iLOVECLIM (here in version 1.1) is a code fork of the LOVECLIM 1.2 model . The core of the model is a combination of a quasi-geostrophic atmospheric model solved on a T21 (∼5.6∘×5.6∘) spectral grid (ECBilt, ); a free surface oceanic general circulation model on a 3∘×3∘ spherical grid which includes a thermodynamic sea ice model (CLIO, ); and a dynamic vegetation and carbon allocation model (VECODE, ). iLOVECLIM has been extensively used to study millennial climate change during the Quaternary. For example, it has proven able to reproduce the glacial–interglacial variability of the hydrological cycle in the tropics . It has also been used to study Heinrich events during the last glacial period or to investigate the processes responsible for changes in the carbon cycle during the last eight interglacial periods . With a similar model configuration to the one used in this work, iLOVECLIM results were included in the fourth phase of the Palaeoclimate Modelling Intercomparison Project (PMIP) contribution to the Coupled Model Intercomparison Project (CMIP) .

Since , the model has also included a 3D thermomechanically coupled ice sheet model GRISLI,. GRISLI solves the ice sheet mass conservation equation on a Cartesian grid. Like most ice sheet models, deformation is computed with a Glen flow law in which anisotropy is artificially accounted for using a flow enhancement factor (Ef) that facilitates deformation induced by vertical shear. For the entire domain, the velocity field is the sum of velocity driven by vertical shearing (shallow ice approximation, SIA) and the velocity driven by horizontal shearing (shallow shelf approximation, SSA). In doing so, the SSA is used as a sliding law . Basal dragging τb is assumed to follow a linear friction law: 1τb=-βub, where β is the basal drag coefficient and ub is the basal velocity. Cold-based grid points have a virtually infinite friction at the base (5×105 Pa yr m-1), while floating ice shelves have no friction. For grid points at the pressure melting point, we use a friction computed from the effective pressure at the base of the ice sheet N: 2β=cfN, where cf is a parameter that has to be calibrated. For the experiments shown here, we impose an ice flux at the grounding line that follows the analytical solution of . Calving at the ice shelf edge occurs if the ice thickness falls below a critical threshold and if the upstream Lagrangian ice flux does not allow us to maintain an ice thickness above this threshold. The threshold is set here to 250 m. Ice sheet model parameters (enhancement factor, basal drag coefficient and hydraulic conductivity) are calibrated in the same way as in to reproduce glacial–interglacial Antarctic ice sheet grounding line migration. In addition, we used a map of sediment thickness to locally reduce basal dragging. We assume that for a sediment thickness greater than 200 m, the basal drag coefficient in Eq. () is multiplied by a dimensionless factor of 0.05. Glacial isostatic adjustment is accounted for in GRISLI using an elastic-lithosphere–relaxed-asthenosphere model , with a relaxation time of the asthenosphere of 3000 years. The ice sheet model is run here on a Cartesian 40 km grid of the Northern Hemisphere using a Lambert azimuthal equal-area projection.

The inclusion of GRISLI into iLOVECLIM has been presented in . However, the coupling procedure has been largely modified from this work. In particular, we have substantially improved the computation of surface and sub-shelf mass balance. Water conservation between GRISLI and the rest of the climate model has also been considerably improved. Details on this coupling are given in the following, while its schematic representation is shown in Fig. . It is important to mention that only the Northern Hemisphere ice sheets are interactively simulated, while the Antarctic ice sheet topography and ice mask remain prescribed at their Last Glacial Maximum following the PMIP4 protocol.

