SCALE INVARIANCE OF TOPOGRAPHIC DEPRESSIONS ON HIMALAYAN DEBRIS-COVERED GLACIERS

Meltwater runoff from Himalayan debris-covered glaciers supplies a substantial volume of freshwater to hundreds of millions of people in Asia. However, spatially variable melt rates on debris-covered glaciers create highly irregular glacier surfaces, characterized by thousands of topographic depressions that intermittently store meltwater. But topographic depressions are more than passive water storage features, rather they are a topographic signature of the complex dynamics relating surface melt processes with long-distance meltwater drainage systems on debris-covered glaciers. Little attention has been given specifically to their distribution and geometry as a means for better understanding melt and drainage processes. This work shows scale invariant area-abundance distributions of topographic depressions on 15 debris-covered glaciers in the Khumbu Region and distinct power law perimeter-to-area and depth-to-area scaling relationships. The observed scale invariance demonstrates that there is no characteristic length scale for topographic depressions, and depression growth is only meaningfully limited by the dimensions of the glacier. Topographic depressions on the Ngozumpa Glacier were examined more closely over the 2010-2019 time period. Interestingly, the total depression area on the Ngozumpa Glacier did not necessarily increase from one year to the next, nor did the largest depression always gain area. We use a simple numerical model to simulate possible growth mechanisms that reproduce the observed scaling relationships.