Modelling of glacial inceptions, i.e. the relatively fast (compared to the duration of glacial cycles) transitions of the Earth system from an interglacial (no significant ice sheets over the northern continents, except for Greenland) to a glacial state, caused by lowering of the boreal summer insolation, is a crucial test for the Milankovitch theory of glacial cycles . Milutin Milankovitch was the first who used mathematical modelling to test the hypothesis that the lowering of boreal summer insolation associated with precession and obliquity cycles is sufficient to cause growth of northern ice sheets. In his “Cannon of insolation”, using a simple energy balance model and taking into account the ice–albedo feedback, Milankovitch estimated that a typical decrease in summer insolation would cause a lowering of the snow line by about 1 km and would cause a southward expansion of ice cover up to 55° N.

A set of transient and equilibrium experiments with the Earth system models of intermediate complexity (EMIC) CLIMBER-2 demonstrated that glacial inception could be interpreted as a bifurcation transition in the Earth system in the phase space of orbital forcing, defined as the maximum summer insolation at 65° N. This idea was explicit already in classical work by but was not tested before with geographically explicit climate–ice sheet models. traced both equilibrium states in summer insolation-phase space and found a wide range of insolations for which multistability of the climate cryosphere system exists. They also show that there is a second important dimension of the phase space, the atmospheric CO2 concentration. This finding was confirmed using a completely different model in . A detailed analysis of the critical relationship between summer insolation and CO2 was performed with the CLIMBER-2 model in , where a logarithmic relationship between critical CO2 concentration and insolation was found. This result has been recently corroborated by the new CLIMBER-X model .

Since the most recent glacial inception, which began between 120 and 115 ka, is, compared to previous glacial inceptions, relatively well covered by paleoclimate data and occurred during one of the deepest (the second lowest during the late Quaternary) boreal summer insolation minima, it is often used for testing Milankovitch theory. Until recently, complex climate models based on general circulation models (GCMs) did not include ice sheet components and thus could not simulate the evolution of ice sheets, which can be directly compared with existing paleoclimate data. So-called time slice simulations with fixed orbital parameters and greenhouse gas (GHG) concentrations corresponding to the insolation minimum (115 or 116 ka) have been traditionally performed instead. In such simulations, an establishment of perennial snow cover over at least several model grid cells in northern North America and/or Eurasia was considered to be the criterion for a successful simulation of glacial inception. A number of such simulations have been performed during the past 4 decades e.g.. Similar time slice experiments using climate model output to force a standalone ice sheet model have also been performed e.g.. Overall, the results of these simulations in terms of simulated (or not simulated) areas of perennial snow cover and their locations have been diverse. In many simulations, perennial snow cover did not appear even under such extreme orbital forcing or appeared in locations not supported by paleoclimate reconstructions. This is not surprising, since climate models used for paleoclimate studies usually have a coarse spatial resolution, which has been shown to have a significant impact on simulations of glacial inception e.g.. No less important is the fact that climate models tend to have climate biases often comparable in magnitude with the simulated climate response to orbital forcing. Some studies e.g. demonstrated a significant influence of climate biases on the simulation of glacial inception. It was also proposed that the failures to simulate glacial inception in climate models can be related to the omission of some positive feedbacks, such as the climate–vegetation feedback . Several studies demonstrated that a weakening of the Atlantic Meridional Overturning Circulation (AMOC) during glacial inception e.g. could potentially affect ice growth in North America or Scandinavia . The role of GHGs was also investigated e.g., but since the last glacial inception began when concentrations of CO2 and other GHGs were close to pre-industrial values, it is clear that climate–carbon cycle feedbacks can contribute to the rate of ice sheet growth but not to the initial ice growth.

So far, only a few attempts have been made to simulate the last glacial inception with ice sheet models asynchronously coupled to atmospheric GCMs but have generally failed to grow enough ice to match sea level reconstructions, even when using permanent coldest orbit (116 ka). Many more simulations of the last glacial inception and even full glacial cycles have been performed with different types of simplified, geographically explicit climate–ice coupled models. In particular, 2D energy balance climate models were coupled with 2D  and later 3D thermomechanical ice sheet models to simulate the last glacial cycle. More recently, different EMICs were applied in transient simulations of the last glacial inception and the entire last glacial cycle (or even several glacial cycles) . While EMICs are much more computationally efficient than GCMs, which allows for the performance of many long-term (orbital timescale) simulations, they usually have even larger climate biases than GCMs. This often causes significant misplacement of simulated ice sheets during glacial inception compared to paleoclimate reconstructions , and it was shown that the correction of temperature biases significantly improves the agreement between simulated and reconstructed ice sheets evolution during glacial inception .

