Supraglacial debris is significant in many regions and complicates modeling of glacier melt, which is required for predicting glacier change and its influences on hydrology and sea-level rise. Temperature-index models are a popular alternative to energy-balance models when forcing data are limited, but their transferability among glaciers and inherent uncertainty have not been documented in application to debris-covered glaciers. Here, melt factors were compiled directly from published studies or computed from reported melt and MERRA-2 air temperature for 27 debris-covered glaciers around the world. Linear mixed-effects models were fit to predict melt factors from debris thickness and variables including debris lithology and MERRA-2 radiative exchange. The models were tested by leave-one-site-out cross-validation based on predicted melt rates. The best model included debris thickness (fixed effect) and glacier and year (random effects). Predictions were more accurate using MERRA-2 than on-site air temperature data, and pooling MERRA-2-derived and reported melt factors improved cross-validation accuracy more than including additional predictors such as shortwave or longwave radiation. At one glacier where monthly ablation was measured over 4 years, seasonal variation of melt factors suggested that heat storage significantly affected the relation between melt and energy exchange at the debris surface.
Modelling ablation of glacier ice under a layer of mineral debris is increasingly important, because the extent of supraglacial debris is expanding worldwide due to glacier recession. Physically based models have been developed, but the uncertainty in predictions is not yet well constrained. A new one-dimensional model of debris-covered ice ablation that is based on the Simultaneous Heat and Water transfer model is introduced here. SHAW-Glacier is a physically based, vertically integrated, fully coupled, water and energy balance model, which includes the advection of heat by rainwater and lateral flow. SHAW-Glacier was applied to North Changri Nup, a high elevation alpine glacier in the monsoon-dominated Central Himalaya. Simulations were compared with observed debris temperature profiles, snow depth, and ablation stake measurements for debris 0.03–0.41 m thick, in a 2500 m2 study area. Prediction uncertainty was estimated in a Monte Carlo analysis. SHAW-Glacier simulated the characteristic pattern of decreasing ablation with increasing debris thickness. However, the observations of ablation did not follow the characteristic pattern; annual ablation was highest where the debris was thickest. Recursive partitioning revealed a substantial, non-linear sensitivity to the snow threshold air temperature, suggesting a sensitivity to the duration of snow cover. Photographs showed patches of snow persisting through the ablation season, and the observational data were consistent with uneven persistence of snow patches. The analyses indicate that patchy snow cover in the ablation season can overwhelm the sensitivity of sub-debris ablation to debris thickness. Patchy snow cover may be an unquantified source of uncertainty in predictions of sub-debris ablation.
A supraglacial debris layer controls energy transfer to the ice surface and moderates ice ablation on debris-covered glaciers. Measurements of vertical temperature profiles within the debris enables the estimation of thermal diffusivities and sub-debris ablation rates. We have measured the debris-layer temperature profiles at 16 locations on Satopanth Glacier (central Himalaya) during the ablation seasons of 2016 and 2017. Debris temperature profile data are typically analysed using a finite-difference method, assuming that the debris layer is a homogeneous one-dimensional thermal conductor. We introduce three more methods for analysing such data that approximate the debris layer as either a single or a two-layered conductor. We analyse the performance of all four methods using synthetic experiments and by comparing the estimated ablation rates with in situ glaciological observations. Our analysis shows that the temperature measurements obtained at equispaced sensors and analysed with a two-layered model improve the accuracy of the estimated thermal diffusivity and sub-debris ablation rate. The accuracy of the ablation rate estimates is comparable to that of the in situ observations. We argue that measuring the temperature profile is a convenient and reliable method to estimate seasonal to sub-seasonal variations of ablation rates in the thickly debris-covered parts of glaciers.
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