A Scaling Relation for Cryoconite Holes

Abstract

Tiny cryoconite holes are commonly found on glacier surfaces. Despite a long history of research on them, their influence on glacier-scale mass balance and runoff are not well understood. We model the absorption of solar radiation at the bottom of cylindrical cryoconite holes, incorporating the three-dimensional geometry. The simulated holes achieve a limiting steady-state depth, where the daily melt rate at the bottom of the holes matches that at the glacier surface. This implies a feedback loop restricting the excess ice melt due to the presence of dark supraglacial impurities. The modeled steady-state depth scales approximately linearly with the radius, consistent with in situ observations at several glaciers across the world. Given the areal coverage and radius distribution of cryoconite holes on a glacier, this scaling yields first-order estimates of their melt contribution.