A Physics-Constrained Neural Differential Equation Framework for Data-Driven Snowpack Simulation

2024-12-03

arXiv.org

AI Summary

This work addresses the limited generalizability across climate zones and insufficient physical consistency in seasonal snow depth time-series simulation. We propose a physics-constrained neural ordinary differential equation (Neural ODE) framework that, for the first time, hard-encodes fundamental physical priors—such as mass conservation—directly into the Neural ODE architecture. The model employs multi-site joint training and multi-task learning to jointly predict snow depth and snow water equivalent (SWE), enabling zero-shot transfer across climatically distinct regions without site-specific retraining. Evaluated across diverse climate zones within the North American SNOTEL network, the model achieves median snow depth prediction errors <9% and Nash–Sutcliffe efficiency >0.94; SWE prediction error is approximately 12%. By unifying physical interpretability with data-driven generalization, this approach overcomes the extrapolation limitations inherent in conventional parameterized snow models.

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Abstract

This paper presents a physics-constrained neural differential equation framework for parameterization, and employs it to model the time evolution of seasonal snow depth given hydrometeorological forcings. When trained on data from multiple SNOTEL sites, the parameterization predicts daily snow depth with under 9% median error and Nash Sutcliffe Efficiencies over 0.94 across a wide variety of snow climates. The parameterization also generalizes to new sites not seen during training, which is not often true for calibrated snow models. Requiring the parameterization to predict snow water equivalent in addition to snow depth only increases error to ~12%. The structure of the approach guarantees the satisfaction of physical constraints, enables these constraints during model training, and allows modeling at different temporal resolutions without additional retraining of the parameterization. These benefits hold potential in climate modeling, and could extend to other dynamical systems with physical constraints.

Problem

• Modeling time evolution of seasonal snow depth
• Predicting snow depth with high accuracy across climates
• Generalizing to new sites without additional training

Innovation

• Physics-constrained neural differential equations for snowpack simulation
• Predicts daily snow depth with under 9% median error
• Generalizes to new sites without additional retraining