All results in this paper are from CESMv2.1 CESM2.1;, a model which includes components for the atmosphere, ocean, sea ice, land, and ice sheets. The model has participated in the Climate Model Intercomparison Project 6 (CMIP6). Of the CMIP6 models, it is the only model providing an interactive calculation of the Greenland ice sheet (GrIS) SMB for all simulations and dedicated interactive GrIS simulation .

The atmosphere is simulated by a hybrid version of the Community Atmosphere Model CAM5; which combines version 5 (CAM5) physics with the sub-grid orographic form drag parameterization of CAM6. CAM5 physics was preferred over the standard CAM6 that was used in CMIP6 simulations due to the CAM6 physics yielding unrealistically high cooling under last glacial forcings . This excessive cooling is due to a high equilibrium climate sensitivity of 5.3 K that has been attributed to updates in cloud parameterizations introduced in CAM6 . A detailed comparison of CAM5 and CAM6 simulation of contemporary polar climate is given in .

The land model used in our simulations is the Community Land Model version 5 CLM5;. We turn off the anthropogenic influence (e.g. harvesting and irrigation) on vegetation. We use the River Transport Model RTM; rather than the default and more advanced Model for Scale Adaptive River Transport (MOSART), as the latter requires high-resolution input, which is not available for the LGM. CLM5 calculates the SMB over the ice sheets via an energy-balance model and uses an advanced simulation of snow and firn processes . The model simulates realistic contemporary ice sheet climate and SMB and has been applied to projections for the GrIS (). Sub-grid variations in the SMB are simulated with the use of 10 elevation classes . These elevation classes are active in CLM5 grid cells where both the land ice model is active and there is land ice present. We make two minor modifications to the default settings for the elevation classes parameterizations with the aim of reducing the magnitude and extent of the ablation zone. The first modification is an increase in the bare ice albedo from 0.4 to 0.5. The former relative low albedo used in Greenland simulations was partially motivated to account for the low albedo in the “dark zone” of the present-day southwestern ablation area. Second, we use different thresholds for repartitioning the precipitation phase between snow and rain. Precipitation falls exclusively as rain above 2 ∘C and snow below 0 ∘C, with mixed-phase precipitation between this range. These repartition thresholds are the same as used over vegetation by default in CESM2.1.

The atmosphere and land model are run at a horizontal resolution of 0.9∘ (latitude) × 1.25∘ (longitude); the ocean model (POP2) and sea ice model (CICE5) are run on a 1∘ displaced Greenland grid. In POP2 we do not include ocean biogeochemistry (MARBL), but the estuary model from is adopted. The overflow parameterization in POP2 was adjusted from the model's modern values due to the narrowing of Denmark Strait as a result of the larger-than-present GrIS. Also, part of Baffin Bay was closed due to excessive sea ice formation in connection with a narrower bay from the larger-than-present GrIS. This part is treated as covered with land ice.

The Community Land Ice Model version 2.1 CISMv2.1; is used as a diagnostic component, i.e. we do not run it with interactive ice sheets. The 4 km CISMv2.1 grid (Fig. ) provides high-resolution information for CLM5's elevation classes, as well as downscaled SMB (at 4 km resolution) by horizontal bilinear and vertical interpolation from the elevation classes. (Note that at present, precipitation is not downscaled.) In our simulations we produce elevation class information for SMB, 2 m air temperature across the CISM2.1 grid (Fig. ) of the Northern Hemisphere ice sheets but also across the Antarctic and Patagonia ice sheets (however, the latter are not analysed here).

We ran two 500-year simulations for a 26 ka BP (LG-26 ka) and a 21 ka BP (LG-21 ka) climate using the boundary conditions and glacial forcings listed in Table . The LG-21 ka simulation was initialized using two published 21 ka CESM simulations for the climate and ocean (Table ). The climate and ocean state at year 100 of LG-21 ka was used as the initial conditions for LG-26 ka. An offline glacial isostatic adjustment (GIA) model (see general description in ) was run to produce the initial 21 ka input boundary conditions which define the paleo-coastlines, topography, land–ocean mask, and ice sheet extent. The input ice sheet reconstruction used for the GIA model combines the Antarctic and Patagonia ice sheets from ICE5G ; the NAISC from GLAC1D , the GrIS from HUY3 , and the Eurasian ice sheet complex (BIIS; BKIS and SIS) from BRITICE-CHRONO (Fig. ). The GIA model output was regridded to a reference 10 min grid (bilinear interpolation) following the protocol as defined in PMIP4 (see Fig. 3 in ). An offline vegetation model BIOME4; was run with climate forcing from the LG-21 ka simulation to generate the vegetation distribution (see Appendix ).

