HadCM3 is a coupled atmosphere–ocean general circulation model (Gordon et al., 2000; Valdes et al., 2017). It has been shown to be capable of accurately reproducing the heat budget of the present-day climate (Gordon et al., 2000) and has been used for future climate projections in the IPCC AR4 (Solomon et al., 2007) as well as paleoclimate reconstructions such as PMIP2 (Braconnot et al., 2007) and PlioMIP (Haywood and Valdes, 2003; Dolan et al., 2011, 2015; Haywood et al., 2013). The atmosphere module of HadCM3 covers the entire globe with grid cells of 2.5∘ latitude by 3.75∘ longitude, giving a north–south resolution of about 278 km, whereas east–west resolution varies from about 70 km over northern Greenland (80∘ latitude) to about 290 km over southern Canada (45∘ latitude, the southern-most area covered by the ANICE grid). The ocean is modelled at a horizontal resolution of 1.25∘ by 1.25∘, with 20 vertical layers.

In their 2010 study, Singarayer and Valdes used HadCM3 to simulate global climate during the LGM, the pre-industrial period (PI), and several time slices in between. Orbital parameters representative of the era are used according to Laskar et al. (2004), atmospheric CO2 concentration is prescribed according to the Vostok ice-core record (190 ppmv at the LGM; Petit et al., 1999; Loulergue et al., 2008), and orographic forcing follows the ICE-5G ice distribution reconstruction by Peltier (2004), shown in Fig. 1. Temperature and precipitation fields resulting from these two experiments are shown in Figs. 2 and 3.

The modelled glacial–interglacial global mean temperature difference is 4.3 K, which is in good agreement with results from other model studies (Hewitt et al., 2001; Braconnot et al., 2007), as well as reconstructions from multiple proxies (Jansen et al., 2007; Annan and Hargreaves, 2013). Comparisons of the model results with ice-core isotope temperature reconstructions from Greenland (GRIP; Masson-Delmotte et al., 2005) and Antarctica (EPICA Dome C; Jouzel et al., 2007), as well as borehole-derived surface temperature reconstructions (Dahl-Jensen et al., 1998), indicate that glacial–interglacial temperature changes at these high latitudes are slightly underestimated by the model, by up to 1.5 K over Antarctica and up to 4 K over Greenland.

To simulate the ice evolution on Earth we use ANICE, a coupled 3-D ice-sheet–shelf model (Bintanja and Van de Wal, 2008; de Boer et al., 2013, 2014, 2015). It combines the shallow ice approximation (SIA) for grounded ice with the shallow shelf approximation (SSA) for floating ice shelves to solve the mechanical equations and incorporates a thermodynamical module to calculate internal ice temperatures. In ANICE, the applied mass balance is calculated using the parameterization by (Bintanja et al., 2005; Bintanja and van de Wal, 2008), which uses present-day monthly precipitation values for which changes in precipitation follow from a Clausius–Clapeyron relation as a function of free atmospheric temperature. Time- and latitude-dependent insolation values according to the reconstruction by Laskar et al. (2004) are used to prescribe incoming radiation at the top of the atmosphere. Ablation is calculated using the surface temperature–albedo–insolation parameterization by Bintanja et al. (2002). In the transition zone near the grounding line, SIA and SSA ice velocities are averaged using the approach by Winkelmann et al. (2011), as explained by de Boer et al. (2013). Sub-shelf melt is calculated based on a combination of the temperature-based formulation by Martin et al. (2011) and the glacial–interglacial parameterization by Pollard and DeConto (2009) tuned by de Boer et al. (2013) to produce realistic present-day Antarctic shelves and grounding lines. A more detailed explanation is provided by de Boer et al. (2013) and references therein. Ice calving is treated by a simple threshold thickness of 200 m, whereby any shelf ice below this thickness is removed. ANICE calculates ice-sheet evolution on four separate grids simultaneously, covering the areas of the large Pleistocene ice sheets: North America, Eurasia, Greenland, and Antarctica. The areas covered by the four model domains are shown in Fig. 4. Horizontal resolution is 20 km for Greenland and 40 km for the other three regions. Splitting North America and Greenland into separate model domains means the Laurentide and Greenland ice sheets can no longer merge in the north, which they might have done during the LGM. However, we assume this to be not important for the large-scale evolution discussed in this study.

