Probabilistic scenario-based decision making for water resources planning and management

Uncertainty is an unavoidable part of decision making. Decisions always have to be made before perfect knowledge on their consequences is known. However, there is no ‘perfect knowledge’ in hindsight. To research uncertainty and take actions proactively becomes the challenge to scientists and decision makers. In water resources planning and management, uncertainty is presenting at all stages of planning, developing and managing a water system (Loucks, Van Beek et al. 2005). The water systems are dynamically driven by factors such as climate, environment, demographics, socio-economy, technology, policies and regulations, etc. For example, climate change will affect hydrological and water conditions such as rainfall, temperature, water availability for irrigation; socio-economic development causes the change of water demand. However, the variation of these driving forces is unknown and beyond the control of decision makers, so as their impact on water systems. To plan and manage water systems without addressing uncertainty will invite surprises and potential risk subject to unexpected consequences and losses. Therefore, the objective of this thesis is to contribute knowledge to decision making under uncertainty for water resources planning and management. Scenarios have been widely used to explore uncertainty for long-term strategic planning. Scenarios are defined as “a coherent and plausible description of possible future states of the world” by the IPCC. They are distinguished from the deterministic or most-likely prediction of future states. Scenario-based approaches have been applied largely to analyse future water- related issues, and support water managers and decision makers to put forward strategies for potential problems. Two criteria ‘robustness’ and ‘rationality’ are proposed for decision making in face of uncertainty. Unlike traditional decision analysis which makes decisions based on the ‘most-likely’ futures, robust decisions are those who perform satisfactorily over a wide range of plausible future states. Rationality was usually modelled to maximize the expected profits in economic terms. Von Neumann and Morgenstern (1947) added the risk attitudes and satisfaction of decision makers to economic outcomes, and introduced expected utility theory to model rationality as maximizing the expected utility. To apply scenario-based approaches to support decision making in a rational and robust way, the crucial task is to develop scenarios that can describe and quantify future states under uncertainty. Two research questions are raised in the research: (1) How to develop scenarios for future water circumstances to cope with uncertainty? (2) How to make robust and rational decisions based on the developed scenarios? Scenarios are defined as qualitative storylines about the future, however, quantitative projections and numerical information should be included to inform decision making. Traditional scenarios were quantified according to each storyline, and leaves out possible situations in between them. The ignorance of in-between scenarios constrains the explorative characteristic of scenarios. Besides, each storyline is assumed to be equally likely without attaching probabilities. Future states with equal chance are not realistic, and it forces decision makers to pick up any scenario arbitrarily. Conversely, the application of probabilities encourages representing uncertainty and explaining assumptions behind scenarios explicitly. It is also more approachable for risk quantification, and informs decision makers the different chances of future situations. The thesis advances scenario development by combining numerical information and attaching probability distributions. Probability distributions of future states can only be estimated subjectively, and they are highly conditional on the assumptions being made. Bayesian probabilities and expert judgement are two main techniques to combine subjective probabilities and scenarios. Subjectivity cannot be avoided or stopped when talking about uncertainty and the important thing is to make the assumptions and expert judgement about scenarios as explicit and transparent as possible. Besides, the principle of Maximal entropy can be used to choose probability distributions with the largest uncertainty. To estimate climate change impact on water availability in the Yellow River Basin (YRB), China in the next 30 years, probabilistic scenarios of water availability were generated which are based on the climate scenarios (precipitation and temperature) based on the projections of General Circulation Models (GCMs). To investigate socio-economic development impact on water demand in the Yellow River Delta (YRD), China, probabilistic scenarios of water demand were developed using expert judgement. Four storylines comprising two extremes (urbanization speed-up/ agriculture intensive, water-saving/ water consumptive) were constructed to describe the future development of the YRD. An existing expert elicitation technique, i.e. the SHELF method, is used to elicit prior probabilities of socio-economic driving variables from local experts. Probability distributions from individual experts are then aggregated, and correlations between different variables are taken into account by using a multivariate probability distribution based on the Gaussian Copula. The thesis developed the probabilistic scenario-based decision making framework to handle uncertainties and support decision making in a systematic, robust and rational manner. The framework relies on a full probabilistic distribution of scenarios and outcomes, and ranks decision alternatives based on expected utility theory. The framework not only investigated the monetary objective, but also further engaged the decision makers by investigating their preferences and risk attitudes (risk averse, risk neutral, risk taking) under uncertainty. The risk attitudes of decision makers were modelled using a negative exponential utility function. The decision making framework was applied for a case study of long-term water resources planning and management in the YRD. Evaluation and ranking of candidate strategies was performed against the full probability distribution of water supply and demand scenarios. Sensitivity analysis was performed to test the robustness of the decisions with respect to uncertain factors such as water supply and demand, market prices and the risk attitudes of decision makers. In summary, the thesis contributes knowledge on uncertainty management and decision making, which includes: achieve better understanding of the state-of-the-art in scenario science; advance scenario development – from qualitative storylines to quantitative projections, discrete states to continuous states, equal- likelihood states to probabilistic states; develop the probabilistic scenario-based decision making framework to handle uncertainties and support decision making in a systematic, robust and rational manner; taking into account risk from both the engineers’ and decision makers’ perspectives; and analyse the influence of decision makers’ risk attitudes on the choice of decisions