Modeling surface-roughness/solar-ablation feedback: application to small-scale surface channels and crevasses of the Greenland ice sheet

Surface roughness enhances the net ablation rate associated with direct solar radiation relative to smooth surfaces, because roughness allows solar energy reflected from one part of the surface to be absorbed by another part. In this study we examine the feedback between solar-radiation-driven ablation and growth of surface roughness on the Greenland ice sheet, using a numerical model of radiative transfer. Our experiments extend previous work by examining: (1) the effects of diurnal and seasonal variation of solar zenith angle and azimuth relative to incipient roughness features, (2) the evolution of roughness geometry in response to radiatively driven ablation and (3) the relative solar energy collection efficiencies of various roughness geometries and geographic locations and orientations. A notable result of this examination is that the time evolution of the aspect ratio of surface features under solar-driven ablation collapses onto a roughly universal curve that depends only on latitude, not the detailed shape of the feature. The total enhancement of surface melt relative to a smooth surface over a full ablation season varies with this ratio, and this dependence suggests a way to parameterize roughness effects in large-scale models that cannot treat individual roughness features. Overall, our model results suggest that surface roughness at the latitudes spanned by the Greenland ice sheet tends to dissipate as the ablation season progresses.