The simulated global mean surface temperature evolution for the synchronously coupled ice sheet climate experiments is shown in Fig. , together with the strength of the AMOC. In response to the forcings, the different experiments produce a gradual warming from the Last Glacial Maximum towards its maximum value during the Holocene. The glacial–interglacial temperature difference ranges from 3.1 to 3.8 ∘C and is in good agreement with a palaeo-temperature stack , even though iLOVECLIM is one of the warmest models at the LGM within the PMIP4 ensemble . The glacial–interglacial temperature difference is mostly explained by the cold temperatures at the LGM resulting from the large ice sheets that induce higher surface elevations and a strong albedo effect. A polar amplification is simulated since the northern and southern high latitudes both show a greater temperature difference from the pre-industrial period compared to the tropics (Fig. ). This pattern is consistent with recent reconstructions (e.g. , shown in Fig. d), even though with a smaller amplitude in our model. However, our simulated glacial–interglacial temperature difference is within the range of other estimates (4±0.8 ∘C, ).

For all the experiments, we simulate a gradual warming with no abrupt climate transitions. If the different experiments show a similar temperature evolution, they also display subtle differences. First, the experiments that use a reduced freshwater flux resulting from ice sheet melting present a more rapid warming compared to the reference experiment (e.g. DGL_noFWF with respect to DGL). Second, the experiments show a diverging temperature evolution after around 13 ka. After this date, the reference DGL simulation shows a slight decrease in temperature for about 2 kyr followed by a moderate warming until ∼7 ka. By contrast, the experiment in which the freshwater fluxes are discarded (DGL_noFWF) displays a brief period during which the temperature ceases to increase followed by a sharp temperature increase. In this case, the maximal surface temperature is reached at 10 ka after which there is a slight decrease until 7 ka. DGL_FWF/3 shows a very similar temperature change as DGL_noFWF, while DGL_FWF/2 presents similarities with both DGL and DGL_noFWF. This temperature evolution is in overall agreement with the temperature reconstruction of , which shows a pause in the deglacial warming trends at about 13.5 ka, synchronous with the carbon dioxide plateau. The experiment with the parameterisation of brines sinking, DGL_brines, displays a comparable temperature evolution to the reference simulation DGL for most of the simulated time period. However, the brine parameterisation induces a cooling of about 0.5 ∘C in the first years after its activation due to increased sea ice extent around Antarctica. In addition, at 4 ka, the global mean temperature starts to rise again after a relatively steady state for the rest of the Holocene. At 0 ka the temperature in the DGL_brines experiment is close to the temperature in the DGL_noFWF and DGL_FWF/3.

These differences in terms of global mean surface temperature amongst the different experiments are mostly explained by the differences in the state of the simulated Atlantic oceanic circulation. The reference experiment DGL simulates a decrease in the AMOC from the Last Glacial Maximum. After a 50 % reduction in its glacial values, the oceanic circulation strengthens at 13.5 ka for about 500 years before an abrupt collapse. This AMOC collapse is synchronous with the simulated pause in the temperature increase. From 12 ka onwards, the model simulates virtually no meridional overturning circulation. The evolution of the AMOC is drastically different when the freshwater flux to the ocean resulting from ice sheet melting is not considered (DGL_noFWF). In this case, the AMOC remains strong during the whole 26 kyr, with a maximum in the middle of the deglaciation towards 14 ka. This explains why the temperature rises more rapidly during the deglaciation in this experiment compared to the reference DGL experiment. Due to the weak AMOC in this case, the Northern Hemisphere remains colder, which ultimately delays the deglaciation of the ice sheets. The simulated pre-industrial period is also 0.8 ∘C colder in DGL with respect to DGL_noFWF since the absence of oceanic meridional heat transport results in much colder high latitudes, especially in the North Atlantic (Fig. ). The release of only half the meltwater flux to the ocean (DGL_FWF/2) does not allow us to maintain an active AMOC during the Holocene either, but the collapse of the AMOC is delayed here with respect to the reference experiment. In addition to the DGL_noFWF experiment, only the experiment in which only one-third of the meltwater flux is released to the ocean (DGL_FWF/3) is able to maintain an active AMOC during the Holocene. In this case, there are several abrupt oscillations in the strength of the circulation from 14 to 10 ka, but the model recovers and simulates an AMOC similar to the DGL_noFWF from 10 ka onwards. For most of the simulated time period, the experiment in which the sinking of brines around Antarctica is parameterised (DGL_brines) shows a very similar evolution than the reference DGL experiment, except that the AMOC shut-down occurs a few centuries earlier. However, at 4 ka the AMOC abruptly recovers and explains the final increase in the global mean temperature.

