{
  "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.",
  "abstract_shown": true,
  "affiliations": [
    "University of Twente (Enschede, Netherlands)",
    "University of Sheffield (Sheffield, United Kingdom)"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Konstantin A. Maslov",
      "orcid": "0000-0002-9616-4979"
    },
    {
      "name": "Thomas Schellenberger",
      "orcid": "0000-0002-2501-3700"
    },
    {
      "name": "Claudio Persello"
    },
    {
      "name": "Alfred Stein"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ntbdjb8fsfab.bib",
  "cited_by": 0,
  "doi": "10.5194/tc-20-6045-2026",
  "fulltext_url": null,
  "id": "8ntbdjb8fsfab",
  "issns": [
    "1994-0424"
  ],
  "landing_url": "https://tc.copernicus.org/articles/20/6045/2026/",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1902|Cryospheric studies and observations"
    ]
  ],
  "openalex": "W7131719983",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": "Copernicus GmbH",
  "ris": "https://research.draconitic.com/paper/8ntbdjb8fsfab.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:37Z",
      "native_id": "10.5194/tc-20-6045-2026",
      "source": "crossref",
      "url": "https://tc.copernicus.org/articles/20/6045/2026/"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "openalex:1902|Cryospheric studies and observations",
      "subfield": "atmospheric"
    }
  ],
  "title": "GlaUnTI: a hybrid physics–machine learning model enables transferable glacier surface mass balance estimation",
  "title_text": "GlaUnTI: a hybrid physics–machine learning model enables transferable glacier surface mass balance estimation",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:20:37Z",
  "url": "https://research.draconitic.com/paper/8ntbdjb8fsfab",
  "venue": "The Cryosphere",
  "versions": [
    {
      "doi": "10.5194/egusphere-2026-515",
      "pid": null,
      "relation": "preprint",
      "title": null,
      "venue": null
    }
  ]
}