Estimation of ice ablation on a debris-covered glacier from vertical debris-temperature profiles

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.