Supraglacial channel inception: Modeling and processes

Supraglacial drainage systems play a key role in glacial hydrology. Nevertheless, physical processes leading to spatial organization in supraglacial networks are still an open issue. In the present work we thus address from a quantitative point of view the question of what is the physics leading to widely observed patterns made up of evenly spaced channels. To this aim, we set up a novel mathematical model describing a condition antecedent channel formation, i.e., the down-glacier flow of a distributed meltwater film. We then perform a linear stability analysis to assess whether the ice-water interface undergoes a morphological instability compatible with observed patterns. The instability is detected, its features depending on glacier surface slope, ice friction factor, and water as well as ice thermal conditions. By contrast, in our model channel spacing is solely hydrodynamically driven and relies on the interplay between pressure perturbations, flow depth response, and Reynolds stresses. Geometrical features of the predicted pattern are quantitatively consistent with available field data. The hydrodynamic origin of supraglacial channel morphogenesis suggests that alluvial patterns might share the same physical controls.