We have constrained the value for thermal diffusivity of near-surface snow and firn at Summit Station, Greenland, using a Fourier-type analysis applied to hourly temperature measurements collected from eight thermistors in a closed-off, air-filled borehole between May 2004 and July 2008. An implicit, finite-difference method suggests that a bulk diffusivity of ∼25 ± 3m2 a−1 is the most reasonable for representing macroscale heat transport in the top 30 m of firn and snow. This value represents an average diffusivity and, in a conduction-only model, generates temperature series whose phase shifts with depth most closely match those of the Summit borehole data (rms difference between measurements and model output is ∼6 days). This bulk value, derived numerically and corroborated analytically, is useful over large tracts of the Greenland ice sheet where density and microstructure are unknown.

Abstract. Few surface energy balance models for debris-covered glaciers account for the presence of moisture in the debris, which invariably affects the debris layer's thermal properties and, in turn, the surface energy balance and sub-debris melt of a debris-covered glacier. We adapted the interactions between soil, biosphere, and atmosphere (ISBA) land surface model within the SURFace EXternalisée (SURFEX) platform to represent glacier debris rather than soil (referred to hereafter as ISBA-DEB). The new ISBA-DEB model includes the varying content, transport, and state of moisture in debris with depth and through time. It robustly simulates not only the thermal evolution of the glacier–debris–snow column but also moisture transport and phase changes within the debris – and how these, in turn, affect conductive and latent heat fluxes. We discuss the key developments in the adapted ISBA-DEB and demonstrate the capabilities of the model, including how the time- and depth-varying thermal conductivity and specific heat capacity depend on evolving temperature and moisture. Sensitivity tests emphasize the importance of accurately constraining the roughness lengths and surface slope. Emissivity, in comparison to other tested parameters, has less of an effect on melt. ISBA-DEB builds on existing work to represent the energy balance of a supraglacial debris layer through time in its novel application of a land surface model to debris-covered glaciers. Comparison of measured and simulated debris temperatures suggests that ISBA-DEB includes some – but not all – processes relevant to melt under highly permeable debris. Future work, informed by further observations, should explore the importance of advection and vapor transfer in the energy balance.

Abstract. Few surface energy balance models for debris-covered glaciers account for the presence of moisture in the debris, which invariably affects the debris layer's thermal properties and, in turn, the surface energy balance and sub-debris melt of a debris-covered glacier. We adapted the Interactions between Soil, Biosphere, and Atmosphere (ISBA) land surface model within the SURFace EXternalisée (SURFEX) platform to represent glacier debris rather than soil. The new ISBA-DEBris model includes the varying content, transport, and state of moisture in debris with depth and through time. It robustly simulates not only the thermal evolution of the glacier-debris-snow column but also moisture transport and phase changes within the debris – and how these, in turn, affect conductive and latent heat fluxes. We discuss the key developments in the adapted ISBA-DEB and demonstrate the capabilities of the model, including how the time- and depth-varying thermal conductivity and specific heat capacity depend on evolving temperature and moisture. Sensitivity tests emphasize the importance of accurately constraining the roughness lengths and surface slope. Emissivity, in comparison to other tested parameters, has less of an effect on melt. ISBA-DEB builds on existing work to represent the energy balance of a supraglacial debris layer through time in its novel application of a land surface model to debris covered glaciers. Comparison of measured and simulated debris temperatures suggests that ISBA-DEB includes some – but not all – processes relevant to melt under highly permeable debris. Future work, informed by further observations, should explore the importance of advection and vapor transfer.

Mapping patterns of supraglacial debris thickness and understanding their controls are important for quantifying the energy balance and melt of debris-covered glaciers and building process understanding into predictive models. Here, we find empirical relationships between measured debris thickness and satellite-derived surface temperature in the form of a rational curve and a linear relationship consistently outperform two different exponential relationships, for five glaciers in High Mountain Asia (HMA). Across these five glaciers, we demonstrate the covariance of velocity and elevation, and of slope and aspect using principal component analysis, and we show that the former two variables provide stronger predictors of debris thickness distribution than the latter two. Although the relationship between debris thickness and slope/aspect varies between glaciers, thicker debris occurs at lower elevations, where ice flow is slower, in the majority of cases. We also find the first empirical evidence for a statistical correlation between curvature and debris thickness, with thicker debris on concave slopes in some settings and convex slopes in others. Finally, debris thickness and surface temperature data are collated for the five glaciers, and supplemented with data from one more, to produce an empirical relationship, which we apply to all glaciers across the entire HMA region. This rational curve: 1) for the six glaciers studied has a similar accuracy to but greater precision than that of an exponential relationship widely quoted in the literature; and 2) produces qualitatively similar debris thickness distributions to those that exist in the literature for three other glaciers. Despite the encouraging results, they should be treated with caution given our relationship is extrapolated using data from only six glaciers and validated only qualitatively. More (freely available) data on debris thickness distribution of HMA glaciers are required.

Pakistan is the most glaciated country on the planet but faces increasing water scarcity due to the vulnerability of its primary water source, the Indus River, to changes in climate and demand. Glacier melt constitutes over one-third of the Indus River’s discharge, but the impacts of glacier shrinkage from anthropogenic climate change are not equal across all eleven subbasins of the Upper Indus. We present an exploration of glacier melt contribution to Indus River flow at the subbasin scale using a distributed surface energy and mass balance model run 2001–2013 and calibrated with geodetic mass balance data. We find that the northern subbasins, the three in the Karakoram Range, contribute more glacier meltwater than the other basins combined. While glacier melt discharge tends to be large where there are more glaciers, our modeling study reveals that glacier melt does not scale directly with glaciated area. The largest volume of glacier melt comes from the Gilgit/Hunza subbasin, whose glaciers are at lower elevations than the other Karakoram subbasins. Regional application of the model allows an assessment of the dominant drivers of melt and their spatial distributions. Melt energy in the Nubra/Shyok and neighboring Zaskar subbasins is dominated by radiative fluxes, while turbulent fluxes dominate the melt signal in the west and south. This study provides a theoretical exploration of the spatial patterns to glacier melt in the Upper Indus Basin, a critical foundation for understanding when glaciers melt, information that can inform projections of water supply and scarcity in Pakistan.