In their 2013 study, de Boer et al. simulated global ice distribution and sea-level variation over the last 1 million years, forcing ANICE with the LR04 benthic δ18O record using an inverse routine. Their simulated LGM ice sheets are shown in Fig. 5. They showed that their results are in good agreement with existing independent literature in terms of sea-level contributions (Rohling et al., 2009; Thompson and Goldstein, 2006), seawater heavy isotope enrichment (Duplessy et al., 2002; Lhomme and Clarke, 2005), and other modelling studies (Huybrechts, 2002; Bintanja et al., 2005; Bintanja and van de Wal, 2008; Pollard and DeConto, 2009), although ice-sheet location and extent do not agree well with evidence from geomorphology (Ehlers and Gibbard, 2007; de Boer et al., 2013, and references therein). The latter is likely a result from the absence of feedback from the growth of large ice sheets onto large-scale atmospheric circulation patterns in the model, e.g. failing to reproduce the decrease in precipitation over the Barents Sea–Kara Sea area caused by the appearance of the large Fennoscandian ice dome, resulting in the appearance of an unrealistically large ice dome over the Barents Sea. The highly parameterized climate forcing and resulting computational efficiency of ANICE allow these transient simulations of multiple glacial cycles to be carried out within 10–100 h on single-core systems, making ensemble simulations feasible.

A climate matrix, as defined by Pollard (2010), is a collection of output data from different steady-state GCM simulations that differ from each other in one or more key parameters or boundary conditions, such as prescribed atmospheric pCO2, orbital configuration, or ice-sheet configuration. At every point in time during the simulation, the location of the model state within this matrix is extracted from the matrix by interpolating between its constituent precalculated climate states. The pair of climate states generated by Singarayer and Valdes (2010) using HadCM3 is based on otherwise identical input parameters that differ in two respects: pCO2 and ice-sheet coverage. These climate states can be viewed as points on a two-dimensional climate matrix, with pCO2 constituting one dimension and ice-sheet coverage constituting another. In order to calculate a climate state for intermediate pCO2 and ice-sheet coverage values, simple weight functions yielding linear interpolation in this climate phase space will yield the corresponding monthly temperature and precipitation fields. The weighting factor wCO2 is calculated as wCO2=pCO2-pCO2,LGMpCO2,PI-pCO2,LGM, with pCO2,PI=280 ppmv and pCO2,LGM=190 ppmv. Although the dependence of radiative forcing on pCO2 is logarithmic rather than linear, preliminary experiments showed that changing this in the calculation of the weighting factor did not result in significant changes in modelled sea level at the LGM considering the uncertainty from other model parameters.