EMICs are computationally fast enough to allow large ensemble of simulations to be performed, exploring the dependence of simulated glacial inception on model parameters e.g. and its sensitivity to different factors e.g. and found that the transition from interglacial to glacial state is characterized by two timescales associated with different mechanisms. They have shown that the initial growth of ice sheets begins nearly simultaneously at several nucleation centres in high latitudes and high elevations of the Northern Hemisphere, and the lateral spreading occurs only through the slow motion of ice sheets, resulting in rather low initial rate of ice volume increase. However, at a certain time corresponding to a sufficiently low summer insolation, an abrupt expansion of the ice sheet area occurs through the positive albedo feedback. This leads to a rapid increase in accumulation area and causes a significant acceleration of the ice volume growth rate. Over the past 20 years since the publication of , the phenomenon of rapid expansion of ice sheet accumulation area through albedo feedback mechanisms was either not found or not properly discussed by other authors, although it is likely that a similar mechanism operated in simulations described in . This is why it is essential to revisit this topic as new and improved modelling tools become available.

In this study we build on our experience in modelling glacial cycles with the CLIMBER-2 model and employ the newly developed Earth system model CLIMBER-X with interactive ice sheets, visco-elastic solid Earth response and dynamic vegetation to simulate the last glacial inception from 125 to 100 ka. CLIMBER-X operates at a relatively high horizontal resolution of 5° for the climate model and 32 km for the ice sheet model and includes a rather detailed representation of the processes which have been found to be potentially important to simulate the interglacial–glacial transition, making it a powerful tool to explore mechanisms and feedbacks at play during the last glacial inception.

The paper first describes the model and in particular the ice sheet surface mass balance computation and the ice sheet coupling strategy (Sect. ), with more details provided in the Appendix. The experimental setup is then presented (Sect. ) followed by a description of the results of the model simulations (Sect. ) and finally discussions and conclusions.

To simulate the last glacial inception we use the Earth system model CLIMBER-X , which is a major step forward in modelling capabilities compared to its predecessor CLIMBER-2, with a much higher spatial resolution both in climate and ice sheets and substantial improvements in all components: atmosphere, ocean, sea ice, vegetation, ice sheets, and surface mass balance scheme. The CLIMBER-X climate model component includes a semi-empirical, statistical dynamic atmosphere model, a 3D frictional geostrophic ocean model, a dynamic thermodynamic sea ice model, and a land surface and dynamic vegetation model, all with a horizontal resolution of 5° × 5°.

Additionally, the two ice sheet models SICOPOLIS and Yelmo are part of CLIMBER-X . In the present study we employ SICOPOLIS to model the Northern Hemisphere (NH) ice sheets since it has already been extensively applied to NH glaciation studies, particularly in the framework of the CLIMBER-2 model e.g., the predecessor of CLIMBER-X. In CLIMBER-X we make use of one of the latest versions of SICOPOLIS (v5.3; ), which is based on the shallow-ice approximation for grounded ice, the shallow-shelf approximation for floating ice and hybrid shallow-ice–shelfy-stream dynamics for ice streams . The enthalpy method of is used as thermodynamics solver. The ice sheet model is applied to the NH at a default horizontal resolution of 32 km. The performance of the standalone SICOPOLIS model for present-day Greenland has been presented in . Since we concentrate on the NH, Antarctica is prescribed at its present-day state in this study based on the assumption that the Antarctic ice sheet contribution to global ice volume changes during the glacial inception is small. Different modelling studies confirmed that during this time period the Antarctic contribution to global sea level drop is only about 5 m e.g., about 10% of global sea level variations reconstructed for this period.

The coupling of the ice sheet model to the other CLIMBER-X components is schematically illustrated in Fig.  and further details of SICOPOLIS are presented in Appendix .

