Comparative analyses of covariance matrix adaptation and iterative ensemble smoother on high-dimensional inverse problems in high-resolution groundwater modeling

Abstract

Parameter estimation is an inverse problem which is crucial to reliable groundwater model predictions and management. Numerous techniques have been developed to address this challenging problem. This study aims to compare the performance of a stochastic optimization method, covariance matrix adaptation-evolution strategy (CMA-ES), and a data assimilation method, Levenberg-Marquardt based iterative ensemble smoother (ES-LM), on solving inverse problems in groundwater modeling. This study also presents a parallelization strategy to accelerate their implementation. The comparative analysis involves synthetic inverse problems and a real-world case study of calibrating a high-resolution groundwater model. Results from the synthetic problems suggest that both the CMA-ES and the ES-LM are able to achieve desirable data fitting, but the ES-LM generally exhibits greater efficiency than the CMA-ES. Also, with appropriate stopping criteria, both methods can perform well on propagating uncertainty of model predictions. However, both methods can underestimate the uncertainty of model parameters derived from Bayesian posterior. The underestimation is particularly pronounced by the ES-LM when using a small ensemble size, whereas uncertainty quantification by the CMA-ES is less affected by population size. Moreover, calibration of the highly parameterized groundwater model in Louisiana and Southwest Mississippi indicates that the ES-LM can outperform the CMA-ES for high-dimensional inverse problems regarding both data match and computational costs. With proper ensemble size, the two methods can produce comparable uncertainty of model parameters and predictions. This study contributes to the scientific understanding and efficient application of the CMA-ES and the ES-LM.