As debris-covered glaciers (DCGs) become a more prominent feature of the shrinking mountain cryosphere (Shukla et al., 2009; Thakuri et al., 2014; Gaddam et al. 2016; Tielidze et al., 2019), there is an increasing need to understand how they will respond to climate change. In particular, there is a requirement to improve our understanding of both the current and future spatial distribution of supraglacial debris thickness. This knowledge is indispensible because the mass balance response of DCGs is dependent on the distribution of its debris thickness, given that debris cover can either enhance or inhibit ablation depending on its thickness (Østrem, 1959; Nakawo and Young, 1981; Mattson et al., 1993; Nicholson and Benn, 2006). This knowledge is particularly applicable in the cryosphere of High Mountain Asia (HMA) where ~18% of the total ice mass is stored under a debris mantle (Nuimura et al., 2012; Bolch et al., 2012; Kraajienbrink et al., 2017) and 1.4 billion people rely on glacial runoff (Immerzeel et al., 2010; Kamp et al., 2011; Shukla and Qadir, 2016).

To improve our understanding of the current spatial distribution of debris thickness in HMA, this study aims to improve the empirical calculation of debris thickness from surface temperature. This study undertakes the first systematic comparison of different forms of the empirical relationship between debris thickness and surface temperature (linear, rational curve and two types of exponential curve) to determine which derives the most accurate debris thickness distribution for six different glaciers (Baltoro Glacier, Satopanth Glacier, Lirung Glacier, Ngozumpa Glacier, Changri Nup Glacier and Hailuogou Glacier). This method is only successful when the in situ debris thickness data is well distributed. When well-distributed data is provided, the rational curve and the linear relationship consistently perform best. Tentatively, it is suggested that the rational curve performs best for glaciers with a thinner debris cover, whilst a linear relationship performs best for glaciers with a thicker debris cover.

Data is collated from the six glaciers to produce an empirical relationship applicable to multiple glaciers over the HMA region, including those with no in situ debris thickness data where the glacial-scale method of derivation cannot be undertaken. The novel application of the rational curve to a dataset collated from multiple glaciers, deemed to be representative of the region, produced a regional scale debris thickness distribution with a similar accuracy, but a greater precision than the current regional scale derivation of debris thickness that uses an exponential form of the relationship (Kraaijenbrink et al., 2017).

To improve our understanding of the future spatial distribution of debris thickness in HMA, this study quantifies the influence of glaciological characteristics (elevation, slope, aspect, curvature, velocity) on debris thickness spatial variability. This will allow for more accurate predictions concerning the evolution of debris thickness distribution in the future. This study quantifies the interplay between the controlling variables by demonstrating the covariance of velocity and elevation and of slope and aspect, in addition to revealing the dominance of velocity and elevation over slope and aspect in explaining the distribution of debris thickness. In the majority of cases, thicker debris is expected at low elevations, on slowly flowing ice. However, the relationship between debris thickness and slope/aspect varies. On Satopanth Glacier, thicker debris occurs on flatter, W-facing slopes, but on Ngozumpa, Changri Nup and Hailuogou Glaciers, thicker debris occurs on steeper, E-facing slopes. The first empirical evidence of the influence of curvature was found on Hailuogou Glacier, where thick debris occurs on concave slopes. The percentage of debris thickness variability explained by these factors alone varies between 1% and 50% for the different glaciers. It is suggested that the variation in the relationship between debris thickness and slope/aspect, in addition to the variation in the proportion of debris thickness variability explained, could be explained by the varying strength of the influence of rockfall and the melt out of englacial debris, neither of which are explicitly accounted for in this study.

Overall, this study improves the understanding of the current and future distribution of the spatial distribution of debris thickness, by (i) assessing which form of the surface temperature/debris thickness relationship produces the most accurate and precise debris thickness distribution, on six individual glaciers, (ii) improving the empirical derivation of debris thickness at the regional scale and (iii) quantifying the interplay and dominance of glaciological characteristics in controlling the spatial distribution of debris thickness. Understanding both the current and future distribution of supraglacial debris thickness is essential for better understanding the future response of DCGs to climate change.