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1. Scalable Riemann Solvers with the Discontinuous Galerkin Method for Hyperbolic Network Simulation

   https://doi.org/10.1145/3592979.3593421  

   Hamilton, Aidan; Qiu, Jing-Mei; Zhang, Hong (July 2023, Platform for Advanced Scientific Computing (PASC))

   We develop a set of highly efficient and effective computational algorithms and simulation tools for fluid simulations on a network. The mathematical models are a set of hyperbolic conservation laws on edges of a network, as well as coupling conditions on junctions of a network. For example, the shallow water system, together with flux balance and continuity conditions at river intersections, model water flows on a river network. The computationally accurate and robust discontinuous Galerkin methods, coupled with explicit strong stability preserving Runge-Kutta methods, are implemented for simulations on network edges. Meanwhile, linear and nonlinear scalable Riemann solvers are being developed and implemented at network vertices. These network simulations result in tools that are added to the existing PETSc and DMNetwork software libraries for the scientific community in general. Simulation results of a shallow water system on a Mississippi river network with over one billion network variables are performed on an extreme-scale computer using up to 8,192 processor with an optimal parallel efficiency. Further potential applications include traffic flow simulations on a highway network and blood flow simulations on a arterial network, among many others. 

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2. ChemLotUS: A Benchmark Data Set of Lotic Chemistry Across US River Networks

   https://doi.org/10.1029/2024WR039355  

   Fernandez, N.; Cohen, M_J; Jawitz, J_W (May 2025, Water Resources Research)

   Abstract We present a curated water chemistry data set for lotic systems across the contiguous US containing 35,000,000 records from 290,000 locations. These records are spatially joined to high‐resolution national hydrography data sets, providing information on watershed area, network position, and other hydrographic information. Our curation process follows best practices applied to raw query results from the Water Quality Portal, followed by assigning network context (position and watershed attributes) to each site from the high‐resolution National Hydrography Data set. The ChemLotUS data set currently includes 11 analytes selected to represent geogenic, biogenic, and anthropogenic processes: calcium, conductivity, pH, total suspended solids, turbidity, dissolved oxygen, total organic carbon, chlorophyll a, nitrate, soluble reactive phosphorus, and total phosphorus. All records from the raw query were modified during curation, most notably by removing duplicated observations, converting units, and aggregating strongly correlated chemical forms. Following curation, 65% of the original records were preserved, with significant reductions from raw to curated data in the means of nine constituents and, more notably, in the standard deviations of all constituents. 95% of monitored river reaches were linked to three or fewer monitoring sites, with sample patterns revealing a strong measurement bias to high order streams. We demonstrate the functionality of ChemLotUS by identifying spatiotemporal patterns in water quality at the CONUS‐scale, including diurnal variations of dissolved oxygen, pH in headwaters compared to their corresponding river mouths, and total suspended solids as a function of stream order. ChemLotUS enables new opportunities for investigations of continental scale variation in and controls on water quality. 

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3. Fair Graph Learning Using Constraint-Aware Priority Adjustment and Graph Masking in River Networks

   https://doi.org/10.1609/aaai.v38i20.30212  

   He, Erhu; Xie, Yiqun; Sun, Alexander; Zwart, Jacob; Yang, Jie; Jin, Zhenong; Wang, Yang; Karimi, Hassan; Jia, Xiaowei (March 2024, Proceedings of the AAAI Conference on Artificial Intelligence)

   Accurate prediction of water quality and quantity is crucial for sustainable development and human well-being. However, existing data-driven methods often suffer from spatial biases in model performance due to heterogeneous data, limited observations, and noisy sensor data. To overcome these challenges, we propose Fair-Graph, a novel graph-based recurrent neural network that leverages interrelated knowledge from multiple rivers to predict water flow and temperature within large-scale stream networks. Additionally, we introduce node-specific graph masks for information aggregation and adaptation to enhance prediction over heterogeneous river segments. To reduce performance disparities across river segments, we introduce a centralized coordination strategy that adjusts training priorities for segments. We evaluate the prediction of water temperature within the Delaware River Basin, and the prediction of streamflow using simulated data from U.S. National Water Model in the Houston River network. The results showcase improvements in predictive performance and highlight the proposed model's ability to maintain spatial fairness over different river segments. 

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4. Using Machine Learning Models for Short-Term Prediction of Dissolved Oxygen in a Microtidal Estuary

   https://doi.org/10.3390/w16141998  

   Gachloo, Mina; Liu, Qianqian; Song, Yang; Wang, Guozhi; Zhang, Shuhao; Hall, Nathan (July 2024, Water)

   This paper presents a comprehensive approach to predicting short-term (for the upcoming 2 weeks) changes in estuarine dissolved oxygen concentrations via machine learning models that integrate historical water sampling, historical and upcoming 2-week meteorological data, and river discharge and discharge metrics. Dissolved oxygen is a critical indicator of ecosystem health, and this approach is implemented for the Neuse River Estuary, North Carolina, U.S.A., which has a long history of hypoxia-related habitat degradation. Through meticulous data preprocessing and feature selection, this research evaluates the predictions of dissolved oxygen concentrations by comparing a recurrent neural network with four other models, including a Multilayer Perceptron, Long Short-Term Memory, Gradient Boosting, and AutoKeras, through sensitivity experiments. The input predictors to our prediction models include water temperature, turbidity, chlorophyll-a, aggregated river discharge, and aggregated wind based on eight directions. By emphasizing the most impactful predictors, we streamlined the model-building processes and built a hindcast system from 2015 to 2019. We found that the recurrent neural network model was most effective in predicting the dissolved oxygen concentrations, with an R2 value of 0.99 at multiple stations. Different from our machine learning hindcast models that used observed upcoming meteorological and discharge data, an actual forecast system would use forecasted meteorological and discharge data. Therefore, an actual operational forecast may have lower accuracy than the hindcast, as determined by the accuracy of the predicted meteorological and discharge data. Nevertheless, our studies enhance our understanding of the factors influencing dissolved oxygen variability and set the basis for the implementation of a predictive tool for environmental monitoring and management. We also emphasized the importance of building station-specific models to improve the prediction results. 

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5. Estimating a Directed Tree for Extremes

   Ngoc Mai Tran, Johannes Buck (October 2023, Journal of the Royal Statistical Society Series B Methodological)

   The Extremal River Problem has emerged as a flagship problem for causal discovery in extreme values of a network. The task is to recover a river network from only extreme flow measured at a set V of stations, without any information on the stations' locations. We present QTree, a new simple and efficient algorithm to solve the Extremal River Problem that performs very well compared to existing methods on hydrology data and in simulations. QTree returns a root-directed tree and achieves almost perfect recovery on the Upper Danube network data, the existing benchmark data set, as well as on new data from the Lower Colorado River network in Texas. It can handle missing data, has an automated parameter tuning procedure, and runs in time O(n |V|^2), where n is the number of observations and |V| the number of nodes in the graph. Furthermore, we prove that the QTree estimator is consistent under a Bayesian network model for extreme values with noise. We also assess the small sample behaviour of QTree through simulations and detail the strengths and possible limitations of QTree. 

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