nonlinearities, where: uek = α(yk )uk−δu , Tke

= β(yk )Tk−δk

(2.4a) (2.4b)

in which it will be seen that both SDPs are dependent on the flow variable yk , as discussed further in the next sub-section. The simulated output xˆk of this model is given by, xˆk =

Bˆ 1 (z−1 ) e u + ˆ −1 ) k A(z

Bˆ 2 (z−1 ) e T ˆ −1 ) k A(z

(2.5)

and this is used for computing the coefficient of determination RT2 of the model in subsequent model evaluation. 2.3.2 State-Dependent Parameter modelling of the nonlinearities The nonparametric estimates of the SDPs α(yk ) and β(yk ) in Eq. (2.4) are obtained using the SDP estimation algorithm in the CAPTAIN Toolbox. They are plotted against the flow

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Fig. 2.4. Nonparametric estimate of the state-dependent parameters α and β (full lines), with the estimated standard error bounds shown as dotted lines. The dash-dot lines are the optimized parametric functions (both power law). The marks on these graphs are discussed in the text.

yk in Fig. 2.4 (the dash-dot lines are discussed later). These two curves can be interpreted in physically meaningful terms. Considering first the precipitation SDP α(yk ) in Fig. 2.4a, the flow state dependency has the well-known saturating shape that has been interpreted in previous research as a catchment storage effect (see Young, 2003 and previous references therein). In this previous research, the flow is assumed to be a surrogate or proxy indicator of the catchment storage. However, in the present context where the whole precipitation (rainfall plus snowfall) is important, this prior interpretation needs to be revised to some extent. Depending on the season, the estimate of the SDP α(yk ) at the low flow values in Fig. 2.4a can be explained in two ways: either as the normal effect of the dry summer soil, as considered previously in rainfall–flow modelling; or as the effect of the prevailing snowy nature of the winter precipitation, which simply adds depth to the snowpack and does not generate any immediate flow increase. This latter effect is acting as a ‘seasonal reservoir’, releasing in the summer the water stored as snow during the winter. As an example of the first behaviour, consider the two precipitation events marked as A and B in Fig. 2.2b. Although they have similar intensities, the flow values they produce are significantly different: the A precipitation event occurs in August, on completely dry soil, and so the rainfall acts only to wet the soil, without accompanying run-off. However,

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the precipitation peak in B occurs after a very wet period, during which the soil has been saturated and run-off occurs, resulting in a higher flow. Finally, the event marked as C is a sample of the winter behaviour, when most of the precipitation is trapped in the snowpack. Note how the SDP estimate has a higher standard error for small values of the flow. This is probably due to the intense activity of alpine hydropower reservoirs modulating the flow of many tributaries of the River Ticino (see later discussion on this effect). The estimate of the SDP β(yk ) in Fig. 2.4b modulates the effect of the temperature on the flow. The graph clearly shows that the temperature-related contribution to the flow increases as the flow ranges between 60 to 200 m3 /s. This can be explained as follows. For the very steep Ticino River basin, temperature cannot be assumed uniform over the basin and should be a decreasing function of altitude. The altitude–temperature relationship can be assumed to be approximately linear. The snow-melt process starts when the daily average temperature is higher than a threshold value4 . As temperature is not uniform over the basin, the temperature in the early spring exceeds the threshold only at the lower altitudes, so that the surface Sk involved in the snow-melt process (accordingly called the active surface) is limited to the lower band of the basin and the snow-melt contribution is rather limited. As time progresses, however, the temperature rises all over in the basin, the active surface Sk becomes increasingly larger and the snow-melt intensifies. In order to account for this snow-melt phenomenon, the dynamic behaviour of Sk is generally introduced into conceptual models and the snow-melt volume vk is assumed to be proportional to both temperature and active surface area, i.e. vk = kSk Tk .

(2.6)

This can be interpreted to mean that the proportionality coefficient β(yk ), between the flow arising from snow-melt and the temperature, is an increasing function of Sk . However, provided that yk is increasing with Sk , β(yk ) must also be an increasing function of yk . This is exactly what Fig. 2.4b shows (see trend 1) and suggests that the flow yk is a proxy indicator of Sk . When the temperature exceeds the threshold even at the highest altitude, the whole basin surface is involved in the snow-melt process. Consequently, the coefficient β(yk ) saturates. In this condition, the snow-melt volume vk does not depend upon Sk and, as a result, Eq. (2.6) turns into the form of the classical degree-day formulation, which assumes that the snow-melt is linearly proportional to the difference between the air temperature and a threshold temperature, below which no melting occurs (see, for example, Martinec et al., 1983). As the season proceeds, the snow-pack disappears at the lower altitude, so that the active surface Sk decreases and the contribution to the flow decreases too. The dynamic behaviour of vk is, therefore, once again expressed by Eq. (2.6) and it can be explained by the parameter β(yk ) varying with yk as in Fig. 2.4b (see trend 2). This hypothesis of the snow-melt behaviour suggests that the β(yk ) curve provides a single path approximation to underlying hysteretic behaviour in the system, with different 4 Indeed the snow-melt process starts a few days after the temperature reaches the threshold value. The reason is that the snow-melt occurs along the snowpack base surface; but since air temperature influences snow-melt through the snow-pack top surface, it takes some time for the heat flux to reach the bottom and start the melting process.

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16 14 12 10 (1) 8 6 4

(2)

2 0 -2

80

100

120

140 160 y (active surface)

180

200

220

Fig. 2.5. Comparison of the nonparametric estimate of β computed on the original time series (full line), with that relevant to the increasing phase (dashed line) and that to the decreasing phase (dash-dot line). Only the range of flow values generated by snow-melting is shown.

behavioural mechanisms for increasing and decreasing Sk , and its proxy indicator yk , corresponding to different phases of the snow-melt process. As a consequence, the values it provides must be considered as an average of the actual values in these two phases. This argument can be justified by plotting the nonparametric SDP estimates of β for two time series obtained by considering separately increasing (1) and decreasing (2) phases, as shown in Fig. 2.5, where the hysteresis effect is very pronounced. For simplicity, in the present example, we have not included this hysteretic effect in the model, but it is likely that the model’s explanatory ability could be improved by its introduction. 2.3.3 Parameterization and optimization The final stage of DBM modelling is the parameterization of the effective input nonlinearities, whose form and location has been identified by the nonparametric SDP estimation. Many different parameterizations could be used, such as a power law, polynomial and radial basis functions. However, reasonable results have been obtained using a simple power law in flow: i.e., α(yk ) = ykc1 ,

(2.7a)

β(yk ) = ykc2 .

(2.7b)

Initial estimates of the parameters in these nonlinear functions are obtained using the lscurvefit function in Matlab, applied to the nonparametric estimation results in Fig. 2.4.

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This allows for the identification of the best model order for the transfer function in Eq. (2.3) using RIV estimation applied to the input-output data, with the original inputs replaced by the effective inputs generated using the optimized parameterizations in (2.7). The best identified model structure using these effective inputs is [2 2 2 0 1]. It is now possible to further improve the model through a final iterative optimization procedure that has been used in previous rainfall–flow modelling examples (see previous references). Here, at each iteration, estimates of all the model parameters are obtained using the leastsq optimization function in Matlab, starting with the ci , i = 1, 2, parameters optimized on the basis of the nonparametric SDP estimation results and exploiting the RIV algorithm to estimate the associated transfer function model parameters: Iterate for j = 1 to convergence: 1. the effective inputs uek , Tke are calculated, based on the previous (j − 1)th estimate of the ci parameters; 2. the linear transfer function in Eq. (2.3) is estimated using the RIV algorithm, and the corresponding simulated deterministic model output xˆk is used to evaluate a quadratic cost function based on the model error ek = yk − xˆk ; 3. the new ci estimates provide the basis for the next (j + 1)th iteration. end iteration The final estimated model, obtained in this manner, takes the form yk =

bˆ10 + bˆ11 z−1 bˆ21 + bˆ22 z−1 e u + T e + ξk 1 + aˆ 1 z−1 + aˆ 2 z−2 k 1 + aˆ 1 z−1 + aˆ 2 z−2 k−1

(2.8a)

with   uek = ykcˆ1 uk ,  cˆ2  e Tk−1 , Tk−1 = yk−1

(2.8b) (2.8c)

where the noise ξk is identified by reference to the AIC criterion (Akaike, 1974) as the following autoregressive AR(7) model: ξk =

1 + γˆ1

z−1

1 ek , + · · · + γˆ7 z−7

  ξk = N 0, σξ2 ,

  ek = N 0, σ 2 .

(2.9)

As shown here, in theory ek should be a zero mean, normally distributed, white noise sequence with variance σ 2 . If this were the case, then model estimation could have been made more statistically efficient if this noise model had been incorporated in the optimization and estimated simultaneously, with the ek used as the basis for maximum likelihood estimation. However the estimated noise ξk in this case has two characteristics that affect ek and mean that it does not conform to these assumptions. These are the presence of the periodic component in the flow, arising from the hydropower induced fluctuations; and the ‘heteroscedastic’ nature of the noise, where its variance fluctuates considerably over the observation interval. As a result of these complications, the simpler algorithm

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described above was used for estimation. In these circumstances, this algorithm has the advantage that the optimal instrumental variable nature of the associated RIV estimation algorithm makes it robust to residuals that do not comply fully with the theoretical assumptions (see Young, 1984). The parameter estimates associated with the above model Eqs (2.8a)–(2.8c) and (2.9) are: aˆ 1 = −1.3188(0.0001), aˆ 2 = 0.3285(0.0001),     bˆ10 = 0.1796 0.0059 × 10−3 , bˆ11 = −0.1700 0.0055 × 10−3 ,     bˆ21 = 0.0378 0.0019 × 10−3 , bˆ22 = −0.0382 0.0019 × 10−3 , cˆ1 = 0.6298(0.0002), cˆ2 = 0.7613(0.0013),     γˆ1 = −0.4677 0.4276 × 10−3 , γˆ2 = 0.0956 0.5189 × 10−3 ,     γˆ3 = −0.1066 0.5190 × 10−3 , γˆ4 = −0.0222 0.5239 × 10−3 ,     γˆ5 = −0.0949 0.5194 × 10−3 , γˆ6 = −0.0899 0.5194 × 10−3 ,   γˆ7 = −0.1234 0.4280 × 10−3 , σˆ 2 = 373, σˆ ξ2 = 618, where the figures in parentheses are the estimated standard errors based on the assumption that ξk is a white noise process with estimated variance 618 (see above). Since this assumption is not correct in this case, as pointed out above, these standard errors, as well as the associated parametric covariance matrix used later for uncertainty analysis, can only be considered as approximations. Nevertheless, previous experience and analysis using MCS has suggested that the approximations are acceptable and normally provide a reasonable basis for uncertainty assessment. The estimated parametric SDP functions, with these estimates of the ci parameters defining the power law relationships, are shown as the dash-dot lines in Fig. 2.4. This model explains the data reasonably well, as we see in Fig. 2.6a, which compares xˆk with the measured flow: here the coefficient of determination RT2 = 0.847, based on deterministic output of the model xˆk (see earlier equation (2.5)). The performance of the model is confirmed on a validation data set different from the one used for model estimation, as shown in Fig. 2.6b, where RT2 = 0.836, only marginally less than that obtained in the model estimation. These values of RT2 should be compared with the linear model in Table 2.1, where RT2 is only 0.595. Finally, in line with our objectives, Fig. 2.7 shows the constituent output flows from the two parts of the model that are added together to produce the total flow output. The upper panel is the flow from the first transfer function in the model (2.8a), namely the flow arising from the effective rainfall input uek ; while the lower panel shows the component associated with the effective temperature input Tke . These are plotted on the same scale so that their relative effects are apparent: clearly most of the model output is explained by the effective rainfall transfer function, with the effective temperature transfer function acting to ‘adjust’ this model output, upwards or downwards, to allow for the temperature induced effects.

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Fig. 2.6. Comparison of model output (dots) and measured flow (continuous line) over: (a) a sample of the estimation data set; and (b) a sample of the validation data set.

(a)

flow [m3/s]

600 400 200

(b)

flow [m3/s]

600 400 200 0 J F M A M J J A S O N D J F M A M J J A S O N D

Fig. 2.7. The nonlinear effects of (a) the rainfall, and (b) the temperature on the flow variable, plotted to the same scale to show their relative contributions.

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2.3.4 Physical interpretation of the model The final stage in DBM modelling is the physical interpretation of the model. We have already considered the physical interpretation of the SDP nonlinearities associated with the precipitation and temperature inputs, but we have not yet considered the linear, transfer function part of the model. Using partial fraction decomposition, as in all previous applications of DBM modelling to rainfall–flow data (see earlier references and Young, 2006), each second order transfer function is characterized by real eigenvalues and so it can be decomposed into a parallel connection of first order processes. For illustration, let us consider the transfer function associated with the precipitation– flow process (a similar analysis can be applied to the effective temperature–flow transfer function). The deterministic output xˆ1,k of this transfer function, in response to the effective precipitation input uek , is given by  xˆ1,k =

 βq βs ue , + 1 − αq z−1 1 − αs z−1 k

(2.10)

where βq , βs and αq , αs are the parameters of the first order components revealed by the decomposition. Following the earlier references, the residence times (time constants) of the two parallel processes have very different values, suggesting that they are characterising different flow pathways associated with the quick and slow dynamics of the flow propagation in the catchment. In particular, the quick pathway, with a residence time of Tq = 1/ loge (α1 ) = 0.91 days, appears to reflect the more immediate effects of the various surface and near surface processes; while the slow pathway, with a very large residence time of Ts = 1/ loge (αs ) = 68.62 days, can only be connected with the snow-melt, subsurface and groundwater processes. The ‘partition percentages’ (i.e. the percentages of the flow associated with the two pathways), computed on the basis of the steady state gains of the sub-processes, are Pq = 25.4% for the quick pathway and Ps = 74.6% for the slow pathway. The upper panel (a) of Fig. 2.8 shows the full deterministic output xˆk of the model, compared with the observed flow; while the estimated flow from the quick and slow pathways are shown in the lower two panels, (b) and (c), respectively. In a similar manner, the full line in Fig. 2.9 shows the normalised response of the estimated transfer function to a unit impulsive input of effective precipitation. This represents the unit hydrograph of the effective precipitation–flow component. The decomposed quick and slow components of this hydrograph are shown as dash-dot and dashed lines, respectively. It is clear from both of these Figures that the quick pathway effects dominate the initial response of the catchment to precipitation; while the slow pathway dominates the subsequent response and elevates the tail of the hydrograph. In conventional hydrological terms, therefore, the quick pathway would appear to represent the outcome of the surface and near-surface flow processes; while the slow pathway is a consequence of the deeper groundwater dynamics and the displacement of ‘old water’ into the river channel when effective rainfall events occur (base flow).

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flow [m3/s]

(a) 600 400 200 0 (c) flow [m3/s]

600 400 200 0 (b) flow [m3/s]

600 400 200 0

J F M A M J J A S O N D J F M A M J J A S O N D

Fig. 2.8. Decomposition of the flow: (a) full simulated deterministic model output xˆk compared with the measured flow yk ; (b) the decomposed ‘quick flow’ response; and (c) the decomposed ‘slow flow’ response.

0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0

0

20

40

60

80

100

120

Fig. 2.9. Comparison of the full normalised model impulse response (full line) and the impulse responses of the two decomposed pathways: quick (dash-dot line) and slow (dashed line).

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2.3.5 Uncertainty analysis One aspect of the DBM approach to modelling which differentiates it from alternative deterministic top-down approaches is its inherently stochastic nature. This means that the uncertainty in the estimated model is always quantified and this information can then be utilized for uncertainty and sensitivity analysis based, for example, on the application of MCS methods (see e.g. Young, 1999a). Figure 2.10 shows typical MCS results obtained in the present example: these are the normalized histograms of the derived residence time parameters, as obtained using 5000 Monte Carlo realizations based on the covariance matrix of the estimated parameters (i.e. both the linear TF parameters and the nonlinear SDP s). It is clear that the uncertainty in the quick residence time is relatively small and has an approximately normal distribution; whereas the slow residence time is very uncertain and shows considerable skew towards higher values. The uncertainty on any derived, physically meaningful parameters can be evaluated in this manner, often providing useful insight into the strengths and weaknesses of the model. In addition, MCS can be used to investigate the propagation of uncertainty in the model and the way in which this affects model variables, such as the output flow or the flows in the quick and slow pathways. It can also help in evaluating how well the model parameters, either directly estimated or derived, are identified statistically by plotting the RT2 values for each member of the

Fig. 2.10. MCS analysis: normalized histograms of the residence times associated with the ‘quick’ (a) and ‘slow’ (b) pathways, based on 5000 realizations.

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Monte Carlo ensemble against the associated parameter values (see above reference). In the present example this confirms the poor identification of the slow residence time. 2.3.6 Model developments The present DBM model could be used as a basis for a flow forecasting and flood warning system but, for such an application, it would need to be provided with one-day-ahead rainfall forecasts because, in contrast to the effective temperature–flow transfer function, the effective rainfall–flow transfer function does not incorporate a one day pure time delay (refer to Eq. (2.8a) and the associated definitions). Another possibility would be to re-estimate the model with a false one day time delay in the effective rainfall–flow transfer function (see e.g. Young, 2002) but this has not been investigated so far. The present model does not explain the flow data quite as well as previous DBM rainfall–flow models that have not had to account for snow-melt effects, where the coefficient of determination RT2 is normally in excess of 0.9 (> than 90% of the output flow variance explained by the model), compared with RT2 = 0.847 here. However, it is well known that the modelling of rainfall–flow in rivers where snow-melt effects are important is difficult. Nevertheless, we believe the present model should be considered as a preliminary one that could be enhanced in various ways. For instance, the hysteretic effect associated with the snow-melt has been identified but not included in the present model: there seems no doubt that its inclusion would improve the explanatory ability of the model. Also, the noise component ξk could be improved by allowing for heteroscedasticity and including an explanation of the periodic component in the flow, arising from the hydropower induced fluctuations. In fact, DBM models can include periodic components when considered within a wider, ‘Unobserved Component’ context (e.g., Young et al., 1999). Finally, the present model could provide the basis for the development of a DBM simulation model, as shown in Young (2003), where the SDP based directly on the flow measurement (acting as a surrogate measure of the catchment storage) is replaced by an SDP based of a simple conceptual model for the catchment storage. More recent research has shown that a suitable conceptual model for this purpose is the Matlab/Simulink version of TOPMODEL (Romanowicz, 1997) and this would allow for information obtained from digital terrain data to be included in the overall DBM simulation model. However, such simulation model developments will require further research since the task will be made more difficult by the complex nature of the Ticino Basin and the added complication of the snow-melt effects. 2.4 Conclusions This chapter has outlined the DBM approach to the modelling of environmental systems and applied it, for the first time, to the modelling of flow in the Ticino River basin, where snow-melt effects are important. In this sense, the modelling described in the chapter represents an exploratory exercise, since the inclusion of the snow-melt dynamics considerably complicates the model identification and estimation. As such, there is no doubt that the model could be improved in various ways to enhance its performance and allow for its use in forecasting and simulation modelling applications, as discussed in Sec. 2.3.6

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of the chapter. Nevertheless, the synthesis of the DBM model obtained here does not require any measurements other than flow, temperature and raw precipitation; and it does not depend to any large extent on any a priori assumptions. It is a simple, parametrically efficient (parsimonious) model that is straightforward to identify and estimate using algorithms available in the CAPTAIN toolbox for Matlab. The model is computationally efficient, in contrast to recent rainfall–flow models that rely on numerical Bayesian methods (Thiemann et al., 2001); it explains the data reasonably well on both the estimation and validation sets; and it can also be interpreted in physically meaningful terms, taking into consideration both the rainfall and the snow-melt contributions to the flow. Consequently, even in this initial, preliminary form, the model provides a useful, reasonably validated tool for evaluating the relationship between rainfall–flow and snow-melt on the Ticino River flow. And it provides the basis for rainfall–flow modelling at the catchment scale in other river basins that are similar to the Ticino, where snow-melt is an important part of the flow generation process. Bibliography Akaike, H. (1974). A new look at statistical model identification. IEEE T. Automat. Contr. 19, 716– 723. Beck, M.B. and P.C. Young (1975). A dynamic model for BOD-DO relationships in a nontidal stream. Water Res. 9, 769–776. Beck, M.B. (1979). Model structure identification from experimental data. In: Theoretical Systems Ecology (E. Halfon, Ed.). Academic Press. New York, NY. pp. 259–289. Beven, K.J. and A. Binley (1992). The future of distributed models: model calibration and uncertainty prediction. Hydrol. Process. 6, 279–298. Beven, K.J. and P.C. Young (2003). Comment on ‘Bayesian recursive parameter estimation for hydrologic models’ by M. Thiemann et al. Water Resour. Res. 39(5), 1116. Bryson, A.E. and Y.-C. Ho (1969). Applied Optimal Control. Blaisdell Publishing Co.. Waltham, MA. Jarvis, A.J., P.C. Young, C.J. Taylor and W.J. Davies (1999). An analysis of the dynamic response of stomatal conductance to a reduction in humidity over leaves of Cedrella odorata. Plant Cell Environ. 22, 913–924. Konikow, L.F. and J.D. Bredehoeft (1992). Ground water models cannot be validated. Adv. Water Resour. 15, 75–83. Martinec, J., A. Rango and E. Major (1983). The snowmelt runoff model users manual. Tech. Report 1100. NASA. Washington DC. Norton, J.P. (1986). An introduction to identification. Academic Press. New York, NY. Oreskes, N., K. Shrader-Frechette and K. Belitz (1994). Verification, validation, and confirmation of numerical models in the earth sciences. Science 263, 641–646. Parkinson, S. and P. C. Young (1998). Uncertainty and sensitivity in global carbon cycle modelling. Climate Res. 9, 157–174. Pedregal, D.J. and P.C. Young (2002). Statistical approaches to modelling and forecasting time series. In: A Companion to Economic Forecasting (M.P. Clements and D.F. Hendry, Eds.). Blackwell. Oxford, UK. pp. 69–104. Popper, K. (1959). The Logic of Scientific Discovery. Hutchinson. London, UK. Price, L., M.A. Bacon, P.C. Young and W.J. Davies (2001). High-resolution analysis of tomato leaf elongation: the application of novel time-series analysis techniques. J. Exp. Bot. 52, 1925–1932.

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Price, L., P. Goodwill, P.C. Young and J.S. Rowan (2000). A data-based mechanistic (DBM) approach to understanding dynamic sediment transmission through Wyresdale Park Reservoir, Lancashire, U.K. Hydrol. Process. 14, 63–78. Price, L., P.C. Young, D. Berckmans, K. Janssens and J. Taylor (1999). Data-based mechanistic modelling and control of mass and energy transfer in agricultural buildings. Annu. Rev. Control 23, 71–82. Romanowicz, R.J. (1997). A MATLAB implementation of TOPMODEL. Hydrol. Process. 11, 1115–1129. Thiemann, M., M. Trosset, H. Gupta and S. Sarooshian (2001). Bayesian recursive parameter estimation for hydrological models. Water Resour. Res. 37, 2521–2536. Young, P.C. (1984). Recursive Estimation and Time-Series Analysis. Springer-Verlag. Berlin, D. Young, P.C. (1993). Time variable and state dependent modelling of nonstationary and nonlinear time series. In: Developments in Time Series Analysis (T. Subba Rao, Ed.), Chapman and Hall. London. pp. 374–413. Young, P.C. (1998). Data-based mechanistic modelling of engineering systems. J. Vib. Control 4, 5– 28. Young, P.C. (1999a). Data-based mechanistic modelling, generalised sensitivity and dominant mode analysis. Comput. Phys. Commun. 117, 113–129. Young, P.C. (1999b). Nonstationary time series analysis and forecasting. Progress in Environmental Science 1, 3–48. Young, P.C. (2000). Stochastic, dynamic modelling and signal processing: time variable and state dependent parameter estimation. In: Nonlinear and Nonstationary Signal Processing (W.J. Fitzgerald, A. Walden, R. Smith and P.C. Young, Eds.). Cambridge University Press. Cambridge, UK. pp. 74–114. Young, P.C. (2001a). Data-based mechanistic modelling and validation of rainfall–flow processes. In: Model Validation: Perspectives in Hydrological Science (M.G. Anderson and P.D. Bates, Eds.). John Wiley. Chichester, UK. pp. 117–161. Young, P.C. (2001b). The identification and estimation of nonlinear stochastic systems. In: Nonlinear Dynamics and Statistics (A.I. Mees, Ed.). Birkhauser. Boston, MA. pp. 127–166. Young, P.C. (2002). Advances in real-time flood forecasting. Philos. T. Roy. Soc. A 360(9), 1433– 1450. Young, P.C. (2003). Top-down and data-based mechanistic modelling of rainfall–flow dynamics at the catchment scale. Hydrol. Process. 17, 2195–2217. Young, P.C. (2006). Transfer function models. In: Encyclopedia of Hydrological Sciences (M.G. Anderson, Ed.). Vol. 3. Part II, 128. John Wiley. Chichester, UK. pp. 1985–2000. Young, P.C. and D.J. Pedregal (1999). Macro-economic relativity: government spending, private capital investment and unemployment in the USA 1948-1998. Struct. Change Econ. Dynam. 10, 359–380. Young, P.C. and K.J. Beven (1994). Data-based mechanistic modelling and the rainfall–flow nonlinearity. Environmetrics 5, 335–363. Young, P.C. and M.J. Lees (1993). The active mixing volume: a new concept in modelling environmental systems. In: Statistics for the Environment (V. Barnett and K.F. Turkman, Eds.). John Wiley. Chichester, UK. pp. 3–43. Young, P.C., D. Pedregal and W. Tych (1999). Dynamic harmonic regression. J. Forecasting 18, 369–394. Young, P.C., S.D. Parkinson and M. Lees (1996). Simplicity out of complexity in environmental systems: Occam’s razor revisited. J. Appl. Stat. 23, 165–210.

CHAPTER 3

Bayesian Networks as a Participatory Modelling Tool for Groundwater Protection Hans J. Henriksen1 , Per Rasmusssen1 , Gyrite Brandt2 , Dorthe von Bulow2 and Finn V. Jensen3 1 Geological Survey of Denmark and Greenland (GEUS)

Copenhagen K, Denmark 2 Copenhagen Energy (CE)

Copenhagen K, Denmark 3 Aalborg University, Department of Computer Science

Aalborg, Denmark

3.1 Introduction Participatory approaches help to better control and accelerate the integration, to make the decision making process more transparent and comparable across transboundary river basins and scales, and to increase confidence in an integrated model-based planning process. Integration and participation can be significantly enhanced by using Decision Support Systems (DSS) to assist the planning process, as they provide tools and platforms for collecting data from many sources, integrating models of different nature (physical, socioeconomical and decisional), evaluating the effects of different planning alternatives and, in some cases, negotiating them. Models are an essential component of DSSs since they provide the system representation on the basis of which the planning process is carried on. It is key for the succeeding of this process that stakeholders and water managers share the same representation of the system, i.e. agree on the same model. There are many types of models that can be used to inform and support decision, each of which has its strength and weakness. In this chapter we will describe the use of Bayesian Networks (BNs) – a relatively recent modelling techniques (Pearl, 1988) which is encountering wide diffusion in the environmental modelling community (see for instance Batchelor and Cain, 1991; Varis and Kuikka, 1997; Borsuk et al., 2001, 2004) – in groundwater protection problems. More precisely, we will demonstrate through a case study, the Havelse well field 49

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catchment in Denmark, how BNs can be employed in modelling the ecological, social and economic effects of different management actions aimed at reducing the negative impact of agricultural practices on groundwater quality. As part of an integrated water management strategy the use of pesticides in agriculture is one of the problems to be dealt with. In order to secure good groundwater quality, farming contracts could be one way of decreasing pesticide use. In order to achieve this goal active participation of local farmers, farmers’ associations as well as the local population is necessary in order to convince and carry through the groundwater protection strategy. Farming contracts will influence a number of issues. Therefore, an inter-disciplinary analysis of the possibilities and problems connected with five or ten year farming contracts, with totally stop of the use of pesticides in return for compensational payment is required. The aim of the case study is to describe in what way the introduction in some areas of farming contracts with no pesticide applications may influence farming economics, groundwater quality, biodiversity and the aquatic environment. The classical modelling methods used in groundwater studies (comprehensive models) are not broad enough and cannot encompass other ‘non-technical’ data. This means that these types of classical models can be used for information and consultation but are not really applicable for active involvement. The advantages of the BNs are that they are graphical, focus dialogue, integrate different types of data and are interactive, trans- and interdisciplinary and can quantify difficult cases. The graphical nature of BNs facilitates formal discussion of the structure of proposed model. Also the ability of a BN to describe the uncertain relationships amongst variables is ideal to describe the relationship between events which may not be well understood and intrinsically uncertain. The construction process of Bayesian Networks with stakeholder involvement followed a seven-step procedure. There is no single best way to involve stakeholders, but that does not mean that there is no need for guidelines for how to construct Bayesian Networks with stakeholder involvement. In a recent EU research project (Bromley, 2006) one main deliverable was to establish such a proposal for guidelines for BNs, and the seven step procedure roughly follows this proposal. This chapter is structured in the following way. After the present introduction, Section 3.2 two describes the theoretical basis of Bayesian Networks. Section 3.3 three describes the case study and Section 3.4 four the case study BN model. Section 3.5 is about the pros and cons of BNs for participatory modelling and finally discussion and conclusions. 3.2 Bayesian Networks A Bayesian Network (BN), also called a belief network, is a type of graphical models used for areas where uncertainty is an integral part of the reasoning (Pearl, 1988; Cowell et al., 1999; Jensen, 2001a; Korb and Nicholson, 2004). The structural part is a graph consisting of nodes and directed edges (see Fig. 3.1). A node represents a variable with states, and a directed edge from a node A to a node B represents a cause–effect relation; it indicates that the state of A is likely to have an impact on the state of B. The cause–effect relation needs not be deterministic. For example, the arrow from Water Price to Domestic Abstraction (Fig. 3.1) indicates only, that the price of water is likely

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Fig. 3.1. Example of a simple Bayesian Network representing a river catchment.

to have an impact on domestic consumption, and given a certain price, you will only be able to provide a probability distribution over the domestic abstraction. Therefore, the strength of a cause–effect relation is represented by conditional probabilities. If A is a node with parents B and C, then the model shall include P (A|B, C), the probability distribution for A given any configuration over B and C. For the node Domestic Abstraction for example, you shall specify the probability of each value of domestic abstraction for each combination of values of price and weather (net precipitation). BN s have become a highly successful technique in medical diagnostic systems, analysis, artificial intelligence, and decision-making in real-world domains. They have been applied for many years in practice in a variety of fields, including engineering, science, and medicine (Andreasen et al., 1989; Abramson and Finizza, 1991; Jensen et al., 2001b; Marcot et al., 2001; Borsuk et al., 2002; Gomez, 2004). BN s have gained a reputation of being powerful techniques for modelling complex problems involving uncertain knowledge and uncertain impacts of causes. This is due to the following two characteristics: • BNs as a modelling language has a straightforward semantics, namely that of cause– effect. A domain expert without particular skills in probability theory can easily use them. The transparent semantics, supports communication between humans and a BN model can form a solid basis for discussion. • A BN model over a universe U is a compact representation of the joint probability distribution, P (U ). That is, a BN model holds all sufficient information for reasoning over P (U ). Furthermore, computer systems are available, which efficiently perform the required probability calculations. For example in Fig. 3.1, if water price and land use is known (evidence), these computer systems will very fast calculate (belief propagation) the consequences for the other variables in the model.

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Thanks to their characteristics BNs are a powerful technique to assist decision-making, especially when there is scarcity and uncertainty in the data used in taking the decision and the factors are highly interlinked, all of which makes the problem highly complex. BN s can help formulating environmental management strategies by (Henriksen et al., 2006): • Allowing users to build their own Environmental Decision Support System (EDSS). By building it themselves, users can ensure that the decision support system meets their needs. • Helping users to understand the nature of their decisions better. An EDSS should help users make a better decision, not an easier one. It should not make the decision for the user. Instead, it should encourage the user to identify all relevant information and to analyse it more in depth. • Encouraging users to deal with uncertainty, when appropriate. It must be recognized that is impossible to be certain about the consequences of any environmental management decision, and the uncertainty has to be explicit in the responses from the EDSS . • Encouraging consultation with stakeholders. Without stakeholder consultation, it is unlikely that an environmental management decision can be implemented. The graphical nature of BNs facilitates formal discussion of the structure of a proposed model and the ability of a BN to describe the uncertain relationships amongst variables is ideal to describe the relationship between events, which may not be well understood. When used in integrated water resource management for participatory processes e.g. negotiation and active involvement of stakeholders, BNs are used as a tool that enable and support decision makers to make rational and informed choices between different alternatives. BNs are excellent tools for quantification of the whole picture, e.g. economics, hydrology, hydraulics, environmental and sociological impacts of various instruments and offers a transparent, inclusive, coherent and equitable methodology for dealing with groundwater management that incorporates both formal and informal institutional arrangements (including social norms) of different stakeholder groups (Henriksen et al., 2006). 3.3 The Havelse case study Groundwater is the ‘backbone’ for drinking water supply, industrial supply and supply for aquatic environment in the greater Copenhagen area. In Denmark, 99% of the water supply is groundwater. Furthermore, most Danes agree that clean groundwater and drinking water has the highest priority of all environmental issues. Chemical treatment of groundwater is rarely accepted before it is supplied to the consumers. Agriculture currently accounts for two-thirds of land use in Denmark, and the farmed area covers some 2.7 million ha. More than half of the agricultural area is used to grow cereals, mainly winter cereals. These crops have a high leaching potential, because they need additional fertilisers and pesticides. Pork accounts for about a third of agricultural production value, and diary products have a share of 20% of total production value.

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Denmark is one of the leading countries in the world exporting pork. Agriculture is a rather marginal activity, if measured in terms of the share of agriculture of the Gross Domestic Product. From a preventive groundwater protection point of view, the goal should be no pesticides in the groundwater above the maximum limit value. Perhaps the vulnerability of the area with respect to the deeper aquifers is less than for other Danish aquifers, but we do not know in detail which parameters or factors we should base such an assessment on. In fact, we know very little about the vulnerability of the deep groundwater in the Havelse area at the depths from which groundwater is abstracted. We do know that pesticides have a very low degradation rate (nearly none) once they have reached the anaerobic parts of the aquifer, which in this area is located a few meters below the surface. In the Danish case study the water company responsible for decision making and actions toward well field protection is Copenhagen Energy representing the Municipality of Copenhagen. Copenhagen Energy (CE), is the largest water supply company in Denmark. It supplies roughly one million inhabitants in the greater Copenhagen area with drinking water each day. CE operates Havelse well field together with 55 other large well fields located in northern and eastern Zealand (Fig. 3.2). The aim of the case study was to identify a groundwater protection strategy for CE against pesticide application to agricultural areas, which could be a threat to good groundwater quality. We know a great deal about the quality of the deep groundwater in Denmark from work on a national scale (Jorgensen, 2003). However, we have little knowledge about the quality of the young groundwater and we do not know exactly to which extend pesticide contaminated shallow groundwater, in the long run affects deep groundwater. The application of pesticides to agricultural fields according to regulative guidelines, accidents, point sources, past mistakes, and the spread of pesticides (e.g. BAM) all contribute to a high frequency of findings both in shallow and deep groundwater, as well as in surface water (Henriksen et al., 2004). The most common pesticide found in existing monitoring data is BAM – 2,6-dichlorbenzamide, which is a metabolite of the herbicides dichlobenil or chlorthiamide. BAM is the greatest threat to groundwater quality at the moment (Jorgensen, 2003; Brusch et al., 2004). The use of the BAM herbicide is now prohibited. In the case study area pesticides were found in wells in a village, and it is probably more point source related pollution than diffuse pollution. Similar vulnerable or very vulnerable areas are also found inside the catchment area and in the present well field zone. The vulnerability is here an expression of the thickness of the clay layer above the primary reservoir and whether the aquifers are unconfined or confined. However new pesticide analysis from five drilled wells, four dug wells and Havelse Creek showed various herbicides (BAM and Mechlorprop) in two dug wells and one drilled well, but also AMPA (a degradation product of Glyphosate) in Havelse creek, all with findings above the MAC (maximum admissible concentration for drinking water (0.1 μg/l)). Active groundwater protection from pesticides requires innovative solutions (Brandt and Henriksen, 2003), coordination of actions by various authorities and commitment to implementation from the different stakeholder groups. Lack of knowledge about different sources of pesticide pollution, vulnerability and spreading of pesticides to drinking

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Fig. 3.2. Havelse well field case study area (35 km2 ).

water may hamper and threaten existing protection initiatives and undermine the overall efficiency. In order to identify actions that can be implemented in practice, discussion and dialogue with stakeholders and general public about the factors and consequences are necessary. The traditional approaches taken by CE for groundwater protection are afforestation, establishment of monitoring wells and establishment of local waterworks cooperation forums. Until now farming contracts have only been considered as a possible (novel) future action, not a measure that is a part of CE’s current strategy for groundwater protection. Farming contracts will influence a number of issues. Therefore, an inter-disciplinary analysis of the possibilities and problems connected with five or ten-year farming contracts, with total stop of the use of pesticides in return for compensational payment is required. The aim of the case study is to describe in what way the introduction in some areas of farming contracts with no pesticide application may influence farming economics, groundwater quality, biodiversity and the aquatic environment.

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The involvement of farmers and other stakeholders is vital for developing novel actions for CE’s groundwater protection strategy, because the response and behaviour of these groups are critical for the implementation of such novel initiatives. This situation introduces the need for a participatory modelling and decision-making support tool. The intricate properties of the BNs (interdisciplinary/transdisciplinary, etc.) justified the idea of using BNs for the Havelse case. Section 3.4 describes the way the BNs were applied in the case study, i.e. how the BN was constructed, populated and used. 3.4 The Havelse BN model 3.4.1 BN construction The BN construction process is a complex and tricky process that often require to interactively repeat many steps. For this reason a procedural approach is essential to drive the modeller and the stakeholders through it. Such a procedure makes it easier for all parties to participate in framing the problem and to focus on the dialogue toward areas, which are associated with ambiguity. Problem-framing includes existing views on the problem, how the problem is interwoven with other problems, possibly relevant aspects of the problem that are not dealt with in the management, the role the BN construction is expected to play in the policy process, and the way the BN construction is related to previous studies on the subject. Ambiguity refers to a lack of clarity or consistency in reality, causality, or intentionality. Ambiguous situations are situations that cannot be coded precisely into mutually exhaustive and exclusive categories, which means that the assumptions necessary for rational decision making are not met. The problem in ambiguity is not that the real world is imperfectly understood and that more information will remedy that. The problem of ambiguity is that information may not resolve misunderstandings (Weick, 1995). Although the word ambiguity also means the presence of two or more interpretations, it can also mean something quite different, namely, a lack of clarity, which makes it quite similar to uncertainty. The shock attendant to uncertainty is one of ignorance. So uncertainty comes from imprecision in estimates of future consequences conditional on present actions. To reduce uncertainty and remove ignorance, more information is required. But to remove confusion or ambiguity (multiple meaning), a different kind of information is needed, namely, the information that is constructed in face-to-face interaction that provides multiples cues. To reduce multiple meanings, people need access to more cues and more varied cues, and this is what happens when rich personal media such as meetings (with BN construction and involvement of stakeholders in focused dialogues with managers and researchers as the tool) and direct contact take precedence over less rich impersonal median such as formal information systems and special reports. To resolve confusion, people need mechanisms that enable debate, clarification, and enactment more than simply provide large amounts of data (Daft and Lengel, 1986). The problem with ambiguity is that people are unsure what questions to ask and whether there even exists a problem they have to solve (Weick, 1995). In conclusion, BNs can be characterised as a rather powerful tool for ‘sense-making’, which comes before and is required if subsequent decision making and implementation

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Define the context (Step 1)

Identify factors actions and indicators (Step 2)

Build pilot Network (Step 3)

Collect data (Step 4)

Define states (Step 5)

Construct CPTs (Step 6)

Collect feedbacks from stakeholders (Step 7)

Fig. 3.3. The general procedure for the construction of a tables).

BN

model (CPT: conditional probability

of decisions shall turn vision and innovative instruments into reality. Especially where there are confusion and multiple meanings about management goals and outcomes, BNs are a possible tool, which can enable debate, clarification, and enactment. The activities of relating beliefs and actions are the sense-making process (Weick, 1995). The outcome of such a process is a ‘unit of meaning’ (= the constructed BN), where beliefs and actions are tied together by socially and scientifically acceptable implications. The BN construction in the Havelse case study was undertaken in a stepwise fashion with the scheme of Fig. 3.3. It was considered from the start of the project, if necessary subsequently to repeat Step 3-7 several times based on the character of the feedback. The activities implemented within each step are the following:

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Step 1 Physical and socio-economic boundaries, area of interest, the input to the network (factor, actions and scenarios). A scenario is the background over which the effects of the alternative are evaluated, i.e. the input to the network that cannot be decided, and the outputs (indicators) are tentatively defined. The degree of stakeholder involvement (information, consultation, active involvement) is also determined. Afterwards, at meetings with stakeholders and general public, working groups are set up, stakeholder interests analysed and responsibilities clarified. Step 2 A list of stakeholder and general public concerns is drawn up, and the tentative list of actions and indicators provided at Step 1 is properly modified in accounts of the stakeholder suggestions. A synopsis of data sources, reports, stakeholders and models is described and agreed upon. Step 3 The important variables are identified, and the topology of their direct interconnection (cause–effect relationships) is defined in collaboration with the stakeholders. A tentative network structure is obtained. On the basis of the stakeholder technical expertise and of their willingness to participate the rules for participation are set up and the platform for information decided. Step 4 The data required to fill in the network are collected from different sources (including stakeholders and general public). Data are analysed, processed, and initially the tentative network obtained in Step 3 is presented as an illustration of the type of analysis that will be carried out in the following steps. Step 5 The stakeholders and the public provide the first feedback on the tentative BN, on the basis of which this is adjusted and redefined with additional variables and links. For each variable of the network the range of values (states) which it can assume are specified and agreed upon. Step 6 The BN is populated, i.e. the CPTs (conditional probability tables) of each variable are filled in using the quantitative information obtained from domain models and experts. This includes a review of the networks at individual stakeholder meetings. The BN should also be carefully checked for internal consistency at this stage. Parameter learning is encouraged as a method of bridging data and CPTs. At the end of this Step a populated and ready-to-work BN is obtained. Step 7 Stakeholder and general public opinions on the network obtained at Step 6 are collected. If all the stakeholders and the public agree on the network the final BN is documented and implemented. Otherwise, if additional adjustments are required Steps 3 to 7 are iteratively repeated. Once the procedure ends, the network obtained is run (i.e. the belief is forward propagated from the roots to the outputs) by varying the evidence on the action nodes, so that the values of the indicators are computed for different combinations of actions. In this way a ‘what if’ analysis is conducted through which the stakeholders and the public may look at the effects that the divergent proposed actions have on their interests. Information, consultation and active involvement of professional stakeholders and general public is a necessary part of the BN construction and can be carried out using announcements and facilitated public meeting (Step 1-2), working group meetings (Step 1-3), newsletters, a Web site, individual meetings (Step 4-6) and a joint working group (Step 7).

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In the Havelse case study the facilitator of the public meeting and workshops was the Agenda 21 Centre in Frederikssund. Various subcontractors have participated in the project that, e.g. farm economics (Rasmussen, 2003) and value of biodiversity, land use, etc. (Schou, 2003). By applying the above procedure to the Havelse modelling, the network in Fig. 3.4 was obtained. We will illustrate it in the following section. 3.4.2 The BN model The general idea with the BN for farming contracts was to analyse the effects of compensation payments to farmers for not using pesticides on agricultural fields. The higher the compensation level, the more farmers will join such a voluntary farming contract. However, farmers signing a contract will also try to optimise land use by growing crops more suitable for farming without pesticides, and this means that contracts will also affect land use. Farming contract restrictions and land use affect the farmers’ bottom line (Fig. 3.4), so to speak, and this, together with the compensation payment, has an impact on farm economics as a whole. All the relationships in this part of the farming contract BN were initially provided by subcontractor Svend Rasmussen from the Royal Veterinarian and Agricultural University (KVL), which also collected the data for pesticide application for different crop rotations (Rasmussen, 2003). The other part of the BN shows variables concerning environmental impacts of pesticide application. If farming contracts are established then the pesticide load is reduced, which again has a knock-on effect on diffuse load (the non-point discharge to groundwater from the root zone) and the surface water quality, to an extent dependable of soil and non-point application (whether it is herbicides, fungicides or insecticides we have chosen to analyse). Diffuse load influence shallow groundwater quality, but this variable is also influenced by point sources. Finally, shallow groundwater quality influences deep groundwater quality. These variables were based on information from monitoring programmes at GEUS and CE (Jorgensen, 2003; Brusch et al., 2004). Furthermore, research had shown that high concentrations of herbicides in surface water impacts the reproductive capability of leopard frogs (expressed by the variable biological a BN normality). The types of variables in the BN in Fig. 3.4 can be grouped into five categories: 1. Objectives. Things that are affected: Shallow groundwater quality, Biological abnormality, Biodiversity, Surface water quality, Recreative value and Deep groundwater quality. Overall objective: Safe supply. 2. Actions. Things, which must be implemented or included in CE policy: Compensation, Non-point application and Remove point sources. 3. Intermediate factors. Variables, which link objective variables with action variables: Farming contracts, Land use, Farm economics, Pesticide load, Diffuse, Surface water quality, Point sources and Hunting/fishing. 4. Controlling factors. Factors that control the environmental system: Sand/clay, Animal/vegetable production, SFL area (vulnerable farming areas). Uncertain controlling factors: Perception of vulnerability (stakeholders do not agree).

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Fig. 3.4. Final BN for voluntary farming contracts.

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H.J. Henriksen et al. 5. Decision and Utility variables. Variables that are included in order to calculate and visualise a certain utility: All-farm economy and Utility node.

The decision variable All farm economy is simply added to the BN in order to make the total utility for farmers fully transparent (production exclusive fixed costs for machinery, etc. plus compensation payment). One variable is aimed at directly focusing on overall outcome of BN: Safe supply of drinking water, a boolean variable which can be true or false: true means that clean groundwater will have a content of pesticides below the maximum allowed concentration, for at least 50 years. 3.4.3 Population of BN The next step is to complete the conditional probability tables (CPT) that lie behind each of the variables. This is a task that requires care and patience because if the CPT are wrong, the network output will be equally wrong. As well as being one of the most important, it is also the step that causes most difficulty for the network designer and the stakeholders who provide information for the table. The procedure used to complete CPTs in the Havelse case were based on (1) monitoring data and model data sets and (2) stakeholder opinion/knowledge and expert opinion. Data for variables such as land use, pesticide load and farm economics often have to be simulated using a model. This means that for different scenarios there are model results available providing input for CPT for these variables. Variables like diffuse, point sources, shallow groundwater, deep groundwater quality and surface water quality was available from monitoring programmes covering more than a decade of measurement. In cases where data linking two variables was scarce, or none existent, particularly when the link is difficult to quantify, a turn to local stakeholder knowledge or expert knowledge was chosen. Among the variables difficult to quantify are those dealing with social or cultural issues, but economic factors can also be problematic. The variables compensation and farming contracts are examples of such variables, where it was important to carefully elicit proper values for the case study ‘context’ (which is partly social constructed). Since we are relying on stakeholder input and expert opinion in the Havelse case study, the data (for the CPTs) were carefully elicited and input into the tables manually. It was also possible to handle data manually from the monitoring and model data which was used, because the BN has a reasonable (not too many) number of variables and states. At the workshop meetings the input data were discussed and adjusted based on feedback from stakeholders and experts. A number of things were learned throughout the process using this approach, in order to allow data to be entered manually. It is important to minimise the size of the tables, using expert inputs to input probabilities means that values can be entered directly into the table since he or she is likely to be familiar and comfortable doing so, and some stakeholders may be experts in their own right. A good example is offered by the variable farm economics which has 3 parent nodes: farming contracts, animal/vegetable and land use. A combination of three parameters and a combined number of 21 states meant that the CPT for farm economics required 384 values. However, despite the size and complexity, the CPT was successfully completed in conjunction with an expert familiar with the economics of agriculture in the area, and drawing on farm economic modelling results.

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Parameter learning calculating the conditional probabilities for variables, given the link structures and data is an efficient method available for BN constructors if sufficient extensive data sets to generate enough cases (experiences) for the resulting probability distributions to be robust are available. One of the most common used methods for parameter learning is the expectation-maximisation (EM) algorithm (Jensen, 2001a). However, this method was not applied in the present case study, because the number of cases was too limited to relay on the automated approach. Instead, data were manually entered and adjusted, and by simulation with values in CPTs for different combination of parent variable and a range of actions, the resulting probability distributions for various variables were examined and discussed with experts and stakeholders. Different approaches were subsequently used to check the network for consistency (structure, values placed in CPTs and checks in diagnostic mode) before the completed network and different combination of actions or scenarios on the objective variables were presented to the stakeholders. A first step here is to check whether the network behaves in a logical way, which was done by noting the impact of each implementation and controlling variable one by one, and by setting all implementation and controlling nodes to represent the current situation. Next by changing one of these to another state to represent a different action or scenario (instantiating the node) the impact and response on the variables linked to it was examined to see if it responded in a logical way. A check of the network in diagnostic mode is a test where a child node is fixed, which then propagates back to describe the states of the parents needed to generate that condition. In the Havelse case we can give an example of such a diagnostic test. If the variable land use is in the state 22% ‘set aside’ and 78% ‘grass’, then the hunting and fishing income from the land will be 200 DKK per ha. Now, fixing the hunting and fishing income in diagnostic mode at 200 DKK per ha, this then propagated back to indicate that the best combination of land use to achieve this income is 22% ‘set aside’ and 78% ‘grass’, which confirms the original prediction. The diagnostic mode can thus be used to determine the land cover required to generate any selected level of income. 3.5 Use of the BN As already anticipated, the populated BN was used to perform a ‘what if’ analysis by putting the evidence on different values of the input variables representing actions and, via belief propagation, computing the effects on different indicators (output). Two class of alternatives were analysed (Henriksen et al., 2004): 1. Farming contracts: voluntary farming contracts (different compensation level), in the following denoted as A. 2. Both actions: voluntary farming contracts plus removal of point sources (it is assumed that all point sources are simply removed), in the following denoted as B. Figure 3.5 illustrates that the compensation payment must be corresponding to MVJ high level compensation agreement. The Danish acronym MVJ stands for ‘Environmental friendly agricultural agreements’ that beside no pesticide application includes other restrictions, e.g. use of fertilizers, choice of vegetation, etc. The level of compensation for MVJ is DKK 4400 per ha/year, of this up to 60% financed by the EU .

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Fig. 3.5. Comparison of overall indicator (safe supply) for the two alternatives: farming contracts and removal of point sources (two actions) (a) and water quality indicators (probability of water quality exceeding 0.1 μg/l (b) for different levels of compensation.

The only way to achieve the ‘preventive goal’ (minimum a 95% probability for the state ‘true’ of the safe supply) is by the high level compensation of the standardized MVJ agreement. Even if both actions are taken, with an additional cost for removing all the point sources, the result is the same. We have not considered the move of the wellfield away from the Havelse creek in the present analysis. This could both increase the probability of the safe supply being in the state of ‘true’, but other effects could also adversely decrease this probability (intrusion of salt water closer to the Roskilde Fjord or unknown point sources close to the new wellfield location). For a compensation of DKK 500 per ha/year, few farmers (4%) would join voluntary farming agreements prescribing no pesticide application. For DKK 1000 per ha/year,

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a slightly larger fraction would join (11%). At DKK 2500 per ha/year, nearly 50% would join, but their willingness to sign voluntary preventive farming contracts (no pesticides) is much less than the input from the expert indicated (Rasmussen, 2003), which indicated a break-even point of below DKK 1500 per ha/year. The main problem is related to a lack of commitment to realistic levels of compensation. Farmers in the area have suggested compensation payment levels of about DKK 5000 per ha/year. Farmers’ organizations (NOLA and Sjaellands Familielandbrug) have indicated that such agreements should either offer a very high compensation (up to DKK 7000 per ha/year) or not be part of groundwater protection at all (expropriation may be necessary and a more feasible method). The value that alternative A produce for the indicator surface water quality show that the probability of polluted deep groundwater above MAC drops to below 5% at a compensation level of DKK 2500 per ha/year. This probability varies for the different compensation level from 8.3% (none) to 7.3% (500), 7.5% (1000), 6.6% (1500), 5.8% (2000), 4.3% (2500) to 1.3% (DKK 44 per ha/year). Alternative B reaches the 5% level at DKK 1000 per ha/year, signifying that action directed at point sources (removal) may be a necessary element of groundwater protection policy. With alternative A, shallow groundwater has a probability of pesticide content of between 41.7% (none) and 33.2% (DKK 1500 per ha/year). Not until DKK 4400 per ha/year does the probability drop below 10% for clean groundwater (6.6% probability). Alternative B results in an achieved goal of a 5% level at DKK 4400 per ha/year including removal of point sources. Similar results were found for surface water. Furthermore, the exercise demonstrated that cost/benefit issues and especially the implementation of management action plans are associated with many more issues than expert knowledge normally takes into consideration. In our case, a barrier for voluntary farming contracts is not data or information on economic conditions in farming, but, to a much greater extent, perception among stakeholders of the soundness of the action. Attitudes, beliefs and group behaviour (Robbins, 2003) among farmers and their organizations, and the uncertainty and lack of data, play a more important role than a possible financial benefit in the short run. Since farming contracts also are rather difficult to manage (Brouwer, 2003), at least as voluntary agreements negotiated within a wellfield catchment area as part of a groundwater protection plan, the entire approach is both costly and difficult to implement. 3.5.1 Stakeholder involvement The starting point for identifying stakeholders was trying to list categories of water users, potential groundwater pollution sources, and authorities in the area: local waterworks, other water consumers, farmers, industry, anglers, the county and the municipalities. All professional stakeholder organisations that were found to have a potential or even marginal interest in groundwater protection in the specific area were invited to a one-day workshop in October 2002. Many ‘green’ NGOs did not show up and the industrial sector preferred to use their political contacts on groundwater issues. The workshop resulted in the formation of a professional stakeholder working group with ten institutions, including the project end user (Copenhagen Energy, the local

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Agenda 21 Centre (was also used as facilitator in relation to citizens’ group), and the Geological Survey Denmark and Greenland (GEUS). In November 2002, a public meeting was held in the local community hall. Invitations were distributed to more 1100 local households and the meeting was announced in the local newspaper. About 100 people and the local TV station showed up for the meeting. The meeting resulted in a local citizen-working group. At both meetings, stakeholders were asked to present issues and problems they found important in relation to groundwater protection. The idea behind splitting up the stakeholders into two groups, was the perception that the professional stakeholders are already deeply involved in groundwater management and protection, whereas local citizens might have another starting point for their involvement in groundwater management and protection (Henriksen et al., 2004). At meetings and workshops with citizens’ group, we used a facilitator from the local joint municipality Agenda 21 Centre. Facilitation in relation to the group of professional stakeholders was not systematic throughout the project, but the first meeting was facilitated by Agenda 21 Centre. The citizen group met five times in the first half of 2003. The facilitator guided the meetings. GEUS and CE only participated in two of the five meetings to answer specific questions and to introduce and discuss the development of the BNs. The citizen group published two newsletters in the first half-year of 2003. A third newsletter was published in July 2004 after finishing the final MERIT report. They were distributed to 1000 households in the local area. The newsletters included mainly articles related to groundwater protection, water supply and water quality, and introduced the members of the citizen group. The production and distribution of the newsletter was financed by the MERIT project. At the final joint meeting in March 2004, the stakeholder groups were asked to comment on the involvement process on the basis of four questions (Henriksen et al., 2004): 1. Is there a need for further initiatives for the protection of groundwater and the stream/bay? 2. How have you experienced the MERIT project progress (BNs, citizens’ meeting, workshops, citizen groups, newsletter, individual meetings, etc.)? 3. How should stakeholders be involved in the future in, for example, active groundwater protection and the establishment of wetlands? 4. Other comments to the process? Furthermore, comments and suggestions from the stakeholders and citizens’ group to the draft report were collected by consultation (from questionnaires and hearing in May 2004) and consequences for the final reporting addressed. The overall idea was to begin the process as openly as possible, to get an idea of how stakeholders could contribute to an improved protection of the groundwater resources in the area. Problems encountered in BN development were: • Stakeholder input to networks and probability tables (numbers) required individual meetings. • It was not that easy to understand the networks (a way of thinking that requires a little practice, if not properly explained.

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Table 3.1. Strengths, weaknesses, opportunities and threats (SWOT) analysis of stakeholder engagement process. Strengths Public participation can. . .

Weaknesses Public participation can be weakened by. . .

Opportunities Public participation offers the opportunity to. . . Build trust and capacity

Make use of local and citizen knowledge not known by authorities

A lack of resources (time, money, staff)

Encourage diverse perspectives (and thus encourage issues not thought of)

A lack of rules for participation

Empower people by starting a dialogue and improving openness

Enable a better evaluation of the issues

A lack of in-depth involvement of authorities

Expand the limits of understanding (working together to solve problems)

A lack of hands-on BN for stakeholders

Improve the accountability of stakeholders

Threats Public participation can be threatened if. . . The public thinks that the process is a formality (that minds are already made up)

A vocal minority dominates public meetings

A lack of professional supervision of the stakeholder involvement process

• Difficult to motivate stakeholders to become involved in BN development. • Problems with conditional probability tables in different stakeholder groups. • We did not receive as much input to the BNs as expected from stakeholders. BN s can help formulate environmental management strategies by allowing users to build their own decision support system that meets their needs, helping users to better understand the nature of their decisions, and encouraging users to deal with uncertainty and to consult stakeholders and members of the general public. Table 3.1 and Table 3.2 contains an interpretation of BNs with respect to strengths, weaknesses, opportunities and threats based on our experience. An important characteristic of BNs is that the tool can be used ‘interactively’ for uncertainty assessment and communication with the stakeholders involved. However, it is important to apply a kind of ‘protocol’ for BN construction in order to be able to explain to stakeholders, experts, users, etc. what input is required at different stages of the BN development.

3.6 Discussion The results of the case study showed ‘a paradox’. On the one hand, BNs can create space for an open and non-deterministic dialogue with stakeholders due to the flexibility of the decision support tool. This allowed factors (nodes), associations (directed links) and probabilities of the graphical model to be adjusted, reconstructed and validated throughout the

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Table 3.2. Strengths, weaknesses, opportunities and threats (SWOT) analysis of tory modelling tool for water resources management. Strengths Excellent for structural learning, elegant statistical approach and data mining for analysis of complex systems

Weaknesses Difficult to understand for non-experts

Easy to develop a BN with nodes and directed links and update it with input from stakeholders

Feedback nodes are not allowed; some problems in the real world cause strong feedback

Social and ecological issues can be incorporated and coupled with hydrology

The interdisciplinary approach raises problems with organising knowledge input and data input (academic territories, illusion of techniques)

BN s

as participa-

Opportunities Possible to understand for representatives of general public if explained properly by the specialists

Threats Not easily understood if not properly explained

The opportunity to work with more disciplines

Over-expectations with respect to modelling capabilities

Excellent for strategic considerations (indicators, actions and additional data requirements) Expert knowledge and data can be combined and modified/balanced through stakeholder involvement

Requires panel of expert input for all domains ⇒ resources and time (equivalent to numerical models)

Improves conversation/ dialogue with stakeholders

Too much ‘hot air’/soft discussion (difficult to govern the process; ‘focused stakeholders’)

Very useful for complex systems

There is a danger that use of BNs causes ignoring of real data and knowledge

Excellent for integration and breakdown of barriers between different domains, e.g. economy, hydrology, ecology, social (different time and spatial aggregation)

Not useful for implementation of specific protection zones (physical-based model required)

New problems can be structured and analysed quickly

Political manipulation

Holistic approach

BN s describe an understanding of the system and processes that are not physically based (more information flow than mass flow)

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Table 3.2. Continued. Strengths Non-linearity not incorporated

Weaknesses Can be used even if data sets are incomplete

Opportunities The BN hides the complexity of the system from the users (underlying conditional probability tables are rather complex!)

Threats

Ability to predict future state of systems based on simplified assumptions

Data manipulation is possible (it is easy to get carried away)

A possible tool when dealing with water managers sceptical about comprehensive models and questioning the need for catchment modelling

Experts do not want to provide input for the conditional probability tables (numbers): defending academic territories!

