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MANY OBJECTIVE WATER RESOURCES PLANNING AND MANAGEMENT GIVEN DEEP UNCERTAINTIES, POPULATION PRESSURES, AND ENVIRONMENTAL CHANGE
Abstract
Climate change and population growth require adaptation strategies that can ensure a sufficient amount of water supply over long planning horizons. In the past, water resources planning has been done using single-objective benefit-cost analysis, where a single estimate of a project’s costs and benefits is calculated to select funded projects. The calculation of monetary benefit functions, however, is heavily dependent on several critical assumptions. For example, the analysis must assume that the preferences of diverse stakeholder groups will not change in the future system states. Moreover, operational design and implementation of engineered water resources systems must consider a broad suite of risk-based performance objectives. This dissertation research advances water resources planning and decision support techniques that can confront the limiting challenges associated with classical approaches. We specifically advance a many objective approach using multiobjective evolutionary algorithms (MOEAs) that allows planners to generate and evaluate planning alternatives that can balance diverse planning goals and objectives.
This dissertation contributes two new many objective planning frameworks, collections of techniques that use many objective analysis to further our understanding of how to improve planning under uncertainty. The first framework, termed de Novo Planning, incorporates the concept of “learning” into many objective planning formulations. De Novo Planning addresses the fact that planning formulations themselves change as decision makers solve problems and analyze results. Global sensitivity analysis using Sobol’ variance decomposition is used to determine an appropriate level of complexity for decision variables in the system. Multiple problem formulations are then constructed and solved using a MOEA to test the insights learned through the sensitivity analysis.
The second planning innovation is termed Many Objective Robust Decision Making (MORDM). MORDM addresses deep uncertainty, a situation in which stakeholders do not know or cannot agree on the full suite of risks that are posed
to their system. Deep uncertainty can severely impact the expected performance of planning alternatives in ways that are difficult to predict. This issue is especially relevant since most system planning under uncertainty is evaluated using a single best estimate of the distributions of data. Estimates from historical system information and their associated likelihoods, though, could be incorrect. For example, climate change can alter the magnitude and timing of streamflow availability, which makes the historical data an unreliable indicator of future events. Robust Decision Making (RDM) has been advocated as a way to address this issue, by evaluating a wide array of plausible futures to show future system vulnerabilities. The MORDM framework introduced in this thesis bridges many objective analysis with RDM, by evaluating solutions in the many objective tradeoff with an ensemble of alternative futures that investigate key assumptions and uncertainties, quantifying the solutions’ robustness, and facilitating choice of robust solutions for a final negotiated decision.
The dissertation’s planning innovations are demonstrated using two test cases with differing hydrologic characteristics and regulatory structures. The first test case explores how to improve the supply reliability of a single city in the Lower Rio Grande Valley (LRGV) of Texas. The LRGV case study uses risk-based planning triggers to control a city’s use of a water market, with transfers between agricultural use and municipal supply. The goal is to highlight how non-structural adaptation such as water marketing can aid water management in the arid western U.S. Problems of water availability are also becoming more apparent in the eastern U.S., where water planning was traditionally focused on flood management and droughts were not often considered a serious issue. The second test case explores multi-sector long-term supply planning for the Lower Susquehanna portion of the Susquehanna River Basin in Pennsylvania and Maryland. Two many objective problem formulations for the Lower Susquehanna expose biases and challenges of classical planning formulations. Subsequent exploration of deep uncertainty suggests critical modeling assumptions for the test case. Insights from the Susquehanna test case have the goal of assisting reservoir planning for infrastructure systems in the eastern U.S.
