Debris-covered glaciers are ubiquitous in the Himalaya, and supraglacial debris significantly alters how glaciers respond to climate forcing. Estimating debris thickness at the glacier scale, however, remains a challenge. This study inverts a subdebris melt model to estimate debris thickness for three glaciers in the Everest region from digital elevation model difference-derived elevation change. Flux divergences are estimated from ice thickness and surface velocity data. Monte Carlo simulations are used to incorporate the uncertainties associated with debris properties, flux divergence, and elevation change. On Ngozumpa Glacier, surface lowering data from 2010 to 2012 and 2012 to 2014 are used to calibrate and validate the method, respectively. The debris thickness estimates are consistent with existing in situ measurements. The method performs well over both actively flowing and stagnant parts of the glacier and is able to accurately estimate thicker debris (>0.5m). Uncertainties associated with the thermal conductivity and elevation change contribute the most to uncertainties of the debris thickness estimates. The surface lowering associated with ice cliffs and supraglacial ponds was found to significantly reduce debris thickness, especially for thicker debris. The method is also applied to Khumbu and Imja-Lhotse Shar Glaciers to highlight its potential for regional application. Plain Language Summary Debris-covered glaciers are ubiquitous in the Himalaya, and this debris significantly alters the evolution of these glaciers. Estimating the thickness of debris on these glaciers, however, remains a challenge. This study develops a novel method for estimating the debris thickness on three glaciers in the Everest region of Nepal based on digital elevation models, surface velocity data, ice thickness estimates, and a debris-covered glacier energy balance model. The method was calibrated and validated on Ngozumpa Glacier, one of the largest debris-covered glaciers in Nepal, and was found to accurately estimate debris thickness. Specifically, this method was able to estimate thick debris (>0.5m), which has been a major limitation of previous studies. This is important because thick debris significantly reduces glacier melt rates by insulating the underlying ice. This study creates a step-change in our ability to model the past, present, and future evolution of debris-covered glaciers.

We developed a simple model to estimate ice ablation under a debris cover. The ablation process is modelled using energy and mass conservation equations for debris and ice and heat conduction, driven by input of either i) debris surface temperature or ii) radiation fluxes, and solved through a finite difference scheme computing the conductive heat flux within the supra-glacial debris layer. For model calibration, input and validation, we used approximately bi-weekly surveys of ice ablation rate, debris cover temperature, air temperature and solar incoming and upwelling radiation during for Summer 2007. We calibrated the model for debris thermal conductivity using a subset of ablation data and then we validated using another subset. Comparisons between calculated and measured values showed a good agreement (RMSE = 0.04 m w.e., r = 0.79), thus suggesting a good performance of the model in predicting ice ablation. Thermal conductivity was found to be the most critical parameter in the proposed model, and it was estimated by debris temperature and thickness, with value changing along the investigated ablation season. The proposed model may be used to quantify buried ice ablation given a reasonable assessment of thermal conductivity.