It is possible to ‘validate’ the importance of value and belief when consulting stakeholders

BN s work on ‘aggregated data’ (probabilities)

Not possible to utilise all collected data (temporal and spatial variation/information in data)

process and based on inputs from all involved stakeholders and experts. This means that BN s were powerful for integrating data and knowledge from different domain experts and capable of handling uncertain information in a practical and easily understandable manner. Constructing the qualitative part of a belief network (nodes and links), although elaborate, seemed relatively straightforward and experts seemed comfortable doing so. This part of the net was relatively easily communicated to stakeholders. On the other hand, getting stakeholders, general public and even experts to understand and accept the idea behind the BNs used for decision making was a demanding task (Varis and Kuikka, 1999). Especially the required probability assessments for the BNs were not easy to understand or accept by stakeholders. Even domain experts had problems to express all these probabilities numerically, something they were reluctant to do. So the quantitative part, with the probabilities over the variables, was more problematic. Probabilities offer an alternative approach to communicating data and model results which takes advantage of the ability of people to understand outcomes presented in probabilistic language. Instead of a pesticide concentration of 0.12 μg/l simulated by a model, which is likely to be received with scepticism by stakeholders because it does not account for natural variability in the system, the information should be presented categorically in the following form: ‘There is a 37% probability that the concentration will be below 0.01 μg/l, a 51.5% probability that it will be between 0.01 and 0.1 μg/l, and a 11.5% probability that it will be greater than 0.1 μg/l.’ One reason why probabilistic information of this form is useful is that it lends itself to evaluating the risk associated with different alternatives. Probabilities can be multiplied by the potential cost or benefit of different outcomes in order to elicit the ‘expected value’ of a decision. Expected values of different management alternatives can then be compared

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to aid decision-makers in selecting an option. Additionally, the risk of an outcome can be interpreted as a margin of safety associated with the option. In a BN, this is done by introducing ‘utility nodes’ that perform risk assessment by multiplying and adding total costs or benefits (in monetary value or other type of utility). When applying the precautionary approach in groundwater protection, the role of uncertainty is vital: the higher it is, the lower the pressures allowed from various non-point and point pollution sources should be. In addition, recent paradigms for risk-informed decision-making call for a participatory procedure in which the various stakeholders become involved early on in the risk assessment process to ‘characterize’ risks even before a formal assessment of them is made. This does not diminish the role of modelling and quantification, but is aimed at eliciting the ‘values’ and the perspectives of the community involved so that the multiple dimensions of risk can be taken into account early in the assessment. Decision-makers need to be informed not only of the available scientific knowledge but also of policy-relevant uncertainties and lacunae in the knowledge base (Levin et al., 2004). For this to be possible, uncertainties must be transparently discussed and communicated. A key problem with the probabilistic approach is that most people feel more at ease with verbal probability expressions than with numbers. When people communicate probabilities, they frequently do so in words rather than in numbers. So when it comes to reasoning and to communicating the results of BNs to users, the mode in which people normally represent probability must be taken into account as well (Renooij et al., 1999). This has often been considered a major obstacle, one of the reasons being that experts are reluctant to provide numerical probabilities. However, recent research activities have made some progress in this field by developing a probability scale that contains words as well as numbers (Renooij et al., 1999; Witteman and Renooij, 2003 and Gaag et al., 2002). This leads us to the following conclusions regarding BNs as a participatory modelling tool. BNs demonstrated several advantages compared to traditional approaches. BNs enabled locally based solutions (more than before). They provided local acceptance of decisions and solutions and improved the dialogue between the water company, local stakeholders and authorities. They encouraged diverse perspectives (and thus identified issues not thought of). They enabled a better evaluation of the issues. They made use of local and citizen knowledge not known by the authorities (Henriksen et al., 2004), see Fig. 3.6. The weaknesses of BNs as a participatory modelling tool were the time-consuming and long-lasting process in construction and evaluation of BNs, which had to be properly organised and conducted. This means that, if there is a lack of resources (time, money, staff), rules for participation, in-depth involvement of authorities, hands-on BN for the stakeholders and professional supervision of the stakeholder involvement process, then the credibility of the BNs are likely to be questioned by stakeholders and general public. Regarding involvement of stakeholders and general public (Mostert, 2003a), in BN development the following observations can be made: Stakeholders have an impact on the BN development (on variables, links and CPTs, e.g. ‘perception of vulnerability’ variable and behaviour of farmers in relation to compensation payment).

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Benefits of BNs in stakeholder involvement process

Low Type of stakeholder involvement Type 1 information

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Fig. 3.6. The Negotiation Support System.

Evaluation of BNs with input from stakeholders and general public is a necessary step. In the early, more qualitative stages, broader groups of stakeholders and the general public may provide relevant input to BN development. In the later, more quantitative stages, it is better to consult stakeholders and members of the general public at individual meetings or maybe in stakeholder and citizens’ groups that each focused on a ‘domain of interest’ because they were reluctant to give quantitative inputs in larger groups. Experts are necessary for quantitative input to BNs. In the case study, we had two experts in farming economics and socioeconomics in addition to the geological and hydrological experts from CE and GEUS. It would have been an advantage in BN development if the panel of experts had included an expert on biodiversity and/or pesticide-exposed aquatic environment as well. The results of BNs must be followed by a detailed description of the parameters used and why, plus a description of the results and their consequences in order to make BNs as transparent as possible. It is much too risky to allow politicians or civil servants to make decisions based on the ‘naked’ data. So one should rather allow stakeholders and citizens to become more involved. It is important to provide users with more easily understandable explanations of the results, for which numbers not necessarily was the best option, and verbal communication is a necessary alternative. Furthermore, an expert’s assessments may reflect various biases, where an expert consistently gives probability assessments that are higher or lower than they should be.

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In order to provide a credible BN it is necessary to engage stakeholder groups in the validation of BNs. This is a crucial and demanding task. 3.7 Conclusion In conclusion, the use of BNs went beyond information and consultation and required the full involvement of stakeholders in their construction and validation. The advantage was a reduced risk of lack of support by stakeholders during the implementation phase of a given action plan. The benefits of BNs were greatest when there was a high degree of interaction between researchers, users, water managers, stakeholders and general public. BN s are most powerful when integrating different domains, e.g. physical, social, economic and ecological, in the early stages of preparing a management plan with the involvement of stakeholder groups and general public (Mostert, 2003a, 2003b). A panel of experts is valuable in covering each domain included, for providing proper input and/or for reviewing the results from the BNs developed. Clear rules of the game are important: it is necessary to prepare a stakeholder involvement plan describing how to involve stakeholders and general public which is balanced with respect to problem framing and the type of decision support system used for planning and implementation. It is better to involve stakeholders and public in ‘temporary’ groups or at individual meetings when direct input is required, especially when collecting data for BNs; feedback on states, links and CPTs than it is to run the process with broad, permanent groups of stakeholders and citizens. Do not be afraid of actively involving citizens: but be careful to inform and explain properly about the tasks and goals and do always allow feedback and comments on the BN development process by presenting the graphical model and easily understood descriptions and results. If representatives of the general public are involved, be sure there is enough time and money to run the process according to the stakeholder involvement plan. Acknowledgements The present work was carried out within the Project ‘Management of the Environment and Resources using Integrated Techniques’ (MERIT), which is partly funded by the EC Energy, Environment and Sustainable Development programme (Contract EVK 1- CT 2000-00085). Bibliography Abramson, B. and A. Finizza (1991). Using belief networks to forecast oil prices. Int. J. Forecasting 7(3), 299–315. Andreassen, S., F.V. Jensen, S.K. Andersen, B. Falck, U. Kjærulff, M. Woldbye, A.R. Sørensen, A. Rosenfalck and F. Jensen (1989). Computer-Aided Electromyography and Expert Systems. Chap. MUNIN – an expert EMG assistant. Elsevier. Amsterdam, NL, pp. 255–277. Batchelor, C. and J. Cain (1991). Application of belief networks to water management studies. Agr. Water Manage. 4(1), 51–57.

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Borsuk, M.E., C.A. Stow and K.H. Reckhow (2004). A Bayesian network of eutrophication models for synthesis, prediction, and uncertainty analysis. Ecol. Modell. 173, 219–239. Borsuk, M.E., C.A. Stow, D. Higdon and K.H. Reckhow (2001). A Bayesian hierarchical model to predict benthic oxygen demand from organic matter loading in estuaries and coastal zones. Ecol. Modell. 143, 165–181. Borsuk, M.E., P. Reichert and P. Burkhardt-Holm (2002). Integrative environmental prediction using Bayesian networks. In: Integrated Assessment and Decision Support, Proceedings of 1st Biennial Meeting of IEMSS, June 24–27 (A.E. Rizzoli and A.J. Jakeman, Eds.). Lugano, CH, pp. 102–107. Brandt, G. and H.J. Henriksen (2003). Protection of drinking water sources for quality and quantity. Groundwater protection in the Greater Copenhagen area. In: Future Scenarios for Water Management in Europe. FIRMA Conference, 19–20 February. Barcelona, SP. Bromley, J. (2006). Guidelines for the use of Bayesian networks as a participatory tool for Water Resource Management. Management of the Environment and Resources using Integrated Techniques (EVK1-CT-2000-0085 MERIT). Centre for Ecology and Hydrology. Wallingford, UK. Brouwer, F. (2003). Co-operative agreements in agriculture. National report: Denmark. Technical report. Agricultural Economics Research Institute (LEI). Brusch, W., J. Stockmarr, Fv. Platen-Hallermund and P. Rosenberg (2004). Pesticide pollutent water from small waterworks. Technical report. Geological Survey of Denmark and Greenland. Copenhagen, DK. in Danish. Cowell, R.G., A.P. Dawid, S.L. Lauritzen and D.J. Spiegelhalter (1999). Probabilistic Networks and Expert Systems. Springer Verlag. Berlin–Heidelberg–New York. Daft, R.L. and R.H. Lengel (1986). Organizational information requirements, media richness, and structural design. Manage. Sci. 32, 554–571. Gaag, L.Cv., S. Renooij and C.L.M. Witteman (2002). Probabilities for a probabilistic network: a case study in oesophageal cancer. Artif. Intell. Med. 25, 123–148. Gómez, M. (2004). Advances in Bayesian Networks. Chap. Real-world applications of influence diagrams. Springer-Verlag. New York, NY, pp. 162–180. Henriksen, H.J., P. Rasmussen, G. Brandt, D. v. Bülow and F.V. Jensen (2006). Public participation modelling using Bayesian networks in management of groundwater contamination. Environ. Modell. Softw. in press. Henriksen, H.J., P. Rasmussen, G. Brandt, Dv. Bülow, L.F. Jørgensen and P. Nyegaard (2004). Test of Bayesian Belief Network and stakeholder involvement. Groundwater management and protection at Havelse well field in Northern Zealand. Evk1-2000-00085. Geological Survey of Denmark and Greenland and Copenhagen Energy. Copenhagen, DK. Jensen, F.V. (2001). Bayesian Networks and Decision Graphs. Springer Verlag. New York, NY. Jensen, F.V., U. Kjærullf, B. Kristiansen, H. Langseth, C. Skaanning, J. Vomlel and M. Vomlelova (2001). The SACSO methodology for troubleshooting complex systems. Artificial Intelligence for Engineering, Design, Analysis and Manufacturing 15, 321–333. Jorgensen, L.F. (2003). Groundwater monitoring 2003. Technical report. Geological Survey of Denmark and Greenland. Copenhagen, DK. Korb, K.B. and A. Nicholson (2004). Bayesian Artificial Intelligence. Chapmann and Hall. Boca Raton, FL. Levin, R., S.O. Hansson and C. Rudén (2004). Indicators of uncertainty in chemical risk assessment. Regulatory and Pharmacology 39, 33–43. Marcot, B.G., R.S., Holthausen, M.G. Raphael, M. Rowland and M. Wosdom (2001). Using Bayesian Belief Networks to evaluate fish and wildlife population viability. Forest Ecol. Manag. 153(1–3), 29–43. Mostert, E. (2003a). The challenge of public participation. Water Policy 5(2), 81–97.

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Mostert, E. (2003b). Public participation and the European Water Framework Directive. A framework for analysis. Inception report of the HarmoniCOP project – Harmonising Collaborative Planning. EU-FP5. Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann Publishers. San Francisco, CA. Rasmussen, S. (2003). Economic losses by pesticide free agriculture in Havelse catchment. Technical report. Royal Danish Veterinary and Agricultural University. Copenhagen, DK. Renooij, S. and C. Witteman (1999). Talking probabilities: communicating probabilistic information with words and numbers. Int. J. Approx. Reas. 22, 169–194. Robbins, S.P. (2003). Organizational Behaviour. Pearson Education International. San Diego, CA. Schou, J.S. (2003). Economic analysis of pumping strategies for groundwater abstraction in the Havelse stream catchment. Technical report. National Environmental Research Institute. Roskilde, DK. Varis, O. and S. Kuikka (1997). Bayesian approach to expert judgment elicitation with case studies on climatic change impact assessment on surface waters. Climatic Change 37(3), 539–563. Varis, O. and S. Kuikka (1999). Learning Bayesian decision analysis by doing: lessons from environmental and natural resources management. Ecol. Modell. 119, 177–195. Weick, K.E. (1995). Sensemaking in Organizations. Foundations for Organizational Science. Sage Publications. London, UK. Witteman, C and S. Renooij (2003). Evaluation of a verbal-numerical probability scale. Int. J. Approx. Reas. 33, 117–131.

CHAPTER 4

Exploring Water Conservation Behaviour through Participatory Agent-Based Modelling

Andrew Rixon, Magnus Moglia and Stewart Burn CSIRO Manufacturing and Infrastructure Technology Highett, Victoria, Australia

4.1 Introduction The pre-industrial period found water utilities developing ‘big pipe networks’, with centralised structures aimed at controlling disease outbreaks (Livingston et al., 2004). Since then population growth, technological development, trends in urban and rural development, and human-induced climate change are have been driving future water use (Kuylenstierna et al., 1997). This has meant that urban water utilities have continued to evolve as socio-economic and environmental conditions have changed. With large pipe networks having been established within cities, a strong supplyoriented logic of development prevailed. Water utilities were driven by the basic assumption that economic growth generates new demands for services. However, during the last decade, corporatized water utilities, guided by regulatory frameworks, have had to address environmental concerns, decaying infrastructure, water shortages and the inability to continue the supply-side expansion (Marvin et al., 1999). What has emerged is a demand management paradigm. Under this paradigm, the water utility attempts to influence and reshape demand by mechanisms such as metering, where variable tariff schemes are used to impact on peak demand periods, and initiatives such as water recycling, and the promotion of water-saving technologies and behaviours. With such programs, the water utility can find itself embedded in a complex sociopolitical landscape. How willing are people to accept these water-demand management strategies, and how fair are tariff structures in lower socio-economic areas (Turton, 1999)? It has been suggested that policy debates could start to recognise a much wider role for water utilities within their regions, and the potential for strengthening their contribution to social cohesion (Marvin et al., 1999). 73

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Although such demand-side strategies employed by the water utility focus directly on human behaviour, studies involving human beliefs, behavioural factors on water conservation and adoption rates of water-smart technologies are in their infancy. Although there are a few exceptions (see Clark et al., 2000; Corral-Verdugo et al., 2003; Syme et al., 2004). The growing importance of public participation and engagement within sustainability science has led to a reformulation of tools and methodologies which can be meaningful to both the researcher and the participants (Kasemir et al., 2003). One key strength of tools such as the agent-based modelling approach over more traditional equation-based approaches is that mathematical equations can be represented by soft sentences which make more sense to those not involved in model-building on a daily basis (Tillman et al., 2001). The problem of how to obtain relevant data and rules to incorporate into agent-based models, as well as seeking model validation by participants has been clearly recognised within the literature (Tillman et al., 2001; D’Aquino et al., 2002; Pahl-Wostl, 2002; Barreteau, 2003). The methodology of participatory agent-based modelling (companion modelling) has provided a framework for addressing such issues (Barreteau, 2003). Here, public participation and engagement is a vital ingredient in a three-stage process of field study, modelling and simulation (or game playing). Such a methodology provides access to knowledge elicitation and social learning, developing a dual mechanism with implicit added value for both the participants and the modeller (Pahl-Wostl, 2002). This chapter explores the effects of social networks and imitation on water conservation, and lay some groundwork for further exploration of water conservation behaviour using the participatory agent-based modelling approach. Two agent-based models are discussed and developed. The first is a simple model to explore the effects of social networks and tariff structures on a small population of agents, where the utility who collects the tariffs has constraints on the level of tariffs it may set. The second model, evolved from the first, seeks to explore the effect of imitation of water use behaviour within a population of agents and builds a case for the need for further studies into the potential for imitation being a key driver in water use behaviour and uptake of new technology. In both cases, social interaction forms the basis for the agent behaviour and the agents are characterised with degrees of belief for water saving. 4.2 Water conservation 4.2.1 Urban water use In Australia, the average household residence consumes 250 000 litres of water per year. On average, 34% of domestic water is used in the garden, 20% is used in both the toilet and shower, 12% in the washing machine, and the last 14% is used in the remaining water devices in the house (WSAA, 2001). Studies have shown that water use per capita declined in most large urban centres during the 1990s due to increases in water pricing, consumer education, use of watersaving appliances and higher residential densities being linked to lower outdoor water use (Senate, 2002). Australia’s population is estimated to grow to between 24 and 28 million by the year 2051 (ABS, 2001) and such population growth leads to total water

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consumption levels increasing, placing pressures on resources. It has been estimated that water-efficient devices could potentially reduce consumption by 50% in both the toilet and shower, 35% for the washing machine and 20% for the dishwasher (WSAA, 2001). The issue of technological adoption has been addressed by mainly focusing on the rate of diffusion of the innovation. Clark et al. (2000) has demonstrated an individual-based approach to the study of innovation within the water industry. In particular, it was shown that understanding the diversity of motivations and perceptions which characterise individual organizations’ operational experience is central to managing the implementation of new technology. 4.2.2 The social dilemma of water conservation Water conservation can be thought of as a social dilemma, a conflict between private and public interest. For example, in a hot summer period, the common consensus approach to conserve water may be ignored by a select few who decide to use water without regard for the consensus. If everyone used this strategy of ‘defection from the norm’, then the water resource would deplete rapidly. Water metering, pricing and the effect of tariff structures on water conservation have received a lot of attention in the literature (Saleth et al., 2000; Arbues et al., 2003; Chambouleyron, 2003). Few studies, however, have explored the effects of social cohesion on water conservation. An exception is Vugt (2001), who, treating water conservation as a natural social dilemma, identified two key approaches: the structural and the socialpsychological. The structural approach contains strategies that intervene directly in the outcome structure of the dilemma. For example, installation of domestic water meters makes it possible to charge based on usage, giving a financial incentive to consume less water. The social-psychological approach consists of interventions altering the way people value and think about the resource. Such an example can be found with public education campaigns. Vugt (2001) demonstrated that a community’s social cohesion moderates the effects of tariff structures on resource use. In particular, tariff systems in which overuse is penalised are particularly effective when a community’s social cohesion is low. Greater community social cohesion is suggested as a way to help promote restraint by increasing within the community thus increasing peoples willingness to exercise restraint when needed. 4.2.3 Water use: beliefs, attitudes and memetics On average, a person in Australia uses 350 litres of water a day, with this usage being split across activities in the kitchen, bathroom, toilet, laundry and garden. The garden represents the highest use area, consuming approximately 34% of total daily water use. Garden watering is strongly correlated with lifestyle beliefs and conservation attitudes (Syme et al., 2004). Water usage is also affected by the type of device and the associated behaviour with that device. For example, brushing teeth using a glass instead of leaving a tap running will save 9100 litres per person per year. Similarly, using a AAA-rated shower head instead of a normal shower head will save 28 000 litres per person per year1 . 1 Information drawn from http://www.southeastwater.com.au/sewl/index.asp?link_id=27.521 last visit 05/2006.

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Water user beliefs can be classified into two main classes (Corral-Verdugo et al., 2003). The first class is the water utilitarians - those who believe water is an unlimited resource to be used in an arbitrary way. The second class are the water ecologists (water savers) - those who believe water is a limited resource to be conserved. Corral-Verdugo et al. (2003) showed that water utilitarian beliefs are related with increased water consumption. Similarly, water ecologists’ beliefs on water consumption – believing that water is a resource to save leads to a decrease in consumption. Motives for saving water are significant predictors of water use. That is, the more motives, the greater the chance for water conservation behaviour (Corral-Verdugo et al., 2003). Although attitudes and beliefs of residents have been shown to have a direct effect on external water use (Corral-Verdugo et al., 2003; Syme et al., 2004), no studies on imitation of water-use behaviours have been found. Imitation is considered to be a founding block for learning in humans (Blackmore, 1999), and has been acknowledged to provide a mechanism beyond the rational actor paradigm, where individuals have perfect knowledge and try to optimise their outcomes (Jager et al., 2000). Although a controversial theory, the meme has been described as anything passed on by imitation (Blackmore, 1999) and is considered analogous to the gene and is embedded within an evolutionary process where selection, variation and inheritance operate. For the purposes of this chapter, the adoption of both water-use behaviours and smart water devices is considered memetic. Memetics has been criticised for being merely a conceptual framework (Edmonds, 2002), however it is considered to provide a strong software engineering framework by which technology adoption and beliefs can be implemented within the software models described in this chapter. Using a memetic representation for the description of the behaviours and devices allows a decoupling of the water-use behaviour from the resident’s behaviour in the implementation. This decoupling at the software development level provides flexibility, allowing for scenarios such as investigating the impact of advertising campaigns on residents. Under the memetic framework, the effect of an advertising campaign is captured by introducing a specific meme into the population of residents. Whilst this chapter explores the application of memetics within the community the validity of the approach is still to be shown. 4.3 The models 4.3.1 The agent-based modelling framework Agent-based models differ from equation-based mathematical models in that they are computational models focusing on algorithms to implement the behaviour within the model, rather then evaluating sets of system variables and equations (Parunak et al., 1998). For a full treatment and review on building agent-based models see Rixon et al. (2005). Whether a modeller chooses to use a agent-based modelling platform or build from scratch there are three key phases to the development of an agent-based model (Rixon et al., 2005): Phase 1 requirements; Phase 2 model storming;

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Phase 3 implementation. In Phase 1 Designs for multi-agent systems generally require mechanisms for (Gilbert and Terna, 1999) 1. receiving input from the environment; 2. storing a history of previous inputs and actions (audit trails); 3. carrying out actions and distributing outputs (scenarios). In Phase 2 it is common to work through higher level issues that are not well addressed with code. This might be an inclusive modelling session with stakeholder(s) to understand their requirements, or it could be a quick design session with other developers to determine how to build something. The technique of class responsibility collaborator or CRC cards has been shown to be an effective tool for facilitating group model storming processes (Biddle et al., 2002). Finally, when building agent-based simulations from scratch, there are two methods for dealing with time and events those being the discrete event simulation; and time stepped simulation. With a time stepped simulation, there is an internal ‘clock’ which ticks the model over to where the next group of events takes place. A discrete event simulation, however, does not use the ‘tick’ within the model; instead it utilises a stack of events which are queued and then scheduled and released once conditions are met (Tyszer, 1999). Table 4.1 details the key elements of the two agent-based models described in this paper based on the taxonomy provided by Hare et al. (2004) . By using an object-oriented approach for software development of agent-based models, it becomes possible to create a flexible framework of classes (and objects) that can be Table 4.1. Key characteristics of the explored agent-based models. Criterion Coupling of social and environmental models

Simple model Spatially non-explicit Collection of agents with friend networks not geo-referenced

Memes models Spatially explicit – Collection of geo-referenced households each containing residents with friend networks

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extended and evolved as the modelling process proceeds and the questions under investigation become clarified. 4.3.2 Model validation: understanding robustness and prediction In this paper, two models are described which aim at exploring some aggregated properties relating to water use behaviour that emerge from the interactions between individuals in a society. This is done for two key reasons. The first reason is to provide understanding and the second goal is to provide prediction. The focus however is put on developing an understanding because prediction is not a good indicator of the validity of a complex system model, in particular for a micro-simulation model. This is because of: • Non-linear features: the object of study is a non-linear system where only one ‘true’ model exists, but there is often an infinite number of models that all provide perfectly accurate prediction (Richardson, 2003). • Emergent features: even a perfect understanding of the micro-behaviour of all components (i.e. individuals) is insufficient to predict group behaviour (Gilbert et al., 1999). In addition to the non-linear and emergent features, the studied system also has second order emergence which is typical of human social systems. Second-order emergence refers to when institutions result from behaviour which takes into account emergent features, for example governments, churches and business organisations (Gilbert et al., 1999). There is hence second order emergence within our studied system because institutions and organisations adjust, at least on the long time scale, reflexively according to the expected emergent behaviour of the collection of individuals. This provides a selfreferential property (i.e. feedback) which again makes prediction very difficult. Therefore, while a solid understanding of micro-behaviour, and a reasonable predictive capacity are both indicators of a reasonable model, absolute validation of a model is virtually impossible, and a common path towards ensuring legitimacy of social simulation models is validation through stakeholders (Tillman et al., 2001; D’Aquino et al., 2002; Pahl-Wostl, 2002; Barreteau, 2003), which is typically attempted within Companion Modelling and Participatory Agent-Based Modelling (Barreteau et al., 2003). In line with the Companion Modelling approach, D’Aquino et al. (2001) distinguish between three types of validation processes: • Confrontation to the present reality: in essence a reality check. • Reconstruction by the model of a real past dynamics: can the model be used to reproduce and understand past dynamics (assuming data is available)? • Model acceptance by concerned people: can the model be understood and does it make sense? This requires transparency in terms of being able to understand the components of the model In the Participatory Agent-Based Modelling framework, a pragmatic constructivism is applied in the sense that validation of the model is not strictly necessary, but legitimacy is critical because models are used in a framework to support discussion and social learning.

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Within this process, the model and methodology is used for exploratory purposes and to generate theories in order to ask new questions on the real systems (Barreteau et al., 2004). A model is then legitimate, rather than valid, when it provides participants with new theories about the real system and is an acceptable representation of the real system. However, it should also be remembered that agent-based simulations can sometimes provide a false sense of realism, which makes stakeholder validation difficult. Other key methods to improve the validity and to increase understanding is to apply • Simplicity: make the model as basic or simple as possible so that assumptions or potential errors can easily be evaluated. • Sensitivity analysis: by varying the model’s parameter values, it is possible to explore the solution space of qualitatively different results, and to evaluate robustness, or in other words, evaluate how sensitive the model is to individual parameter values in terms of what is needed to achieve a qualitatively or quantitatively different result. Further work remains on the models explored in this paper around the areas of sensitivity analysis and stakeholder validation. 4.3.3 A simple model for exploring tariff structures The first simple agent-based model uses social networks to embed resident agents within a water-use environment where a water utility agent controls the tariff structure. The tariff structures explored are fixed and variable. The fixed tariff structure refers to a flat daily cost for water (independent of actual usage) determined by the water utility. The variable tariff structure sees a charge dependent on the amount of water used by the resident. All resident agents belong to a social network. The social network is either randomly generated or reconstructed from a ‘real’ data set of friendship links2 . Resident agents unable to get the amount of water that they require, due to the price placed on water usage by the water utility and their income levels, become water stressed. This water stress leads residents to seek out friends who are using more water and place peer pressure on them to reduce water use. Figure 4.1 details the properties and behaviours of the resident and utility classes. The integer variables of the resident agent, such as IncomeLevel and BlockSizeLevel, are chosen to represent high, medium and low scaling. Extrapolating from Syme et al. (2004) water use becomes a function of the resident agent’s IncomeLevel, BlockSizeLevel, Occupancy, WaterTechnology Level, LifestyleLevel, GardenRecreationLevel and GardenState. This water usage figure is then multiplied by a compensating factor based on whether the resident is a water saver or water utilitarian. The utility agent’s ‘willingness to pay’ algorithm is constrained by the acceptable degree of water stress within the resident population, and whether or not the water levels have reached critical levels. The algorithm for increasing or decreasing the tariff is described in Fig. 4.2. 2 Data sourced from http://www.sfu.ca/∼insna/INSNA/data_inf.html last visit 05/2006.

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Fig. 4.1. UML diagram of agent classes within the simple model.

Current water levels

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Fig. 4.2. Utility agent’s ‘willingness to pay’ algorithm.

4.3.4 Model calibration The simple model is initialised first with either a real social network loaded from file or by creating a random friend network as discussed earlier. Acceptable water stress is determined as a percentage proportion of the chosen agent population level. Resident agents demographic variables are assigned random values, leading to a distribution of income levels, block sizes, occupancies etc. Since the water utility agent maximises its profits there is no need to calibrate the initial level of cost for each tariff.

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4.3.5 Results Figures 4.3 and 4.4 show 100 iterations with 21 resident agents and random social networks (3 friends per resident). In these simulations, the utility agent is allowing a 40% water stress within the population and the tariff is fixed; residents pay per day independent of volume used. 3000

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Fig. 4.5. Variable tariff total water use for a population of 21 agents and 100 iterations (daily).

The periodic nature of Fig. 4.3 reflects the decision-making behaviour of the residents who can no longer afford water based on the cost per day imposed by the utility. The residents who can’t afford the daily tariff for water have no option but to cease water use. This creates water stress amongst the resident agents and leads to the water utility temporarily reducing its daily tariff, resulting in the periodic equilibrium of the fixed tariff price shown in Fig. 4.4. Figures 4.5 and 4.6 demonstrate the effects on resident water usage of a utility operating under the variable pricing tariff with the same initial conditions as the fixed tariff simulation. Figure 4.6 shows the fluctuation in cost per litre as the utility agent attempts to maximise its profit. Unlike the fixed tariff regime, the variable tariff regime produces more complex dynamics regarding total water use (see Fig. 4.5). To further understand the dynamics of this simulation model, 1000 simulations each of 200 time steps were run. Tables 4.2 and 4.3 describe the key results obtained from fixed and variable tariff regimes. Tables 4.2 and 4.3 demonstrate the increase in the utility’s profit resulting from the variable tariff regime. Table 4.3 clearly illustrates the effect of increasing the number of friends in the friend network per resident agent on the mean water use. Interestingly, the real social network data appears to fit between the random four and eight friend networks. 4.3.6 The water memes model In the water memes model, residents are considered to have a selection of water memes, some which are water saving memes and some which are not. These memes have a direct mapping between the type of device, the frequency of use and the amount of water used. In this model, ten types of water meme will be used (see Table 4.4). A view of a resident’s set of memes is: M1M2M3M4M5M6M7M8M9M10, where M1 could represent the garden meme, M2 a shower meme, and so on. Each meme, Mi,

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Mean water use Mean utility profit

No social network 124.13 1466.49

Random 4 friends 124.42 1483.13

Random 8 friends 124.87 1476.03

Real social network 124.69 1490.65

Table 4.3. Effect of variable tariff and social networks on mean water use and mean utility profit.

Mean water use Mean utility profit

No social network 163.12 2153.76

Random 4 friends 128.56 2008.27

Random 8 friends 110.83 1925.02

Real social network 117.10 1942.66

has a cost associated with imitation. This cost is implemented as a required belief in water saving. For example, a resident who comes into contact with a rainwater tank meme would have to have a strong belief in water saving to copy and implement this meme. The memes that are inactive within a resident agent are determined not to be enabled. Resident agents are born with a degree of belief in water saving. This water saving belief is dynamic and is calculated by the percentage of water saving memes in their current meme set. A resident agent’s water worry is an inverse function of the current dam level’s capacity – the closer to full capacity, the less worried the agent. Water worry is scaled by the resident agent’s degree of belief in water saving. The stronger the belief in water saving, the more the resident will care about the state of the water reserves. Water memes are copied based on social interaction. Residents within a household tend to become more like each other, sharing a common set of beliefs. Resident agents who are water worried look to their friendship networks to seek out water savers. In the

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Table 4.4. Names and descriptions of the ten water memes used in the water memes model. Name Garden Shower Toilet Brush teeth Prepare food Wash clothes Leaking tap Leaky toilet Dishwasher Rainwater tank

Description Five types of garden watering technology available, each with differing water use. These are bucket, hose, hose sprinkler, fixed sprinkler and drip system AAA-rated shower head is 45% more efficient than normal head Dual-flush toilet saves water over the single flush Brushing the teeth using a glass saves over having a tap running Preparing food in the kitchen sink with the plug in is more efficient than with a running tap Ensuring that the washing machine is full each wash The knowledge of how much water is saved by stopping leaking taps The knowledge of how much water is saved by diagnosing a leaky toilet Whether dishes are washed in the kitchen sink or in a dishwasher Installing a rainwater tank can reduce external water demands

case of no water worry, resident agents generally seek to become more like their friends, independent of whether their friends are water savers or water utilitarians. The key algorithms for the propagation of memes belong to the resident agent and are the SeekSimilarBeliefs and SeekWaterSavers functions. Resident agents who employ the SeekSimilarBeliefs algorithm iterate through their friend networks seeking a friend who shares a similar degree of belief in water saving. Once found, the resident agent employs the BecomeMoreLike(Friend) function, which randomly picks a meme out of the friends set of memes and copies it into their meme set. Similarly, resident agents who employ the SeekWaterSavers algorithm iterate through their friend networks to find a friend who has greater water saving beliefs then themselves, once found the resident agent then employs the BecomeMoreLike(Friend) function ensuring the transfer of a water saving meme. A simple water balance equation is used for the garden (Cook et al., 2003). This water balance incorporates rainfall, evapotranspiration and block size data to determine the level of water use required for a green garden. Figure 4.7 illustrates the core classes with attributes and behaviours for the water memes model. Finally, this agent-based simulation uses fixed increment time steps with conditional events. The core algorithm ticks the simulation through its daily routine. Here, each household (containing residents) is made to do the ‘activities’ which consist of using each of the core water usage areas: toilet, bathroom, kitchen, laundry and garden. Using an object-oriented approach enables events to be used which can fall outside the ticked simulation. For example, the garden object fires a ‘Needs water’ event whenever its stored water level is below what is required to keep it green. This event initiates the gardener of the household to go and water the garden. 4.3.7 Model calibration The model first loads real climate data from a file which includes rainfall and evapotranspiration data. All households were artificially created for the simulation, this includes selecting the number of residents per household and the type of residence (apartment or house) which were both randomised. Each resident agents created has a random friend

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Fig. 4.7. UML diagram containing classes within water memes model.

networks assigned. Resident agents are randomly assigned income levels, lifestyle levels and their water saving beliefs. Each resident agent is assigned a set of 10 random memes which form the basis for the water use behaviours. Finally the rainwater tank objects are initialised with a maximum volume of 1500 litres and the garden objects belonging to each household object are initialised with crop factors, garden areas, soil storage level, maximum soil storage levels, and green garden storage levels realistic for urban environments.

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4.3.8 Results No water worry. The following results were obtained for a simulation run with 30 households over 730 days (2 years). Real rainfall and evapotranspiration data were used. The residents had no water worries (the dam levels were always close to capacity), and each resident had 3 friends in their friend network. The simulation begins in January which is summer time in the southern hemisphere. Figure 4.8 clearly shows seasonal fluctuation in water use, with the highest usage occurring during the summer months (with gardens requiring most watering), and then dropping off as the winter months arrive (when gardens require least watering). Moreover, the mean total water use per household is around 800 litres per day, remarkably close to actual reported figures of 750 litres per household per day. Runoff water from garden watering or water lost through leaks is defined as water waste. Figure 4.9 shows an increase in mean water waste at the very beginning of the simulation. In this scenario, with no water worry, the water utilitarians outnumber the water savers (see Fig. 4.10). Water worry. The next results were obtained using a simulation scenario identical to the previous set. However, in this case the residents face a depleting water resource (dam levels are below 50% capacity). As with Fig. 4.8, Fig. 4.11 shows the seasonal fluctuations in water use, however in the case of Fig. 4.11, it is clear that the peaks and troughs of the seasonal fluctuations are decreasing. Interestingly, Fig. 4.12 shows an initial increase in mean water waste, followed by a reduction in water waste, which corresponds to an increase in the number of water savers in the simulation. 1000 900 800 700

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Fig. 4.10. Distribution of water savers and water utilitarians for no utility campaigning and no water worry.

Finally, in contrast to the previous simulation where the water utilitarian was the predominant belief, Fig. 4.13 demonstrates the flip to the water saver being the major belief within the population. Effects of friend networks on water saving beliefs. To explore the apparent alternate states of water saving beliefs detailed in Figs. 4.10 and 4.13 (the water saver belief is dominant

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Fig. 4.12. Simulation showing effect of targeting campaign on water waste running for 730 days.

in water worried scenarios, and the water utilitarian belief is predominant in non-waterworried scenarios), a Monte Carlo simulation was carried out with 250 scenario runs. Each scenario had 30 households with 730 days of simulations being run. Random friendship networks of 0, 3, 6 and 9 friends per resident were simulated. Figures 4.14 and 4.15 demonstrate a general declining trend for water saver beliefs as the number of friends per resident increases, independent of water worry. In particular,

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80 70 60

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Fig. 4.13. Distribution of water savers and water utilitarians under water worry.

Figs. 4.14 and 4.15 demonstrate that the water-utilitarian belief is a dominant attractor within the simulations. That is, in general, resident agents within the simulation scenario will tend to become more oriented towards non-water-saving beliefs as the number of friends in their friend network increases. Utility campaigning and water worry. Introducing the ability for a water utility to campaign to its population of residents when the water resources reach critical levels is simple with the memetic approach. In this case, the utility agent simply monitors the current water levels and, when they reach critical levels (in this case, capacity below 50%), the utility sends out a random water-saving meme with the bill (analogous to sending specific water-saving information kits in the mail). Residents who are water worried are able to copy and implement this meme. Figure 4.16 demonstrates the marked decline in mean water waste. Curiously, the wintertime water usage is seen to increase during this scenario. Using this memetic approach, the water usage is dependent on which water memes are dominant within the population of residents. As discussed earlier, memes are embedded within an evolutionary process of variation, inheritance and selection. Figure 4.17 illustrates the initial and final distributions for the various memes (described in Tab. 4.4) in this simulation. Memes which are water saving are listed as, for example, GARDEN1, GARDEN2, GARDEN3. The frequency of use – low, medium or high – is then represented as F1, F2 and F3 respectively. In the case of the GARDEN label: 1 = water by bucket, 2 = water by hose, 3 = water by hose sprinkler, 4 = water by fixed sprinkler and 5 = water by drip system. Interestingly, several memes have become extinct within this scenario. Specifically, washing clothes with many loads (CLOTHES2F2), medium and high hose sprinkler usage (GARDEN3F2,3), and low usage drip systems (GARDEN5F1).

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Profile of the water saver and water utilitarian. Table 4.5 profiles the set of water memes of the strongest water utilitarian belief resident and the strongest water saver belief resident for the previous simulation where residents are facing depleting water resources and the utility is actively campaigning water saving ideas. Each of these memes were initially assigned randomly to the residents.

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Fig. 4.17. Change in distribution of water memes throughout the population of residents from the initial situation (dark grey) to the final one (light gray).

4.4 Discussion This chapter describes an approach to implementing a simple agent-based model to explore the effects of social networks and tariff structures on water use behaviour. Social networks were demonstrated to have no effect on simulated water usage under the fixed tariff structure, as residents are unable to place pressure on their friends to cease their water use, only reduce it. Compared to the fixed tariff regime, the variable tariff regime

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80% Water Utilitarian Born 5% Water Saver Shower Normal Shower Medium

90% Water Saver Born 47% Water Saver Shower AAA Shower Low

Key Name

Toilet Dual Flush

Toilet Dual Flush

Key Name

PrepareFood Running Tap

PrepareFood Kitchen Sink

Key Enable

CheckLeakyToilet False

CheckLeakyToilet True

Key Name Frequency

DishWasher Kitchen Sink High

DishWasher Kitchen Sink High

Key Enable

RainwaterTank False

RainwaterTank True

Key Name Enable

BrushTeeth Tap Low

BrushTeeth Glass Medium

Key Enable

CheckLeakingTap False

CheckLeakingTap False

Key Name Frequency

Garden Fixed Sprinkler Low

Garden Bucket High

Key Name Frequency

WashClothes Many Loads Medium

WashClothes Ensure Full Load High

provides the most equitable and fair allocation of water to residents, with residents always being able to afford daily water usage under the variable tariff regime. This is due to the fact that under the fixed tariff regime, there are residents who are unable to afford the daily cost of water and so completely cease their usage for that day (see Fig. 4.3). Most interesting in this simple agent-based model, however, is that under the variable tariff regime, social networks result in a significant reduction in simulated water use. This result suggests that within small communities where social cohesion is strong, there is an ability for non-tariff-based strategies to successfully impact on water use. Further, the result provides a mechanism for decentralisation of water management, with residents empowered to seek sustainable usage of their precious resource. The first criticism of the simple model, however, is that the mean water use predicted per day is inaccurate. Estimations show that actual usage is on average around 350 litres per person per day, or 730 litres per household per day, this simple model shows mean water use of approximately 120 litres per day (see Tables 4.2 and 4.3). Secondly, although the simple model provided a framework for exploring the effects of social networks on water usage, the reality of this functionality is limited to, at best, small communities

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where hardships in the supply of water are common. Thirdly, the simple model provides no flexibility in how beliefs and actions are actually manifested. As discussed earlier, there is strong evidence for beliefs affecting water use and conservation behaviour. Finally, although water utilities today are interested in assessing customers willingness to pay, their roles also now require a water conservation component using advertising campaigns and more complex social involvement. The simple agent-based model contained no such behaviour for the utility agent. The agent-based water memes model was formulated to extend on these limitations of the simple model. In particular, it sought to explore the effects and transfer of watersaving beliefs on water conservation using a memetic framework. The water memes model demonstrated realistic seasonally fluctuating water use behaviour, with households using approximately 800 litres per day (see Fig. 4.8). Furthermore, with water worry, residents are found to reduce their water usage significantly, explained primarily by the uptake of water-smart garden technologies such as using a bucket or medium/high usage drip systems to water the garden. It was found that with increasing numbers of friends in residents’ friendship networks, there was a greater trend towards water utilitarian beliefs irrespective of water worry (see Figs 4.14 and 4.15). Underlying this trend towards water utilitarian beliefs is the implicit cost associated with copying water saver memes. For example, if a resident finds a water saver resident who uses a bucket to water the garden, then this resident would have to believe strongly in water saving to change from hose watering, to this method of watering the garden. Hence, even with water worry, where residents are concerned about the capacity of the dams and seek out water savers to copy, the extent of their friendship networks can have a large impact on the uptake of water saving behaviours. In this case, the water saving memes are lost from the population based on cliquey friendship networks. This selection on the basis of water memes was demonstrated in Figs 4.16 and 4.17, where the water utility can seek to influence residents’ behaviour when the capacity of the dam becomes critical. In this case, the water utility engages in a water saving campaign, where water saving ideas (water saver memes) are distributed to residents with the water bills. Ironically, even though the summertime water usage is seen to decline marginally with the uptake of rainwater tanks and water saving garden technologies, the winter water usage is seen to increase. Those water memes lost from the system were unsuitable for the current water-using environment. For example, the low frequency usage drip system did not satisfy residents gardens’ water requirements. Further study is required into the actual imitation behaviours of people to water use and technology uptake. In particular, further observation and empirical studies of the effects of friends on imitation behaviour is needed. The basis of the water memes model assumes that friends and family have a large effect on the degree of imitating behaviour. Such studies will allow for the rates and degree of infection to be determined more accurately. Studies to determine the actual distribution of memes within communities and the impact this has on spread and infection rates will aid in calibration/validation issues relating to the water memes model. Finally, there is a tendency to use agent-based models in a predictive exploratory capacity. Such uses are fraught with problems such as calibration, validation and sensitivity which all serve as inputs into the variability of the output of an agent-based model. As

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observed in Richardson (2002), a strong focus on the model rather than the modelling process dominates the field of bottom-up computer simulation. It is the authors view that the use of a participatory modelling process is a powerful inclusion into the method of agent-based modelling helping to take the focus away from the model itself and to address issues of validation. Future residential demand models are expected to analyse alternative demand programs, such as the promotion of low-consumption technologies (Arbues et al., 2003). This chapter has demonstrated the utility of an agent-based approach for incorporating aspects such as social networks and imitation into the study of water conservation behaviour. In particular, the water memes approach has been shown to be a productive framework for the exploration of different scenarios for the adoption of different water use technologies, producing realistic water usage based on residential water use behaviours and beliefs. Furthermore, it is concluded that utilising a memetic framework in the software development of an agent-based model, where the specifics of the behaviours are encapsulated within the meme, provides an extremely flexible object-oriented implementation. With further research into the role and importance of imitation in the uptake of water use beliefs, behaviours and devices, it would be possible to use this approach to study and forecast the potential impact of campaigns targeted for specific water user profiles. Embedding such a study within the participatory agent-based methodology can start a dialogue with participants and stakeholders, engaging and increasing their awareness surrounding the issues of water use and water conservation as well as providing a valuable validation process for the modeller. Acknowledgements All authors would like to thank Andrea Castelletti. Without his generosity of spirit, patience and willingness to share his time and expertise with LaTex and Matlab this book chapter would be only a possibility. Thank you so much Andrea. We are in your debt. Bibliography ABS (2001). Australia’s environment: Issues and trends. Australian Bureau of Statistics Catalogue. Arbues, F., M.A. Garcia-Valinas and R. Matrinez-Espineira (2003). Estimation of residential water demand: A state-of-the-art review. J. Socio-Econ. 32, 81–102. Barreteau, O. (2003). Our companion modelling approach. JASSS. Barreteau, O., F. Bousquet, C. Millier and J. Weber (2004). Suitability of multi-agent simulations to study irrigated system viability: application to case studies in the Senegal river valley. J. Appl. Stat. 80, 255–275. Biddle, R., J. Noble and E. Tempero (2002). Reflections on crc cards and oo design. In: Proceedings 40th International Conference on Technology of Object-Oriented Languages and Systems (TOOLS Pacific 2002). Vol. 10. Sydney, AUS. Blackmore, S. (1999). The Meme Machine. Oxford University Press. Oxford, UK. Chambouleyron, A. (2003). An incentive mechanism for decentralized water metering decisions. Water Resour. Manag. 17, 89–111. Clark, T., P. Jeffrey and T. Stephenson (2000). Complex agendas for new technology adoption in the UK water industry. Technovation 20, 247–256.

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Cook, F.J., C.E. Pankhurst, H.P. Bohl, C. D’Amato, D. Fanning, G.E. Rayment and G.D. Carlin (2003). Fate of split sugars from cane harvest: Investigation and modelling of the phenomena. Technical Report 48/03. CSIRO. Canberra, AUS. Corral-Verdugo, V., R.B. Bechtel and B. Fraijo-Sing (2003). Environmental beliefs and water conservation: An empirical study. J. Environ. Psychol. 23, 247–257. D’Aquino, P. and F. Bousquet (2001). Accompanying governing processes in land use management with linking role playing games, gis and mas: The selfcormas experiment in the Senegal river valley. In: Special Workshop on Agent-based Models of Land Use / Land Cover Change. Irvine, CA. D’Aquino, P., O. Barreteau, M. Etienne, S. Boissau, S. Aubert, F. Bousquet, C. Le Page and W. Dare (2002). The role playing games in an abm participatory modelling process: Outcomes from five different experiments carried out in the last five years. In: Integrated Assessment and Decision Support, Proceedings of 1st Biennial Meeting of IEMSS, June 24–27 (A.E. Rizzoli and A.J. Jakeman, Eds.). Lugano, SW. Edmonds, B. (2002). Three challenges for the survival of memetics. Journal of Memetics – Evolutionary Models of Information Transmission 6, 1–6. Gilbert, N. and K.G. Troitzsch (1999). Simulation for the Social Scientist. Open University Press. Philadelphia, PA. Gilbert, N. and P. Terna (1999). How to build and use agent-based models in social science. http://web.econ.unito.it/terna/deposito/gil_ter.pdf. Hare, M. and P. Deadman (2004). Further towards a taxonomy of agent-based simulation models in environmental management. Math. Comput. Simulat. 64, 25–40. Jager, W., M.A. Janssen, H.J.M. De Vries, J. De Greef and C.A.J. Vlek (2000). The human actor in ecological-economic models: Behaviour in commons dilemmas: Homo economicus and homo psychologicus in an ecological-economic model. Ecolog. Econ. 35, 357–379. Kasemir, B., J. Jager, C.C. Jaeger and M.T. Gardner (2003). Public Participation in Sustainability Science: A Handbook. Cambridge University Press. Cambridge, UK. Kuylenstierna, J.L., G. Bjorklund and P. Najlis (1997). Sustainable water future with global implications: Everyone’s responsibility. Nat. Resour. Forum 21(3), 181–190. Livingston, D.J., N.J. Ashbolt and H.K. Colebatch (2004). Urban water management as a changing socio-technical system: Participation, decentralisation and sustainability. In: First Int. Conf. on onsite Wastewater Treatment and Recycling/6th Specialist Conf. on Small Water Systems and Wastewater Systems, Freemantle, Australia 11–13 February. Marvin, S., S. Graham and S. Guy (1999). Cities, regions and privatised utilities. Prog. Plann. 51, 91–169. Pahl-Wostl, C. (2002). Agent based simulation in integrated assessment and resources management. Integrated Assessment and Decision Support, Proceedings of the First Biennial Meeting of the International Environmental Modelling and Software Society 2, 239–244. Richardson, K. (2002). Methodological implications of complex systems approaches to sociality: Some further remarks. JASSS 5(2), 1–11. Richardson, K. (2003). On the limits of bottom-up computer simulation: Towards a nonlinear modelling culture. In: 36th Hawaii International Conference on System Science, Hawaii. Rixon, A., M. Moglia and S. Burn (2005). Bottom-up approaches to building agent-based models discussing the need for a platform. In: Proceedings CABM-HEMA-SMAGET Joint Conference on Multi-Agent Modelling for Environmental Management Bourg St Maurice Les Arcs, France 21–25 March/mars 2005 5(2), 1–11. Saleth, R.M. and A. Dinar (2000). Satisfying urban thirst: Water supply augmentation and pricing policy in Hyderabad city, India. Technical Report 395. The World Bank. Washington, DC.

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Senate (2002). The value of water: Inquiry into Australia’s urban water management – report of the senate environment, communications, information technology and the arts reference committee. Technical report. Parliament of the Commonwealth of Australia. Canberra, AUS. Syme, G.J., Q. Shao, M. Po and E. Campbell (2004). Predicting and understanding home garden water use. Landscape Urban Plan. 68, 121–128. Tillman, T., T.A. Larsen, C. Pahl-Wostl and W. Gujer (2001). Interaction analysis of stakeholds in water supply systems. Water Sci. Technol. 43(5), 319–326. Turton, A.R. (1999). Water scarcity and social adaptive capacity: Towards an understanding of the social dynamics of water demand management in developing countries. MEWREW Occasional Paper No. 9. Tyszer, J. (1999). Object Oriented Computer Simulation of Discrete Event Simulations. Kluwer Academic Publishers. Dordrecht, NL. Van Dyke Parunak, H., R. Savit and R.L. Riolo (1998). Agent-based modelling vs. equation-based modelling: A case study and user’s guide. Proceedings of Multi-agent Systems and Agent-based Simulation (MABS’98) 1534, 10–26. Van Vugt, M. (2001). Community identification in a natural social dilemma. Pers. Soc. Psychol. Bull. 27, 1440–1449. WSAA (2001). The Australian urban water industry wsaafacts 2001. Technical report. Water Services Association of Australia. Melbourne, AUS.

Part III

Managing and MODSS

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CHAPTER 5

Decision Support Systems for Integrated Water Resources Management with an Application to the Nile Basin

Aris P. Georgakakos Georgia Water Resources Institute Georgia Institute of Technology, Atlanta, USA

5.1 Integrated water resources management: science in support of public policy Integrated Water Resources Management (IWRM) is the process of formulating and implementing shared vision planning and management strategies for sustainable water resources development and utilization with due consideration of all spatial and temporal interdependencies among natural processes and human and ecological water uses. The IWRM process is conceptualized in Fig. 5.1. The knowledge to support planning and management decisions resides in various disciplines including climatology, meteorology, hydrology, ecology, environmental science, agro-science, water resources engineering, systems analysis, remote sensing, socioeconomics, law, and public policy. Public policy actors (such as politicians, judges, government agencies, financial institutions, Non-Governmental Organizations, citizen groups, industries, and the general public) are often in a position to make critical decisions that reflect society’s shared vision for water resources utilization. Public policy actors develop consensus and decide on shared vision strategies based on information generated and communicated by Decision Support Systems (DSSs) and associated processes. Thus, the role of DSS is to leverage current scientific and technological advances in developing and evaluating specific policy options for possible adoption by the IWRM process. DSSs are developed and used by research institutions, government agencies, consultants, and the information technology industry. By its nature, IWRM is a process where information, technology, natural processes, water uses, societal preferences, institutions, and policy actors are subject to gradual or rapid change. To keep current, IWRM should include a self-assessment and improvement mechanism. This mechanism is indicated by dashed arrows in Fig. 5.1 and starts with monitoring and evaluating the impacts of decisions made. These evaluations identify the need for 99

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Fig. 5.1.

IWRM:

science in support of public policy.

improvements pertaining to the effectiveness of the institutional set-up, the quality and completeness of the information generated by decision support systems and processes, and the validity and sufficiency of the current scientific knowledge base. IWRM processes can lead to great successes just as they can cause costly failures. In a world where water disputes are on the rise and the delay between science and technology advances and their consideration by management practices widens, IWRM faces important challenges: • lack of integrative tools to support planning and management decisions; • segmentation of institutions responsible for water resources planning and management; • limited participation of stakeholders in decision making processes; • lack of disinterested self-assessment and improvement mechanisms; • continuing specialization of science and engineering education at the expense of interdisciplinary training. Specifically on decision support tools, lack of integration is common with respect to disciplines (water resources, agriculture, environmental science, ecology, energy, public health, socio-economics, etc.) as well as with respect to decision levels (assessment, planning, and operational management). Current DSS tools are narrowly focused, developed by overspecialized professionals, working for institutions operating in silo mode. Thus, lack of integration undermines the effectiveness of tools, people, and institutions and is a major challenge of IWRM processes.

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However, challenges create opportunities, and the design, development, and use of is an excellent opportunity that can thread together a broad range of disciplines, people, and institutions to address the complex IWRM challenges. This is the chapter’s overarching message. DSS

5.2 Decision support systems for IWRM 5.2.1 DSS elements Decision Support Systems (DSS) are technical tools intended to provide valid and sufficient information to IWRM decision makers. A typical DSS for IWRM includes five main components (Fig. 5.2): data acquisition system, user–data–model interface, database, data analysis tools, and a set of interlinked models. The data acquisition system consists of all means by which generic data are collected and made available to IWRM through the DSS. Data may be collected by conventional sensors (rain-gages, stream-gages, etc.), remote sensors (satellite, radar), as well as by manual compilation efforts (e.g., surveys, interviews, and literature reviews). The purpose of the user–data–model interface is to (1) transfer the data to the database, and (2) provide easy and meaningful access to data, data analysis tools, and models. The database is the depository of all data acquired by the data acquisition system and generated by the data analysis tools and application programs. The data analysis tools provide user-friendly means to visualize and analyse various data sets. Geographic Information Systems (GIS) packages are especially important for the visualization and analysis of georeferenced (spatial) data. Lastly and most importantly, the purpose of the DSS models is to quantify the holistic response of the water resources system to alternative scenarios of basin development, hydrology, water use levels, and management policies. In some form, the above-described DSS elements exist in most useful information and modelling tools for water resources planning and management. However, beyond these

Fig. 5.2. Typical DSS elements.

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elements, the effectiveness of a DSS depends on its ability to provide valid, sufficient, and consistent information at all levels of the IWRM process. A generic DSS structure that has the potential to achieve this goal is described next. 5.2.2 DSS conceptual structure for systems with multiple objectives, temporal and spatial scales, and decision makers The key DSS challenge is to support decisions that are made by several decision makers, pertain to various temporal and spatial scales, and concern multiple stakeholder groups and water uses. Experience with the development and application of such DSSs in various regions and institutional settings suggests that the multilayer structure illustrated in Fig. 5.3 emerges naturally and can meet this challenge. This DSS structure includes multiple interconnected layers each of which models the system at a particular temporal and spatial scale, addresses a certain subset of objectives, and involves an appropriate subset of decision makers and stakeholder groups. The linkages among and within the layers ensure that (1) system data, models, and outputs provide an integrative understanding of the system response and (2) decision maker choices are prioritized and implemented consistently as the IWRM process evolves. While this structure is generic, the layers appropriate for each application are system specific. In the example of Fig. 5.3, the three modelling layers shown include (1) near real time models (with an hourly time resolution over a horizon of one day), (2) short/mid range models (with a daily, sub-daily, or hourly resolution and a horizon of one month),

Fig. 5.3. A generic DSS structure.