Table of Contents
List of Figures ix
List of Tables xi
Acknowledgments xii
Chapter 1
Introduction 1
1.1 Overview of Chapters . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.1 Chapter 2: Background . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 Chapter 3: de Novo Planning . . . . . . . . . . . . . . . . . 4
1.1.3 Chapter 4: Many Objective Robust Decision Making . . . . 5
1.1.4 Chapter 5: Formulation Biases for the Lower Susquehanna . 6
1.1.5 Chapter 6: Concluding Remarks . . . . . . . . . . . . . . . . 7
Chapter 2
Background 8
2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 Many Objective Analysis . . . . . . . . . . . . . . . . . . . . 9
2.1.2 Many Objective Analysis of the LRGV . . . . . . . . . . . . 11
2.1.3 Impact of Changing Assumptions: Drought Analysis for the
LRGV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Planning Innovations . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 The Challenge of Deep Uncertainty . . . . . . . . . . . . . . 17
2.2.2 de Novo Planning . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.3 Many Objective Robust Decision Making . . . . . . . . . . . 19
2.3 Quantitative Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1 Multi-Objective Evolutionary Algorithms . . . . . . . . . . . 20
2.3.1.1 Epsilon-Dominance . . . . . . . . . . . . . . . . . . 23
2.3.1.2 ε-NSGAII . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.1.3 The Borg MOEA . . . . . . . . . . . . . . . . . . . 26
2.3.2 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.2.1 Sobol’ Sensitivity Analysis . . . . . . . . . . . . . . 27
2.3.2.2 Scenario Discovery and PRIM . . . . . . . . . . . . 27
2.3.3 Interactive Visual Analytics . . . . . . . . . . . . . . . . . . 30
2.4 Regional Problem Motivation . . . . . . . . . . . . . . . . . . . . . 31
2.4.1 Lower Rio Grande Valley . . . . . . . . . . . . . . . . . . . . 31
2.4.2 Lower Susquehanna . . . . . . . . . . . . . . . . . . . . . . . 35
Chapter 3
Many Objective de Novo Planning Under Deep Uncertainty 38
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.1 Handling Uncertainty in MOEAs . . . . . . . . . . . . . . . 41
3.2.2 Performance Metrics . . . . . . . . . . . . . . . . . . . . . . 44
3.2.2.1 Efficiency Metrics . . . . . . . . . . . . . . . . . . . 45
3.2.2.2 Risk Indicator Metrics . . . . . . . . . . . . . . . . 47
3.2.2.3 Market Use Metrics . . . . . . . . . . . . . . . . . 50
3.2.3 A Priori Problem Formulation . . . . . . . . . . . . . . . . . 51
3.2.4 Drought Scenarios . . . . . . . . . . . . . . . . . . . . . . . 53
3.3 Computational Experiment . . . . . . . . . . . . . . . . . . . . . . 54
3.3.1 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.2 Parameterizing Multi-Objective Search and Handling Un-
certainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4.1 Sobol Sensitivity Indices . . . . . . . . . . . . . . . . . . . . 57
3.4.1.1 Ten Year Sensitivity . . . . . . . . . . . . . . . . . 57
3.4.1.2 Drought Sensitivity . . . . . . . . . . . . . . . . . . 59
3.4.2 Sensitivity-Informed Problem Modifications . . . . . . . . . 60
3.4.3 Multi-Objective Tradeoffs . . . . . . . . . . . . . . . . . . . 65
3.4.3.1 Exploration of Solutions through the Drought Sce-
nario . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Chapter 4
Many Objective Robust Decision Making 78
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . 83
4.2.2 Generating Alternatives Using MOEAs . . . . . . . . . . . . 85
4.2.3 Uncertainty Analysis . . . . . . . . . . . . . . . . . . . . . . 85
4.2.4 Scenario Discovery . . . . . . . . . . . . . . . . . . . . . . . 87
4.2.5 Interactive Visual Analytics . . . . . . . . . . . . . . . . . . 87
4.3 LRGV Case Study Implementation . . . . . . . . . . . . . . . . . . 89
4.3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.3.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . 90
4.3.3 Multi-objective Evolutionary Algorithm . . . . . . . . . . . 94
4.3.4 Uncertainty Sampling . . . . . . . . . . . . . . . . . . . . . . 94
4.3.4.1 Scaling Factors . . . . . . . . . . . . . . . . . . . . 95
4.3.4.2 Scalar Model Parameters . . . . . . . . . . . . . . 99
4.3.4.3 Quantifying Robustness . . . . . . . . . . . . . . . 100
4.3.5 Scenario Discovery . . . . . . . . . . . . . . . . . . . . . . . 101
4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.4.1 Generating Alternatives . . . . . . . . . . . . . . . . . . . . 101
4.4.2 Percent Deviation of Performance Measures . . . . . . . . . 103
4.4.3 Negotiation of a Robust Solution . . . . . . . . . . . . . . . 105
4.4.4 Scenario Discovery . . . . . . . . . . . . . . . . . . . . . . . 108
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Chapter 5 Planning in the Susquehanna: Formulation Biases and Conse-
quences of Deep Uncertainty 117
