LOVECLIM (version 1.3) is a coupled Earth systems model of intermediate complexity (EMIC), which consists of atmosphere (ECBilt), ocean with dynamic sea ice (CLIO) and vegetation (VECODE) modules. It is fast enough to simulate the last glacial inception (120 to 100 ka) in less than 3 weeks using a single computer core. Therefore, it has been used to simulate a wide range of different climates from the last glacial maximum through the Holocene and the last millennium to the future . Atmosphere

The atmospheric component ECBilt, is a spectral global quasi-geostrophic model, with T21 truncation, three vertical layers at 800, 500, and 200 hPa, and a time step of 4 h. The quasi-geostrophic structure of the model limits its ability to simulate equatorial variability and, hence, atmospheric interactions between the tropics and higher latitudes. To partially compensate for this, it has additional ageostrophic terms to improve the representation of Hadley cell dynamics . Precipitation is computed from the precipitable water of the first layer according to a precipitation threshold for relative humidity (default 85%). The model contains simple schemes for short-wave and long-wave radiation, with radiative cloud cover prescribed by default .

The GSM is built around a thermo-mechanically coupled ice sheet model. It includes a 4 km deep permafrost-resolving bed thermal model , fast surface drainage and lake solver , visco-elastic bedrock deformation , positive degree day surface mass balance with temperature dependent degree-day coefficients derived from energy balance modelling results , sub-grid ice flow and surface mass balance for grid cells with incomplete ice cover , and various ice calving schemes for both marine and proglacial lake contexts . For the results herein, ice shelves are treated using a crude shallow ice approximation with fast sliding. The GSM is run at a 0.5∘ longitude by 0.25∘ latitude grid resolution.

The GSM has three new features that have not been previously documented. First, ice calving has been upgraded to the more physically based scheme from . However, our implementation imposes the additional condition that the ice cliff failure mechanism is only imposed at ice marginal grid cells. Second, a temperature-dependent sub-shelf melt scheme that also depends on adjacent subglacial meltwater discharge from the grounded ice sheet has been added. The melt is proportional to the water temperature to the power 1.6 and to proximal subglacial meltwater discharge following the Greenland fjord modelling results of . We also impose a quadratic dependence on ice thickness to concentrate sub-shelf melt near deep grounding lines in accord with the results of process modelling e.g.,. Finally, a first-order approximation to geoidal deflection is now included. Details of these schemes will be in an upcoming submission that fully describes the revised GSM.

For the results herein, PD and glacial inception model runs are initiated with PD ice sheet thickness. The initial bed-thermal temperature field is set to the PD resultant field from a mix of best-fit past calibrated and ongoing calibration model runs (i.e., without LOVECLIM as in for North America).

To initialize the temperature field of existing ice sheets, results from previous transient runs are usually used in the GSM. However, this does not work for a cold start from PD fields, as the PD ice thickness fields will not line up fully with model results. As such, the ice temperature field is initially linearly interpolated from surface temperature to a basal temperature of -3 ∘C. This enforces a frozen base to ensure a smooth spin-up and also provides warm enough ice to generate significant ice velocities. Ice velocity fields are then computed. The ice thermodynamics are subsequently partially spun-up over 5000 years (with fully coupled bed-thermal evolution). When the results of pre-Eemian Greenland and Antarctic calibrations become available, this will be used to initialize the respective Eemian ice sheet temperature and ice thickness fields.

Glacial inception surface topography is also offset from PD by the amount required to remove PD topographic discrepancies (to observed) from some past best fit calibration model runs.

As detailed below, the climate model is spun-up over an ensemble parameter dependent time interval prior to onset of the coupled model run.

At the end of each coupling time step, the coupler receives climate fields averaged over the last 10 years from ECBilt and converts them to monthly-mean values. These fields include the following:

2 m near surface air temperature and standard deviation;

Sub-ice shelf melt is a challenge for paleo coupled ice sheet climate modelling given the dependence on unresolved basin-scale circulation. As a first-order approximation, we assume that upstream ocean temperature at the same depth corresponds to the local sub-shelf temperature. To facilitate fast and simplified coupling, given the complexity of ocean grids in most ocean general circulation models, we only extract upstream ocean temperature vertical profiles from LOVECLIM at the end of each coupling time step for a number of chosen index sites as indicated in Fig.  and use these for downstream marine sectors. We selected these sites (seven over NA + Greenland and four over EA) by examining the PD ocean temperature climatologies from CLIO (at various depths) while taking ocean currents into account. Our site selection was predicated on the constant bathymetry and land mask of CLIO and would need updating for a model with dynamic land mask/bathymetry. The downstream masks for the profile sites extend onto land where applicable when grounding line retreat beyond the fixed ocean mask of CLIO (i.e., onto the land mask) is possible.

