A Comparative Study of Methods for Estimating the Thickness of Glacial Debris: A Case Study of the Koxkar Glacier in the Tian Shan Mountains

The local or overall mass balance of a glacier is significantly influenced by the spatial heterogeneity of its overlying debris thickness. Accurately estimating the debris thickness of glaciers is essential for understanding their hydrological processes and the impact of climate change. This study focuses on the Koxkar Glacier in the Tian Shan Mountains, using debris thickness data to compare the accuracy of three commonly used approaches for estimating the spatial distribution of debris thickness. The three measurement approaches include two empirical relationships between the land surface temperature (LST) and debris thickness approaches, empirical relationship approach 1 and empirical relationship approach 2, and the energy balance of debris approach. The analysis also explores the potential influence of topographic factors on the debris distribution. By incorporating temperature data from the debris profiles, this study examines the applicability of each approach and identifies areas for possible improvement. The results indicate that (1) all three debris thickness estimation approaches effectively capture the distribution characteristics of glacial debris, although empirical relationship approach 2 outperforms the others in describing the spatial patterns; (2) the accuracy of each approach varies depending on the debris thickness, with the energy balance of debris approach being most accurate for debris less than 50 cm thick, while empirical relationship approach 1 performs better for debris thicker than 50 cm and empirical relationship approach 2 demonstrates the highest overall accuracy; and (3) topographic factors, particularly the elevation, significantly influence the accuracy of debris thickness estimates. Furthermore, the empirical relationships between the LST and debris thickness require field data and focus solely on the surface temperature, neglecting other influencing factors. The energy balance of debris approach is constrained by its linear assumption of the temperature profile, which is only valid within a specific range of debris thickness; beyond this range, it significantly underestimates the values. These findings provide evidence-based support for improving remote-sensing methods for debris thickness estimation.