Estimation of the total sub-debris ablation from point-scale ablation data on a debris-covered glacier

Glaciological ablation is computed from point-scale data at a few ablation stakes that are usually regressed as a function of elevation and averaged over the area-elevation distribution of a glacier. This method is contingent on a tight control of elevation on local ablation. However, in debris-covered glaciers, systematic and random spatial variations of debris thickness modify the ablation rates. We propose and test a method to compute sub-debris ablation where stake data are interpolated as a function of debris-thickness alone and averaged over the debris-thickness distribution at different parts of the glacier. We apply this method on Satopanth Glacier located in Central Himalaya utilising similar to 1000 ablation measurements obtained from a network of up to 56 stakes during 2015-2017. The estimated mean sub-debris ablation ranges between 1.5 +/- 0.2 to 1.7 +/- 0.3 cm d(-1). We show that the debris-thickness-dependent regression describes the spatial variability of the sub-debris ablation better than the elevation dependent regression. The uncertainties in ablation estimates due to the corresponding uncertainties in the measurement of ablation and debris-thickness distribution, and those due to interpolation procedures are estimated using Monte Carlo methods. Possible biases due to a finite number of stakes used are also investigated.