A new sub-grid surface mass balance and flux model for continental-scale ice sheet modelling: testing and last glacial cycle

Abstract. To investigate ice sheet evolution over the timescale of a glacial cycle, 3-D ice sheet models (ISMs) are typically run at "coarse" grid resolutions (10–50 km) that do not resolve individual mountains. This will introduce to-date unquantified errors in sub-grid (SG) transport, accumulation and ablation for regions of rough topography. In the past, synthetic hypsometric curves, a statistical summary of the topography, have been used in ISMs to describe the variability of these processes. However, there has yet to be detailed uncertainty analysis of this approach.

We develop a new flow line SG model for embedding in coarse resolution models. A 1 km resolution digital elevation model was used to compute the local hypsometric curve for each coarse grid (CG) cell and to determine local parameters to represent the hypsometric bins' slopes and widths. The 1-D mass transport for the SG model is computed with the shallow ice approximation. We test this model against simulations from the 3-D Ice Sheet System Model (ISSM) run at 1 km grid resolution. Results show that none of the alternative parameterizations explored were able to adequately capture SG surface mass balance and flux processes. Via glacial cycle ensemble results for North America, we quantify the impact of SG model coupling in an ISM. We show that SG process representation and associated parametric uncertainties, related to the exchange of ice between the SG and CG cells, can have significant (up to 35 m eustatic sea level equivalent for the North American ice complex) impact on modelled ice sheet evolution.