Predicting Mean Depth and Area Fraction of Antarctic Supraglacial Melt Lakes with Physics-Based Parameterizations

Abstract Supraglacial melt lakes have been implicated in decreasing albedo and increasing flow speed of the Greenland Ice Sheet and ice shelf disintegration in Antarctica. However, supraglacial melt lakes are largely not represented in current large-scale climate and ice sheet models due to their small size compared to typical model grid spacing. In this study, we first use extensive surface elevation measurements from the ICESat-2 satellite altimetry mission to show that roughness on the Antarctic Ice Sheet surface is largely self-affine, consistent with prior observations of bed roughness beneath ice sheets and geomorphic surfaces more broadly. This self-similarity of ice sheet surfaces across scales enables us to develop a broadly applicable set of simple mathematical expressions parameterizing the average supraglacial melt lake area fraction and lake depth. These parameterizations depend only on two ice sheet roughness parameters and the depth of water supplied as runoff from the surface melt. We derive these parameterizations from statistical fitting of large Monte Carlo ensembles of numerical simulations of water flow on random, self-affine surfaces and show that they provide predictions that are generally consistent with observations. Finally, we predict that on large portions of Antarctic ice shelves supraglacial lakes are likely to, on average, stay less than one meter deep and occupy less than 40% of the ice area, absent changes in ice shelf surface roughness.