Development of objective-oriented groundwater models: 2. Robust experimental design

Abstract

This paper continues the discussion in part 1 by considering the data collection strategy problem when the existing data are judged to be insufficient for constructing a reliable model. Designing an experiment for identifying a distributed parameter is very difficult because the identification of a more complex parameter structure requires more data. Moreover, without knowing the sufficiency of a design, finding an optimal design becomes meaningless. These difficulties can be avoided if we turn to the construction of objective-oriented models. The identifiability of a distributed parameter, as defined in this paper, contains the reducibility of parameter structure. Sufficient conditions for this kind of identifiability are given. When the structure error associated with a structure reduction is too large, these conditions may not be satisfied no matter how much data are collected. In this paper we formulate a new experimental design problem that consists of two objectives: minimizing the cost and maximizing the information content, with robustness and feasibility as constraints. We develop an algorithm that can find a cost-effective robust design for objective-oriented parameter identification. We also present a heuristic algorithm that can find a suboptimal design with less computational effort for real case studies. The proposed methodology is used to design a pumping test for identifying a distributed hydraulic conductivity. We verify the robustness of the obtained design by assuming that the true parameter may have continuous, discrete, random, and fractured structures. Finally, the presented procedure of constructing objective-oriented models is described step by step. Copyright 2007 by the American Geophysical Union.