To test the impact of this regional disaggregation of ocean temperatures, we generated three test cases: ocean temperature forcing set to PD value, to -2 ∘C, and to the contemporaneous average across the above index sites. Starting from a 110 ka restart, all three options have local ice thickness differences greater than 1 km after 2 kyr compared to that with the standard coupling (Fig. ).

Changes in both the topography and the ice mask can affect the global circulation patterns by influencing the stationary waves and the jet stream. At the end of each coupling time step, the coupler receives the updated topography and ice thickness fields from the GSM. The topography field is upscaled to the ECBilt grid and then used for the next LOVECLIM run step. Given the large difference in grid resolution, the choice of upscaling scheme is not clear a priori. Therefore, we have implemented three different schemes to upscale the topography from the GSM high-resolution grid to the ECBilt low-resolution grid.

Changes in the snow and ice area and type have an amplifying effect on climate by modifying the surface albedo. During summer, the balance between absorbed and reflected solar energy at the ice sheet surface is the dominant factor controlling surface melt variability in the ablation zone . The parameterization of the surface albedo in LOVECLIM takes the state of the surface (frozen or melting) and the thickness of the snow and ice covers into account . We include all types of snow and ice albedo (i.e., snow, melting snow, and bare ice) in our ensemble parameter set.

The snow albedo, bare ice albedo, and melting ice albedo rows in Table  show the range of albedo values for each type and their climate sensitivity. Increasing snow albedo results in a reduction of winter precipitation over all four regions with an extended effect over summer temperatures, as expected. However, the same feedback is not as straightforward for bare ice albedo and melting ice albedo. Although the increase in bare ice albedo shows an expected cooling effect over all regions with a smaller influence on precipitation, an increase in melting ice albedo causes all regions to get between 4 and 6 ∘C warmer and increases the winter precipitation.

Before starting a coupled transient climate simulation, it is necessary to allow the atmosphere and ocean to adjust to the initial boundary conditions and external forcings. Model spin-up, and therefore the initial state of the climate system, can be a major source of uncertainty in climate modelling especially given the millennial timescale of deep ocean circulation.

The general approach to spin-up the ocean is to run the ocean to an equilibrium state under fixed external forcings e.g.,. However, as the climate system is unlikely to ever be in equilibrium, this choice lacks justification. We include two parameters to control the initial state of the system: LOVECLIM spin-up start year, and LOVECLIM spin-up length. All spin-ups are performed using transient orbital and CO2 forcings ranging from 3000 to 5000 years but without the GSM coupling. The combination of these two spin-up control parameters results in slightly different coupled transient start times, each with different initial ocean and atmosphere states. For the runs herein, we constrain the spin-up to end between 1400 and 1600 CE. Increasing the spin-up length has a cooling and drying effect in the coupled model with PD boundary and initial conditions, while starting the transient coupled run from earlier years results in slightly warmer and wetter conditions (Table ).

The three different upscaling methods described in Sect.  are evenly distributed between ensemble members as shown in Table . By switching between three methods, we calculate the highest temperature and precipitation changes over four regions and plot them in the last column of Table . The highest temperature sensitivity to the upscaling method is recorded in NorthNA followed by the NorthEA zones, and the highest precipitation sensitivity is seen in the SouthEA zone.

ECBilt only accounts for humidity, and thus precipitable water, between the surface and the 500 hPa layer. Above 500 hPa, the atmosphere is assumed to be dry, meaning that all the water transported by atmospheric flows into this region precipitates. Below the 500 hPa layer, ECBilt precipitates all the excess water above a fixed threshold (default 0.83) multiplied by the vertically integrated saturation specific humidity . This parameter has the largest relative impact for NorthEA temperature (4 ∘C over the parameter range equivalent to 60 % of mean).

The representation of clouds is one of the largest sources of uncertainty in models. They play an important role in regulating the surface energy balance of ice sheets, with competing warming and cooling effects at the surface through changes to short-wave and long-wave radiative fluxes. The effect of ice sheets on cloud formation is also significant. The growth of ice sheets results in tropospheric cooling and a reduction in humidity. This colder and drier troposphere displaces the upper tropospheric stratiform clouds downward, and reduces the low level stratiform cloud cover around the ice sheets .

The total downward and upward long-wave radiative scheme in ECBilt is a function of the vertical profile of the temperature, the concentration of various GHGs, and the humidity, and is computed for both clear sky and cloudy conditions. The radiation computed for each grid cell is then the weighted average of these two conditions based on the cloud coverage. The default ECBilt configuration prescribes radiative cloud coverage to the PD ISCCP D2 dataset . The total downward and upward short-wave radiative fluxes depend on the transmissivity of the atmosphere, which also relies on the prescribed cloud cover .