A physically based surface energy and mass balance scheme (SEMIX, Surface Energy and Mass balance Interface for CLIMBER-X) is used to interface the ice sheet model with the atmosphere. In the ice sheet modelling community it is still common to use the simple positive-degree-day (PDD) model e.g. for the computation of surface melt. However, this simplified approach computes melt only from near-surface air temperature, with potentially important implications on the simulated response of the surface mass balance to orbital forcing and climate change e.g.. To address some of the limitations of the PDD scheme, so-called insolation–temperature methods (ITMs) have been developed that explicitly account for absorbed surface solar radiation . Recently, energy balance schemes or land surface models have also been applied to compute the surface mass balance of ice sheets (e.g. ). Similarly to these models, SEMIX also explicitly resolves the surface energy balance and is largely based on the ideas in , but with notable modifications and improvements. The climate model fields needed by SEMIX are first bilinearly interpolated from the coarse-resolution climate model grid (5°×5°) onto the high-resolution ice sheet model grid, where SEMIX operates. Subsequently, temperature, humidity, and radiation fields are elevation corrected. We do not account for the additional orographic effect on precipitation. Such an effect is crudely accounted for by the atmospheric component of CLIMBER-X, which has a much higher resolution compared to CLIMBER-2, where a parameterization of the orographically forced precipitation was included . Snow albedo depends on snow grain size and the concentration of dust in snow, while bare ice sheet albedo transitions between firn-like values, clean-ice values, and dirty-ice values depending on the age of ice and the time it has been exposed to the atmosphere. CLIMBER-X includes an interactive dust cycle , and the dust concentration in snow is computed from the simulated dust deposition flux. The surface energy balance equation is then solved following a similar approach as over land and sea ice as described in and , and the surface mass balance is finally derived accounting for snowfall, rainfall, evaporation or sublimation, melt, refreezing, and runoff. The performance of SEMIX for Greenland in the fully coupled CLIMBER-X configuration has already been presented in . In order to compute the annual surface mass balance, SEMIX is called every 10 years over a full year with a time step of 1 d. As long as the forcing is slow enough, a higher frequency of SEMIX calls is not needed to accurately capture the climatological evolution of the surface mass balance because CLIMBER-X does not resolve weather and internal inter-annual variability. SEMIX is described in detail in Appendix .

The surface mass balance of ice sheets is largely controlled by air temperature and precipitation and relatively small climate model biases can result in large changes in simulated ice sheets e.g.. In accordance with Milankovitch theory, ice sheets are particularly sensitive to summer temperatures, which control snow and ice melt. Thus, even small summer temperature biases, which are common even in state-of-the-art climate models e.g., can therefore preclude a realistic simulation of ice sheet growth and decay. In CLIMBER-X, present-day summer temperature biases over NH land are generally within a few degrees (Fig. a). However, in the area around Hudson Bay and the Labrador Peninsula, simulated summer temperatures are up to ∼ 5 °C too warm. Biases of this order of magnitude are comparable to the temperature changes induced by changing orbital configuration (Fig. b) and can consequently strongly affect the simulated ice sheet distribution. Therefore, similarly to , in SEMIX we implemented a temperature bias correction over northern North America as shown in Fig. . The bias correction is applied throughout the year as a constant offset in the computation of the surface energy balance. The reasoning behind the choice of applying summer temperature bias correction throughout the year is guided by the fact that, following Milankovitch theory, ice sheet surface mass balance is largely determined by ablation during summer, which is highly sensitive to temperature. We have actually also tested the use of bias correction applying monthly mean temperature differences, but the model results indicated absolutely negligible differences compared to using the mean summer bias. We also assume that the bias is a persistent feature of the model also under different boundary conditions and therefore apply the same bias correction at all times. Since the focus of our study is on the last glacial inception and the boundary conditions at ∼ 120 ka (just before the expected onset of ice sheet growth) are similar to pre-industrial values in terms of GHG concentrations and orbital parameters, we do not expect significant differences in temperature biases compared to the present day. The assumption on stationarity of the temperature biases is therefore, at least during the initial ice growth phase, well justified. Furthermore, since air temperature is closely related to the downwelling long-wave radiation at the surface, which affects the surface energy balance, we additionally correct the downwelling long-wave radiation using a simple quadratic relation derived from ERA5 reanalysis data. For more details, see Appendix .

