GlaUnTI: a hybrid physics–machine learning model enables transferable glacier surface mass balance estimation
- 1University of Twente (Enschede, Netherlands)
- 2University of Sheffield (Sheffield, United Kingdom)
Abstract
Glacier surface mass balance (SMB) is a key climate indicator and a central driver of glacier change. Direct SMB observations remain sparse and unevenly distributed. Hence, transferable SMB models are essential for large-scale assessments and projections. Here, we propose the GLAcier-UNiversal Temperature Index model (GlaUnTI) for this purpose. This hybrid physics–machine learning model modifies a fully differentiable temperature index (TI) SMB model by introducing a shallow convolutional neural corrector. It learns spatially and temporally varying adjustments to a small set of physically interpretable TI parameters, using glacier geometry and aggregated climate information. We calibrate four models – a basic TI model, a purely data-driven recurrent neural network with no physical inductive bias and two GlaUnTI variants, with and without glacier facies maps as predictors – using a dataset of 65 European glaciers spanning 1995–2024 and covering the Alps, Scandinavia, Iceland, Svalbard and the Pyrenees. Their spatial transferability is evaluated on a held-out, spatially independent test subset of 13 glaciers across climatically and geometrically contrasting European regions. The evaluation uses 793/756/314 (annual/winter/summer) point SMB measurements and 312/235/233 glacier-wide SMB estimates. On the test glaciers, the baseline TI model achieves annual point-level performance with r =0.854 and an RMSE equal to 1.707 m w.e. With GlaUnTI, r increases to 0.940 and the RMSE reduces to 1.068 m w.e. At the glacier-wide scale, the baseline TI model attains an r equal to 0.606 and an RMSE of 0.805 m w.e. With GlaUnTI, r increases to 0.700 and the RMSE reduces to 0.627 m w.e. Including glacier facies maps from the end of the ablation season to the corrector yields moderate benefits in glacier-wide summer (11.0 %) and annual (12.2 %) SMB estimates. In contrast, the purely data-driven baseline model overall shows the weakest spatial transferability. Beyond modelling accuracy, end-to-end differentiability enables efficient gradient-based calibration, transfer learning, inverse optimisation of effective forcing perturbations, formal model explainability and propagation of forcing-driven aleatoric uncertainty through long SMB trajectories. These results demonstrate that parameter-corrected hybrid models improve SMB transferability across diverse climate regimes while preserving a physically grounded structure, suitable for integration into broader glacier evolution workflows and for informing climate-related policies.
Versions
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BibTeX
@article{maslov2026glaunti,
title = {{GlaUnTI: a hybrid physics–machine learning model enables transferable glacier surface mass balance estimation}},
author = {Konstantin A. Maslov and Thomas Schellenberger and Claudio Persello and Alfred Stein},
journal = {The Cryosphere},
year = {2026},
month = oct,
doi = {10.5194/tc-20-6045-2026},
url = {https://tc.copernicus.org/articles/20/6045/2026/},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - GlaUnTI: a hybrid physics–machine learning model enables transferable glacier surface mass balance estimation
AU - Konstantin A. Maslov
AU - Thomas Schellenberger
AU - Claudio Persello
AU - Alfred Stein
PY - 2026
DA - 2026/10/21
JO - The Cryosphere
DO - 10.5194/tc-20-6045-2026
UR - https://tc.copernicus.org/articles/20/6045/2026/
AB - Glacier surface mass balance (SMB) is a key climate indicator and a central driver of glacier change. Direct SMB observations remain sparse and unevenly distributed. Hence, transferable SMB models are essential for large-scale assessments and projections. Here, we propose the GLAcier-UNiversal Temperature Index model (GlaUnTI) for this purpose. This hybrid physics–machine learning model modifies a fully differentiable temperature index (TI) SMB model by introducing a shallow convolutional neural corrector. It learns spatially and temporally varying adjustments to a small set of physically interpretable TI parameters, using glacier geometry and aggregated climate information. We calibrate four models – a basic TI model, a purely data-driven recurrent neural network with no physical inductive bias and two GlaUnTI variants, with and without glacier facies maps as predictors – using a dataset of 65 European glaciers spanning 1995–2024 and covering the Alps, Scandinavia, Iceland, Svalbard and the Pyrenees. Their spatial transferability is evaluated on a held-out, spatially independent test subset of 13 glaciers across climatically and geometrically contrasting European regions. The evaluation uses 793/756/314 (annual/winter/summer) point SMB measurements and 312/235/233 glacier-wide SMB estimates. On the test glaciers, the baseline TI model achieves annual point-level performance with r =0.854 and an RMSE equal to 1.707 m w.e. With GlaUnTI, r increases to 0.940 and the RMSE reduces to 1.068 m w.e. At the glacier-wide scale, the baseline TI model attains an r equal to 0.606 and an RMSE of 0.805 m w.e. With GlaUnTI, r increases to 0.700 and the RMSE reduces to 0.627 m w.e. Including glacier facies maps from the end of the ablation season to the corrector yields moderate benefits in glacier-wide summer (11.0 %) and annual (12.2 %) SMB estimates. In contrast, the purely data-driven baseline model overall shows the weakest spatial transferability. Beyond modelling accuracy, end-to-end differentiability enables efficient gradient-based calibration, transfer learning, inverse optimisation of effective forcing perturbations, formal model explainability and propagation of forcing-driven aleatoric uncertainty through long SMB trajectories. These results demonstrate that parameter-corrected hybrid models improve SMB transferability across diverse climate regimes while preserving a physically grounded structure, suitable for integration into broader glacier evolution workflows and for informing climate-related policies.
SN - 1994-0424
ER -