While some experiments show very abrupt shifts in the ocean, the atmospheric temperature evolution is nonetheless mostly gradual. This is visible at the global scale (Fig. b) but also when examining the temperature change above the Greenland ice sheet (Fig. a). The local temperature change closely resembles the global mean temperature change, even though with a larger amplitude. There are a few abrupt changes: slightly less than 4 ∘C in about 200 years at 10.7 ka and at 3.8 ka for the DGL_FWF/3 and DGL_brines experiments, respectively. These are direct consequences of the AMOC recoveries visible in Fig. c. These simulated abrupt warming events over the Greenland ice sheet look similar to the ones of the ice core record (Fig. b). The North GRIP (North Greenland Ice Core Project) δ18O is generally used to reconstruct the past local temperature changes with a conversion factor of 0.67 ‰ per degree to 0.8 ‰ per degree e.g., suggesting a glacial–interglacial difference of more than 15 ∘C. On comparable timescales, the Bølling–Allerød warming at 14.7 ka displays a similar temperature change amplitude compared to our simulated abrupt warming events, even though slightly larger. This suggests that, in our model, abrupt changes in the Atlantic oceanic circulation can induce large temperature changes over the Greenland ice sheet, similar to the ones deduced from the ice core records. However, the timing of the simulated abrupt events in the experiments shown here does not correspond to the ones of the ice record.

The large-scale differences amongst the different experiments discussed in Sect.  are largely driven by differences in the amount of the freshwater released to the ocean related to ice sheet melting. This freshwater flux is shown in Fig. a for the reference experiment DGL. Even though this flux displays some variability, its evolution is generally gradual and shows a maximum around 14 ka where it peaks above 0.3 Sv (1 Sv corresponds to 106 m3 s-1) with 100-year mean values about 0.23 Sv. In Fig. a we also show the meltwater flux computed from the ice thickness changes in the ICE-6G_C and GLAC-1D geologically constrained reconstructions. These fluxes have the same order of magnitude of the simulated flux in the DGL experiment. However, the model fails to reproduce the two distinct accelerations in ice sheet retreat visible in the reconstructions for the meltwater pulse 1A at 14.6 ka and the meltwater pulse 1B at 11.45 ka . Instead, the model produces important fluxes (greater than 0.1 Sv) over a few thousand years. Another way to discuss these fluxes is to integrate them in time to have an idea of the total ice sheet volume evolution through the deglaciation (Fig. b). In doing so, we can see that the coupled iLOVECLIM-GRISLI model setup produces an ice volume evolution in general agreement with the reconstructions since it lies between the two estimates of ICE-6G_C and GLAC-1D most of the time. However, the coupled model seems to deglaciate too fast since it displays a lower total ice sheet volume than the two reconstructions from 12.5 ka. In Fig. b we also show the eustatic sea level reconstruction of which displays a larger ice sheet volume, in particular around the Last Glacial Maximum. Since we do not simulate the Antarctic ice sheet changes, the ice volume shown in this figure only represents the Northern Hemisphere ice sheet volume. Interactive simulation of the Antarctic ice sheet would result in a larger ice volume during the glacial period reducing partially the mismatch with the reconstruction. At the end of the simulation, the model has an overestimation of the present-day ice volume. This overestimation corresponds to about 4.5 m of sea level equivalent and is explained by an overestimation of the Greenland ice sheet volume and remaining small ice sheets in the Ellesmere Island, Iceland, Norway and offshore of Newfoundland (Grand Banks).

