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  1. It can be expensive and difficult to collect direct bathymetry data for nearshore regions, especially in high-energy locations where there are temporally and spatially varying bathymetric features like sandbars. As a result, there has been increasing interest in remote assessment techniques for estimating bathymetry. Recent efforts have combined Kalman filter–based techniques with indirect video-based observations for bathymetry inversion. Here, we estimate nearshore bathymetry by utilizing observed wave celerity and wave height, which are related to bathymetry through phase-averaged wave dynamics. We present a modified compressed-state Kalman filter (CSKF) method, a fast and scalable Kalman filter method for linear and nonlinear problems with large numbers of unknowns and measurements, and apply it to two nearshore bathymetry estimation problems. To illustrate the robustness and accuracy of our method, we compare its performance with that of two ensemble-based approaches on twin bathymetry estimation problems with profiles based on surveys taken by the U.S. Army Corps of Engineer Field Research Facility (FRF) in Duck, North Carolina. We first consider an estimation problem for a temporally constant bathymetry profile. Then we estimate bathymetry as it evolves in time. Our results indicate that the CSKF method is more accurate and robust than the ensemble-based methods with the same computational cost. The superior performance is due to the optimal low-rank representation of the covariance matrices.

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  2. Abstract

    High‐resolution characterization of hydraulic properties and dense nonaqueous phase liquid (DNAPL) contaminant source is crucial to develop efficient remediation strategies. However, DNAPL characterization suffers from a limited number of borehole data in the field, resulting in a low‐resolution estimation. Moreover, high‐resolution DNAPL characterization requires a large number of unknowns to be estimated, presenting a computational bottleneck. In this paper, a low‐cost geophysical approach, the self‐potential method, is used as additional information for hydraulic properties characterization. Joint inversion of hydraulic head and self‐potential measurements is proposed to improve hydraulic conductivity estimation, which is then used to characterize the DNAPL saturation distribution by inverting partitioning tracer measurements. The computational barrier is overcome by (a) solving the inversion by the principal component geostatistical approach, in which the covariance matrix is replaced by a low‐rank approximation, thus reducing the number of forward model runs; (b) using temporal moments of concentrations instead of individual concentration data points for faster forward simulations. To assess the ability of the proposed approach, numerical experiments are conducted in a 3‐D aquifer with 104unknown hydraulic conductivities and DNAPL saturations. Results show that with realistic DNAPL sources and a limited number of hydraulic heads, the traditional hydraulic/partitioning tracer tomography roughly reconstructs subsurface heterogeneity but fails to resolve the DNAPL distribution. By adding self‐potential data, the error is reduced by 24% in hydraulic conductivity estimation and 68% in DNAPL saturation characterization. The proposed sequential inversion framework utilizes the complementary information from multi‐source hydrogeophysical data sets, and can provide high‐resolution characterizations for realistic DNAPL sources.

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