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To investigate ice sheet evolution over the timescale of a glacialcycle, 3-D ice sheet models (ISMs) are typically run at "coarse" gridresolutions (10–50 km) that do not resolve individualmountains. This will introduce to-date unquantified errors in sub-grid(SG) transport, accumulation and ablation for regions of roughtopography. In the past, synthetic hypsometric curves, a statisticalsummary of the topography, have been used in ISMs to describe thevariability of these processes. However, there has yet to be detaileduncertainty analysis of this approach.  We develop a new flow line SG model for embedding in coarse resolutionmodels.A 1 km resolution digital elevation model was used to compute the localhypsometric curve for each coarse grid (CG) cell and to determine local parameters to represent thehypsometric bins' slopes and widths. The 1-D mass transport for the SGmodel is computed with the shallow ice approximation. We test thismodel against simulations from the 3-D Ice Sheet System Model(ISSM) run at 1 km grid resolution. Results show that none ofthe alternative parameterizations explored were able to adequatelycapture SG surface mass balance and flux processes. Viaglacial cycle ensemble results for North America, we quantify theimpact of SG model coupling in an ISM. We show that SG processrepresentation and associated parametric uncertainties, related to theexchange of ice between the SG and CG cells, can havesignificant (up to 35 m eustatic sea level equivalent for the North American icecomplex) impact on modelled ice sheet evolution

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