Relative control of bedrock roughness versus topography on global glacier bed friction

Friction at the base of ice-sheets has been shown to be one of the largest uncertainty of model projections for the contribution of ice-sheet to future sea level rise. On hard beds, most of the apparent friction is the result of ice flowing over the bumps that have a size smaller than described by the grid resolution of ice-sheet models. To account for this friction, the classical approach is to replace this under resolved roughness by an ad-hoc friction law. In an imaginary world of unlimited computing resource and highly resolved bedrock DEM, one should solve for all bed roughnesses assuming pure sliding at the bedrock-ice interface. If such solutions are not affordable at the scale of an ice-sheet or even at the scale of a glacier, the effect of small bumps can be inferred using synthetical periodic geometry. In this presentation,  beds are constructed using the superposition of up to five bed geometries made of sinusoidal bumps of decreasing wavelength and amplitudes. The contribution to the total friction of all five beds is evaluated by inverse methods using the most resolved solution as observation. It is shown that small features of few meters can contribute up to almost half of the total friction, depending on the wavelengths and amplitudes distribution. This work also confirms that the basal friction inferred using inverse method  is very sensitive to how the bed topography is described by the model grid, and therefore depends on the size of the model grid itself.