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We use a spatially distributed and physically based energy and mass balance model to derive the ostrem curve, which expresses the supraglacial debris-related relative melt alteration versus the debris thickness, for the Djankuat Glacier, Caucasus, Russian Federation. The model is driven by meteorological data from two on-glacier weather stations and ERA-5 Land reanalysis data. A direct pixel-by-pixel comparison of the melt rates obtained from both a clean ice and debris-covered ice mass balance model results in the quantification of debris-related relative melt-modification ratios, capturing the degree of melt enhancement or suppression as a function of the debris thickness. The main results show that the distinct surface features and different surface temperature/moisture and near-surface wind regimes that persist over debris-covered ice significantly alter the pattern of the energy and mass fluxes when compared to clean ice. Consequently, a maximum relative melt enhancement of 1.36 is modeled on the glacier for thin/patchy debris with a thickness of 0.03 m. However, insulating effects suppress sub-debris melt under debris layers thicker than a critical debris thickness of 0.09 m. Sensitivity experiments show that especially within-debris properties, such as the thermal conductivity and the vertical debris porosity gradient, highly impact the magnitude of the sub-debris melt rates. Our results also highlight the scale-dependency as well as the dynamic nature of the debris thickness-melt relationship for changing climatic conditions, which may have significant implications for the climate change response of debris-covered glaciers. The presence of rocks, boulders and sediments on top of glacier ice can highly modify the behavior of mountain glaciers. As such, compared to a clean ice surface, a debris-covered ice surface is subject to a modified melting regime. In our study, we quantify this melt-modification effect for the Djankuat Glacier, a well-studied glacier situated in the Caucasus. The results are expressed by a so-called ostrem curve that quantifies the debris-related melt-modification effect and compares it to the corresponding debris thickness. Here, we present the first attempt to construct such a glacier-specific ostrem curve through sophisticated 2D glacier-wide energy and mass balance modeling. Our results show that the energy and mass balance at the glacier surface are greatly modified due to the debris, resulting in different melting regimes over both surface types. Hence, ice melt is enhanced for thin and patchy debris layers, whereas melt is increasingly suppressed for thick and continuous debris layers due to an insulating effect. The degree of melt modification and the shape of the ostrem curve are found to depend on the debris properties, the spatio-temporal distribution of the debris, and the local climatic conditions. Quantifying such melt-modification effects is important to more accurately understand and assess the behavior of (partly) debris-covered glaciers under a future warming climate. We use a spatially distributed and physically based energy and mass balance model to derive the ostrem curve for the Djankuat Glacier The sub-debris melt rates are especially sensitive to within-debris properties, such as the thermal conductivity, the debris porosity and its gradient The relative melt suppression of the debris cover is modeled to increase in a warming climate, regardless of the changes in debris thickness

来源平台：JOURNAL OF GEOPHYSICAL RESEARCH-EARTH SURFACE