Inverse problem and parameter structure identification in groundwater modeling

Although model calibration in groundwater modeling has been studied for many decades, parameter structure identification is not fully recognized and solved. The main difficulties of identifying model parameters emerge from the inherent heterogeneity of the aquifer. Since scarcity of observations can not fully describe the aquifer heterogeneity, parameter structure identification needs to be conducted in the groundwater inverse problem.; Parameter structure identification aims at identifying distributed parameters in groundwater modeling with the least parameter dimensions for a given problem. To do so, parameterization is suggested for the space optimization. Voronoi Tessellation and Natural Neighbor Method are mainly used for parameterization as well as spatial optimization. A universal parameterization method is developed to enhance flexibility of handling non-smooth distribution. In this study, parameter structure identification is formulated into three types of inverse problem problems. An extended inverse problem (EIP) identifies the parameter structure based on available observations and prior information. In order to incorporate the model application in the model calibration process, a generalized inverse problem (GIP) is introduced based on both fitting residual and parameter structure error. In addition, parameter structure discrimination provides an alternative criterion for parameter structure identification. Utilizing a genetic algorithm, BFGS and grid search, a global-local optimization scheme and a hybrid genetic algorithm are developed as a complete optimization package to identify the best parameter structure. Sensitivity-equation method is used to calculate the sensitivities for gradient evaluation and parameter uncertainty analysis. MODFLOW and MT3DMS are employed to solve the flow and transport equations as well as the sensitivity equations. They are also linked with optimization solvers (MINOS and PCx) to deal with model management problems. The proposed methodology is validated and demonstrated in the numerical examples where the distributed transmissivity field is unknown in two and three-dimensional aquifers. The identified transmissivity structures are well approximated to the true distributions in terms of parameter values and distribution variation. Following the structure identification procedure, over parameterization is avoided, low parameter uncertainty is achieved, and accuracy requirement of model application is satisfied.