Purpose of Review This paper reviews the recent literature on numerical modelling of the dynamics of the Greenland ice sheet with the goal of providing an overview of advancements and to highlight important directions of future research. In particular, the review is focused on large-scale modelling of the ice sheet, including future projections, model parameterisations, paleo applications and coupling with models of other components of the Earth system. Recent Findings Data assimilation techniques have been used to improve the reliability of model simulations of the Greenland ice sheet dynamics, including more accurate initial states, more comprehensive use of remote sensing as well as paleo observations and inclusion of additional physical processes. Summary Modellers now leverage the increasing number of high-resolution satellite and air-borne data products to initialise ice sheet models for centennial time-scale simulations, needed for policy relevant sea-level projections. Modelling long-term past and future ice sheet evolution, which requires simplified but adequate representations of the interactions with the other components of the Earth system, has seen a steady improvement. Important developments are underway to include ice sheets in climate models that may lead to routine simulation of the fully coupled Greenland ice sheet-climate system in the coming years.
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