To determine the position of the model state along the pCO2 dimension of the climate matrix, we use the EPICA ice-core record by Lüthi et al. (2008). However, the ice-sheet coverage dimension of the matrix, described by wice, is more complicated and cannot be adequately described by a single scalar weight function. Since a continental-sized ice sheet affects both local and global temperature mainly because of the increase in albedo, we chose to represent this process in the model by making the ice-sheet coverage dimension of the climate matrix a spatially variable field wicex,y calculated by scaling between the local absorbed insolation at present day and at the LGM. In this way the albedo feedback is captured more realistically. The absorbed insolation Iabs is calculated by multiplying incoming insolation at the top of the atmosphere QTOA (from Laskar et al., 2004) with the surface albedo α, the latter being calculated internally by ANICE: Iabsx,y=1-αx,y⋅QTOAx,y. The weighting field is calculated by scaling between the PI and LGM reference fields, winsx,y=Iabs,modx,y-Iabs,LGMx,yIabs,PIx,y-Iabs,LGMx,y, running from 0 at the LGM to 1 for the PI. To account for both local and regional effects, a Gaussian smoothing filter F with a radius of 200 km and a total average value are added to the weighting field: wicex,y=17winsx,y+37Fwinsx,y+37wins‾, with the weights of the respective unsmoothed, smoothed, and average values determined experimentally such that the precipitation on the ice-sheet flanks, resulting from applying the Roe precipitation model, has values similar to those on the flanks of the ice sheets in the reference GCM snapshots. The value of 200 km for the smoothing radius is based on de Boer et al. (2014), who used a similar smoothing procedure in their precipitation model. Preliminary experiments showed that changing this value did not result in significant changes in modelled LGM sea level, within the uncertainty arising from other model parameters. For all four ice sheets, these spatially variable ice-weighting fields are combined with the scalar pCO2 weight wCO2 to yield the final weighting parameter wtot: wtot=wCO2+wice2, which is used to linearly interpolate between the states in the climate matrix and calculate the reference temperature, precipitation, and orography. Preliminary experiments showed that changing the distribution of contributions from wCO2 and wice did not result in significant changes in modelled LGM sea level within the uncertainty arising from other model parameters. Since the two variables generally show coherent temporal behaviour, the two weighting factors are usually close together, meaning wtot does not change much when altering the distribution. When too much weight is given to wice (between 2 and 4 times more than wCO2), eventually a threshold is reached at which the drop in pCO2 during the early phase of the glacial cycle does not result in a strong enough cooling to trigger the growth of ice, thus breaking down this similarity.

Precipitation is customarily interpolated logarithmically to accurately reflect relative changes and to prevent the occurrence of negative values. Tref,GCMx,y=wtot⋅TPIx,y+1-wtot⋅TLGMx,yPref,GCMx,y=ewtot⋅log⁡PPIx,y+1-wtot⋅log⁡PLGMx,yhref,GCMx,y=wtot⋅hPIx,y+1-wtot⋅hLGMx,y

Being linear combinations of output data from a relatively low-resolution GCM, these three data fields necessarily have a lower resolution than the ice-sheet model to which they will be applied. To correct for this, the temperature and precipitation are adapted based on the difference between the interpolated reference orography href,GCM and the actual model orography using the approach by de Boer et al. (2013) described in Appendix A.

Since the relative changes in ice-sheet size for Greenland and Antarctica are much smaller than those for North America and Eurasia, the relative changes in absorbed insolation in those regions are proportionally smaller and should therefore have had less impact on local climate. For example, for North America the total absorbed insolation over the model grid at the LGM is 32 % lower than at present day, whereas for Antarctica this change is only 5 %. This is reflected in the model by giving more weight to the pCO2 parameter: GRL,ANT:wtot=3⋅wCO2+wicex,y4.

Preliminary experiments showed that here, too, the sensitivity of the modelled ice volume to this distribution is relatively low.

One of the major simplifications in the ANICE mass balance model is the assumption that temperature decreases linearly with altitude – the spatially and temporally constant lapse rate of -8 K km-1. As has been shown by de Boer et al. (2014), the methodology of combining this constant lapse rate with a global temperature offset derived from external forcing produced realistic results in terms of global and regional ice volume when simulating Pleistocene glacial cycles. However, even though the reference orography field obtained from the climate matrix is already close to the model orography and the correction applied to the GCM reference temperature field is therefore much smaller, preliminary experiments showed that even making these relatively small corrections using a constant lapse rate resulted in distorted results.

