An identification approach to subsurface hydrological systems

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Abstract
A method for the optimal determination of the transmissivity function in a model of a horizontal two‐dimensional saturated aquifer, using time histories of the heads at a number of observation points, is developed. In this method the transmissivity function is assumed to be represented by a continuous spline surface over the entire domain of the aquifer and is given in terms of unknown nodal values disposed over a rectangular grid. These nodal values are then determined by requirements of optimality, i.e., by minimization of an error functional denoting the deviations of the observed and predicted heads at several strategically distributed observation wells. The method is complemented by using a hierarchical identification approach which consists of gradually increasing the number of nodal values employed in the analytical representation of the transmissivity function. Finally, a numerical example involving the determination of the transmissivity map of an aquifer by employing simulated head histories is presented to illustrate the feasibility of the proposed method.