The main computational costs of gradient-based inverse methods for solving high-dimensional groundwater inverse problems usually include (a) the storage and computation of large-dimensional spatial covariance matrices, which regularize the smoothness of the parameter field to be estimated, (b) a large number of iterative forward model implementations to determine the Jacobian matrix, and (c) forward model simulations on high-resolution parameter fields (Kitanidis, 2015). Many research efforts have been devoted to improving the storage and computation of large matrices and reducing the number of forward model runs. For example, adjoint state methods were developed to evaluate the Jacobian by solving an additional forward model system for each measurement (Sun & Yeh, 1990a, 1990b, 1992, reducing the number of forward model runs to the number of measurements. Geostatistical approach (GA) has been improved to compute large-dimensional covariance matrices and reduce the number of forward model runs (
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