The ice volume evolution of individual ice sheets is presented in Fig  for both the reference DGL and the DGL_noFWF experiments. In this figure, the individual ice sheet break-up is also represented for the ICE-6G_C and the GLAC-1D reconstructions. The ice volume partitioning is well reproduced. The North American ice sheet is by far the largest contributor for the last glacial sea level fall. At 26 ka, we simulate an ice volume of 81 m of sea level equivalent within the range of the geological reconstructions (75 and 86 m). However, in our experiments, the North American ice sheet volume increases until 20.5 ka where the reconstructions suggest a decline already as early as 26 ka (ICE-6G_C) or 23.8 ka (GLAC-1D). This is mostly due to our methodology used to define the initial state for the coupled experiments. When the coupling starts, at the beginning of our experiments, there is an abrupt change in the climate model in terms of ice mask and surface elevation from GLAC-1D to our spun-up ice sheets. Our spun-up ice sheets at 26 ka (Fig. a) show a higher North American ice sheet surface elevation than the GLAC-1D reconstruction used during the climatic spin-up, suggesting an overestimation of the precipitation in this area. When the coupling starts, this precipitation bias is amplified due to higher surface elevation and related increased orographic precipitation. The iLOVECLIM climate model likely shows an underestimation of the elevation desertification effect over the ice sheets . The simulated volume of the Eurasian ice sheet displays a similar evolution than the North American ice sheet with a maximum around the Last Glacial Maximum. This agrees well with the GLAC-1D reconstruction. Given its smaller volume, the absolute rate of volume loss is smaller for the Eurasian ice sheet (1.3 m per millennium) compared to the one of the North American ice sheet (5.7 m per millennium). However, the Eurasian ice sheet has already lost half its volume by 14.5 ka, whereas this occurs at 12.8 ka for the North American ice sheet. The Greenland ice sheet presents only a small volume reduction of 2.6 m of sea level equivalent, in good agreement with the reconstructions. However, the Greenland ice sheet volume at the end of the simulation is largely overestimated compared to the present-day observations (about 40 % volume overestimation). As for the total volume, the individual ice sheets deglaciate faster in the DGL_noFWF experiment. This is particularly visible for the North American ice sheet for which there is a difference of 1000 years at about 11 ka.

A map of the simulated ice sheet configuration for selected snapshots is shown in Fig. . This figure shows the results for the reference DGL experiment, while the other synchronously coupled experiments show a similar deglacial pattern although with differences in timing. At 26 ka, the North American ice sheet presents some very active ice streams on its northern margin from east to west: the Hudson Strait ice stream, the Lancaster Sound ice stream and the Amundsen Gulf ice stream. In these regions, grounded ice velocities are greater than 500 m yr-1. Elsewhere, the ice sheet does not present well-identified ice streams but the margins generally present large velocities, greater than 200 m yr-1. The other ice sheets present a smaller ice flow. From 26 to 21 ka, there is only little change in the ice sheet except the Eurasian ice sheet retreat from the British Isles and the development of an ice shelf at the outlet of the Hudson Strait ice stream. The simulated topography at 21 ka (Fig. b) is close to the spun-up ice sheets used at 26 ka and generally remains in good agreement with the geologically constrained reconstructions. From 21 ka, we simulate a gradual ice sheet retreat for both the North American and the Eurasian ice sheets. The North American ice sheet mostly retreats in its southern continental part due to decreased surface mass balance related to the gradual warming. The deflected bedrock in this area leads to the apparition of proglacial lakes, already visible at 14 ka. Similarly, at this date, the southern flank of the Eurasian ice sheet also displays proglacial lakes. The eastern part of the Eurasian ice sheet, the Barents–Kara ice sheet, rapidly collapses due to a grounding line instability in the Kara sea. This instability is initiated at about 14.5 ka and results in a complete disintegration of the Barents–Kara ice sheet in about 1.2 ka. Such instability is favoured by the depressed bedrock, with a ∼300 m deepening in the Kara sea with respect to the present-day bathymetry, resulting in steeper retrograde slopes. Another grounding line instability occurs later for the continental part of the North American ice sheet. The grounding line retreat is clearly visible at 12 ka. This lake-induced instability considerably facilitates the North American ice sheet deglaciation . At 8 ka, we simulate a very small North American ice sheet and only a relic of the Eurasian ice sheet over the Scandinavian mountains. At this time, the bedrock is still depressed below sea level over the northern most part of America but slowly returns to its present-day value. During the last 1000 years of the simulation, the bedrock uplift rate in the vicinity of the Hudson Bay is about 0.5 to 1.2 m per century, a value comparable to modern observations . The Greenland ice sheet expands considerably onto the continental shelf during the glacial period and retreats until about 10 ka. It does not display any substantial change in the ice extent during the Holocene, but it displays some ice elevation changes. The ice elevation evolution near the summit shows a maximum at about 10 ka and decreases afterwards in agreement with palaeo-elevation reconstructions at the deep ice core drilling sites .

