Estimation of parameter geometry

Abstract

It is well known that to use a groundwater model as a predictive tool, model parameters have to be calibrated against measurements (heads, concentrations or other state variables). For this reason, groundwater literature is plenty of results and theory on inverse problems. Usually, the physical parameters are discretized using a parameterization defined through some variables (the so called model parameters) that can be estimated (calibrated). Most of the effort on inverse modeling has been done in estimating the values of the model parameters, but not their spatial variability, that customarily is considered as fixed except in some few works.

Among different alternatives, we have chosen zonation as the way of discretizing spatial variability of parameters, that is one of the most employed ways of parameterization. In this paper a methodology for the estimation of both parameter values at the zones and their shape (geometry) is presented. A model structure identification criterion (developed on the framework of the bayesian theory) has been defined to account for the consistency between model and real system. This criterion leads to a optimization problem with a objective function that is minimized using several integer algorithms. The differences and similarities between our proposed methodology and other approaches are highlighted, as well as their respective limitations. Examples are included to show the applicability and restrictions of the methodology.