Given the importance of cloud radiative feedbacks on ice sheet evolution, the use of a prescribed PD cloud cover for paleoclimate modelling lacks justification. Therefore, we have added a simple cloud parameterization scheme similar to the precipitation parameterization scheme described in Sect. . The only difference here is the humidity threshold for cloud formation, which is assumed to be 10 % less than the precipitation threshold, allowing cloud cover without precipitation. Including the dynamic cloud cover radiation feedback in the coupled model slightly decreases the total ice volume at glacial inception (Fig. ) through reduced humidity during glacial conditions reducing the cloud cover.

As evident in the “Temperature and precipitation sensitivity” column in Table , regional temperature and precipitation are sensitive to each of our ensemble parameters in the coupled model. However, due to the non-linearity of the climate system, the combined effect can be significantly different. In the next section, we explore the coupled model response to all these parameters in an ensemble of simulations.

The ensemble distribution of the annual mean global T2m anomaly with respect to observations shows that the majority of the ensemble members fall within ±3 ∘C of observations (grey bars in Fig. ). However, as ice sheet build up is a function of both temperature and precipitation, most of the warm biased simulations fail to maintain ice-free conditions over NA and EA during PD due to a high winter precipitation bias (Table ).

Our four latitudinal bands defined in Sect.  (Table ) provide more relevant temperature metrics for NH ice sheet contexts. All four regions have higher ensemble mean seasonal T2m and precipitation compared to observations. However, the observations are covered well within two standard deviations for all regions, and temperature is covered within one standard deviation for most regions.

The seasonal cycle provides a partial test of a model's response to orbital forcing on Milankovitch scales. The ensemble mean seasonal cycle (difference between mean summer and mean winter) is within one standard deviation of the reanalysis data for all regions and for both temperature and precipitation (Table ). Furthermore, aside from NorthEA, the diagnostic regions have a mean difference between summer and winter ensemble temperatures within a degree Celsius of that of the reanalysis climatology.

Jet stream latitude and oscillations have a strong control over storm tracks and the boundary between polar and subtropical air masses. Therefore, they are critical factors in controlling where and when an ice sheet margin advances or retreats. Due to the low vertical resolution of ECBilt, we compare the ensemble zonal mean of the 200 hPa zonal wind (as opposed to the more usual 300 hPa diagnostic level) with observations in winter and summer over NA and EA (Fig. a). The ensemble shows good agreement in capturing the maximum zonal velocity, but there is a 10 to 15∘ shift northward in the latitude of the jet in both seasons. This is likely due to the reduced temperature gradient between low and high latitude.

We also compare the 30–80∘ N meridionally averaged meridional wind at 200 hPa of the ensemble mean and the observations to diagnose the Rossby waves. In the summer, the longitudes of the troughs and ridges from the Pacific Ocean to the Atlantic Ocean largely match the reanalysis output within ensemble range (red line in Fig. b) with the largest discrepancies over the Eurasian region. During the winter, although the general pattern of the jet stream oscillations still agrees between the model and the observations (troughs over Eurasia and North America), the mismatch between ensemble members and observations becomes more significant given the higher Rossby wave number of the model ensemble.

High latitude sea ice acts as an insulator for both heat and moisture between the atmosphere and ocean, which are the two controlling factors for terrestrial ice sheet surface mass balance. We use the area and minimum latitude extent of the NH sea ice as relevant diagnostics. The general warm bias of the ensemble is reflected in the reduced ice area of the ensemble for both seasons, barely capturing the observed area within the one standard deviation range of the ensemble (Fig. ). Both March (maximum) and September (minimum) NH sea ice areas show gradual decreases in the ensemble mean as the greenhouse gas concentration increases in the model.

Our filter condition for our sub-ensemble still permits a wide response of modelled components. For instance, averaging from 1950 to 1980 CE, the Pacific Ocean sea ice shows higher sensitivity to ensemble parameters during its maximum seasonal extent than the Atlantic. The sea ice minimum latitude in the Pacific ranges from 60 to 45∘ N (not shown), in comparison to the observed value of 60∘ N .

The AMOC transports large amounts of heat and salinity between high and low latitudes. Both paleoclimate proxy records and climate model simulations show that the AMOC experiences significant changes over a glacial cycle.

Our “bounding reality” criteria is not met for at least two AMOC features of the sub-ensemble. The PD ensemble mean AMOC strength is weaker than the reanalysis data from European Centre of Medium-Range Weather Forecasts ECMWF ORA-S3,. The temporal mean of the reanalysis data is only captured by the maximum ensemble range (Fig. a). The ensemble mean shows a slight increase in the AMOC strength from 1965 to 1980 CE, which is not seen in ORA-S3. Furthermore, the temporal variability of the CLIO AMOC lacks the strong amplitude of the low frequency component of observations (as displayed by the maximum and minimum – time averaged – AMOC strength runs in Fig. a).

The maximum AMOC stream function strength is seen around 50∘ N at 1 km depth. The ensemble variance is also highest in the same region, in addition to 0∘ latitude at the same depth (Fig. b).