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and (3) long range models (with a 10-day or monthly resolution and a horizon of one to two years). The DSS also includes an assessment model which evaluates the system response under various inflow scenarios, system configurations, demand scenarios, and policy options. This DSS is designed to operate sequentially. In a typical application, the long range models are activated first to consider long range planning issues such as appropriate water conservation strategies for the upcoming one to two years. In carrying out these evaluations, the long range models utilize climate-hydrologic and demand forecasts with a 10 day or monthly resolution. A central part of this analysis is to quantify all tradeoffs in which the planning authorities and system stakeholders may be interested. The tradeoffs quantify the benefit-cost (or impact) relationships among (1) water users and (2) water uses, and delineate the capacity of the system to meet the various demands placed upon it. Interesting tradeoffs pertain to benefits and costs that would accrue to upstream and downstream users or to specific water uses (e.g., power and agriculture, or agriculture and ecosystem health) if relative water shares were to change. The tradeoffs are provided to planning authorities and stakeholders (water, power, environmental protection, etc.) to use in their decision process. After a consensus is reached, key decisions are made on relative water shares, monthly releases, energy generation, lake levels, and reservoir coordination strategies. The short/mid range models are activated next to consider system operation at finer time scales. The objectives addressed here are more operational rather than planning and may include flood control, power plant scheduling, irrigation management, and environmental flow regulation. This model uses hydrologic and demand (water and power) forecasts with a daily, 6-hour, or hourly resolution and can also quantify the relative importance of upstream versus downstream flooding risks, power generation versus flood control, water supply versus fishery management, and other applicable tradeoffs. Such information is provided to the forum of management authorities and stakeholders to use in their effort to reach consensus on the most preferable operational policy. Such policies are revised as new information on reservoir levels, flow forecasts, and demands becomes available. The model is constrained by the long range planning decisions, unless current conditions indicate that a departure is warranted. The near real time models are activated last to determine the hour to hour operations (e.g., turbine dispatching and flow regulation). All decisions made by the upper levels of the IWRM process are realized at this stage. In developing the above-described DSS, particular attention must be placed on ensuring consistency across modelling layers, both with respect to physical system representations as well as with respect to decisions made. Consistency with respect to decisions is achieved by constraining lower layers to stay within the limits established by the upper layers. Thus, the purpose of the lower layers is to distribute the bulk upper layer decisions (e.g., monthly volumes or energy amounts) at finer temporal scales (e.g., daily, 6-hour, or hourly releases and energy generation) such that system objectives of these finer resolutions are best met. Consistency with respect to system representation is achieved by (1) utilizing models of increasing resolution (temporally and process-wise) and (2) using lower level models to derive (off or on line) aggregate performance functions associated with potential upper layer (bulk) decisions. An example of such an aggregate function is the relationship of power versus plant discharge that provides optimal plant generation

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as a function of reservoir level and total plant discharge. Such functions can be derived by the real time (turbine dispatching) models by determining the optimal turbine loads corresponding to particular reservoir level and plant discharge combinations. These functions are derived for each system plant and are provided to the short/mid range models to ensure that they ‘know’ the power that will actually be generated from a particular level of hourly plant release. Similar aggregate performance functions are derived by each modelling layer for each system use and are communicated to the upper DSS layers. In this manner, each layer has an accurate and consistent representation of the benefits and implications of its decisions. The three modelling layers in this particular example address planning and management decisions for a given system configuration. The scenario/policy assessment model addresses longer term planning issues such as increasing demands, infrastructure change (basin development options), water sharing compacts and policies, potential hydro-climatic changes, and mitigation measures. The approach taken in this DSS layer is to simulate and inter-compare the system response under various inflow, demand, development, and management conditions. Altogether, the DSS provides a comprehensive modelling framework responsive to the information needs of the IWRM process at all relevant time scales. 5.3 Nile DSS The Nile River Basin (Fig. 5.4) covers about 10% of the African continent and is spread over ten countries (Burundi, Congo, Egypt, Eritrea, Ethiopia, Kenya, Sudan, Tanzania, Uganda, and Rwanda). Almost all Nile water is generated on an area covering 20% of the basin, while the remainder is in arid or semi-arid regions. Egypt and Sudan are almost totally dependent on the Nile for their water uses. Most other Nile countries are close to water stress, if not already below the water scarcity threshold of 1000 m3 of water per inhabitant per year. Water stress is compounded by rapid population growth, occurring at nearly twice the average global rate. Hence severe water scarcity conditions are looming over most Nile countries. Nile Basin economies are heavily dependent on agriculture which accounts for more than half of the gross domestic product and employs more than 80% of the workforce. However, lack of water supply infrastructure, climate variability, and poor cultivation practices have seriously restrained, if not completely halted, economic growth. These complex challenges are at the forefront of an unfolding initiative by the Nile Basin nations to set forth equitable and lasting water development and utilization agreements. The goal of the Nile Basin Initiative (NBI) is poverty alleviation and sustainable economic growth. Thus, water sharing is intended to facilitate the creation of efficient markets for food and energy and stimulate environmentally-sound industrial and economic growth. However, effective policy dialogue requires that the countries assess and weigh the benefits and impacts of various water development and management strategies accrued to themselves and other Nile partners. Prerequisite elements in this process are the existence of an institutional cooperative framework, information and modelling systems, and the technical expertise to use them. The Nile Decision Support System (Nile DSS) is the outgrowth of several projects implemented in the course of the last 10 years. These were collaborative efforts of the Geor-

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Fig. 5.4. The Nile River Basin; shaded areas represent wetlands.

gia Water Resources Institute at Georgia Tech, the Nile Governments and their agencies, and various international organizations including the Food and Agriculture Organization of the United Nations (FAO) and the World Bank. The Nile DSS includes planning and operational components developed for and used by individual countries as well as basin planners. Operational management systems have been developed and used in Egypt (High Aswan Dam) and Uganda (Lake Victoria), while a planning DSS was recently completed

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for all Nile countries. In what follows, we describe the elements of the latter. The operational components are being published separately. The following general principles governed the development of the Nile DSS: • The data of the Nile DSS should be shared and agreed upon by the Nile Basin nations. • The Nile DSS should be based on sound and current scientific and engineering approaches able to handle the Nile Basin size, complexity, and range of development and management options. it should also include functionalities useful for users of varying technical backgrounds and experience from novice to advanced. • The Nile DSS should be a neutral decision support tool. Thus, its overriding purpose should be to objectively assess the benefits and tradeoffs associated with various water development and sharing strategies that may interest the Nile Basin partners individually or as an interdependent community of nations. • The Nile DSS should be sustainable and adaptable as future needs arise. The implications of this are twofold: first, the Nile DSS should be based on widely supported computational technology and should be expandable to incorporate new data and effective applications; second, technology and know-how building mechanisms should be implemented during the Nile DSS development as well as in the long term. The Nile DSS follows the concepts illustrated in Figs 5.2 and 5.3 and includes a database, a set of models (for river simulation and management, agricultural planning, hydrologic modelling, and remote sensing), and a user-data-model interface. 5.3.1 Database and interface The Nile DST database is an object-oriented, databasing structure developed to (1) house all types of data (existing as well as future) required by a comprehensive water resources decision support system and (2) to optimize data entry, access, visualization, and analysis. To support the process of water resources planning and management, the data base is designed with the ability to grow, namely, to accept new data, regardless of its type and size. Further, the database tools are capable of visualizing and analysing the data in efficient and meaningful ways. Database contents: The Nile DST database is comprised of several national databases and is of considerable size. Each Nile country has painstakingly compiled station data with measurements of more than 30 hydro-climatic parameters. In addition, the project has compiled 10 years of remotely sensed data that covers the entire basin. The temporal resolution of the remotely sensed data is 30 minutes, and the special resolution is approximately 5 km × 5 km. All together, this data represents nearly 37 GB of information. Data visualization: The data visualization tool in the Nile DSS provides a seamless system to look at all databases. This is a tree-style exploring tool (data tree) that shows the entire contents of the Nile DST database and allows the user to navigate to greater and greater levels of detail. Due to the database size, the data tree is useful in providing a better understanding of the database. Each database has a georeferenced component and a time series component. The geo-referenced data is viewed in the mapping tool,

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which holds a GIS. The mapping tool incorporates the ESRI Incorporated Map Objects to ensure compatibility of the system with industry standard GIS files. The time series data is viewed in the charting tool, which features a powerful chart and aggregation and statistics calculators. Together, the charting tool, mapping tool, and the data tree work seamlessly to provide the user with an ability to view any piece of information in the system quickly and meaningfully. Data analysis: The data analysis tool provides extensive data manipulation capabilities for current and future applications. The user can instruct the Nile DSS to take information from its databases in user specified forms, operate on the data, and construct maps of the output. One example of this is the generation of mean areal precipitation (MAP) and evapotranspiration estimates over user-specified areas. The tool allows the user to save a graphical map of the analysis and revisit/continue the work at a later time. 5.3.2 River and reservoir simulation and management The Nile DSS River Simulation and Management system aims at simulating the Nile response under different hydrologic, development, and management scenarios. Thus, its overriding purpose is to objectively assess the benefits and tradeoffs associated with various water development, sharing, and management strategies that may interest the Nile Basin partners individually or as an interdependent community of nations. Tradeoffs exist among water uses in the same country and across the Nile countries. The river basin planning and management Nile DST component has several unique features: This module includes extensive data in five major categories: (a) river network configuration, (b) river hydrology, (c) existing and planned hydro facilities, (d) water use, and (e) reservoir/lake regulation rules. Data can be viewed, added, or modified as necessary through a userfriendly interface. The actual river system is represented by a network of river nodes, reaches, and reservoirs, each with its own attributes. River nodes represent locations of local inflow and/or water withdrawals and returns. River reaches represent physical river segments and their water transport characteristics. Reservoirs represent man-made or natural lakes that may support various water uses including water supply, flood control, drought management, hydropower, and wetland protection, among others. Models: This module integrates streamflow forecasting, river and reservoir simulation, and reservoir management. Ten-day streamflow forecasts are generated at key basin nodes including Lakes Victoria, Kyoga, and Albert, Torrents, Bahr el Ghazal, Sobat, the Blue Nile, Dinder, Rahad, and Atbara. The forecasts have the form of equally likely realizations reflecting historical streamflow characteristics such as seasonal and long-term variability. Streamflow forecasts are generated by the hydrologic watershed models, or via statistical procedures where hydrologic models are unavailable. The river and reservoir routing models simulate the movement of water through the river reaches and quantify transmission losses and time lags. The routing models are based on statistical or physically-based relationships (depending on available information) and incorporate model error characterizations. Reservoir and lake outflow through hydropower facilities and spillways is modelled with sufficient detail for use in operational applications. The purpose of reservoir management is to determine release sequences from each system reservoir such that sub-basin and basin-wide objectives are met as best as pos-

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sible. System objectives include meeting water supply targets and avoiding water shortages, minimizing losses, maintaining land use patterns (Sudd), regulating river flows, avoiding spillage, and generating as much firm and average energy as possible. The task of the reservoir control module is complicated by the system size, non-linear response, and intrinsic uncertainties. The optimization process is based on the Extended Linear Quadratic Gaussian (ELQG) control method (developed by Georgakakos and associates (1987) through present), a trajectory iteration optimization algorithm suitable for multidimensional, dynamic, and uncertain systems. Applications: The Nile-DST river simulation and management model can be used to provide answers to various important questions. Typical applications are listed below: • Value of various regulation, hydro-power, and irrigation projects along the White, Blue, and Main Nile branches. Such assessments could quantify the incremental benefits from individual development projects as well as the combined benefits from various project configurations. • Implications of reservoir regulation policies for local, upstream, and downstream riparians. • Marginal value (gain or loss) of irrigation with respect to hydropower at various basin locations. • Irrigation versus hydropower tradeoffs for each nation, region, and the entire basin. • Impacts of flow regulation on wetlands. The Nile-DST utilizes several assessment criteria of interest to the Nile Basin nations. These criteria include: 1. severity and frequency of shortages with respect to user-specified water supply targets; 2. water withdrawals and losses over user selected regions and times of the year; 3. reservoir and lake level drawdown and spillage statistics; 4. in-stream flow availability at user-selected river nodes and reaches; 5. flood and drought severity and frequency; 6. annual and firm energy generation statistics; 7. seasonal and permanent extent of wetlands. Figure 5.5 presents an assessment of the flow and hydropower impacts of two development scenarios in the Blue Nile Basin. The first scenario (dark gray) is the baseline of current conditions. The second scenario (light gray) assumes that 4 large hydropower projects have been built in Ethiopia and are operated using dynamic inflow forecasts and multi-reservoir control methods. The results show that flow changes can be significant with benefits both at the high and the low ends (reduction of excessive floods as well as low flow augmentation). Furthermore, energy generation in Ethiopia would increase very substantially with the potential to benefit not only Ethiopia, but also Sudan and Egypt. Other benefits (not shown) include drastic reductions of the drought risk for Sudan and Egypt.

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5.3.3 Agricultural planning Agriculture is a major water consumer in the Nile Basin. It is the main source of income for a large part of the population, and many people rely predominantly on crops they grow themselves. Agricultural products are also an important source of foreign currency, as commodities like coffee, cotton, and sugarcane are exported in large quantities and sold on the world market. The Nile Basin contains many regions of high agricultural potential, some of which are already fully exploited, while others await development. Given the importance of agriculture in the basin, decision makers would benefit from reliable assessments regarding potential crop yield in undeveloped lands, irrigation needs, drought vulnerability, and the potential tradeoffs between agriculture and other water uses. The purpose of the agricultural planning model is to address these issues. Models: The Georgia Water Resources Institute at Georgia Tech has developed a comprehensive Agricultural Planning Model (GT -AgroPlan), which combines state-of-thescience irrigation scheduling and crop yield prediction tools with a user-friendly graphical interface. Physiologically-based crop models form the agronomic simulation core of GT -AgroPlan. These models, adapted from the Decision Support System for Agrotechnology Transfer (DSSAT; Tsuji et al., 1994), simulate the daily life-processes of crops using input data for soils, meteorology, and genetics. Currently, GT -AgroPlan includes crop models for eleven crops (maize, cassava, groundnuts, wheat, rice, sorghum, millet, barley, potatoes, soybeans, and dry beans), but five additional crops (including sugarcane)

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have recently been added to the DSSAT and will be incorporated into GT -AgroPlan. The models produce outputs of yield and total irrigation needs as well as daily timeseries of soil moisture and biophysical parameters. GT -AgroPlan requires data on soils, terrain, hydro-meteorology, crop characteristics, and agricultural and irrigation practices. All of these data are integrated within a GIS and graphical user interface (GUI). The GUI allows program users to easily select input data scenarios for simulation by the crop models and to view results in on-screen tables and graphs. Applications: GT -AgroPlan has been used for a wide variety of analyses, such as the assessments of gains from irrigation, spatial distribution of irrigation needs, regional drought vulnerability, and regional calorie supply. Other potential GT -AgroPlan applications include investigating the consequences of deficit irrigation relative to water demand and crop production, assessing various irrigation scheduling scenarios, climate variability impacts on agriculture, and determining water-efficient and high-calorie crop combinations. Figure 5.6 shows a regional assessment carried out in the Lake Victoria Basin (Georgakakos et al., 2000). The purpose was to assess the vulnerability of the agricultural sector to climate variability. The figure includes results for maize assuming only rain-fed conditions. Results are presented for both growing seasons (long rains – March to May; and short rains – October to November) and for typical wet and dry years. The results show that during long rains, Kenya is immune to climate variability while Tanzania, Rwanda,

Fig. 5.6. Agricultural assessments in the Lake Victoria Basin.

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Burundi can experience serious shortages. During the short rains, Kenya becomes most vulnerable with the rest of the basin exhibiting mild potential deficits. Such information is useful in formulating equitable water and benefit sharing strategies. 5.3.4 Hydrologic modelling Hydrologic models are necessary to translate climatic forcing (rainfall and temperature) to lake rainfall, evaporation, and watershed inflow. The temporal scales of interest are ten days for water resources planning and one day for operational applications; the applicable spatial scale varies from a few hundred to several thousand square kilometres. Models and applications: The Nile DSS and its derivatives include Sacramento type watershed models (Peck, 1976) that simulate the hydrologic processes of surface and subsurface runoff through physically-based conceptual elements. Such models are very useful for applications that require flow predictions over daily to sub-daily time steps. Another hydrologic model type that is also part of the Nile DSS is especially suited for medium size (1000 to 10 000 km2 ) to large watersheds (larger than 10 000 km2 ), as well as for weekly, ten-day, and monthly time steps. The model has been developed by Georgakakos and Yao (2000) and has successfully been tested in the Southeastern US and elsewhere. Figure 5.7 shows a comparison of observed and simulated flows for the Nzoia basin in Kenya and indicates that predicted and observed streamflows exhibit good agreement. Some hydrologic model features are summarized below: • Input data include watershed rainfall (weekly, ten-day, or monthly) and temperature or evapotranspiration. Model calibration additionally requires observed stream0.04 0.035

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• Model output includes streamflow at the watershed outlet and spatially-averaged soil moisture. The latter is also important for agricultural planning applications. • The model (a) simulates the watershed water balance processes (rainfall, evapotranspiration, streamflow, and soil moisture storage) on weekly, ten-day, or monthly time steps, and (b) uses a historical analog approach to determine streamflow from current conditions of rainfall, evapotranspiration, and soil moisture. • A particular basin can be sub-divided into smaller sub-basins leading to a semidistributed model implementation. However, this would be appropriate for sub-basins with streamflow measurements. • This model is also used to assess the sufficiency of hydrologic data and develop data monitoring plans. An additional hydrologic module has recently been added to simulate the seasonal and permanent extent of the Sudd wetlands (Sutcliffe and Parks, 1999) in southern Sudan. The wetlands are critical resources for the local population, fauna, and flora, and can adversely be impacted by water conservation projects and reservoir regulation policies. The wetland module enables the DSS river and reservoir simulation and management models to identify policies that minimize wetland impacts. 5.3.5 Remote sensing Rainfall drives the response of the Nile Basin at all spatial and temporal scales, and its reliable estimation is a requisite DSS component. Traditional rainfall estimation techniques rely on conventional rain-gages. However, in many areas of the world, including large portions of the Nile Basin, the raingage network is sparse, and satellite data provide an attractive alternative. The purpose of this Nile-DSS model is to combine existing rain-gage data with data from operational satellites (currently received by the Nile Basin hydro-meteorological agencies) to provide reliable rainfall estimates over the Nile subbasins. Models: At present, no universal method exists for satellite-based rainfall estimation, but several techniques have been developed and are currently used. Georgia Tech’s (GT’s) experience in the Lake Victoria Basin (De Marchi and Georgakakos, 2000) has shown that rain from convective storms (most common over the Nile Basin) can successfully be determined for daily time intervals using a combination of Meteosat visible and infrared (VIS/IR) images. This method also captures rain produced by non-convective cells, though with somewhat less accuracy. For a 10-day time scale, this approach provides reliable total rainfall estimates with correlation to ground stations as high as 0.8 to 0.9. The principle idea of the GT’s rainfall estimation approach is to identify characteristic ‘signatures’ of rain-producing events in the VIS/IR data signals. More specifically, a typical tropical convective storm exhibits a certain visible and infrared signal pattern. Initially, the cloud is low and relatively thin, resulting in a high infrared temperature and

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low visible signal. As the convective storm matures and its top approaches the tropopause, the cloud gets thicker and colder. This leads to a rising visible count and falling infrared temperature. Then, as the convective cell dissipates, the visible count decreases while the infrared temperature increases. This pattern represents a distinct signature for all rainproducing cells. The GT’s rainfall estimation approach exploits this characteristic relationship between rain-producing storms and Meteosat infrared (IR) and visible (VIS) images in a two-step procedure. First, the existence of convective cells (which produce the highest rain rates) is determined for each satellite pixel (5 × 5 km2 ) by screening the VIS/IR signals exhibiting these rain-indicating signatures. Two specifically trained neural networks (one for daytime and one for nighttime) have been developed for this task. Then, based on the temporal and spatial distribution of convective cells and other characteristics of the cloud system, the daily mean areal precipitation (MAP) is estimated over the areas of interest. The method has been calibrated and validated for three years in several locations around the Nile Basin. These tests show that the approach can successfully identify strong convective cells and provide reliable MAP estimates for daily time steps (correlation with ground measurements of 0.7), ten-day time steps (correlation of 0.80–0.9), and monthly time steps (correlation of 0.87–0.98). The good performance of this approach is attributed to the use of the full VIS/IR signal information rather than simply considering specific threshold levels. Figure 5.8 illustrates the value of satellite-based rainfall estimation over Lake Victoria. The top graphs present rainfall estimates based on rain-gages (located at the lake shores), while the lower graphs make use of the GT’s satellite rainfall estimation scheme. The resulting rainfall distributions are rather different, with the satellite estimates being considerably wetter. The lake level changes experienced during the same period provide strong evidence of the accuracy of the satellite estimation procedure. The above-described Nile DSS modules can express the response of the Nile system in terms of river flow, water supply, food production, and energy generation. Building on these developments, the next modelling phase will introduce models that can translate physical outputs into economic and social benefits and impacts. Furthermore, a water quality component is planned to enable fully integrated assessments. 5.4 Conclusion Decision support systems are integral parts of IWRM processes facilitating the use of science and technology advances in public policy. Although generic DSS development principles exist, much is system specific and a thorough understanding of the interdependence of natural processes, water uses, institutional setting, and decision maker objectives is necessary for a successful DSS design. Participatory DSS development: As indicated earlier, DSS generate a wide array of quantitative system response measures including water use tradeoffs, risks, and benefits. A key effort during the DSS development phase is to determine the necessary and sufficient information that decision makers need to make good decisions. This information set is expected to vary by decision type (planning, management, or near real time), management agency, and stakeholder group, and significant interaction should take place with the decision makers defining the most suitable informational content and form.

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Fig. 5.8. Rainfall estimation over the Lake Victoria region (left) and over the lake itself (right) without (top) and with satellite information (bottom).

In view of the inter-disciplinary DSS application scope, the formation of an interdisciplinary DSS expert group is recommended to participate in all DSS development phases, to ensure the effective transfer of the new technology to user groups, and to contribute to DSS sustainability beyond the development phase. Institutional implementation aspects: Decisions in the Nile Basin involve a multitude of agencies and involve various stakeholders. The DSS provides some useful information to all parties. However, some modelling components are more relevant to particular decision maker groups, and there is a need to consider how to best implement this system in view of the current institutional framework. The DSS structure of Fig. 5.3 suggests that higher DSS modelling layers are more suitable for agencies with planning functions (e.g., environmental, water, and energy planning departments), while lower DSS layers are more suitable for agencies with operational mandates (e.g., flood control, power scheduling, and water distribution). This issue should be addressed in close collaboration with all relevant agencies and stakeholders by reviewing past practices and experience, and by developing a shared vision institutional decision framework. In the assessment phase

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of the project, the operational experience with the DSS and the agreed-upon inter-agency decision process should be documented and possible enhancements should be made. Long term sustainability: Lastly, the greatest challenge in the development and effective use of integrated decision support systems is the availability of qualified water resources professionals. To varying degrees, this challenge applies everywhere including the Nile Basin. The answer is not to develop simple DSS tools that address parts of the overall problem and provide simplistic answers to the complex questions asked by policy makers. Doing so would only trivialize and discredit the role of DSS and defeat the purpose of addressing water resources challenges in a holistic manner. Instead, a comprehensive professional training and capacity building program must be part and parcel of DSS development. Sufficient training, retention of qualified personnel, continuing education, and long term capacity building must all be part of a general educational strategy. Specifically, capacity building is a long term endeavour and requires engaging and focusing the academic community. While university programs cover many of the areas underlying the above described DSS, they lack a program extending across and integrating the disciplines of climatology, meteorology, hydrology, hydraulics, sensor technology, water resources management, power systems analysis, environmental and ecological assessments, economic valuation, conflict resolution, public health, and information technology. The key to sustainable water resources development and management is at the interface of these disciplines. It is thus opportune for the Nile Basin nations to institute cross disciplinary programs that can provide future engineers and scientists with a holistic understanding of the IWRM process. It is these qualified people that will create and use better DSS tools and will invent hopeful and amicable solutions to the ever-emerging Nile Basin challenges. Acknowledgements The work referred to herein has been sponsored by various organizations. Specifically, I am grateful to FAO, World Bank, and US Agency for International Development (AID) for funding and continuing to support my involvement in various DSS development efforts. Several of my graduate students and associates contributed to the development of the Nile DSS including Huaming Yao, Kelly Brumbelow, Carlo De Marchi, Stephen Bourne, Lori Visone, and Amy Tidwell. I am very fortunate to have the opportunity to teach and learn from such gifted individuals. Many people from the Nile Basin Countries have contributed to the Nile DSS. I specifically wish to thank the team of National Modelers from all ten Nile countries that have worked closely with us in developing and testing the various Nile DSS modules. Their continued interest, collaboration, and friendship are highly rewarding. Lastly, I wish to thank Professor Rodolfo Soncini-Sessa for inviting me to participate at the IFAC workshop on Modelling and Control for Participatory Planning and Managing Water Systems that was held in Venice, Italy. Bibliography Brumbelow, K. and A. Georgakakos (2000). An assessment of irrigation needs and crop yield for the United States under potential climate changes. J. Geophys. Res.-Atm. 106(21), 27383– 27406.

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Brumbelow, K. and A. Georgakakos (2001). Agricultural planning and irrigation management: The need for decision support. The Climate Report 4(1), 2–6. De Marchi, C. and A. Georgakakos (2001). A satellite based rainfall estimation method for the Lake Victoria basin. In: Proceedings of Remote Sensing and Hydrology, April 2000. IAHS. IAHS Publication. Santa Fe, NM. Georgakakos, A. (1989a). Dynamic Programming for Optimal Water Resource System Analysis. Chap. Extended Linear Quadratic Gaussian Control for the Real-Time Operation of Reservoir Systems, pp. 329–360. Prentice-Hall. Englewood Cliffs, NJ. Georgakakos, A. (1989b). Extended Linear Quadratic Gaussian (ELQG) control: Further extensions. Water Resour. Res. 2(25), 191–201. Georgakakos, A. (1991). Decision Support Systems. Chap. Computer-Aided Management of the Southeastern U.S. Reservoir System, pp. 407–428. Vol. G 26. NATO ASI Series. Georgakakos, A. (1993). Operational tradeoffs in reservoir control. Water Resour. Res. 11(29), 3801–3819. Georgakakos, A. and H. Yao (1995). A Decision Support System for the Equatorial Lakes. Technical Report GIT/CEE-HYDRO-957. School of Civil and Environmental Engineering, Georgia Tech. Atlanta, GA. Georgakakos, A. and H. Yao (2000). Climate change impacts on Southeastern US basins. Open File Report 00-334. USGS. Georgakakos, A., H. Yao and Y. Yu (1995). Control models for hydropower system analysis and operation. Technical Report 158. School of Civil and Environmental Engineering, Georgia Tech. Atlanta, GA. Georgakakos, A., H. Yao and Y. Yu (1997a). A control model for dependable hydropower capacity optimization. Water Resour. Res. 10(33), 2349–2365. Georgakakos, A., H. Yao and Y. Yu (1997b). A control model for hydroelectric energy value optimization. J. Water. Res. Pl.-ASCE 1(123), 30–38. Georgakakos, A., H. Yao and Y. Yu (1997c). Control models for hydroelectric energy optimization. Water Resour. Res. 10(33), 2367–2379. Georgakakos, A., H. Yao, K. Brumbelow, C. DeMarchi, S. Bourne and M. Mullusky (2000a). The Lake Victoria Decision Support System. Technical Report GWRI-20001. Georgia Water Resources Institute, Georgia Tech. Atlanta, GA. prepared for FAO. Georgakakos, A., H. Yao, K. Brumbelow, C. DeMarchi, S. Bourne, L. Visone and A. Tidwell (2003). The Nile Decision Support Tool. Technical report. Georgia Water Resources Institute, Georgia Tech. Atlanta, GA. prepared for FAO. Georgakakos, A., H. Yao, M. Mullusky and K. Georgakakos (1998). Impacts of climate variability on the operational forecast and management of Midwestern Water Resources Systems. Water Resour. Res. 4(34), 799–821. Georgakakos, A.P. and D.H. Marks (1987). A new method for real-time operation of reservoir systems. Water Resour. Res. 23(7), 1376–1390. Georgakakos, K., N. Graham and A. Georgakakos (2000b). Can forecasts accrue benefits for reservoir management? The Folsom Lake case study. The Climate Report 4(1), 7–10. Peck, E.L. (1976). Catchment modelling and initial parameter estimation for the national weather service river forecast system. Technical Report NWS HYDRO-31. Office of Hydrology, NWS. Silver Spring, MD. Sutcliffe, J.V. and Y.P. Parks (1999). The Hydrology of the Nile. number 5. In: IAHS Special Publication. IAHS Press. Wallingford, UK. Tsuji, G.Y., G. Uehara and S. Balas, Eds.) (1994). DSSAT: A Decision Support System for Agrotechnology Transfer. Version 3. University of Hawaii. Honolulu, HI. Yao, H. and A. Georgakakos (2001). Assessment of Folsom Lake response to historical and potential future climate scenarios. J. Hydrol. 249, 176–196.

CHAPTER 6

Water Reservoirs Management under Uncertainty by Approximating Networks and Learning from Data Marco Baglietto1 , Cristiano Cervellera2 , Marcello Sanguineti1 and Riccardo Zoppoli1 1 Department of Communications, Computer and System Sciences (DIST)

University of Genoa, Genova, Italy 2 Institute of Intelligent Systems for Automation (ISSIA-CNR)

National Research Council of Italy, Genova, Italy

6.1 Introduction Finite-horizon management of water reservoirs systems under uncertainty can be formalized as a T -stage stochastic optimal control problem. As is well-known, T -stage stochastic optimal control problems can be solved analytically by Dynamic Programming (DP), if suitable hypotheses on the state equation, the cost function, and the random variables (river inflows and stochastic rain inflows) are verified. Typically, the analytical solution by DP can be obtained in the so-called LQG framework: linear state equation, quadratic cost, and Gaussian random variables. However, in realistic operating conditions water management problems are far from satisfying such hypotheses, so one has to search for approximate solutions. When the state of the water reservoirs system can be observed perfectly, approximate solutions can be obtained by discretizing the state space and applying DP. In such a way, the functional equation defining the DP procedure has to be solved only in correspondence of a finite number of state values. A suitable interpolation technique is then used to obtain approximate values of the cost function for points not belonging to the discretization set. However, given a fixed number d of discretization grid points in each of the n components of the state vector, the use of a full tensor-product grid makes the total number of discretization points grow as d n . This exponential growth is known as curse of dimensionality (Bellman, 1957), and limits to small dimensions the applicability of discretization techniques. In the deterministic case, various methods to cope with the curse 117

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of dimensionality have been proposed since the first appearance of dynamic programming in Bellman’s paper; among them, we mention State Incremental Dynamic Programming (Larson, 1968) and Differential Dynamic Programming (Jacobson and Mayne, 1970). A realistic model for water management tasks has to take into account the presence of uncertainties, represented, e.g., by river inflows and stochastic rain inflows. This makes things more complex, as in such a case the random variables have to be discretized, too. When stochastic DP is used, the efforts to cope with the curse of dimensionality have followed two main approaches: (i) simplification of the problem by using simpler models, and (ii) use of smart approximators for the cost-to-go functions (in such a way as to reduce the number of grid points). In applications to water reservoirs management, among the methods using the first approach we cite the aggregation/disaggregation of grid points to diminish the dimension of the state space (Turgeon, 1981) and the partition of the original problem into smaller separable problems (Archibald et al., 1997). The major drawback of these methods lies in their lack of generality, since they are highly dependent on the particular reservoir operation problem they are applied to. As to the second approach, among the various methods proposed for a suitable approximation of the cost-to-go functions one can trace an evolution starting from polynomial approximation (Bellman et al., 1963) and continuing with cubic Hermite polynomials (Foufoula-Georgian and Kitanidis, 1988) and spline interpolation (Johnson et al., 1993). In Johnson et al. (1993), the use of cubic splines instead of tensor–product linear interpolating functions, allowed to solve a water supply problem up to dimension five. More recently, by incorporating in the DP procedure information on first and second derivatives of the cost-to-go functions, reservoir control problems with up to seven state variables and two random inputs have been faced (Philbrick and Kitanidis, 1999). Although these strategies allow one to reduce the number of grid points required to obtain a given precision in the approximation of the cost-to-go functions, they still need a uniform discretization of the state space, thus leaving the curse of dimensionality eventually unavoided and their employ still impracticable for high values of n. In Chen et al. (1999), by using an approximation technique based on multivariate adaptive regression splines and a statistical perspective for the choice of the discretization points, an inventory forecasting application (defining a stochastic control problem with a structure similar to the one associated with water resources management) has been faced with a number n of state variables higher than those considered before, but still limited to nine. In this paper we propose two general approaches to solve non-LQ T -stage stochastic optimal control problems. Both approaches aim at coping with the curse of dimensionality and are specialized to the problem of optimally controlling a system of water reservoirs over a finite time horizon. Both methods rely on the use of approximating networks (ANs; see Zoppoli and Parisini, 1992; Zoppoli et al., 2001; Kainen et al., 2003; Kurková and Sanguineti, 2001, 2002 and the references therein), which are a family of nonlinear approximators with powerful approximation properties. The first method exploits ANs for the approximation of the cost-to-go functions and combines this with deterministic sequences generation (Cervellera and Muselli, 2004), whereas in the second method ANs are used in the context of a methodology of functional optimization, called Extended Ritz Method (ERIM), that has proved itself to be effective in a large number of applications (see Zoppoli and Parisini, 1992; Zoppoli et al., 2001; Kurková and Sanguineti, 2005a;

Reservoir Management by Approximating Networks and Learning from Data 119 Zoppoli et al., to appear; Giulini et al., to appear, the references therein). We discuss several theoretical features of the proposed solution methodologies and describe numerical results. The outline of the paper is the following. In Section 6.2 we give an overview of the two proposed methods, which are dealt with in detail in Sections 6.3 and 6.4, respectively. Upper bounds on the error associated with the two methodologies of approximate solution are discussed in Section 6.5. Efficient sampling techniques in high dimensions are considered in Section 6.6. Numerical results are presented in Section 6.7. 6.2 Overview of the proposed approaches We begin this section providing a very general definition of dynamic system and cost of the decisional process. In the following we will narrow such concepts down to simple problems that are practical to reservoirs management. The reader may find this approach that goes from the generic to the particular rather abstract. Actually it is more useful, for the purposes we aim at, to start from a general description, since this allows us to employ methods for the solution of optimal control problems to solve a very large spectrum of applicative cases in various fields of Engineering. Since the above mentioned concepts of ‘dynamic system’ and ‘cost of the decisional process’ will be presented in as simplified as possible fashion, the reader should be able to apply easily the general issues to the applicative cases of his particular interest. Consider the following equation xt+1 = ft (xt , ut , εt ),

t = 0, 1, . . . , T − 1,

(6.1)

where xt ∈ n is the state vector (x0 = xˆ is a given initial state), ut ∈ Ut (xt ) ⊆ m is the control vector (Ut (xt ) is the set of admissible controls), and εt ∈ q is a random noise. The state is assumed to be perfectly measurable and the stochastic vectors εt , t = 0, . . . , T − 1 to have a known probability density function. Let us see the physical meaning of the three vectorial variables that appear in (6.1), i.e., xt , ut , and εt . In rather informal terms, the state xt is made up of the minimum number of variables the knowledge of which, at the discrete time t, allows one to determine what the evolution will be, at stages t + 1, t + 2, . . . , of all the variables that can be ‘interesting’ to understand the behaviour of the physical (or economic, logical, etc.) system that we aim at modelling with (6.1). Obviously, among these variables, there is the state vector itself. Clearly, what said above has no meaning if, in addition to the knowledge of the state xt , we do not have also knowledge of the external variables that, at stages t + 1, t + 2, . . . , influence the behaviour of the system. Such variables are of two kinds: (i) the ones that can be controlled by the decision maker in charge of managing the system and (ii) those that do not depend on its control, but are generated by the so-called external environment. The first variables are called control variables, and lumped together in the vector ut ; the second can be named exogenous variables and are generally unpredictable. We call them generically random variables and lump them together into the random vector εt . If, as we have said, the vectors εt , εt+1 , . . . are unpredictable, the trajectory of the state xt+1 , xt+2 , . . . will be unpredictable as well. Nevertheless, the mechanism of transition of the

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state (and of all the ‘interesting’ variables that depend on it) from the value xt to the value xt+1 under the action of ut and remains univocally determined. What said above allows us to call (6.1) state equation and to state that it represents the model of the dynamic system we want to describe. In this chapter, we consider mathematical models that describe only the behaviour through time of water levels in reservoirs and the interactions among interconnected reservoirs. It follows that the state of the system is simply given by state vectors having the form xt = col(st1 , . . . , stn ), where st1 , . . . , stn are the amounts of water in the reservoirs 1, . . . , n, respectively, at the beginning of the tth decision stage (see, e.g., the models in (6.14) and, for a more general model of a single j reservoir, Ch. 5 in Soncini-Sessa et al., 2007). In these models the natural inflows ξt (j = 1, . . . , n) of water into the reservoirs are random variables that are mutually independent over the time (not among the reservoir). Then we let εt = col(ξt1 , . . . , ξtn ) and ε0 , ε1 , . . . , εT −1 are mutually independent random vectors. However, this hypothesis is usually not true and therefore, to cope with the more realistic case where the inflows are not independent, we need to model suitable dynamics. This requires the definition of more state equations (and then more state variables), and the state xt of the global dynamic system must have in its components the aforementioned state variables too (see Ch. 6 in Soncini-Sessa et al., 2007). Whenever we need to consider also the dynamic behaviour of other entities related to the reservoirs system, such as cultures that benefit from irrigation, the catch basins that feed the reservoirs, aqueducts and urban agglomerates, etc., new dynamic systems have to be aggregated to the system of reservoirs, and the state xt must contain other suitable state variables. The cost of the decisional process is given by J=

T −1

ht (xt , ut , εt ) + hT (xT ).

(6.2)

t=0

The functions ht (·) represent the costs of transitions that must be paid from stage t to stage t + 1 and hT (·) the final cost. Examples of such functions are (6.15) and (6.16). It has to be noticed that we assume that the time horizon of the decisional process is finite and fixed: the number T of decisional stages is in fact assigned a priori. Such context is correct when we want to study ‘manoeuvres’ on the controlled system or problems of intrinsically limited duration. However this assumption often is not satisfied: the time horizon is very large or tending to infinity and the optimization problem becomes even more difficult. To solve it, we need to recur to approximate techniques. A frequently adopted one is the so-called receding-horizon optimization, in which one assumes that the decisional process lasts for T stages. Thus the problem is led back to the one considered in this chapter, assuming that it is defined between stage t and stage t + T . We determine the optimal control law at stage t and we neglect those relative to the following stages. At time t + 1, we reformulate the problem for the temporal range that goes from t + 1 to t + T + 1, we compute again the control laws, but we employ just the one relative to stage t + 1. We repeat the procedure at stages t + 2, t + 3, . . . and we obtain a control law that, with intuitive meaning, takes the name of open-loop feedback control (OLFC) law. It must be considered, as we end the present introductory lines, that the optimal

Reservoir Management by Approximating Networks and Learning from Data 121 control problem over infinite horizon (as many problems where the LQ hypotheses are not verified) remains an open research problem. We can now formulate the following T -stage stochastic optimal control problem. Problem SOC. Find the sequence of optimal control laws u∗t = m∗t (xt ), t = 0, 1, . . . , T − 1, that minimize the expected cost J (x0 ) = Eε0 ,...,εT −1 (J ). As the initial state x0 = xˆ is fixed, in stating Problem SOC it would be sufficient to determine the optimal control vector u∗0 instead of the optimal control law u∗0 = m∗0 (x0 ). However, it may be useful the controller to be provided with this control law once and for all in order to face any possible initial condition x0 = xˆ without solving a new optimization problem every time the information xˆ is acquired. Then, in the statement of Problem SOC, we leave the function m∗0 (x0 ) as an unknown. It is common knowledge that Problem SOC can be solved analytically by DP only if suitable hypotheses are verified: typically, if Problem SOC is stated in the LQ framework and if the random vectors are mutually independent over the time. Note that for DP the vectors ε0 , . . . , εN −1 are assumed to be mutually independent over the time, but the components of each εt , t = 0, . . . , N − 1 may be highly cross-correlated (e.g., the natural flows in different watersheds are such). A standard way of searching for approximate solutions to Problem SOC consists in discretizing the state space and applying DP. Thereby, the functional equation of DP has to be solved only in correspondence of a finite number of state values. Suppose that, at (l) each stage t, L discretization points xt , l = 1, . . . , L have been selected (in order to simplify the notation, we suppose the number L of discretization points to be the same at 

(l)

all stages). Let XtL = {xt , l = 1, . . . , L}. Then we can write  (l)    (l)  J˜T∗−1 xT −1 = JT∗−1 xT −1   (l)    (l) 

= min E ht xT −1 , uT −1 , εT −1 + hT ft xT −1 , uT −1 , εT −1 , uT −1 ∈UT −1 εT −1

(l)

xT −1 ∈ XT −1,L ,   (l)  (l)    J ∗

J˜t∗ xt = min E ht (xt , ut , εt ) + Jˆ ft xt , ut , εt , θt+1 ,

(6.3a)

ut ∈Ut εt

(l)

t = T − 2, . . . , 0; xt ∈ XtL ,

(6.3b)

J ∗ ] is a function parameterized by θ J ∗ , by which we approxwhere Jˆ[ft (xt(l) , ut , εt ), θt+1 t+1 imate the cost-to-go function at stage t + 1, while the notation J˜t∗ (xt ) is used to differentiate this quantity from the true cost-to-go Jt∗ (xt ) (as we are using the aforementioned approximations). At stage T − 1, this approximation is not needed (see (6.3a)). • Approximation of the cost-to-go functions by approximating networks. The first method that we propose resorts to the DP procedure by using approximating networks (ANs), i.e., linear combinations of simple ‘mother’ basis functions dependent on some free inner parameters. We call this method ANDYM (Approximating Networks in DYnamic programming Method).

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The coefficients of the linear combination and the inner parameters have to be determined in such a way as to minimize the cost functional in the water management problem at each decision stage t = 0, 1, . . . , T − 1, with the purpose of approximating (for example, in the sense of least squares) the cost-to-go functions of the DP procedure. Clearly, approximating the cost-to-go functions entails the solution of nonlinear programming problems, in which the parameters vectors have to be optimized at each decision stage. Various nonlinear programming algorithms have been proposed to find the optimal value of the parameters; see, e.g., Grippo (2000), Alessandri et al. (2002), Alessandri et al. (to appear) and the references therein. Here we shall apply stochastic approximation techniques (Kushner and Yin, 1997). The basis functions have to be chosen with care, as their linear combinations must benefit by suitable properties in the spaces of the functions to be approximated (in our case, the optimal cost-to-go functions). For example, certain sigmoidal basis functions and some radial basis functions have such properties; see Barron (1993), Kurková and Sanguineti (2001, 2002), and the references therein for details. The idea of approximating cost-to-go functions by neural networks is not new and goes under the naming of Neuro-Dynamic Programming (NDP) (Bertsekas and Tsitsiklis, 1996), which, however, focuses mainly on the case of infinite-horizon than on the T -stage optimal control problems. Moreover, here we consider more general approximating architectures and we combine the use of neural networks (either for the cost-to-go functions or for the control law) with recent results from approximation theory (Barron, 1993; Kurková and Sanguineti, 2001, 2002), statistical learning (Barron, 1994) and deterministic learning (Cervellera and Muselli, 2004), which provide our method with strong theoretical foundations. • Minimization of the total expected cost by the Extended Ritz Method. This method presents a different way of dealing with the problem of T -stage stochastic optimal control, quite different from dynamic programming. The presence of uncertainty in an optimal water management problem suggests or even makes mandatory searching for optimal management strategies that are functions of the state vector. In other words, the stochastic optimal control task becomes a functional optimization problem: one has to minimize a functional with respect to water management laws belonging to an infinite-dimensional space of functions, often dependent on a large number of variables (i.e., the number n of components of the state vector). Infinite dimension makes most mathematical tools typically used in nonlinear programming inapplicable and requires the development of new approaches based on functional analysis theory and techniques. The key idea of the method consists in assigning to the control functions the structure of approximating networks, in which a finite number of parameters have to be determined in order to minimize the cost functional in the stochastic optimal control problem. The sequence of control laws is then composed of a ‘chain’ of approximating networks. This makes it possible to approximate the original functional optimization problem by a nonlinear programming one. In this way we skip the computation of the cost-to-go functions, whose values remain implicit in the minimization process for the total cost. Such a cost is then minimized by using a stochastic approximation technique (Kushner and Yin, 1997). As the methodology outlined above extends the classical Ritz method (Gelfand and Fomin, 1963) for the calculus of variations (the latter corresponds to the particular case in which one considers linear combinations of fixed basis functions instead of basis functions dependent on free parameters), we call it ERIM (Extended RItz Method). It turns

Reservoir Management by Approximating Networks and Learning from Data 123 out to be simple (it does not require the construction of any grid in the state space) and surprisingly effective in solving optimal control problems with a large number of state components (see Zoppoli and Parisini, 1992; Parisini and Zoppoli, 1994, 1996, 1998; Baglietto et al., 2001, 2003; Alessandri and Sanguineti, 2005; Zoppoli et al., to appear; Giulini et al., to appear, the references therein). The theoretical foundations of such approach can be found in Zoppoli et al. (2001), Kainen et al. (2003), Kurková and Sanguineti (2005a). 6.3 ANDYM: approximation of the cost-to-go functions by approximating networks As mentioned in Section 6.2, the basic feature of this method consists in searching for an approximation Jˆ(xt , θtJ ∗ ) of Jt∗ (xt ) by constraining the cost-to-go to take on the structure of an AN. In the following we briefly describe such networks. For a positive integer ν, a one-hidden-layer network (shortly, OHL network) is a function γν (x, θν ): n × k → s of the form γν (x, θν ) = col

 ν

cij ϕ(x, κi ), j = 1, . . . , s ,

(6.4)

i=1

where ϕ(·, ·) is a given basis function, cij ∈  and the components of the vectors 

κi ∈ k are parameters to be determined. The parameter vector θν is defined as θν = col(cij , κi , i = 1, . . . , ν, j = 1, . . . , s). Then we have θν ∈ N (ν) , where N (ν) = ν(k + s). As the latter is a linear function of ν, ν measures, in some sense, the model complexity of functions γν (x, θν ) and so we call ν model complexity. From (6.4) it is apparent that, in general, an OHL network is a vectorial function of dimension s. Indeed the problem considered in this section would require just a scalar network (s = 1), but we prefer to define multi-dimensional networks because they will be required in the following sections. Following Zoppoli et al. (2001), let the set of functions to be approximated be a linear space H . Since the distance between the functions γ and γν has to be measured, the space H is equipped with a norm  · . Aν ⊂ H is defined as the parameterized set of 

all functions of the form (6.4), that is, Aν = {γν (x, θν ) ∈ H, θν ∈ N (ν) }. The sequence {Aν }∞ ν=1 has the infinite nested structure A1 ⊂ A2 ⊂ · · · ⊂ Aν ⊂ · · · . In the approximation methods that are going to be presented, the following assumption plays a basic role (Zoppoli et al., 2001). A1. The functions γν (x, θν ) are such that the set

+∞

ν=1

Aν is dense in H .

We call functions of the form (6.4) that verify Assumption A1 H -approximating networks. Feedforward neural networks with one hidden layer and linear output activation functions, linear combinations of sinusoidal functions with variable frequencies, and linear combinations of radial basis functions of the Gaussian type are examples of H approximating networks in the space C(K, s ) of continuous functions on a compact set K with the supremum norm and in the space L2 (K, s ) of square-integrable functions

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on K with the L2 norm. Hence, such approximators are both C- and L2 -approximating networks. The proofs of the related density properties can be found in several papers (see, e.g., Leshno et al., 1993; Park and Sandberg, 1991). We call linear approximating networks those in which the basis functions ϕ(·) do not contain the parameter vectors κi ; when such vectors are present, we have nonlinear approximating networks. Examples of C- and L2 -linear approximating networks are classical linear approximators such as algebraic and trigonometric polynomials. The reason that motivates one to use nonlinear approximating networks instead of the simpler linear ones is the following. An important property to be taken into account in the choice of a OHL network is its ability to approximate within a fixed desired accuracy every function belonging to a given subset S ⊂ H of functions of interest, with a number ν of basis functions that grows ‘not too fast’ with the number of variables of the functions in S. If the rate of growth were too fast, the nonlinear programming problem of determining the values of the optimal parameters might become computationally unfeasible for a large dimension of the state vector. Nonlinear ANs may show, for a given desired accuracy, a polynomial rate of growth of ν with the number of variables, in cases in which linear ANs may be ruled out by the curse of dimensionality (see for details Barron, 1993; Kurková and Sanguineti, 2001, 2002, 2005a; Kainen et al., 2003; Zoppoli et al., 2001). Coming back to the approximate DP procedure, we constrain the tth cost-to-go function, t = T − 1, . . . , 1, to take on the structure of an AN, that is, νt     ci (t)ϕ xt , κi (t) , Jˆ xt , θtJ =

t = T − 1, . . . , 1.

i=1

The ANs are assumed to maintain the same structure stage after stage. The parameter (l) vector θtJ ∗ is obtained on the basis of the values of J˜t∗ (xt ) by using some approximation criterion like the least-squares one, i.e., θtJ ∗ = argmin θtJ

L   ∗  (l)   (l)  2 J˜t xt − Jˆ xt , θtJ ,

t = T − 1, . . . , 1.

(6.5)

l=1

Of course, there is the need to assume that the cost functions to be approximated are sufficiently ‘smooth’ in the sets of the admissible states, so that such functions belong to suitable subsets of linear spaces with the norm  · . There are two techniques for determining the optimal controls on line: reoptimization and approximation of the optimal control laws by ANs. 1. Reoptimization. Using this technique the computation of the optimal controls u˜ ∗t , t = 0, 1, . . . , T − 1, is performed on line by exploiting the values of the cost-to-go Jˆ(xt , θtJ ∗ ) stored in memory, that is, 

 J∗ u˜ ∗t = argmin E ht (xt , ut , εt ) + Jˆ ft (xt , ut , εt ), θt+1 , ut ∈Ut εt

t = 0, 1, . . . , T − 1.

2. Approximating the optimal control laws by ANs. In this case the optimal control laws m∗t (xt ) are approximated by another family of ANs, denoted by m(x ˆ t , θtu ),

Reservoir Management by Approximating Networks and Learning from Data 125 t = 0, 1, . . . , T − 1. Such a second family of ANs is derived as follows. While apply(l) (l) (l) ing Eqs. (6.3), the L pairs [xt , m ˜ t (xt )] are obtained at each stage. Then the optimal  u∗ ˜ ∗t (xt(l) ) − vectors θt can be computed by minimizing the approximation error L l=1 m (l) u 2 m(x ˆ t , θt ) , for t = T − 1, . . . , 1. Again, the optimal control laws m∗t , t = 0, 1, . . . , T − 1, are assumed to belong to normed linear spaces in which the ANs are dense. By using the second technique, it is possible to obtain the important advantage of performing all computations off line. Indeed, reoptimization requires on-line computations whereas the use of ANs permits the on-line generation of the control vectors ‘almost instantaneously’. 6.4 ERIM: minimization of the total expected cost by approximating networks The ANDYM may not be an easy tool to handle, for it may require cumbersome numerical procedures. Therefore, we consider another method of approximate solution of Problem SOC. Such a method consists in assigning the control laws mt (xt ) a fixed structure ˆ ·) is an AN and θt is the vector of parameters to m(x ˆ t , θt ), t = 0, 1, . . . , T − 1, where m(·, be determined. By substituting the control laws m(x ˆ t , θt ) into the state equation (6.1) and in the cost 

(6.2), the cost function assumes the form J (θ, x0 , ε0 , . . . , εT −1 ), where θ = col(θt , t = 0, 1, . . . , T − 1). As stated in Problem SOC and pointed out after the statement of the problem, it may be useful to compute the optimal control law for any possible initial state x0 instead that for ˆ This can be obtained directly in applying dynamic programming. a specific value x0 = x. On the contrary, if the ERIM is used, some changes in the statement of Problem SOC is needed. We assume x0 to be a random vector uniformly distributed in its domain (if some information on the possible value of x0 , a probability density p(x0 ) can be introduced). Thus, we have to average the cost J (θ, x0 , ε0 , . . . , εT −1 ) not only with respect to the 

random vector ε = col(ε0 , . . . , εT −1 ), but also with respect to x0 . Then the vector θ ∗ that minimizes the expected cost Ex0 ,ε [J (θ, x0 , ε)] has to be found. It follows that the functional optimization Problem SOC has been approximated by a nonlinear programming problem, which can be solved by using some gradient descent method. Provided that the numbers νt of basis functions in each AN are sufficiently large, the new problem can approximate Problem SOC to any degree of accuracy. The concept of epi-convergence is useful to state correctly the meaning of the term ‘approximation’ of Problem SOC by a sequence of nonlinear programming problems parametrized by νt (Zoppoli et al., 2001). Due to the general statement of Problem SOC, it is generally impossible to express the average cost Ex0 ,ε [J (θ, x0 , ε)] in explicit form. This leads to the computation of the realization ∇θ J [θ (k), x0 (k), ε(k)] instead of ∇θ Ex0 ,ε [J (θ, x0 , ε)], thus giving rise to the stochastic approximation algorithm  θ (k + 1) = θ (k) − α(k)∇θ J θ (k), x0 (k), ε(k) ,

k = 0, 1, . . . ,

(6.6)

where the realizations of x0 (k) and of the sequence {ε(k), k = 0, 1, . . .} are generated by randomly selecting such vectors according to their probability density functions.

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As is well known, a necessary condition for convergence is that the step-size α(k) suitably decreases (Kushner and Yin, 1997). A commonly employed choice is α(k) = c1 /(c2 + k), c1 , c2 > 0. To implement algorithm (6.6) at each iteration step k, the components of the gradient ∇θ J [θ (k), x0 (k), ε(k)] have to be computed, i.e., the partial derivatives ∂ i J [θ (k), x0 (k), ε(k)], for t = 0, 1, . . . , T − 1 and for i = 1, . . . , N (νt ), ∂θt

where θti denotes the ith component of the vector θt . It is possible to write: ∂J /∂θti = ∂J /∂ut ∂ m(x ˆ t , θt )/∂θti , and then, by using some algebra, it is easy to see that ∂J /∂ut is given by ∂J ∂ ∂ = ht (xt , ut , εt ) + λ ft (xt , ut , εt ), t+1 ∂ut ∂ut ∂ut

t = 0, 1, . . . , T − 1,



where λ t = ∂J /∂xt . Moreover, λt can be computed as λ t =

∂ ˆ t , θt ) ∂ ∂J ∂ m(x ht (xt , ut , εt ) + λ ft (xt , ut , εt ) + , t+1 ∂xt ∂xt ∂ut ∂xt

t = T − 1, . . . , 0, λ T =

(6.7)

∂ hT (xT ). ∂xT

It is worth noting that (6.7) is the classical adjoint equation of T -stage optimal control theory, with the addition of one term (the third) to take into account the introduction of the parameterized feedback control law. Note also that the structure of (6.7) does not depend on the type of AN used to implement the control law. Furthermore, notice that the ERIM, unlike the ANDYM, does not require the random vectors ε0 , . . . , εT −1 to be mutually independent over the time (note that both methods do not require that the components of each εt be independent, which would be completely unrealistic in water resources management problems). The ERIM has turned out to be simple (it does not require the construction of any grid in the state space), and very effective in solving optimal control problems with a large number of state components (see Zoppoli and Parisini, 1992; Parisini and Zoppoli, 1994, 1996, 1998; Baglietto et al., 2001, 2003; Alessandri and Sanguineti, 2005 and the references therein). Although the authors are not yet completely able to motivate analytically such powerful capabilities, recent results (Kainen et al., 2003; Kurková and Sanguineti, 2005a, 2005b) show that some of the properties that will be discussed in Section 6.5 can be in force not only to approximate functions belonging to suitable spaces, but also to solve approximately functional optimization problems by using a ‘moderate’ number of free parameters and samples, provided that the optimal solutions are characterized by appropriate smoothness properties. 6.5 Bounds on the generalization error in ANDYM and ERIM ANDYM

and the ERIM share the following important features:

• the approximation of unknown functions by approximating networks, consisting of linear combinations of a certain number ν of parametrized basis functions;

Reservoir Management by Approximating Networks and Learning from Data 127 • the use of a certain number P of samples. If the ANDYM is used, an effective methodology for deriving an approximate solution of Problem SOC should require a limited number ν of basis functions (the model complexity) and a limited number of samples ([state-optimal cost-to-go functions] and possibly [state-optimal controls] values) to obtain a good approximation of the optimal cost-to-go and control laws. In analogy with the expression ‘model complexity’, we call the number of samples ‘sample complexity’. If the ERIM is used, a limited number ν of basis functions and of samples of stochastic variables should be required to obtain good approximations of the control laws. In both cases, we want to avoid an unacceptably fast growth of the number of basis functions and of samples, with the dimension n of the state vector, in order not to incur the curse of dimensionality neither in model complexity nor in sample complexity. Recent theoretical results show that the use of nonlinear ANs may allow one to fulfil these requirements. Loosely speaking, by suitable nonlinear ANs one can approximate ‘sufficiently smooth’ functions γ : n → s up to any fixed degree of accuracy, using a number of basis functions and a number of samples that grow only polynomially (sometimes with a slow degree) with the dimension n of the state vector. In such a way, the curse of dimensionality is avoided with respect to both model complexity and sample complexity. The remaining of this section presents the (rather technical) theoretical results that support the above qualitative statement. Let P be a set of P samples [x (p) , y (p) = γ (x (p) )], p = 1, . . . , P . For a function γ : n → s and for each x (p) ∈ P , we denote by γν,P (x (p) , θν , P ) the approximation of the value γ (x (p) ) obtained by an AN with the parameter vector θν , using the set P of P samples. The quantity that can be minimized by using an AN with model complexity ν and a set P with sample complexity P is the so-called empirical risk, defined as the mean square error P     1  γ x (p) − γν,P x (p) , θν , P 2 P p=1

between γ (x (p) ) and γν,P (x (p) , θν , P ). Let P       1  ∗  γ x (p) − γν x (p) , θν 2 . γνP = γνP x, θν∗ , P = argmin θν ∈N(ν) P

(6.8)

p=1

Let B ⊂ n be the compact set from which the state x takes its values. If, ideally, we had at our disposal an infinite number of samples, it would be possible to find    γν∗ = γν x, θν∗ ,

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where 2    θν∗ = argmin E γ (x) − γν (x, θν ) θν ∈N(ν)



= argmin

θν ∈N(ν) B

  γ (x) − γν (x, θν )2 ρ(x) dx.

The expected value is taken with respect to a the probability measure ρ on B, which models the a-priori knowledge on the distribution of the state in B. In case of no such knowledge, the uniform distribution over B is used. The quantity of interest to evaluate the effectiveness of the approximation is the dis∗ , called generalization error and defined as tance between γ and γνP     ∗ 2 . EνP (γ , θν , P ) = E γ − γνP By using the triangle inequality, we can write       γ − γ ∗   γ − γ ∗  + γ ∗ − γ ∗ , ν ν νP νP which evidences the two factors contributing to the generalization error. The term γ − γν∗ 2 , called approximation error, is due to the impossibility of perfectly representing a function belonging to an infinite-dimensional space by an element of a finite-dimensional ∗ 2 ), known as estimation error, is due to the fact that a space. The term E(γν∗ − γνP limited number of samples contains insufficient information about the target function. Some analytical results are available concerning the relationship among generalization error, model complexity ν, sample complexity P and dimension n, for a random extraction of the set P according to the probability density ρ and for ANs corresponding to feedforward sigmoidal neural networks, widely diffused in applications. However, the results that are going to be presented hold in a similar form for wider classes of nonlinear AN s (e.g., for radial basis function networks Niyogi and Girosi, 1996). To avoid burdening the notation and without losing generality, the case of a scalar function (s = 1 in (6.4)) is considered. A feedforward neural network with one hidden layer is expressed as: γν (x, θν ) =

ν 

  ci σ x  αi + βi ,

(6.9)

i=1

where σ (·) is a sigmoidal function, i.e., a bounded measurable function on the real line such that limz→+∞ σ (z) = 1, limz→−∞ σ (z) = 0. For functions γ : n →  with a Fourier transform γF , let 

Cγ =

 n

  ω1 γF (ω) dω

Reservoir Management by Approximating Networks and Learning from Data 129  (see Barron, 1993), where ω1 = ni=1 |ωi |, with ωi denoting the ith component of the vector ω, and

  = γ : n →  such that Cγ < ∞ .

Let Aν be the set of sigmoidal feedforward neural networks with ν hidden units,   ∗  ∗ γνP = γνP x, θν∗ , P , and 

θν∗ = argmin

θν ∈N(ν)

P     1  γ x (p) − γν x (p) , θν 2 . P p=1

Finally, let γ ∈ , B ⊆ [−1, 1]n and suitable assumptions on the parameters vector be satisfied (Barron, 1994). Then it has been proved by Barron (1994) that 



EνP γ , θν , P

 O

Cγ2 ν





 νn +O ln P . P

(6.10)

A number of important remarks can be made about this result. • The upper bound (6.10) is stated for an integral squared error on the set B ⊆ [−1, 1]n , but this is not a major limitation, since other compact domains may be considered (see Barron, 1993 for details). • To apply the upper bound (6.10) to ANDYM or ERIM for the approximate solution of Problem SOC, the optimal cost-to-go functions or each component of the optimal control laws, respectively, must belong to the class . However, this is not a major limitation, since  contains a large variety of functions of interest in applications (Barron, 1993). • For a fixed dimension n of the state, the approximation error goes to zero when ν → ∞. The estimation error goes to zero when ν, P → ∞ only if ν/P ln P → 0, i.e., only when the sample complexity ν grows slower than P / ln P . • For functions with Cγ showing a moderate growth with n, the bound O(Cγ2 /ν) allows to avoid the curse of dimensionality with respect to the model complexity.  P 1/2 , the upper bound on the generalization error is • When one takes ν ∼ Cγ n ln P 1/2    n . ln P O Cγ P

(6.11)

This implies that, for functions with Cγ showing a moderate growth with n, also the curse of dimensionality with respect to the sample complexity can be avoided. • With respect to the choice in the previous item, it must be pointed out that the number of units ν cannot generally be selected as a function of Cγ , since this latter

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It is worth comparing the nonlinear ANs with the linear ones. By ignoring the logarithmic factor, for a given Cγ the bound (6.11) provides a rate of convergence O(n/P )1/2 for the generalization error. In contrast, the rate of convergence by using linear ANs (e.g., fixed-knots splines and polynomials) for functions belonging to classical smoothness classes, such as Sobolev spaces of order s, is O(1/P )2s/(2s+n) (Nussbaum, 1986). The dependence of the exponent on the dimension n implies that, in order to keep the generalization error below a fixed threshold, the smoothness s has to grow with the dimension n. In other words, to avoid the curse of dimensionality with respect to the sample complexity, the class of functions to be approximated has to be constrained more and more as the dimension increases. However, it must be considered that also the condition of finiteness of Cγ , used to define the class , represents a smoothness constraint, although in a less evident form. As noticed in Girosi et al. (1995), functions in  become more and more constrained as the dimension n grows. In other words, the effect of the dimension reveals itself in a different way on  with respect to Sobolev spaces. Note also that in the bound (6.11) the dimension n of the state is somehow ‘hidden’ in Cγ . Such a bound allows to avoid the curse of dimensionality with respect to the sample complexity only for classes of functions with Cγ not exponentially large in n. The same problem arises if one remembers that the bound (6.11) corresponds to a model complexity  P 1/2 ν ∼ Cf n ln , which is characterized by the curse of dimensionality for exponentially P large values of Cγ . However, a wide variety of functions of interest for which Cγ shows a moderate growth with the dimension is reported in Barron (1993). 6.6 Efficient sampling in high dimension Let B ⊂ n be a compact set and γ (x): B →  denote the target function representing, each time, the optimal tth cost-to-go or the optimal tth control law. In the ANDYM, the P points of the discretization of B should be spread in the ‘most uniform’ way, without leaving regions undersampled, and they should be close enough to each other. There are different possibilities of sampling a compact subset B of n uniformly. For example, the following ones can be cited. (i) A full uniform grid. Each component of the state space is discretized by a fixed number of values. This is the simplest choice, and the first used since the introduction of the DP algorithm. As mentioned before, its main drawback lies in the curse of dimensionality. (ii) A random sequence of independent and identically distributed (i.i.d.) points drawn with an uniform probability distribution. In this way the dimension of the training set does not depend ‘structurally’ on n (as in the full uniform grid case), but such a dependence is related to the accuracy of the approximation (in fact, it can be expected that functions with higher dimension n require larger training sets in order to guarantee the same level of accuracy). A possible drawback of this choice is that the original ‘deterministic’ problem (i.e., the approximation of a fixed unknown function) is transformed into a statistical one. In other words, a probability measure on the generation of the samples, is arbitrarily

Reservoir Management by Approximating Networks and Learning from Data 131 introduced (even if it is the most reasonable probability). In this way, the available theoretical results (Barron, 1994; Vapnik, 1995) are applied to a problem that is not statistical in nature. Anyway, by using an uniform distribution such results can be helpful to give reasonable hints about the required model complexity and sample complexity. (iii) A deterministic sequence of points, which tries to spread them in the most uniform way. Examples are Orthogonal Arrays, Latin Hypercubes, quasi-Monte Carlo sequences (see, e.g., Niederreiter, 1992; Chen et al., 1999). In this case the sequences are deterministic, hence they enable one to obtain ‘deterministic’ results. Furthermore, generally the resulting training sets are more uniformly spread than the ones generated by a random uniform distribution (Niederreiter, 1992). In the following we investigate in more detail this last possibility. The notions of uniformity and good spreading have been largely discussed in the literature. The concept of discrepancy is commonly employed to measure the uniformity of a set of points in a closed and bounded domain. Next discussion refers to sampling from 

the n-dimensional unit cube I n = [0, 1]n , but by applying suitable transformations one n can consider the discretization nof other sets. Let BP be a set of P points in I . For every subinterval M of the form i=1 [0, si ], where si ∈ [0, 1], let c(M, BP ) be the counting function for the number of points of BP in M (i.e., c(M, BP ) is the number of points of BP that belong to M). Then the discrepancy of BP is defined as     c(M, BP )  − λ(M), D(BP ) = sup  P M∈M˜  where M˜ is the family of all subintervals of the form ni=1 [0, si ] and λ(M) is the Lebesgue measure of M. The following are quantitative definitions of ‘good scattering’ of points. For a positive integer n and a compact B ⊂ n , a set BP ⊆ S of P points is called uniformly scattered on S if   D(BP )  O P −1/2 (6.12) and well uniformly scattered on S if   D(BP )  O P −1+ ,

(6.13)

where  > 0 (see, e.g., Fang and Wang, 1994). Various methods have been developed for the generation of well uniformly scattered deterministic sets. A common procedure consists in taking finite portions of suitably generated infinite sequences, such as the Good Lattice Points sequences, the Niederreiter sequence, the Halton sequence, the Hammersley sequence and the Sobol’ sequence (Fang and Wang, 1994; Niederreiter, 1992). The construction of such sequences, sometimes informally called low-discrepancy sequences, varies from method to method. In Niederreiter (1992) a common framework for the construction of (t, n)-sequences, which generalizes many of the aforementioned techniques, is presented, together with the most relevant theoretical properties.