The chronology and pattern of the deglaciation is largely affected by the biases in the climate model. We present these biases in terms of mean annual temperature and total precipitation rate in Fig. . To construct this figure we use a reference pre-industrial experiment (with fixed ice sheets), performed with a similar setup to the deglaciation experiments. Notably, this pre-industrial experiment uses the same last glacial oceanic bathymetry with a closed Bering Strait. The Northern Hemisphere topography and ice mask are nonetheless at their present-day reference value for GRISLI . The model presents a cold bias associated with an overestimation of the precipitation in the northwestern part of the North American continent. This explains why this region of the North American ice sheet deglaciates much later than its eastern sector where a warm bias is present. Also, Grand Banks and Iceland remain ice covered at the end of the simulation where the model is generally too cold and too wet. More generally, the climate model tends to overestimate the precipitation over mountainous areas which can induce a positive feedback over some ice caps such as Iceland, Grand Banks, Ellesmere Island and the Scandinavian mountains.

In Fig.  we present the rate of total ice mass change and its individual components: surface mass balance, basal mass balance and calving. The total mass change remains positive until 20.5 ka due to a positive integrated surface mass balance, not entirely compensated for by the basal mass loss (mostly sub-shelf melt) and calving. After this date, the total mass change becomes negative for the rest of the duration of the experiment. The total mass loss peaks at -9.7×103 Gt yr-1 at 13.8 ka when surface ablation and loss by calving almost synchronously display a maximum (surface ablation slightly precedes the calving increase). At this date, the mass loss due to the ocean and lake represent more than half the loss by surface mass balance. In fact, if both basal mass loss and calving remain almost constant until 14.5 ka (-1.4×103 Gt yr-1), they nonetheless show some variability after this date. These fluxes are maximal at the time of the grounding instabilities shown in Fig.  for both the Eurasian (14.5–13.5 ka) and the North American (12.8–10 ka) ice sheets. While the mass loss is primarily driven by surface ablation until 12.8 ka, after this date the oceanic and lake forcing become the major driver for the ice sheet retreat. The total mass loss finally reaches zero (ice sheet equilibrium) at 6.5 ka. The lesser importance of the sub-shelf melt rate for the first phase of the deglaciation could arise from the simple model we use to represent this process. Notably, we use a linear melting rate dependency on temperature change, while a quadratic dependency could best reproduce this process . A quadratic dependency would result in more sensitive melt rate changes to temperature changes.

The aim of this section is to assess the sensitivity of the simulated climate evolution to the choice of critical ice sheet model parameters and assumptions. To do so, we have performed additional experiments in which the forcings are accelerated. Three major sources of uncertainties have been explored: ice sheet mechanics (deformation and grounding line dynamics), surface mass balance and sub-shelf melting rates.

