GlaUnTI: A hybrid physics–machine learning model enables transferable glacier surface mass balance estimation

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 performance is evaluated on a spatially independent test subset of 13 glaciers across heterogeneous 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. We found that the purely data-driven baseline model overall shows the weakest spatial transferability. Also, 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.