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In the Jutulgryta area of Dronning Maud Land, Antarctica, subsurface melting of the ice sheet has been observed. The melting takes place during the summer months in blue-ice areas under conditions of below-freezing air and surface temperatures. Adjacent snow-covered regions, having the same meteorological and climatic conditions, experience little or no subsurface melting. To help explain and understand the observed melt-rate differences in the blue-ice and snow-covered areas, a physically based numerical model of the coupled atmosphere, radiation, snow and blue-ice system has been developed. The model comprises a heat-transfer equation which includes a spectrally dependent solar-radiation source term. The penetration of radiation into the snow and blue ice depends on the solar-radiation spectrum, the surface albedo and the snow and blue-ice grain-sizes and densities. In addition, the model uses a complete surface energy balance to define the surface boundary conditions. It is run over the full annual cycle, simulating temperature profiles and melting and freezing quantities throughout the summer and winter seasons. The model is driven and validated using field observations collected during the Norwegian Antarctic Research Expedition (NARE) 1996–97. The simulations suggest that the observed differences between subsurface snow and blue-ice melting can be explained largely by radiative and heat-transfer interactions resulting from differences in albedo, grain-size and density between the two mediums.