The limitations of this constant lapse rate procedure can be seen over the western part of Canada, an area that is hypothesized to have remained ice-free for the larger part of the last glacial cycle until a few thousand years before the LGM. Here, results from the LGM experiment with HadCM3 (Singarayer and Valdes, 2010) indicate mean annual surface temperatures of around 235 K, or -38 ∘C. When calculating this surface temperature following the approach by de Boer et al. (2014), starting with the present-day surface temperature at bedrock and scaling with the constant lapse rate of -8 K km-1 to the ice-sheet surface (with an ice thickness of up to 5000 m, as indicated by ICE-5G), the resulting value is about 220 K, or -53 ∘C, which is about 15∘C colder than calculated with the GCM, as shown in Fig. 6. A problem occurs during the inception and the subsequent build-up towards the LGM, when this area is still ice-free in the model. Using the GCM-generated temperature field as a reference and scaling this down to bedrock level will then result in surface temperatures that are actually warmer than present day. This is unlikely and results in overestimated melt rates near the ice margins.

A solution to this is to slightly adapt the constant lapse rate approximation. Assuming the GCM-generated temperature field at the LGM is still based upon the present-day temperature field plus a global offset and a (local) lapse rate correction, similar to the old ANICE method, this local lapse rate correction field is then calculated as λLGMx,y=-TLGMx,y-TPIx,y+ΔTLGMhLGMx,y-hPIx,y, and the downscaling from the GCM grid to the ice model grid, previously described by Eq. (A1), now being calculated as Tx,y=Trefx,y+λLGMx,yhx,y-hrefx,y, where the local lapse rate at the LGM, λLGM, is calculated by dividing the difference between the local GCM-calculated surface temperature, TLGM, and the extrapolated temperature at local bedrock altitude, Tbedx,y,t=TPIx,y,t+ΔTLGM, by the change in local orography, hLGM, with respect to present day (hPI). The temperature offset ΔTLGM is the mean difference in GCM-calculated temperature between the LGM and PI fields over the ice-free area in the respective model region (either North America or Eurasia) at the LGM. For North America, this results in a value of ΔTLGM=-14.9 K. This methodology ensures that when the modelled ice sheet is identical to the ICE-5G ice sheet at the LGM and the CO2 concentration is at the LGM value (190 ppmv pCO2), the temperature field that is used to calculate the mass balance is still identical to the GCM-calculated temperature field. It also guarantees that, when pCO2 is at 190 ppmv but no ice is present in the model, mean annual surface temperatures are uniformly lower than present day by ΔTLGM.

Of course, the latter scenario only occurs during non-physical steady-state experiments such as forcing ANICE with the LGM GCM climate but initializing with present-day ice cover. During transient experiments, the modelled ice sheets generally resemble those “expected” by the mass balance model through the climate state on which it is based, so the applied lapse rate correction is generally small. This variable lapse rate solution is used in the surface mass balance models for North America and Eurasia, since those regions see the dramatic changes in orography that require this correction. For Greenland and Antarctica, where the changes in ice cover are relatively small even during glacial cycles, the constant lapse rate is still applied with a value of 8 K km-1 based on earlier work with ANICE by Helsen et al. (2013) and de Boer et al. (2014).

