LSQR AND TIKHONOV REGULARIZATION IN THE CALIBRATION OF A COMPLEX MODFLOW MODEL

Employing a-priori parameter parsimony to solve the inverse problem in groundwater modeling is conceptually appealing, but has several downfalls – not least of which is that the solution of the inverse problem is restricted to a very limited subspace of the true parameter space. The alternative is to estimate a very large number of parameters and allow the calibration process to determine where heterogeneity may exist. Estimating a large number of parameters during model calibration requires rapid and memory-lean matrix solution techniques that can accommodate highly parameterized models. We demonstrated (Muffels et al, 2006) that although the LSQR - an iterative matrix solution technique similar to the methods of conjugate gradients - can solve the large matrix equations that are produced when thousands of parameters are estimated, convergence can be disappointing. Here, we explore the role of Tikhonov regularization, when employed together with LSQR, for stabilizing the inverse problem and for improving the convergence of a local-approximation to the true inverse problem. The model application is a synthetic approximation to the real-world regional MODFLOW model of the Trout Lake Basin, Wisconsin. Since the number of parameters greatly exceeds the number of observations, parameter sensitivities are calculated using the adjoint-state method. We compare the results to the most commonly employed subspace method, the truncated singular valued decomposition (TSVD). Discussions focus on the advantages – or otherwise – of the Tikhonov regularization, and on the improvement(s) in inference gained through the use of a large number of parameters.

Muffels, C., M. Tonkin, H. Zhang, M. Anderson, and T. Clemo. 2006. Application of LSQR to Calibration of a MODFLOW Model: A Synthetic Study. MODFLOW and More 2006, Managing Ground-Water Systems, International Ground Water Modeling Center, Colorado School of Mines Golden, Colorado, May 22-24, 2006. Vol. 1. 283-287.