Controls on the relative melt rates of debris-covered glacier surfaces

Supraglacial debris covers 7% of mountain glacier area globally and generally reduces glacier surface melt. Enhanced energy absorption at ice cliffs and supraglacial ponds scattered across the debris surface leads these features to contribute disproportionately to glacier-wide ablation. However, the degree to which cliffs and ponds actually increase melt rates remains unclear, as these features have only been studied in a detailed manner for selected locations, almost exclusively in High Mountain Asia. In this study we model the surface energy balance for debris-covered ice, ice cliffs, and supraglacial ponds with a set of automatic weather station records representing the global prevalence of debris-covered glacier ice. We generate 5000 random sets of values for physical parameters using probability distributions derived from literature, which we use to investigate relative melt rates and to isolate the melt responses of debris, cliffs and ponds to the site-specific meteorological forcing. Modelled sub-debris melt rates are primarily controlled by debris thickness and thermal conductivity. At a reference thickness of 0.1 m, sub-debris melt rates vary considerably, differing by up to a factor of four between sites, mainly attributable to air temperature differences. We find that melt rates for ice cliffs are consistently 2-3× the melt rate for clean glacier ice, but this melt enhancement decays with increasing clean ice melt rates. Energy absorption at supraglacial ponds is dominated by latent heat exchange and is therefore highly sensitive to wind speed and relative humidity, but is generally less than for clean ice. Our results provide reference melt enhancement factors for melt modelling of debris-covered glacier sites, globally, while highlighting the need for direct measurement of debris-covered glacier surface characteristics, physical parameters, and local meteorological conditions at a variety of sites around the world.