Fractal perimeter dimensions of topographic sinks may reveal clues to dominant melt processes on Himalayan debris covered glaciers

Abstract:

Most Himalayan debris covered glaciers are melting rapidly; however, significant melt rate variability exists between glaciers in close geographic proximity and melt processes remain poorly understood. Spatially variable melt rates, as well as meltwater storage and drainage generate hummocky glacial topography. Topographic sinks are bowl-like depressions in the hummocky surface, indicative of localized rapid melt. We applied Mandelbrot’s area-perimeter method of fractal analysis to topographic sinks on 18 Himalayan debris covered glaciers to better understand the growth of these melt features. To ensure that the measured fractal dimensions were independent of DEM resolution, we applied the area-perimeter method to sinks isolated from 1m, 5m and 8m resolution DEMs of the Ngozumpa Glacier in the Everest Region and removed all sinks with areas smaller than 100x(cell area) from the analysis. This revealed the same fractal dimension, independent of raster resolutions and data acquisition years. We then estimated the fractal dimensions of 17 additional Everest Region glaciers using the 2016 High Mountain Asia 8m DEM data set, revealing a unique topographic sink fractal dimension for each glacier. Fractal dimensions range from 1.14-1.62. We compared topographic sink fractal dimensions to available short (<20 year mean) and long term (>20 year mean) mass balance data from three published remote sensing studies. All of the correlations suggest a positive relationship between sink fractal dimension and glacier mass balance, but most are not statistically significant (p>0.05). However, for the longest duration mean mass balance data (comprising 8 glaciers, 1970-2007), increasingly negative mass balance correlates with decreasing fractal dimension (p=0.028). We speculate that the fractal dimension relates to the processes that drive the enlargement of topographic depressions. Ice cliffs are disproportionately responsible for high ice mass loss rates on debris covered glaciers, and ice cliff backwasting processes act over time to smooth the irregular perimeters of topographic sinks, thus reducing the fractal dimension. Because ice cliffs are usually adjacent to meltwater lakes, the fractal dimension may indicate the importance of lake melt processes versus sub-debris melt processes on each glacier.