Problem‐Dependence of Ground‐Water Model Identification: Significance, Extent, and Treatment

Because geologic settings are not fully known (data are sparse) and because geologic properties vary spatially, flow modelers resort to simplifying conceptualization (simplified geological models) of the settings to perform modeling. But as results of identification of a simplified model depend on identification problem formulation, simplification poses two issues: (1) Since coupled identification and prediction problems are differently formulated problems, successful identification (calibration) of a model does not mean that the model will be good in prediction, so the goal of model identification should be the model's parameters effective in an intended application. (2) Since the identification results are problem‐dependent, they may be deprived of geological meaning. Therefore, they should be interpreted in the terms of their relation to the real world: To use them without understanding their meanings is potentially damaging. The key to both issues is explicit mathematical presentation of the spatially variable geologic properties transformations to the ground‐water model parameters. Canonical forms of the transformations, displaying readily inherent features of those transformations, are introduced. Two‐level modeling, exploiting the canonical forms, is suggested as an approach to address the above‐mentioned issues. The higher level models represent real geologic settings. The lower level model presents a conventional geological model. Comparison of responses to the same impact between the higher level models and the geological model should permit inference of the canonical forms for the given geological model. The forms can be used to choose predictive model effective parameters, interpret observed data, and optimize field investigation. Two simple examples illustrate the main notions of the approach.