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Intuitively, a simple condition to ensure a good uniform spreading of sampling points over a set is to divide the set in suitable ‘basic’ subsets, and then make sure that every basic subset contains a number of points of the discretization that is somehow proportional to the volume of the subset. To this purpose, let us define an elementary interval in base q over [0, 1)n as an ndimensional subrectangle with component intervals of the form  αj αj + 1 , [aj , bj ) = l , qj q lj 

for integers lj  0 and 0  αj < q lj . A (t, m, n)-net in base q on [0, 1)n consists of q m points such that every elementary interval in base q of volume q t−m contains exactly q t points. A (t, n)-sequence in base q is an infinite sequence of points {si } such that for all integers k  0 and m  t, the finite sequence {skq m +1 , . . . , s(k+1)q m +1 } is a (t, m, n)-net in base q. In particular, it can be shown that it is possible to construct (t, n)-sequences {sP } that satisfy deterministically     D {sP }  O P −1 (log P )n−1 . Therefore, the corresponding sets BP are well uniformly spread according to (6.13). When used in a context of function learning from data, low-discrepancy sequences have been proved (Cervellera and Muselli, 2004) to provide bounds on the estimation error that are better, in terms of sample complexity, than those coming from random sampling (e.g., those discussed in Section 6.5). In fact, if the function we want to approximate satisfies suitable regularity conditions, we obtain a bound on the estimation error of the same order   O P −1 (log P )n−1 , which is not only better than the quadratic rate of random sampling, but also deterministic, i.e., not subject to a given confidence interval. Construction of such sequences is generally not straightforward and, as said, it varies from method to method. As an example, we consider the Halton sequence (see Fang and Wang, 1994). Any natural number k has an unique m-digits representation k = b0 + b1 m + b2 m2 + · · · + br mr , where m is a natural number  2 and mr  k < mr+1 . Then, for any k represented in such way, define the radical inverse of k with base m as ym (k) = b0 m−1 + b1 m−2 + · · · + br m−r−1 ∈ (0, 1). Let pi , i = 1, . . . , n, be n distinct prime numbers. Then, the kth point of the Halton sequence is defined as   x(k) = yp1 (k), . . . , ypn (k) ,

k = 1, 2, . . .

Reservoir Management by Approximating Networks and Learning from Data 133 1

0.8

0.6

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0.2

0

0

0.2

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Fig. 6.1. Random sampling of the 2-dimensional unit cube. 1

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0

0

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1

Fig. 6.2. Low-discrepancy sampling of the 2-dimensional unit cube.

Figure 6.1 shows the sampling of the 2-dimensional unit cube by a sequence of 500 points i.i.d. according to the uniform distribution; Figure 6.2 shows the sampling of the same cube by 500 points coming from the low-discrepancy sequence called Sobol’ sequence (Sobol’, 1967). It can be clearly seen how better is the space covered in the second case, as well as how the largest spaces between points appear in the first sampling scheme.

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6.7 Numerical results In order to present numerical results concerning the use of learning techniques for the solution of reservoirs management problems, two test systems of reservoirs on a finite time horizon are considered. These problem were often used in literature to test some DP based algorithms (Foufoula-Georgian and Kitanidis, 1988; Johnson et al., 1993; Yakowitz, 1982; Philbrick and Kitanidis, 1999) and thus they become a sort of benchmark. Here we use the first system to compare ANDYM and ERIM, and the second to compare deterministic versus random sampling in the ANDYM method. 6.7.1 A numerical comparison between ANDYM and ERIM For this test, the 10-reservoir system considered in Yakowitz (1982) (see Fig. 6.3) has been chosen, with a time horizon T = 5. The state equation has the form: j st+1

   j j j j h t = 0, 1, . . . , 5; j = 1, 2, . . . , 10, = min st − ut + ut + ξt , smax j

j

0  ut  st +

h∈I+ j j uht + ξmin ,



(6.14)

h∈I+ j j

where st is the water level in the j th reservoir at the beginning of the tth period and j ut is the release decision from the j th reservoir for same period (planned at the beginning of the period). I+ j denotes the set of indexes of the reservoirs that release water j

directly into the j th one, and ξt is the natural inflow of water into the j th reservoir during the tth period. The inflows are modelled as mutually independent stochastic variables

Fig. 6.3. Ten-reservoir system configuration.

Reservoir Management by Approximating Networks and Learning from Data 135 drawn from the uniform density, ranging from ξmin = col(1, 1, 1, 0, 0.7, 0.7, 0, 1.5, 0, 0) to ξmax = col(1.5, 1.5, 1.5, 0, 1.2, 1.2, 0, 2, 0, 0), that simulate the sum of deterministic minimum river inflows and random rain inflows. Without loss of generality for what concerns the applicability of the ANDYM and ERIM methods, in (6.14) we assumed that the superficial spill from each reservoir, which occurs whenever the corresponding storage overcomes the maximum storage smax = col(10, 10, 10, 10, 10, 10, 10, 10, 18, 25), does not reach the reservoirs downstream from it. The benefit function to be maximized is given by J=

5 10      j j 2 cp ut + cf u10 − 100 max 0, smin − s5 , t t=0

(6.15)

j =1

where cp = col(1.1, 1, 1, 1.2, 1.1, 1, 1.2, 1, 1.2, 2.5) describes the benefits for the release of water from each reservoir in terms of power generation, and cf = 1.9 is the coefficient corresponding to an irrigation benefit, produced downstream from the 10th reservoir. J contains a penalty function to induce the condition s5  smin , where smin = col(3, 3, 3, 3, 3, 3, 3, 3, 5, 6). For what concerns ANDYM, approximating networks having the structure of feedforward neural networks have been used to approximate the optimal cost-to-go functions J˜t∗ (st ), t = 1, 2, . . . , 4. For each network, ν = 40 neural units have been employed, and L = 1800 sample pairs [state vector – optimal cost-to-go function] drawn from a random uniform distribution were used. Feedforward neural networks were employed also for the ERIM solution, this time to approximate the optimal control laws m∗t (st ), t = 1, 2, . . . , 4. Each network has ν = 40 neural units. Since ERIM utilizes unconstrained optimization techniques, suitable differentiable penalty functions have been added to benefit (6.2) in order to implement the various constraints. The results obtained from both methods have been tested by computing a mean benefit over 500 different sequences of the inflows, randomly extracted according to the uniform density in the proper range, all with s0 = smin . The mean benefit for ANDYM turned out to be 282, while the mean benefit for ERIM turned out to be 285. Other examples have been considered with different values of the parameters in the model of the controlled system and in the cost. The mean benefits obtained with ANDYM and ERIM have turned out to be generally very close to themselves. Thus, we can deduce that (i) the values of the mean benefits are reasonably close to the optimal values (unfortunately, a comparison with the incremental dynamic programming approach mentioned in Yakowitz (1982) is not possible due to the fact that the problem considered in the aforementioned work is deterministic), (ii) ANDYM and ERIM are both reliable techniques. Obviously, there are differences in the implementation of the two methods. ANDYM needs an a-priori evaluation of the domains of the state space over which the optimal cost-to-go functions and the optimal control functions have to be computed. ERIM is simpler, but it requires a rather delicate choice of the parameters c1 and c2 that appear in the step-size α(k) (see (6.6)) and of the initial value of the parameter vector θ (0).

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6.7.2 A numerical comparison between deterministic versus random sampling For the second comparison, the 7-reservoir system proposed by Philbrick and Kitanidis (1999) (see Fig. 6.4) has been adopted, with a time horizon of 6 stages (T = 6). The system is still described by (6.14), with only the following difference: (i) the index j j spans from 1 to 7; (ii) the maximum storage smax is equal to 12 for all the reservoirs; (iii) uncontrolled inflows affect only the two upstream reservoirs (1 and 3, see Fig. 6.4) and the inflow processes are white and Gaussian, with mean values 2 and 4 and standard deviations 4 and 2.5, respectively. The cost function to be minimized is J=

5  7  t=0 j =1

7  j 2 2  j j s6 − s˜ j , cp ut − 1 +

(6.16)

j =1

with cp = col(1.1, 1.2, 1, 1.3, 1.1, 1, 1) and s˜ = col(5, 5, 5, 7, 7, 7, 7). In other words the goal is to minimize the sum of the squared deviation of the releases from 1 and of the final storages from s˜j . The choice of a different system of reservoirs with respect to the one considered in Subsection 6.7.1 and, especially, of a cost J structurally different from cost (6.15) and of sequences of white Gaussian inflows is motivated by the need of obtaining further experimental confirmation of the robustness of ANDYM and ERIM in different contexts of modelling for optimization problems. Anyway, we report only results concerning ANDYM for low-discrepancy sequences and uniform random sequences. For what concerns the implementation of ANDYM, ANs having the structure of feedforward neural networks have been used to approximate the optimal cost-to-go functions

Fig. 6.4. Seven-reservoir system configuration.

Reservoir Management by Approximating Networks and Learning from Data 137 J˜t∗ (st ), t = 1, 2, . . . , 5. Each network has ν = 15 neural units, and it has been trained by using L = 1000 sample pairs [state vector – optimal cost-to-go function]. Two different sampling schemes have been tested, one based on a low-discrepancy sequence (specifically, a Niederreiter sequence in base 7, Niederreiter, 1992) and the other given by an i.i.d. sequence with uniform distribution. The results obtained for both schemes have been tested by computing a mean cost over 100 different sequences of the inflows, randomly extracted according to their probability density functions, each one starting from s0 = s˜ . The mean cost for the Niederreiter sequence has turned out to be 68.7, while the random uniform sequence has given a cost of 69.3. Also in other numerical results we have detected a certain superiority, even if mild, of low-discrepancy sequences with respect to uniform random sequences. However, the kind of approximation problems for which low-discrepancy sequences clearly outperform uniform random sequences is still an open problem. Figure 6.5 compares the trajectories of the water levels through the horizon of 6 temporal stages for 2 different reservoirs (2 and 4), when the optimal releases are computed using solutions of the ANDYM method obtained from low-discrepancy and random sampling with the same sequences of the random inflows. Obviously, the behaviours of the trajectories of the water levels depend in a decisive way on the components of the vector cp appearing in (6.16). As can be noticed in Fig. 6.5, due to the particular values chosen for cp , the control functions try to force the water levels in the reservoirs 2 and 4 to the final values of 5 and 7, respectively. This is done while avoiding that the values of the control variables get too far from 1. As said, the best compromise is given by lowdiscrepancy sequences; within this compromise, such sequences lead to a better result for what concerns the closeness of the final level to the desired one. Summing up, the numerical results obtained in the two different tests show how, by using powerful approximating structures and efficient learning techniques, one can successfully face high-dimensional problems, which would be impossible to cope with by using classical techniques.

9

water storage level (reservoir n.4)

water storage level (reservoir n.2)

7 6.5 6 5.5 5 4.5 4 1

2

3

4

time stage t

5

6

8.5 8 7.5 7 6.5 6 5.5 1

2

Fig. 6.5. Water levels of random and low-discrepancy sampling for sampling; - - low-discrepancy sampling; -·- desired final level.

3

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time stage t ANDYM

solutions. – random

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Bibliography Alessandri, A. and M. Sanguineti (2005). Optimization of approximating networks for optimal fault diagnosis. Optim. Method. Softw. 20, 235–260. Alessandri, A., M. Cuneo, S. Pagnan and M. Sanguineti (to appear). A recursive algorithm for nonlinear least-squares problems. Comput. Optim. Appl. Alessandri, A., M. Sanguineti and M. Maggiore (2002). Optimization-based learning with bounded error for feedforward neural networks. IEEE T. Neural Networ. 13, 261–273. Archibald, T.W., K.I.M. McKinnon and L.C. Thomas (1997). An aggregate stochastic dynamic programming model of multireservoir systems. Water Resour. Res. 33, 333–340. Baglietto, M., M. Sanguineti and R. Zoppoli (2003). Facing the curse of dimensionality by the extended Ritz method in stochastic functional optimization: dynamic routing in traffic networks. In: High Performance Algorithms and Software for Nonlinear Optimization (G. Di Pillo and A. Murli, Eds.). pp. 23–56. Kluwer Academic Publishers. Baglietto, M., T. Parisini and R. Zoppoli (2001). Distributed-information neural control: the case of dynamic routing in traffic networks. IEEE T. Neural Networ. 12, 485–502. Barron, A.R. (1993). Universal approximation bounds for superpositions of a sigmoidal function. IEEE T. Inform. Theory 39, 930–945. Barron, A.R. (1994). Approximation and estimation bounds for artificial neural networks. Mach. Learn. 14, 115–133. Bellman, R. (1957). Dynamic Programming. Princeton University Press. Princeton, NJ. Bellman, R., R. Kalaba and B. Kotkin (1963). Polynomial approximation – a new computational technique in dynamic programming. Math. Comput. 17, 155–161. Bertsekas, D.P. and J.N. Tsitsiklis (1996). Neuro-Dynamic Programming. Athena Scientific. Belmont, MA. Cervellera, C. and M. Muselli (2004). Deterministic design for neural network learning: An approach based on discrepancy. IEEE T. Neural Networ. 15, 533–544. Chen, V.C.P., D. Ruppert and C.A. Shoemaker (1999). Applying experimental design and regression splines to high-dimensional continuous-state stochastic dynamic programming. Oper. Res. 47, 38–53. Fang, K.-T. and Y. Wang (1994). Number-Theoretic Methods in Statistics. Chapman & Hall. London, UK. Foufoula-Georgiou, E. and P.K. Kitanidis (1988). Gradient dynamic programming for stochastic optimal control of multidimensional water resources systems. Water Resour. Res. 24, 1345– 1359. Gelfand, I.M. and S.V. Fomin (1963). Calculus of Variations. Prentice-Hall. Englewood Cliffs, NJ. Girosi, F., M. Jones and T. Poggio (1995). Regularization theory and neural networks architectures. Neural Comput. 7, 219–269. Giulini, S., M. Sanguineti and R. Zoppoli (to appear). Approximation schemes for functional optimization problems. Journal of Optimization Theory and Applications. Grippo, L. (2000). Convergent on-line algorithms for supervised learning in neural networks. IEEE T. Neural Networ. 11, 1284–1299. Jacobson, D. and D. Mayne (1970). Differential Dynamic Programming. Academic Press. New York, NY. Johnson, S.A., J.R. Stedinger, C. Shoemaker, Y. Li and J.A. Tejada-Guibert (1993). Numerical solution of continuous-state dynamic programs using linear and spline interpolation. Oper. Res. 41, 484–500. Kainen, P.C., V. Kurková and M. Sanguineti (2003). Minimization of error functionals over variable-basis functions. SIAM J. Optimiz. 14, 732–742. Kurková, V. and M. Sanguineti (2001). Bounds on rates of variable-basis and neural-network approximation. IEEE T. Inform. Theory 47, 2659–2665.

Reservoir Management by Approximating Networks and Learning from Data 139 Kurková, V. and M. Sanguineti (2002). Comparison of worst case errors in linear and neural network approximation. IEEE T. Inform. Theory 48, 264–275. Kurková, V. and M. Sanguineti (2005a). Error estimates for approximate optimization by the extended Ritz method. SIAM J. Optimiz. 15, 461–487. Kurková, V. and M. Sanguineti (2005b). Learning with generalization capability by kernel methods of bounded complexity. J. Complexity 21, 350–367. Kushner, H.J. and G.G. Yin (1997). Stochastic Approximation Algorithms and Applications. Springer-Verlag. New York, NY. Larson, R. (1968). State Increment Dynamic Programming. Elsevier. New York, NY. Leshno, M., V. Ya, A. Pinkus and S. Schocken (1993). Multilayer feedforward networks with a nonpolynomial activation function can approximate any function. Neural Networks 6, 861–867. Niederreiter, H. (1992). Random Number Generation and Quasi-Monte Carlo Methods. SIAM. Philadelphia, MA. Niyogi, P. and F. Girosi (1996). On the relationship between generalization error, hypothesis complexity, and sample complexity for radial basis functions. Neural Comput. 8, 819–842. Nussbaum, M. (1986). On nonparametric estimation of a regression function that is smooth in a domain on Rk . Theor. Probab. Appl. 31, 118–125. Parisini, T. and R. Zoppoli (1994). Neural networks for feedback feedforward nonlinear control systems. IEEE T. Neural Networ. 5, 436–449. Parisini, T. and R. Zoppoli (1996). Neural approximations for multistage optimal control of nonlinear stochastic systems. IEEE T. Automat. Contr. 41, 889–895. Parisini, T. and R. Zoppoli (1998). Neural approximations for infinite-horizon optimal control of nonlinear stochastic systems. IEEE T. Neural Networ. 9, 1388–1408. Park, J. and I.W. Sandberg (1991). Universal approximation using radial–basis–function networks. Neural Comput. 3, 246–257. Philbrick, Jr. C.R. and P.K. Kitanidis (1999). Improved dynamic programming methods for optimal control of lumped-parameter stochastic systems. Oper. Res. 49, 398–412. Sobol’, I.M. (1967). The distribution of points in a cube and the approximate evaluation of integrals. Zh. Vychisl. Mat. i Mat. Fiz. 7, 784–802. Soncini-Sessa, R., A. Castelletti and E. Weber (2007). Integrated and Participatory Water Resources Management. Theory. Elsevier. Amsterdam, NL. to appear. Turgeon, A. (1981). A decomposition method for the long-term scheduling of reservoirs in series. Water Resour. Res. 17, 1565–1570. Vapnik, V. N. (1995). The Nature of Statistical Learning Theory. Springer-Verlag. New York, NY. Yakowitz, S. (1982). Dynamic programming applications in water resources. Water Resour. Res. 18, 673–696. Zoppoli, R. and T. Parisini (1992). Learning techniques and neural networks for the solution of n-stage nonlinear nonquadratic optimal control problems. In: Systems, Models and Feedback: Theory and Applications (A. Isidori and T.J. Tarn, Eds.). pp. 193–210. Birkhäuser, Boston. Zoppoli, R., T. Parisini and M. Sanguineti (2001). Approximating networks and extended Ritz method for the solution of functional optimization problems. J. Optimiz. Theory Appl. 112, 403– 440. Zoppoli, R., M. Sanguineti, M. Baglietto and T. Parisini (to appear). Neural Approximations for Optimal Control and Decision. Springer-Verlag, London, “Control and Communications Systems Series”.

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CHAPTER 7

Optimising Irrigation Management at the Plot Scale to Participate at the Regional Scale Water Resource Management Jacques-Eric Bergez1 , Frédérick Garcia2 , Delphine Leenhardt1 and Laure Maton1 1 UMR-ARCHE, INRA – Castanet Tolosan, France 2 UBIA, INRA – Castanet Tolosan, France

7.1 Introduction According to the FAO, a great challenge for the coming decades will be the task of increasing food production to ensure food security for the steadily growing world population. Most of that increase will have to come from intensified agriculture, supported by irrigation. Where irrigated agriculture is developed, water used for irrigation can represent more than 90% of water consumption. In an increasing number of countries existing resources are fully exploited (Smith, 2000; FAO, 2002). An answer therefore lies in improving agricultural productivity and water use efficiency (FAO, 2002). Where water is plentiful, water demand for other purposes increases and can become a source of conflict between different components of society (Ramonet, 2002). Drinking water supplies and the maintenance of a continuous minimum water flow in rivers are often given priority over irrigation. Planning and management of water resources have become a very important issue everywhere in the world. In particular, accurate estimation of water demand by agriculture is a key need for water management. Water management includes planning (with decisions on a multi-year time scale, such as building dams), strategic management (seasonal decisions with possible adjustment during the season, such as determining the total water volume used for irrigation) and tactical management (daily decisions, such as releasing water from particular dams) (Trouvat, 1997). In the past few years a lot of attention has been given by the water management community to Decision Support Systems (DSS) (Fontane, 1995). Numerous DSS for strategic and tactical water management are described in the literature, although few of them are operational (Mateos et al., 2002). To account for variable phenomena such as annual weather and economic factors and ‘users’ psychology’ (Hammel, 1994), these 141

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DSS often include models which most often simulate irrigation scheduling. Crop water needs are rarely or very roughly simulated (Yamashita and Walker, 1994; Gouy et al., 1996). When they are simulated, FAO guidelines (Smith, 2000) are often used to estimate crop evapotranspiration from observed (Ray and Dadhwal, 2001) or standard (Herrero and Casterad, 1999) values of crop development. Developing tools by integrating knowledge in models may be of some help for planners. However, modelling water management is complex because it concerns different scales (scale of decision, scale of action, scale of planning, scale of management) and different actors (water users including farmers, factory managers and general public, policy makers and water manager). Crop models which simulate the dynamic of plant growth and water demand of one or several crops can provide quantitative contributions to the environmental impact assessment and be very useful for water management (Lilburne et al., 1998; Bergez et al., 2002). However they do not explicitly represent farmers’ decision. One of the keys to improving agricultural water management is therefore to better understand the way farmers manage their irrigation and to model it. Decisional models have to be based on decision rules in order to integrate how farmers adapt management to context. For the farmers, combining a decision model with a crop model makes it possible to calculate the best strategy1 that optimises water consumption and maximises revenue. For the planner, such models can be used to mimic farmer strategy (optimal or not) in order to anticipate water demand. In France, a national framework (PSDR) has been established in order to promote research projects involving stakeholders and the national research institute for Agronomy (INRA). The project whose results are presented in this chapter was developed within this framework and involved researchers and engineers in agronomy, sociology, economy, biometry, meteorology and remote sensing, advisors and water managers faced with the problem of managing water resources from the plot scale up to the regional scale. The chapter will not follow the classical organization in ‘material and methods’ and ‘results’ sections. Instead, it will present the work carried out at the different scales. The first section presents the bio-decisional simulation model at the scale of an irrigation block. The second section presents the optimisation methods developed to improve irrigation management. The third section moves to the farm scale and presents the statistical analyses used to estimate the spatial distribution of irrigation management strategies using easily accessible data and how relationships between irrigation practices and other agricultural practices are taken into account. The last section presents a global DSS model, emphasizing the prediction of the spatial distribution of crops using Markov Chain methods.

7.2 MODERATO: a bio-decisional simulation model at the irrigation block scale MODERATO is a management-oriented, growth simulation model aimed at describing the effects of an Irrigation Strategy for an irrigated maize crop at the irrigation block scale. However, as it takes into account other practices than irrigation (sowing, fertilizing and harvesting), it can be described as a Cultivation Strategy simulation model. It embeds a biophysical model that describes the dynamics of the plant-soil system, which is described in detail in Wallach et al. (2001). This biophysical model is linked dynamically 1 A strategy is a set of decision rules to target a given goal, taking into account some known constraints.

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with a decision model that provides daily action to be performed (‘Do I have to sow?’, ‘Do I have to irrigate?’). Decisions are taken depending on indicators provided by the biophysical model. Details on the decision model may be found in Bergez et al. (2001). As this paper is based on water resource management, more information are given on Irrigation Strategy modelling. Different constraints have to be taken into account in order to model Irrigation Strategy. These constraints included in MODERATO are divided into three categories: • Equipment constraints: maximum water flow rate as determined by pumping capacity per hectare; maximum and minimum applicable water amount per irrigation round. • Resource constraints: total volume of water for irrigation. • Regulatory or human constraints: irrigation bans on some days of the week, farmer’s reluctance to work for all or part of certain days, decreased flow rate availability during the irrigation period due to administrative restrictions, etc. The major irrigation decisions of the farmer are when to start a new irrigation round, the quantity of water to apply and when to stop irrigation. These decisions are usually based on almost daily observations of crop physiological stage and soil water content. In surveys carried out in south-western France, it was found that different farmers use different rules to irrigate and different indicators to trigger the rules. For example, farmer’s answers to the question of how they decide when to start irrigation, included: ‘when leaves start to roll’, ‘when the soil changes colour’, ‘when the soil thrown up by moles becomes drier’, ‘when tensiometer values reach a given threshold’, ‘when the neighbour starts to irrigate’, etc. All these indicators are difficult or even impossible to translate into a decision model. We chose to simplify this complex decision strategy and to base each elementary rules on a two-step condition algorithm: 1. a condition related to crop development [Cond1] 2. a condition related to soil water [Cond2] The Boolean process to decide on any rule is then very simple: ‘If Cond1 is true, then Cond2 is checked; If Cond2 is true, then an action occurs’. Each condition has two alternative forms: either the condition depends simply on the data (the date for Cond1 and weather data for Cond2, e.g. the sum or average rainfall or potential evapotranspiration) or on simulated indicators, calculated by the biophysical model (stage of the crop described by accumulated thermal units for Cond1, soil water deficit for Cond2). MODERATO has two options for fixing the applicable water amount per irrigation round: either it is a fixed quantity or is calculated on the basis of the soil water deficit. A Cultivation Strategy is composed by three simple rules (Sowing, Fertilizing and Harvest) and by the Irrigation Strategy, which, in its turn, is defined by five elementary rules: (i) a rule to determine if irrigation is to be used to facilitate plant emergence (Irrigation at Sowing Rule); (ii) a rule to decide when to start the main irrigation period (Starting Rule); (iii) a rule to determine when to start a new irrigation round (Returning Rule); (iv) a rule to delay irrigation due to weather conditions (Delaying Rule); (v) a rule to decide when

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Table 7.1. Description of an example of a Cultivation Strategy that can be simulated with ERATO .

MOD -

Sowing Rule

Sowing is between 20 April and 30 May as soon as the cumulative rainfall during the previous 3 days is less than 15 mm. Variety Cécilia is sown at 80 000 plants ha−1 .

Fertilizing Rule

A single application of 200 kg N ha−1 is made at sowing.

Harvest Rule

The crop is harvested when grain moisture content reaches 20% or cumulative thermal units from sowing reach 2100 CTU and if the cumulative rainfall during the previous 3 days is less than 15 mm. In any case, the crop must be harvested before 15 October.

Irrigation Strategy

Irrigation at Sowing Rule: A 10 mm irrigation is performed if less than 15 mm rainfall occurs during the 10 days after sowing to facilitate plant emergence. Starting Rule: The main irrigation period starts after 650 CTU as soon as the soil water deficit reaches 60 mm, with an application of 20 mm. Returning Rule: 25 mm is applied every 8 days, if no rainfall occurs. Delaying Rule: Precipitation delays irrigation: when the cumulative rainfall over the 5 previous days is more than 10 mm, a delay of one day is applied for every 4 mm. The delay cannot exceed 7 days. Ending Rule: For the irrigation round following 1st September, if the soil water deficit is greater than 90 mm before the irrigation round starts, a last irrigation round is performed with an application of 20 mm. Otherwise irrigation ends.

to stop irrigation (Ending Rule). Table 7.1 gives an example of a Cultivation Strategy that can be tested with MODERATO. The structure of MODERATO has been validated through a survey of farmers and irrigation advisors in a large irrigated area in south-western France. This survey allowed to check the modelled indicators used to trigger irrigation and the consistency of the hierarchy of the different rules. For some farmers, a monitoring of irrigation was performed. Results of a comparison between simulation and reality was quite consistent. Discrepancies were explained by other factors than agronomical factors (Salles, 2003).

7.3 Optimising irrigation policies at irrigation block scale An optimal Irrigation Strategy π ∗ can be defined as the solution of a stochastic Optimal Control Problem  π ∗ = arg max E J (π, ξ ) , (7.1) π

ξ

where E[·] is the expected value operator and the objective function J depends on the Irrigation Strategy π and on an exogenous, uncertain vector ξ = |ξ0 , . . . , ξh |, the tth component of which is the vector of all the variable that are necessary and sufficient to describe the weather condition at time t; in other words the vector ξ describes the trajectory of the weather condition all over the simulation horizon 0, . . . , h. The solution of problem (7.1) has been tackled through two different approaches: control-based optimisation and simulation-based optimisation.

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7.3.1 Control-based optimisation In an initial study we considered optimisation of just the Starting Rule, given for granted all the other rules that defines a Cultivation Strategy. We compared two solution algorithms for the Optimal Control Problem: Stochastic Dynamic Programming and Reinforcement Learning. With both optimization methods the consequences of a strategy were calculated using the simulation model MODERATO, coupled with a stochastic weather generator. The problem of optimizing the Starting Rule is a sequential decision problem under uncertainty. Each day, farmers observe the physiological stage of development of the crop and the soil water deficit, that is a measure of the soil water content. On the basis of these daily observations they must decide whether to start the first irrigation round or to continue waiting. Once irrigation is begun, a fixed Cultivation Strategy is followed. Crop yield, total volume of water used for irrigation, gross margin and soil dynamics depend on the weather which is a stochastic process. We modelled the problem of choosing an optimal Starting Rule as a Markov Decision Problem (MDP). The element of such a problem are a controlled Markov chain (i.e. a model that is defined by a set of possible states, a set of possible decisions, the probabilities of transitions between successive states conditioned to decision) and an objective function to be maximized, defined as the expected sum of transition returns. Each day t the state xt of the process is the couple (dt , at ), where dt is the soil water deficit, and at is the Cumulative Thermal Units (CTU) above 6◦ C since sowing. The ranges of dt and at are the intervals D and A respectively. In any state (dt , at ) there are only two possible decisions, namely wait (W ) until the next day (t + 1), or start (S) irrigation today. When the decision S is taken or when at becomes greater than the upper bound of A, a fixed Irrigation Strategy is applied up to the end of the irrigation season, and the decision process terminates. That fact is formally represented by a ‘final state’ xend (which has not to be confused with the crop state at the end (h) of the simulation horizon). In this final state xend no decision has to be taken. A Starting Rule is thus a function π that maps each possible state (dt , at ) of DA into a decision: W or S. An usual Objective Function J is the direct margin obtained after harvest (i.e. the gross margin minus specific costs for a given activity, here irrigation), defined by J = pY − lN − qC − X,

(7.2)

where Y is the final yield, p the price of crop, l the labor cost per irrigation round, N the number of irrigation rounds, q the unit cost of water, C the total volume of water used for irrigation and X a fixed production cost. Y , N and C depend on the weather condition ξ and on the state (d, a) where irrigation started. This problem is similar to the so-called Optimal Stopping Problem (Puterman, 1994), which is characterised by a system that evolves uncontrolled (possibly non-stationary) and by a decision-maker (DM) who needs to decide whether to stop waiting or to continue waiting and postpone a decision to the next time step. The solution of this problem can be found with two different alternatives procedures. The first relies on the discretization of the intervals D and A of the state variables d and a. The discrete transition probabilities are then estimated by simulation, and an approx-

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imate numerical solution of the optimal solution is obtained by Dynamic Programming (Kennedy, 1986). The second approach, called Reinforcement Learning (Sutton and Barto, 1998) does not require an a priori estimation of the transition probabilities. An approximation of the optimal solution is directly obtained from simulation of the Markov chain trajectories with sampled realizations of the weather series ξ ij and random initial conditions (d0 , a0 ). Both these approaches lead to an approximate optimal Starting Rule, due to domain discretization for Dynamic Programming and value function approximation for Reinforcement Learning. Note also that Reinforcement Learning only provides an approximate optimal Starting Rule for the states visited during simulation. 7.3.2 Simulation-based optimisation In order to solve the optimisation problem for the full Irrigation Strategy, we developed a second approach based on simulation optimisation methods that directly optimize a parametrized strategy π(θ ), θ ∈ , without modelling explicitly the dynamics of the process, but instead considering the simulation model as a black box  θ ∗ = arg max E J (θ , ξ ) . θ∈ ξ

(7.3)

7.3.2.1 The P2P algorithm We developed the P 2 P algorithm, a stochastic branching method, by analogy with the DIRECT (Jones et al., 1993) and the MCS (Huyer and Neumaier, 1999) algorithms, dedicated to deterministic problems. The algorithm is based on a hierarchical decomposition of  into 2 P-trees. The principle of the algorithm is simple. At each iteration of the search, a promising region is selected from a list of ‘pending regions’ (see below). This selected region, a p-dimensional rectangle, is then broken down into 2p smaller ones, whose sides are half the length of the original rectangle. Each of these 2p new pending regions is then randomly sampled, and the sample points are used for estimating, via simulation, some indices for the region, on the basis of which the region is ranked in the pending list. From the initial region , this algorithm generates a tree of rectangles, whose leaves form a partition of . The maximum depth of the tree is achieved when pending regions cannot be broken down any further, since the maximum precision is reached. Indices are used as heuristics for selecting promising regions to explore. In Bergez et al. (2004), the average value f of a region was the only index used for ranking them: for each of the sampled points θ j within a region, the simulation model is run and the value f (θ j ) = E[J (θ j , ξ )] is estimated by averaging the objective function J (θ j , ξ ) for N sampled realizations of the weather condition series ξ ij f (θ j ) ≈

1  J (θ j , ξ ij ). N

(7.4)

i

The number M of sampled points θ j drawn randomly from within each new region can be either fixed (e.g. one point in the centre of the region), or based on the size of the region

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(e.g. proportional to its volume). The average value f of the region is then estimated by f≈

1  f (θ j ). M

(7.5)

j

As f is just an empirical indicator, its exact value does not need to be precisely estimated, and small values for N and M are sufficient in practice (Ólafsson and Shi, 1999). The main drawbacks of the P 2 P algorithm are underlined in Bergez et al. (2004): (i) indices are chosen on the basis of the expected value of the objective function only and (ii) when the number of parameters increases, the time to perform the optimisation is a strong limiting factor. We therefore propose to modify the P 2 P algorithm in order to speed up the process. 7.3.2.2 P2 The first modification is inspired by the Tree-Direct algorithm. Instead of dividing the promising region in 2p sub-cells, it is divided only into 2 sub-cells, with respect to the dimension i ∗ that has the largest relative range ri , i.e. i ∗ = arg max ri i=1,...,p

with ri =

rimax − rimin , i

(7.6)

where rimax and rimin are respectively the upper and lower bounds of the ri interval, and i is the discretization step (i.e. the smallest permissible range) for the dimension i. This modification of the algorithm is called P 2. 7.3.2.3 P2β The second modification is to modify the index used to sort the promising cells. Instead of sorting the cells on the basis of the average value f only, they are sorted according to a combination of f and the cell variance v, estimated as v=

M N 1 1   f − J (θ j , ξ ij ) 2. MN

(7.7)

j =1 i=1

The next region to be divided is the one that maximise the linear score function β = v + tan(α)f, where α is chosen in [0, π/2], in order to select nondominated elements of the Pareto domain for the two criteria v and f . We call this modification P 2 β algorithm. 7.3.3 Application To test these different algorithms, we used the simulator MODERATO for a specific case based on data from south-western France. Information on the pedoclimatic context can be found in Bergez et al. (2004). The objective function J to be maximised is the direct margin over the whole planning horizon defined in Eq. (7.2). As the reader remembers, we applied control-based optimisation approach to determine the optimal Starting Rule, while the other rules of the Irrigation Strategy were taken for granted. In particular we considered the following rules:

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• Irrigation at sowing rule: no irrigation is performed after sowing. • Returning rule: 30 mm are applied every 7-day, if no rainfall occurs. • Delaying rule: if rainfall occurs during the irrigation round, the round is delayed by one day every 5 mm of rainfall. • Ending rule: after September 1st, if the soil water deficit is less than 50 mm, irrigation ends; otherwise a last irrigation round is performed. For the simulation-based optimisation approach, a more complicated Irrigation Strategy was tested: • Sowing irrigation rule: no irrigation is performed after sowing. • Staring rule: the main irrigation period starts after T 1 CTU have been reached, as soon as the soil water deficit reaches D1 with an application of I 1. • Returning rule: a new round starts when the soil water deficit reaches D2 with an application of I 2. • Delaying rule: when the cumulative rainfall over the 5 previous days is more than 10 mm, a delay of one day is applied for every 4 mm. The delay cannot exceed 7 days. • Ending rule: as soon as T 3 CTU have been reached, if the soil water deficit is greater than D3, a last irrigation round is performed with an application of I 3; otherwise the irrigation campaign ends. T 1 and T 3 (in ◦ C day) are cumulative thermal unit; D1, D2, D3 are soil water deficit (in mm) and I 1, I 2 and I 3 are applicable water amount per irrigation round (in mm) and the vector θ is the vector |T 1, T 3, . . . , I 3|. We defined three criteria to test the algorithm efficiency: 1. the number of runs performed to reach the solution; 2. the time required to reach the solution; 3. the expected value of J at the solution. 7.3.4 Some results The two alternative procedures for solving the Control-based Optimisation Problem gave different but close approximate optimal Starting Rules. Instead of directly representing these Starting Rules (incomplete for Reinforcement Learning as explained in Section 7.3.1), we preferred to represent in Fig. 7.1 the state (dt , at ) of the Markov chain trajectory at which the Starting Rule triggers irrigation, for 1000 randomly simulated Markov chain trajectories with a0 = 0 and d0 ∈ [0; 50 mm]. We recall that a Starting Rule is defined as a partition of DA between the wait (W ) and the start (S) areas, and thus these maps represent the most frequent condition of the Starting Rules. As we can see in Fig. 7.1, both procedures mainly state that the irrigation must start when 650–700 CTU have been reached. This result is consistent with the knowledge of irrigation practitioners.

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Fig. 7.1. States (d, a) of the system where irrigation is triggered (black dots) for optimal Starting Rules obtained with Dynamic Programming (upper panel) and Reinforcement Learning (lower panel), for 1000 randomly sampled realizations of the weather series ξ ij and random initial conditions (d0 , a0 ).

Two methodological results emerged: (i) Reinforcement Learning performs better (i.e. a better expected value of J at the solution) than Dynamic Programming when only a small number of simulation runs are available; (ii) for a given number of simulation runs, a smaller number of grid points for the discretization of the domains of the state variables d and a is preferable. Concerning simulation optimization methods, P 2 and P 2 β reached the solution faster than P 2 P (Fig. 7.2). The maximum value of the objective function is quite similar with all the three algorithms. The faster algorithm (P 2 β ) reaches the solution in 5000 s, a reasonable amount of time for a user.

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Fig. 7.2. Simulation-based optimisation. Compared performance of P 2 (dotted line), P 2 β (dashed line) and P 2 P (solid line). The x-axis is the logarithm of the simulation time.

7.4 Linking Irrigation Strategies to Production Systems Irrigation is a complex activity whose determinants are technical and agronomic knowledge (Bergez et al., 2001), sociological factors (Salles, 2003) and negotiations between irrigators (Barreteau, 1998). If one wants to apply knowledge about Irrigation Strategy at a larger scale two main problems arise. The first is to link the Irrigation Strategy and the Farming System (how a strategy is affected by other farm activities, by farm constraints, by farmer objectives). The second is to determine the importance of each farm types within the regional irrigated area (finding spatial keys). In the first study presented in this section we will analyse the links between easily accessible data from national databases and Irrigation Strategies obtained from surveys. Irrigation Strategy (as described in Section 7.2) is highly influenced by some other aspects of the Cropping Systems. For example, the farmer’s choice for maize precocity and sowing dates are very important because they determine the plant development cycle and therefore the temporal dynamic of water demand. However the relationships between Irrigation Strategy, precocity and sowing date choices are not well known. The second study in this section focuses on the relationships between Irrigation Strategies and farmer’s choices for Precocity and Sowing Strategy. 7.4.1 Spatial distribution of the Irrigation Strategies Data on farming system types can be obtained easily from large national databases. The idea is then to link these types to Irrigation Strategies (Maton et al., 2005). Our study is based on two zones located in the south-western France: the Agout [A] and the Baïse [B] valleys. The two zones are naturally rainfall deficient in July and August (cumulative rainfall is 94 mm). The main Farming System types are cereal crops and mixed farming and livestock. Irrigated maize covers on average 80% of the irrigated areas in B and 60% in A. Regarding water resources for irrigation, B is part of the hydraulic

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Fig. 7.3. General diagram of the multivariate analyses approach. See main text for explanation of the different steps. PCA: Principal Component Analysis; HAC: Hierarchical Ascending Clustering; MCA : Multiple Correspondence Analysis; Glm: General Linear Modelling; CART: Classification And Regression Tree.

system called ‘Neste system’ while A is an irrigated perimeter fed by the Tarn and the Agout rivers. Surveys on Irrigation Strategies were carried out in 2001 among 56 farmers in the two regions (32 in A and 24 in B). All surveyed farmers were irrigated maize growers. Some 70 variables describing the Farming System were available for all the farms. In a first step (Fig. 7.3), we partitioned these variables according with the three sub-systems which constitute the Farming System: the Production System, the Equipment System for irrigation and the Water Resources described by the Theoretical Irrigation Capacity2 [TIC], the last two describing the Hydraulic System. Due to the small number of farmers compared to the number of variables, we chose to create typologies for each sub-system by using multivariate analyses (Principal Component Analysis (PCA), Multiple Correspondence Analysis (MCA) and Hierarchical Ascending Clustering (HAC)) as proposed by Köbrich et al. (2003), for Production System and Equipment System (Step 2). The same approach was used for the Irrigation Strategies (IS) by using the formalism of the bio-decisional simulation model MODERATO (Bergez et al., 2001). Water Resources classes were based on expert knowledge. Regarding Production System, we obtained six classes, farmers being homogeneously distributed amongst them, related with the proportion of irrigated field crops and the type of other productions. Regarding Equipment System, we obtained four classes but 70% of the farmers are in the same type (those using mainly travelling gun sprinklers). Regarding Water Resources, we obtained three classes. Finally, regarding Irrigation Strategy, the classes obtained were defined by: (i) the duration of the irrigation round (DUR) (longer or 2 TIC = (theoretical equipment flow rate/irrigated area)×24 × 0.1.

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shorter than 6 days) (ii) the applied water amount per day (higher or lower than 5 mm/day) and (iii) the presence or not of a pause between two consecutive irrigation rounds. However, only two classes were not empty: the one (denoted with IS1) that group farmers with ‘extensive practices’ (long irrigation round, low applied water amount per day, pause), and the one (IS2) of farmers with rather ‘intensive practices’ (short irrigation round, high applied water amount per day, no pause). Regarding farmers’ behaviour in case of rainfall (as described in the Delaying Rule, see Section 7.2) and how they manage the beginning and the end of the irrigation campaign some tendencies inside the two classes could be discerned but there was a large variability within classes. The number of Irrigation Strategies classes (just two: IS1 and IS2) seems to be rather limited compared to the number of classes in the farm sub-systems. But all surveyed farmers from B belong to IS1 while, in A, 41% belong to IS2 and 59% to IS1. This small number of classes may be due to standard answers to the survey. Farmers in the two zones receive county by county advice from agricultural county advisors, co-operative agribusiness and local agricultural newspapers which tends to standardise maize irrigation management. The two classes differ mainly in the variables corresponding to the strategic choices of farmers and in the way they convey the general knowledge provided by county advisors. The other variables more related to operational irrigation like starting and ending irrigation or reacting to rainfall are more intuitive and correspond to answers to contextual and risky situations for the farmers. These variables create the recorded variability in the farmers’ answers. Such gap is in agreement with a study conducted in region B which showed that Irrigation Strategies and decisions rules are diversified because of sociological and economical factors (Salles, 2003). Institutional context is also of importance. In the following step (Step 3), the typologies obtained from the three sub-systems were used as explanatory variables to explain the Irrigation Strategies typology. Two statistical methods were used: MCA and classification and regression tree (CART). Results shows that it is not possible to directly determine the Irrigation Strategies classes from the different typologies on Production System, Equipment and Water Confort. However, by using Generalised Linear Models (GLM) (Step 4-1 in Fig. 7.3), we found that there is a linear relationship between (DUR) and the Water Confort classes: IF TIC is smaller or equal to 5 mm day−1 THEN DUR is greater than 6 days OTHERWISE DUR is smaller than 6 days. As DUR is the most discriminant variable of the irrigation strategies (IS1 and IS2) it was then possible to define a relation between the Water Confort class and Irrigation Strategies (Step 4-2): IF TIC is smaller or equal to 5 mm day−1 THEN Irrigation duration is greater than 6 days and the irrigator uses IS1, OTHERWISE the irrigator uses IS 2. This simple algorithm classifying Irrigation Strategy is well adapted to the regional scale because data on Water Resources are accessible at this scale (yearly farmer’s administrative declaration on his Equipment System for irrigation and Production System). To determine the other Irrigation Strategy variables (starting irrigation, ending irrigation or reacting after rainfall decision rules), several estimations may be performed: (i) using an average value over the region (see Leenhardt et al., 2004a); (ii) using a stochastic approach by drawing thresholds from our survey. Another possibility may be to improve the rules themselves by increasing the number of surveyed farmers.

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7.4.2 Effects of some other Agricultural Practices on the irrigation water demand at Farm scale We investigated the relationships between the different element of the Sowing Strategy3 for maize growers in the Baïse sector (the B zone) using part of the methodology used in the first study. The Sowing Strategy is considered is based on 4 Rules: date of sowing, choice of precocity, density and duration of sowing. Data from about 96 maize growers were available on 10 variables describing sowing organization (starting date for sowing, number of sowing sessions, etc.) and the choice of precocity (number of different precocities, type of precocity, proportions of precocity on the sown area, etc.). There is a large diversity of sown precocities. Even if the majority of sown maize belongs to the very late, late and mid-late growing varieties, the three classes of early growing maize varieties are present. Sowing takes place from beginning of April up to mid-June. Some farmers have short sowing work (1 to 3 days) whereas some others required up to 16 days. This variability is not due to the area to be sown but to some organisation and material aspects. Statistical analyses reveal that sowing work do not determine the choices of precocity. However, it is possible to characterise some general strategy. Each Sowing Strategy is described by the characteristics of the 10 studied variables. For example, two of them can be simply described by: ‘The farmer sows in 1 day. He uses only 1 precocity covering 100% of the maize area. He chooses 1 or 2 varieties’; ‘The farmer sows in several sowing sessions. He uses 3 or 4 different precocities. The late and middle late varieties cover more than 50% of the maize area. He chooses 5 or 6 varieties’. Surveys performed on agribusiness enterprises and on an independent group of maize growers from the Baïse sector show that these Sowing Strategy appear to be mainly linked to (i) the organisation of the sowing and the harvesting task on the farm (for example, the presence of a maize drier in the farm) and (ii) maize fields soil and weather condition. Then, it should be possible to locate these types within the Baïse sector. There is still works to be done in order to determine the links between the farmer’s Sowing Strategy and the Irrigation Strategy. New Surveys will be performed in order to determine: (i) if farmers irrigate differently the different precocities; (ii) if farmers start irrigation on late varieties first, or if farmers do not care about the differences between crop stages and manage homogeneously the maize sown area. 7.5 Regional scale Regarding water resource management, a key problem is to satisfy various uses. In Southwestern France, in summer, agriculture represents the main water consumer because of irrigation. A correct prediction of irrigation withdrawals is therefore necessary. This is why the ADEAUMIS simulation platform (Leenhardt et al., 2004a), linking a bio-decisional simulation model to a geo-referenced data base, has been developed. The methods used to collect data have been chosen: (1) to be applicable to a large area (such as the whole Neste system area covering 12 000 km2 ); (2) for their generic charac3 A more detailed description of the decision making process concerning sowing than the Sowing Rule introduced in Sec. 7.2.

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Table 7.2. Land use information from processing of images available in June of year N . Nature of information

Number of satellite images

Dates of shots

Map of various summer crops in year N − 1

Generally 3 images

Spring, early summer, late summer of year N − 1

Possibly one only

Early September of year N − 1

Map of bare soil in spring of year N

One

March or April of year N

teristics which allow their application to other irrigation areas; (3) to satisfy specific time and cost constraints on data collection. In this section we will focus on a method to provide early estimation of land use by coupling a crop transition model with remote sensing information. Details about the biodecisional simulation model, alternative methods for early estimation of land use and the validation of the ADEAUMIS platform may be found in Leenhardt et al. (2004a,b). 7.5.1 Method principle The proposed method consists in estimating land use map for the current year, denoted as N , from (i) a land use map for year N − 1, (ii) partial land use information for year N , if available, and (iii) crop transition probabilities from year N − 1 to year N . In the following, we explain (1) how land-use data for a single past year can be obtained, (2) how crop transition probabilities are obtained and (3) how land-use maps are predicted. 7.5.1.1 Land use data A land use map is a continuous description of an area specifying the crops that are cropped. It can be obtained by field survey or satellite image processing. But field surveys require a hard, long and fastidious work. On the other hand, satellite image processing allows an automatic identification of land use over very large areas. Image processing methods are in constant evolution due to continuous development of new sensors. A land cover map can be obtained by combining information derived from the analysis of multi-date SPOT images. The precision of the map depends on the correspondence between the acquisition dates of the shots and the development of the crops (phenological stages). To differentiate between the various summer crops (maize, sunflower, soybean, sorghum, etc.), it is necessary to obtain images in late summer (September). But at this time, problems of water management are over. To satisfy the time constraints of water management, we can only use early remote sensing images (acquired in spring), which allow us to identify areas of bare soil that can potentially be sown with summer crops. Table 7.2 summarizes the information that can be obtained from image processing at a date at which water demand prediction is expected by water managers, i.e. in June of year N . 7.5.1.2 Crop transition model For estimating crop transition probabilities, we used a crop transition model based on data mining techniques and applied to a historical land use data base relative to the study area. The Ter-Uti database (Slak, 1997), elaborated by the French Agricultural Administration on the whole metropolitan territory, describes the land use both in the temporal domain (annual survey) and the spatial domain, but on a sample of points (1 point per km2 ).

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Fig. 7.4. Crop transitions output by the CarroTage model applied to the 1992–2000 Ter-Uti database for a zone including the Sousson sector (755 points). On the y axis crops or crop associations are specified and the symbol ‘?’ denotes non-identified crops. Lines represent the successions of crops in time and their width is proportional to the probability of the succession (no representation when probability lower than 1%).

It includes all yearly survey data since 1992 without any break. Land use is classified in 49 modalities (e.g. wheat, maize, forest, urban area, etc.). Mari and Le Ber (2006) developed a stochastic model (CarroTage4 ), based on a Hidden Markov Model estimated on the historical Ter-Uti data base. It describes annual transitions between crops for the different years up to the current year N (Fig. 7.4). One specific output of the CarroTage model is the set of estimated transition probabilities Pij from the crop i in a given year to the crop j in the following year. Let note that the estimation process of CarroTage needs a data base that covers an extended zone (at least 750 points) to provide a representative estimates of the crop transition probabilities. That is, the study area cannot be too small. 7.5.1.3 Predicting land use for the incoming year N The prediction procedure consists in using the transition probabilities Pij to predict, for each spatial unit5 s, the crops that could occur in year N . If some land use information is available in year N (e.g. if soil is bare or not, thanks to the spring satellite images), the transition probabilities Pij are updated to account for the fact that some crops cannot occur (e.g., in France, wheat cannot occur if bare soil is observed in April). For each unit s, knowing the crop i observed at year N − 1, we can draw randomly one next crop j for year N with probability Pij . This procedure is done for all s of the study area, leading to a predicted land use map for year N . In order to approximate the distribution of predicted land use maps, the procedure is repeated 100 times, leading to 100 possible predicted maps. Our land use prediction for year N can be either any of these possible maps (MEAN prediction), or a new map obtained by choosing for each unit s the most frequent crop (MODE prediction). 4 Software under a GPL licence (Gnu Public Licence) available on http://www.loria.fr/∼jfmari/App last visited 04/2006. 5 The spatial units s are homogeneously cropped pieces of land, usually agricultural fields.

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7.5.1.4 Evaluating the prediction The evaluation of this prediction procedure consists in checking that predicted land use maps for year N are close to the observed land use map of year N , and that the proposed method is better than other methods (already developed and/or more simple). To evaluate if the spatial distribution of crops of the whole study area is correctly estimated by a predicted land use map, we used the statistic C1 , which is the mean squared error of the number of spatial units s corresponding to each possible land use crop  K  2 1 n(k) − n(k) ˆ , C1 =  S k=1

with S, the total number of units s; K, the number of possible crops k; n(k) and n(k), ˆ the number of spatial units with crop k, observed or predicted respectively. To evaluate if a predicted land use map correctly estimates the crops location, we used a second statistic C2 , which expresses the ratio between the number of the spatial units the crops of which are correctly predicted and the total number of the spatial units C2 =

S 1 1c(s)=c(s) ˆ , S s=1

where 1c(s)=c(s) is a Boolean variable whose value is 1 when the crop observed (c(s)) ˆ and predicted (c(s)) ˆ in unit s coincide. For the MODE prediction, C1 and C2 are calculated with the map of most frequent crops. For the MEAN prediction, C1 and C2 are calculated on the 100 possible predicted maps and we keep their average values. 7.5.2 A first application The method has been applied to the Sousson sector, which is part of the Neste system area and is included in the French department of Gers. The agricultural features of the sector are described in Puech et al. (1999). The sector has been chosen because an exhaustive land use survey was made in 1995 and 1996, which allowed us to test the prediction procedure for the year 1996 on high number units (3710). However, we could not test the gain provided by a spring information since neither a land use survey had been done, nor a satellite image had been taken in March or April 1996. The Ter-Uti data base was used to estimate Pij . However the Sousson sector is small (118 km2 ) and the Ter-Uti points strictly included in the Sousson sector were not sufficient to provide representative estimates of such probabilities. Therefore, we applied CarroTage to a larger zone, which includes the Sousson sector and 755 points of Ter-Uti, for which information was available for 1995 and 1996. With these crop transition probabilities, we applied the prediction procedure both to the 755 points Ter-Uti sample to check the pertinence of the method, and to the smaller Sousson area to illustrate the method. To evaluate the prediction procedure presented in this paper, we calculated the C1 and C2 criteria (Table 7.3). To evaluate the benefit of this procedure, we compared it with a

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Table 7.3. Criteria C1 and C2 calculated for the land use prediction for year 1996 on the Ter-Uti sample (755 points) and for the Sousson area (3710 units). The MEAN and MODE prediction maps are compared to the PERSISTENT predictor. Sample Ter-Uti (755 points)

Prediction map PERSISTENT MEAN MODE

Sousson (3710 fields)

PERSISTENT MEAN MODE

C1 2.4 2.0 1.3 4.6 7.4 8.6

C2 67% 59% 69% 57% 49% 60%

method that assumes that crops remain unchanged from year to year, i.e. land use in 1996 is equal to the observed land use in 1995. We call this method, the PERSISTENT predictor. Table 7.3 shows the pertinence of the method: using the Ter-Uti sample, we can see that the global proportion of crops is correctly predicted with C1 = 2.0 for the MEAN map and C1 = 1.3 for the MODE one. The choice of the descriptor (MEAN or MODE) is of importance: the probability that a spatial unit is correctly classified is better for the MODE map than for the MEAN map. The mean implies a normality that does not seem to be verified in this case, while the mode does not have such exigence and therefore can make a better use of the information provided by the 100 maps. On the Sousson area, the procedure does not perform as well: C1 = 8.6 with only 60% of well classified fields. This can arise from the fact that transition probabilities have been calculated on a zone much larger than the Sousson area. Moreover, because of the low sample density of Ter-Uti points, probabilities may not be well estimated when crops are not homogeneously distributed in the landscape, as it is the case here (woods, sunflower mainly on the hills, maize and soybean mainly close to rivers). The benefit of the procedure (when compared to the PERSISTENT predictor) appears for the global estimation of the crop distribution and when it is applied to the Ter-Uti sample. It is not the case when the procedure is applied to the Sousson area because of the sampling problem described just before. The benefit of the procedure for classifying correctly the various spatial units of the area appears for both samples (Ter-Uti and Sousson) only when using the mode as descriptor. Finally, the procedure presents a low benefit compared to the PERSISTENT predictor. The same results are obtained if we compute C1 and C2 for areas of each crop instead of number of fields of each crop. The procedure should be tested on various application cases to give some definitive conclusions. For example, the relevance of early (spring) forecast of land use could not have been tested here. On the other hand, this application case can lead to draw some conclusion and recommendation about the method itself in order to improve its applicability: 1. carefully ascertain that the area used for estimating the crop transition probabilities is well representative of the area where crop forecast is required; 2. impose some spatial constraints, either by modelling the spatial dependencies between units or using geographical features (soil, topography, etc.) when estimating crop transition probabilities; 3. consider exogen factors, such as agricultural subsidies.

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Satellite images seem to be a means for land use forecasting that cannot be bypassed, but the kind of sensor and the classification procedure to be used should be defined taking into consideration the water management objectives. 7.6 Conclusions Managing irrigation water involves various actors, scales and stakes. In this work, we focused mainly on the farmers’ behaviour in irrigation. From surveys and expertise we developed a bio-decisional simulation model, based on hierarchical decision rules. It allows one to predict water demand at the irrigation block scale. Optimal Irrigation Strategies were determined by using Control-based optimisation (Dynamic Programming and Reinforcement Learning) and Simulation-based optimisation. These studies showed that optimisation based on structured decision rules is much easier to use and to transfer than more complex Artificial Intelligence (AI) methods. AI methods may help in finding new decision rule structures (as no structure is given) but seem to be poorly suited for larger problems (more than a few thresholds to be optimised). Irrigation is only a part of the farm functioning. Multivariate statistical analyses were used to determine relationships between crop management and the variables of the farm enterprise (Production System, Equipment System, etc.) and to classify the farms according to farmer behaviour. One of the main problems is to determine the spatial distribution of the farm types and to determine the input variables for applying a model of cropping system at a regional scale. At a regional scale, the extent of irrigated area is a key factor in water demand for agricultural use. Water managers need to forecast land use (in particular irrigated land use) at the start of the irrigation period. To face such challenge, we developed a method coupling a land use map of the previous year and past land use database for estimating possible land use maps for the current year. The method could be improved by introducing early land use information, available from spring satellite photos, but this has not been tested in our study. Predicting irrigation needs at a regional scale could be based on the various tools presented in this chapter. An early land cover map could be linked with a bio-decisional simulation model and initialisation could be performed by some survey or some internet declaration. Such a tool could then be used to negotiate water requirements, dam storage and to analyse modifications due to the climate change or to new policies (for example elimination of subsidies). Bibliography Barreteau, O. (1998). Un système Multi-Agent pour explorer la viabilité des systèmes irrigués : dynamique des interactions et modes d’organisation. Ecole Nationale du Génie Rural, des Eaux et des Forêts. Montpellier, FR. Bergez, J.-E., F. Garcia and L. Lapasse (2004). A hierachical partitioning method for optimizing irrigation strategies. Agric. Syst. 80, 235–253. Bergez, J.-E., J.-M. Deumier, B. Lacroix, P. Leroy and D. Wallach (2002). Improving irrigation schedules by using a biophysical and a decisional model. Eur. J. Agron. 16, 123–135. Bergez, J.-E., P. Debaeke, J.M. Deumier, B. Lacroix, D. Leenhardt, P. Leroy and D. Wallach (2001). MODERATO : an object-oriented decision tool for designing maize irrigation schedules. Ecol. Modell. 137, 43–60.

