Solving and Calibrating Groundwater Flow Systems with the Penalty Method

Abstract

Calibration of the two-dimensional steady state groundwater flow equation can be formulated as an optimization problem with a quadratic objective function and nonlinear constraints. The quadratic objective function is the weighted sum of squares of measurement residuals and regularization residuals which contain the original estimates of model parameters. Weighting matrices are formed by taking the inverse of the covariance estimates of measurements and original parameter estimates, respectively. The minimization can be perfomed with the penalty method. In a single step, the penalty method provides an updated set of parameter estimates and the solution of the groundwater flow equation. The use of nondiagonal weighting matrices for the regularization residual portion of the objective function greatly improves estimates in the presence of over-parameterized systems. It may be possible to estimate nondi-agonal covariance matrices from soft geological information, providing a method for incorporating soft geological information into numerical models.KeywordsGroundwater FlowCovariance MatriceHydraulic HeadPenalty MethodGroundwater Flow ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.