The importance of bed roughness on ice sheet flow investigated using a full-Stokes ice flow model

We present detailed modelling of ice flow over a synthetic topography using the full-Stokes ice flow model ELMER-ICE. Our results indicate that landforms/obstacles under 1000 m wavelength contribute importantly to basal drag, implying that predictive ice sheet models that are initialised using static parameterisations of basal drag will greatly underestimate the possible mediating effects of bedrock topography. We conducted numerous simulations using a 10 m resolution, 40 x 22 km model domain with a uniform ice thickness of 1000 m and with sliding restricted to a 20 km-wide central corridor to negate ice leaving the lateral margins. Basal slipperiness (i.e. skin drag) in all simulations used the value obtained during an initial simulation using an entirely flat bed and an imposed surface velocity of 150 m a^-1. Subsequent simulations used a synthetic bed with wavelength 5 km, amplitude 200 m, and randomised superimposed smaller-scale roughness. Because ice sheet beds are bumpy at a range of scales - from landforms reflective of km-scale patterns of glacial bedrock erosion down to m-scale obstacles characteristic of bedrock structure – roughness was introduced gradually into the simulations by stepwise reduction of the degree of smoothing applied to the synthetic topography using a band-pass filter. Our results demonstrated that around two-thirds of observed surface velocity was by sliding, and that mean sliding velocity (and thus surface velocity) declined rapidly when introducing roughness with length scale smaller than 1000 m. Further, the observed decline appeared broadly exponential in relation to obstacle size as smaller roughness length scales were added, down to the smallest length scale (10 m) permitted by present model resolution. The results therefore highlight the potential importance of form drag provided by sub-km scale bed roughness in stabilising ice flow, including flow in grounding line locations that are critical to marine ice sheet stability. The results also have implications for predictive ice sheet models, which typically use static fields of basal drag derived from inversions of present-day surface observations, and do not distinguish between form and skin drag. As such, current models could imprecisely predict ice discharge and grounding line behaviour in regions of evolving bedrock or sedimentary landforms, which are ubiquitous to ice sheet beds.