A Scaling Relation for Cryoconite Holes

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. Dark particles deposited on glacier surfaces absorb more solar radiation than the surrounding ice, and melt into the surface to create approximately cylindrical holes with a layer of dark cryoconite substance at their bottom. Such cryoconite holes are commonly seen on glacier surfaces all over the world. These holes continue to deepen, reducing the exposure of the dark cryoconite to solar radiation, and eventually leading to a steady-state depth. We combine modeling and in situ observations to show that the steady depth is approximately proportional to the radius of the hole. This simple geometric property proves useful in estimating the net contribution of all the cryoconite holes present on a glacier to its mass balance and runoff. Our estimates suggest that these holes efficiently negate the melt-enhancing effects of the dark impurities on glacier surface. Effects of shortwave radiation on cryoconite holes modeled in three dimensionsUnder steady clear-sky conditions, cryoconite holes deepen up to a steady depth which scales with radiusThis depth-diameter scaling yields estimates of cryoconite-hole contribution to glacier mass balance

Automated summary

Tiny cryoconite holes commonly found on glacier surfaces have a significant impact on glacier mass balance and runoff. By modeling and in situ observations, it is discovered that the steady depth of these holes is approximately proportional to their radius, providing a useful tool for estimating their contribution to glacier mass balance and runoff.