Approximating 3D bedrock deformation in an Antarctic ice-sheet model for projections

Abstract. The bedrock deformation in response to a melting ice sheet provides negative feedback on ice mass loss. When modelling the future behaviour of the Antarctic Ice Sheet, the impact of bed deformation on ice dynamics varies but can reduce projections 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 computationally expensive and has only recently been shown to be necessary over centennial time scales, sea-level projection ensembles often exclude the Earth's response or apply a globally constant relaxation time or viscosity. We use a coupled model to investigate the accuracy of various approaches to modelling the bedrock deformation to ice load change. Specifically, we compare the sea-level projections from an ice-sheet model coupled to (i) an elastic lithosphere, relaxed asthenosphere (ELRA) model, with either uniform and laterally varying relaxation times, (ii) a glacial isostatic adjustment (GIA) model with a radially varying Earth structure (1D GIA model), and (iii) a GIA model with laterally varying earth structures (3D GIA model). Furthermore, using the 3D GIA model we determine a relation between relaxation time and viscosity which can be used in ELRA and 1D models. We conduct 500-year projections of 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. Using a rigid Earth model, this results in ∼3–7.5 m of barystatic sea-level rise with significant retreat in various basins due to marine ice sheet instability. The results show that using a uniform relaxation time of 300 years in an ELRA model leads to a total sea-level rise that deviates less than 40 cm (6 %) from the average of the 3D GIA models in 2500. This difference in the projected sea-level rise can be further reduced to 20 cm (4 %) by using an upper mantle viscosity of 1019 Pa s in the 1D GIA model, and to 10 cm (2 %) in 2500 by using a laterally varying relaxation time map in an ELRA model. Our results show that the Antarctic Ice Sheet contribution to sea-level rise can be approximated sufficiently accurate using ELRA or a 1D GIA model when the recommended parameters derived from the full 3D GIA model are used.