As soon as an ice sheet gets in contact with the ocean its mass balance is also influenced by melting and freezing at the base of the floating ice shelves. At present, basal melt is important mostly for the Antarctic ice sheet, which is in extensive contact with the ocean, and for the interactions of the Greenland ice streams with the fjords. However, little is known about the role played by basal melt for ice sheets in the NH during the last glacial cycle. The basal melt is strongly influenced by the ocean circulation on the continental shelf and by the turbulent plume dynamics generated at the ice–water interface by the density difference between the fresh meltwater and the surrounding saline seawater e.g.. These processes can not be properly represented at the typically applied resolutions of global ocean circulation models, and several simple parameterizations have been put forward to represent the basal melt process in ice sheet models based on large-scale ambient properties of seawater and on the ice shelf base topography . Simple box models have also been developed to describe the ocean circulation in the cavities below the ice shelves , but they are specifically designed to be applied to Antarctica, and an extension to the NH is not straightforward. In CLIMBER-X we have therefore implemented the simple and general basal melt parameterizations of and , both of which rely on the difference between the ambient ocean temperature simulated by the ocean model and the freezing point temperature of seawater at the ice shelf base. The linear model of has been used in the simulations presented in this work. A more general 2D plume model also including the Coriolis effect that is general enough to be applied to any ice shelf geometry has been recently developed and will be considered for a future implementation in CLIMBER-X. See Appendix  for more details on the basal melt schemes in CLIMBER-X.

The presence of ice sheets also affects the simulated freshwater fluxes into the ocean. Freshwater produced by melt occurring at the surface of the ice sheets is routed to the ocean following the steepest surface gradient, and the same runoff directions are used also to route the water originating from basal melt of grounded ice to the ocean. The freshwater flux from basal melt of floating ice and ice shelf calving is applied locally to the ocean model. Both liquid water runoff and calving fluxes are distributed uniformly over several coastal grid cells. For calving fluxes the latent heat needed to melt the ice is also accounted for in the ocean model. CLIMBER-X so far does not include an iceberg model to explicitly simulate the fate of ice originating from ice shelf calving.

The glacial isostatic adjustment (GIA), which controls regional sea level change and surface displacements, is computed by the viscoelastic solid Earth model VILMA . In VILMA, mass conservation between ice and ocean water is considered, and the loading effect of the ice and gravity-consistent redistribution of water in the ocean is solved applying the sea level equation including the rotational feedback . VILMA takes the ice sheet loading as input and computes the relative sea level (RSL) changes. The sea-level equation at the surface is solved on a Gauss–Legendre grid of 512 × 256 grid points (n128), which is consistent with the spectral resolution in spherical harmonics up to a Legendre degree or order of 170, corresponding to a wavelength of ∼ 120 km. In this study we use the 3D viscosity structure from , which is based on a 3D tomography model of the upper mantle seismic velocity structure that is converted into viscosity variations considering further constraints by geodynamics and lithospheric structure. In CLIMBER-X, the solid Earth dynamics determines the bedrock elevation through simulated changes in relative sea level. The relative sea level computed by VILMA is substracted as an anomaly from the reference high-resolution (≈ 10 arcmin) bedrock elevation from . This is done in order to preserve the small-scale structure, which is important both for runoff routing and for surface mass balance. Surface elevation, land–sea mask, and runoff routing directions are then updated accordingly. The surface elevation is then aggregated to the coarse climate model resolution, and the land and ocean grid cell fractions on the climate model grid are then derived. The climate model in CLIMBER-X can deal with land–sea mask changes, a feature that is rather exceptional for contemporary Earth system models e.g.. VILMA is called every 10 years, implying that the ice sheet model gets an update of the bedrock elevation field every 10 years and that the topography, the land–sea mask and the runoff directions are also updated every 10 years. Experiments using a higher coupling frequency of 1 year showed negligible differences. In a recent study coupling VILMA with the PISM ice sheet model showed a coupling time step of 100 years as being sufficient.

We first performed a transient Holocene simulation from 10 ka to present day (2000 CE) to make sure that no glacial inception is simulated at present. Since for this purpose we are mainly interested in the growth of ice sheets outside of Greenland, the Holocene simulation was performed with a prescribed present-day Greenland ice sheet. In this simulation, the model is driven by prescribed changes in the orbital configuration and atmospheric concentrations of CO2, CH4 and N2O from ice core data and historical observations . Note that NH summer insolation is continuously decreasing over the Holocene, although not enough to cause a glacial inception at present . At the end of the transient Holocene simulation ice cover is consistently simulated only over parts of Baffin Island and Ellesmere Island, in the southeast of Iceland, on Svalbard, over part of Novaya Zemlya, and in a small area over the Rocky Mountains (Fig. ), in good agreement with glacier inventories .

