Simulating Topographic Inversion during Deglaciation

High-relief hummocky moraine is thought by many to form by the non-uniform accumulation of supraglacial debris atop downwasting, stagnant ice during deglaciation. Long-lived supraglacial depressions, when filled with debris transported downslope, become hills in the postglacial landscape, while the surrounding highs on the ice surface become inter-hummock valleys and basins. On debris-covered glaciers, debris transport occurs by gradual, slope-dependent processes as well as discrete mass wasting events. Debris production and surface lowering occur during ablation of underlying ice, which in turn depends on the spatial distribution of debris thickness. The coupled heat and mass transport problem lends itself to study using numerical methods similar to those used in mainstream landscape evolution models. A better understanding of the complex relationships between these processes is essential both for more accurate predictions of future ice mass loss and better reconstruction of former ice margins.

A one dimensional evolution model has been constructed for investigation of the temporal and spatial relationships between supraglacial processes and postglacial relief. While the heat transfer relationships are well known from field studies on debris-covered glaciers, debris transport relationships are poorly known. Preliminary model analysis suggests that moraine characteristics depend strongly on the ratio of characteristic timescales for surface lowering by ablation and slope degradation by downslope transport. This ratio is therefore sensitive to the form and rate constant of the selected transport relationship, plausibly yielding both high-relief hummocks and nearly-flat plains. Simulations with rapid ablation and relatively slow debris transport yield the greatest initial supraglacial relief, and are most sensitive to the initial configuration of debris sources (e.g., englacial debris bands). However, for such relief to persist as the debris cover thickens, ablation must involve a term proportional to upslope contributing length, and therefore likely requires heat transfer from meltwater.