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Fontane, D.G. (1995). Decision Support Systems: Water Resources Planning. Water in the Balance Report Series. Colorado Water Resources Research Institute. Fort Collins, CO. Gouy, D., J. Miquel, J. Pinte and V. Hammel (n.d.). Les prévisions et les simulations de débits en période d’étiage: du modèle au tableau de bord opérationnel. Study report. EDF-AEAG. Toulouse, FR. Hammel, V. (1994). Engineering Risk in Natural Resources Management. Chap. Planning and management of water resources in the Southwest of France in a dynamical, social and economic environment, pp. 449–454. Kluwer Academic Publishers. Dordrecht, NL. Herrero, J. and M.A. Casterad (1999). Using satellite and other data to estimate the annual water demand of an irrigation district. Environ. Monit. Asses. 55, 305–317. Huyer, W. and A. Neumaier (1999). Global optimization by multilevel coordinate search. J. Global Optim. 14, 331–355. Jones, D.R. Perttunen C.D. and B.E. Stuckman (1993). Lipschitzian optimization without the Lipschitz constant. J. Optimiz. Theory Appl. 79, 157–181. Kennedy, J.O. (1986). Dynamic Programming: Application to Agricultural and Natural Resources. Elsevier Applied Science. London, UK. Köbrich, C., T. Rehman and M. Khan (2003). Typification of farming systems for constructing representative farm models: two illustrations of the application of multi-variate analyses in Chile and Pakistan. Agric. Syst. 76, 141–157. Leenhardt, D., J.-L. Trouvat, G. Gonzalès, V. Pérarnaud, S. Prats and J.-E. Bergez (2004a). Estimating irrigation demand for water management on a regional scale. i. adeaumis, a simulation platform based on bio-decisional modelling and spatial information. Agric. Water Manage. 68, 207–232. Leenhardt, D., J.-L. Trouvat, G. Gonzalès, V. Pérarnaud, S. Prats and J.-E. Bergez (2004b). Estimating irrigation demand for water management on a regional scale. ii validation of adeaumis. Agric. Water Manage. 68, 233–250. Lilburne, L., J. Watt and K. Vincent (1998). A prototype DSS to evaluate irrigation management plans. Comput. Electron. Agr. 21, 195–205. Mari, J.-F. and F. Le Ber (2006). Temporal and spatial data mining with second-order hidden Markov models. Soft Comput. 10(5), 406–414. Mateos, L., I. Lopez-Cortijo and J. Sagardoy (2004). SIMIS; the FAO decision support system for irrigation scheme management. Agric. Water Manage. 56, 193–206. Maton, L., D. Leenhardt, M. Goulard and J.-E. Bergez (2005). Assessing the irrigation strategies over a wide geographical area from structural data about farming systems. Agric. Syst. 86(3), 293–311. Multimedia group, FAO (2002). Water: Precious and Finite Resource. Food and Agriculture Organization. Rome, I. Ólafsson, S. and L. Shi (1999). Optimization via adaptive sampling and regenerative simulation. In: Proceedings of the 1999 Winter Simulation Conference. Squaw Peak, Phoenix, AZ. pp. 666– 672. Puech, C., F. Cernesson and B. Balas (1999). Approche spatiale de la pollution par les nitrates. Bois et forêts des agriculteurs. In: Actes du colloque de restitution de l’AIP AGRIFOR. ClermontFerrand, FR. pp. 191–213. Puterman, M.L. (1994). Markov Decision Processes. Wiley. New York, NY. Ramonet, I. (2002). Une ressource stratégique. Le Monde diplomatique, Manière de voir : La ruée vers l’eau 65, 6–7. Ray, S.S. and V.K. Dadhwal (2001). Estimation of crop evapotranspiration of irrigation command area using remote sensing and gis. Agric. Water Manage. 49, 239–249.

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Salles, D. (2003). Gestion collective et stratégies individuelles. Gestion de l’eau et pratiques d’irrigation dans le système irrigué neste. In: Actes du 71ème congrès de l’ACFAS. Rimouski, CA. Slak, M.F. (1997). L’évolution des paysages girondins vue par ter-uti. Agreste-Les Cahiers 21, 23– 33. Smith, M. (2000). The application of climatic data for planning and management of sustainable rainfed and irrigated crop production. Agric. For. Meteorol. 103, 98–108. Sutton, R.S. and A.G. Barto (1998). Reinforcement Learning: An Introduction. MIT Press. Cambridge, MA. Trouvat, J.-L. (1997). Concepts de base de la gestion quantitative de la ressource en eau. In: Irrigation, outil de qualité et de régularité de la production agricole pour les marchés et les industries d’aval. Journées Techniques Nationales, AFEID - AGPM. Pau, FR. pp. 121–136. Wallach, D., B. Goffinet, J.-E. Bergez, P. Debaeke, D. Leenhardt and J.-N. Aubertot (2001). Parameter estimation for crop models: a new approach and application to a maize model. Agron. J. 93, 757–766. Yamashita, S. and W.R. Walker (1994). Command area water demands. i: Validation and calibration of uca model. J. Irrig. Drain. E.-ASCE 120, 1025–1042.

CHAPTER 8

Multi-Objective Optimization of Water Distribution System Design under Uncertain Demand and Pipe Roughness Artem V. Babayan, Dragan A. Savic and Godfrey A. Walters Department of Engineering School of Engineering, Computer Science and Mathematics University of Exeter, Exeter, UK

8.1 Introduction The vast majority of mathematical models use deterministic approaches to describe various processes and systems. In contrast all real life problems incorporate uncertainty in one way or another. It could be uncertainty in measurement, uncertainty in estimation of parameters, uncertainty as to which processes one should include into the model, etc. Such contradiction between ‘mathematical determinism’ and ‘natural uncertainty’ can seriously affect the reliability of the results of mathematical modelling. So design methodologies which allow us to take into account uncertainty when predicting the behaviour of the system is of great practical interest. In designing water distribution networks (WDS) the most uncertain quantities are, probably, water consumption and pipe roughness coefficients. While it is possible to estimate the present water demand reasonably well (Obradovic and Lonsdale, 1998), the situation becomes much worse when future demands need to be predicted. Also, the pipe roughness factor can change significantly with age – depending on pipe material and water corrosive characteristic. Given the above, the need for considering the design of WDS under uncertainty in input parameters within an optimization framework is obvious. Water distribution system design optimization is one of the most heavily researched areas in the hydraulics profession (see Goulter, 1992; Lansey, 2000 for detailed review). Recently, Genetic Algorithms (GA) have become the preferred water system design optimization technique for many researchers (Dandy et al., 1993; Savic and Walters, 1997) because GAs demonstrate good ability to deal with complex, nonlinear and discrete optimization problems. 161

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When uncertainty is taken into account, the following questions should be answered: 1. how to include it in problem formulation; 2. how to quantify the influence of input parameter uncertainty on the solution’s quality. The first problem is usually resolved by incorporating uncertainty into the problem formulation as a constraint on minimal system robustness, or a penalty for fitness function (Lansey et al., 1989; Xu and Goulter, 1999; Kapelan et al., 2003; Tolson et al., 2004; Babayan et al., 2005), which results in a single-objective optimization problem. In this way the result of each run of optimization process is one minimal-cost WSD which provides at least this predefined level of robustness (here under robustness we understand the ability of the system to satisfy the specifications despite the possible errors in input parameters). This type of optimization is useful as a tool which should provide decision makers with insights into the nature of the problem, but usually cannot provide a set of alternative solutions that trade different objectives against each other. On the contrary, in a multi-objective optimization with conflicting objectives, there is no single optimal solution. The interaction among different objectives gives rise to a set of compromised solutions, largely known as the trade-off, non-dominated, non-inferior or Pareto-optimal solutions. The consideration of many objectives in the design or planning stages provides three major improvements to the procedure that directly supports the decision-making process (Cohon, 1978): • A wider range of alternatives is usually identified when a multi-objective methodology is employed. • Consideration of multiple objectives promotes more appropriate roles for the participants in the planing and decision-making processes, i.e. ‘analyst’ or ‘modeller’, who generates alternative solutions, and ‘decision maker’, who uses the solutions generated by the analyst to make informed decisions. • Models of a problem will be more realistic if many objectives are considered. The need to identify as many solutions as possible within the Pareto-optimal frontier often represents a problem for standard optimization techniques. By maintaining and continually improving a population of solutions, a Genetic Algorithm can search for many non-dominated solutions at the same time (in a single run), which makes it a very attractive tool for solving multi-objective optimization problems. The answer to the second question requires from the engineer application of one of the methodologies for quantifying the influence of uncertainty on the system performance. These methods can be divided into two groups: one using stochastic simulation (sampling methods), the other replacing stochastic formulation with deterministic one (analyticallybased methods). The simplest way is to use one of the sampling techniques (Monte Carlo simulation and its modifications, Bao and Mays, 1990), however such a straightforward approach requires an unreasonable amount of computational effort, especially when using GA , as one needs to calculate the fitness function for a large number of network configurations. The main area of usage of sampling-based methods is checking robustness of the final solution and verification of deterministic approaches (Xu and Goulter, 1999; Tolson

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et al., 2004; Babayan et al., 2005). Still, it is possible to exploit the stochastic nature of the GA and to incorporate stochastic approach into optimization process as was done in Kapelan et al. (2003). Analytically-based methods usually allow the engineer to get results much faster (up to several orders of magnitude), which makes them the preferable instrument for optimization problems. Today several techniques are available (see Haldar and Mahadevan, 2000 and Zhao and Ono 2001, for review), some of them were applied to WDS optimization problem. In Xu and Goulter (1998) a probabilistic hydraulic model was used for the first time in the water distribution system design optimization. The WDS hydraulic model uncertainties were quantified using the analytical technique known as the First-Order Second-Moment (FOSM) Reliability method. This method assumes that relationship between uncertain and response variables is very close to linear, which is often not the case for water distribution systems. In addition to this it cannot use information about probability distribution function (pdf ) of uncertain parameters when such information is available. The same authors (Xu and Goulter, 1999) later used the more accurate First-Order Reliability Method (FORM). To calculate the uncertainties, the FORM requires repetitive calculations of the first-order derivatives and matrix inversions, which are computationally very demanding even in the case of small networks and may lead to a number of numerical problems. Also when using this method it is difficult to determine how uncertainty in different parameters affects the system’s robustness. The least-cost design problem was, in both cases, solved using the generalized reduced gradient optimization algorithm. However, being a local search method, it can easily be trapped in the local minimum (Savic and Walters, 1997). Recently, Tolson et al. (2004) overcame the problem associated with the use of gradient search methods by using GAs to solve the optimal water distribution system design problem. However, the authors still used the First-Order Reliability Method (FORM) to quantify uncertainties. To overcome the limitations of all the aforementioned WDS design approaches, a new robust design methodology was developed recently (Babayan et al., 2005), based on numerical integration. In this chapter the improved methodology is used to solve the multi-objective problem. The chapter is organized as follows: after this introduction a robust, least-cost design problem is formulated. This is followed by the presentation of the methodology used to solve the aforementioned problem and of its application to a case study. At the end, relevant conclusions are drawn.

8.2 Problem definition The objectives of the robust, least-cost design problem presented here are to minimize total design or rehabilitation cost J and maximize the level of design robustness. More specifically, the optimization problem is formulated as follows (8.1a)

Minimize J (d1 , d2 , . . . , dnd ),  Maximize min P (hi  hi,min ), subject to

i = 1, . . . , nn



(8.1b)

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(a) Mass and energy balance constraints np,i 

qm,i − wi = 0 (i = 1, . . . , nn ),

(8.1c)

hi,u − hi,d − hi = 0 (i = 1, . . . , np ).

(8.1d)

m=1

(8.1e) (b) Decision variables constraint di ∈ D

(i = 1, . . . , nd ),

(8.1f)

where: J : total design or rehabilitation cost; di : value of the ith discrete decision variable, in general design/rehabilitation option index (i = 1, . . . , nd ); D: discrete set of available design/rehabilitation options; hi : head at the ith network node (i = 1, . . . , nn ); hi,min : minimum acceptable head at the ith node (i = 1, . . . , nn ); P (hi  hi,min ): probability that the head hi is not lower than hi,min ; qm,i : flow in the mth pipe (m = 1, . . . , np,i ) connected to the ith node; wi : demand at ith node; hi,u : head at the upstream node of the ith pipe (i = 1, . . . , np ); hi,d : head at the downstream node of the ith pipe (i = 1, . . . , np ); hi : difference between ith pipe’s total headloss and pumping head (i = 1, . . . , np ); nd : number of decision variables; np : number of network pipes; nn : number of network nodes. The non-linearity of the problem is associated with the hi term, which can be calculated using the Hazen–Williams or the Darcy–Weisbach formula. The former one can be writing as follow  a l q h = ω , c db where ω: numerical conversion constant which depends on the units used; c: pipe Hazen–Williams roughness coefficient;

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q: flow through the pipe; l: length of the pipe; d: diameter of the pipe. The constants a and b here are chosen to be 1/0.54 and 2.63/0.54 respectively, but some other values have also been adopted in the literature (Obradovic and Lonsdale, 1998). In the model presented here it is assumed that nodal demands (wi ) and pipe roughness coefficients (ci ) are the only sources of uncertainty, i.e. it is assumed that all other model parameters are deterministically known. In addition to this, all uncertain parameters are assumed to be independent random variables, each of them following some pdf. In the following we will denote the vector of the uncertain parameters with θ and the number of its components with M. 8.3 Solution technique 8.3.1 Genetic algorithm Genetic Algorithms are stochastic search procedures based on the evolutionary mechanisms of natural selection and genetics (Holland, 1975). They use the rapid iterative processing ability of computers to simulate the methods by which species adapt themselves to suit their environments. In other words, GAs mimic the very effective optimization model that has evolved naturally for dealing with large, highly complex systems. Good descriptions of GAs are given by Goldberg (1989) and Michalewicz (1992). A brief summary is presented here for completeness. A population of random trial solutions to the problem are created, each trial solution being defined by the values of its design variables, which are encoded as a data string (chromosome), usually using a binary coding. Every solution (individual) is evaluated using the objective function, and its ‘fitness’ is determined relative to the entire population. This value determines the probability that an individual will contribute offspring to the next generation of solutions, the offspring being created by a ‘breeding’ process. The breeding process uses three simple operators: selection, crossover and mutation. Selection produces a pool of individuals with, in effect, multiple copies of fitter members from the old population appearing alongside small numbers of less fit members. From this pool, random selections of ‘parents’ are made, thus biasing the selection of parents towards the fitter members of the old population. Once two parents have been selected, their data codes are rearranged by the crossover process, which breaks the data strings at a random point and crosses the tail ends of the strings over. Two new individuals (offspring) are thus formed, each having characteristics inherited from its parents. The third genetic operator, mutation, changes, with a low probability, randomly selected digits of the offspring’s data string. The breeding process continues until a complete new generation has been formed, at which point the old generation is discarded and the process starts a new iteration. Note, that, when using GA to solve the optimization problem (8.1a)–(8.1f), constraint (8.1f) can be automatically satisfied by using the appropriate GA coding. The potential solution can be represented as a vector each element of which corresponds to a pipe to be installed and may take on a value of the available pipe diameters only.

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Constraints (8.1c)–(8.1d) constitute a separate subsystem, which is usually solved using deterministic WDS solver such as EPANET. 8.3.2 Uncertainty quantification The main idea behind the approach here proposed is to replace the stochastic objective (8.1b) with a deterministic one (R) that expresses the level of system’s robustness, which is defined as follows   μhi − hi,min (8.2) Maximize R = min , i = 1, . . . , nn , σhi where R is the robustness index of the solution and μhi and σhi are the mean and the standard deviation of the head hi at node i. With the following formulas  μhi =

σhi =

+∞  −∞

 +∞  −∞

hi (θ )

m 

 ηj (θj ) dθ ,

j =1

 m  2  hi (θ ) − μhi ηj (θj ) dθ. j =1

μhi and σhi could be computed, given the known probability distribution function ηj (θj ) of the j th of m uncertain parameters. However, because of the implicit relationships between demands and heads it is impossible to calculate the above integrals directly: a straightforward numerical evaluation would require an unreasonable amount of computational effort. Therefore we will use a simplified method of evaluating μhi and σhi , based on some assumptions we are going to introduce. First of all assume the validity of the superposition principle hi (μθ1 + θ1 , μθ2 + θ2 , . . . , μθm + θm ) − hi (μθ1 , μθ2 , . . . , μθm ) m    hi (μθ1 , . . . , μθi + θi , . . . , μθm ) − hi (μθ1 , μθ2 , . . . , μθm ) , ≈

(8.3)

i=1

where μθi is the mean and θi a random fluctuation of the ith uncertain parameter θi . Note that the pdf of an uncertain parameter is non-zero in some area only (e.g. uniform distribution) or decreases exponentially with distance from the mean value (e.g. normal distribution). Hence, all we need is that a superposition principle is satisfied in some area around μθ : two standard deviations are generally enough in most cases. It is worth to note also, that assumption (8.3) is less strict than requirement of linear relationship between uncertain and response variables. For example, equality (8.3) is satisfied if hi (θ1 , θ2 ) = θ12 + θ22 . Assumption (8.3), together with the assumption that nodal demands and pipe roughness are independent, lead to the following approximation formulas for the means and standard deviations of the nodal-heads

Multi-Objective Optimization of Water Distribution System Design μhi ≈ hi (μθ ) +

m 

167

(8.4)

αij ,

j =1

σhi ≈

m  

j =1 −∞

 αij =

+∞ 

2 hi (θj ) − hi (μθ ) − αij ηj (θj ) dθj ,

+∞ 

−∞

 hi (θj ) − hi (μθ ) ηj (θj ) dθj .

(8.5)

(8.6)

Integrals in (8.5) and (8.6) are 1D and can be calculated using conventional numerical formulas. To estimate the standard deviation for all nodes in a network with m uncertain parameters using formulas (8.4)–(8.6) one needs to perform (k − 1)m + 1 model runs, where k is the odd number of points in the formula for numerical integration: when k is odd the point in the centre corresponds to μθ and is common for all dimensions, thus the value of the head at that point can be computed only once. It is clear from (8.6) that amendments αij in (8.4) and (8.5) account for non-symmetry of heads around mean value of uncertain parameters. In case of non-independent uncertain parameters the mean still can be computed with formula (8.4), but the formula for the standard deviation becomes σcorr,hi ≈ σnoncorr,hi +

 m m  

+∞  +∞ 

j =1 k=1,k=j −∞

−∞

hi (θj ) − hi (μθ ) − αij



  × hi (θk ) − hi (μθ ) − αik ηj k (θj , θk ) dθj dθk ,

where σnoncorr,hi is given by (8.5). The numerical computation of the above integral does not require more model runs, however one has to provide the joint pdf, which is not always readily available. Formula (8.5) allows us to estimate the relative contribution of uncertainty in each variable to the nodal heads uncertainty. This information can be used to build up the list of ‘significant’ variables and model the rest of the network as certain, leading to significant computational time savings. To summarize, the following algorithm is proposed to solve the least-cost design problem under uncertainty using GA: 1. Identify the sets of critical nodes and significant variables. Take some initial configuration of the network (e.g. the existing network configuration). Then, compute the head mean and deviation at each node using formulae (8.4)–(8.6). Nodes at which (μhi − hi,min )/σhi < 3 are added to the set  of ‘critical nodes’. Uncertain variables whose relative contribution to standard deviation in critical nodes is more then some prescribed level (say, 5%) form the set  of ‘significant variables’. Note that this step requires m × k state estimate calculations, where m is the number of uncertain variables and k is the number of points in the quadrature formula used. 2. Run GA to find the optimal robust design. Use the GA to obtain solution of problem (8.1a), (8.2). Note that the total number of state estimate calculations (i.e. hydraulic

168

A.V. Babayan et al. solver runs) necessary to obtain the value of fitness function for the second objective (8.2) is ||(k − 1) + 1 where || is the number of significant variables (i.e. the cardinality of ) and k is the number of quadrature formula points. Finally, note that as the GA run progresses, the sets of critical nodes and significant variables may have to be updated periodically. This can be done using the procedure described in the previous step.

In comparison with First-Order Second-Moment (FOSM) Reliability method the methodology described here can provide better accuracy for the same computational overheads. Another commonly used method, First-Order Reliability Methods (FORM), although providing higher accuracy, is much more computationally demanding, with complexity increasing rapidly as the number of uncertain parameters increases: for each network configuration it requires conversion of matrix of order m (operation with complexity ∼ m3 ) and solving of the system of non-linear equations of the same order. 8.4 Case study 8.4.1 Problem description The robust least-cost design methodology presented here is tested and compared on the well-known literature problem of New York Tunnels reinforcement. This problem dates back to the late sixties when Schaake and Lai (1969) attempted to use linear programming optimization to analyse the New York City water supply tunnels system. The City was looking to increase the capacity of its water supply system to meet future demands by adding one or more pipes to the existing network of 21 tunnels. The tunnel system layout is shown in Fig. 8.1. Because of age and increased demands the then existing gravity flow tunnels have been found to be inadequate to meet the pressure requirements (nodes 16, 17, 18, 19 and 20 in Fig. 8.1) for the projected consumption level. The proposed method of expansion was the same as in previous studies, i.e., to reinforce the system by constructing tunnels parallel to the existing ones. For 15 available diameters, i.e., 16 possible decisions including the ‘do nothing’ option, and 21 pipes to be considered for duplication, the total solution space is 1621 ≈ 1.9 × 1024 ) possible network designs. So far, a number of authors have solved the problem as a deterministic one. A review of these approaches can be found in Savic and Walters (1997). The two deterministic solutions identified previously on the opposite ends of the cost domain are presented here in Table 8.1. Unlike in the deterministic approaches, it is assumed here that some parameters in problem formulation are uncertain. To demonstrate that the methodology presented here is able to handle uncertainties in different types of parameters and with various probability distribution functions, the following case is considered: (1) nodal demands are assumed to be uncertain variables following Gaussian pdf with mean equal to the deterministic demand value and standard deviation equal to 10% of the mean value; (2) the friction coefficients in the old pipes are assumed to be uniformly distributed stochastic variables on the interval [90, 110]. The deterministic demands, friction coefficients and other network data used here are taken from Murphy et al. (1993). The EPANET hydraulic solver (Rossman, 2000) was used to calculate unknown heads and flows for each demand sample.

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Fig. 8.1. Layout for New York City water supply system.

During the first step of the algorithm the set  of significant uncertain variables, consisting of demands in 7 nodes (9, 11, 16, 17, 18, 19 and 20) and pipe roughness coefficients in two pipes (13 and 14) was formed (then the cardinality of  was 9). The quadrature formulae with 3 integration point were chosen (i.e. k = 3) in order to estimate R in (8.2). Therefore, each fitness function evaluation required 9 × (3 − 1) + 1 = 19 runs of the EPANET solver. 8.4.2 Results and discussion The results obtained for the problem formulated in the previous section are shown in Fig. 8.2. The curve represents part of the Pareto frontier obtained by solving the optimization problem (8.1a), (8.2) using the Non-Dominating Sorting GA (NSGA - II) (Deb et al., 2000) with population size 400 and 1000 generations. Note that the level of robustness of each solution shown in Fig. 8.2 was re-calculated using 100 000 Monte Carlo

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A.V. Babayan et al. Table 8.1. Selected Deterministic and Optimal Robust Solutions. Pipe

Det. Solutions

Stoch. Solutions

Quindry et al. (1981)

Murphy et al. (1993)

90%

95%

99%

1–6 7 8–10 11 12 13 14 15 16 17 18 19 20 21

– – – 302 341 337 337 334 49 233 185 185 – 140

– – – – – – – 305 213 244 213 183 – 183

– – – – – – – 488 274 243 243 243 – 183

– 305 – – – – – 518 243 243 243 243 – 183

– – – – – 366 – 427 213 274 213 182 – 213

Cost (mln.$)

63.58

38.80

49.03

52.64

57.45

Robust.

58.5%

48.0%

91.6%

95.0%

99.1%

100

Robustness (%)

90

80

70

60

50

40

45

50

55

60

Cost (mln. $) Fig. 8.2. Trade-off curve cost vs. robustness.

samples once the relevant optimization process was finished. As one would expect the cost of solution raises exponentially with the robustness level. Non-smoothness and nonconvexity of the parts of the curve can be explained (1) by the discrete nature of the

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problem, (2) by the use of the indirect index R for robustness measurement and (3) by errors caused by using simplified methodology. Details of the two optimal robust solutions for robustness levels 90% and 95% are shown in Table 8.1. The following can be noted from this table: (1) Both stochastic (i.e. robust) solutions have higher cost than the optimal deterministic solution identified by Murphy et al. (1993); this is the price that has to be paid for increased robustness. (2) The robustness of the two deterministic solutions is quite low. In the case of the Murphy et al. (1993) solution this is the consequence of the deterministic optimization which left no or very little redundancy in the system to cope with demand fluctuations. In the case of the Quindry et al. (1981) solution, even though the rehabilitation cost is very high, the robustness is low because of the inappropriate selection of duplication diameters. This solution also demonstrates that spending a lot of money on rehabilitation does not guarantee that a high level of system robustness will be achieved. 8.5 Conclusions In this chapter a methodology for the multi-objective least-cost robust design of water distribution networks under uncertain demand is presented. The problem is solved using GA s after converting the original problem formulation to an equivalent, simplified deterministic optimization problem. This way computational efficiency of the methodology is significantly increased. The methodology is verified on a case study where, among other things, optimal robust solutions obtained are compared to well-known deterministic solutions from the literature. The results clearly demonstrate that neglecting uncertainty in the design process may lead to serious underdesign of water distribution networks. The methodology proposed here is of a general type in terms that different uncertain parameters with different pdf types can be considered. Its disadvantage is that the target level of the design robustness cannot be specified explicitly in the problem formulation phase, i.e. it has to be specified indirectly (by specifying the target value of parameter). As a consequence, the actual level of robustness can be calculated only once the optimization process has converged and the final solution is obtained. Bibliography Babayan, A.V., D.A. Savic and G.A. Walters (2005). Least cost design of water distribution network under demand uncertainty. J. Water. Res. Pl.-ASCE 131(5), 375–382. Bao, Y. and L.W. Mays (1990). Model for water distribution system reliability. J. Hydr. Eng. Div.ASCE 116(9), 1119–1137. Cohon, J.L. (1978). Multiobjective Programming and Planning. Academic Press. New York, NY. Dandy, G.C., A.R. Simpson and L.J. Murphy (1993). A review of pipe network optimisation techniques. In: Proceedings of WATERCOMP ’93, 30 May–1 April. Melbourne, AU. pp. 373–383. Deb, K., S. Agrawal, A. Pratap and T. Meyarivan (2000). A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Proceedings of Parallel Problem Solving from Nature VI Conference, 16–20 September. Paris, F. pp. 849–858. Goldberg, D.E. (1985). Genetic Algorithms in Search, Optimisation, and Machine Learning. Addison Wesley. Reading, MA. Goulter, I.C. (1992). Systems analysis in water-distribution network design: From theory to practice. J. Water. Res. Pl.-ASCE 118(3), 238–248.

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Haldar, A. and S. Mahadevan (2000). Probability, Reliability and Statistical Methods in Engineering Design. John Wiley. New York, NY. Holland, J.H. (1975). Adaptation in Natural and Artificial Systems. University of Michigan Press. Ann Arbor, MI. Kapelan, Z., D.A. Savic and G.A. Walters (2003). Robust least cost design of water distribution systems using gas. In: Proceedings Computer Control for Water Industry (CCWI) (C. Maksimovic, D. Butler and F.A. Memon, Eds.). London, UK. pp. 147–155. Lansey, K.E. (2000). Optimal design of water distribution systems. In: Water Distribution System Handbook (L.W. Mays, Ed.). McGraw-Hill. New York, NY. Lansey, K.E., N. Duan, L.W. Mays and Y.K. Tung (1989). Water distribution system design under uncertainties. J. Water. Res. Pl.-ASCE 115(5), 630–645. Michalewicz, Z. (1992). Genetic Algorithms + Data Structure = Evolution Programs. SpringerVerlag. Berlin, D. Murphy, L.J., A.R. Simpson and G.C. Dandy (1993). Pipe network optimization using an improved genetic algorithm. Technical Report R109. Department of Civil and Environmental Engineering, University of Adelaide. Adelaide, AU. Obradovic, D. and P. Lonsdale (1998). Public Water Supply Models, Data and Operational Management. E & FN Spon. London, UK. Quindry, G.E., E.D. Brill and J.C. Liebman (1981). Optimisation of looped water distribution systems. Journal of the Environmental Engineering, ASCE 107(4), 665–679. Rossman, L.A. (2000). EPANET2 Users Manual. U.S. Environmental Protection Agency (USEPA). Cincinnati, OH. Savic, D.A. and G.A. Walters (1997). Genetic algorithms for the least-cost design of water distribution networks. J. Water. Res. Pl.-ASCE 123(2), 67–77. Schaake, J. and D. Lai (1969). Linear programming and dynamic programming applications to water distribution network design. Technical Report 116. Dept. of Civil Engineering, MIT. Boston, MA. Tolson, B.A., H.R. Maier, A.R. Simpson and B.J. Lence (2004). Genetic algorithms for reliabilitybased optimisation of water distribution systems. J. Water. Res. Pl.-ASCE 130(1), 63–72. Xu, C. and I.C. Goulter (1998). Probabilistic model for water distribution reliability. J. Water. Res. Pl.-ASCE 124(4), 218–228. Xu, C. and I.C. Goulter (1999). Reliability-based optimal design of water distribution networks. J. Water. Res. Pl.-ASCE 125(6), 352–362. Zhao, Y.G. and T. Ono (2001). Moment methods for structural reliability. Structural Safety 23, 47– 75.

Part IV

Planning and MODSS

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CHAPTER 9

Sustainable Floodplain Management and Participatory Planning in the Red River Basin, Canada

Slobodan P. Simonovic Department of Civil and Environmental Engineering and Institute for Catastrophic Loss Reduction The University of Western Ontario, London, Ontario, Canada

9.1 Introduction Flood management in general comprises of different water resources activities aimed at reducing potential harmful impact of floods on people, environment and economy of a region. Sustainable flood management decision-making requires integrated consideration of economic, ecological and social consequences of disastrous floods. While economic consideration gets priority in traditional approaches of decision-making, empowerment of stakeholders is an issue that is demanding increasing attention now a days in many decision-making processes. Flood management activities (i.e., disaster mitigation, preparedness and emergency management) may be designed and achieved without the direct participation of stakeholders. However, it cannot be implemented without them (Affeltranger, 2001). In order to decide about the flood control measure to be adapted in a floodplain, the decision-making process should include different stakeholders. Government policy makers and professional planners are first to name. However, others like general public, communities affected by the decision outcomes, non-governmental organizations and different interest groups should be included as well. In the wake of the 1997 flood that devastated communities along the Red River in Canada and the USA, research continues to progress, working to minimize the impact of future flooding on flood victims. A common criticism among the communities in Canada affected by the Red River flooding is the lack of their involvement concerning decisions made on flood control and flood protection measures implemented by the government (Simonovic and Carson, 2003). The International Joint Commission task force was formed by the US and Canadian governments to evaluate the existing flood management plan, 175

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after the severe flood in 1997. In 2000, they published a report (IJC, 2000) with the following recommendation: ‘The city of Winnipeg (largest community in the floodplain), province of Manitoba, and the Canadian federal government should cooperatively develop and finance a long-term flood protection plan that fully considers all social, environmental and human effects of any flood protection measures and respects both the needs of Winnipeg and the interests of those outside the city who might be affected by such a plan’. The objective of the collaborative research performed by the University of Western Ontario and the communities in the Red River Basin is to develop a multi-criteria decision-making methodology for participatory process governing the flood management in the Red River Basin. This methodology is able to: (1) evaluate potential alternatives based on multiple criteria under uncertainty; (2) accommodate the high diversity and uncertainty inherent in human preferences; and (3) handle a large amount of data collected from stakeholders in the Red River Basin. This chapter presents a new methodology and its application to the Red River Basin flood management. A set of conclusions is provided at the end. 9.2 Methodology The flood management process in Canada, as elaborated for the Red River Basin by Simonovic (1999), has three major stages: (a) planning, (b) flood emergency management, and (c) post-flood recovery. Appropriate decision-making in each of these stages is very important to establish an efficient flood management process. During the planning stage, different alternative measures (both structural and non-structural) are analysed and compared for possible implementation in order to minimize future flood damage. Flood emergency management includes regular evaluation of the current flood situation and daily operation of flood control works. The evaluation process includes identification of potential events that could affect the current flood situation (such as dike breaches, wind set-up, heavy rainfall, etc.) and identification of corresponding solution measures for flood fighting (including building temporary structures or upgrading existing ones). Also, from the evaluation of current situation, decisions are made regarding evacuation and re-population of flood-affected areas. Post-flood recovery involves numerous decisions regarding return to normal life. Main issues during this stage include assessment and rehabilitation of flood damage, and provision of flood assistance to flood victims. In all these three stages, the decision-making process takes place in a multi-disciplinary and multi-participatory environment. Flood management decision-making problems are complex due to their multi criteria nature. For a given goal, many alternative solutions may exist that provide different level of satisfaction for different issues, such as environmental, social, institutional and political. These concerns naturally lead to the use of multi criteria decision-making techniques, in which, trade-off is performed among the single objectives to find out the most desirable solution. Multiple criteria decision-making becomes more complicated with the increase in number of individuals/groups involved in the decision-making process. In reality, the decision-making process often involves multiple stakeholders/decision makers. Moving to a multiple stakeholders’ participation introduces a great deal of complexity into the analysis. The decision problem is no longer limited to the selection of the most

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Table 9.1. Conceptual decision matrix for a discrete multi criteria multi participant decision problem.

A1 ... Am DM1

... DMn

O1

...

Op

a11 ... am1 w11 ... wn1

... ... ... ... ... ...

A1p ... Amp w1p ... wnp

preferred alternative among the non-dominated solutions according to a single set of preferences. The analysis must also be extended to account for the conflicts among different stakeholders with different objectives. Therefore, it is a real challenge to have a group decision outcome that can satisfy all who are involved in the decision-making process (Arrow, 1963). In general, the process of decision-making basically involves deriving the best option from a feasible set of alternatives. Most of the existing approaches in multiple criteria decision-making with a single stakeholder/decision maker consist of two phases (Zimmerman, 2001): (1) the aggregation of the judgements with respect to all criteria and per decision alternatives; and (2) the ranking of the decision alternatives according to the aggregated judgment. In the case of multiple stakeholders, an additional aggregation is necessary with respect to the judgements of all the stakeholders. Group decision-making under multiple criteria involves a diverse and interconnected fields like preference analysis, utility theory, social choice theory, voting, game theory, expert evaluation analysis, aggregation, economic equilibrium theory and so on (Hwang and Lin, 1987). Consider a multi criteria multi participant decision-making problem where m alternatives are to be evaluated by n decision makers, who are using p objectives. The general conceptual decision matrix for the discrete multi criteria multi-participant problem is shown in Table 9.1. In Table 9.1, A denotes the alternative, O is the criterion or objective (used alternatively in this chapter with some meaning) and DM is the decision maker/stakeholder. The preference of the decision maker k (k = 1, . . . , n) for the objective j (j = 1, . . . , p) is expressed by wj k , and aij is the performance evaluation of the alternative i (i = 1, . . . , m) for each objective j . The classical outcome of the decision matrix is the ranking of the alternatives. To obtain that, a number of steps are necessary like establishing the preference structure, the weights and also the performance evaluations. All these can be termed as the inputs for the decision matrix. These inputs come from the stakeholder/decision maker. The decision matrix shows that the inputs can be for the preference of criteria as well as for the performance evaluations. The decision maker might also have a preference structure for the alternatives. In case of multi participant decision-making problem, these inputs are to be collected from all the stakeholders. Following is a general mathematical formulation of this multi criterion, multi participant problem (Hwang and Lin, 1987). A payoff matrix can be obtained for the problem

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where m alternatives are to be evaluated by n stakeholders/decision makers, who are using p criteria: ⎞ ⎛ a11 . . . a1p ⎜ a21 . . . a2p ⎟ ⎟ ⎜ (9.1) Ak = [aij ]k = ⎜ . . . ⎟ k = 1, . . . , n. ⎝ .. . . .. ⎠ am1 . . . amp Here Aki = [ai1 , . . . , aip ]k means that alternatives i are being evaluated by criteria from 1 to p by decision maker k. The symbol Akj = [a1j , . . . , amj ]k means that the objective j is being used by decision maker k to evaluate all alternatives from 1 to m. The solution to this problem is to have each alternative evaluated by all the decision makers using all criteria. The process can be summarized as the following mapping function: 

 : Ak | k = 1, . . . , n → G, (9.2) where G is a collective weighted agreement matrix. It is crucial that this mapping function represents all criteria that the decision makers use in judging all the alternatives. Flood management decision-making is always associated with some degree of uncertainty. This uncertainty could be categorized into two basic types: uncertainty caused by inherent hydrologic variability and uncertainty due to a lack of knowledge (Simonovic, 2000). Uncertainty of the first type is associated with the spatial and temporal changes of hydrologic variables such as flow, precipitation, and water quality. The second type of uncertainty occurs when the particular value of interest cannot be assessed exactly because of the limitation in the available knowledge. The second type of decision uncertainty is more profound in the area of public decision-making such as in the case of flood management. Capturing views of individuals present the problem of uncertainty. The major challenge while collecting these views is to find out the technique that will capture those uncertainties, and also be usable in a multi-criteria tool. 9.2.1 Participation of multiple stakeholders An aggregation procedure is one of the ways to include information from the participating decision makers into the decision matrix. The available methods do not seem to be appropriate for flood management for two reasons. The first is that all available methods collect the information from the multiple participants using relatively complicated procedures. Where the participating decision makers, as in case of flood management, are from both technical and non-technical backgrounds, the application of the complicated procedures is not feasible. The second reason is that when the responses are collected from a large number of participants, there may be a number of common responses. This overlap will not be reflected in the results if traditional (direct aggregation) methods are applied. The methodology of the present study (Akter and Simonovic, 2005) includes representation of inputs from a large number of participants and the analysis of inputs to make them usable for the application to various multi criteria decision-making methods. Fuzzy

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set theory and fuzzy logic are used to represent the uncertainties in stakeholders’ opinions. Three possible types of fuzzy input have been considered to capture the subjectivity of the responses from stakeholders. When a stakeholder is asked to evaluate an alternative against a particular criterion, the answer may take one of the following forms: (a) a numeric scale response; (b) a linguistic answer (for example: poor, fair, good, very good, etc.); or (c) an argument (for example: ‘if some other condition is satisfied then it is good’). For the first type, the input is quite straightforward. For type (b) answer, it will be necessary to develop the membership functions for the linguistic terms. Type (c) input can be described by using fuzzy inference system, which includes membership functions, fuzzy logic operators and if-then rule. For this, the membership functions for the input arguments need to be developed first. Then fuzzy operator and fuzzy logic are applied to obtain the output. It should be noted that the interpretation of type (b) and type (c) input values are highly dependent on the shape of the membership functions and the degree of severity chosen by the expert for a particular application. After receiving the inputs from all stakeholders, the next step is to aggregate those inputs to find a representative value. It is obvious that for all input types considered above, the responses are sure to be influenced by a number of repetitions. This means many respondents can provide the same response. This implies that the general methodologies of fuzzy aggregation cannot be applied for deriving the resultant input from a large number of decision makers. Fuzzy Expected Value (FEV) method can be used instead to get the resulting opinion of the stakeholders. Following is the definition of the fuzzy expected value: Let χA be a B-measurable function such that χA ∈ [0, 1]. The FEV of χA over the set A, with respect to the fuzzy measure μ, is defined as FEV(χA ) =

sup

T ∈[0,1]

 

min T , μ(ξT ) ,



ξT = x | χA (x)  T ,   μ x | χA (x)  T = fA (T ),

(9.3)

(9.4) (9.5)

where fA (T ) is a function of the threshold T . Figure 9.1 provides a geometric interpretation of the FEV. Performing the minimum operator, the two curves create the boundaries for the remaining triangular curve. The supremum operator returns the highest value of fA (T ) which graphically represents the highest point of the triangular curve. This corresponds to the intersection of the two curves where T = H . FEV can be computed for all three types of inputs mentioned earlier in this section. For type (a) input, the resultant FEV should be a numeric value between 0 and 1. For both type (b) and type (c) inputs, the resultant FEVs are membership functions. The crisp numeric equivalents of these membership functions can be obtained by applying defuzzification method and can then be compared with type (a) answers. The Centroid of Area defuzzification method has been used that returns a value obtained by averaging the moment area of a given fuzzy set. Mathematically, the centroid,

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1

T H

H

1

T

Fig. 9.1. A geometric interpretation of the FEV.

x, ¯ of a fuzzy set, A, is defined as 1

xμA (x) dx x¯ = 0 1 , 0 μA (x) dx

(9.6)

where μA (x) is the membership function of the fuzzy set A. The resultant FEVs are now the aggregated evaluation of the alternatives from all the stakeholders. They can now be used as the input value in the decision matrix (Table 9.1) for the multi criteria analysis. 9.2.2 Participatory multi criteria decision-making under uncertainty In this chapter an innovative modification has been made to the Compromise Programming multi criteria decision-making technique to accommodate participatory flood decision-making under uncertainty. Bender and Simonovic (2000) fuzzified Compromise Programming entirely and thus formulated Fuzzy Compromise Programming (FCP). The driving force for the transformation from a classical to a fuzzy environment is that there is a need for accurate representation of subjective data in the flood decision-making. It is the theory of fuzzy sets that can represent the subjective data well. Thus, instead of using crisp numbers in the Compromise Programming distance metric equation, fuzzy numbers are used; instead of using classical arithmetic, fuzzy arithmetic is applied; instead of simply sorting distance metrics, fuzzy set ranking methods must be applied to sort the fuzzy distance metrics. In other words, the fuzzy transformation complicates the interpretation of the results but, on the other hand, models the decision-making process more realistically.

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Mathematically, Compromise Programming distance metric in its discrete form can be presented as  ∗ p  1/p  t  p fz − fz Lj = wz , (9.7) fz∗ − fz− z=1 where z = 1, 2, 3, . . . , t and represents t criteria; j = 1, 2, 3, . . . , n and represents n alternatives; Lj is the distance metric of alternative j ; wz corresponds to a weight of a particular criteria; p is a parameter (p = 1, 2, . . . , ∞); and fz∗ and fz− are the best and the worst value for criteria z, respectively (also referred to as positive and negative ideals); and fz is the actual value of criterion z. The parameter p is used to represent the importance of the maximal deviation from the ideal point. Varying the parameter p from 1 to infinity, allows one to move from minimizing the sum of individual regrets (i.e. having a perfect compensation among the criteria) to minimizing the maximum regret (i.e. having no compensation among the criteria) in the decision making process. The choice of a particular value of this compensation parameter p depends on the type of problem and desired solution. The weight parameter, wz , characterizes decision makers’ preference concerning the relative importance of criteria. Simply stated, the parameter places emphasis on the criteria the decision maker deems important. The parameter is needed because different participants in the decision-making process have different viewpoints concerning the importance of a criterion. Bender and Simonovic (2000) fuzzified Compromise Programming and thus formulated Fuzzy Compromise Programming (FCP). The driving force for the transformation from a classical to a fuzzy environment is that there is a need for accurate representation of subjective data in the flood decision-making. It is the theory of fuzzy sets that can represent the subjective data well. Thus, instead of using crisp numbers in the distance metric equation (9.7), fuzzy numbers are used; instead of using classical arithmetic, fuzzy arithmetic is applied; instead of simply sorting distance metrics, fuzzy set ranking methods must be applied to sort the fuzzy distance metrics. In other words, the fuzzy transformation complicates the interpretation of the results but, on the other hand, models the flood decision-making process more realistically. In Fuzzy Compromise Programming, obtaining the smallest distance metric values is not easy, because the distance metrics are also fuzzy. To pick out a smallest fuzzy distance metric, from a group of distance metrics, fuzzy set ranking methods have to be used. A study by Prodanovic and Simonovic (2002) compared fuzzy set ranking methods for use in Fuzzy Compromise Programming, and recommended using the method of Chang and Lee (1994). This recommendation was founded on the fact that Chang and Lee’s (1994) method gave most control in the ranking process – with degree of membership weighting and the weighting of the subjective type. The Overall Existence Ranking Index (OERI) suggested by Chang and Lee (1994) has the following mathematical form  OERI = 0

1

 −1 ω(α) χ1 μ−1 j L (α) + χ2 μj R (α) dα,

(9.8)

where the subscript j stands for alternative j , while α represents the degree of membership; χ1 and χ2 are the subjective type weighting indicating neutral, optimistic or

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pessimistic preferences of the decision maker, with the restriction that χ1 + χ2 = 1; parameter ω(α) is used to specify weights which are to be given to certain degrees of distance −1 metric membership (if any); and μ−1 j L (α) represents an inverse of the left part, and μj R (α) the inverse of the right part of the distance metric membership function. For χ1 values greater than 0.5, the left side of the membership function is weighted more than the right side, which in turn makes the decision maker more optimistic. Of course, if the right side is weighted more, the decision maker is more of a pessimist (this is because he/she prefers larger distance metric values, which means the farther solution from the ideal solution). In summary, the risk preferences are: if χ1 < 0.5, the user is a pessimist (risk averse); if χ1 = 0.5, the user is neutral; and if χ1 > 0.5, the user is an optimist (risk taker). Simply stated, Chang and Lee’s (1994) Overall Existence Ranking Index is a sum of the weighted areas between the distance metric membership axis and the left and right inverses of a fuzzy number. 9.3 Red River Basin flood management The proposed methodology is applied to flood management in the Red River Basin (Simonovic, 1999; IJC, 2000; Simonovic and Carson, 2003). One of the flood management problems at the planning stage in the Red River Basin is the complex, large-scale problem of ranking potential flood management alternatives. During the evaluation of alternatives, it is necessary to consider multiple criteria that may be quantitative and qualitative. The flood management process in the basin also involves numerous stakeholders. They include different levels of government, different agencies, private organizations, interest groups and general public. They all have different and specific needs and responsibilities during all stages of flood management – planning, emergency management and flood recovery. Currently, the Government of Manitoba, Canada is responsible for decision-making about flood management measures. The decision-making process involves consulting different organizations for their technical input. Concerns of the general public about the alternatives are gathered through public hearings and workshops. Economic analysis plays an important role in formulating plans for reducing flood damages and making operational decisions during the emergency. One of the main limitations of the existing flood management methodology is high emphasis on the economic criterion. Very minor attention is given to environmental and social impacts of floods. There has been increasing concern of general public about the decisions to be taken on the selection of flood control measures. During the 1997 flood, it was indicated that certain stakeholders in the basin, particularly the floodplain residents, did not have adequate involvement in flood management decision-making. Dissatisfaction has been observed among the stakeholders about evacuation decisions during the emergency management and about compensation decisions during the post-flood recovery (IJC, 2000). The methodology presented in the previous section has been used to collect information from the stakeholders across the Canadian portion of the Red River Basin. In order to evaluate the utility of the methodology, a generic experiment was considered for the study to evaluate three alternative options for improved flood management. A flood management pay-off (decision) matrix with relevant criteria and theoretical alternatives was

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Table 9.2. Flood management pay-off (decision) matrix.

A1 A2 A3 WC

O1

O2

O3

O4

O5

O6

O7

O8

e11 e21 e31 W1

e12 e22 e32 W2

e13 e23 e33 W3

e14 e24 e34 W4

e15 e25 e35 W5

e16 e26 e36 W6

e17 e27 e37 W7

e18 e28 e38 W8

developed for this case study as shown in Table 9.2, where the stakeholder’s preference is emn . Three generic options considered are: (a) structural alternatives (A1), (b) nonstructural alternatives (A2), and (c) a combination of both (A3) alongside with a weighting coefficient (WC) of each objective. The selection of criteria against which the alternatives are ranked is one of the most difficult but important tasks of any multi-criteria decision analysis. For the flood management decision-making in the Red River Basin, the criteria selection is mainly based on prior studies of the Red River flooding (IJC, 2000; Morris-Oswald et al., 1998). Economic objectives [cost (O1), damage (O2), benefit (O3)] are in general the most important ones and also are straightforward to quantify. Environmental objectives [chemical contamination (O3); inter-basin transfer of alien invasive species (O4); and protection and enhancement of floodplain environment (O5)] are highly important too. Generally, most flood management decision-making processes exclude or ignore the social objectives. This is mainly because of the difficulties inherent in selecting and quantifying these objectives. Different studies of the Red River flooding and numerous interviews with its stakeholders reflect that including social impacts is of prime importance for a successful implementation of any flood management policy in the Red River Basin. The following two social objectives have been considered in our case study: (a) level of community involvement (O7), and (b) amount of personal losses (O8), and includes financial, health and psychological losses. A detailed survey has been conducted in the Basin to collect the information on the two selected social criteria (Salonga, 2004). Therefore, the remaining of this chapter focuses on the application of the developed methodology using a generic set of three alternatives and the real data on two social criteria. The survey questionnaire was prepared: (a) to capture the possible views of the stakeholders for the two selected criteria (eight questions for criterion 1 and five questions for criterion 2), and (b) to allow stakeholders to express their views in an easy way. Thirty-five respondents were interviewed and they were asked to answer each question in three forms: (a) using a numeric scale with the range 0–1; (b) using linguistic answers (very low, low, medium, high, very high); and (c) using conditional answers [if flooding is moderate then (very low, low, medium, high, very high)] [if flooding is severe then (very low, low, medium, high, very high)] All three types of inputs obtained from all the stakeholders were processed using the Fuzzy Expected Value method as explained in the methodology section. For the conditional response, the response from each person was first processed to get the crisp value, and then all the responses were further processed to obtain the FEV using the method for scale responses.

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S.P. Simonovic Table 9.3. Resultant FEVs for structural alternatives. Question 1 2 3 4 5 6a 6b 6c 7 8 1 2 3a 3b 4 5

FEV

Type A

0.600 0.529 0.618 0.600 0.700 0.800 0.771 0.700 0.800 0.700 0.800 0.588 0.500 0.700 0.771 0.500

Table 9.4. Resultant tives. Question 1 2 3 4 5 6a 6b 6c 7 8 1 2 3a 3b 4 5

FEV

Type B

0.650 0.517 0.700 0.650 0.700 0.825 0.770 0.700 0.825 0.717 0.770 0.570 0.570 0.717 0.770 0.570

FEV s

Type A

0.647 0.500 0.559 0.657 0.629 0.704 0.714 0.629 0.829 0.700 0.700 0.600 0.559 0.700 0.700 0.700

FEV

FEV

Type C

0.544 0.500 0.529 0.544 0.559 0.677 0.588 0.574 0.735 0.574 0.718 0.544 0.574 0.625 0.574 0.529

for non-structural alternaFEV

Type B

0.650 0.517 0.625 0.650 0.650 0.770 0.717 0.650 0.850 0.650 0.700 0.650 0.625 0.717 0.650 0.570

FEV

Type C

0.544 0.491 0.529 0.559 0.544 0.588 0.574 0.574 0.718 0.574 0.574 0.544 0.574 0.588 0.574 0.544

Tables 9.3–9.5 summarize the results of all three types of inputs (scale, linguistic and conditional types which are termed as A, B and C, respectively, in the table) as the evaluation of three alternatives (structural, non-structural, combination) against two criteria (community development-top questions 1–8, personal loss-bottom questions 1–6). Obtained results show good correlation between the numeric scale type and linguistic type of inputs with an average difference of only 0.029. The conditional type results show consistently a slightly lower value. This can be attributed to the fact that, to obtain the resultant linguistic input from the conditional statements, it is required to select a level of severity for the flooding considered. In this case, we took 1997 flooding of the Red River to be of 0.7 degree of severity on the scale from 0 to 1. This value is subject to change

Sustainable Floodplain Management and Participatory Planning Table 9.5. Resultant tives. Question 1 2 3 4 5 6a 6b 6c 7 8 1 2 3a 3b 4 5

FEV

FEV s

Type A

0.600 0.500 0.600 0.686 0.700 0.800 0.743 0.686 0.857 0.700 0.700 0.600 0.559 0.706 0.700 0.571

185

for combination alterna-

FEV

Type B

0.625 0.570 0.625 0.650 0.650 0.825 0.770 0.700 0.825 0.700 0.717 0.625 0.570 0.717 0.717 0.570

FEV

Type C

0.544 0.544 0.544 0.544 0.544 0.647 0.574 0.574 0.718 0.574 0.671 0.574 0.574 0.588 0.544 0.544

according to the expert opinion, and if a higher value is chosen the results would be closer to the other type values. All the three methods used in this study can be claimed to be equally accurate in representing the stakeholders’ view. The degree of superiority of one above others has not been measured in this study. FEV s obtained in Tables 9.3–9.5 are used further to rank the three generic alternatives. All questions are considered to carry the same weight. A set of ranking experiments has been conducted to evaluate the impact of different stakeholder groups on the final rank of alternatives: (a) experiment 1 – all stakeholders interviewed; (b) experiment 2 – stakeholders from the city of Winnipeg; (c) experiment 3 – stakeholders from the Morris area (south of Winnipeg); and (d) experiment 4 – stakeholders from the Selkirk area (north from Winnipeg). Figure 9.2 shows for illustrative purposes, the criterion 1, the criterion 2 and the resultant distance metric membership functions obtained in evaluation of alternative 1 (structural flood management option) for all participants (top left), participants from the City of Winnipeg (top right), participants from the Morris area (bottom left) and participants from the Selkirk area (bottom right). The final results of four ranking experiments with three generic alternatives and two social criteria are shown in Table 9.6 (defuzzified distance metric value and the rank in brackets). It is obvious that the final rank varies with the experiment, therefore confirming that preferences of different stakeholders are being captured by the developed methodology. 9.4 Conclusions Though flood control (i.e., disaster mitigation, preparedness and management) may be designed and achieved without the stakeholders’ participation, it cannot be implemented

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S.P. Simonovic A1 for all

0.8

C2

0.6

Resultant

0.4 0.2

C1 C2

0.8

Resultant

0.6 0.4 0.2 0.0

0.0 -2

-1

0

1 2 Preference

3

4

-3

5

A1 for Morris

1.0

-2

-1

Resultant 0.6 0.4 0.2

3

4

5

C1

C2 Membership Value

0.8

0 1 2 Preference

A1 for Selkirk

1.0 C1

C2 Membership Value

A1 for Winnipeg

1.0

C1 Membership Value

Membership Value

1.0

0.8 0.6 Resultant

0.4 0.2 0.0

0.0 -2

-1

0 1 Preference

-2

2

-1

0 1 2 Preference

3

4

Fig. 9.2. Distance metric fuzzy membership functions. Table 9.6. Final rank of flood management alternatives. Participants

Alt. 1

Alt. 2

Alt. 3

All

13.224

13.717

13.280

(1)

(3)

(2)

15.435

16.068

13.686

(2)

(3)

(1)

14.635

14.425

14.585

(3)

(1)

(2)

13.746

15.259

13.923

(1)

(3)

(2)

Morris

Selkirk

Winnipeg

without it (Affeltranger, 2001). So, flood management decision-making can be defined as a multi-criteria, multi participant problem where alternatives are evaluated against a number of criteria considering the concerns of all stakeholders. As most of the decision-

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making processes take place in situations where the goals, the constraints and the consequences of the possible actions are not known precisely, it is necessary to include these types of uncertainty into the decision-making methodology. Fuzzy set and fuzzy logic techniques have been used successfully to represent the imprecise and vague information in many fields, and so have been considered as an effective way to represent uncertainties in this study. This work proposes a new methodology that provides alternative ways to extract and aggregate the inputs from a large number of stakeholders for flood management decision-making. Fuzzy Expected Value (FEV) has been used as a method to aggregate those inputs and generate the elements of the multi criteria decision matrix for further analysis (Akter and Simonovic, 2005). Three possible types of responses for flood management have been considered which are numeric input, linguistic input and conditional input. The Fuzzy Compromise Programming technique (Bender and Simonovic, 2000) is combined with the fuzzy membership ranking (Prodanovic and Simonovic, 2002) to analyse the alternative flood management options. The analyses of flood management options in the Red River Basin show the applicability of the methodology for a real flood management decision-making problem. The stakeholders can now express their concerns regarding flood hazard in an informal way, and that can be incorporated into the multi criteria decision-making model. The application of methodology helps in solving the problem of incorporating a large number of stakeholders in flood decision-making process. Bibliography Affeltranger, B. (2001). Public participation in the design of local strategies for flood mitigation and control. Technical Documents in Hydrology 48. UNESCO IHP-V. Akter, T. and S.P. Simonovic (2005). Aggregation of fuzzy views of a large number of stakeholders for multiobjective flood management decision making. J. Environ. Manage. 77(2), 133–143. Bender, M.J. and S.P. Simonovic (2000). A fuzzy compromise approach to water resources planning under uncertainty. Fuzzy Set Syst. 115(1), 35–44. Chang, P.T. and E.S. Lee (1994). Ranking of fuzzy sets based on the concept of existence. Comput. Math. Appl. 27, 1–21. Hwang, C. and M. Lin (1987). Group Decision Making Under Multiple Objectives: Methods and Applications. Springer-Verlag. Berlin. IJC, International Joint Commission (2000). Living with the Red (Available on line: http://www.ijc.org/php/publications/html/living.html). Ottawa, Washington. Morris-Oswald, T., S.P. Simonovic and J. Sinclair (1998). Efforts in flood damage reduction in the red river basin: Practical considerations. Technical report. Prepared for the Environment Canada, Environmental Adaptation Group, Institute for Environmental Studies, University of Toronto. Prodanovic, P. and S.P. Simonovic (2002). Comparison of fuzzy set ranking methods for implementation in water resources decision-making. Can. J. Civil Eng. 29, 692–701. Salonga, J. (2004). Aggregation methods for multi-objective flood management decision making with multiple stakeholders: Red River Basin case study. Technical report. Prepared in partial fulfilment of the requirements for the degree of Bachelor of Engineering Science, The University of Western Ontario, London. Simonovic, S.P. (1999). Decision support system for flood management in the Red River Basin. Can. Water Res. J. 24(3), 203–223. Simonovic, S.P. (2000). Tools for water management: One view of the future. Water Int. 25(1), 1–8.

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Simonovic, S.P. and R.W. Carson (2003). Flooding in the Red River Basin — lessons from post flood activities. Nat. Hazards 28, 345–365. Zimmerman, H.J. (2001). Fuzzy Set Theory and Its Application. Academic Publishers. Boston/Dordrecht/London.

CHAPTER 10

Negotiation Support System for Resolution of Disputes over International Water Resources Lea Kronaveter1 and Uri Shamir2 1 Mekorot Water Company, Israel 2 Technion – Israel Institute of Technology, Israel

10.1 Introduction Available quantities of the naturally renewable fresh waters are being exhausted in many parts of the world, and the problem of international water resources is becoming more acute. International or shared waters are surface and underground water resources whose watersheds are spread over the territory of more than one country. Most of the world’s largest rivers cross or define international borders. There are more than 260 international river systems, with over 50% of the world’s global population (Wolf, 1995). Many of the world’s aquifers are spread under the territory of more than one country (Puri, 2001). When dealing with water shortages, governments frequently take unilateral actions, without considering the needs of their neighbours. Such policies alter the natural balance of quantities and qualities of water resources and, eventually, cause international disputes. Management of international waters is difficult, since issues of control, jurisdiction and sovereignty are extremely complicated. International Law (United Nations, 1997) does not provide unambiguous directive for appropriation and management of international water resources. When claiming rights to shared waters, nations rely on their geographical position, historical rights, and often on their relative power. Conflicts over international waters are extremely complex because of the variety of interests involved and the meanings of water to human society. In some countries water is a matter of culture and religion, often an issue of survival or of economic prosperity, but in most parts of the world it is not merely the scarcity that makes water an important resource. Water resources are of strategic importance and become a matter of a country’s highest policy. Conflicts over international waters are long lasting, often involving military threats and sometimes even military skirmishes, although not wars (Wolf et al., 2003). Negotiations over allocation of shared water resources are frequently a long-drawn process, burdened by mutual mistrust among the parties. Water quantity is often the dom189

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inant feature of the negotiations, even though there are many other aspects which deserve consideration, such as quality and environmental amenities, and thus dividing the waters is viewed as a win-lose situation. Negotiations over shared waters are in most cases conducted as simple, distributive bargaining processes. If a solution is reached, it may be heavily influenced by the power balance between the parties, and at least one of them leaves the table unsatisfied. This work is concerned with competition over shared international water resources, under conditions of potential or actual water scarcity. It has been proven that inefficient management of water resources (such as under-pricing, over-pumping, etc.) can cause artificial water scarcity, and that water markets have a potential to increase the efficiency of water utilization (Becker and Zeitouni, 1998 and Fisher et al., 2002). The water market approach aims at determining an efficient allocation of water resources based on a system of voluntary trade in water, which can bring benefits to all parties involved. The basic assumption of our work is that certain features of a water market system can help in adjusting the allocation of a disputed international water resource to actual hydrological, political and economic circumstances, while insuring improved benefits to the parties. We propose a collaborative Negotiation Support System (NSS) as a dispute resolution technique, to assist the parties in searching for feasible and satisfying solutions to managing the shared resource. A central component of the NSS is the Water Allocation System (WAS) (Fisher et al., 2002) that allocates water in a way which maximizes total social net benefit from water supply to all consumers in a defined region. 10.2 Value of water1 Most solutions to water allocation problems relate to water only in terms of quantities. Demands for water are projected according to needs of various consumers. Supplies of available water are estimated and whenever the balance between the two shows a shortage, engineering and/or political solutions are sought. According to this approach, water allocation between two parties that claim rights from the same water resource is perceived as a zero-sum game: water allocated to one party is not available to the other. This holds for both within-a-country and international water, since the parties can represent different types of demands in a single country or two states (or political entities) that share a water resource. In recent years, there have been attempts to relate to water in terms of values. They are based on the fact that water is valuable not only because it is essential for sustaining human life, but because it is scarce (Eckstein et al., 1994). In the countries that have access to the sea, desalination puts an upper bound to the value of water in dispute (Fisher et al., 2002). Feitelson and Haddad (2001) give as an example the dispute over the Mountain Aquifer between Israel and the Palestinians. With desalination as an alternative water source, the value of the water in dispute is at most in the range of a few hundred million dollars per year – a sum that should be negotiable. The economic value of water is expressed through the willingness of a user to pay for a certain amount of water. For the first few units of water one is willing to pay the highest price, as it will be used to satisfy the most urgent needs. Values of the following units of 1 Following Fisher et al. (2002).

