Application of Physics-Informed Neural Networks in Hydrological Analysis: A Method for Partitioning Fast and Slow Runoff Paths in Mountainous Watersheds

This article introduces an open-source framework based on Physics-Informed Neural Networks (PINN) for distinguishing fast and slow flow paths in snow-dominated mountainous watersheds. The framework integrates hydrological observation data and conservative chloride tracers, providing a new tool for water resource management. The project's code and data are open-source, serving as a reference case for hydrological research and AI for Science.

Mountainous watersheds are important sources of freshwater, but their hydrological processes are complex (coupling of snowmelt, soil infiltration, etc.). Traditional models struggle to accurately distinguish between fast (surface/interflow, hours to days) and slow (deep groundwater, months to years) paths. Challenges include: observation data only measuring total runoff, complex coupling of physical processes (difficulty solving partial differential equations), and pure data-driven models lacking physical constraints (poor generalization).

PINN embeds physical laws into neural network training, with loss functions including data loss (fitting observations) and physical loss (satisfying physical constraints). The PINN architecture in this project: inputs are meteorological forcing, upstream hydrology, and time information; outputs are fast/slow path contributions, storage changes, and tracer concentrations; physical constraints include water mass conservation, chloride tracer conservation, and boundary conditions.

The model uses data from the snow-dominated East River Watershed in Colorado, USA: hydrological observations (river discharge, meteorology, snow cover), and conservative chloride tracers (chemically stable, used to infer path contributions). The data are publicly available via ESS-DIVE: Dataset 1 (https://doi.org/10.15485/1668054), Dataset 2 (https://doi.org/10.15485/1779721).

The project compares PINN with two baseline methods: 1. Pure hydrological PINN (without tracers, difficult to distinguish paths); 2. LSTM (pure data-driven, prone to violating physical laws). Results show PINN's advantages: physical consistency (satisfies mass conservation), interpretability (supported by physical equations), data efficiency (good generalization with limited data), and extrapolation capability (strong robustness).

Scientific value: Methodological innovation (application of PINN in hydrology), revealing watershed path contributions, and demonstrating data fusion. Practical value: Improving flood forecasting accuracy, drought assessment (groundwater quantification), climate change impact assessment, and decision support for water resource management. Educational value: Open-source code and data can be used for learning PINN, hydrological model development, and reproducible research.

Current limitations: Dependence on observation data quality, high computational cost, significant impact of hyperparameter tuning, and cross-watershed generalization needing verification. Future directions: Multi-watershed validation, lightweight models for real-time prediction, uncertainty quantification (Bayesian PINN), and integration of more complex processes (snow-soil-vegetation interactions).