Present-day observations from Greenland indicate that the effect a continental-sized ice sheet has on local precipitation is mostly due to geometry; more precipitation falls on the flanks due to orographic forcing, and as a result the dome becomes a plateau desert (Roe and Lindzen, 2001; Roe, 2002). The different character of this process calls for a different representation in the model than the absorbed insolation-based temperature calculation. In order to calculate monthly precipitation values, for North America and Eurasia we use the “local ice-weighting” method described by Pollard (2010). For every element of the spatial grid, ice thickness relative to the ice thicknesses at that element for the different reference GCM states, limited by the total volume of the ice sheet, is used to obtain the interpolation parameter for the ice dimension of the climate matrix. Although physically, precipitation is influenced by surface altitude and not ice thickness, the fact that the weight is calculated based on scaling the model state between two extremes means the end result is the same as long as the rate of change of ice thickness and surface altitude is the same. The discrepancy between the two is caused by isostatic adjustment. During the inception phase of the glacial cycle, the ice grows slowly enough that there is hardly any discernible time lag between ice thickness and surface altitude. During the deglaciation this is not true anymore, but since ice-sheet evolution during that phase is dominated by ablation rather than precipitation, a parameterization based on elevation instead of ice thickness yields similar results. The interpolation parameter for the “ice” dimension of the climate matrix wice is expressed as wicex,y=Himodx,y-HiPIx,yHiLGMx,y-HiPIx,y⋅Vmod-VPIVLGM-VPI, where Himod is the modelled local ice thickness and HiPI and HiLGM are the local ice thickness values in the reference fields from the GCM states. Vmod, VPI, and VLGM are the modelled and reference ice-sheet volumes. For Greenland and Antarctica, only the total ice volume limitation is applied and the interpolation weight is calculated as wicex,y=Vmod-VPIVLGM-VPI.

The first term in Eq. (12) describes the local ice-weighting method by Pollard (2010), whereas the second term describes the total ice volume scaling. Combining these two terms ensures that precipitation prescribed to the model only decreases over areas where the model actually simulates ice and that the drop in precipitation caused by the ice–plateau–desert effect scales appropriately with ice-sheet size. Since the thickness of a growing ice sheet levels off much earlier than its horizontal extent, an ice sheet only a quarter of its LGM extent can already have nearly the same maximum thickness. Scaling precipitation based on local thickness alone will therefore result in the ice plateau becoming too dry too early in the growth phase, limiting further growth. Preliminary experiments showed that including the total ice-sheet volume in the calculation of the weighting factor solved this problem, resulting in a growth rate more in line with expectations from sea-level records.

The reason that the local ice thickness term is absent in the calculation for Greenland and Antarctica shown in Eq. (13) is that the ICE-5G LGM ice sheets that were used to calculate the corresponding GCM states are, in many places, thinner at the LGM than at present day, even though the total volume of the ice sheet is larger. This would mean that an increase in modelled ice thickness would lead to an increase in applied local precipitation, causing unrealistic ice growth. Therefore, in order to prevent such unrealistic scenarios, precipitation is scaled only by the total ice-sheet volume.

For Greenland and Antarctica, the reference GCM precipitation field PGCM,ref is downscaled from the GCM to the ice-sheet model resolution based on the difference in temperature between the model state Tmod and the reference GCM state TGCM, as shown in Eq. (14), according to a Clausius–Clapeyron relationship similar to the approach by de Boer et al. (2014) described in Appendix A. This ensures that smaller-scale topographical features present in the model but not in the lower-resolution GCM have an influence on local precipitation through their effect on local surface temperature. Pmodx,y=PGCM,refx,y⋅1.0266Tmodx,y-TGCMx,y

Similarly, for North America and Eurasia, precipitation is adjusted using the Roe (2002) parameterization for the wind-orography-based correction of precipitation as described in Eqs. (A3)–(A6), but now by using the GCM-generated precipitation and orography as reference fields instead of their ERA-40 equivalents. This allows for a better representation of the orographic forcing of precipitation on the migrating ice flanks as these ice sheets advance and retreat, an effect that cannot be captured by interpolating by different GCM snapshots alone.

As a benchmark experiment, the new model set-up was used to perform a simulation of the last glacial cycle. The climate matrix for this experiment consists solely of the PI_Control and LGM experiments by Singarayer and Valdes (2010). Following the approach by Bintanja et al. (2002), the model was tuned by adjusting the ablation parameter c3 in Eq. (A9) individually for all four ice-sheet regions such that their modelled sea-level contribution at the LGM matched the values postulated by ICE-5G (Peltier, 2004). The resulting c3 values, which are hereafter kept fixed, are shown in Table 1. This 120 kyr simulation took about 12 h to complete on a single-processor system, meaning it is feasible to use this model set-up to perform ensemble simulations without demanding excessive amounts of computation time.