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2.1 System Representation . . . . . . . . . . . . . . . . . . . . . 121
5.2.1.1 IRAS-2010 Water Resource Simulator . . . . . . . 121
5.2.1.2 Lower Susquehanna Network . . . . . . . . . . . . 123
5.2.2 Performance Measure Definitions . . . . . . . . . . . . . . . 126
5.2.3 Stochastic Hydrology . . . . . . . . . . . . . . . . . . . . . . 130
5.2.4 Problem Formulations . . . . . . . . . . . . . . . . . . . . . 132
5.2.4.1 Design Levers . . . . . . . . . . . . . . . . . . . . . 132
5.2.4.2 Deterministic Formulation . . . . . . . . . . . . . . 133
5.2.4.3 Stochastic Formulation . . . . . . . . . . . . . . . . 134
5.2.5 Many Objective Search . . . . . . . . . . . . . . . . . . . . . 135
5.2.6 MORDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.3 Computational Experiment . . . . . . . . . . . . . . . . . . . . . . 138
5.3.1 Stochastic Hydrology . . . . . . . . . . . . . . . . . . . . . . 138 5.3.2 Implementation of the Borg MOEA . . . . . . . . . . . . . . 139
5.3.3 Uncertainty Sampling and Robustness Analysis . . . . . . . 141
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.4.1 Comparing Formulations . . . . . . . . . . . . . . . . . . . . 142
5.4.2 Selecting Robust Alternatives . . . . . . . . . . . . . . . . . 148
5.4.3 Identifying Critical Thresholds . . . . . . . . . . . . . . . . . 152
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
Chapter 6 Concluding Remarks 157
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.3.1 Improved Decision Support Systems . . . . . . . . . . . . . . 161
6.3.2 New Application Areas . . . . . . . . . . . . . . . . . . . . . 163
6.3.3 Stakeholder Interaction . . . . . . . . . . . . . . . . . . . . . 164
Chapter 1
Introduction
Water resources planners and managers have long operated under the assumption that the historical record of water supply and demand provided a reliable estimation of future conditions. However, the validity of this approach is threatened by population pressures and environmental change, which can cause past records of streamflow availability to inadequately capture the future performance within these systems [1] . For example, climate change modifies the hydrologic cycle [2] , changing surface water availability and increasing the likelihood of droughts. Water demand is highly uncertain [3] , affected by climate change [4] and population growth [5] . Additionally, new water uses can emerge, such as water to support hydraulic fracturing for electricity generation [6] . These challenges can be considered deeply uncertain [7–9] , meaning that decision makers cannot fully conceptualize or agree upon the range of possible risks in their system. This dissertation will utilize multi-objective tools and improved planning frameworks for identifying robust planning alternatives under conditions of deep uncertainty.
Water projects are typically evaluated using cost-benefit analysis [10] , where project benefits are commensurated or transformed into their expected monetary value and compared to the project’s costs to determine if benefits outweigh the costs. The classical approach of expressing benefits in terms of their dollar values has several significant limitations. In order to perform the transformation of benefits into dollar amounts, the analyst’s assumptions (such as the discount rate) must maintain valid in the future system states [11] . Also, the recipients of the benefits (such as the residents of a river basin) may have preferences that change in the future. Simply providing a proper baseline for a project’s cost-benefit analysis is a significant challenge (i.e., what the state of the world would be like without the project [12] ), especially when multiple policy alternatives are considered [13] . Some have argued that under cost-benefit analysis, political pressure is the only determinant of whether or not a project gets implemented [14] .
Cost-benefit analysis is equivalent to a single-objective maximization, which finds a single optimal design that maximizes benefits for a system. The optimal solution to this problem, though, may prove to be inferior [15] when new objectives such as preservation of environmental quality or meeting conflicting water uses are considered. Banzhaf [16] outlines a historic disagreement between economists that advocated the single benefit-cost ratio and Arthur Maass and others at the Harvard Water Program that believed that a set of multiple objectives could be explicitly used in the design and funding negotiations for federal projects[1] . While multiobjective planning could have helped address some fundamental flaws of singleobjective welfare economics [16] , traditional benefit-cost ratios were adopted in U.S. Water Resources Council standards.
