We used a spatially distributed and physically based energy and mass balance model to derive the Østrem curve, that is the supraglacial debris-related relative melt alteration versus the debris thickness, for the Djankuat Glacier, Caucasus, Russian Federation. The model is driven by meteorological input data from two on-glacier automatic weather stations and ERA-5 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. In doing so, our model is the first attempt to derive the glacier-specific Østrem curve through spatially distributed energy and mass balance modelling. The main results show that a maximum relative melt enhancement occurs on the Djankuat Glacier for thin and patchy debris with a thickness of 3 cm. However, insulating effects suppress sub-debris melt under debris layers thicker than a critical debris thickness of 9 cm. Sensitivity experiments show that especially within-debris properties, such as the thermal conductivity, the vertical porosity gradient and the moisture content of the debris pack, highly impact the magnitude of the sub-debris melt rates. The Østrem curve is also shaped by the local climate. Our results highlight the need to account for site-specific debris properties and their variation with depth, as well as for the effects of changing local climatic conditions in order to accurately assess (partly) debris-covered glacier behavior and its climate change response.