Coupling debris transport to 3D higher-order ice flow dynamics to model the behavior and climate change response of debris-covered glaciers

We use a three-dimensional time-dependent glacier model that couples higher-order ice flow dynamics with multi-dimensional englacial and supraglacial debris transport to investigate the behavior of debris-covered glaciers and their response to climate change. By applying the model to a synthetic idealized glacier, our simulations allow for multi-dimensional, physically-based and general insights into debris-ice interactions. The model incorporates a melt-modification parameterization based on a synthesis of Østrem curves from previous debris-covered glacier studies, which is coupled to submodules for the spatio-temporal evolution of debris. The debris submodule also includes an off-glacier debris evacuation scheme which allows our simulations to reach a steady state debris mass, while explicitly ensuring debris mass conservation. Results reveal that the presence of a debris cover significantly alters the steady state glacier geometry and dynamics, as well as its climate change response. Debris-covered glaciers in some specific environmental settings are also found to be prone to the formation of stagnant, isolated dead ice bodies during glacier recession. The results highlight the importance of representing a more complete and multi-dimensional set of key debris processes in debris-covered glacier models, including (i) a melt-modification curve that captures melt enhancement for thin debris, (ii) resolving dynamic debris-ice interactions in three dimensions with higher-order ice flow, (iii) explicitly modelling the multi-dimensional, spatio-temporal evolution of a supra- and englacial debris mass, and (iv) a mass-conserving debris off-loading procedure which allows the model to reach steady state. Our main findings therefore emphasize the need to incorporate robust debris modelling in future glacier projections.