A Structural-State Closure Model for Glacier Basal Friction and Its Validation with Daily Argentiere Glacier Data

<title>Abstract</title> <p>Glacier basal friction controls basal sliding, subglacial erosion, sediment deformation, glacier seismicity, and the basal boundary condition in glacier and ice-sheet models. However, a real glacier bed cannot be treated like an ordinary laboratory friction pair. It is deeply buried, spatially extensive, hydrologically active, and composed of bedrock, cavities, water films, till, debris-rich contacts, frozen patches, and localized sticky spots. Laboratory experiments can constrain local ice-rock, icetill, ice-ice, or debris-rich friction, but they cannot directly measure the total instantaneous friction force of a whole glacier bed. A glacier-scale friction law therefore has to act as an effective field closure, converting observable or inferable quantities such as sliding velocity, proglacial discharge, borehole water pressure, seismicity, and inverted basal drag into basal resistance. Here, the structural-state friction formula proposed by Pan (2026) is extended to glacier basal motion. The proposed basal closure decomposes basal shear stress into a hydrology/effective-pressure background channel and a structural-state production-loss channel. The structural channel uses the fixed response shape 𝑥/(1 + 𝑥1+𝑞), representing competition between sliding-induced formation of load-bearing basal structures and destruction of those structures by rapid sliding, hydrologic perturbation, cavity expansion, or bed reorganization. The model is tested with daily field data from Argentiere Glacier. The dataset includes sliding velocity, proglacial discharge, and inferred basal shear stress; after date matching and data cleaning, 6871 daily records remain. A physically constrained structural-hydrology model outperforms power-law, Gaussian-hump, and hydrology-only power baselines in training RMSE, AIC, and BIC. With a fixed structural response shape 𝛽 = 0.05, 𝑞 = 0.05, the model gives a mean holdout RMSE of 0.005453 MPa in five year-block folds, better than 0.005732 MPa for the hydrology-only power model. Failure analysis shows that the fixed-characteristic-speed model loses mainly under extreme discharge, summer melt, decadal nonstationarity, and speed-range extrapolation. A corrected closure is therefore proposed in which the fixed structural response shape is retained but the characteristic speed drifts with hydrologic state and slow bed state: ln 𝑢𝑐,eff = ln 𝑢𝑐0 + 𝑘𝑄 log(𝑄norm) + 𝑘𝑇 trend. The corrected model wins all RMSE, AIC, and BIC comparisons across 20 partition tests involving year, season, decade, sliding-speed quantile, and discharge quantile, with a weighted mean RMSE advantage of 0.002394 MPa. The results support a strong internal conclusion for Argentiere Glacier: basal friction is effectively described by a fixed structural response shape with a hydrology- and bedstate- dependent characteristic speed. This is not yet a proof of an externally universal glacier slip law; external validation requires transfer to independent glaciers or laboratory bed-slip datasets.</p>