The evolution of some large-scale climate variables for these additional experiments are shown in Fig. . Since we do not feed back the freshwater related to ice sheet melting to the ocean in the accelerated experiments, they have to be compared to the DGL_noFWF experiment. The reference accelerated experiment ADGL (black in Fig. ) is in fact similar to the DGL_noFWF (blue): rapid temperature increase and active Atlantic circulation throughout the deglaciation. However, the accelerated experiment displays larger ice sheets than the non-accelerated (about 8 m of sea level equivalent at 14 ka) and as a result a colder climate (∼0.4 ∘C in global mean surface temperature at 14 ka). If the timing of the ice sheet retreat can be slightly different, the overall pattern of this retreat is only weakly affected by the acceleration factor.

The two experiments related to ice sheet dynamics (ADGL_ef and ADGL_schoof) do present some differences in their simulated ice sheet volume. The increased enhancement factor (ADGL_ef) leads to thinner ice sheets (smaller ice volume) and, as such, deglaciates faster than the reference accelerated experiment (ADGL). The experiment in which we use the formulation of instead of (ADGL_schoof) also produces a lower ice sheet volume during the glacial period. However, this experiment shows a slower ice sheet retreat during the deglaciation compared to the reference ADGL experiment. This is mostly related to the greater grounding line sensitivity in the formulation of , already shown in for the Antarctic ice sheet. These differences in terms of ice sheet evolution nonetheless only have a limited impact on the climate evolution. The ADGL_ef produces a slightly more rapid warming during the deglaciation (related to the smaller ice sheets), while it is the opposite for the ADGL_schoof (slower ice sheet retreat). The Atlantic circulation is also weakly impacted by the different ice sheet evolution. Only the ADGL_ef produces a slightly earlier decrease in the overturning circulation than the ADGL experiment, while the ADGL_schoof displays insignificant differences.

The two experiments related to modification of the surface mass balance parameters induce larger simulated ice sheet volume differences. Associated with a larger ice sheet surface mass balance, the ADGL_accplus produces larger ice sheet volumes throughout the whole simulated time period. For this experiment the maximal ice volume is reached by circa 19 ka, and it is larger by about 15 m of sea level equivalent than the ADGL experiment. This excess ice also explains the delayed ice sheet retreat: at 10 ka the simulated ice sheets still represent about 45 m drop in eustatic sea level in the ADGL_accplus experiment compared to about 8 m in the ADGL experiment. This has consequences for the simulated climate: (i) the global mean temperature rises more slowly, eventually reaching a comparable value to the reference simulation at 0 ka; (ii) the phase of very active overturning in the middle of the deglaciation is extended by 2 kyr. Even though the ADGL_accplus experiment displays larger ice sheet volume, the pattern of the ice sheet retreat is similar to the one of the ADGL experiment. By contrast, the ADGL_nocor experiment provides alternative ice sheet histories. In the ADGL experiment the Barents–Kara sector of the Eurasian ice sheet is almost fully deglaciated at 13.5 ka, while it is the case only after 8.5 ka in the ADGL_nocor experiment. Conversely, the North American ice sheet retreats faster in the ADGL_nocor experiment. This is a direct consequence of the cold temperature bias in northern Europe and the warm bias in North America. If the climate evolution is not drastically changed as a result of these different ice sheet chronologies, it nonetheless shows some interesting differences. The overturning circulation remains moderate for a longer time period compared to the ADGL experiment since it increases only after 15 ka (with respect to 17.5 ka in ADGL). As a result the global mean temperature in ADGL_nocor is colder than in ADGL even though it shows smaller ice sheets at least until 15 ka. The oceanic circulation in the model seems largely affected by the Eurasian ice sheet size.

Finally, the experiment in which we increase the sub-shelf melting rate, ADGL_bmbplus, shows only negligible changes with respect to the ADGL experiment. This suggests that, in our model, the ice sheet retreat is mostly driven by surface ablation and not sub-shelf melt.