Shown in Fig. 7 are the results of this experiment in terms of the global mean sea-level contributions of the four separate ice sheets over time, as well as the total global mean sea level, together with the same values from a simulation of the same period of time with the default ANICE model forced with the LR04 benthic δ18O record using an inverse routine. As can be seen, the new model set-up obtains a close match to the postulated ICE-5G LGM ice volume for all ice sheets except Greenland. The resulting ice sheets at the LGM are shown in Fig. 8. As can be seen, the north-west Canadian corridor is now blocked by ice, which was still open in the default ANICE simulation shown earlier in Fig. 5. Although the main dome of the ice sheets is not as thick as in the ICE-5G reconstruction, it now lies more westward than in the simulation with the default ANICE model, forming a ridge running from midwest Canada to the eastern shores of Hudson Bay, which is in better agreement with the reconstruction. The southern margin lies too far to the north, varying from 400 km near the Atlantic coast to up to 950 km in the midwest. The Antarctic ice sheet now shows a much stronger increase in ice volume around the LGM, matching the 16 m of eustatic sea-level contribution postulated by ICE-5G (Peltier, 2004). Most of the ice mass increase takes place in West Antarctica; as can be seen, both the Ross and Ronne shelves become fully grounded. The Greenland ice sheet does show some minor growth over the glacial cycle, though not as much as postulated. It must be noted that several modelling studies of Greenland using the ANICE model (de Boer et al., 2013, 2014) have had trouble in this regard, mostly because of the difficulty in simulating the ice shelves that might have formed around the continent at the time but are not there now (Bradley et al., 2018).

The simulated Eurasian ice sheet is now in better agreement with the consensus regarding the Fennoscandian dome, as well as with the total ice volume or sea-level contribution. When simulated with the default ANICE version, the main dome of the Eurasian ice sheet forms over the Barents Sea, extending eastward to about 70∘ E. The new model set-up results in a dome over Fennoscandia and a smaller dome over the Barents Sea. The present-day southern North Sea area, formerly Doggerland, remains ice-free, in agreement with paleo-data (Hughes et al., 2016). Compared to the recent DATED-1 reconstruction of the Eurasian ice sheet (Hughes et al., 2016) at the LGM shown in Fig. 9, the modelled ice sheet does not extend as far south over northern Germany, Poland, and Lithuania. The simulated Atlantic side of the ice margin agrees well with the reconstruction, reaching the edge of the continental shelf everywhere.

Peltier (2004) provides an ice volume of the Eurasian ice sheet of about 17 m sea-level equivalent based on GPS observations of isostatic rebound, whereas Hughes et al. (2016) state a volume of 24 m based on geomorphological evidence of the extent and a logarithmic linear regression between ice-sheet area and volume. By slightly increasing the ablation tuning parameter, thus decreasing ablation and increasing ice volume, we were able to produce a Eurasian ice sheet with a volume of 24 m sea-level equivalent that matches the DATED-1 horizontal extent very well, as shown in Fig. 10. However, we believe that a “chain” of simulations such as this (an ice-sheet reconstruction, forcing a GCM, forcing an ice-sheet model) should aim for consistency first, meaning that the ice sheet produced at the end of the chain should match the one that was used as forcing at the start of the chain. Although there are more recent, more extensive data available for the volume and extent of the Eurasian ice sheet, prescribing to the ice-sheet model a climate that was calculated based on the presence of a different ice sheet would make it much more difficult to determine the cause of any model–data mismatch in the final results. We therefore did not use this new, probably more physically realistic Eurasian ice sheet as our benchmark.

