What does steady state mean for debris-covered glaciers?

Debris-covered glaciers accumulate supra-glacial debris on the glacier surface in the ablation zone. As long as this debris layer is not at least partly removed, it can be expected that glaciers continue to grow in length, because the thickening debris layer continuously reduces surface melt rates. Removal of the debris layer, on the other hand, is a complicated process, which depends on a number of parameters, like surface slope, debris thickness, grain size distribution and water content to name just a few. However, the way how supra-glacial debris is removed might strongly influence the dynamic reaction of the glacier itself.

A realistic study of these interactions can only be performed, if the ice flow and the debris-influenced melt is treated with a high degree of detail. In our study, we coupled a 2-D full Stokes ice dynamic and surface debris transport model with a sophisticated description of energy transfer through the debris layer. This approach ensures that ice flow and surface melt rates are simulated at high detail, including the enhanced melt rates for very thin debris cover just below the equilibrium line. We restricted our experiments to rather simple initial conditions, in order investigate the fundamental feedback mechanisms between melt rates and glacier dynamics. Therefore, we introduced rather simple, but realistic formulations of debris unloading at the glacier front. The coupled experiments show that steady-state conditions are highly unlikely for glaciers with the debris layer remaining on the glacier. However, a balance of the debris budget and the glacier mass flux is possible, when introducing debris removal from the glacier tongue. We focussed on an as realistic as possible representation of the snout geometry, in order to allow a physically sensible debris discharge. The results show that for some removal processes debris-covered glaciers have an inherent tendency to enter an oscillating state, where glacier mass balance and debris balance are out of phase. In specific experiments glacier advance periods end with the separation of the heavily debris-loaded lowermost glacier tongue, at time scales of decades to centuries, followed by an advance of the remaining clean glacier. In such cases we assume that long-term “mean-steady-state” conditions modulated by oscillations in glacier length exist and are independent from climatic variations. This makes it difficult to interpret short-term geometry observations of debris-covered glaciers in the context of climate impact.