A Physics-Based Parameterization of Mean Melt Lake Depth and Area Fraction of Supraglacial Melt Lakes

Over the past several decades, the abundance of melt lakes appearing on Antarctic ice shelves has increased. Most notably these melt lakes have led to large-scale fracturing and calving events such as the Larsen B Ice Shelf collapse during the 2001-2002 melt season. In this work, we analyze the surface roughness of the Antarctic Ice Sheet to determine its self-affinity, which quantifies the repeating topographical scaling pattern of the surface, using ICESat-2 land ice elevation altimeter tracks. We find a relationship between roughness parameters and mean melt lake depth and area fraction by developing a workflow of Monte Carlo simulations that simulate the distribution of melt lakes as they form on the glacial surface. From this workflow, we derive two mathematical parametrizations, that utilize the roughness parameters and melt supply, to estimate the mean melt lake depth and mean area fraction of melt lakes on a self-affine surface. We validate the effectiveness of these parameterizations by computing the estimated mean melt lake depth and area coverage from 2013-2018 using estimated runoff from RACMO and the analyzed ICESat-2 tracks and compare this estimation with a Landsat-based set of observations. In the future, we plan to implement these parameterizations into large-scale climate and ice sheet models to improve albedo and ice damage simulation.