In order to estimate the uncertainty in modelled global mean sea level following from the uncertainty in the EPICA pCO2 record, we performed simulations with the forcing record adjusted to its respective upper and lower bounds based on an LGM uncertainty of 10 ppmv (Lüthi et al., 2008). Additionally, we investigated the model sensitivity to the four ablation tuning parameters c3 for the different ice sheets mentioned earlier by performing simulations in which these parameters had been either increased or decreased by 10 % relative to their benchmark value. We also assessed model sensitivity to the SSA and SIA flow enhancement factors, with the upper and lower limits determined by Ma et al. (2010), in order to test the sensitivity to the ice-sheet dynamics. Results from these different sensitivity tests are shown in Fig. 11. The resulting uncertainty in simulated LGM ice volume amounts to about 6 m sea-level equivalent in either direction, about 6 % of the total signal, for both the CO2 and ablation parameter experiments. Sensitivity to the flow enhancement factor ratio is lower at about 4 % of the total signal.

Included in ANICE is a module that tracks the oxygen isotope abundances of the ocean (δ18Osw), precipitation, and the ice sheets. In the default ANICE version, an inverse routine is used to calculate a global temperature offset using the difference between modelled and observed benthic oxygen isotope abundance, implying that modelled and observed are per definition in agreement. In our new model set-up, the isotopic content of the ice sheets is still tracked, but now the global mean temperature anomaly from the climate matrix is used to determine a deep-water temperature anomaly (ΔTdw) and hence a modelled value for benthic δ18O. This deep-water temperature anomaly is calculated from the modelled mean annual surface temperature anomaly over the ocean following the approach by de Boer et al. (2014) using a 4000-year running average and a scaling factor of 0.25. As opposed to the approach by de Boer et al. (2014), in which an inverse method was used to match modelled benthic δ18O to an externally prescribed record, modelled δ18O can now be independently compared to such a record in order to test the performance of the matrix method.

We compared our modelled benthic oxygen isotope abundance and the relative contributions to this signal by seawater heavy oxygen enrichment and deep-water temperature change to the LR04 benthic oxygen isotope stack (Lisiecki and Raymo, 2005) to data by Shakun et al. (2015), who analysed 49 ODP drilling locations at which both surface-dwelling planktonic and benthic foraminiferal oxygen isotope abundance data were available, thereby allowing them to make a data-based decoupling of the contributions from ice volume and deep-water temperature to the benthic oxygen isotope signal. This model–data comparison is shown in Fig. 12. As can be seen, the results from the LGM benchmark experiment are in good agreement with the data, similar to the default ANICE model. The drop in benthic δ18O at the LGM of about 1.7 ‰ is reproduced comparably well by both the inverse-method-forced model by de Boer et al. (2014) and the new matrix-method-forced model set-up. The contribution from the change in deep-water temperature is slightly smaller in the new model set-up, though still in good agreement with the calculated global mean offset of 2 to 3 K at the LGM. The new model set-up fails to reproduce the strong drop in benthic δ18O during the inception of the glacial cycle, “catching up” at only 75 kyr.

Shown in Fig. 13 are the modelled mean annual surface temperature anomalies over the Antarctic and Greenland ice sheets for the simulation with the default ANICE version and for the LGC benchmark experiment compared to the EPICA Dome C reconstruction by Jouzel et al. (2007), a stack of the GISP2 reconstruction by Alley (2000), and the NGRIP reconstruction by Kindler et al. (2014). As can be seen, both model versions agree well with each other and reasonably well with the Greenland isotope-based reconstructions (Alley, 2000; Kindler et al., 2014) regarding Greenland surface temperature anomalies. The Greenland records have been smoothed with a 4 kyr running mean to filter out Dansgaard–Oeschger events, which are not present in our model forcing or climate reference runs and are also not included as feedback mechanisms in our model physics. Regarding Antarctic surface temperature anomalies, the new model set-up agrees particularly well with the EPICA isotope-based reconstruction (Jouzel et al., 2007), showing almost no significant deviations except for the first 20 kyr of the inception, during which the model fails to reproduce the observed rapid cooling.