Abstract
Abstract. Retreat and advance of ice sheets perturb the gravitational field, solid surface and rotation of the Earth, leading to spatially variable sea-level changes over a range of timescales O(100−6 years), which in turn feed back onto ice-sheet dynamics. Coupled ice-sheet–sea-level models have been developed to capture the interactive processes between ice sheets, sea level and the solid Earth, but it is computationally challenging to capture short-term interactions O(100−2 years) precisely within longer O(103−6 years) simulations. The standard forward sea-level modelling algorithm assigns a uniform temporal resolution in the sea-level model, causing a quadratic increase in total CPU time with the total number of input ice history steps, which increases with either the length or temporal resolution of the simulation. In this study, we introduce a new “time window” algorithm for 1D pseudo-spectral sea-level models based on the normal mode method that enables users to define the temporal resolution at which the ice loading history is captured during different time intervals before the current simulation time. Utilizing the time window, we assign a fine temporal resolution O(100−2 years) for the period of ongoing and recent history of surface ice and ocean loading changes and a coarser temporal resolution O(103−6 years) for earlier periods in the simulation. This reduces the total CPU time and memory required per model time step while maintaining the precision of the model results. We explore the sensitivity of sea-level model results to the model temporal resolution and show how this sensitivity feeds back onto ice-sheet dynamics in coupled modelling. We apply the new algorithm to simulate sea-level changes in response to global ice-sheet evolution over two glacial cycles and the rapid collapse of marine sectors of the West Antarctic Ice Sheet in the coming centuries 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 time increase from quadratic to linear. This improvement would increase with longer simulations than those considered here. Our algorithm also allows for coupling time intervals of annual temporal scale for coupled ice-sheet–sea-level modelling of regions such as West Antarctica that are characterized by rapid solid Earth response to ice changes due to the thin lithosphere and low mantle viscosities.
Highlights
It is well established that sea-level changes in response to icesheet changes feed back onto the evolution of ice sheets (e.g., Gomez et al, 2012, 2015; de Boer et al, 2014; Konrad et al, 2015; Larour et al, 2019)
This algorithm allows users to assign non-uniform time steps across simulations by dividing the simulations into as many as four time intervals, which we call “internal time windows (ITWs)”. (We note that our model can be modified to adopt a greater number of internal time windows, but we found that four is sufficient for a range of applications such as long paleo-simulations and short simulations with rapidly retreating ice sheets.) During set-up, users define the internal time window length (L_ITWk) and temporal resolution such that each L_ITWk is divisible by dtk and each dtk is divisible by the finest temporal resolution of the simulation time window
Input ice history based on the equation for an equilibrium ice surface profile for viscous ice provided in Cuffey and Paterson (1969, The Physics of Glaciers), with the ice sheet centred at the South Pole (Fig. 2g)
Summary
It is well established that sea-level changes in response to icesheet changes feed back onto the evolution of ice sheets (e.g., Gomez et al, 2012, 2015; de Boer et al, 2014; Konrad et al, 2015; Larour et al, 2019). Changes in grounded ice cover perturb the Earth’s gravitational field, rotation and viscoelastic solid surface, leading to spatially non-uniform changes in the heights of the sea surface geoid and the solid Earth, i.e., sea-level changes (e.g., Woodward, 1888; Peltier, 1974; Farrell and Clark, 1976; Mitrovica and Milne, 2003). The spatial and temporal scales of the solid Earth response to ice loading changes depend on the rheological structure of the lithosphere and mantle, which are both radially and laterally heterogeneous The contribution from viscous deformation to sealevel changes in regions with thinner lithosphere and lowermantle viscosities such as West Antarctica occurs on shorter timescales O(≤ 102 years) (e.g., Barletta et al, 2018) and has greater spatial variation for given loading changes compared to regions with thicker lithosphere and higher mantle viscosities such as North America (e.g., Mitrovica and Forte, 2004), calling for higher spatiotemporal resolution for modelling applications in these regions
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