Multi-Objective Groundwater Quantity Management. A Stochastic Approach

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Abstract

The question of managing groundwater resources is one of implementing institutions that regulate the use of the resource so as to harvest maximum benefits without imparting undesirable consequences on the system. Traditionally, regional groundwater management problems have been solved deterministically. However, predictions made through this deterministic modelling approach are inherently based on the belief that the present is the key to the future. However, this presumption can only be true if the present situation is known with high precision. This assumption, therefore, commonly proves invalid when applied to most regional groundwater systems because typically too few data are available to define uniquely the current state of the system, and the system properties can be estimated only with a large degree of uncertainty. The research investigated how parameter uncertainty affects regional scale groundwater optimal strategies. Results show that by approaching the optimization problem deterministically, the realized optimal management strategies may exhibit an optimistic bias, and hence may encourage a decision maker to accept an investment for the alternative which in the future will fail to deliver the estimated performance. This is because such solutions are very sensitive to data perturbations. However, when uncertainty in parameters is taken into account through multiple scenario and second-order cone optimization approaches, the resulting optimal strategies are robust (i.e., not very sensitive to small perturbations within the input parameters). Thus, recalling that well field development is a very expensive exercise, it certainly pays to implement such robust solutions because one would avoid a situation whereby in future, it would be recommended that some pumping wells be relocated as a result of excessive violation of constraints due to uncertainty in the input parameters. The main contributions in this research are twofold: (1) the optimization is carried out within a multi-objective framework and therefore a decision support system is incorporated in order to assist a decision maker choose one among the many optimal solutions for final implementation and (2) uncertainty due to input parameters is explicitly taken into account. Thus, it is the view of the researcher that one of the proposed approaches (i.e., second-order cone optimization approach) holds the key to the solution of many problems whose input data are uncertain and the near future is likely to witness enormous interest in this optimization approach.