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The study introduces the Mass-Conserving Perceptron (MCP), a novel framework that reformulates traditional hydrologic models into conceptually interpretable neural networks, specifically focusing on snow-water dynamics. Evaluating the MCP across 513 CAMELS-US basins, the researchers demonstrate that the predictive performance of the MCP is comparable to that of established hydrologic models while utilizing fewer parameters. Notably, the findings reveal that increasing the number of states in the MCP architecture enhances predictive accuracy, with a median KGEss of 0.90 achieved using five-state networks, although gains diminish beyond two states.
Transforming hydrologic modeling, the Mass-Conserving Perceptron achieves state-of-the-art predictive accuracy with fewer parameters than traditional methods.
The Mass-Conserving Perceptron (MCP) establishes a modeling paradigm in which conceptual hydrologic models can be reformulated as physically constrained, conceptually interpretable neural networks. Here, we develop a snow-water MCP network framework and evaluate it across 513 CAMELS-US basins. We first recast a coupled two-state SOIL-MCP and SNOWMCP conceptual model as a mass-conserving neural network and show that the hydrologic-model and neural-network formulations achieve comparable predictive performance. We then examine cross-node state-information sharing within two-state HYDROMCP architectures and evaluate broader single-layer networks constructed from three types of interpretable MCP units with one to five states. Across CONUS, the median KGEss increases from 0.82 for one-state networks to 0.89 for two-state networks and 0.90 for five-state networks, suggesting diminishing aggregate gains beyond two states. Basin-specific MCP and LSTM selection yields the same median KGEss of 0.90, while the selected MCP networks use fewer parameters on average. Complementary AIC- and KGE-based selection identifies compact, basin-specific directed-graph representations that balance predictive accuracy and model complexity. These analyses provide an empirical basis for identifying the numbers, types, and interactions of states needed for hydrologic representation. Future studies should test joint training against multiple hydrologic responses, such as streamflow, snow water equivalent, and groundwater storage.
