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

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 the 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.

The SNOTEL data utilized in this study were available via the National Water and Climate Center, which lies under the United States Department of Agriculture. Data reports of the SNOTEL data were generated using the online portal found at https://www.nrcs.usda.gov/wps/portal/wcc/home/. The data from Col de Porte (Lejeune et al. 2019) can be found at the Observatoire des Sciences de l’Univers de Grenoble DOI portal at https://doi.osug.fr/public/CRYOBSCLIM_CDP/CRYOBSCLIM.CDP.2018.html, and data from Kühtai (Krajči et al. 2017) can be found as the supplemental material from https://doi.org/10.1002/2017WR020445. Raw data from Sodankyla (Essery et al. 2016) can be found from the Intensive Observation (sensors 8, 11) data portal at https://litdb.fmi.fi/ioa.php and automated weather station (sensor 15, portal at https://litdb.fmi.fi/luo0015_data.php). Reynolds Mountain East (Reba et al. 2011) data were obtained from an ESM-SnowMIP repository https://www.geos.ed.ac.uk/∼ressery/ESM-SnowMIP.html. Raw Yala Basecamp (Stigter et al. 2021; Shea et al. 2015) data were retrieved from https://rds.icimod.org/Home/DataDetail?metadataId=26859 and https://rds.icimod.org/Home/DataDetail?metadataId=1972554. Rofental (Warscher et al. 2024) data were retrieved from https://datapub.gfz-potsdam.de/download/10.5880.FIDGEO.2023.037-MNveB/. The data in this study were processed from these sources. Code for scraping and cleaning SNOTEL data and tutorials for data retrieval and training/modifying the neural models are available at https://clima.github.io/ClimaLand.jl/dev/generated/standalone/Snow/base_tutorial/. CSVs of the training/testing data are also available here, as a quality-controlled fully observational dataset of physical variables for calibration and ML applications.