Distributed glacier melt models generally assume that the glacier surface consists of bare exposed ice and snow. In reality, many glaciers are wholly or partially covered in layers of debris that tend to suppress ablation rates. In this paper, an existing physically based point model for the ablation of debris-covered ice is incorporated in a distributed melt model and applied to Haut Glacier d'Arolla, Switzerland, which has three large patches of debris cover on its surface. The model is based on a 10 m resolution digital elevation model (DEM) of the area; each glacier pixel in the DEM is defined as either bare or debris-covered ice, and may be covered in snow that must be melted off before ice ablation is assumed to occur. Each debris-covered pixel is assigned a debris thickness value using probability distributions based on over 1000 manual thickness measurements. Locally observed meteorological data are used to run energy balance calculations in every pixel, using an approach suitable for snow, bare ice or debris-covered ice as appropriate. The use of the debris model significantly reduces the total ablation in the debris-covered areas, however the precise reduction is sensitive to the temperature extrapolation used in the model distribution because air near the debris surface tends to be slightly warmer than over bare ice. Overall results suggest that the debris patches, which cover 10% of the glacierized area, reduce total runoff from the glacierized part of the basin by up to 7%.