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  1. The solution of partial differential equations (PDEs) on modern high performance computing (HPC) platforms is essential to the continued success of groundwater flow and transport modeling in Pacific islands where complex regional groundwater flow is governed by highly heterogeneous volcanic rocks and dynamic interaction between freshwater and seawater. For accurate simulations of complex groundwater flow processes in the Hawaiian islands, the PISALE (Pacific Island Structured-AMR with ALE) software has been developed to offer an innovative combination of advanced mathematical techniques such as arbitrary Lagrangian-Eulerian method (ALE) and Adaptive Mesh Refinement (AMR). The software uses parallel programming models to accelerate the time to solution and dynamically adapt the grids using AMR. This allows for the solution of equations that can reproduce the sharp freshwater-seawater interface in large-scale coast aquifers. In this work, we summarize our ongoing efforts to create a publicly available sustainable branch of the software focused on the groundwater problem. The island-scale numerical groundwater flow modeling will play an important role in predicting the sustainable yields and potential contaminant transport for the volcanic aquifer systems and planning groundwater resources management. 
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  2. Abstract

    Submarine groundwater discharge (SGD) is an important driver of coastal biogeochemical budgets worldwide. Radon (222Rn) has been widely used as a natural geochemical tracer to quantify SGD, but field measurements are time consuming and costly. Here, we use deep learning to predict coastal seawater radon in SGD‐impacted regions. We hypothesize that deep learning could resolve radon trends and enable preliminary insights with limited field observations of groundwater tracers. Two deep learning models were trained on global coastal seawater radon observations (n = 39,238) with widely available inputs (e.g., salinity, temperature, water depth). The first model used a one‐dimensional convolutional neural network (1D‐CNN‐RNN) framework for site‐specific gap filling and producing short‐term future predictions. A second model applied a fully connected neural network (FCNN) framework to predict radon across geographically and hydrologically diverse settings. Both models can predict observed radon concentrations withr2 > 0.76. Specifically, the FCNN model offers a compelling development because synthetic radon tracer data sets can be obtained using only basic water quality and meteorological parameters. This opens opportunities to attain radon data from regions with large data gaps, such as the Global South and other remote locations, allowing for insights that can be used to predict SGD and plan field experiments. Overall, we demonstrate how field‐based measurements combined with big‐data approaches such as deep learning can be utilized to assess radon and potentially SGD beyond local scales.

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  3. Abstract

    Gridded monthly rainfall estimates can be used for a number of research applications, including hydrologic modeling and weather forecasting. Automated interpolation algorithms, such as the “autoKrige” function in R, can produce gridded rainfall estimates that validate well but produce unrealistic spatial patterns. In this work, an optimized geostatistical kriging approach is used to interpolate relative rainfall anomalies, which are then combined with long-term means to develop the gridded estimates. The optimization consists of the following: 1) determining the most appropriate offset (constant) to use when log-transforming data; 2) eliminating poor quality data prior to interpolation; 3) detecting erroneous maps using a machine learning algorithm; and 4) selecting the most appropriate parameterization scheme for fitting the model used in the interpolation. Results of this effort include a 30-yr (1990–2019), high-resolution (250-m) gridded monthly rainfall time series for the state of Hawai‘i. Leave-one-out cross validation (LOOCV) is performed using an extensive network of 622 observation stations. LOOCV results are in good agreement with observations (R2= 0.78; MAE = 55 mm month−1; 1.4%); however, predictions can underestimate high rainfall observations (bias = 34 mm month−1; −1%) due to a well-known smoothing effect that occurs with kriging. This research highlights the fact that validation statistics should not be the sole source of error assessment and that default parameterizations for automated interpolation may need to be modified to produce realistic gridded rainfall surfaces. Data products can be accessed through the Hawai‘i Data Climate Portal (HCDP;

    Significance Statement

    A new method is developed to map rainfall in Hawai‘i using an optimized geostatistical kriging approach. A machine learning technique is used to detect erroneous rainfall maps and several conditions are implemented to select the optimal parameterization scheme for fitting the model used in the kriging interpolation. A key finding is that optimization of the interpolation approach is necessary because maps may validate well but have unrealistic spatial patterns. This approach demonstrates how, with a moderate amount of data, a low-level machine learning algorithm can be trained to evaluate and classify an unrealistic map output.

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  4. 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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  5. 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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