We use a spatially distributed and physically based energy and mass balance model to derive the Østrem 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.