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Price

Quantity Fig. 10.1. Demand curve.

Price Demand Curve Cost

P*

Q*

Quantity

Fig. 10.2. Optimal allocation.

water decrease, since it is used to satisfy less essential needs. The willingness to pay as a function of the amount of water is presented by the demand curve (Fig. 10.1). When an amount Q of water is supplied to a user the total value of that amount of water to that user equals to the area below the demand curve, to the left of Q (Pmax is a cutoff price, which makes the area finite). Summation of demand curves of all users (urban, industrial or agricultural) in a specified region yields the aggregate demand curve for that region, and the area under the curve gives the benefits. These are gross benefits because there are costs of providing the amount Q of water. The cost function (Fig. 10.2) is an increasing function of the amount of water, and may rise smoothly or in steps corresponding to different supply sources (Fisher et al., 2002). For any allocation Q the net benefit is calculated by subtracting the total costs of providing the water (the area under the cost curve, to the left of Q) from the gross benefits (the area under the demand curve to that point).

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L. Kronaveter and U. Shamir Price Private Value Private

Social Value

Subsidy Amount

Quantity Fig. 10.3. Private and social value of water.

If the allocation is designed to maximize net benefits, the amount Q* (given by the intersection of the two curves, in Fig. 10.2) should be delivered. A lesser amount of water would mean that the consumer would be willing to pay more for additional units than the cost of such additional units. A greater amount of water delivered than Q* would mean that the consumer would not be willing to pay the costs of providing the additional units. Such demand curves capture the private value of water, the value to the consumer. But water also has a social value, which can exceed the private one. For example, one of the ways for a government to support the agricultural sector is to subsidize its water. In the case of a subsidy by a fixed amount at all quantities, the demand curve would move up as shown in Fig. 10.3. This means that this water is worth to society more than farmers are willing to pay for it. The optimal allocation is now determined as the intersection of the cost curve and the new demand curve. Such a water policy would make farmers use more water than without the subsidy. 10.2.1 Shadow prices and scarcity rents Prices in competitive markets measure the willingness of buyers to pay for additional units of the goods in question (marginal value). When a price is higher than the cost of providing an additional unit (marginal cost), that unit is worth providing. A price less than the marginal cost means that production of that good should be cut back. This system of prices and the profits and losses is a guide for an optimal allocation of goods. There are many reasons why the laws of perfect competitive markets can rarely be applied in the case of water. A competitive market assumes many private competing producers and buyers, but water is usually not supplied privately and competitively by many sellers. Other reasons are that pumping in one location may affect the availability or cost of water at another location of the same source (e.g., aquifer). If, in Fig. 10.2, Q∗ were the maximum amount of water available, then, P ∗ would represent the price which consumers would be willing to pay to obtain an additional unit of water. This price is called the shadow price of water. It can also be defined as the amount of increase in net-benefit to water users that would result from the availability of that additional unit of water.

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Lake

the shadow value of water a

the marginal cost of supply shadow value of water at the source (scarcity rent)

b

c Fig. 10.4. Scarcity rent and shadow prices.

The shadow price of water at a given location is not necessarily equal to the direct (marginal) cost of producing it there. If demand from a limited water source exceeds its capacity then the water in the source has a value in situ, called scarcity rent. When direct costs of providing the water are zero, the scarcity rent equals the shadow price of water. Accordingly, at a given location, the shadow price is the sum of the scarcity rent of water and the direct marginal costs of providing it at that location (Fig. 10.4). 10.3 The Water Allocation System The methodology for optimal allocation of water has been embedded in the Water Allocation System (WAS) model (Fisher et al., 2002). The area in question, covering the territory of one or more political entities, is divided into ‘districts’. Each has sources, consumer sectors (urban, agriculture, industry, nature), and is connected to other districts or to a central conveyance system. Physical and economic data are given for the districts, consumer sectors, and the connecting conveyance system. The model maximizes the total net benefit by allocating water among all districts and sectors, subject to physical, political, administrative and any other imposed constraints. The model can also include recycling of wastewater. Depending on the users’ definition, water resources in the WAS model can be treated as common pools with respect to a group of consumers, so that there are no constraints on the allocation among them. Another possibility is to constrain the allocations by defining a minimum, maximum, or a fixed quantity of water to be allocated to particular consumers, districts, or countries (or any other political entities).

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WAS can be run in a countrified version, where the area in question is a single country, with water inputs from sources shared with its neighbours a priori defined. Another option is to run WAS for the region of two or more countries (the regional version), in which case shared water resources are treated as common pools. Both types of WAS runs can be performed to reflect various sets of physical, political, administrative and other constraints. Each set of constraints produces a water allocation alternative (countrified or regional). The set of WAS output data includes the optimal allocations, total net benefit from water use, shadow prices of water for the consumers and districts, shadow values of constraints, including scarcity rents for water in the sources.

10.4 Optimal allocation of water between parties The basic principles of economically optimal water allocation serve as the basis for the proposed Negotiation Support System. Suppose that a total quantity Q of water is allocated to the two parties, A and B, in quantities QA and QB (QA + QB = Q), so that the marginal value of water to party A is higher than that of party B (Fig. 10.5). For zero water supply costs, the total net benefit to A and B from using quantity Q of water is equal to the sum of the areas below the two demand curves. According to the principles outlined above, if a unit of water were transferred from party B to party A, the sum of the areas, i.e. the total net benefit, would increase. By transferring additional units of water from B to A, we continue to increase the total net benefit, reaching the maximum at the point at which the two marginal values, PA and PB , are equal. Hence, if we wanted to allocate the total quantity Q of water to A and B so as to maximize the total net benefit, the optimal quantities for allocation would be QA and QB . Relative to the starting allocation (QA and QB ), the transfer of water from B to A increases the total value by the shaded area in Fig. 10.5.

A’s price $

B’s price A’s demand curve B’s demand curve





Fig. 10.5. Water transfer: creating a ‘new’ value.

$

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10.5 Supporting negotiations Negotiation support systems are designed to provide assistance in situations where there is disagreement among the parties on which decision to adopt. They can be categorized according to their functions (Hipel et al., 1993 and Thiesen et al., 1992) as: 1. Negotiations Preparation Systems, which assist each party to analyse its positions and to decide what choices to make during negotiations; 2. Negotiation Information Management Systems that include • Context Support Systems, which simulate the behaviour of the system that is the subject of negotiations, and can be used to analyse its performance under different circumstances (alternatives/scenarios); • Process Support Systems, which are concerned with the dynamics of the negotiation process. 10.6 The Negotiation Support System (NSS) Our NSS is designed to support bilateral negotiations, although the same concepts can be extended to negotiations with more than two parties (Kronaveter, 2005). The NSS is based on symmetry, and provides an identical set of tools to both parties. The negotiation is modelled as a combination of two processes: individual decision-making and joint problem solving. Individual decision support is aimed at assisting the parties in structuring their systems of preferences related to the water allocation problem. Each party establishes its utility for negotiated alternatives, using the Analytic Hierarchy Process (AHP) algorithm (Saaty, 1980) to weight and combine its different objectives, with the economic objective being one of them, into a single utility figure. Joint problem solving is modelled as an interaction, supported by tools from game theory, in which the parties have the opportunity to design and select jointly preferred solutions. The central component of the NSS is the WAS model which provides assistance in both individual and joint decision making (Fig. 10.6). It supports interactive communication in two senses: first, each party can use the WAS alone, by introducing various waterallocation alternatives into the model, receiving feedback information about the implications of such alternatives on its country’s domestic water economy and consequently on its other objectives. Second, the two parties can perform a WAS analysis jointly, in search of joint gains. While exploring alternatives for resolving the allocation of the joint water resources and negotiating ‘around’ the WAS model, the parties have an opportunity to improve communication, evaluate each other’s expectations and goals, and interact in a manner that is less distributive and more integrative. Within the framework of the NSS, the negotiation process is modelled as an alternating sequence of individual and joint activities by which the parties manipulate the set of alternative solutions, aimed at enlarging the negotiation space by creating and proposing new alternatives, and narrowing it by removing non-efficient ones. An alternative can be designed by a single party, by a mediator, or by the two parties jointly. Removal of nonefficient offers is determined by the individual preference structures and utility values of both parties, and by a game-theoretic device based on the Nash bargaining solution, which

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Fig. 10.6. The Negotiation Support System.

operates within the joint ‘utility space’. Enlarging and narrowing the set of alternatives are repeated in an iterative manner, regulated by the protocol of interaction. The iterative nature of the negotiation process enables the parties to revise their preference structures during the negotiations and negotiate around a dynamic set of the alternative solutions, and is supposed to lead eventually to an agreed solution. The design of the NSS is based on conclusions drawn from a number of real-world cases of international water disputes. It recognizes the usual absence of confidence between the parties, and assures a level of confidentiality in the manipulation of revealed information. Also, the approach does not assume that agreement between the parties has to be based necessarily on cooperation in the management of the disputed water resources. It searches for the ‘best outcome’ as perceived jointly by both parties, given the level of their mutual trust, and given the present ‘state of the world’. 10.6.1 Negotiation protocol (protocol of interaction) Negotiation is a joint problem solving process during which the parties have to communicate and interact. The NSS includes an interaction protocol, designed to assist the parties in problem solving, since the quality of the outcome depends on the quality of the communication between them. Parties who claim rights to the same water resource presume, by themselves, to have mutually conflicting interests and are inclined to bargain in a distributive manner. The negotiators often find themselves locked in situations when it seems impossible to overcome the differences, and at least one of them prefers to break off the negotiation process. The protocol of interaction is aimed at reducing the probabil-

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ity that this will occur. It is motivated by normative (prescriptive) models of interaction, such as the models of Game Theory. The protocol of interaction consists of the rules, which specify the steps of interaction. The protocol of a typical bargaining interaction is an alternating sequence of offers and counter-offers. In our approach, the negotiation protocol does not require an exchange of offers. In contrast, it prescribes a sequence of two procedures, alternative-generation and alternative-evaluation, aimed at searching for those negotiated solutions that improve the achievements for both parties. A new alternative solution may be offered by one or both parties, or by a mediator, disregarding the fact who offered the previous one. Generation of alternatives is supported by the WAS model which enables analysis of various inter- and intra-country water allocation alternatives. Each of the parties then conducts its own evaluation based on a pair-wise comparison of the proposed alternative negotiation solutions as well as other elements of the negotiators’ preference structures. These two processes, alternative-generation and alternative-evaluation, are repeated in a sequence of iterations, which seeks to terminate when a stable solution is reached. 10.6.2 Design of alternatives The parties design alternatives while interacting, individually or jointly, with the WAS model. Each party can analyse the effects of an alternative using the complete set of WAS outputs. However, there are only few results of the WAS output that are relevant on the public level and which figure in the bargaining process. Let: QDS = the average annual renewable quantity of water in the disputed resource; Qi (a) = quantity of water from the disputed resource, allocated to party i, i = A, B, in alternative a; qi (a) = WAS-optimal quantity of water from the disputed resource, to be supplied to the consumers in i, given Qi (a) (qi (a) ≤ Qi (a)). qi (a) can vary as a function of intracountry water allocation arrangements; Vi (a) = the annual net economic benefit of party i from the use of water as a result of the negotiation alternative a. It is the net benefit from the total annual consumption of water in i, when the annual available supply of water includes qi (a): Vi (a) = Vi (Qi + qi (a)), where Qi is the annual renewable quantity of water available to i that is not subject of the negotiations. Like qi (a), Vi (a) varies as a function of the domestic water arrangements (scenarios). In any negotiated alternative a, QDS can be allocated in one of the two following ways: 1. It can be a priori allocated to the parties in quantities QA (a) and QB (a), (so that QA (a) + QB (a) = QDS ), where each party analyses the intra-country waterallocation scenarios a posteriori, given Qi (a), i = A, B; 2. QDS can be defined as a common pool; in this case, the regional version of the WAS model determines the optimal allocation so as to maximize the joint net benefit from the annual water consumption in both countries – without any restrictions or pre-judgement on the final negotiated allocations. Allocated quantities of the disputed resource (QA (a) and QB (a)) and the net benefit from the water use in the two countries will be different for different regional scenarios.

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On a public level (in terms of shared information), the parties negotiate the allocation of two commodities: water and an economic value. From the perspective of party i, i = A, B, a negotiation alternative a is represented by the allocated quantity of water from the disputed resource, Qi (a), measured in units of volume, and a monetary value vi (a). The sum of the quantities allocated to the two parties, QA (a) + QB (a), is constant over all the alternatives and equals the amount of water in the disputed source. Since water sources are always subject to random variability, this is usually set to be an agreed upon average annual renewable potential of the water source. vi (a) is the net economic gain to party i from alternative a, relative to some reference alternative, ar , assured to party i (vi (a) = Vi (a) − Vi (ar )). If, for example, alternative a reallocates the disputed water resource so that party A gains an additional quantity of water, the economic value of the total quantity of water available to A increases according to its demand curve. Correspondingly, party B loses the same quantity of water, so that the economic value of its available water decreases according to its own demand curve. If the gain to A is greater than the loss to B then they may agree to share in some manner the net total gain. In order to make such an alternative attractive to party B, A can offer B a side payment. vA (a) and vB (a) are then, the net economic values that the two parties gain by selecting alternative a over the reference alternative ar . The sum vA (a) + vB (a), varies over the alternatives. If alternative a is (economically) efficient, this sum will be equal to the change in the total annual economic value of water in the two countries, achieved by selecting alternative a over ar . On a private level (in terms of confidential information), each party evaluates the efficiency of alternative solutions to the problem according to a set of his own criteria. The set of criteria of one party is independent of the set of criteria of the other party. In terms of decision-making theory, these criteria are the parties’ objectives or attributes. Party i can assess the ‘quality’ of alternative a by analysing the ‘performance’ of the correspondj ing bundle, (Qi (a), vi (a)), with respect to each of his objectives. If ui (a) is a subjective measure (score) of the degree to which alternative a satisfies objective j , j = 1, . . . , n, then, for party i, alternative a represents the n-tuple [u1i (a), . . . , uni (a)], with n being j the number of party i’s objectives (criteria). The subjective measures, ui (a), result from an evaluation of alternative a, as part of i’s individual decision making process, and are explained next. 10.6.3 Individual decision support The negotiation framework is based on the idea of a dynamic evaluation of the objectives, which reflect the party’s interests, goals, and perceptions. Generally, the objectives (criteria) can be of the two following types: 1. Quantitative objectives, which can take values measurable in their characteristic units. For example, water quantity and economic efficiency (net benefit) from water use are objectives measured in units mcm and millions of dollars, respectively; 2. Qualitative objectives that cannot be measured by any standard units, such as national security or social stability. The dynamics in the set of the objectives is a function of the change in the negotiation conditions (e.g., knowledge, information, relationship and trust, previous proposals). For

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Allocation of a shared water resource

International goals

National goals

Relations in the region

Development

Costs

Reliable water supply

International reputation

Environment

National Identity

Religion

Alternative solution 1

Alternative solution 2

Alternative solution

Fig. 10.7. Individual preference structure.

given negotiation conditions, a ‘state of the world’, and a set of L alternative solutions, party i, i = A, B, has a subjective utility function, Ui which assigns a single score to every n-tuple [u1i (al ), . . . , uni (al )], l = 1, . . . , L. This score is a real number from the interval [0, 1], which expresses the level of overall satisfaction that party i accords to each of the L alternatives. Individual decision support consists of preference-setting procedures (performed by the party’s decision maker) and calculations (performed with the tool for individual decision support). The final result of the quantitative and qualitative analysis is party’s individual utility function, relevant for particular negotiation conditions. The model for individual decision support utilizes the Analytic Hierarchy Process (Saaty, 1980 and Shamir et al., 1985) for individual structuring (presentation and evaluation) of the water allocation problem. The AHP is a multi-objective decision support designed to select the best from a number of alternatives evaluated with respect to several criteria. It is suitable as decision support in this kind of water allocation problems, since it assists the decision maker in dealing with both quantitative and qualitative objectives. The AHP utilizes the assumption that human decision makers make good judgements for small groups of objects. It prescribes pair-wise comparisons of the elements of individual preference structure, organized in a hierarchical manner. These comparisons are used to develop overall priorities for ranking of the alternatives. Within the framework of the NSS, the hierarchy of each party consists of three levels as shown by an example in Fig. 10.7. The first level represents the overall aim of the party, the second lists the party’s objectives (criteria) which are affected by the negotiation outcome, while the third level consists of the available negotiation alternatives. The first and the third level of both parties’ hierarchies are identical and publicly known at each stage of the negotiations. The elements of the second level, the set of

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criteria, as well as the weights assigned by the party to the criteria and to alternatives vis-à-vis the criteria, are individual and confidential. The individual utility function which describes the overall satisfaction of party i by alternative negotiation solution a, obtained by the AHP model, is of the linear additive form: n  j Ui (a) = wi1 u1i (a) + · · · + win uni (a), wi = 1, j =1 j

where wi1 , . . . , win are the weights of n objectives (criteria), and ui , j = 1, . . . , n is the ‘performance’ of alternative a with respect to criterion j . Once party i has established its overall utility function, its individual objective becomes a standard optimization problem: find alternative a for which Ui (a) will be maximized. 10.6.4 Joint consequence space When parties have opposed interests, the solution, which maximizes the utility function of one party, will be unacceptable by the other. A negotiation agreement will be achieved only if the parties manage to find a jointly acceptable solution. Within the framework of the NSS, a Game Theory model is included, which assists the parties in selecting an efficient and equitable alternative, among the set of known, feasible alternative solutions to the problem. Selection of the ‘best’ negotiation solution is performed by accounting for the utility functions of both parties. Once the parties have evaluated their utility functions for a given set of negotiation alternatives, their individual overall rankings can be presented in a joint utility space (Fig. 10.8). Reservation values in a joint utility space mark the utility values of the alternative assured to the parties in case one of them breaks away from the negotiations. In Negotiation

Utility of party A

Efficient (Pareto) alternatives

Reservation value for A

Reservation value for B

Fig. 10.8. Joint utility space.

Utility of party B

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 Efficiency Frontier



 Fig. 10.9. The Nash rationale for the selection of the ‘best’ alternative: find the point which maximizes the product UV.

Theory, this threshold value of the consequence of a ‘no agreement’ alternative is called BATNA – the best alternative to a negotiated agreement. In other words, a rational party, who acts to maximize his utility function, will not accept an alternative which gets him a utility value lower than his BATNA. Another constraint for the selection of the ‘jointly best’ alternative arises from the concept of efficiency. Of all feasible alternatives, the efficient ones are those from which one cannot move to improve the utility of one party without decreasing the utility of the other. These lie on the Efficient (Pareto) Frontier. With these two constraints, the problem is reduced to the selection of one of the efficient alternatives, which are beyond the lines that mark the parties’ reservation values. This is a difficult task, since by moving along the efficient frontier, improvement of one party’s gains can be achieved only at the expense of other party’s loses. Of the several Game Theory models (Binmore, 1992) which propose solutions for such difficulty, within the framework of our NSS, the Nash bargaining solution is adopted as the criterion for the selection of an efficient and equitable negotiation resolution. According to the Nash solution, the best alternative is the one which belongs to the efficient frontier and maximizes the product of the utility values of the two parties. According to the rationale of the Nash point (Fig. 10.9), the parties should move from the point (V , U ) on the efficient frontier to point (V − V , U + U ) if U/U is greater than V /V (the proportional gain for one player is larger than the proportional loss for the other). They should continue to move along the frontier, up to the point at which δU/U = −δV /V , or, at which the product U · V is maximized (Raiffa, 1982). 10.6.5 Iterative progress of the negotiations The dynamic evolution of the set of alternative solutions can be shown as a progression in the joint consequence (utility) space (Fig. 10.10). The NSS is designed to assist the parties in advancing towards solutions which (jointly) improve their overall satisfaction. The utility function, as a measure of a party’s overall satisfaction, is formulated based on that party’s preference structure. The NSS allows the parties to change their sets of objectives and systems of preferences, and hence the utility evaluations, in response to changes in the negotiation conditions. Stages of the negotiation process in which the negotiation conditions are constant

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2 3

1

2 1 3

2

Efficiency Frontier 0

1

t and U t are utility values for parties A and B in Fig. 10.10. Iterative process of negotiations. UA B negotiation iteration t; UABATNA and UBBATNA are the reservation values of the two parties; art is the reference alternative in iteration t.

are called iterations. In a new negotiation iteration, the parties can change their sets of the objectives by adding and/or removing objectives, and/or by changing their relative importance. In Fig. 10.10, UAt and UBt are utility values of parties A and B, in negotiation iteration t. In each iteration, the parties negotiate over a set of alternatives with the aim of (eventually) selecting a single alternative as ‘the best’ (proposed by the Nash bargaining solution). The alternative selected as the ‘best’ in one iteration is the reference alternative for the next iteration. This means that alternatives negotiated in iteration t are compared relative to one another, as well as to the reference solution selected as ‘the best’ in iteration t − 1. In a general case, utility scores of a reference solution selected in iteration t − 1, UAt−1 and UBt−1 , can be different from the utility scores of that same alternative in iteration t, UAt and UBt , since the utilities are re-evaluated for each iteration. The reference alternative of the first iteration is the ‘no agreement’ alternative, which corresponds to (UABATNA ; UBBATNA ). If no alternative in iteration t has a better performance than the reference alternative art−1 , then this solution is proposed as the final negotiation resolution. 10.6.6 Relaxing the weights of the criteria For a given alternative a, which is supposed to challenge the stability of the last reference alternative ar , the parties are allowed to ‘relax’ the weights of their objectives, by assigning an upper and a lower limit to the weight of each objective. The final weights of the objectives are then obtained by a maximization procedure.

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j

i i = 1, . . . , n and w , j = 1, . . . , m, be the weights of the objectives of parties Let wA B j A and B in iteration t. Next, let uiA (a) and uB (a), i = 1, . . . , n and j = 1, . . . , m, be the scores of alternative a with respect to n objectives of party A and m objectives of party B. Then, the product of the overall utilities of the two parties resulting from alternative a, is

 1 1  n n uA (a) + · · · + wA uA (a) UA (a) · UB (a) = wA   × wB1 u1B (a) + · · · + wBm um B (a) or, in vector-matrix form 1 UA (a) · UB (a) = w T C1 w, 2

 C1 =

0 CT

 C , 0

1 , . . . , w n , w 1 , . . . , w m ], and C is where w is the vector of weights of the two parties [wA B A B the matrix obtained by multiplication of the vectors of the scores of alternative a:

⎤ u1A (a) ⎥ ⎢ C = uA (a) · uB (a) = ⎣ ... ⎦ u1B (a) ⎡

...

um B (a) .

unA (a) The search for optimal weights of the objectives of both parties is a quadratic maximization problem: max w

1 T w C1 w 2

subject to the following constraints: 1. i i i wA min  wA  wA max ,

i = 1, . . . , n,

j wB min

j = 1, . . . , m.

j  wB

j  wB max ,

2. The sum of the weights of the objectives of each party sum up to one: n  i=1

i wA = 1;

m 

j

wB = 1.

j =1

3. Overall utility of a party is greater than or equal to the utility of that party assured by a reference alternative: & ' & ' UAT (a) UARef (a) 0  . 0 UBT (a) UBRef (a) If there is a feasible solution to this optimization problem, the alternative a will become the new reference alternative, and in case there are no new proposed alternatives, it will be the final negotiation resolution.

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10.7 Experimental evaluation Concepts of the NSS were tested in two types of simulation experiments. The first was performed as simulated negotiations with real actors who played a ‘negotiation game’ based on a case study. Half of the participants performed the exercise with the NSS and the other half without, and the results were compared and statistically analysed. These exercises were limited by the feasible duration of the ‘game’ and by the computer skills of the participants, so that the efficiency of only a part of the NSS features could have been assessed. The second type of experiments were performed with simulated actors in which the initial preference structures were obtained from ‘random participants’ not related to the research, while the remaining dynamics in the systems of preferences of the ‘negotiating parties’ was simulated by the researcher. The aim of these experiments was to test and explore in detail the role and capabilities of the WAS within the framework of the NSS, which was not possible in simulations with real actors. 10.8 Summary and conclusions The Negotiation Support System is designed to assist parties involved in a dispute over international (shared) water resources, with a real or potential water scarcity. It utilizes an economic perspective, which is accepted as a rational criterion for management of scarce resources. The NSS introduces an economically based water allocation optimization model (WAS) into negotiations, with the aim of emphasizing the potential gains to all parties which can result from relating to water in terms of values and not only quantities. We believe that the WAS model, by which the parties can explore the effects of various domestic and international water allocation schemes, contributes to their creativity in searching for alternative negotiation solutions. The NSS includes tools based on the concepts of multi-criteria decision making that enable the negotiating parties to evaluate their systems of preferences and recognize opportunities for tradeoff between differently valued objectives and for joint gains. The parties to negotiation over international waters often tend to lack mutual confidence, which causes them to consider distributive solutions. The proposed protocol of interaction and the iterative manner of negotiation are designed to improve the interaction between the parties and assist them in gradually advancing from distributive win–lose alternatives to alternatives which bring joint gains. The combination of the AHP model for individual decision support and the Nash bargaining solution enables the parties to recognize mutually preferred alternatives, which might otherwise be overlooked. Bibliography Becker, N. and N. Zeitouni (1998). A market solution for the Israeli–Palestinian water dispute. Water Int. 23(4), 238–244. Binmore, K. (1992). Fun and Games: A Text on Game Theory. D.C. Heath and Company. Lexington, MA. Eckstein, Z., D. Zakai, Y. Nachtom and G. Fishelson (1994). The allocation of water sources between Israel, the West Bank and Gaza: An economic viewpoint. Technical report. Tel-Aviv University. Tel Aviv, IL.

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Feitelson, E. and M. Haddad (2001). Management of Shared Groundwater: The Israeli–Palestinian Case with an International Perspective. Kluwer. Boston, MA. Fisher, F., S. Arlosoroff, Z. Eckstein, M. Haddadin, S. Hamati, A. Huber-Lee, A. Jarrar, A. Jayyousi, U. Shamir and H. Wesseling (2002). Optimal water management and conflict resolution: The Middle East water project. Water Resour. Res. 38, 1243–1260. Hipel, W.K., L. Fang and D.M. Kilgour (1993). Game theoretic models in engineering decision making. Journal of Infrastructure Planning and Management 470/IV-20, 1–16. Kronaveter, L. (2005). A negotiation support system for resolution of disputes over international water resources. PhD thesis. Faculty of Civil Engineering, Technion. Haifa, Israel. Nations, United (1997). Convention on the Law of Non-Navigational Uses of International Water Courses. Puri, S. (2001). A framework document: Internationally shared transboundary aquifer resources – their significance and sustainable management. Technical report. UNESCO. Paris, F. Raiffa, H. (1982). The Art and Science of Negotiation. Belknap Press of Harvard University Press. Cambridge, MA. Saaty, T.L. (1980). The Analytic Hierarchy Process. McGraw-Hill. New York, NY. Shamir, U., J. Bear, N. Arad, Y. Gal-Noor, N. Selbst and Y. Vardi (1985). Water Policy for Israel. The Samuel Neaman Institute for Advanced Studies in Science and Technology, Technion-Israel Institute of Technology. Haifa, IL. (in Hebrew, with summary in English.) Thiessen, E.M., D.P. Loucks and J.R. Stedinger (1992). Computer-assisted negotiations of multiobjective water resources conflicts. Water Resour. Bull. 28(1), 163–177. Wolf, A.T. (1995). Hydropolitics Along the Jordan River. United Nations University Press. Tokyo, J. Wolf, A.T., S.B. Yoffe and M. Giordano (2003). International waters: identifying basins at risk. Water Policy 5(1), 29–60.

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CHAPTER 11

Workflow Oriented Participatory Decision Support for Integrated River Basin Planning

Joerg Dietrich1 , Andreas H. Schumann1 and Alexander V. Lotov2 1 Institute for Hydrology and Water Management Ruhr-University Bochum, Germany 2 Department of Higher Mathematics for Economists

State University, Moscow, Russia

11.1 Introduction The Integrated Water Resources Management (IWRM) approach considers water as an integral part of ecosystems, a natural resource and a social and economic good. The European Water Framework Directive (WFD) specifies guidelines for integrated river basin management which are implementing this holistic view by means of a coherent water policy within all member states of the European Union. The WFD sets the goal of a ‘good ecological status’ as the objective of water management in surface waters. This ecological objective should be reached within the year 2015. The WFD also specifies the aim to improve public participation in river basin management planning. The planning cycle of implementation is based on the general scheme of Driving forces, Pressure, State, Impact and Responses (DPSIR) adopted by EEA (1999). A relatively large number of criteria has to be considered for assessing the complex interactions between water and society. Decision support systems (DSS) are appropriate tools for this purpose. Considering the variety of stakeholders (with regard to water everybody is a stakeholder) balancing the interests of various groups could be very difficult. That’s why DSS which are designed to support the implementation of the WFD should be open and interactive usable systems, capable to provide a platform for the public discussions of measures among stakeholders. One approach based on this philosophy is presented in this contribution. From a semantic model of planning and decision making processes, an interactive spatial decision support system (SDSS) was developed. The SDSS was applied for the elaboration of an exemplary river basin management plan for the Werra River basin in central Germany. 207

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11.2 Management options implementing the European Water Framework Directive The WFD specifies the protection of surface waters, transitional waters and groundwater in order to achieve a good ecological and chemical status as the main objective of water management within the EU. The good ecological status is defined in terms of the quality of the biological community, the hydrological characteristics and the chemical characteristics. As no absolute standards for biological quality can be set which apply across the community (caused by the extreme ecological variability within Europe), the targets of planning are specified indirectly. The main objective consists in a slight departure only from the biological community which would be expected in conditions of a minimal anthropogenic impact. As the biological reference conditions vary with the natural character of the surface waters, also the objectives vary spatially. To consider this variability, the WFD specifies ‘water bodies’ as key units for which environmental objectives are set. In Article 2, the directive defines them in the following way: ‘Body of surface water means a discrete and significant element of surface water such as a lake, a reservoir, a stream, river or canal, part of a stream, river or canal, a transitional water or a stretch of coastal water.’ A river basin usually contains a number of ‘water bodies’. For each water body the actual conditions have to be compared with reference conditions which would be necessary to ensure the good ecological status. The significant human pressures and impacts have to be specified which are responsible for gaps between the existing and the demanded good ecological status. According to the DPSIR-scheme presented before, measures to improve the ecological status by modifications of human pressures have to be planned with regard to the different quality elements (Fig. 11.1). The programmes of measures are an essential component of the river basin management plans. They should contain detailed descriptions how the ecological objectives will be reached by 2015.

Fig. 11.1. The causal framework for describing the interactions between society and environment (EEA, 1999) and related planning activities in WFD implementation.

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The general objectives of the WFD are mandatory (‘top down’). However a set of uses which adversely affect the status of water, but which are considered essential on their own terms, are seen as overriding policy objectives. If it can be shown that measures to improve the ecological status are technically impossible, that they would be prohibitively expensive, or that they would produce a worse overall environmental result, exceptions from the general demand are possible. These exceptions could be prolongations of deadlines and even modifications of the objectives if such changes are needed to ensure specific water uses with high socio-economic importance. Obviously the specification of such exceptional cases demands a comprehensive characterisation of all circumstances connected with the specific water utilization. Not only technical, but also socio-economic analyses of the boundary conditions of such human pressures are needed. The local authorities have to take the ‘polluter pays principle’ into account, but they are also encouraged to find the most cost efficient combination of measures. These two basic principles of European environmental policy might be conflicting in specific local situations. Water managers have some freedom to decide about the suitability of measures and their distribution in space and time. They might also address different ‘driving forces’ to take social and economic criteria into consideration. The active involvement of stakeholders in the planning process can influence the negotiation of measures (‘bottom up’), but also strategic political decisions about the RBMP. 11.3 Demand for workflow support and collaborative decision support The demand for planning and decision support implementing the WFD is manifold. First of all, the river basin is subdivided into a number of spatial elements (e.g. water bodies). The interaction between society and environment takes place on different spatial, temporal and functional scales. The object of planning is a natural system which depends on a complex of combining factors (hydro-morphological, physico-chemical and biological conditions). A DSS should be able to handle different temporal scales (e.g. short-term phosphorus peaks during a runoff event affecting the biological quality have to be considered as well as long term effects of socio-economic developments determining the emissions of phosphorous in total. A large variety of data and information has to be considered. These data are provided by different disciplines. Integrated river basin management demands a cooperation of ecologists, hydrologists, water managers, computer scientists and socio-economists (Fig. 11.2). Local measures and regional management strategies have to be planned and synchronized in cooperation with local and regional authorities and stakeholders. Under consideration of their different spatial scales the possible ecological consequences of measures can be assessed based on simulation models or expert knowledge. In some cases monitoring programmes have to be initiated to provide better data and information about the different quality elements. Costs, benefits and possible conflicts have to be estimated with socio-economic methods under different management schemes and under consideration of different baseline scenarios. Decisions about the River Basin Management Plan will be based on an assessment of the cost efficiency of various possible management strategies at river basin scale mainly. The possible exceptions from the environmental objectives at water body scale demand a comprehensive consideration of the socio-economic circumstances as well as the interdependencies within the river network. Setting exceptions at one water body can influ-

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Fig. 11.2. Relationship between the different disciplines in integrated river basin management for the Werra pilot basin. The IT-disciplines (column in the centre) provide services for planners and decision makers.

ence the achievement of the good ecological status of other water bodies (e.g. regarding ecological continuity for long-distance travelling fishes). Here decision makers need aggregated information about possible strategies and their effects. But also the boundary conditions which form the constraints have to be analysed to determine the chances to realize these strategies. The economic importance of existing water and land uses and existing legal restrictions should be known. The negotiation of different proposals for the programme of measures under consideration of ecological, economic and social criteria can be supported by methods of multicriteria decision analysis (MCDA), which have often been applied in water resources management (Nandalal and Simonovic, 2003). These methods can be applied in the WFD implementation in order to explore and reduce the presumably large set of management options according to the preferences of decision makers. The different steps of the decision process developed in the Werra IRBM project are shown schematically in Fig. 11.3. Measures are prepared in the design (or planning) phase, where they are also aggregated into alternatives (= alternative proposals for the programme of measures on basin scale). Decision making is seen as a collaborative process. Thus the exploration of the decision space and the application of a multi-criteria analysis take part in the choice phase. The WFD asks the EU member states to encourage active involvement of all interested parties. Public participation can be supported at different levels: information, consultation or active involvement. Participation demands new tools which ensure transparency within the decision processes. These tools should be able to visualize the different criteria mentioned above in a way that supports the negotiations among stakeholders.

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Fig. 11.3. Phases of a participatory decision making process in integrated river basin management (changed from Malczewski, 2001).

11.4 Tools for decision support in the WFD implementation The design of the spatial decision support system for integrated management of the Werra River basin is based on a central logical model of workflow, objects and methods on the one hand. On the other hand software services are provided to planners, decision makers, administration, NGO’s and stakeholders for support of decentralized collaborative negotiation and decision procedures: • display and analysis of the state of the water bodies, deficits, spatial representations of measures and their consequences using an internet enabled Geographic Information System; • support for access, organization and documentation of the different steps of decision making via an assistant like, internet based, user interface; • multi-criteria exploration of the decision set, setting of a reasonable goal and search for efficient measures close to the goal. The required system interaction demanded a completely new functionality and user interfaces. So the development of the SDSS was started with a comprehensive requirement analysis. The software development followed an incremental, iterative use case driven approach (Fig. 11.4). New use cases according to the required work package were defined incrementally. New functionality was added by iterative refinement of use cases. This software development approach helps synchronizing parallel system analysis tasks

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Fig. 11.4. Incremental and iterative software development process phases. The main products related to workflow and data modelling are written italic.

between interdisciplinary working groups. Changes in EU and national guidance papers for the WFD implementation can also be accounted. The WFD redefines existing water management procedures. Many tasks of river basin management can be seen as business processes: A business process is a collection of activities that takes one or more kinds of input and creates an output that is of value to the customer. A business process has a goal and is affected by events occurring in the external world or in other processes (Hammer and Champy, 1993). Business process modelling is a technique which can be applied to get a clear view on the planning and decision making processes in the WFD implementation. A business process model can be the starting point for the development of a decision support system. The Unified Modelling Language (UML, Booch et al., 1997) is an industry standard to support a model driven software development approach. Eriksson and Penker (2000) extended the UML with business process modelling capabilities. For modelling business processes and workflow, use cases are specified in detail in activity diagrams. These diagrams were significantly revised in the latest UML 2.0 standard, which was used in the Werra project. The example in Fig. 11.5 shows an activity ‘Setting exceptions for economic reasons’. From the activity start, a sequence of actions is connected with action flows. Decision points with guard conditions direct the flow through the activity (imagine tokens following the flow). Expansion regions allow the iterative treatment of a collection of inputs, e.g. for the redefinition of objectives for multiple water bodies. Activity models for ecological assessment, planning of measures and for decision processes have been developed in corporation of the Werra IRBM project partners. The models allowed all partners to evolve and communicate a clear logical view on the workflow of river basin managers and decision makers – not only from the software point of view, but also as a general business process model of parts of the WFD implementation. The use of complex physical models and interdisciplinary assessment tools is not practicable in a participatory decision process. One option to support the negotiation of a

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Fig. 11.5. UML activity diagram showing an exemplary workflow for the socio-economic assessment of the total costs of the program of measures.

consensus is an interactive collaborative exploration of the variety of possible decision alternatives by administration and stakeholders (‘explore, what is possible’), e.g. during a focus group meeting. Here the preferences of decision makers may not be defined a priori. Instead of modelling in the decision phase, a database of measures and strategies was prepared during the previous planning phase, spanning a discrete set of feasible decision vectors. The object model proposed by the European Commission working group (CIS, 2002) was extended to integrate and link socio-economic and management aspects (e.g. census data, agro-economic statistics, database of measures and strategies). The database of measures can be interactively filtered in several steps: • set restrictions (e.g. budget maximum), • explore only strategies responding to specific elements of the DPSIR scheme, • analyse the consequences of setting exceptions, • set exceptions like heavily modified water bodies, less stringent objectives, extension of deadlines, • start a multi-criteria analysis. When a filter is applied, the set of selected strategies is dynamically reduced. At this stage of the decision support process the relationships between the different objects and scales are evaluated (Fig. 11.6). Finally, a decision matrix is computed from the actually selected subset of strategies. 11.5 Interactive multi-criteria decision analysis To select the most cost-efficient, ecologically effective management strategy, a multicriteria visualisation-based decision and negotiation support technique, named the Rea-

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Fig. 11.6. Conceptual object model of the spatial information system. The decision matrix will be dynamically computed from the measure and strategy classes according to the users’ preliminary filtering of the database.

Fig. 11.7. General workflow of the RGM / IDM method (changed from Lotov et al., 1997).

sonable Goal Method/Interactive Decision Map (RGM / IDM) technique, is applied. In the framework of the technique, it is assumed that the decision alternatives (strategies) are given in the form of rows of a rectangular table (matrix), whose columns contain selection criteria. The rows of the matrix (that is, strategies) are associated with points in criterion space. The technique is based on approximation of the convex hull of the criterion points and subsequent interactive visualization of its Pareto frontier. To be precise, the maximal set is approximated that has the same Pareto frontier as the convex hull of criterion points (Convex Edgeworth-Pareto Hull, CEPH). Approximation of the CEPH is carried out to simplify the visualization of the Pareto frontier. Exploration of the Pareto frontier helps user to understand the criterion tradeoffs and to identify a preferred criterion point directly at the Pareto frontier (the goal point). Since user explores the Pareto frontier of the convex hull, the goal is usually not feasible. However, it is close to the set of criterion points; therefore it is denoted as the reasonable goal. Several criterion points that are close to the identified goal and related decision alternatives are selected by computer and used for further detailed discussion (see Fig. 11.7).

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Fig. 11.8. Criterion points related to decision alternatives.

Let us provide a more detailed informal introduction of the RGM / IDM technique. Mathematical description of the technique along with its applications is considered in the book by Lotov et al. (2004a). We illustrate the technique by a water management example, in the framework of which decision alternatives (strategies) are given by such attributes as cost, conflicts, residual pollution, etc. We begin with the case when only two attributes are used as choice criteria, namely cost of the strategy and resulting conflicts. Though the use of the RGM / IDM technique is not particularly advantageous in the case of two criteria, we use it anyway to explain the fundamentals of the technique. In Fig. 11.8, about two dozens of strategies are depicted by points and crosses in the criterion plane (cost and conflicts plane, in this example). Non-dominated (Pareto) points, from which the decision must be selected, are given by crosses. Since the number of decision criteria (in the above example) is two, Fig. 11.8 provides full information about the variety of alternatives. However, one is unable to construct a similar graph for the case of three, four, five and more criteria, and so a different graphic technique must be used. In the IDM technique, the frontier of the Convex EdgeworthPareto Hull (CEPH) is displayed instead of points in Fig. 11.9. Convex hull also includes artificial criterion points, which help to explore the properties of the variety of feasible alternatives. Since the user is interested in minimizing both cost and conflicts, the ‘south-western’ frontier of the convex hull should be of interest (curve ABC in Fig. 11.9). This part of the frontier is denoted as the Pareto (efficiency, non-dominated) frontier of the convex hull. The Pareto frontier shows the efficient (criterion) tradeoffs between two criteria: how much the increment of cost is related to the decrement of conflicts if points from the convex hull are used. At the same time, the Pareto frontier of the convex hull roughly describes location of the non-dominated criterion points for the variety of original feasible alternatives, and so it can be considered as the proxy efficient (criterion) tradeoff curve for feasible alternatives. Note that the notion of the efficient (criterion) tradeoff differs from the notion of the value tradeoff, which is related to preferences and which means the subjective compensation of losses in one criterion by gains in another. After the exploration of the Pareto frontier is completed, user has to identify a preferable combination of criterion values, which belongs to the Pareto frontier of the CEPH (the reasonable goal). In the case of two criteria, it can be done at the graph of the CEPH. In Fig. 11.10, the identified reasonable goal is displayed by a small circle. It is important to

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Fig. 11.9. Convex Edgeworth-Pareto Hull.

Fig. 11.10. The reasonable goal.

note that user does not need to be involved in complicated interactive procedures aimed at eliciting his/her preferences. Instead, user can identify the most preferable criterion point (the goal) after visual inspecting the Pareto frontier. It is assumed that user will identify the goal consciously, in accordance with his/her preferences. In contrast to other goal-based methods, the RGM / IDM technique restricts the identification of the goal to the Pareto frontier of the convex hull. Due to this, the identified goal is close to feasible points. Since the goal is identified on the graph, which displays the Pareto frontier of the CEPH , the goal is likely to coincide with feasible points only occasionally. For this reason, a computer algorithm is used to select several non-dominated feasible points, which are close to the identified goal. The selected points (and the corresponding alternatives) are of interest to user since they reflect both his/her subjective preferences expressed in the form of the goal and the objective situation represented by the criterion points. The short list of selected alternatives may be studied by other tools. Say, spatial alternatives can be visualized on thematic maps. They can be displayed to user by photos and films, too. Actually, all multimedia tools can be used to support selecting from the short list. If more than two attributes are used as the screening criteria, the IDM technique is used to generate and display tradeoffs among the criteria. Let us first include the third attribute, say, residual pollution into the list of decision criteria. It is expected that user prefers to

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Fig. 11.11. Decision map.

decrease pollution. To include pollution into the analysis, let us approximate the CEPH of the criterion points in the three-dimensional criterion space. Then two-criterion slices of the CEPH can be displayed to user. Each of them looks as the CEPH given in Fig. 11.11 and is related to a certain value of pollution in the following sense: its frontier displays a tradeoff among cost and conflicts if pollution is not greater than its given value. Such differently coloured two-criterion slices of the CEPH are superimposed one over another. Fig. 11.11 provides an example of the graph that contains five two-criterion slices related to five different pollution values. A pollution value is related to a certain colour of the slice provided on display (to a certain shading in Fig. 11.11). Note that the frontiers of these slices do not intersect, and so the graph is fairly simple to interpret. The graphs of this type, which display the Pareto frontier for two criteria depending on the value of the third one, are called the decision maps. Changing one frontier for another, one can see how constraints imposed on the value of the ‘third’ criterion influence the criterion tradeoff curve among the initial two criteria. Remember that this information is provided for the convex hull of criterion points. So, the decision map displays efficient criterion tradeoffs among three criteria for the convex hull. Due to it, the decision map at Fig. 11.11 informs roughly about the influence of the value of pollution on the tradeoffs among cost and conflicts for the set of criterion points. In the RGM / IDM technique, the decision maps for three and more criteria are displayed on-line. The most important feature of the technique is related to the way of how decision maps are computed in the case of three, four, five and more selection criteria: the CEPH is approximated in advance for the entire set of criteria under consideration (three to eight criteria can be studied). Then, several two-dimensional slices of the CEPH related to several equidistant values of the third criterion (and fixed values of other criteria in the four and more criterion case) are computed and superimposed. They provide decision maps such as given in Fig. 11.11. Since the CEPH is approximated in advance, various decision maps may be displayed on request very fast. Hundreds of decision maps related to various values of the fourth and fifth criterion can be computed and displayed in a matter of few seconds. By this, animation of decision maps is possible. This option is very important in the case of four and more criteria. The information on the Pareto frontier displayed by the IDM technique helps user to identify a preferable goal. The goal is identified on a decision map (specified by user) by a simple click of the computer mouse. After a moment, a short list of non-dominated

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alternatives, which are close to the identified goal, is constructed and displayed to the user. Various procedures for selecting of the goal-proximate alternatives can be used, and so we do not describe them. One particular selection procedure is given in the book of Lotov et al. (2004a). It is clear that, in the framework of the RGM / IDM technique, the approximation of the CEPH and its exploration may be easily separated in time and space. This feature of the technique can be effectively used in its Web applications. 11.6 Results from the Werra pilot study In the joint research project introduced in Fig. 11.2, a collaborative spatial decision support system was developed for the integrated management of the Werra River basin following the approach described above. The system architecture is shown in Fig. 11.12. A DSS client application provides assistance for the iterative filtering of the database of measures and the dynamic calculation of a decision matrix. The SDSS implements the RGM / IDM technique in the form of an application server (RGDB-Server, a detailed description of the RGM / IDM technique in Web is given in Lotov et al., 2004b). The calculation server constructs an approximation of the CEPH from the decision matrix. The graphic presentation window is a Java applet executed at the client computer, which displays the Pareto frontier in the form of decision maps and helps the users to negotiate a common goal point. Then, the applet transmits the goal to the server, and the server returns the selected rows to user. The system was spatially enabled using ESRI enterprise GIS technology. Deviations from the good ecological status of the Werra River and its main tributaries are mainly caused by deficits of the hydro-morphological conditions and of the trophic status. Recently developed tools for type specific ecological assessments of river reaches (e.g. AQEM, Hering et al., 2004), a hydrological model (SWAT, Neitsch et al., 2001) and two water quality models were applied by the three environmental subprojects in order to design and optimize measures. Several combinations of measures were aggregated to strategies, which could achieve the environmental objectives after implementation. All information needed by and produced by all planners were organized in a modelled spatial database and can be accessed via the SDSS (Fig. 11.13). Pilot focus groups initiated by local water management authorities were accompanied by the socio-economy subproject. Socio-economic constraints like existing water use rights, which cannot be compensated (e.g. small hydropower plants) and small farms, which cannot abandon their land, were considered in the planning phase.

Fig. 11.12. Implementation of the RGM / IDM technique in Web.

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Table 11.1 lists four representative strategies and their socio-economic assessment. The following socio-economic criteria were calculated (for a detailed discussion see Hirschfeld et al., 2005): • costs: estimated from prior studies or technical guidance papers; • benefits: use and non-use values of the river ecosystem, e.g. tourism, biodiversity which are promoted implementing the WFD (calculated with benefit transfer method for a 50 years project duration with declining use value);

Fig. 11.13. User interface of the prototype of the interactive spatial decision support system for integrated management of the Werra River basin.

Table 11.1. Strategies for the programme of measures developed in the Werra IRBM project. Strategy

Cost [mill. €] 94.2

Reduction of nutrient emissions from point sources where possible, additionally from diffuse sources, morphological measures Reduction of nutrient emissions from diffuse 96.6 sources where possible, additionally from point sources, morphological measures Distribution of measures for nutrient reduc- 97.6 tion according to the polluter pays principle on water body scale, morphological measures Most cost-efficient measures for nutrient re- 97.0 duction, polluter pays principle on river basin scale via nutrient emission trading, morphological measures

Benefit [mill. €] 104.3

Cooperation [–] 0.63

112.1

0.47

118.1

1.24

127.2

0.54

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• cooperation: an index was calculated from actors analysis, cost recovery and other ‘soft’ socio-economic criteria related to stakeholders. This criterion expresses the relative possibility of cooperation among stakeholders and with river basin managers for each strategy (as a positive formulation of ‘conflicts’, the highest level of cooperation is expressed by a criterion value of 0). 11.7 Conclusion The implementation of the Water Framework Directive in the EU is a new task of policy for many water authorities, coinciding or even conflicting with spatial planning. Based on the traditional planning approach decision makers implementing the WFD by measures would mainly consider the cost–efficiency of the combinations of measures. Hence it would follow that the WFD contains no multi-criteria problem. In the real world planning is much more complicated as multiple social and economic criteria have to be considered within political planning and decision making processes. Within the Werra River Basin Management Project such criteria were considered explicitly with the main aim to bring together the top-down approach of the European framework legislation and the bottom-up approach of active involvement of stakeholders in regional aspects of river basin management planning. Further more, the placement of exceptions due to budget restriction should be directed by the best ecological and economic benefit. Multi-criteria methods allow water resources managers to search for efficient measures, which take into account ecological and socio-economic criteria according to the preferences of decision makers including stakeholders. Learning based interactive methods provide a suitable solution for collaborative participatory decision making in a dynamic decision environment like the implementation of a new directive. With regard to the WFD especially ecological assessment tools used to specify the ecological status and tools to predict the effects of changing quality elements on the ecological status are subject to uncertainty. Here the uncertainty of the planned strategies, resulting from model uncertainties, unknown socio-economic developments, etc. were not considered explicitly. To give a qualitative assessment of it, the relative certainty of the planning results was expressed for each strategy. Further research has to be done for a more detailed assessment of the planning uncertainty as well as for an extension of the RGM / IDM technique to apply the Pareto principle also on uncertain criteria. Simulation models and tools for environmental assessment were not integrated in the SDSS due to performance issues and a demand for reducing the complexity of the participatory negotiation and decision making process. This might limit the application of the SDSS , because the decision space is limited by the prepared database of measures. Thus the generation of measures and strategies was one of the most critical tasks of the project. Further research should be done in the development of scenario generators, which could produce a large amount of alternatives in a semi-automatic process, and meta-models, which could be integrated in an SDSS without the performance issues of numerical models. An incremental and iterative software development process is a suitable way to cope with rapidly changing requirements of river basin managers during the implementation of the WFD. Formal models of workflow and objects allow a detailed discussion between water management experts and system analysts. They can further be used as a standard

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template for the description of river basin managers’ business processes and the model based development of software solutions supporting these complex processes. Acknowledgements We thank all participants of the Werra River Basin Management project for their input, especially the cooperating partners Federal State of Hesse, Free State of Thuringia and Flussgebietsgemeinschaft Weser, who provided a huge amount of data and knowledge about business processes of the responsible authorities. The German Federal Ministry of Education and Research (BMBF) is acknowledged for financial support of the project. Bibliography Booch, G., J. Rumbaugh and I. Jacobson (1997). Unified Modelling Language User Guide. Addison Wesley. CIS Common Implementation Strategy Working Group 3.1 GIS (2002). Guidance document on implementing the GIS elements of the WFD, 04-12-2002. Eriksson, H.-E. and M. Penker (2000). Business Modelling with UML. Business Patterns at Work. John Wiley. New York, NY. European Environment Agency (1999). Environmental indicators: Typology and overview. Technical Report 25. EEA. Hammer, M. and J. Champy (1993). Reengineering the Corporation: A Manifesto for Business Revolution. HarperBusiness. New York, NY. Hering, D., O. Moog, L. Sandin and P.F.M. Verdonschot (2004). Overview and application of the aqem assessment system. Hydrobiologia 516(1–3), 1–20. Hirschfeld, J., A. Dehnhardt and J. Dietrich (2005). Socioeconomic analysis within an interdisciplinary spatial decision support system for an integrated management of the Werra River basin. Limnologica 35(3), 234–244. Lotov, A.V., A.A. Kistanov and A.D. Zaitsev (2004a). Visualization-based data mining tool and its web application. In: Data Mining and Knowledge Management (Y. Shi, W. Xu and Z. Chen, Eds.). Vol. 3327 of Lecture Notes in Artificial Intelligence. Chinese Academy of Sciences Symposium CASDMKD 2004, Beijing, China, July 12–14, 2004. Springer-Verlag, Berlin. pp. 1–10. Lotov, A.V., V.A. Bushenkov and G.K. Kamenev (2004b). Interactive Decision Maps. Approximation and Visualization of Pareto Frontier. Kluwer Academic Publishers. Boston, MA. Lotov, A.V., V.A. Bushenkov, A.V. Chernov, D.V. Gusev and G.K. Kamenev (1997). Internet, GIS and Interactive Decision Maps. J. Geogr. Inform. Decis. Anal. 1(2), 118–149. Malczewski, J. (2001). GIS and Multicriteria Decision Analysis. John Wiley. New York, NY. Nandalal, K.D.W. and S.P. Simonovic (2003). State-of-the-art report on systems analysis methods for resolution of conflicts in water resources management. Technical documents in hydrology. Technical Report PC-CP Series No. 4. UNESCO IHP. Neitsch, S.L., J.G. Arnold, J.R. Kiniry and J.R. Williams (2001). Soil and water assessment tool, theoretical documentation. Technical Report Version 2000. Temple, Texas.

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CHAPTER 12

Comprehensive Testing and Application of the PIP Procedure: the Verbano Project Case Study Andrea Castelletti1 , Francesca Cellina2 , Rodolfo Soncini-Sessa1 and Enrico Weber1 1 Dipartimento di Elettronica e Informazione

Politecnico di Milano, Milano, Italy 2 POLIEDRA

Politecnico di Milano, Milano, Italy

12.1 Introduction Lake Verbano, also known as Lake Maggiore, is a natural lake located south of the Alps between Italy and Switzerland (Fig. 12.1). It is the most important water system of the sub-alpine area on account of its multiple – occasionally conflicting – socioeconomic uses. Its large alpine watershed (6600 km2 ) is characterized by extremely variable weather conditions, which cause important outbreaks of flood and drought periods of both the lake and its outflow – the River Ticino – with consequent substantial damages to the socio-economic systems. The Miorina dam, built by Italy in 1943 to meet the needs of the downstream water users, regulates the lake outflow. An international agreement, signed in the same years, states that the Release Manager (RM) can operate the dam arbitrarily only when the lake water level is between −0.5 and +1.0 meters in summer, and between −0.5 and +1.5 meters in winter. When the upper bound of this range is reached, the RM is obliged to completely open the dam gates, thus allowing the maximum possible outflow1 , with the aim of reducing the risk of flooding on the lake’s shores. The downstream interests are on one hand related to the agricultural activities of two important farmer leagues (Est-Sesia and Villoresi), and on the other to the hydropower generation needs (three hydroelectric and one thermal power stations). The water demand for hydropower does not show distinctive seasonal fluctuations, while a seasonal peak (between April and September) characterizes the water demand for agriculture. As the inflow rises, the RM increases the water storage in order to create a water reserve to supply the downstream demand in the 1 Note that, when the dam was built, the lake outlet was excavated to increase the outflow capacity.

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Fig. 12.1. The Lake Verbano water system.

low inflow periods. However, when the inflow rises, an increase in the probability of extreme meteorological events is expected. Therefore, the satisfaction of the downstream users implies an increase of flooding risk for both the Swiss and Italian communities living by the lake and the river shores. According to the ends of the Italian–Swiss agreement of 1943, the introduction of a time-variant regulation range should have addressed all the concerns of the lake shoreline communities with respect to the risk of flood, especially on the Swiss side. However, it is common opinion among these communities, particularly in the Swiss city of Locarno, that the regulation of the lake has increased the flood frequency and intensity. The disastrous flood events in 1993 and 2000 sharpened the population sensitivity to the problem, and the requests for resolute intervention became ever more insistent. The Swiss authorities replied to these requests by devising some proposals, in the following denoted as structural actions, aimed at increasing the outflow capacity by dredging the outlet, so that in flood conditions the lake could be emptied more quickly. The Swiss proposals, however, did not encounter the agreement of the Italian party, as they do not bring any advantage for the downstream users, while enhancing the risk of flooding for the populations on the River Ticino. The Italian farmer leagues in their turn suggested accompanying the Swiss proposal with a modification of the regulation range, which would allow the RM to regulate the lake up to a level of +1.50 meters even in the summer period, thus reducing the

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risk of water deficit for the downstream users. Such an action (in the following denoted as normative action) can be therefore regarded as a second action, complementary to the structural one. Nevertheless, it is not supported by the lake shoreline population, which fears once again flooding. To overcome this difficulty and avoid an uncontrolled increase of the lake level, the decisional freedom of the RM can be reduced with a suitable regulation policy, i.e. a rule that every day specifies the amount of water to be released as a function of the lake level. The definition of such a policy is a third possible action we will refer to in the following as regulatory action. With the purpose of exploring whether any combination of the aforementioned actions (that in the following we will denote as alternative) might be suitable for addressing the conflict among the different water uses/users, the Verbano Project was funded at the end of 1999, within the INTERREG II EU framework. The project gave us the opportunity to follow the adage ‘practice what you preach’ and apply the Participatory and Integrated Planning procedure (PIP) – theoretically framed in Ch. 1 of this book – to the Verbano Project, in order to support the decision-making process accordingly with the requirements of the Water Framework Directive (WFD) and the Integrated Water Resource Management (IWRM) paradigm. Two issues make the Project extremely challenging and significantly more complicated than the common planning tasks: the combined presence of planning and management decisions, due to the highly dynamical nature of the water system, and its transboundary position, which results in the presence of more than one decision maker (DM). In what follows we will assume that the reader knows the PIP procedure and we will present how it has been instantiated in the Verbano Project at hand, by following phase by phase its logic flow (see Fig. 12.2) and describing the activities carried out within each phase2 . 12.2 Phase 0 – Reconnaissance The above considerations should have already given an idea of the Goal of the Verbano Project. Formally, this can be formulated as: ‘to evaluate the actions proposed by the parties in a integrated way’, i.e. ‘to assess and analyse the effects they would produce on the whole system, and to identify the alternatives to be submitted to the decision makers (DMs) for the final decision, together with the list of the stakeholders supporting and opposing each one of them’. The DMs are the Governments of Italy and Switzerland, which will negotiate the final (political) decision. However, when proposing the final decision, each DM is sensible to the viewpoint of the stakeholder group she represents. Therefore the stakeholders might influence the final political choice by indicating the alternative (or the set of alternatives) that best fits their concerns. The Lake Verbano stakeholders are numerous: in addition to the lacustrine and riverine communities, the farmer leagues and the hydropower company, one may consider the navigation company, the fishermen, the tourist operators, one natural reserve located at the top of the lake and two natural parks placed along the downstream River Ticino. The 2 A comprehensive and exhaustive description of the Verbano Project can be found in Soncini-Sessa et al. (2007b).

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0. Reconnaissance

1. Defining Actions

2. Defining Criteria and Indicators

3. Identifying the Model CONCEPTUALIZATION

4. Designing Alternatives

8. Mitigation and Compensation

5. Estimating Effects

6. Evaluation

7. Comparison NO

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9. Final decision

Best compromise alternative

Fig. 12.2. The phases of the PIP procedure.

