UC Santa Barbara

This work deals with a theoretical analysis of parameter uncertainty in groundwater management models. The importance of adopting classical, Bayesian, or deterministic distribution assumptions on parameters is examined from a mathematical standpoint. In the classical case, the parameters (e.g., hydraulic conductivities or storativities) are assumed fixed (i.e., nonrandom) but unknown. The Bayesian assumption considers the parameters as random entities with some probability distribution. The deterministic case, also called certainty equivalence, assumes that the parameters are fixed and known. Previous work on the inverse problem has emphasized the numerical solution for parameter estimates with the subsequent aim to use them in the simulation of field variables. In this paper, the role of parameter uncertainty (measured by their statistical variability) in groundwater management decisions is investigated. It is shown that the classical, Bayesian, and deterministic assumptions lead to analytically different management solutions. Numerically, the difference between such solutions depends upon the covariance of the parameter estimates. The theoretical analyses of this work show the importance of specifying the proper distributional assumption on groundwater parameters, as well as the need for using efficient and statistically consistent methods to solve the inverse problem. The distributional assumptions on groundwater parameters and the covariance of their sample estimators are shown to be the dominant parameter uncertainty factors affecting groundwater management solutions. An example illustrates the conceptual findings of this work. Copyright 1987 by the American Geophysical Union.