High‐Dimensional Groundwater Flow Inverse Modeling by Upscaled Effective Model on Principal Components
Yue Zhao, Quan Guo, Chunhui Lu, Jian Luo
Abstract
Abstract The main computational costs of gradient‐based inverse methods for high‐resolution groundwater flow inverse problems include costly forward model simulations and the large number of such simulations required to determine the Jacobian matrix. We develop an upscaling‐based inverse approach, named upscaled principal component inverse approach (UPCIA), which achieves dimensionality reduction and reduces computational cost of forward model simulations by evaluating the Jacobian through upscaled effective models on a coarse‐resolution grid constructed from upscaled principal components. UPCIA integrates downscaling into the inverse problem by estimating principal component coefficients based on the coarse‐resolution forward model, which are then used to generate high‐resolution parameter fields. Various numerical experiments demonstrate the effectiveness and efficiency of UPCIA, including 2‐D/3‐D high‐dimensional steady‐state and transient hydraulic tomography with known storativity to estimate multi‐Gaussian transmissivity or hydraulic conductivity fields. Results show that the hydraulic head is insensitive to small‐scale variability of conductivity, and UPCIA provides high‐quality inversion results similar to inverse methods with high‐resolution forward model simulations and significantly reduces computation time by orders of magnitude. In addition to supporting the characterization of heterogeneity in sufficient detail, UPCIA can also be used to examine whether finer resolution is necessary and possibly to determine an optimal inverse resolution.