Evaluating the effect of Tikhonov regularization schemes on predictions in a variable-density groundwater model

Abstract

Calibration of highly‐parameterized numerical models typically requires explicit Tikhonovtype regularization to stabilize the inversion process. This regularization can take the form of a preferred parameter values scheme or preferred relations between parameters, such as the preferred equality scheme. The resulting parameter distributions calibrate the model to a user‐defined acceptable level of model‐to‐measurement misfit, and also minimize regularization penalties on the total objective function. To evaluate the potential impact of these two regularization schemes on model predictive ability, a dataset generated from a synthetic model was used to calibrate a highly-parameterized variable‐density SEAWAT model. The key prediction is the length of time a synthetic pumping well will produce potable water. A bi‐objective Pareto analysis was used to explicitly characterize the relation between two competing objective function components: measurement error and regularization error. Results of the Pareto analysis indicate that both types of regularization schemes affect the predictive ability of the calibrated model.