Glacial melt under a porous debris layer

In this paper we undertake a quantitative analysis of the dynamic process by which ice underneath a dry porous debris layer melts. We show that the incorporation of debris-layer airflow into a theoretical model of glacial melting can capture the empirically observed features of the so-called Ostrem curve (a plot of the melt rate as a function of debris depth). Specifically, we show that the turning point in the Ostrem curve can be caused by two distinct mechanisms: the increase in the proportion of ice that is debris-covered and/or a reduction in the evaporative heat flux as the debris layer thickens. This second effect causes an increased melt rate because the reduction in (latent) energy used for evaporation increases the amount of energy available for melting. Our model provides an explicit prediction for the melt rate and the temperature distribution within the debris layer, and provides insight into the relative importance of the two effects responsible for the maximum in the Ostrem curve. We use the data of Nicholson and Benn (2006) to show that our model is consistent with existing empirical measurements.