Model Structure Identification in Three Dimensions and Observation Design in Groundwater Modeling

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0001082YehThe development of a reliable model for basin water resources management is a challenging problem because real aquifer structure is highly complex and mostly unknown and that we only have very limited data to calibrate the model. The three major difficulties are: (1) How to determine an appropriate level for model complexity; (2) How to parameterize and identify the unknown distributed parameter values; and (3) How to judge the sufficiency of existing data for the chosen model. In our recent studies, we have developed a new approach to fix model complexity and to estimate a model structure and its corresponding parameter values for groundwater modeling in a 2-dimensional distributed parameter system. We have defined a generalized inverse problem, in which the model complexity level is set by available data and the accuracy requirements of model applications. We have further developed a stepwise regression method to solve the generalized inverse problem in two dimensions as well as a new methodology for constructing groundwater models. The utility of the new methodology was demonstrated by an application to a water resources management problem of a groundwater basin in Southern California. We have found that management requirements were satisfied by a simple model structure with a few identified parameters to represent various hydraulic and mass transport properties. We also found that existing data are insufficient to identify certain boundary conditions with the required accuracy.This work explores new frontiers in groundwater modeling. The key objectives are: (1) To make our methodology for model structure identification more general. We will consider zonation and such other parameterization methods as finite element interpolation and kriging. We will extend the methodology to three dimensions. Parameter structures to be identified will include not only hydraulic conductivity but also initial and boundary conditions and source terms. (2) To build the theoretical basis of the generalized inverse inverse problem. We will define model structure identifiability and find its sufficient conditions. We will also consider how information on geological structure can be incorporated into model structure identification procedure in three dimensions. (3) To develop methodology for observation design. After the least complex model structure is found, we can formulate the observation design problem into an optimization to find the most cost-effective design from all sufficient and feasible designs. Our ultimate goal is to quantitatively link observation design to model structure complexity, model parameter identifiability, and model application reliability. Results will be compared to Monte Carlo simulations. We will apply our research results with a water resources agency in Southern California.