The transient last glacial inception simulations are started from the Eemian interglacial at 125 ka and run until 100 ka. This time interval is characterized first by a decrease in NH summer insolation, with a minimum reached at ∼ 116 ka followed by an increase in insolation until ∼ 105 ka (Fig. a). The model is driven by prescribed changes in the orbital parameters and atmospheric concentrations of CO2, CH4 and N2O from ice core data (Fig. b). The initial conditions of the model runs correspond to the climate model in equilibrium with 125 ka boundary conditions. We therefore make the reasonable assumption that climate was in quasi-equilibrium at 125 ka. Because the Greenland ice sheet was likely not in equilibrium with climate at this time, for practical reasons we choose to start from the Greenland ice sheet prescribed from present-day observations with a uniform ice temperature of -10 °C. This is justified because Greenland is not the focus of our study and plays a negligible role in the glacial inception over the NH continents. With this general setup we performed different simulations to test the importance of different processes, namely (i) vegetation feedback, (ii) ice sheet feedback, and (iii) role of CO2 variations, and additional experiments to explore the sensitivity of the simulated last glacial inception to (i) the temperature bias correction in SEMIX, (ii) snow albedo parameterization, (iii) ice sheet model resolution, and (iv) climate acceleration factor. The full set of experiments is listed in Table .

We have presented the results of a set of transient simulations of the last glacial inception with the CLIMBER-X Earth system model, which includes an ice sheet model and a model for the solid Earth response to changes in ice sheet loading. This paper also describes the ice sheet coupling with the atmosphere and ocean, which will serve as a reference for future studies using the model with interactive ice sheets.

We have shown that, as a response to the decreasing summer insolation at high northern latitudes, the model simulates a rapid expansion of ice sheets over northern North America and Scandinavia between ∼ 120 and ∼ 116 ka, which is driven mainly by large-scale snowfield thickening. This result is fully consistent with the concept of glacial inception as a bifurcation in the climate system caused by a strong albedo feedback . The rapid expansion of the ice sheet area was followed by ice volume growth that corresponds to a global sea level drop of nearly 40 m at 110 ka, which is in reasonable agreement with paleoclimate reconstructions. Compared to the CLIMBER-2 results from , as expected the CLIMBER-X model results are in better agreement with available paleoclimate reconstructions in terms of simulated ice volume and spatial distribution of ice sheets. The abrupt increase of the North American ice sheet extent simulated in CLIMBER-X is nearly half that shown in , and this increase happens in two steps. Less ice is formed in eastern Siberia and Alaska in CLIMBER-X than in CLIMBER-2. At the same time, despite substantial differences in model formulations and spatial resolution, the results of the simulations with CLIMBER-X confirm the main findings presented in . The abrupt increase in the North American ice sheet area occurs in CLIMBER-X approximately at the same time and in the same area as in and through the same mechanisms. Our results confirm the critically important role of vegetation feedback demonstrated in . The albedo feedback associated with an increase in snow-covered area, sea ice extent, and the southward retreat of the boreal forest plays a crucial role in the rapid ice area expansion in our simulations. The vegetation feedback alone increases the maximum simulated ice sheet area by 50 %.

Our new modelling results show a strong sensitivity of simulated ice sheet evolution to the parameterization of clean snow albedo and to the impact of impurities on snow albedo. The ice sheet feedback and the variations in GHGs concentrations are of minor importance during the ice growth phase associated with decreasing summer insolation prior to ∼ 115 ka but are fundamental in maintaining the system in a glacial state during the subsequent period of increase in summer insolation, resulting in an only partial deglaciation.

The results of model simulations demonstrate that the reduction of climate biases (too high summer air temperatures over eastern North America) leads to significant improvements in the simulated spatial extent of the North American ice sheet, as also shown by .

The model results are not very sensitive to climate acceleration up to a factor ∼ 10, confirming earlier findings by and . Assuming that this finding also holds for more complex Earth system models, a climate acceleration factor of 10 would allow these models to run transient glacial inception simulations in a reasonable time using less computational resources. The resolution of the ice sheet model only marginally affects the model results, at least in the tested range between 16 and 64 km. This is because a large-scale ice expansion over relatively flat terrain is the dominant mechanism leading to glacial inception in our model, while ice caps, which can be captured only if the topography is highly resolved, have only a very localized effect and are therefore not of fundamental importance.

The glacial inception simulations presented here are a first step towards simulating the full last glacial cycle with CLIMBER-X.