A proposed stepwise regression method for model structure identification

This paper proposes a new methodology for constructing groundwater models. The proposed methodology, which determines simultaneously both model structure and model parameters, is based on the following ideas: (1) When solving the inverse problem, different model structures always produce different model parameters; (2) since the number of possible model structures of an aquifer is infinite, the number of possible representative parameters is also infinite; (3) to obtain a set of appropriate representative model parameters, we must have an appropriate model structure; and (4) an appropriate model structure should be determined not only by observation data and prior information but also by the accuracy requirements of model applications. In this proposed methodology we start with a homogeneous model structure and, step by step, gradually increase the complexity of the model structure. At each level of complexity we calculate not only the fitting residual of parameter identification but also the error of model structure to determine if a more complex model structure is needed. The model structure error of using one model structure to replace another model structure is defined by a maximum-minimum (max-min) problem that is based on the distance between the two models and is measured in parameter, observation, and prediction (or decision) spaces. This proposed methodology is used to solve a hypothetical remediation design problem in which the true hydraulic conductivity is a random field with a certain trend. We have found that for the example problem: virtually identical pumping policy is obtained when a five-zone model with an optimized zonation pattern is used to represent the nonstationary random field. We have also found that observation errors have minimum impact ori management solution in comparison with structure errors. To calculate the model structure error for this example, the inverse solution is coupled with a management problem. We have also developed an effective iteration method to handle nonlinear water quality constraints.