This dissertation demonstrates a many objective approach, in which planners can generate and evaluate alternatives with respect to four or more objectives simultaneously, avoiding lower-dimensional, myopic problem formulations that seek to confirm decision-makers’ preconceptions of the best alternative for their system. Our approach generates high quality approximations to the Pareto optimal set of solutions, solutions that are better than all other feasible solutions in at least one objective. Considering multiple objectives lends problem insight; we demonstrate in Chapter 2, for example, that commonly-employed decision maker heuristics (rules of thumb based on intuition) that attempt to minimize water surplus and wasted water transfers inadvertently lower the reliability of water supplies in a modeled system. To generate our planning alternatives, we use multi-objective evolutionary algorithms (MOEAs) [23] , modern solution tools that use selection of good solutions and variation on those solutions to generate high-quality approximations to the Pareto optimal set in a single algorithm run. Use of MOEAs does not require many simplifications of the planning problem, since the analyst can integrate a full-complexity simulation model into the optimization routine. Although the benefits of combining simulation models were clearly recognized in early water resources planning and management efforts [24–26] , very recent breakthroughs in computational power and MOEA-based search are now enabling studies to fully realize the benefits of these tools. This computation approach, coupled with advanced three-dimensional visualizations, allows us to visualize the tradeoffs between planning objectives in a manner originally intended by the Harvard Water Program (see Maass et al., page 308 [24] ) but previously unavailable due to computational and conceptual limitations.
While improved planning frameworks and MOEAs strengthen water resources systems analysis, analysts must also consider the fact that planning formulations themselves change as decision makers solve problems and analyze results. In this sense, the problem formulation itself is “nonstationary”, and decision makers form new hypotheses and pursue modified decision-making objectives as they solve their problems [27,28] . Modern decision support uses the paradigm of “constructive decision aiding” [29] , allowing a collaborative process for discovering problem formulations that capture evolving decision-making goals. In chapter 3 this dissertation proposes and demonstrates ade Novo Planning framework that will incorporate this new problem learning into many objective planning formulations.
A key limitation of planning studies is that they often use a single best estimate of the distributions of future inflows, supply costs, and demand trajectories to evaluate alternatives. Recent studies evaluating risks as broad as climate change planning [30] and terrorism risk insurance [31] have shown that decision makers should be cognizant of the ramifications when estimates of problem information and likelihoods are wrong. Robust Decision Making (RDM) [9] has been advocated as a way to address this issue, by evaluating a wide array of plausible futures and plan for system vulnerabilities. RDM approaches, though, have not emphasized the role of generating planning alternatives, as mentioned above. Chapter 4 contributes a framework termed Many Objective Robust Decision Making (MORDM) that bridges many objective analysis with RDM to facilitate decision-makers’ choice of robust solutions for planning.
The planning innovations are demonstrated using two test cases: a single city’s municipal supply using a water market in the Lower Rio Grande Valley (LRGV) of Texas (chapters 3-4), and multi-sector long-term supply planning for the Lower Susquehanna basin on the border of Pennsylvania and Maryland (chapter 5). Each basin has a unique set of challenges and exhibits different hydrologic characteristics and regulatory structures. The following section outlines the remainder of the dissertation and provides a brief summary of each chapter.
1.1 Overview of Chapters
1.1.1 Chapter 2: Background
Chapter 2 provides the reader with background information on the core topics covered in this dissertation. The chapter defines many objective analysis and provides a motivating example of how it can enhance environmental decision-making. Then, the challenge of deep uncertainty is introduced, motivating the planning innovations that will be introduced in this work. Technical details on the quantitative methods used are then given. Finally, the chapter concludes with information about the motivations for the regional case studies used to test the frameworks.
1.1.2 Chapter 3: de Novo Planning
The first planning innovation in this dissertation moves beyond the idea of using a single, static problem formulation (i.e., decision variables, objectives, and constraints) for decision support. Chapter 3 presents de Novo planning, which uses multiple problem formulations to help incorporate learning into the decision support process. We use global sensitivity analysis using Sobol’ variance decomposition to determine an appropriate level of complexity for decision variables and aid in choosing an appropriate set of objectives and constraints. A suite of multiple problem formulations is then constructed and solved using a MOEA to explore the insights learned through sensitivity analysis. The chapter uses the LRGV risk-based water supply management problem to demonstrate the framework. Use of the framework illustrates how to adaptively improve the value and robustness of our problem formulations by evolving our definition of optimality while discovering key tradeoffs. Chapter 3 was adapted from a study published in Environmental Modelling and Software [32] co-authored with Patrick M. Reed, Gregory W. Characklis, and Brian R. Kirsch.
