A major impact of anthropogenic climate change is the crossing of tipping points, which may have severe consequences such as the complete mass loss of the Greenland ice sheet (GrIS). At present, the GrIS is losing mass at an accelerated rate, largely due to a steep decrease in its surface mass balance (SMB; the balance between snow accumulation and surface ablation from melt and associated runoff). Previous work on the magnitude and nature of a threshold for GrIS complete melt remains controversial. Here, we explore a potential SMB threshold for complete melt of the GrIS; the impact and interplay of surface melt and glacial isostatic adjustment (GIA) in determining this threshold; and whether the GrIS exhibits characteristics commonly associated with tipping points, such as sensitivity to external forcing. To this end, we force the Community Ice Sheet Model v.2 (CISM2) by cycling different SMB climatologies previously calculated at multiple elevation classes with the Community Earth System Model v.2 (CESM2) in a two-way coupled CESM2-CISM2 transient simulation of the global climate and GrIS under high CO₂ forcing. The SMB calculation in CESM2 has been evaluated with contemporary observations and high-resolution modelling and includes an advanced representation of surface melt and snow-firn processes. We find a positive SMB threshold for complete GrIS melt of 230 ± 84 Gtyr^-1, corresponding to a 60 % decrease in SMB and to a global mean warming of +3.4 K compared to pre-industrial CESM2-CISM2 simulated values. In our simulations, a small change in the initial SMB forcing (from 255 to 230 Gtyr^-1) and global mean warming above pre-industrial levels (from +3.2 to +3.4 K) causes an abrupt change in the GrIS final volume (from 50 % mass to nearly complete deglaciation). This nonlinear behaviour is caused by the SMB-elevation feedback, which responds to changes in surface topography due to surface melt and GIA. The GrIS tips from ∼ 50 % mass towards nearly complete melt when the impact of melt-induced surface lowering outweighs that of GIA-induced bedrock uplift and the (initially positive) SMB becomes and remains negative for at least a few thousand years. We also find that the GrIS tips towards nearly complete melt when the ice margin in the central west unpins from a coastal region with high topography and SMB. We show that if we keep the SMB fixed (i.e. no SMB-elevation feedback) in this relatively confined region, the ice sheet retreat is halted and nearly complete GrIS melt is prevented even though the initial SMB forcing is past the threshold. Based on the minimum GrIS configuration in previous paleo-ice-sheet modelling studies, we suggest that the surface topography in the central west might have played a role in preventing larger GrIS loss during the last interglacial period ∼ 130-115 kyrBP.

We describe and evaluate version 2.1 of the Community Ice Sheet Model (CISM). CISM is a parallel, 3-D thermomechanical model, written mainly in Fortran, that solves equations for the momentum balance and the thickness and temperature evolution of ice sheets. CISM's velocity solver incorporates a hierarchy of Stokes flow approximations, including shallow-shelf, depth-integrated higher order, and 3-D higher order. CISM also includes a suite of test cases, links to third-party solver libraries, and parameterizations of physical processes such as basal sliding, iceberg calving, and sub-ice-shelf melting. The model has been verified for standard test problems, including the Ice Sheet Model Intercomparison Project for Higher-Order Models (ISMIP-HOM) experiments, and has participated in the initMIP-Greenland initialization experiment. In multimillennial simulations with modern climate forcing on a 4 km grid, CISM reaches a steady state that is broadly consistent with observed flow patterns of the Greenland ice sheet. CISM has been integrated into version 2.0 of the Community Earth System Model, where it is being used for Greenland simulations under past, present, and future climates. The code is open-source with extensive documentation and remains under active development.