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stakeholders that share the same interests are grouped tentatively in a sector3 , however this does not mean that stakeholders that are affected by the same problem form a group. For example, the fluctuation of the lake induced by the regulation is often responsible for a seasonal mosquitoes proliferation. These cause annoyance to both the lake shoreline population and the tourists, thus resulting in a potential income loss for tourist operators. However tourist operators and lake shoreline communities do not constitute a sector, because they value the effects of mosquitoes from a different viewpoint: on the one side in terms of the monetary loss due to the decrease of tourists and on the other side as a nuisance. It is worthwhile to keep in separate sectors interests that are quite different in nature: e.g., the lake shoreline population is affected by the lake flooding and mosquitoes, but the damage caused by the first is incommensurable larger than the one produced by the seconds, and therefore two different sectors have to be considered for them. A list of the project’s stakeholders and sectors is shown in Fig. 12.3. 12.3 Phase 1 – Defining Actions Some of the (meta-)4 actions proposed within the Project have already been introduced above. Namely, the dredging of the lake outlet, the modification of the regulation range, and the modification of the regulation policy. However, in the phase of Reconnaissance another significant proposal emerged: the revision of the existing Minimum Environmental Flow (MEF) value that was proposed by the downstream natural parks, which care for the environmental quality5 of the River Ticino downstream of the lake. Once defined, each (meta-) action must be instantiated, i.e. the values that it may assume should be clearly defined. For example three values were considered for the structural action: ‘leaving things as they presently are’ (the business-as-usual option, labelled in the following as ‘0’), and two levels of dredging that would modify the stage-discharge function at the lake outlet as shown in Fig. 12.4, and are labelled as ‘+300’and ‘+600’ according to the increase of lake outflow they would produce at a given reference lake level. A regulatory action is implemented by means of a regulation policy, that is designed, as we will see in Phase 4, by solving a Multi-Objective Optimal Control Problem (MOOCP). A policy is univocally associated to a point of the Pareto frontier that is obtained by solving the MOOCP and it is therefore univocally specified (instantiated) by the parameters that characterize that point (weights or constraints). In order to consider the full range of regulatory actions, all the possible combinations of parameters (weights or constraint values) have to be explored. Designing an alternative means selecting a coordinated mix of a structural action, a couple of normative actions (regulation range and MEF) and a regulatory action (i.e. a regulation policy). The alternatives considered in the Project were obtained by combining in all the possible ways the values that each one of the actions 3 The introduction of ‘sectors’ proves to be quite useful in the next phases of the procedure, because it allows a significant reduction of the variables to be considered during the Comparison (Phase 7) and simplifies the interaction with the stakeholders, especially in the more technical phases. However only in the phase of Evaluation (Phase 6) it is possible to check the consistency of the sectors’ definition adopted in the current phase. A more detailed and technical description of the concept of ‘sector’ and of its use can be found in Soncini-Sessa et al. (2007a, Ch. 3). 4 The difference between ‘action’ and ‘meta-action’ is explained in Section 1.3.2. 5 Nowadays actions concerning the water quality status would not be optional in Europe, as they are imposed by the WFD, but the Project started (1999) before the directive came in force (2000).

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Fig. 12.3. Stakeholders, sectors and evaluation (sector) criteria of the Verbano Project.

can assume. In this way the action tree of Fig. 12.5 was generated, where each branch between the root and a leaf node (a policy) constitutes an alternative. 12.4 Phase 2 – Defining Criteria and Indicators Once the stakeholders are identified and agree on the definition of the Goal of the Project, they are asked to specify the criterion (evaluation criterion) with which they would judge the performance of an alternative from their own viewpoint. Due to the high number of stakeholders involved in the Project this operation was not carried out separately for each stakeholder, but sector-by-sector, thus obtaining as many evaluation criteria as the sectors individuated in Phase 0 (see Fig. 12.3). In order to be used within the PIP procedure, every evaluation (sector) criterion needs to be associated with a value (an index) expressing the degree to which the criterion is satisfied. Since the sector criterion is characterised by an high level of abstraction, it was not possible to obtain the indexes directly by interviewing the stakeholders. Thus for

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3500 3000

3

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2500 2000 1500 1000 500 0 −0.5

0

0.5

1

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4

Fig. 12.4. The stage-discharge functions that would be produced by the three structural actions ‘0’ (dashed line), ‘+300’ (continuous line) and ‘+600’ (dot-dashed line).

Fig. 12.5. The actions considered within the Verbano Project.

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Fig. 12.6. The evaluation hierarchy for the Irrigation sector.

each sector the corresponding criterion was resolved into lower level criteria and these in turn into other lower level criteria up to the point that the stakeholders were able to associate an indicator – i.e. a function of the trajectories of the variables describing the system condition – to each one of the criteria at the lowest level. In this way a hierarchy of criteria (evaluation hierarchy) was obtained for each sector. An example of evaluation hierarchy is given in Fig. 12.6, in which the hierarchy of the Irrigation sector is depicted: the sector criterion is the ‘farmers’ income’, which increases with the ‘harvest’ and decreases with the ‘costs of water distribution’. If the harvest, i.e. the biomass of the harvested crop, could have been computed by a mathematical model of the crop growth, the harvest would have been a leaf-criterion and the annual average biomass produced would have been the corresponding indicator. However growth models are very complex (high state dimensionality) and therefore they are not suitable for the design of regulation policies (see Soncini-Sessa et al., 2007a, Ch. 12). As a consequence the harvest had to be subdivided into lower level criteria, for which easier computable indicators were devisable. These criteria were identified by analysing the crop growth model proposed by FAO (FAO, 1986 and 1994), which allowed understanding that the water supply deficit and the crop stress drive the value of the harvest. Thus, they were added to the hierarchy as leaf-criteria, since they can be transformed into indicators. For example, the following indicator quantified the water supply deficit in the irrigation district managed by the Est-Sesia Farmer League ES iirr =

+ 1  ES wt − qtES , H

(12.1)

t∈H

where qtES is the water supplied to the irrigation district on the day t, wtES is the water demand of the same day, and H is the evaluation horizon (25 years), over which the effects of the alternatives are evaluated. The water demand {wtES }1,...,|H | represents a parameter that had to be defined over the entire evaluation horizon H . It has been provided by the farmers and reflects their current water needs, thus can be considered as an element of the project scenario. Eventually 53 indicators were defined for the 11 sectors.

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12.5 Phase 3 – Identifying the Model To compute the values of the indicators with respect to a given alternative, the trajectories of the system variables that such an alternative would produce have to be determined. They can be obtained by simulating the system behaviour under the assumption that the alternative is implemented. To accomplish this task the models of the single system’s components (the catchment, the lake, the distribution network, the irrigation district, the power plants, etc.) were aggregated to form a model of the whole system (Fig. 12.7). This model is dynamical and stochastic, it takes as inputs the alternative, whose effects are being evaluated, and the disturbances (i.e. the inflows to lake), and gives as output the lake level, the release and the water flows both in the distribution network and in the River Ticino. Different modelling approaches have been used to describe the different components, depending both on the type of processes taking place in each of them and on the data available. For instance, the catchment has been described by means of an autoregressive stochastic model, the lake and the distribution network with simple

Lake Verbano

Po

catchment diversion reservoir

power plant

junction

Fig. 12.7. The model of the Verbano water system as an aggregation of single components.

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mechanistic models, while the flood propagation along the River Ticino with a neural network. The model identification process has been carried out in strict collaboration with the stakeholders. 12.6 Phase 4 – Designing the Alternatives As already said, the actions identified in Phase 1 are combined in all the possible ways to produce the set of the alternatives to be evaluated. Given a couple of structural and normative actions the efficient regulation policies are designed by formulating and solving a stochastic MOOCP. The stochasticity is the effect of the lake inflow, which is described as a stochastic process. As a straightforward consequence also the indicators identified in Phase 2 are stochastic variables and therefore a statistic was applied to them in order to obtain the objectives of the MOOCP. Moreover, in order to make the computation times for the solution of the problem acceptable, only a subset of the indicators identified in Phase 2 was considered to formalize the problem objectives. The statistic and the indicators were chosen in collaboration with the stakeholders, who, stimulated through interviews and decision support tools based on proper communication techniques, proposed to filter the stochasticity through the expected value (Laplace criterion) and selected some indicators of the following sectors: Lake Flood, River Environment, Irrigation and Hydropower generation. The Italian law (the Galli’s act) states the priority of environment protection, flood control and irrigation with respect to the hydropower generation. This suggested to use a lexicographic approach to design the regulation policy: a primary control problem was solved considering the objectives from the first three sectors, and a secondary problem was then formulated considering only the hydropower generation. For each given pair of structural and normative actions this cascade MOOCP was solved6 many times by varying the weights of the objectives, in order to obtain the Pareto frontier for that pair. By considering all the combinations of structural and normative actions, and by discretizing the Pareto frontier, 195 alternatives were designed in two phases7 (see page 237). 12.7 Phase 5 – Estimating Effects With the model of the system the system behaviour was simulated over the entire evaluation horizon for each alternative. The trajectories so obtained allowed computing the values of the 53 indicators for each one of the alternatives. The simulations were performed using the historic scenario (catchment inflow and water demands for farming and electricity generation), as suggested by the stakeholders, since they were only able to value the effects of the alternatives under the conditions which had already taken place in 6 The algorithm ASA (White, 1963) based on Stochastic Dynamic Programming was used. 7 The adoption of the weight method for solving the MOOCP was imposed by the form of the objective that

were obtained by using the Laplace criterion. This method provides the so-called supported alternatives (see Lotov et al., 2004) that cover the whole Pareto frontier only when the set of the feasible alternatives in the objective space is convex. Due to the non-linearities of both the model and the objectives it was not possible to prove mathematically the satisfaction of this property. Therefore it cannot be formally stated that the full range of regulatory actions was actually considered, but a visual inspection of the elements of the above mentioned set gave the feeling that it was indeed. The inspection can be greatly facilitated by using the Iteractive Decision Maps proposed in the above mentioned book (Ch. 7).

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the past. The indicators were then validated, by checking if their variations were significantly greater than the precision of the model by which they had been computed and by testing if they were properly describing the phenomenon they were expected to: a couple of indicators did not pass the test. These were the indicators for the River floods sector, whose values were estimated by means of a neural network model of the flood propagation along the River Ticino. Since the precision of the model turned out to be less than the difference among the values of the indicators, the indicators could not be regarded as representative of the effects of the alternatives. For this reason, the sector River floods was temporarily kept out of the decision-making process; however, detailed analysis of the effects on the River floods sector was accomplished in the Mitigation phase, focusing on the limited group of the reasonable alternatives (more details can be found in Soncini-Sessa et al., 2007b). Thereafter a correlation analysis between all couples of the indicators was carried out to test if the indicators used to define the objectives of the MOOCP were good representatives of the whole set of indicators. The reply was positive. The final product of the phase was a Matrix of the effects that shows the value assumed by each indicator for each one of the alternatives (see upper part of Fig. 12.8). 12.8 Phase 6 – Evaluation The Evaluation of the alternatives was performed according to the strict Multi Attribute Value Theory (Keeney and Raiffa, 1976), with the active participation of the stakeholders involved. The physical indicators in the Matrix of the effects were translated into dimensionless numbers by specifying a partial value function that was identified by means of interviews to the stakeholders (see lower part of Fig. 12.8). Once the mutual preferential independence [ibidem] within the set of indicators was verified, the partial value functions within each sector were linearly aggregated to form a dimensionless sector index, namely the index mentioned in Phase 2. Both the partial value functions and the aggregation weights were suggested by the stakeholders themselves, being supported by ad hoc prototypical software tools. An example of these functions is shown in Fig. 12.9 for the case of the sector Lake Environment. In this way the Matrix of the effects is transformed into the Matrix of values, which has on the rows the sector indexes and on the columns the alternatives (see Fig. 12.10). Since the sector indexes were determined sector by sector working with the stakeholder representing each sector, in order to increase the group’s perception of the problems posed by the whole system, a common knowledge base was created through an open workshop. During this workshop every stakeholder was invited to explain the others the meaning of the sector indexes he had identified and the reasons supporting his/her evaluation. For example, the municipality of Locarno explained why 2 km2 of flooded area are definitively worse than 1 km2 , by comparing pictures of the same street in these two conditions (see Fig. 12.11). The images and charts they used to make their point proved to be particularly helpful to the audience. 12.9 Phase 7 – Comparison Once all the alternatives generated have been evaluated, the next step is to choose among them the best compromise alternative. With a single DM this operation can be easily issued

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Fig. 12.8. An excerpt of the rows of the evaluation and partial value matrices corresponding to the sector Lake Environment. The code denoting each indicator is composed by the Italian acronym of the sector (AmbM = LakeEnvironment) and by a number that identifies the different indicators: (1) Distance between regulated and natural lake regime; (2) Mean annual number of days in which the lake level is in the range of the reed bed erosion; (3) Fraction of the spawning period in which the Cyprinids cannot access the reed beds; (4) Fraction of the nesting period in which the lake level is higher than the threshold of the nests; (5) Fraction of the normal period of emersion of the shores in which the lake level is higher than the threshold of emersion.

in two steps: the DM expresses her preferences among the sectors by means of weights, on the basis of which the sector indexes are aggregated to form a single index for each alternative. The alternatives may be then sorted from the most to the least desirable. The first alternative of the ranking is the best compromise alternative. However, as we have already outlined, in the Verbano Project there are two DMs and the final decision has to be negotiated between the Governments of Italy and Switzerland. During the negotiation, the two Governments may be driven and strongly supported by the knowledge of the stakeholders preferences. For this reason, they should know which alternative(s) is (are)

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Fig. 12.9. The partial value functions for the indicators of the sector Lake Environment. For the meaning of the indicator code see Fig. 12.8.

SECTORS Lake environment

ALTERNATIVES A22

A27

A31

A240

0.17

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Fig. 12.10. An excerpt of the row of the value matrix corresponding to the sector Lake Environment.

judged to be an acceptable compromise by all the stakeholders con without opposition from anyone, i.e. the set of the reasonable alternatives, and for each one of these alternatives who the supporters and who the opponents are. In such a situation the final political decision is transparent, since both the Governments and the stakeholders clearly know who is favoured and who is penalised. To obtain this information a negotiation process among the stakeholders was established with the purpose of identifying the alternatives that collect the largest consent. The procedure adopted was and ad hoc modification (see again Soncini-Sessa et al., 2007b) of the Pareto Race (Korhonen, 1988 and Korhonen and Wallenius, 1988): starting from a sector, the stakeholders that belong to that sector are invited to single out the alternative they consider the best from their point of view. The value of the indexes that this alternative produce in each one of the sectors are then compared in a diagram such the one in Fig. 12.12.a. The stakeholders that are unsatisfied with the alternative are asked to specify why. To help them the trajectories of the system variables and the values of the indicators produced by the alternative can be shown (see Fig. 12.12.b,c). The set of

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Fig. 12.11. The presentation of the partial value function of the indicator ‘max flooded area in Locarno’. The left figure represents practical effects of 1 km2 flooded area, while the right figure represents practical effects of 2 km2 flooded area.

Fig. 12.12. The exploration of the alternatives effects.

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the (Pareto optimal) alternatives is then explored to find out, if it exists, an alternative than would increment the benefit of the ‘most penalized’ stakeholders and at the same time would lower the indexes of its supporters only of an ‘acceptable amount’, i.e. of an amount that does not transform them into opponents. If such an alternative exists, this phase is iteratively repeated by considering the stakeholders that are still opponents to the new alternative, until an alternative is found such that it is impossible to transform an opponent into a supporter, without transforming a supporter into an opponent. This alternative is then an attractive alternative. By repeating the procedure starting from each sector the set of the attractive alternatives may be determined. In the Verbano Project the negotiation process took place in two phases: in the first phase a preliminary analysis of the level of social conflict was conducted, thus allowing the process to focus on the area of the Pareto frontier where the majority of the stakeholder preferences were concentrated (attractive alternatives). With such a piece of information, that area was explored in deeper detail and a number of new alternatives was generated. In the second phase a further negotiation workshop took place among the new alternatives, thus producing the reasonable alternatives and a map of the stakeholder preferences with respect to them. 12.10 Phase 8 – Mitigation and Compensation The attractive alternatives are not yet reasonable alternatives since the agreement on some of them might still be enlarged by means of mitigation actions, i.e. actions aimed at reducing the disagreement of the opponents. The alternative A34 is an attractive alternative and gathers a large agreement among the sectors. However, the sector Lake Environment is not among its supporters, because the value of its sector index (0.27) is nearly as unsatisfactory as the present situation (alternative A0, see Fig. 12.14). Mitigation measures were then studied and it was discovered that, by extending the Natural Reserve’s present surface (labelled as ‘A’ in Fig. 12.13) to cover the areas labelled as ‘B’ and ‘C’ in the same figure, the sector would become strongly favourable to the alternative A34 (the sector index grows up to 0.85). The cost for acquiring this land was estimated in 10.15 millions of Euro, and the stakeholders of the Lake Floods sector, which are strong supporters of A34, declared to be willing to cover it if the stakeholders group would accept A34 as the best compromise alternative. Other types of mitigation measures which induced the relevant stakeholders to turn into supporters of the A34 were identified also for the River Floods sector. For a detailed description see Soncini-Sessa et al. (2007b). 12.11 The set of the reasonable alternatives It would result too long to describe the features of each one of the 9 reasonable alternatives eventually obtained, however it is worthwhile to provide an idea of their effects. Figure 12.14 shows the values of the sector indexes of these alternatives and of the business-as-usual alternative (A0). The alternative producing the largest agreement (all the sectors, except the River Environment) is A34. Among its supporters are the Irrigation and the Lake Floods sectors. The first because on average A34 increases the water storage in the lake before the drought periods (see Fig. 12.15), the second because it strongly reduces the lake levels during the floods (see Fig. 12.16).

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Fig. 12.13. The Natural Reserve Bolle di Magadino with the currently owned land (A), and the areas to be acquired (B and C) to mitigate the effects of the alternatives A34.

12.12 Phase 9 – Final Decision The two Governments have not yet assumed their final decision. However a step towards it has been already taken: between the set of the reasonable alternatives the Swiss Government proposed to select alternative A34; the Italian Government has not yet responded, claiming the need for further studies on the compromise alternatives. 12.13 Conclusion and remarks An application of the PIP procedure to a real world case study has been presented in this chapter. It is worthwhile noting that: • the PIP procedure produced a bunch of reasonable alternatives, each one of which collects a large agreement among the stakeholders; • for each one of these alternatives the list of the supporter and opponent stakeholders was provided: an information that is extremely useful to support the political DMs (the two Governments); • a real process of social learning was produced: – the Swiss lake shoreline communities, that formerly thought that the RM were the main responsible of floods, were drawn to recognize that flooding can only be slightly reduced without structurally modifying the lake outlet;

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1 0.8 0.6 0.4 0.2 0 Lake floods

Navigation Tourism on Mosquitoes the lake

Fishery

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A54 A168

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Fig. 12.14. The values of the sector indexes for (a) the sectors on the lake and (b) the sectors in the plain.

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level [m]

1 0.8 0.6 0.4 0.2 0 −0.2

J

F

M

A

M

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S

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Fig. 12.15. The trajectories of the median of the lake levels with the alternatives A0 (dashed line) and A34 (continuous line).

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8000 6000 4000 2000 0 5 lake level [m]

4 3 2 1 0 09/15/00 09/20/00 09/25/00 09/30/00 10/05/00 10/10/00 10/15/00 10/20/00 10/25/00

Fig. 12.16. Floods event of October 2000: lake inflow (top panel), and comparison of levels (bottom panel) with alternatives A0 (dashed line) and A34 (continuous line).

– moreover both the Swiss lake shoreline population, who strongly opposed any enlargement of the regulation range as required by the downstream users, and the downstream river users, who strongly opposed the dredging required by the Swiss, understood that, by accepting the requirements of the counterpart, a winwin solution is produced. From a methodological perspective the PIP procedure has shown to be able to deal with complex problems, with many decision makers and many stakeholders, where a mixture of planning and management decisions has to be taken. These kind of problems can be considered as the more complex ones in the field of the integrated water resources management. Acknowledgements The preparation of the chapter was carried on within the Project COFIN 2004 Sistemi di supporto alle decisioni per la pianificazione e gestione di serbatoi e laghi regolati [prot. 2004132971_004]. Bibliography FAO (1986). Yield Response to Water Deficit. number 33 In: Irrigation and Drainage Papers. Food and Agriculture Organization. Rome, I. FAO (1994). CLIMWAT: A climatic database for CROPWAT. number 49 In: Irrigation and Drainage Papers. Food and Agriculture Organization. Rome, I. Keeney, R.L. and H. Raiffa (1976). Decision with Multiple Objectives: Preferences and Value Trade-offs. John Wiley & Sons. New York, NY.

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Korhonen, P. (1988). A Visual Reference Direction Approach to Solving Discrete Multiple Criteria Problems. Eur. J. Oper. Res. 34, 152–159. Korhonen, P. and J. Wallenius (1988). A Pareto Race. Nav. Res. Log. 35, 615–623. Lotov, A.V., V.A. Bushenkov and G.K. Kamenev (2004). Interactive Decision Maps Approximation and Visualization of Pareto Frontier. Springer-Verlag. Heidelberg, D. Soncini-Sessa, R., A. Castelletti and E. Weber (2007a). Integrated and Participatory Water Resources Management. Theory. Elsevier. Amsterdam, NL. to appear. Soncini-Sessa, R., F. Cellina, F. Pianosi and E. Weber (2007b). Integrated and Participatory Water Resources Management. Practice. Elsevier. Amsterdam, NL. to appear. Ufficio Federale dell’Economia delle Acque (1993). Studio di fattibilità per un incremento di deflusso del fiume Ticino a Sesto Calende: relazione tecnica. Studio d’Ingegneria G. Anastasi. Bellinzona, CH. White, D.J. (1963). Dynamic programming, Markov chains, and the method of successive approximations. J. Math. Anal. Appl. 6, 373–376.

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CHAPTER 13

Social Science Contributions to the Participatory Planning of Water Systems – Results from Swiss Case Studies

Berit Junker and Matthias Buchecker Section Landscape and Society Swiss Federal Institute for Forest, Snow and Landscape Research (WSL) Switzerland

13.1 Introduction Participatory approaches to decision-making in water systems planning have gained worldwide a novel significance in Integrated Water Resources Management (IWRM, see GWP , 2000 and Mostert, 2003). They are also an important objective of the European Water Framework Directive (WFD – Directive/2000/60/EC; European Commission, 2000). This is one of the main reasons that there exists besides the engineering and natural sciences a strong call for social science research and expertise to find and facilitate suitable strategies of public involvement and consensus finding (Creighton, 1981; Pahl-Wostl, 2005; Ridder et al., 2005). One special area of water systems planning for which this is especially true is the area of river restorations. Large and numerous river restoration projects are currently carried out throughout Europe and in many other parts of the world (Boon et al., 1994). River restorations are today expected to combine improved flood protection measures with the ecological rehabilitation of the river reaches. This chapter contributes to social science research for new ‘best practise’ in participatory planning of water systems by means of two case studies on river restoration projects in Switzerland. Here the Federal Law on hydraulic engineering (BSE, 1991) explicitly calls for measures combining flood security and an ecological revalorization of the river spaces (BWG, 2001). The guideline of the Swiss Federal Ministry for Water and Geology (BWG) for these measures puts also much emphasis on the social components of such river projects, such as their acceptance by the local public and stakeholders, their participation in the planning and decision-making process, as well as possible compensation measures for affected land owners/users. In order to gain more knowledge on the different aspects of 243

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river rehabilitation, a large transdisciplinary research project – the so-called Rhone-Thur project1 – was initiated by the BWG, the Federal Ministry for Environment, Forest and Landscape (BUWAL), the Swiss Federal Institute for Environmental Science and Technology (EAWAG) and the Swiss Federal Institute for Forest, Snow and Landscape Research (WSL) in 2001. Besides research on engineering and natural science aspects of river revitalisation, also such social science aspects as decision-making, consensus building and participation are studied. Part of this endeavour is the research project ‘Objectives of the population in regard to river restoration’2 . Results of this study can contribute to the design of participatory planning for river rehabilitation projects. While the implementation of computer-aided decisional procedures are helpful for an efficient planning and decision-making process, we argue that the careful evaluation of the social, economic and cultural context of each river project and the design of the participation and consensus finding process are also of high relevance for the success and finally for the acceptance of such projects (Gregory, 2000; Tunstall et al., 2000). Important factors are identified that – according to the results of the concrete project cases studied – should be helpful for successfully implementing (and carrying out) a participatory and decisional process for larger river restoration projects. 13.2 Research design 13.2.1 Methods The results for this contribution stem from qualitative and quantitative data gained in two case studies at the River Thur (river section between Weinfelden and Bürglen) and Flaz (Samedan). The consensus and decision-making process for the Thur project is still ongoing and is negotiated between the river restoration project team from cantonal offices as well as organised stakeholder groups. The same process has already successfully been finished for the Flaz project and here also the local population has been involved next to the project team from canton and community and organised stakeholders. Qualitative interviews along a question guideline were carried out with members of the local population in the respective areas, of involved organised stakeholders and of the project teams. Furthermore, standardised questionnaires were distributed via the community newspapers to all of the households in Bürglen (Thur) and in Samedan (Flaz) and to a random sample of street passengers in Weinfelden (Thur). In the first case study (River Thur), the consensus and decision-making process itself was observed and a questionnaire given out to the participants at the beginning and later at the end of this process. While the first case study on the River Thur was carried out in an explorative way, the gained data was used to derive first hypotheses that established the base for the second case study at the River Flaz. After reworking the hypotheses again from the further data of the second case study, they will be tested by means of a representative Swiss-wide survey3 . This mix of methods allowed for a triangulation of methods which is especially suited to the subject of this study since it offered the chance to first obtain a deeper understanding of the issues at stake (by means of interviews and observation) and then 1 For more information see: http://www.rhone-thur.eawag.ch, last visit 05/2006. 2 See also the project homepage: http://www.wsl.ch/land/society/prorenat-en.ehtml, last visit 05/2006. 3 Conducted between December 2004 and February 2005.

Social Science Contributions to the Participatory Planning of Water Systems 245 to measure and test the general occurrence of certain phenomena (by means of the questionnaires) (Denzin and Lincoln, 1994; Lamnek, 1988; Backhaus, 2000). At present, both case studies on the Thur project have been completed. 13.2.2 Study areas Thur (Weinfelden/Bürglen) The first case study focused on the area between Weinfelden and Bürglen at the River Thur in the Northeast of Switzerland (Canton Thurgau). There the river project team from two cantonal offices for the environment (AfU Thurgau) plans a large river project with the objective to combine flood protection with a river widening and a retention basin. This project is part of the 2nd Thur correction that was started after disastrous floods in 1978 (see Baumann, 2002). Having initiated the project by proposing a first drawn-up sketch of a project scenario the planning team established a regional working group in order to facilitate a participatory decision-making procedure. This circle consists of invited representatives of the following groups: land owners and land users of the affected project perimeter, gravel industry4 , fishing and hunting organisations, regional Farmers Union, Weinfelden community office of tourism, and the mayors of the affected communities5 . In a basic information meeting the project team introduced the following planning actions: a river widening, a retention basin and the restoration of the existing dams. Given these main actions, the participants were given the possibility to negotiate the action space between these framing conditions. The participants where asked to draw up and to explain their own project alternatives (coherent mix of planning actions) in the second meeting. These were supposed to be the basis for the further negotiation process. At the second meeting there existed relatively strong opposition of some members of the regional working group against the project proposed by the project team6 . Participants felt that the participatory decision-making process was only an alibi exercise of the project team. There existed also misunderstanding about the issues of flood protection and the retention basin. The landowners also criticised their lack of concrete information on compensation measures for their land. Since some of the misunderstandings could be erased by the project team, the third meeting indicated some willingness of the participants to find a consensus among the differing claims. At the same time a petition was launched by a member of the regional Farmers Union complaining at the highest cantonal instance about a missing wider participation and discussion of this project, thus discrediting and criticising the project team for the design of the participation process. Flaz (Samedan) In contrast to the Thur project, the Flaz project in Samedan in the Engadin region (Southeast of Switzerland) has already been successfully carried out. After a flood event in 1987, the project was initiated by the canton of Grisons initially centring around the necessity of flood protection measures. But the municipal council and the community actually perceived no need of pursuing a project in this region at that time. The canton reacted by declaring substantial parts of the community ground a highrisk zone thus preventing any new construction in this area. These measures caused the 4 Currently, gravel is worked along the project perimeter. Widening the river bed would produce large amounts

of gravel as well. 5 The mayor of the community Bürglen was asked by the project team to lead the regional working group. 6 These were mainly the representatives of the land owners and users.

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Table 13.1. Overview of the phases of the the Thur and Flaz projects.

PIP

procedure (see Ch. 1) employed/not employed in

Phase

Thur project

0:

Reconnaissance

‘YES’ (hydrological, geological + social ‘YES’ (hydrological + geological surveys; definition of the project teams’ surveys; definition of the project teams strategic objective) strategic objectives)

Flaz project

1:

Defining Actions

‘NO’ (not systematically)

‘YES’

2:

Defining Criteria & Indicators

‘NO’ (not systematically)

‘YES’

3:

Identifying the Model

‘NO’ (not systematically)

‘NO’ (not systematically)

4:

Designing the Alternatives

‘YES’ (as proposed by the involved stakeholders)

‘YES’

5:

Estimating Effects

‘YES’

‘YES’

6:

Evaluation

‘NO’ (not systematically)

‘YES’

7:

Comparison

‘NO’ (not systematically)

‘YES’

8:

Mitigation & Compensation

‘YES’

‘YES’

9:

Final Decision

‘NO’ (open at present)

‘YES’ (proposal of the project team, voted on by the community)

municipality in cooperation with the cantonal offices and federal research institutions to develop a variety of project alternatives. Several of these alternatives included ecological rehabilitation aspects. After a voting of the community against more expensive restoration actions and for a purely technical flood protection project in 1997, a new mayor came to power in 1998. The new mayor of Samedan personally saw the advantages of a rehabilitation project and openly invited everybody interested in and affected by a possible project to work on further project alternatives. Also here a regional working group was launched (lead by the mayor) – together with an additional ecological accompanying commission. These two groups, in cooperation with the responsible cantonal office (Grison Cantonal Office for Civil Engineering) and other cantonal offices, produced three practicable project ideas. Finally the members of the community Samedan voted on one alternative favoured by these groups. This was the maximum alternative, comprising a dismantling of the dams in the area, a relocation of parts of the River Flaz and ecological restoration measures along the new Flaz bed as well as the River Inn in this area7 . It received the majority of votes. This alternative has been implemented by now. Decision-making procedures at Thur and Flaz Neither for the Thur nor for the Flaz projects a computer-aided decision-making procedure was implemented and several of the phases of the PIP procedure by Castelletti and Soncini-Sessa (see Ch. 1) were omitted. Table 13.1 indicates which phases were employed or missing. 7 For more information on the project see: www.flaz.ch, last visit 04/2006.

Social Science Contributions to the Participatory Planning of Water Systems 247 13.3 Social factors for an integrated and participatory decision-making procedure Each water systems and thus also each river rehabilitation project is embedded in a specific social, economic and cultural context. The river spaces concerned play often not only a substantial role as a recreational and leisure time area for the local population in the respective area, but they are for most cases also in agricultural or other economic use (Green and Tunstall, 1992). The necessary acceptance of a project and its efficient realisation depend therefore on the understanding and involvement of the local public and the relevant specific stakeholders (Gregory and Wellman, 2001). The qualitative and quantitative data gained in the two studied projects at the Rivers Thur and Flaz clearly indicates the importance of • a careful evaluation of the local setting (socio-economic and cultural context), • a conscious consideration of social and communicative factors, as well as • a circumspect design of the participation and consensus finding process when planning and implementing the decision-making procedure for such a project. Therefore we argue that the phase Reconnaissance (Phase 0, Ch. 1) should be given especially high emphasis. In what follows several factors that often play a crucial role for the success of a decision-making process – according to the results of the case studies on river rehabilitation projects – will be identified and described. 13.3.1 The socio-economic and cultural setting of a project The importance of the specific local context and setting for a given river project is often underestimated. In case a project team fails to correctly evaluate the different aspects that characterise the locality, the implemented planning and decision-making process bears a high risk of running into difficulties and in the worst-case scenario of failing altogether. Such cases are for example the projects Belpau and Bischofszell-Pfyn, as described by Camenisch et al. (2001) and Zaugg (2003), respectively. Therefore, the effort seems worthwhile to invest sufficient time and finances in pre-project evaluation of the socio-economic and cultural factors that establish the context for any river rehabilitation endeavour. The following factors were found to be relevant in the two case studies: • Current uses of the river space (economic use for agriculture, forestry, industry, but also recreational usesA , etc.). • Meaning of the river space for local communities (other than concrete forms of use; perception, etc.)A . • Past restoration or similar projects in the wider area. • Possibilities and conditions for compensating dispossessed landowners in the project perimeter (financial recompense or land replacement options, etc.). • Past flood events (and its effects). • History of the river (time of channelling, etc.).

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• Usability of agricultural land or forested land, etc. in the project perimeter (also status of agriculture and forestry, etc. in the specific areaA ). • General climate in decision finding in the region (past experiences), i.e. relation to cantonal authorities, former conflicts, etc.)A . • Expectations of the affected communities/stakeholders in regard to their participation in the projectA . Where the types of data marked by the superscript A can be obtained by means of a social survey in the pre-project (Reconnaissance) phase.

13.3.2 Social survey as a preliminary activity In what follows motivations for executing such a survey before designing the actual decision-making and participation process are described. Social surveys can have the following variety of functions: • to gain data for example on the meaning of the river space for the local population, the use of the area as well as the perceived need for action in the respective area (Junker et al., 2003); • to identify possible stakeholders (Mitchell, 1997; Grimble and Wellard, 1997); • to establish a pre-project indicator measurement for a monitoring of the project that might be planned (to be completed with a post-project survey/measurement) (Woolsey et al., 2005; Gloor and Meier, 2001); • to serve as part of the overall public information strategy (House, 1996; Beierle, 1998); • to explore the preferences of the local population and potential stakeholders in regard to their participation in the decision-making as a base for the design of this process (see Fig. 13.1); • to serve as part of the participation process (people perceive a pre-project survey to a certain degree as a way of participating; the survey could for example come along with an invitation to the decision-making process) (Duram and Brown, 1998); • to produce information that can later be used in the decision-making and consensus finding process as a mean of legitimisation and information. In the next paragraphs we will describe an example for the last point in more detail and illustrate it with data from the Thur study. Knowledge of the perceived need for action of different groups in the respective area of concern can be not only very valuable for designing a tailored public relations strategy, but also relativize the magnitude of the respective stakeholders‘ claims in case that they differ from the majority‘s claims. The assignment for the participants of the standardised surveys was to indicate whether they prefer to have done less, the same or more in comparison to the status quo for the

Social Science Contributions to the Participatory Planning of Water Systems 249 25

20

15

10

5

0

A

B

C

D

E

F

G

H

I

J

K

Categories

Fig. 13.1. Expressed request versus perceived ability of the local population to participate in the planning process of the Thur project in Weinfelden and Bürglen. The categories considered are: A: Taking initiative; B: Shipping in ideas (inquiry); C: Making proposals (workshop); D: Working out proposals (working group); E: Raising objections; F: Selection from different proposals; G: Veto; H: Voting on final project; I: Other; J: None; K: Do not know.

different given aspects8 . The reply of the local public in Weinfelden/Bürglen is shown in Fig. 13.2. The same question was asked to the stakeholder groups actually involved in the decision-making process (see Fig. 13.3). When comparing the data from the survey for the local population and the one for the stakeholders different trends in the preferences of these groups in comparison to the status quo can be identified, as shown in Table 13.2. This information could be used in the consensus building process, as was confirmed by the qualitative interviews in Weinfelden and Bürglen. A few of the interview partners from the directly affected land users/owners indicated a higher willingness to cooperate by making parts of their land available to the project and/or by accepting the compensation offered by the canton as soon as they had knowledge of the majority‘s objectives. 8 These aspects were identified to be the relevant ones for the planned Thur project by means of the qualitative interviews.

250

B. Junker and M. Buchecker 100 90 80 70

Evaluation

60 50 40 30 20 10 0

A

B

C

D

E

F

G

H

Aspects

Fig. 13.2. Perceived need for action of the local population Weinfelden/Bürglen (case study Thur). The aspects considered are A: flood protection; B: water quality; C: naturalness; D: leisure time facilities; E: forestry; F: recreation; G: agriculture; H: ground water. Table 13.2. Comparison of trends in perceived need of action. Aspects

Population

Stakeholders

Naturalness Forestry Recreation Agriculture

more same more less

same less same same

13.3.3 Design of the information and participation process Initiative to a project and communication of objectives The majority of flood protection and river restoration projects in Switzerland are not initiated by the local communities, but by the responsible cantonal or federal office. Such an approach is not promising for an efficient realisation of the project since its continuation throughout the project bears a high risk of failure due to a missing acceptance by the local public and stakeholders9 . 9 See for example the failed restoration project Belpau (Camenisch et al., 2001).

Social Science Contributions to the Participatory Planning of Water Systems 251 100 90 80 70

Evaluation

60 50 40 30 20 10 0

A

B

C

D

E

F

G

H

Aspects

Fig. 13.3. Perceived need for action of the stakeholder groups involved in the regional working group Weinfelden/Bürglen (case study Thur). The aspects considered are A: flood protection; B: water quality; C: naturalness; D: leisure time facilities; E: forestry; F: recreation; G: agriculture; H: ground water.

Therefore it is of utmost importance that, once the initiative has been made, the communication and participation process is designed to change this top-down approach of planning into a bottom-up approach, or at least to combine these two in a way acceptable to all participants. When having to launch a project in a top-down manner it further seems important that the project team clearly defines and communicates the necessities as well as the real motives of the project goals to the local public and the personally affected stakeholders. This has proven to be a problem for the Thur project. There a misunderstanding arose when the participants of the regional working group were told that the main goal of the project was flood protection for the project area. They did not recognize the necessity of implementing flood protection measures since the specific area is currently equipped for a safety level of an HQ100. On the basis of this evaluation some of the participants objected to the proposed project goal right from the start10 . The local population did also 10 Information from interviews with the participants of the regional working group and observation of the meetings of the regional working group Thur.

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not perceive of a high need for action in regard to an enhancement of flood security for the communities Weinfelden and Bürglen. Only 29% voted for more flood protection measures in this area, 56% indicated their wish to stay with the status quo11 . Yet the canton’s actual objective is not an improvement of the flood situation for the affected communities per se but a systemic flood protection along the River Thur within which the project measures in the project area are fully justified. As soon as this was communicated clearly by the cantonal project team, the involved stakeholders were suddenly ready to discuss a compromise and to engage in the consensus finding process. Sufficient time for public participation A further factor seems important when planning the information and consensus finding process for a given project. As seems to be the general consensus in the literature (Morrison, 2003; Beierle and Konisky, 2000 and Webler et al., 2001) and as also the experiences from the Thur and Flaz projects show, not only a public relations and information strategy about a planned project and its objectives that starts as early as possible is key. It seems also decisive that sufficient time is calculated for the information of the local public and directly affected stakeholders as well as for their participation in the decision-making process. This time factor seems to be of high relevance especially for the case of river rehabilitations since people living in the respective area are often highly used to the artificial nature of the river space. Thus, overcoming the status quo and recognising the value of a rehabilitation of the area can require relatively much time. Missing to schedule for a sufficiently long time span of the public participation process might result in the perception that this process is implemented solely for the purpose of acting accordingly with the federal guidelines and not for an actual contribution and exertion of an influence of the participating stakeholders to the decision-making. This by itself can prevent a successful course of the consensus finding process. The Thur project was characterised by a very early start of the public information about the project idea, but late personal information of the affected land owners and users by the project team. While the local public seems to generally accept and approve the planned project, the late onset of communication in regard to the land use issue offered most of the land owners/users one more reason to block the consensus finding work creating thus an overall unfavourable climate for this process12 . Once their mistrust had built about the fair proceeding of the project team, it was difficult to be erased. Yet enough time was assigned to the overall participation process in order to make up for this neglect and to establish more trust again during several meetings of the regional working group. The Flaz project team pursued an early information and participation strategy towards both the community and directly affected persons assigning the overall communication and consensus-finding process sufficient length. The latter criterion played a crucial role for the outcome of the project since no need was perceived by the community to launch neither a flood protection nor a restoration project in this area at the beginning. This is partly due to the fact that the highly attractive landscape of the Engadin valley has additionally to its rivers a great variety of different prominent features in store. In contrast to the River Thur, which has a great prominence in the Thur valley of the Thurgau, the channelled River Flaz prior to the project received only relatively little attention by the public. Here the overcoming of the status quo and the recognition of the potential of 11 Results from the questionnaire for the local population Thur project. See Fig. 13.2 for full information. 12 According to the results from the interviews, questionnaires and observations of the case study Thur.

Social Science Contributions to the Participatory Planning of Water Systems 253 a revitalised river landscape needed a relatively long span of time that was sufficiently provided for by the project team13 . Open invitation to the decision-making and consensus finding process One further question for designing the participation and decision-making process is who should be involved (Curtis et al., 1995). Here the experiences of the two researched projects strongly speak for an invitation that is as open as possible to everybody interested in contributing to this process, i.e. not only organized stakeholder groups. This includes also outspoken and potential critics of a project, since it forces them to not only face all other interests and perspectives on such a project, but it also ensures that the opposing standpoints are negotiated openly and not only outside the official consensus finding ground. That is, the chances are higher that the different interests are negotiated within one communicative space under the auspices of the project team. A wide and inviting participation process further seems to be the base for the legitimization of the overall project while its neglect tends to offer opponents an argument for declaring a project illegitimate. If the local public can be involved the project team can in the best case furthermore profit from existing local knowledge that might be conducive to general project success. All of these points proved to be relevant in one or the other way in the Thur and Flaz projects. The invitation to participation in the regional working group in Weinfelden/Bürglen for example seems to have not been sufficiently open and wide enough. Only selected organized stakeholder groups were asked to participate while no invitation went to the local public and recreational user groups14 . While these latter groups have not yet claimed their concrete participation, the Thurgau Farmer’s Union has sent a petition as described above using the missing wider public participation as an argument for pushing their own interests in the decision-making process. In contrast the project team of the Flaz project not only invited all community members to work on the project alternatives, they also offered the opportunity to vote on the resulting proposed alternative. While the alternative that included the largest restoration intervention faced much opposition at the beginning of the planning process, it gained a surprisingly high general acceptance at the end15 . According to interview data, opponents to the finally realized project plan within the community of Samedan noticed their minority status and organised no further protest against the project. 13.4 Conclusions The implementation of computer-aided decision-making procedures for water system planning is without doubt an exigency for the planning and negotiation process of water systems projects. But the study of the river restoration projects at the Rivers Thur and Flaz clearly show that also a careful analysis and evaluation of the projects surrounding social, socio-economic and cultural contexts and settings is highly beneficial to this process. Social surveys among the respective local populations are one way of gathering the information needed for such an evaluation in the run-up of a concrete project. 13 Results from the qualitative interviews with members of the project team, the working groups and the local population in Samedan. 14 See Section 13.2.2 for the groups involved in the regional working group Thur. 15 The community of Samedan voted on November 26, 2000 with 128:6 voices for the project scenario that was realized by now.

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The data gained can serve multiple purposes at the same time, as for example for the identification of stakeholders to be involved, the clarification of the perceived need of action of different groups within the local population, or as a source of local knowledge of the respective area, to name here only a few. A standardised exemplary questionnaire containing items that cover the relevant issues of interests could be incorporated in a Decision Support System (DSS) software specifically designed for river restoration projects. This questionnaire could be complemented by a check-list enabling the project managers to ensure a consideration and evaluation of all typically relevant factors when planning a river restoration project. The utilisation of these tools could be seen as a basis for the subsequent design of an appropriate participation and consensus finding scheme, thus contributing to favourable preconditions for efficiently realising such projects as well as gaining the necessary public approval and support. Bibliography Backhaus, N. (2000). Ecotourism and authenticity in National Parks of Malaysian Borneo. Malays. J. Trop. Geogr. 31(1–2), 65–74. Baumann, M. (2002). Die 2. Thurkorrektion im Thurgau – Hochwasserschutz und Lebensraumgestaltung. In: Internationales Symposium 2002 Moderne Methoden und Konzepte im Wasserbau. ETHZ. Zürich, CH. Beierle, T.C. (1998). Public participation in environmental decisions: an evaluation framework using social goals. Discussion Paper 99-06. Resources For The Future. Washington, D.C. Beierle, T.C. and D.M. Konisky (2000). Values, conflict, and trust in participatory environmental planning. J. Policy Anal. Manage. 19(4), 587–602. Boon, P.J., P. Calow and G.E. Petts, Eds.) (1992). River Conservation and Management. John Wiley & Sons. New York, NY. BSE, Bundesversammlung der Schweizerischen Eidgenossenschaft (1991). Bundesgesetz über den Wasserbau. Technical Report 721.100. Bundesversammlung der Schweizerischen Eidgenossenschaft. Bern, CH. BWG, Bundsamt für Wasser und Geologie (2001). Hochwasserschutz an Fliessgewässern. Wegleitungen des BWG. Bundesamt für Wasser und Geologie. Biel, CH. Camenisch, A., R. Droux, T. Hoeck, A. Huegli and D. Rast (2001). Wer rettet die Belpau? Zur Wahrnehmung und Akzeptanz eines Hochwasserschutz- und Revitalisierungs-projekt. IKAÖ. University Bern, CH. Creighton, J.L. (1981). The Public Involvement Manual. Abt Books/University Press. Cambridge, MA. Curtis, A., J. Birckhead and T. De Lacy (1995). Community participation in landcare policy in Australia: the Victorian experience with regional landcare plans. Soc. Nat. Resour. 8, 415–430. Denzin, N.K. and Y.S. Lincoln (1994). Handbook of Qualitative Research. SAGE Publications. Thousand Oaks, CA. Duram, L.A. and K.G. Brown (1998). Assessing public participation in U.S. watershed planning initiatives. Soc. Nat. Resour. 12, 455–467. European Commission (2000). Directive 2000/60/EC of the European Parliament and of the Council establishing a framework for Community action in the field of water policy. Official Journal. European Commission, Brussels, B. Gloor, D. and H. Meier (2001). Soziale Raumnutzung und ökologische Ansprüche. Grundlagen und Materialien 01/01. Professur Fortspolitik und Forstökonomie, ETH Zürich. Zürich, CH.

Social Science Contributions to the Participatory Planning of Water Systems 255 Green, C.H. and S.M. Tunstall (1992). River Conservation and Management. Chap. The amenity and environmental value of river corridors in Britain, pp. 425–441. John Wiley & Sons. New York, NY. Gregory, R. (2000). Using stakeholder values to make smarter environmental decisions. Environment 42(5), 34–44. Gregory, R. and K. Wellman (2001). Bringing stakeholder values into environmental policy choices: a community-based estuary case study. Ecol. Econ. 39, 37–52. Grimble, R. and K. Wellard (1997). Stakeholder methodologies in natural resource management: a review of principles, contexts, experiences and opportunities. Agric. Syst. 55, 173–193. GWP – Global Water Partnership (2000). Integrated water resources management. TAC Background paper 4. GWP Secretariat. Stockholm, S. House, M.A. (1996). Public participation in water management and the promotion of environmental education. Lake Reserv. Manage 2, 1–5. Junker, B., M. Baumeler, R. Debrunner, P. Nigg, C. Poncini and M. Zschokke (2003). Wie sieht die Bevölkerung aus Weinfelden und Bürglen ihre Thur? Natur + Mensch 5, 4–7. Lamnek, S. (1988). Qualitative Sozialforschung. Methoden und Techniken. Beltz Psychologie Verlags Union. Weinheim, D. Mitchell, R.K. (1997). Toward a theory of stakeholder identification and salience: defining the principle of who and what really counts. Acad. Manage. Rev. 22, 853–886. Morrison, K. (2003). Stakeholder involvement in water management: necessity or luxury? Water Sci. Technol. 47, 43–51. Mostert, E. (2003). The challenge of public participation. Water Policy 5, 179–197. Pahl-Wostl, C. (2005). Information, public empowerment, and the management of urban watersheds. Environ. Modell. Softw. 20, 457–467. Ridder, D., E. Mostert and H.A. Wolters, Eds.) (2005). Learning Together to Manage Together. Improving Participation in Water Management. Institute of Environmental Systems Research. Osnabrück, D. Tunstall, S.M., E.C. Penning-Rowsell, S.M. Tapsell and S.E. Eden (2000). River restoration: public attitudes and expectations. J. Chart. Inst. Water E. 14(5), 363–370. Webler, T., S. Tuler and R. Krueger (2001). What is a good public participation process? Five perspectives from the public. Environ. Manage. 27(3), 435–450. Woolsey, S., C. Weber, T. Gonser, E. Hoehn, M. Hostmann, B. Junker, C. Roulier, S. Schweizer, S. Tiegs, K. Tockner and A. Peter (2005). Handbuch für die Erfolgskontrolle bei Fliessgewasserrevitalisierungen. Rhone-Thur Projekt. WSL, LCH-EPFL, VAW-ETHZ, CH. Zaugg, M. (2003). Mehr Raum den Fliessgewässern! Eine strukturationstheoretische Analyse des institutionellen Wandels im schweizerischen Hochwasserschutz seit den 1970er Jahren. PhD thesis. University Zurich. Zurich, CH.

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CHAPTER 14

Multi-Criterion Decision Making Approach to Assess the Performance of Reconstructed Watersheds

Amin Elshorbagy1 , S. Lee Barbour2 and Clara Qualizza3 1 Centre for Advanced Numerical Simulation (CANSIM)

Department of Civil & Geological Engineering University of Saskatchewan, Saskatoon, Canada 2 Department of Civil & Geological Engineering

University of Saskatchewan, Saskatoon, Canada 3 Syncrude Canada Limited

Fort McMurray, AB, Canada

14.1 Introduction The multi-criterion decision making (MCDM) technique traditionally has been used in water resource literature as a major component of decision support systems (DSS) (Stansbury et al., 1991; Goicoechea et al., 1992; Qureshi and Harrison, 2001; Fassio et al., 2005). It has been applied to an array of problems in water resources, including water transfer options and reservoir operation (Stansbury et al., 1991; Ko et al., 1992; Harboe, 1992; Bogardi and Duckstein, 1992; Roy et al., 1992; Tecle, 1992; Srdjevic et al., 2004; Raju and Duckstein, 2004; Fassio et al., 2005), design of monitoring networks (Woldt and Bogardi, 1992; Harmancioglu and Alpaslan, 1992), various applications in forestry (Huth et al., 2004; Lasch et al., 2005), wastewater treatment alternatives (Tecle et al., 1988; Khalil et al., 2005), and computer-assisted tools for negotiation of water resources conflicts (Thiessen and Loucks, 1992). In this chapter we will demonstrate how it can be usefully applied to assess the performances of different reclamation alternatives for mining-affected watersheds. Mining activities are clear examples of watershed disturbance resulting from human activity. The mining of oilsands in Northern Alberta, Canada, leaves behind large pits, 257

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tailings facilities, and overburden in which the natural hydrology of surface and groundwater has been completely disrupted. The industry is committed to reconstructing functioning landscapes through the design of new reclaimed watersheds in order to restore the different functions of nature, such as habitat function (hosting aquatic ecosystems), production function (e.g., biomass), and carrier function (for dissolved and suspended material). The carrier function plays a central role in land degradation processes such as the leaching of nutrients through moving surface and sub-surface water, erosion, and sedimentation (Falkenmark, 1997). The restoration of the above-mentioned functions relies first and foremost on the restoration of functioning hydrologic systems, a central feature of which is sufficient water to sustain revegetation efforts. Such reclamation and restoration efforts are essential to make the oil sands mining industry as sustainable a development as possible. The mining of oil sands near Fort McMurray, Alberta, involves the stripping of salinesodic overburden to gain access to the oil-bearing formation. The overburden is placed in large mined out pits and surface dumps and is re-contoured before being capped with a mandated one meter soil cover. The potential for slope instability, subsidence, and salinization resulting from the character of the saline-sodic material and its interaction with fresh water makes it imperative that the amount of precipitation percolating below the root zone be minimized (Barbour et al., 2001). Syncrude Canada Ltd is conducting largescale cover experiments at the Mildred Lake mine in order to assess the performance of different reclamation strategies. Four different prototype covers were constructed to study the basic mechanisms controlling moisture movement within the cover systems. The overriding objective is to identify the best reclamation strategy to be adopted by the industry. Adopting a certain strategy implies accepting specific economic, environmental, and regulatory consequences. The compromises resulting from the decision to adopt a certain strategy (alternative) need to be thoroughly investigated and analysed. In this chapter, the problem is formulated within the multi-criterion decision making (MCDM) context (Belton and Stewart, 2003) to evaluate different alternatives towards making a sustainabilityoriented decision. The MCDM technique is used to make a selection or, at least, to aid the decision-making process with respect to the alternative to be adopted. Particular emphasis is given to the selection of the attributes quantifying/qualifying the criteria, and to the a-posteriori analysis of the robustness of the solution provided by the MCMD approach. Moreover, the MCDM framework presented in this chapter is expected to highlight issues that help re-focus the monitoring program and redirect ongoing research on the problem at hand. This chapter is organized as follows: the next section describes the case study from Northern Alberta, Canada, where extensive oil sands mining activities occur. The following two Sections (14.3 and 14.4) present the decision problem to be solved and its formulation within the MCDM context, whereas the task of impact assessment and populating the evaluation matrix with the impact scores is dealt with in Section 14.5. The evaluation and ranking of the various alternatives are conducted in Section 14.6. Section 14.7 focuses on the various types of sensitivity and uncertainty analyses including score and weight sensitivity analysis. The results and the utility of the adopted MCDM technique as well as the main findings and conclusions are discussed in the last section of this chapter.

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Fig. 14.1. The prototype cover site (Boese, 2004).

14.2 Study area Four one-hectare prototype covers were placed on an area referred to as the South Hills Overburden (Fig. 14.1) to study the basic mechanisms controlling moisture movement within the cover systems. Three covers were constructed in 1999 with thicknesses of 1.00 m, 0.50 m and 0.35 m comprised of a thin layer of peat (15–20 cm) overlying varying thickness of secondary soil. A fourth study site, referred to as Bill’s Lake (B.L.), was established in 1996 on a previously reclaimed watershed capped with a 1.00 m cover of peat/secondary mix. A field instrumentation program was carried out consisting of detailed monitoring of matric suction, volumetric water content, and temperature within the different soil profiles as well as measurements of runoff, interflow, and site-specific meteorological conditions. Details of the monitoring program can be found in Meier and Barbour (2002) and Boese (2004). From the hydrologic engineering perspective, assessing the sustainability of the reclamation strategy implies (i) accounting for the different components of the water balance in the reconstructed watershed, (ii) identifying the ability of the watershed to allow for vegetation to be established by securing enough moisture throughout the growing season and allowing for sufficient interflow to leach excessive salt, and (iii) minimizing undesired deep percolation of water to underlying saline/sodic layers. 14.3 Problem definition The problem at hand is a clear example of a complicated decision-making exercise encountered by major oil companies in the region. From a short-term economical perspective, the thinnest cover (D2 in Fig. 14.1) is the cheapest course of action that saves more than 16 million Canadian dollars for the industry. But the apparent multi-dimensionality

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of the problem raises some important issues and makes it more complicated than a singleobjective economical exercise. The ability of different covers to hold sufficient moisture for vegetation and to allow for interflow to leach excessive salts are among major indicators of cover efficiency. Other considerations, such as minimizing deep percolation of water to the underlying shale, minimizing preferential flow through macro-pores, and allowing for vegetation diversity on the covers could be less critical from an engineering perspective than the above-mentioned two indicators yet important from the environmental perspective. Data collected through the in-situ extensive monitoring program reveals that none of the experimental covers dominates others as the best option with respect to all considerations. A more costly cover (e.g. D3) could have better ability to hold moisture and to allow for interflow than a less expensive cover. The least expensive (the thinnest) cover may ecologically provide better vegetation diversity but fails to minimize the preferential flow. The apparent conflicting-objectives (criteria) nature of the problem makes it a suitable candidate for multi-criterion decision making (MCDM) framework. 14.3.1 Multi-criterion decision making framework Formulating the discrete choice problem in a multi-criterion context means constructing a matrix that contains columns of the different soil covers as feasible distinctive alternatives and rows of different criteria that are used in this study to evaluate the performance of different alternatives (Belton and Stewart, 2003). The matrix has to be populated with assessment scores that quantify or qualify the performance of different alternatives with respect to the chosen set of criteria. One of the advantages of the MCDM technique is that it can handle qualitative measures. The performance of different alternatives with respect to some criteria does not have to be a quantitative score. For more details on the different phases of the MCDM process, the readers may also refer to the pip procedure presented in Ch. 1 of this book. 14.4 Definition of criteria In this study, generating or designing different alternatives is not subject to research since the four soil covers (reclamation strategies) have been selected prior to this study and they already exist on the Mildred Lake mining site. However, the multiple criteria used in this chapter are selected to represent the following categories: (a) the resources needed for the project, (b) the reliability of the system, and (c) the effect on the ecology. Based on the discussion provided in previous sections, the following criteria are considered in this study and perceived to be sufficient for representing the problem of assessing the performance of different reclamation strategies: (a) Resources Cost. (b) Reliability of the system Moisture held for vegetation. Interflow to leach excessive salt. Percolation to shale. Preferential flow.

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(c) Ecological effect Vegetation diversity. The last step of formulating the problem into a multi-criterion context is the impact assessment, which identifies the performance of each alternative with respect to each of the criteria, to assess the impact scores. First a measure of performance, or attribute, is chosen as a suitable representative of a criterion. If the attribute is a commensurable value, then it is considered quantitative. Other attributes can be assessed in qualitative terms; for example, using an ordinal scale or an indicator such as ‘+ + +/− − −’ signs. 14.5 Impact assessment Cost: the ‘monetary cost of laying one cubic meter of soil’ is used as the attribute for this criterion. The cost of landscaping is $4.0/m3 , which makes the values of this attribute for different soil covers $2.0, $1.4, $4.0, and $4.0 per m2 of landscape for D1, D2, D3, and Bill’s Lake (B.L.), respectively. The higher the value of this attribute, the worse the alternative. Moisture held for vegetation: the ‘number of days of the growing season (mid May till late October) in which the soil cover holds enough moisture to be taken up by the roots under no stress’ is considered to be the commensurable attribute of this criterion. Data from year 2002 is used in this chapter. Maximum value for this attribute is 170 days. The evapotranspiration values in the study area range between 1.0–10.0 mm/day. The number of days in which the peat layer contains 5.0 mm more than the wilting point is counted for each cover. Regarding the underlying till (secondary) layer, the number of days in which the soil moisture is just above the wilting point is counted. An overall score (number of days) for each cover is calculated as follows: Overall score = 0.7 × No. of days in peat layer + 0.3 × No. of days in till layer.

(14.1)

A higher weight (0.7) is given to the root zone within the upper layer. The attribute values based on year 2002 were found to be 167, 163, 149, and 170 days for D1, D2, D3, and B.L., respectively. The higher the value of this attribute, the better the alternative. Interflow to leach excessive salt: whenever a significant portion of volume of interflow water accumulates in the designated barrels, it is pumped out and measured. ‘Total amount of yearly interflow generated by each cover’ is calculated as depth (mm), and considered to be the commensurable attribute of this criterion. The interflow values in year 2002 were found to be 0.15 mm, 0.21 mm, and 0.15 mm for D1, D2, and D3, respectively. Unfortunately, the interflow from the B.L. cover is not measured. In this study, it is assumed that interflow values for both D3 and B.L. are equal since both covers have equal depth of 1.0 m. The higher the value of this attribute, the better the alternative. Percolation to shale: the field instrumentation provides moisture content at different depths on all covers. An average daily moisture depth (cm) available in the top 50 cm of the underlying shale layer is estimated from available data. A moisture duration curve (moisture depth or content vs. percent of time or probability the moisture is equalled or

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Fig. 14.2. Moisture duration curve of the shale layer under cover D3.

exceeded) is plotted for each soil cover. An example of such a plot is given in Fig. 14.2 for cover D3. From the definition of such a graph, the area under the curve is equal to the expected annual moisture level in the shale layer (Mays, 2001). The area of the rectangle under the dashed line is subtracted from the total area under the curve. The resulting area is the ‘expected annual moisture increase in the shale layer above the firm moisture level’. This value is taken as the commensurable attribute of this criterion. The percolation to shale values in year 2002 were found to be 1.6 cm, 2.1 cm, 3.5 cm, and 1.3 cm for D1, D2, D3, and B.L., respectively. The higher the value of this attribute, the worse the alternative. Preferential flow: detailed study on this phenomenon is still under way for more accurate characterization of preferential flow in all covers. A tentative characterization of this phenomenon is taken from (Boese, 2004). Preferential flow events were observed during or shortly after precipitation events in only the D1 and D2 covers and once in B.L. due to snow melt. A qualitative attribute is chosen for this criterion. The worst covers (D1 and D2) are assigned a score of (− − −), while B.L. and D3 are assigned scores of (−−) and (−), respectively. Vegetation diversity: this criterion is an example of a counter-intuitive criterion or aspect from an engineering perspective. Cover D3 (the thickest) hosts the densest and most uniform vegetation due to the availability of moisture. However, from an ecological perspective, the water stress encountered by vegetation on thinner covers results in competition for moisture, and therefore more vegetation diversity. Following a site visit, the thinnest cover D2 is assigned the highest qualitative score of (+ + +), while D1, D3, and B.L. are assigned the scores of (+ +), (+), and (+), respectively. Table 14.1 shows the final evaluation matrix, sometimes called the pay-off table, populated with impact scores. The MCDM approach adopted in this study does not call for analysis that would require an illusory precision, but it takes into account the data available with the inherent impre-

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Table 14.1. The evaluation matrix.

