Approximating ice sheet – bedrock interaction in Antarctic ice sheet projections

Abstract. The bedrock response to a melting ice sheet provides a negative feedback on ice mass loss. When modelling the future behaviour of the Antarctic Ice Sheet, accounting for the impact of bed deformation on ice dynamics can reduce predictions of future sea level rise by up to 40 % in comparison with scenarios that assume a rigid Earth. The rate of the solid Earth response is mainly dependent on the viscosity of the Earth’s mantle, which varies laterally and radially with several orders of magnitude across Antarctica. Because modelling the response for a varying viscosity is complex, sea level projections often exclude the Earth’s response, or apply a globally constant relaxation time or viscosity. We investigate how accurate such approximations are using an ice sheet model coupled with a glacial isostatic adjustment (GIA) model that simulates the bedrock response to changes in ice loading including lateral and radial variations in viscosity (3D GIA model). Using the 3D model we determined a relation between relaxation time and viscosity which can be used in simpler models. We compare output from an elastic lithosphere relaxed asthenosphere (ELRA) with uniform and laterally varying relaxation times, and a GIA model with a radially varying Earth structure (1D GIA model) and a 3D GIA model. We conducted 500 year projections of the Antarctic ice sheet evolution using two different climate models and two emissions scenarios: the high emission scenario SSP5-8.5 and the low emission scenario SSP1-2.6. The results show that using a uniform relaxation time of 300 years in the ELRA model or an upper mantle viscosity of 10¹⁹ Pa∙s in the 1D GIA model leads to a total sea level rise that deviates less than 40 cm from the average of the 3D GIA models. The difference in the sea level rise predicted with 1D and 3D GIA models can be further reduced to 10 cm by using laterally varying relaxation time maps in an ELRA model. Our results show that the effect of 3D viscosity variations on the AIS contribution to sea level rise can be approximated using the ELRA model or a 1D GIA model when the recommended parameters derived from the full 3D GIA model are used.