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We review the basic equations, numerical solution techniques, and new application areas of a novel multi-purpose computer code framework, PISALE, for the solution of complex Partial Differential Equation (PDE) systems on modern computing platforms. We describe how the code solves equations in the fluid approximation using a novel combination of ALE and AMR methods. Sample problems from areas of ground water flow, high-speed impacts, and X-ray Free Electron Laser (XFEL) experiments are given. 

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. 

Abstract The Surface Water and Ocean Topography (SWOT) satellite has the potential to transform global hydrologic science by offering simultaneous and synoptic estimates of river discharge and other hydraulic variables. Discharge is estimated from SWOT observations of water surface elevation, width, and slope. A first assessment using just the highest quality SWOT measurements, over the first 15 months (March 2023–July 2024) of the mission evaluated at 65 gauged reaches shows results consistent with pre‐launch expectations. SWOT estimates track discharge dynamics without relying on any gauge information: median correlation is 0.73, with a correlation interquartile range of 0.51–0.89. SWOT estimates capture discharge magnitude correctly in some cases but are biased (median bias is 50%) in others. There are already a total of 11,274 ungauged global locations with highest quality SWOT measurements where SWOT discharge is expected to accurately track discharge variations: this value will increase as SWOT data record length grows, algorithms are refined and SWOT measurements are reprocessed. This first look indicates that SWOT discharge is performing as expected for SWOT data that achieve performance requirements, providing observed information on discharge variations in ungauged basins globally. 

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;http://www.hawaii.edu/climate-data-portal). Significance StatementA 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.