Cost ($/m2 ) Moisture (days) Interflow (mm) Percolation to shale (cm) Preferential flow Vegetation diversity

D1

D2

D3

B.L.

2.0 163 0.15 1.6 −−− ++

1.4 149 0.21 2.1 −−− +++

4.0 168 0.15 3.5 − +

4.0 170 0.15 1.3 −− +

cision and indetermination. As will be shown in the following sections, relative scores regarding the performance of different alternatives are important for this type of analysis. As long as consistency in evaluating different alternatives is maintained, high precision of each individual score will have marginal effect on the outcome of the analysis. 14.6 Evaluation of alternatives The concept of non-dominated (Paretian) solution is used to obtain the solution for the problem under consideration. A feasible solution of any multi-objective (multi-criterion) problem is said to be non-dominated if there exists no other feasible solution that will cause an improvement in any one of the objectives (criteria) without making at least one other objective (criterion) worse (Cohon, 1978). This concept of non-dominated solution is the theoretical basis for most of the MCDM methods that aim at ranking different alternatives (Elshorbagy, 1994). In this study, the Weighted Summation method is used as one of the simplest MCDM methods (Parlos, 2000). 14.6.1 Priority structure (weights) An important issue in MCDM methods is to be able to determine the relative weights or importance of a collection of criteria. Usually, such values are between 0 and 1 and they add up to 1. Problems connected to the issue of how relative weights should be assigned and whom they should be assigned by are thoroughly discussed by psychologists (Lakoff, 1973) and in MCDM literature (Parlos, 2000). In this chapter, the results do not rely on any single set of weights; analysis is initiated by assigning equal weights to all criteria followed by weight sensitivity analysis to show the sensitivity of the outcome to changes in the priority structure of the problem. 14.6.2 Weighted summation method This method derives the ranking of alternatives from the weighted sum of standardized impact scores. As a first step all impact scores are standardized to eliminate the problem of multidimensionality (each criterion has its own measuring units). Different standardization schemes are available in the literature; more details can be found in Janssen et al. (2003). An appropriate standardization scheme can help marginalize large but insignificant differences or signify small but significant differences between two scores. An appraisal score is then derived for each alternative by multiplying the standardized impact score by its appropriate weight followed by summing the weighted scores of all criteria.

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14.6.3 Ranking of alternatives The Weighted Summation method is used to rank the four alternatives considering equal weights attached to the six criteria (0.167 each). The final appraisal scores of the four alternatives (Table 14.1) are 0.61, 0.67, 0.44, and 0.52 for D1, D2, D3, and B.L., respectively. Therefore, it can be concluded that D2 (the thinnest cover) outranks the other three alternatives followed by D1, then B.L., and finally D3. Cost, interflow, and vegetation diversity are the three primary criteria that contributed to the performance superiority of the D2 cover. It should be expected that marginalizing or reducing the weights associated with these criteria could lead to D2 cover losing its position as the best alternative. 14.7 Sensitivity and uncertainty analyses The notion of uncertainty is defined here as doubt resulting from a lack of information or knowledge. The results of multi-criterion evaluation are afflicted with a certain amount of uncertainty (Voogd, 1983), which is built up from the following components: (a) criterion uncertainty, which relates to the choice and the definition of the evaluation criteria that fully represent and describe the problem domain; (b) assessment uncertainty, which relates to the sometimes difficult task of arriving at a sharp score or description of the various characteristics of a criterion; (c) priority uncertainty, which relates to the differences that arise as a result of differing priority structures. It cannot be over emphasized that weights may differ from person to person and from time to time, which will affect the outcome of the analysis; (d) method uncertainty, which relates to the assumptions on which different MCDM methods are based. In this section, the second and the third types of uncertainties are discussed. The criterion uncertainty is also addressed briefly in Section 14.8. 14.7.1 Assessment (score) uncertainty Arbitrary uncertainty percentages are assumed for different criteria to reflect inherent randomness and the possibility of inaccurate in-situ measurements. Higher percentages are assumed when less confidence may be associated with the score of certain criteria. Accordingly, 15% uncertainty is assumed regarding the estimates of cost and vegetation diversity, while 50% uncertainty is considered for the criteria of preferential flow and percolation to shale. The scores of these two criteria are affected by the imprecise definition of the phenomena as well as the inaccuracies and failure of measuring instruments. An intermediate level of uncertainty of 30% is assumed for the criteria of moisture and interflow. The matrix scores are randomly changed according to the previous uncertainty levels; 5000 different combinations are tested using Monte Carlo simulation. The results are summarized in Table 14.2. It should be noted that equal criteria weights are assumed for this analysis. Attention should be drawn to three bold values in Table 14.2; in 66% of all cases, D2 still outranks other alternatives. However, there is a significant chance

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Table 14.2. Ranking probabilities for different alternatives using score uncertainty and equal weights. The three bold values are explained in the text. Alternative

D2 D1 B.L. D3

Position 1

2

3

4

0.66 0.33 0.01 0.00

0.30 0.42 0.27 0.00

0.04 0.15 0.71 0.10

0.00 0.10 0.00 0.90

Fig. 14.3. Score interval for different criteria with respect to D1 and D2 alternatives.

(33%) that D1 may outperform other alternatives and occupy the first position. Based on this uncertainty analysis, the thickest cover (D3) is the worst alternative in 90% of the time. 14.7.2 Score interval The purpose of this analysis is to determine the intervals within which the rank order of two alternatives is insensitive to changes in score. This may provide a deeper insight into the robustness of a certain alternative with respect to the scores populated in the evaluation matrix. If the ranking is found to be sensitive to a certain criterion, a feedback to instrumentation program and quantification and analysis processes may be deemed necessary to reduce the uncertainty associated with such a criterion. An example of this analysis is performed with respect to alternatives D2 and D1. The results are shown in Fig. 14.3. If the number of days in which the soil cover D2 holds sufficient moisture for vegetation drops from 149 (the original score in the evaluation matrix) to 141 days, a rank reversal could occur, which results in a conclusion that D1 could outperform D2 given that all other criteria scores are assumed unchanged. This result may divert the attention towards the importance of the moisture criteria. Every possible effort should be made to secure a reasonable estimate of such a score. A similar conclusion could be easily

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D2 D1 B.L. D3

Position 1

2

3

4

0.89 0.07 0.03 0.00

0.07 0.87 0.04 0.00

0.03 0.04 0.87 0.06

0.01 0.01 0.06 0.92

drawn regarding the percolation to shale criterion. D1 could also be perceived as a better alternative than D2 if the interflow value drops from the original estimate of 0.21 mm/year to 0.17 mm/year. This means that the total volume of collected interflow should drop from 2.1 m3 to 1.7 m3 assuming that the total interflow volume in D1 remains unchanged at the value of 1.6 m3 . It is worth mentioning that no rank reversal is observed based on score interval analysis of the preferential flow criterion, but a reverse point in overall ranking is achieved (i.e., D1 becomes better than D2) when vegetation diversity on D1 cover is better than that on D2. 14.7.3 Priority (weight) uncertainty Assigning weights is the issue that raises a strong controversy in the MCDM community. In this chapter, an uncertainty level of 100% is assumed for all criteria weights. This means that the importance of each criterion may range from nil to twice its original value of 0.167. Monte Carlo simulation similar to that performed with respect to the score uncertainty is conducted for weight uncertainty. The results are summarized in Table 14.3. It should be noted that impact scores are assumed unchanged for this analysis. Interestingly, even with such a wide range of weight uncertainty, D2 still outperforms other alternatives in 89% of the time. D3 remains as the worst alternative in 92% of all combinations assumed in this analysis. 14.7.4 Priority (weight) interval This analysis is similar to the score interval discussed earlier. When the weight of a certain criterion is changed (e.g. from 0.167 to 0.3), the remaining portion (0.7) is distributed on the other criteria while preserving their original relative importance. An example of this analysis is shown in Fig. 14.4 with respect to the moisture criterion. If the weight attached to moisture increases up to 0.28, D2 loses its position to D1. If the weight keeps increasing to 0.34, B.L. becomes a better alternative than D2. Even D3 could outperform D2 if the relative importance of the moisture reaches up to 0.43. Similarly, with regard to the cost criterion, B.L. becomes better than D2 if the weight of the cost drops close to zero. If the weight of the interflow criterion decreases to 0.05, D1 outperforms D2. With regard to the percolation to shale criterion, D1 and B.L. outperform D2 when the weight of this criterion increases from 0.167 to 0.44 and 0.53, respectively. The superior performance of D2 is insensitive to change of the weight of the vegetation diversity criterion. Finally,

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Fig. 14.4. Weight interval for moisture criterion.

when the relative importance of the preferential flow criterion increases to 0.38 and 0.43, D3 and B.L. outperform D2, respectively. 14.8 Discussion and conclusions The analysis conducted in this chapter could appear appropriate from the oil industry’s perspective. However, from a regulatory point of view, the problem could be seen differently. A clear example of this is the criterion of cost. The regulatory institution may argue that cost should be eliminated from the evaluation matrix and restoration of premining conditions is a burden on the industry that invested in the area. Therefore, the ranking exercise is repeated here after eliminating the criterion of cost from the matrix. The remaining five criteria are assigned equal weight (0.2 each). In this case, B.L. slightly outperforms D2 followed by D1 and D3 with overall scores of 0.62, 0.61, 0.58, and 0.52, respectively. The MCDM framework is presented in this chapter as a platform for studying the problem at hand from an integrated perspective. The results show that the outcome is sensitive to two major issues: the priority structure and the evaluation criteria. It is recommended that representatives from the oil industry, the regulatory institution, and research personnel reach an agreement on the evaluation criteria that will be included in the evaluation matrix as the first step. Second, a general priority structure listing the criteria in their order of relative importance needs to be identified. Finally, a ranking exercise can be conducted to show the alternatives that satisfy different criteria and priorities set a priori. The sensitivity analysis performed in Section 14.7 reveals that the final outcome is insensitive to changes in the score of the preferential flow criterion. This conclusion may send a signal both to researchers and the instrumentation program that more localized and detailed studies of this phenomenon may not be deemed necessary. The preferential flow phenomenon is greatly interesting both to hydrologists and soil scientists; however, the statement made here is only restricted to the problem of evaluating the above-mentioned discrete choices. The MCDM framework presented in this chapter is neither intended to give the right answer nor does it provide an objective analysis that relieves decision makers of the responsibility of making difficult judgements. The framework is an aid and process that seeks to integrate objective measurement with value judgement (Belton and Stewart, 2003), make judgement explicit, and manage subjectivity. The framework highlights the importance of tackling the problem of reclamation strategy from an integrated perspective. It can also help redirect research and monitoring efforts to focus on issues shown to be highly influential on the final decision.

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More importantly, it should be noted that the evaluation matrix used in this chapter is tentative and considered sufficient as a starting point. However, this matrix should be refined based on the watershed modelling that is going in parallel to this analysis framework. Modelling will help assess the future performance of different covers as well as their risk of failure under different conditions and scenarios. These issues should be considered as additional criteria in the evaluation matrix to capture the currently-missing aspect of the cover sustainability. This MCDM framework can also provide guidance to the modelling efforts by highlighting the most important outputs needed from the model. The watershed model will help populate the evaluation matrix with appropriate scores while receiving signals from the MCDM that help construct more focused and parsimonious models. Acknowledgements The first and second authors thank Syncrude Canada Ltd. and NSERC for financial support through Discovery and CRD grants. Bibliography Barbour, S.L., C. Boese and B. Stolte (2001). Water balance for reclamation covers on oilsands mining overburden piles. In: Canadian Geotechnical Conference. Canadian Geotechnical Society. Calgary, CA. pp. 313–319. Belton, V. and Stewart, T.J., Eds.) (2003). Multiple Criteria Decision Analysis. An Integrated Approach. Kluwer Academic Publishers. Dordrecht, NL. Boese, K. (2004). The design and installation of a field instrumentation program for the evaluation of soil–atmosphere water fluxes in a vegetated cover over saline/sodic shale overburden. M.Sc. Thesis, University of Saskatchewan, Saskatoon, SK, Canada. Bogardi, I. and L. Duckstein (1992). Interactive multiobjective analysis embedding the decision maker’s implicit preference function. Water Resour. Bull 28, 75–88. Cohon, L., Ed.) (1978). Multiobjective Programming and Planning. Academic Press. Washington DC, USA. Elshorbagy, A. (1994). Environment-oriented water resources projects appraisal using the multicriterion decision making technique. Master’s thesis. ITC. Enschede, NL. Falkenmark, M. (1997). Society’s interaction with the water cycle: a conceptual framework for a more holistic approach. Hydrol. Sci. J. 42(4), 451–466. Fassio, A., C. Giupponi, R. Hiederer and C. Simota (2005). A decision support tool for simulating the effects of alternative policies affecting water resources: an application at the European scale. J. Hydrol. 304, 462–476. Goicoechea, A., E.Z. Stakhiv and F. Li (1992). Experimental evaluation of multiple criteria decision models for application to water resources planning. Water Resour. Bull. 28, 89–102. Harboe, R. (1992). Multiobjective decision making techniques for reservoir operation. Water Resour. Bull. 28, 103–110. Harmancioglu, N.B. and N. Alpaslan (1992). Water quality monitoring network design: A problem of multi-objective decision making. Water Resour. Bull. 28, 179–192. Huth, A., M. Drechsler and P. Kohler (2004). Multicriteria evaluation of simulated logging scenarios in a tropical rain forest. J. Env. Manag. 71, 321–333. Janssen, R., M. Van Herwijnen and E. Beinat (2003). Definite 3.0. case studies and user manual. Technical Report R-03/03. Institute for Environmental Studies. Amsterdam, NL.

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Khalil, W.A., A. Shanableh, P. Rigby and S. Kokot (2005). Selection of hydrothermal pre-treatment conditions of waste sludge destruction using multicriteria decision-making. J. Env. Manag. 75, 53–64. Ko, S., D.G. Fontane and J.W. Labadie (1992). Multiobjective optimization of reservoir system operation. Water Resour. Bull. 28, 111–127. Lakoff, G. (1973). Hedges: a study in meaning criteria and the logic of fuzzy concepts. J. Philos. Logic pp. 12–22. Lasch, P., F. Badeck, F. Suckow, M. Lindner and P. Mohr (2005). Model-based analysis of management alternatives at stand and regional level in Brandenburg (Germany). Forest Ecol. Manag. 207, 59–74. Mays, L.W., Ed.) (2001). Water Resources Engineering. John Wiley & Sons. New York, USA. Meier, D. and S.L. Barbour (2002). Monitoring of cover and watershed performance for soil covers placed over saline-sodic shale overburden from oilsands mining. National Meeting of the American Society of Mining and Reclamation, Lexington, KY, June 9–13, Published by ASMR, Lexington, KY 40502. Parlos, P.M., Ed.) (2000). Multi-Criteria Decision Making Methods: A Comparative Study. Kluwer Academic Publishers. Dordrecht, NL. Qureshi, M.E. and S.R. Harrison (2001). A decision support process to compare riparian revegetation options in Scheu Creek catchment in north Queensland. J. Env. Manage. 62, 101–112. Raju, K.S. and L. Duckstein (2004). Integrated application of cluster and multicriterion analysis for ranking water resources planning strategies: a case study in Spain. J. Hydroinformatics 6, 295– 307. Roy, B., R. Slowinski and W. Treichel (1992). Multicriteria programming of water supply systems for rural areas. Water Resour. Bull. 28, 13–31. Srdjevic, B., Y.D.P. Medeiros and A.S. Faria (2004). An objective multi-criteria evaluation of water management scenarios. Water Resour. Manag. 18, 35–54. Stransbury, T., W. Woldt, I. Bogardi and A. Bleed (1991). Decision support system for water transfer evaluation. Water Resour. Res. 27, 443–451. Tecle, A. (1992). Selecting a multicriterion decision making technique for watershed resources management. Water Resour. Bull. 28, 129–140. Tecle, A., M. Fogel and L. Duckstein (1988). Multicriterion selection of wastewater management alternatives. J. Water Resour. Plan. Manag. 114, 383–398. Thiessen, E.M. and D.P. Loucks (1992). Computer assisted negotiation of multiobjective water resources conflicts. Water Resour. Bull. 28, 163–177. Voogd, H., Ed.) (1983). Multicriteria Evaluation for Urban and Regional Planning. Pion Limited. London, UK. Woldt, W. and I. Bogardi (1992). Ground water monitoring network design using multiple criteria decision making and geostatistics. Water Resour. Bull. 28, 45–62.

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Part V

Future Directions

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CHAPTER 15

Outstanding Research Issues in Integration and Participation for Water Resource Planning and Management Anthony J. Jakeman, Rebecca A. Letcher, John P. Norton et al.∗ Integrated Catchment Assessment and Management Centre The Australian National University Canberra, Australia

15.1 Introduction Substantial efforts are being made worldwide to address sustainability issues in catchments, but the approach is everywhere too fragmented and would benefit substantially from more coordination of research, management and their interaction. Typically research and policy have focused on one part of a catchment, or one issue in isolation from others, ∗ Catherine Allen, Charles Sturt University, Australia; Robert Argent, University of Melbourne, Australia;

Sam Banks, Monash University, Australia; Chris Barber, Crisalis International, Darlington, Australia; Guido Bazzani, CNR Ibimet, Bologna, Italy; Phillip Cormack, University of South Australia; Peter Cornish, University of Western Sydney, Australia; Francis Chiew, CSIRO Land and Water, Australia; Barry Croke, The Australian National University, Australia; Susan Cuddy, CSIRO Land and Water, Australia; Stephen Dovers and Rachel Eggins, The Australian National University, Australia; Christy Fellows, Griffith University, Australia; Douglas Fox, University of Melbourne, Australia; Stewart Franks, University of Newcastle, Australia; Carlo Giupponi, Università Statale di Milano, Italy; Neil Gunningham, The Australian National University, Australia; Matt Hare, Seecon Deutschland GmbH, Germany; Christine Johnston, CSIRO Land and Water, Australia; Ling Li, University of Queensland, Australia; Michael McAleer, University of Western Australia, Australia; Alison MacKinnon, University of South Australia, Australia; Holger Maier, University of Adelaide, Australia; Jaroslav Mysiak, FEEM, Venice, Italy; Blair Nancarrow, CSIRO Land and Water, Australia; Rory Nathan, Sinclair Knight Merz, Melbourne, Australia; Claudia Pahl-Wostl, University of Osnabreuck, Germany; Andrea Rizzoli, IDSIA, Lugano, Switzerland; Wendy Proctor, CSIRO Land and Water, Australia; Pradeep Sharma, Murray-Darling Basin Commission, Canberra, Australia; Craig Simmons, Flinders University of South Australia, Australia; Rodolfo Soncini-Sessa, Politecnico di Milano, Italy; Frank Stagnitti, Deakin University, Australia; Robert Vertessy, CSIRO Land and Water, Australia; Alexey Voinov, University of Vermont, USA; Jeffrey Walker, University of Melbourne, Australia; Geoffrey Syme, CSIRO Land and Water, Australia; Peter C. Young, University of Lancaster, UK.

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or on a subset of impacts and related disciplines. Often there has been too little emphasis on socioeconomic aspects, and engagement with managers and the community has been patchy. Continuity has been lacking in many cases. These limitations have led to ineffective and sometimes conflicting attempts to solve environmental problems, and to considerable waste of money. The development of practical, long-term solutions depends on changing this situation in several ways. Much better understanding is needed of the complex interactions between the full range of significant environmental system drivers, processes and impacts in each problem. The extent of uncertainty, the limited reliability of predictions, and fundamental and practical limits to understanding must be taken properly into account. Ways must be developed to achieve satisfactory compromises between the needs and concerns of interest groups, industries and the community at large. Innovative ideas such as water reuse and large-scale vegetation changes must be fostered and tested. Systematic methods of finding solutions that are robust in the face of policy changes and constraints must be developed. These requirements are easy to articulate and widely recognised, but their breadth demands a research framework wider in disciplinary and institutional scope than any current arrangement. To impose some coherence on such a framework, we suggest a research agenda integrated into the following themes and disciplines. 15.2 Themes and disciplines The themes, discussed in detail in Sections 15.2.1 to 15.2.12, are: Integrated Assessment, in which integrated simulation models, supported by stakeholder expertise and collateral knowledge, are used to predict multiple biophysical and socio-economic outcomes in alternative scenarios; Adaptive Management, developing management-revision principles, experiment designs, outcome indicators and monitoring practices to achieve sustainable management in evolving environments; Model Integration, Sensitivity and Uncertainty, tackling the quantification of sensitivity (of outputs to parameter and input values) and uncertainty in integrated, predictive models to aid decision-making; Integrated Decision-Making, designing and evaluating processes in which stakeholders participate to define the problems, design possible solutions, collaborate to implement them, and monitor and evaluate the outcome; Policy and Institutional Analysis, analysing institutional arrangements between various users of natural resources, as well as policy options and implications of alternative policy instruments and institutions; Quality Evaluation, developing standards and protocols for reporting and distributing models and data, and initiating an online resource to promote them. This includes information on model ownership, assumptions and appropriate uses, and data provenance, testing and validation. The disciplines underpinning these programmatic themes are themselves broader than traditional single-science disciplines:

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Ecosystems Management, focusing agricultural as well as ecological research on landscape-scale processes and outcomes; Decision-Making and Socio-Economic Impact Assessment, over a range of social research areas including economics, psychology, sociology and behavioural sciences; Environmental Engineering and Biotechnology, including technological approaches for water reuse and treatment at different scales; Environmental Hydrology, Hydrogeology and Climatic Variability, providing essential information on hydrologic interactions between groundwater, surface water (rivers, lakes, estuaries), marine ecosystems, atmospheric water and ecosystems; Modelling, Environmetrics and Spatial Analysis, incorporating process-based and empirical modelling, environmental data analysis, remote sensing and geographic information systems; Communication, Education and Governance, with innovative approaches to representing and understanding sustainability, and for stakeholders to negotiate policy and act to promote social and ecological sustainability. 15.2.1 Integrated Assessment Integrated Assessment (IA) provides a vehicle for addressing all key issues affecting the sustainability of terrestrial, aquifer and riverine systems. It integrates knowledge and understanding from research areas including social science, economics, ecology and hydrology, as well as from the community and managers, to address real-world management issues. The key features of IA (Jakeman and Letcher, 2003) are that it: • is a problem-focused, iterative, adaptive approach linking research to policy; • possesses interactive transparency that enhances communication; • is enriched by stakeholder involvement and is dedicated to adoption; • takes into account complexities between the natural and human environment, spatial dependence, feedbacks and impediments; • attempts to recognise missing essential knowledge. International research in IA has already demonstrated the success of this approach for natural-resource management. However, it is still at an early stage of development. Thus there is a need for further evolution of the general approach and further experience of how to tailor it to specific types of problems. The IA programme will: • Develop protocols and standards for reporting on IA processes, covering community collaboration and participation and documenting the assumptions, testing and uncertainty of integrated models. This is distinct from documenting the component models making up an IA model; integration of component models entails reconsideration of temporal and spatial scales, propagation of uncertainty, and changes in sensitivity caused by the interactions. Rigorous reporting standards are essential in making the IA process robust and defensible.

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• Develop IA schemes for specific sustainability issues of interest to agencies and other network partners. These schemes will provide the underpinning for research and project prioritization on these issues, as well as recombining problem-specific results from various disciplinary fields.

15.2.2 Adaptive Management Adaptive Management (AM) is about learning from doing (Fig. 15.1). It is a continuous cycle through: • monitoring and evaluating system responses to current management practices, • developing improved understanding and modelling of the system, • assessing alternative policy and management options, • implementing policies as experiments. The AM cycle of learning built on continuing experimentation allows more effective and socially inclusive learning than conventional management practices. By actively fostering the culture of continuing reflection, the AM programme will encourage practical learning from the information created in projects. A culture of reflection will also encourage learning from activities currently considered beyond the scope of formal research. The dual benefits are quicker and more useful learning, and more inclusive participation in managing natural resources.

Policy screening

Developing system understanding and modeling

ADAPTIVE MANAGEMENT CYCLE

Monitoring and evaluating system responses

Fig. 15.1. Adaptive Management Cycle.

Implementing policies as experiments

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Through training, extension and sustained support of philosophy and tools, the AM programme can provide policy makers and managers with the skills to: • determine if an AM approach would benefit their project/programme, and if so whether a passive or active approach is needed, • foster a culture of reflection in natural-resource management projects, • value and incorporate different forms of knowledge, • examine the assumptions underlying resource-management projects, • encourage social learning, • encourage management of whole systems rather than parts, • encourage flexibility in project design to enhance learning opportunities, • develop rewards for learning and sharing. 15.2.3 Model Integration, Sensitivity and Uncertainty Increasingly, simulation models are used to guide management decision-making, by improving understanding of the underlying processes and by predicting consequences of alternative climatic, demographic, economic and policy scenarios. This requires the integration of component models. The Model Integration, Sensitivity and Uncertainty (MISU) programme will focus on how models can be integrated to include all important impacts and how model outputs can be integrated to balance the interests of different stakeholder groups. A crucial aspect of complex, integrated models for environmental management is gauging of model uncertainty and sensitivity. The crux of model-aided decision-making is to determine whether one alternative is superior to another, by comparison of model outputs for the scenarios being considered. However, the outputs from integrated models are highly uncertain, for a number of reasons. The input data (e.g. river flow and temperature) are subject to natural variation, model parameters are estimated from limited data, and model structures are unlikely to represent exactly the complex processes which they mimic. An additional source of uncertainty in integrating outputs of social, environmental and economic models is subjectivity, e.g. in stakeholder selection of weights in multi-criteria decision analysis. The MISU programme will focus on both how to reduce uncertainty at all stages of decision-making and how to assess the sensitivity of the outputs of complex, integrated models to variation in the inputs and parameters. The main output from this programme will be innovative sensitivity-assessment methods to guide modellers towards the simplest adequate integrated model and establish how reliably it can aid environmental management decisions. Specifically, it will enable modellers and managers to: • test model credibility by checking output behaviour against prior knowledge, even if expressed qualitatively; • test model robustness by assessing whether the output requirements are met throughout the uncertainty ranges of the input parameters;

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• test model structure for signs of over-elaboration or over-simplification; • determine the extent of non-linearity in the parameter–output relations; • determine when and how to break up the integrated model for simpler analysis, validation and sensitivity assessment of individual models; • decide what additional data would improve the robustness of the model; • identify the extent to which the outputs can be controlled. 15.2.4 Integrated Decision-Making Integrated Decision-Making (IDM) is a process in which stakeholders participate to define the problems, design possible solutions, collaborate to implement them, and monitor and evaluate the outcomes. Through IDM stakeholders can build relationships and knowledge that will enable them to develop sustainable solutions. It rests on the premise that the successful resolution of environmental challenges depends on the participation of all parties in determining strategies and implementing them. This idea is not new, but the challenge is to ground the underlying philosophy of IDM in knowledge, experience and science. IDM has a focus on areas such as procedural justice, participatory planning and inter-group relations. The key value of IDM is good governance, i.e. direction and regulation incorporating the principles of: • democracy (opportunity for citizens to influence day-to-day decision-making), • participation (all have a voice in influencing decision-making), • equity and justice (processes that are fair and incorporate procedural, distributive and interactive justice), • partnership (cooperation rather than competition), • transparency (open procedures and methods), • open communication (information freely available to all participants), • accountability (checks and balances on decision makers), • responsibility (responsible decisions and actions), • visible influence (participants can see how they influenced the decisions), • unity in diversity (assembling, transforming and maximising knowledge), and • credibility (processes perceived as legitimate and accepted by all concerned. IDM presents a challenge to develop communication by dialogue rather than debate. Core beliefs are that nobody has claim to ‘ultimate truth’ or the ‘right solution’ and that each stakeholder’s perspective and expertise deserve respect and the opportunity to influence decision-making. Interactions must be based on trust, equity, respect, reciprocity and willingness to find consensus. It is expected that honouring each participant’s contribution to the big picture will stimulate creative thinking to devise innovative strategies for sustainability problems. This programme will feed the IA programme directly.

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IDM relies on two types of community integration: multi- and inter-disciplinary collaboration on environmental sustainability, and incorporation of user and general community knowledge, values and preferences in the development of these systems.

15.2.5 Policy and Institutional Analysis Policy and Institutional Analysis (PIA) research is devoted to institutional arrangements between users of natural resources, and to policy options and implications of alternative policy instruments and institutions. Achieving ecologically sustainable management and social and economic viability of related human activities is impossible without suitable policy and institutional settings. The nature of optimal policy and institutional settings for natural resource management and sustainable development is as yet unclear, despite intense research and substantive reform. The PIA programme will make advances in this domain through: closely linking natural- and social-science perspectives, consolidating and developing analytical capacities (theoretical and methodological), and developing operational options for policy and institutional reform. 15.2.6 Quality Evaluation The effectiveness of management decisions relies on the quality and appropriateness of information provided to decision makers and managers. The Quality Evaluation (QE) programme relates to the development of standards and protocols for model and data reporting and distribution. Standards and protocols are required because environmental and natural resource data and models used to guide management decisions often have large uncertainties, questionable underlying assumptions and potential incompatibilities. To ensure their appropriate use and adequate access to information about their scope and limitations, standards for reporting model testing, assumptions, appropriate scales and inherent uncertainties must be applied. The QE programme is intended to push forward development of such standards. It is notoriously difficult to gain widespread acceptance of standards, even in fields much less diverse than environmental modelling and management. A mechanism for doing so is first to establish draft standards through workshop discussions, then to exploit a website to encourage adherence to the standards. Ultimately the public would have access to information on models and data available for making management decisions. The reporting standards developed would be available for international adoption. 15.2.7 Ecosystems Management Ecosystems Management (EM) is a new professional domain which provides the understanding needed to plan and manage future ‘multi-functional’ landscapes that will sustain ecosystem services expected by society. Ecosystem services include agricultural and forestry production, provision of clean water, clean air, social amenity and conservation of biological resources. While the goals of EM include the maintenance of key ecological processes, EM also recognises that landscapes are, in important respects, human constructions reflecting past and present values and social, cultural and economic circumstances.

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Ecological considerations are thus necessarily embedded in debate on the expectations of society and how they might be achieved. EM contributes to setting of targets for catchment or landscape management; improvement of, or new options for, resource use and management; and monitoring of ecosystem performance (‘health’). It provides for branches of ecology and agriculture to focus research on landscape-scale processes and outcomes. The areas of expertise and perspectives in the network include agro-ecological research; fire ecology and management; invasive-species research; biodiversity and habitat assessment; freshwater ecology; molecular ecology; and restoration ecology. To date, many researchers have independently addressed one specific issue without full consideration of other ecosystem services. There is a need for a network, formal or informal, to conduct multi-disciplinary research into these landscape issues. 15.2.8 Decision-Making and Socio-Economic Impact Assessment Sustainable management of natural resources involves decisions on complex issues encompassing not only ecological values but also economic and social considerations. Often significant trade-offs must be taken into account. For these reasons, we need decisionmaking techniques that will simplify and clarify complex decision problems, identify trade-offs and thoroughly analyse the consequences of management and policy options. Management of terrestrial, aquifer and riverine systems should also employ participatory processes which include all stakeholders in decision-making. Such processes involve ‘public good’ resources and require adequate socio-economic impact assessment. The Decision-Making and Socio-Economic Impact Assessment discipline embraces a broad range of social research areas, including economics, psychology, sociology and other behavioural sciences. 15.2.9 Environmental Engineering and Biotechnology The demand for water for urban, industrial and agricultural use is rapidly increasing, resulting in increasing conflicts over water allocation. One solution is to make better use of existing supplies by reusing or recycling water, an increasingly recognised way of improving sustainable management of water. In particular, it can reduce demands on freshwater supplies from existing storages in upper catchments and from aquifers. The Environmental Engineering and Biotechnology discipline provides vital knowledge on water reuse and treatment. Before water can be reused it must often be treated to remove contaminants. The level of treatment depends on the intended use; for instance, water for human consumption requires a much higher level of treatment than irrigation water. Water-treatment technologies range from the conventional chemical and physical technologies used at water-treatment plants to more ‘natural’ technologies such as filtering through constructed wetlands. Other technologies include storage of recycled water in shallow aquifers. For water-recycling technologies to be successful they must consider issues including the source of water targeted (sewage, greywater, stormwater, irrigation tailwater), the use for recycled water (rinking, irrigation of parklands, irrigation of tree plantations or crops), the level of treatment required to meet quality guidelines, the most cost-effective method of treatment, and where the treated water will be stored.

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15.2.10 Environmental Hydrology, Hydrogeology and Climate Variability This discipline provides essential information on the hydrologic interactions between groundwater, surface water (rivers, lakes, estuaries, marine ecosystems), atmospheric water and ecosystems. Also of importance are interfaces between fresh and saline waters (in estuaries and groundwaters) and interactions with sources of contamination. Climate variability and climate change are key factors influencing terrestrial, aquifer and riverine ecosystems. This discipline will build capacity to improve understanding of hydroclimate variability and change. The central question this discipline will address is the influence of land-use change and climate variability on the water cycle. It involves water quantity and quality in surface and groundwater systems. The discipline group will coordinate efforts to understand and quantify flows and contaminant/solute fluxes between environmental compartments (groundwater, aquifer media, biota, surface water and associated ecosystems, atmosphere), and to assess water quantity and quality impacts of changes in one environmental compartment on others connected to it. 15.2.11 Modelling, Environmetrics and Spatial Analysis Effective management of natural resources and the environment requires quantitative assessment and measurement of impacts, processes and interactions. This may or may not be model-based but will require environmental data sets including time series and spatial data. The Modelling, Environmetrics and Spatial Analysis discipline incorporates the knowledge of modellers, environmental data analysis, remote sensing and geographic information systems. Environmental data are notorious for their violation of properties demanded by conventional statistical methods. Their problematic attributes include spatial and temporal correlation, over-dispersion, non-constant variance, paucity and non-standard distributions. Environmetrics aims to develop statistical methods that can be reliably used with environmental data. Currently it is associated with: • the design, evaluation, and placement of environmental monitoring networks; • accounting for meteorological and co-pollutant effects on estimation of status and trends in terrestrial, aquatic, and atmospheric contaminants; • statistical approaches to environmental epidemiology and toxicology; • characterising and reducing uncertainty in environmental risk assessment; • linking information about contaminant source, transport, human and ecosystem interactions and adverse effects; • recognising significant changes in records in the face of large natural variation; • characterising variation in the grey area between stationarity and non-stationarity. 15.2.12 Communication, Education and Governance The long-term goal of eco-social sustainability necessitates dealing with complex patterns of settlement, production, consumption and governance, for which traditional dis-

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ciplines are too narrowly defined. This discipline will bring into dialogue scholars who span the natural sciences, social sciences and humanities. It will integrate interdisciplinary research with policy analysis to build informed public engagement. Its research areas include: • governance and policy in relation to water and land, • river systems ecology, • education about the environment and sustainability, • indigenous knowledge, • economies and work, • rural society and policy, • communication, media and the visual arts. Eco-social sustainability implies socially sustainable cities and rural areas. This discipline will contribute to the development of best practice in social sustainability, and study the relation between increased social stability and equity and increased environmental awareness. There is an urgent need to acknowledge the social sciences as central to this, and to address the social causes of degradation and appropriate responses. ‘Adding in’ social sciences to a model predicated by the physical sciences will not lead to the interdisciplinary solutions that sustainability clearly requires. 15.3 Research directions For Integrated Assessment, significant development is still required in evaluating and reporting models and participatory processes. Frameworks to integrate models and disciplines for multiple issues are also required. Difficulties due to scale differences among component models remain a research topic. In Adaptive Management, future research opportunities stem from problems such as: • a widespread preference for action over reflection, • aversion to public acknowledgement of uncertainty in decision-making, • the narrow focus of target-based programmes, • short time frames of agency planning and implementation, • organisational psychology that guards against learning and change. Significant benefits in Adaptive Management could be obtained through better sharing of existing models and their development. Other opportunities include: • development of non-threatening ways to gather, develop, record and share conventional and unconventional system information, • improved tools to capture and express institutional knowledge, • methods for testing knowledge, identifying gaps and designing experiments,

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• development of monitoring techniques able to distinguish relatively small effects of changed management practices from the large natural variations. Potential difficulties in Model Integration process include data formats impeding exchange between models; software platform incompatibility; error accumulation; large data requirements; high model complexity, and high likelihood of over-parametrization. Although management models are generally less data-intensive than process models, they still need input and output data for calibration and validation. Shortcomings to be addressed are restricted operational range of models, as dictated by the calibration data; lack of transparency in empirical, rather than process-based, models; lack of flexibility in models geared to a particular input/output relationship. For Sensitivity Analysis, alternatives to single-effect perturbations are to be pursued. The best known represents all uncertain inputs/parameters as random variables with distributions obtained from available data, or uniform distributions to represent their likely ranges when detailed information is unavailable. Monte Carlo simulation or first-order approximation is then used to obtain the uncertainty in the model output(s). This approach has obvious limitations when many uncertain items must be considered simultaneously. Another alternative being developed is set-to-set mapping, identifying the ranges of inputs/parameters yielding outputs meeting a number of requirements, with no assumption about relative probabilities within the range. While there is a proliferation of literature on Integrated Decision-Making, there is little evidence of IDM being implemented well in practice. The wealth of claims of the benefits of IDM is rarely substantiated in practice. In recent decades have seen enormous advances in theoretical understanding of equity and fairness in decision-making, but there is general reluctance by decision-makers to implement this knowledge. This can be attributed to time and capacity constraints, but may also be associated with a perceived loss of control. The tradition of overlooking social science or treating it as an afterthought has also been a major impediment. Few have seen the benefits of enriched decision-making through well planned and implemented, participatory IDM. There is also a notable lack of research to determine the long-term effects of different types of participation on, for example, perceptions of the fairness of procedures, commitment to outcomes, and willingness to work towards agreed outcomes. In-depth involvement in decision-making is most effective, yet in practice many participatory models are tokenistic and involve participants only superficially, for example by asking them for feedback well after decisions are made. Tokenistic practices are likely to be inadequate or even detrimental. This area needs more thorough investigation. In regard to Policy and Institutional Analysis, elements of a more comprehensive framework have been developed in recent years. Basic elements include: • a framework for problem definition based on underlying problem attributes; • a heuristic but detailed and environment-specific model of the policy process and a typology of institutional (including statutory) and organisational settings to ensure sensitivity to jurisdictional context; • menus of policy instruments, sustainability-specific selection criteria, and empirically derived insights into instrument choice;

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• more sophisticated schemes for evaluating and prescribing participatory approaches to environmental policy and management, recognising multiple types and purposes of participation and multiple subsets of the community; • principles for institutional design, drawn from analyses of reforms implemented over the past decade. For Quality Evaluation a significant body of literature exists on model validation and evaluation. Traditionally, validation of models has been by a combination of history matching and peer review. However these norms are insufficient, or even impossible, for most integrated assessment models. By contrast, Parker et al. (2001) state that ‘the essential, contemporary questions one would like to have answered when seeking to evaluate a model (are): • Has the model been constructed of approved materials, i.e. approved constituent hypotheses (in scientific terms)? • Does its behaviour approximate well that observed in respect of the real thing? • Does it work, i.e. does it fulfil its designated task, or serve its intended purpose?’ They conclude that evaluating IA models is ‘likely to be less dependent on the previous convention of classical peer review and history matching and more dependent on protocols and tests yet to be developed’. They suggest that an evaluation protocol may be needed more for the ‘evolving structure and content of IA, as opposed to the eventually finished product’. These contentions are arguable. For Ecosystems Management the challenges remain to identify those profitable agricultural systems that possess suitable ecological and physical attributes. The danger is that agricultural systems will appear to be sustainable at the farm scale but prove not to be at catchment scale. Catchment-scale assessment is vital. To achieve desired landscape outcomes based on local actions, management must be co-ordinated within an overall plan, yet there is no real discipline of landscape planning in this sense. Plans are required to ensure biodiversity conservation, water quality and flow, ground water management and perhaps carbon sequestration, while providing rural economic and social wellbeing. The Decision-Making and Socio-Economic Impact Assessment discipline will try to answer such questions as: What matters to people in natural-resource management? How and why do individuals make decisions about resource use and protection? How can individual preferences and constraints influence sustainability? How can policy instruments be designed to complement the constraints and references of individuals to effect better sustainability outcomes? How can a wide range of values and impacts be incorporate into decision-making? How can trade-offs in decision-making be identified and dealt with effectively? How can risk and uncertainty be incorporated? In Environmental Engineering and Biotechnology, there are great opportunities to integrate water re-use schemes into a broader water-management plan and to help address community concerns about recycled water. Environmental Hydrology, Hydrogeology and Climatic Variability has a key link with the IAHS Decade on Predictions in Ungauged Basins (PUB) (http://www.cig.ensmp.fr/∼ iahs), which aims to achieve major advances in the capacity to make predictions in ungauged basins. The science programmes and objectives within PUB identify as areas for

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targeted research: advance the ability of hydrologists to predict water fluxes from ungauged basins, along with estimates of the uncertainty; advance the knowledge and understanding of climatic and landscape controls on hydrologic processes at all scales, to constrain the uncertainty in hydrologic predictions; demonstrate the value of data for hydrologic predictions, and provide a rational basis for future data acquisition, including alternative data sources; advance the scientific foundations of hydrology, provide a scientific basis for sustainable river basin management; and actively promote the development of scientific knowledge and technology to areas and communities where it is needed. For hydroclimate variability, the research priorities are: hydroclimate data interpretation; improved understanding and modelling of hydroclimate and climate variability on different time scales (inter-annual, multi-decadal); improved projections of climate; model-based and statistical approaches to hydrologic sensitivity to changing climate conditions; climate change impact studies on hydrology and water resources, wetlands and riverine environments, biodiversity conservation, rangelands, ecosystems; and ENSO, probabilistic rainfall/streamflow forecasts. The programme outlined, especially in Communication, Education and Governance, will move beyond simple opposition of social development and environmental degradation. The role of the social sciences is not seen solely as a means to promote environmental protection measures and determine their effectiveness. The programme will investigate social policy and institutional structures enabling social and environmental sustainability to be complementary and mutually supporting rather than requiring a series of ‘tradeoffs’. 15.4 Where next? What does this agenda imply about research infrastructure? Plainly a new research effort as broad and as discipline-spanning as the one outlined above poses some questions about the adequacy of present research arrangements. It implies time scales of the order of a decade, funding on a scale allowing continuity for a community large enough to make significant progress on broad and demanding issues, and a means of getting researchers and research users from very different backgrounds to talk to each other and learn each others’ perspectives and priorities. It also poses hard practical problems in sourcing, testing, describing, providing access to and archiving data. One possible way to satisfy these needs is through large, relatively formal, centrally accountable, multi-national research programmes and networks, as exemplified by the European Union Frameworks Programmes. However, other possibilities are beginning to emerge. As the costs of information and communication provision through the internet fall, it becomes feasible to think of an ad hoc research network based on a website, expected to have a life of a decade or so but organised and funded as a large number of relatively modest contributions. Users would be able to take as large or as small a part in the programme as they liked, subject only to definite agreements with their immediate partners and to a commitment to adhere to minimum standards common to the entire network, for instance in data and software reporting, freedom of access with minimal safeguards, proper attribution and crediting, and openness to peer criticism. A network of this type has recently been initiated (see stars.net.au) but is only in its formative stages. Is it Utopian to think that such an informal network could succeed? It would raise difficult

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questions of confidentiality, intellectual property rights, legal liability, depth and continuity of support, and avoidance of jealousies and conflict. Perhaps now is the time to see, by trying, just how large these difficulties are. 15.5 Bibliography IA bibliography CIESIN, Consortium for International Earth Science Information Network (1995). Thematic guide to integrated assessment modelling of climate change. online. Dowlatabadi, H. (1995). Integrated assessment models of climate change: an incomplete overview. Energy Policy 23(4–5), 289–296. Frederick, K.D. (1994). Integrated assessments of the impacts of climate change on natural resources: An introductory essay. Climatic Change 28, 1–14. Hare, M., R.A. Letcher and A.J. Jakeman (2003). Participatory modelling in natural resource management: A comparison of four case studies. Integr. Assess. 4(2), 62–72. Jakeman, A.J. and R.A. Letcher (2003). Integrated assessment and modelling: Features, principles and examples for catchment management. Environ. Modell. Softw. 18, 491–501. Lee, K.N. (1993). Compass and Gyroscope: Integrating Science and Politics for the Environment. Island Press. Washington DC. Letcher, R.A. and A.J. Jakeman (2003). Application of an adaptive method for integrated assessment of water allocation issues in the Namoi River catchment, Australia. Integr. Assess. 4(2), 73–89. Martin, A. and J. Sherington (1997). Participatory research methods – implementation, effectiveness and institutional context. J. Appl. Stat. 55(2), 195–216. Mendelsohn, R. and N.J. Rosenberg (1994). Framework for integrated assessments of global warming impacts. Climatic Change 28, 15–44. Morgan, M.G. and H. Dowlatabadi (1996). Learning from integrated assessment of climate change. Climatic Change 34, 337–368. Pahl-Wostl, C. (2003). The importance of the human dimension in integrated assessment models and processes: actor based analysis and modelling approaches. In: Proceedings of the Modelling and Simulation Society of Australia and New Zealand, MODSIM 2003. Townsville, Queensland, AU. pp. 465–472. Parker, P., R. Letcher, A.J. Jakeman, M.B. Beck, G. Harris, R.M. Argent, M. Hare, C. Pahl-Wostl, A. Voinov, M. Janssen at al. (2002). Progress in integrated assessment and modelling. Environ. Modell. Softw. 17(3), 209–217. Parson, E.A. (1996). Three dilemas in the integrated assessment of climate change. Climatic Change 34, 315–326. Parson, E.A. and K. Fisher-Vanden (1997). Integrated assessment models of global climate change. Annu. Rev. Energ. Env. 22, 589–628. Pretty, J.N. (1995). Participatory learning for sustainable agriculture. World Dev. 23(8), 1247–1263. Risbey, J., M. Kandlikar and A. Patwardhan (1996). Assessing integrated assessments. Climatic Change 34, 369–395. Rothman, D.S. and J.B. Robinson (1997). Growing pains: a conceptual framework for considering integrated assessments. Environ. Monit. Assess. 46, 23–43. Rotmans, J. and M. Van Asselt (1996). Integrated assessment: growing child on its way to maturity. An editorial essay. Climatic Change 34, 327–336. Timmermunn, P. and R. Munn (1997). The tiger in the dining room: designing and evaluating integrated assessments of atmospheric change. Environ. Model. Assess. 46, 45–58.

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Weyant, J., O. Davidson, H. Dowlatabadi, J. Edmonds, M. Brubb, E.A. Parson, R. Richels, J. Rotmans, P.R. Shukla, R.S.J. Tol, W. Cline and S. Fankhauser (1995). Climate Change 1995: Economic and Social Dimensions. Chap. Integrated Assessment of Climate Change: an overview and comparison of approaches and results. Cambridge University Press. Cambridge, UK.

AM bibliography Allan, C. and A. Curtis (2003a). Learning to implement adaptive management. Nat. Resour. Manage. 6, 23–28. Allan, C. and A. Curtis (2003b). Regional scale adaptive management: Lessons from the North East salinity strategy. Australa. J. Environ. Manage. 10, 76–84. Argent, R.M. and B. Houghton (2001). Land and water resources model integration – software engineering and beyond. Adv. Environ. Res. 5, 351–359. Argent, R.M., R.B. Grayson and S.A. Ewing (1999). Integrated models for environmental management: Issues of process and design. Environ. Int. 25, 693–699. Bellamy, J.A. and A.K. Johnson (2000). Integrated resource management: moving from rhetoric to practice in Australian agriculture. Environ. Manage. 25, 265–280. Biggs, S. (1987). Proposed methodology for analysing farmer participation in the Isnar Ofcor study. Overseas Development Institute, London, UK. Ewing, S., R. Grayson and R. Argent (1997). Moving from theory to practice: the use of an adaptive management process in integrated catchment management. In: International Geographical Union Commission on Sustainable Rural Agriculture. IGU, Armidale, AU. pp. 276–282. Holling, C.S. (1995). Barriers and Bridges to the Renewal of Ecosystems and Institutions. Chap. What barriers? What bridges? Columbia University Press. New York, NY. Holling, C.S., Ed.) (1978). Adaptive Environmental Management and Assessment. John Wiley. Chichester, UK. Ladson, A.R. and R.M. Argent (2002). Adaptive management of environmental flows: lessons for the Murray-Darling basin from three large North American rivers. Aust. J. Water Resour. 5, 89– 101. Lee, K.N. (1999). Appraising adaptive management. Conserv. Ecol. 3(2), viewed 16 August 2001, http://www.consecol.org/vol3/iss2/art3. Walters, C., J. Korman, L.E. Stevens and B. Gold (2000). Ecosystem modelling for evaluation of adaptive management policies in the Grand Canyon. Conserv. Ecol. 4(2), 1 ff. Walters, C.J. and C.S. Holling (1990). Large-scale management experiments and learning by doing. Ecology 71, 2060–2068.

MISU bibliography Cukier, R.I., H.B. Levine and K.E. Shuler (1978). Nonlinear sensitivity analysis of multi-parameter model systems. J. Comput. Phys. 26, 1–42. Drechsler, M. (1998). Sensitivity analysis of complex models. Biol. Conserv. 86, 401–412. Hashimoto, T., J.R. Stedinger and D.P. Loucks (1982). Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation. Water Resour. Res. 18, 14–20. Maier, H.R., B.J. Lence, B.A. Tolson and R.O. Foschi (2001). First-order reliability method for estimating reliability, vulnerability and resilience. Water Resour. Res. 37(3), 779–790. Ratto, M. and A. Saltelli (2002). Int. Conf. On Computational Science, 1, Lecture Notes in Computer Science vol. 2329. Chap. An efficient approach to deal with the curse of dimensionality in sensitivity analysis computations, pp. 196–205. Springer-Verlag. Berlin, D. Reichert, P. and M. Omlin (1997). On the usefulness of overparameterized ecological models. Ecol. Modell. 95, 289–299.

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Saltelli, A., Chan, K. and Scott, E.M., Eds.) (2000). Sensitivity Analysis. John Wiley. Chichester, UK. Sitar, N., J.D. Cawlfield and A. Der Kiureghian (1987). First-order reliability approach to stochastic analysis of subsurface flow and contaminant transport. Water Resour. Res. 23(5), 794–804. Sobol, I.M. (1993). Sensitivity analysis for nonlinear mathematical models. Math. Model. Comput. Exper. 1, 407–414. Spear, R.C., T.M. Grieb and N. Shang (1994). Parameter uncertainty and interaction in complex environmental models. Water Resour. Res. 30(11), 3159–3169. Vasquez, J.A., H.R. Maier, B.J. Lence and B.A. Tolson (2000). Achieving water quality system reliability using genetic algorithms. J. Environ. Engin. 126(10), 954–962.

IDM bibliography Arnstein, S.R. (1969). A ladder of citizen participation. Am. Instit. Planners J. 35, 216–224. Batson, C.D., N. Ahmad and J. Tsang (2002). Four motives for community involvement. J. Soc. Issues 58(3), 429–447. Baughman, M. (1995). Fairness and Competence in Citizen Participation: Evaluating Models for Environmental Discourse. Chap. Mediation. Technology, Risk and Society. Kluwer Academic Publishers. Dordrecht. Bellamy, J.A., G.T. McDonald, G.J. Syme and J.E. Butterworth (1999). Evaluating integrated resource management. Soc. Nat. Resour. 12, 337–353. Black, J.S. and H.B. Gregersen (1997). Participative decision-making: An integration of multiple dimensions. Hum. Relat. 50, 859–878. Eggins, R.A., S.A. Haslam and K.J. Reynolds (2002). Social identity and negotiation: Subgroup representation and superordinate consensus. Pers. Soc. Psychol. B. 28, 887–899. El Ansari, W., C.J. Phillips and M. Hammick (1998). Multiple Objective Decision Making for Land, Water and Environmental Management. Chap. Co-learning our way to sustainability: An integrated and community-based research approach to support NRM decision-making, pp. 51– 59. Lewis Publishers. Boston. Ewing, S.A., R.B. Grayson and R.M. Argent (2000). Science, citizens, and catchments: Decision support for catchment planning in Australia. Soc. Nat. Resour. 13, 443–459. Haslam, S.A., R.A. Eggins and K.J. Reynolds (2003). The aspire model: Actualizing social and personal identity resources to enhance organizational outcomes. J. Occup. Organ. Psych. 76, 83– 113. Hemmati, M. (2001). Multi-Stakeholder Processes for Governance and Sustainability – Beyond Deadlock and Conflict. Earthscan. London, UK. Kumar, S. (2002). Methods for Community Participation: A Complete Guide for Practitioners. ITDG Publishing. London, UK. Lawrence, R.L., S.E. Daniels and G.H. Stankey (1997). Procedural justice and public involvement in natural resources decision making. Soc. Nat. Resour. 10, 577–589. Lind, E.A. and T.R. Tyler (1988). The Social Psychology of Procedural Justice. Plenum Press. New York, NY. Maznevski, M.F.L. (1994). Understanding our differences: Performance in decision making groups with diverse members. Hum. Relat. 47(5), 531–552. Seligman, C., G.J. Syme and R. Gilchrist (1994). The role of values and ethical principles in judgments of environmental dilemmas. J. Soc. Issues 50(3), 105–119. Smith, P.D. and M.H. McDonough (2001). Beyond public participation: Fairness in natural resource decision making. Soc. Nat. Resour. 14, 441–452. Soncini-Sessa, R., A. Castelletti and E. Weber (2007). Integrated and Participatory Water Resources Management. Theory. Elsevier, Amsterdam, NL (to appear).

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Syme, G.J. and B.E. Nancarrow (2002). Evaluation of public involvement programs: Measuring justice and process criteria. Water 29(4), 18–24. Syme, G.J. and B.S. Sadler (1994). Evaluation of public involvement in water resources planning: A researcher-practitioner dialogue. Evaluation Rev. 18(5), 523–542. Syme, G.J., B.E. Nancarrow and J.A. McCreddin (1999). Defining the components of fairness in the allocation of water to environmental and human uses. J. Environ. Manage. 57, 51–70. Syme, G.J., E. Kals, B.E. Nancarrow and L. Montada (2000). Ecological risks and community perceptions of fairness and justice: A cross-cultural model. Risk Anal. 20(6), 905–916. Tyler, T.R. and S.L. Blader (2000). Cooperation in Groups: Procedural Justice, Social Identity, and Behavioural Engagement. Psychology Press. Philadelphia, PA.

PIA bibliography Barnett, J., H. Ellemor and S. Dovers (2003). In: New Dimensions in Ecological Economics: Integrated Approaches to People and Nature. Chap. Sustainability and interdisciplinarity. S. Dovers, D. Stern, and M. Young, (Eds). Edward Elgar. Cheltenham, UK. Berkhout, F., Leach, M. and Scoones, I., Eds.) (2003). Negotiating Environmental Change: New Perspectives from the Social Sciences. Edward Elgar. Cheltenham, UK. Connor, R. and S. Dovers (2004). Institutional Change for Sustainable Development. Edward Elgar. Cheltenham, UK. Dovers, S. (1997). Sustainability: demands on policy. J. Public Policy 16, 303–318. Dovers, S. (2002). Sustainability: reviewing Australia’s progress, 1992–2002. Int. J. Environ. Studies 59, 559–571. Dovers, S. (2003). New Dimensions in Ecological Economics: Integrated Approaches to People and Nature. Chap. A policy orientation as integrative strategy. Edward Elgar. Cheltenham, UK. Gunningham, N. and D. Sinclair (2002). Leaders and Laggards: Next Generation Environmental Regulation. Greenleaf. UK. Gunningham, N. and P. Grabosky (1999). Smart Regulation: Designing Environmental Policy. Oxford University Press. Oxford, UK. Gunningham, N., R. Kagan and D. Thornton (2003). Shades of Green: Business, Regulation and Environment. Stanford University Press. Stanford, CA. Page, E. and J.U. Proops (2003). Environmental Thought. Edward Elgar. Cheltenham, UK.

QE bibliography Parker, P., R. Letcher, A. Jakeman et al. (2001). In: Understanding and Solving Environmental Problems in the 21st Century: Toward a New, Integrated “Hard Problem Science” (R. Costanza and S.E. Jorgensen, Eds.) Chap. The potential for Integrated Assessment and Modelling to solve environmental problems: visions, capacity and directions. Elsevier. Amsterdam, NL. Ravetz, J.R. (1997). Integrated Environmental Assessment Forum: developing guidelines for “good practice”. ULYSSES WP-97-1. Darmstadt University of Technology. Darmstadt, D. Risbey, J., Kandlikar M. and Patwardhan A. (1996). Assessing integrated assessments. Climatic Change 34, 369–395. Young, P. (1977). A general theory of modelling for badly defined systems. AS/R9, Centre for Resource and Environmental Studies, The Australian National University, Canberra.

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Subject Index

alternative, 5, 61, 210, 225, 245, 258 BATNA, 201 best compromise, 17, 233 design, 13, 197, 232 ranking, 264 reasonable, 16, 235 Analytic Hierarchy Process, 195, 199 Approximating Networks, 118 BN, 11, 49, 50 compensation, 16, 62 Compromise Programming, 180 criterion, 10, 198, 210, 228, 260 DBM, 27, 29 Decision Support System, see DSS decision-making, 180, 195, 274 procedure, see also PIP, 6, 246, 260 process, 4, 162, 177, 210, 243, 278 discrepancy, 131 discretization, 117, 130, 136 distribution network, 161 DPSIR, 4, 207 DSS, 12, 19, 49, 99, 101, 141, 207 Multi-Objective (MODSS), see DSS Nile, 104 spatial, 207, 211 Dynamic Programming, 117, 146 ANDYM, 121, 123 ELQG, 108 evaluation hierarchy, 11, 230 Extended Ritz Method, 122, 125

farming contract, 54 flood management, 175, 182 protection, 223, 245 Fuzzy Expected Value, 179, 183 Fuzzy Sets, 179, 180 Game Theory, 197, 200 Genetic Algorithms, 161, 165 groundwater management, 52 protection, 49, 53 indicator, 10, 228 Integrated Assessment, 274 Interactive Decision Map, 214, 216 international waters, 189, 225 irrigation, 141, 150 management, 141 strategy, 143, 150 IWRM, 3, 99, 101, 207, 225, 243 Kalman Filter, 31 management, 7, 20, 107, 117, 141, 175, 226, 273 adaptive, 274, 276 Markov chain, 148 Decision Problem, 145 memetic, 76 mitigation, 16, 237 model, 107 activity, 212 agent-based, 74, 76

291

292

Subject Index

agricultural, 109 Bayesian Network, see BN bio-decisional, 142, 153 business process, 212 crop transition, 154 Data-Based Mechanistic, see DBM hydrological, 111 snow-melt, 34 identification, 11, 30, 55, 231 integration, 274 parameter estimation, 30, 60 parsimonious, 12, 28, 35 State Dependent Parameter, see SDP Transfer Function, 30 validation, 31, 78, 284 MODSS, see DSS Monte Carlo simulation, 29, 45, 88, 283 Multi Attribute Value Theory, 15, 233 Multi-Criterion Decision Making, 180, 210, 257 Nash point, 201 Negotiation Support System, 189, 195, 213 negotiations, 16, 189, 195, 201, 210, 237 optimal control, 14, 117, 121, 144, 232 overall existence ranking index, 182 Pareto efficiency, 263 frontier, 13, 201, 214, 232 Race, 16, 235 participation, 6, 50, 57, 65, 74, 113, 175, 178, 210, 243, 247, 250, 280, 283 distributed, 20 PIP procedure, 3, 225, 246 planning, 7, 141, 161, 210, 226, 243 agricultural, 109 integrated, 3, 207, 273 participatory, 3, 175, 273 procedure, see also PIP, 4, 225 process, 4, 49 programme of measures, see alternative

Quality Evaluation, 274 reconstructed watershed, 257 Refined Instrumental Variable, 30, 40 Reinforcement Learning, 146 remote sensing, 112, 154 reservoir, 107, 120, 134, 231 management, 107, 117 River Basin Management Plan, 209 river restoration, 243 scarcity rent, 192 scenario, 12, 14, 107, 209, 230 SDP, 36, 41 sensitivity analysis, 45, 79, 264, 277 shadow price, 192 social factors, 247 learning, 6, 74, 78, 238, 277 survey, 248 stakeholder involvement, see also participation, 63, 175 uncertainty, 18, 45, 51, 161, 180, 264, 274 quantification, 166 utility function, 199 value function, 15, 233 water allocation, 194 conservation, 74 demand, 191 markets, 190 price, 75 Water Allocation System, 190, 193 Water Framework Directive, see WFD Weight method, 263 WFD, 3, 208, 225, 243