Estimating Regional Snow Water Equivalent Using a Physics‐Informed Graph Convolution Network Model

Abstract Snow water equivalent (SWE), which quantifies the amount of water in a snowpack, is critical for water supply forecasting. This study explores machine learning (ML) models' capability of representing the spatial distribution of SWE across the western United States. Nine graph convolution network (GCN) models using different loss functions, including a series of physics‐informed loss functions, are developed and compared to a baseline extra tree (ET) model. Different approaches for physics‐informed loss function are examined according to the correlation among geographic and meteorological conditions and are expected to help ML models better capture SWE variability. Terrain characteristics, meteorological variables, and snow cover products are used as input features for regional SWE estimation. All ML models are trained on data sets at selected in situ sites during 2018–2021 and evaluated with 9 days in January–March 2025. Results show that GCN models generally outperform the ET model, capturing SWE spatial variability more effectively and achieving higher statistical metrics. The use of the SWE‐elevation‐precipitation‐based physics‐informed loss function provides the best results among all models with an improved coefficient of determination ( R 2 ) of 0.28 and the lowest root mean square error (RMSE) of 0.22 m, while underestimation is observed for high SWE. A site‐by‐site comparison reveals that model estimates from the GCN models generally agree with observations with R 2 of 0.5–0.9, showing a reliable capability of estimating SWE at a single given site. However, the GCN models still have limited spatiotemporal generalization affected by the restricted representation of site measurements.