1.1.3 Chapter 4: Many Objective Robust Decision Making
Chapter 3 presents an analysis of a water supply planning problem under uncertainty, where inflows, demands, and prices are characterized by an estimated probability distribution, which is used to estimate a supply portfolio’s expected performance. A key issue with this approach is that we cannot ascertain whether the selected alternative portfolios are robust to core assumptions or changes in likelihoods across the system’s uncertainties. Decision support strategies that use the concept of robustness such as Robust Decision Making (RDM) can help address this issue. RDM seeks to evaluate the performance of policy strategies over an ensemble of deeply uncertain trajectories of the future. It then helps decision makers choose robust alternatives and characterize which deeply uncertain factors are most important in causing performance vulnerabilities. Chapter 4 seeks to overcome an important limitation in the prior RDM literature by bridging MOEA search to generate alternatives with the RDM analysis. This framework represents an innovation termed Many Objective Robust Decision Making (MORDM). MORDM extends the work of chapter 3 by improving the ad hoc method of choosing alternatives by relying solely on the expected values of a single set of assumptions and likelihoods in the Monte Carlo simulation. We use the LRGV test case to demonstrate the framework, with the goal of identifying parsimonious and robust rules for the city to operationally exploit the water market in their supply portfolio. Chapter 4 was adapted from a journal article in press at Environmental Modelling and Software [33] co-authored by Shanthi Nataraj, Patrick M. Reed, and Robert J. Lempert.
Chapters 3 and 4 present a sequence of planning innovations with the goal of helping decision makers identify appropriate problem formulations and choose robust planning alternatives, using the LRGV test case. Although the LRGV test case has significant value, it focuses on a single city’s municipal supply, and augmenting this supply with water marketing transfers is limited to regions in which water marketing is allowed, such as the western United States. In the eastern U.S., water marketing is often prohibited, and water managers must face challenges in managing supply for multiple sectors without the ability to build new infrastructure. This different regulatory context is addressed with a new test case in chapter 5.
1.1.4 Chapter 5: Formulation Biases for the Lower Susquehanna
Chapter 5 builds a new Lower Susquehanna test case to demonstrate how MORDM can be used to test the robustness of management alternatives for water supply infrastructure in the eastern U.S. Two many objective problem formulations are developed using the Interactive River Aquifer Simulation (IRAS)-2010 water resource system simulator and a recently introduced MOEA termed the Borg MOEA. The first formulation is reflective of the classic history-based deterministic water resources systems planning approach that still dominates practice. The second formulation moves beyond the historical record by considering streamflow and evaporation uncertainties modeled using a K-Nearest Neighbor stochastic simulation strategy. MORDM is then used to contrast the robustness of the two formulations’ Pareto approximate solutions’ robustness to deep uncertainties, associated with water demand targets, prolonged droughts, and increased interannual variability of streamflow and evaporation. The optimization-simulation and MORDM components of this study posed severe computational demands in excess 1,000,000 hours of computing. Thus in addition to introducing the test case implementation, chapter 5 also discusses application of High Performance Computing technology to carry out the experiment.
Beyond the case study-specific insights, a key goal in this study is to expose the potential negative consequences or formulation biases that result from the use of deterministic planning based historical hydrology. Although our deterministic many objective formulation contributes a more comprehensive characterization of the Lower Susquehanna test case’s multi-sector demand tradeoffs relative to classic single objective planning [34–39] , deeply uncertain changes in the SRB have the potential to exacerbate drought risks. Moreover, this study explores if the sole consideration of hydrological uncertainties (i.e., stochastic generation of streamflow and evaporation) is sufficient to discover robust alternatives for the system while simultaneously identifying the key deep uncertainties that control its vulnerabilities. A journal article based on this chapter, co-authored by Patrick M.
Reed and Evgenii Matrosov, will be submitted in Spring 2013.
1.1.5 Chapter 6: Concluding Remarks
Chapter 6 suggests the conclusions of this research, its contributions, and provides a guide for future work to expand on the contributions herein.
[1] As cited by Banzhaf [16] , the exchange between the two groups occurred in public [17–22] . Maass argued that the role of public investment in the U.S. was not merely to improve economic efficiency but also to redistribute income. He advocated the political process to determine appropriate tradeoffs between these objectives [17] . In his reply Haveman [18] essentially argued that different types of projects should be designed to either meet economic efficiency or income redistribution, but not both. Maass’ position was that the political system is inherently multiobjective; without considering multiple objectives explicitly, “the tradeoffs are implicit, generally inefficient, and sometimes internally contradictory” [21] .
MANY OBJECTIVE WATER RESOURCES PLANNING AND MANAGEMENT GIVEN DEEP UNCERTAINTIES, POPULATION PRESSURES, AND ENVIRONMENTAL CHANGE
