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Abstract. Retreat and advance of ice sheets perturb the gravitational field, solidsurface and rotation of the Earth, leading to spatially variable sea-levelchanges over a range of timescales O(100−6 years), which in turn feedback onto ice-sheet dynamics. Coupled ice-sheet–sea-level models havebeen developed to capture the interactive processes between ice sheets, sealevel and the solid Earth, but it is computationally challenging to captureshort-term interactions O(100−2 years) precisely within longer O(103−6 years) simulations. The standard forward sea-level modelling algorithmassigns a uniform temporal resolution in the sea-level model, causing aquadratic increase in total CPU time with the total number of input icehistory steps, which increases with either the length or temporal resolutionof the simulation. In this study, we introduce a new “time window”algorithm for 1D pseudo-spectral sea-level models based on the normal modemethod that enables users to define the temporal resolution at which the iceloading history is captured during different time intervals before thecurrent simulation time. Utilizing the time window, we assign a finetemporal resolution O(100−2 years) for the period of ongoing andrecent history of surface ice and ocean loading changes and a coarsertemporal resolution O(103−6 years) for earlier periods in thesimulation. This reduces the total CPU time and memory required per modeltime step while maintaining the precision of the model results. We explorethe sensitivity of sea-level model results to the model temporal resolutionand show how this sensitivity feeds back onto ice-sheet dynamics in coupledmodelling. We apply the new algorithm to simulate sea-level changes inresponse to global ice-sheet evolution over two glacial cycles and the rapidcollapse of marine sectors of the West Antarctic Ice Sheet in the comingcenturies and provide appropriate time window profiles for each application.The time window algorithm reduces the total CPU time by ∼ 50 % in each of these examples and changes the trend of the total CPU timeincrease from quadratic to linear. This improvement would increase withlonger simulations than those considered here. Our algorithm also allows for couplingtime intervals of annual temporal scale for coupled ice-sheet–sea-levelmodelling of regions such as West Antarctica that are characterized byrapid solid Earth response to ice changes due to the thin lithosphere andlow mantle viscosities. 

Abstract. Accurate glacial isostatic adjustment (GIA) modelling in the cryosphere is required for interpreting satellite, geophysical and geological recordsand for assessing the feedbacks of Earth deformation and sea-level change on marine ice-sheet grounding lines. GIA modelling in areas of active ice lossin West Antarctica is particularly challenging because the ice is underlain by laterally varying mantle viscosities that are up to several orders ofmagnitude lower than the global average, leading to a faster and more localised response of the solid Earth to ongoing and future ice-sheet retreatand necessitating GIA models that incorporate 3-D viscoelastic Earth structure. Improvements to GIA models allow for computation of the viscoelasticresponse of the Earth to surface ice loading at sub-kilometre resolution, and ice-sheet models and observational products now provide the inputs toGIA models at comparably unprecedented detail. However, the resolution required to accurately capture GIA in models remains poorly understood, andhigh-resolution calculations come at heavy computational expense. We adopt a 3-D GIA model with a range of Earth structure models based on recentseismic tomography and geodetic data to perform a comprehensive analysis of the influence of grid resolution on predictions of GIA in the AmundsenSea Embayment (ASE) in West Antarctica. Through idealised sensitivity testing down to sub-kilometre resolution with spatially isolated ice loadingchanges, we find that a grid resolution of ∼ 13 of the radius of the load or higher is required to accurately capture the elasticresponse of the Earth. However, when we consider more realistic, spatially coherent ice loss scenarios based on modern observational records andfuture ice-sheet model projections and adopt a viscoelastic Earth, we find that predicted deformation and sea-level change along the grounding lineconverge to within 5 % with grid resolutions of 7.5 km or higher, and to within 2 % for grid resolutions of 3.75 km andhigher, even when the input ice model is on a 1 km grid. Furthermore, we show that low mantle viscosities beneath the ASE lead to viscousdeformation that contributes to the instrumental record on decadal timescales and equals or dominates over elastic effects by the end of the 21stcentury. Our findings suggest that for the range of resolutions of 1.9–15 km that we considered, the error due to adopting a coarser gridin this region is negligible compared to the effect of neglecting viscous effects and the uncertainty in the adopted mantle viscosity structure.