A simple model to estimate ice ablation under a thick debris layer

This paper presents a simple model to estimate ice ablation under a thick supraglacial debris cover. The key method employed in the model is to establish a link between the debris heat flux and the debris temperature at a certain depth when the heat transfer in the debris is described by a diffusion process. Given surface temperature, debris thermal properties and relevant boundary conditions, the proposed model can estimate mean debris temperature at interfaces of different debris layers using an iterative procedure, and then the heat flux for ice ablation. The advantage of the proposed model is that it only requires a few parameters to conduct the modeling, which is simpler and more applicable than others. The case study on Koxkar glacier, west Tien Shan, China, shows, in general, that the proposed model gives good results for the prediction of debris temperatures, except for an apparent phase shift between modeled and observed values. We suggest that this error is mainly due to complex phase relations between debris temperature and debris heat flux. The modeled ablation rates at three experimental sites also show good results, using a direct comparison with observed data and an indirect comparison with a commonly used energy-balance model.