Towards a physically based framework of cryokarst evolution for dynamic modelling of debris covered glaciers

Cryokarst processes such as ice cliffs, ponds and collapsed subglacial cavities have been recognized to substantially enhance surface ablation on debris covered glacier surfaces. Existing flow models for debris covered glaciers, however, still largely ignore their effects, thereby limiting the related predictions and understanding of dynamic feedbacks. We propose here a process based conceptual framework that dynamically simulates the melt enhancing effect along the glacier and can be coupled to a flow-model.

We approximate the enhancing effect of cryokarst through a state variable of ice cliff area density (ICAD) and which is simulated over time and space along the glacier surface through production, advection and reduction. The production of ICAD is assumed to be driven by the processes of meltwater incision, pondsand crevassing through extensional flow; ICAD is then advected at the surface by ice-flow. Reduction in ICAD is simulated through a typical decay timescale related to debris redistribution and burial and, for crevasses, through compressional flow. The drainage of supraglacial streams to the glacier bed under tensile strain rates or through cut-and-closure allows to remove supraglacial discharge, thereby stopping ice-cliff production from supraglacial channel incision. In addition, ICAD growth from full thickness collapse of non-pressurized subglacial channel voids is parametrized through subglacial stream discharge and a threshold in ice overburden pressure. The parametrizations of the above processes are based on variables that are directly available in flow models for debris covered glaciers and encompass ice thickness, surface slope, flow speed, debris thickness and surface ablation. This framework of modelling ICAD evolution is coupled to a flowline model for debris covered glaciers that dynamically tracks debris thickness and then uses ICAD to incorporate melt enhancement relative to clean ice. The effects of including cryokarst processes and the related feedbacks are then investigated for a synthetic debris covered glacier geometry. Modelling results indicate an enhancement of glacier decay in a warming world and are compared to observed relationships of ice cliff area density to variables such as flow speed, surface slope and debris thickness.