An efficient surrogate-based simulation-optimization method for calibrating a regional MODFLOW model

Abstract

Simulation-optimization method entails a large number of model simulations, which is computationally intensive or even prohibitive if the model simulation is extremely time-consuming. Statistical models have been examined as a surrogate of the high-fidelity physical model during simulation-optimization process to tackle this problem. Among them, Multivariate Adaptive Regression Splines (MARS), a non-parametric adaptive regression method, is superior in overcoming problems of high-dimensions and discontinuities of the data. Furthermore, the stability and accuracy of MARS model can be improved by bootstrap aggregating methods, namely, bagging. In this paper, Bagging MARS (BMARS) method is integrated to a surrogate-based simulation-optimization framework to calibrate a three-dimensional MODFLOW model, which is developed to simulate the groundwater flow in an arid hardrock-alluvium region in northwestern Oman. The physical MODFLOW model is surrogated by the statistical model developed using BMARS algorithm. The surrogate model, which is fitted and validated using training dataset generated by the physical model, can approximate solutions rapidly. An efficient Sobol’ method is employed to calculate global sensitivities of head outputs to input parameters, which are used to analyze their importance for the model outputs spatiotemporally. Only sensitive parameters are included in the calibration process to further improve the computational efficiency. Normalized root mean square error (NRMSE) between measured and simulated heads at observation wells is used as the objective function to be minimized during optimization. The reasonable history match between the simulated and observed heads demonstrated feasibility of this high-efficient calibration framework.