Evaluating parameter inversion efficiency in Heterogeneous Groundwater models using Karhunen-Loève expansion: a comparative study of genetic algorithm, ensemble smoother, and MCMC

Groundwater modeling is essential for effective water resource management. However, the heterogeneous distribution of hydrogeological parameters, such as hydraulic conductivity (K), significantly impacts the accuracy and efficiency of simulations. This study investigates the accuracy and computational efficiency of K parameter inversion across varying dimensions. Heterogeneous logarithmic random K (lnK) fields were generated using the Karhunen-Loève Expansion. Three inversion algorithms—Genetic Algorithm, Markov Chain Monte Carlo, and Ensemble Smoother (ES)—were evaluated in conjunction with a Kriging surrogate model. These algorithms were used to invert parameters using different numbers of Inversion Target Features (ITFs) as prediction targets. Results indicate that ES consistently outperformed GA and MCMC in terms of inversion accuracy and computational efficiency across all ITF scenarios (7, 12, 34, 48, and 71 ITFs). Sensitivity analysis revealed that selecting parameters with higher total-order indices for inversion is crucial, as a small subset of ITFs often accounts for a majority of the sensitivity. While increasing the number of ITFs captures greater spatial variability in lnK, high-dimensional cases can lead to less responsive output heads. Furthermore, inadequate grid density may not adequately represent fine-scale lnK distributions. This study provides valuable insights into parameter inversion within heterogeneous groundwater models, furthering our understanding of these complex systems.