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Efficient and responsible use of prior information in inverse methods

Weiss, R., Smith, L.
Ground water 1998 v.36 no.1 pp. 151-163
estimation, simulation models, groundwater flow, solutes, aquifers, data analysis, New Mexico
Prior information on parameters such as hydraulic conductivity or ground water recharge rates is often used to stabilize the inverse problem in parameter estimation. A cautious use of prior information is advisable, however, because it may be biased or unrepresentative of the model parameters and/or it may not significantly stabilize the parameter estimates. Procedures are given: (1) to identify the model parameters for which prior information may best stabilize the parameter set; and (2) to identify the model parameters for which errors in the prior information lead to the smallest possible errors in the final set of parameter estimates. The first case is referred to as the efficient use of prior information; the second case is referred to as the responsible use of prior information. The procedures are based on an analysis of the model parameter space using response surfaces, multiparameter confidence regions, and eigenspace analysis. The guidelines lead to the selection of prior information on those parameters whose axes are most closely aligned with the longest axis of the parameter confidence region. Simple synthetic examples are used to explain the concepts. The advantages gained in screening the model parameters to identify those parameters for which prior information will be most efficient and responsible in determining the final values of the parameter estimates are demonstrated in the calibration of a ground water flow and solute transport model for the San Juan Basin, New Mexico.