Model reliability and experimental design for sustainable groundwater management

Although the concept of sustainability lacks a concise, agreed-upon definition, it is fair to say that sustainable development involves taking care of the needs of the present without compromising the ability of future generations to meet their own needs. This research aims at developing a comprehensive methodology for model reliability assessment and data collection that accounts for the application of numerical models in elucidating the tradeoff relationships between conflicting objectives in groundwater management. A management space is defined as the three-dimensional surface described by the non-dominated solutions of a multiobjective optimization problem. Sensitivity of management solutions to parameter uncertainty is estimated by computing the Hausdorff distance between non-dominated sets. The simulation model reliability is estimated by comparing the effects that a perturbation in the model parameter space has over the model output as well as over the non-dominated surface in the management space. If small perturbations of the parameters yield small perturbations in model output but large changes in the management space then the model is deemed unreliable and more data has to be collected. The problem of experimental design for parameter estimation is formulated as the design of a pumping test that generates noisy observations for the solution of the inverse problem. A genetic algorithm obtains near-optimal number and location of observation wells as well as the pumping rate. Model parameter uncertainty and observation error uncertainty are dealt with by adopting a Bayesian decision theoretic approach for selecting the final design. Prior probability density distributions for the uncertain parameters are sampled using the Gaussian Quadrature method of numerical integration. The proposed methodology is useful for selecting a robust design that will outperform other candidates under most potential "true" states of nature. Results also show that the uncertainty analysis is able to identify complex interactions between the model parameters that may affect the performance of the experimental designs as well as the attainability of management objectives.