A PROPOSED STEPWISE REGRESSION METHOD FOR MODEL STRUCTURE IDENTIFICATION

This paper proposes a new methodology for constructing groundwater mod els. The proposed methodology, which determines simultaneously both mo del 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 rep resentative parameters is also infinite; (3) to obtain a set of approp riate representative model parameters, we must have an appropriate mod el structure; and (4) an appropriate model structure should be determi ned not only by observation data and prior information but also by the accuracy requirements of model applications. In this proposed methodo logy we start with a homogeneous model structure and, step by step, gr adually 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 define d 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 hyd raulic conductivity is a random field with a certain trend. We have fo und that for the example problem: virtually identical pumping policy i s obtained when a five-zone model with an optimized zonation pattern i s used to represent the nonstationary random field. We have also found that observation errors have minimum impact ori management solution i n comparison with structure errors. To calculate the model structure e rror for this example, the inverse solution is coupled with a manageme nt problem. We have also developed an effective iteration method to ha ndle nonlinear water quality constraints.