Both our simulations overestimate the mean monthly sea ice extent relative to GLOMAP (Fig. b and d; Table ), with the area increasing in the colder temperatures of LG-26 ka and during the summer season. The timings of the Northern (Fig. b) and Southern Hemisphere (Fig. d) maximum and minimum sea ice extent are the same as for the present day but are delayed by 1 month relative to GLOMAP. Spatially, the differences are more complicated. During the summer in both the Northern and Southern hemispheres, LG-21 ka overestimates the spatial extent of the sea ice (Fig. a and c). For example, there are large areas of sea ice across the Norwegian and Greenland seas, which are ice free in GLOMAP. In the winter months, the simulation underestimates the sea ice in these regions, but it overestimates across the Bering Sea, Baffin Bay, and into the Labrador Sea.

Generally, LG-21 ka simulates colder ocean temperatures than GLOMAP (Fig. e and f) across large areas of the ocean, with the global mean SST -2.2 and -2.4 ∘C colder in winter and summer, respectively. This colder ocean may be one cause for the consistent overestimation in the sea ice extent. There are warm anomalies (reaching up to 8 ∘C), which are predominately concentrated in the Northern Hemisphere, extending from the NAISC across the North Atlantic Ocean to the BIIS and extending from the North Pacific Ocean (the Gulf of Alaska and Bering Strait) across to the Sea of Japan.

The Atlantic meridional overturning circulation (AMOC) strength (defined as the maximum AMOC transport at 30∘ N) is weaker, and the extent of the overturning cell is shallower in all three LGM simulations relative to the PI (Fig. b). The maximum strengths are 18.4, 17.1, and 16.6 Sv for LG-21 ka, LG-26 ka, and LGM-Zhu, respectively (Fig. b). As stated earlier, the LG-21 ka and LGM-Zhu simulations adopted different ice sheet reconstructions with the former including a revised overflow parameterization around Baffin Bay and Denmark Strait. A recent publication found that the ICE6G reconstruction (similar to LGM-Zhu) resulted in a stronger AMOC relative to GLAC1D (similar to LG-21 ka) due partly to higher elevation across the NAISC complex. This is the opposite of the results from this comparison, which highlights the complex non-linear interplay between the change in elevation across glaciated regions and the resultant impact on sea ice extent and AMOC strength . Two recent transient simulations for the LGM period found either no change in the AMOC between 26 and 21 ka BP or a minor weakening , which is similar to our findings.

The maximum extent of the overturning cell, defined as the depth for which the AMOC strength (at ∼30∘ N) is positive, shoals by ∼240 m for LG-21 ka and LG-26 ka and by 480 m in LGM-Zhu (Fig. b). The shoaling of the simulated glacial AMOC compared with the PI simulation is in agreement with most of the earlier LGM studies e.g..

Evaluating the AMOC strength from a depth–latitude viewpoint (Fig. c, d, and e), south of ∼50∘ N the AMOC is weaker and shallower in all three LGM simulations (LG-21 ka, LG-26 ka, and LGM-Zhu), while north of ∼60∘ N its signal is stronger and of similar vertical extent. Therefore, some of the differences between various studies may result from not adopting the same definition for the AMOC. Previous studies have suggested that the process of deep convection in the Labrador Sea is affected by the advancing of the sea ice in the lower temperatures of the glacial climate which, in turn, impacts the AMOC strength and geometry . As stated above, this is a region where LG-21 ka overpredicts the extent of the sea ice (Fig. a). Indeed, the winter mixed layer depth averaged over the subpolar North Atlantic is shallower by ∼400 m in the glacial simulations compared with the PI (Fig. a, b, and c). Therefore, our weaker AMOC may result from the overestimation of sea ice which limits the deep water formation producing a weaker overturning cell compared with the PI. In the Nordic seas, north of ∼60∘ N, the winter mixed layer depth is deeper in the glacial simulations compared with the PI (Fig. a, b, and c) which corresponds to the region of stronger AMOC ∼60∘ N (Fig. c, d, and e).

The LG-21 ka simulation top of the atmosphere (TOA) SWin is reduced (less insolation) with respect to the PI at northern and southern high latitudes during May–October and October–March, respectively (Fig. a). Tropical and subtropical regions experience a small positive change in insolation for most months, except between August and October where they have a small negative change in insolation. During these periods of reduced TOA SWin (-10 W m2), there is a much larger increase in the surface SWin (Fig. b), up to 100 m2, which can be linked primarily to changes in the cloud cover (Fig. c). Additionally, the presence of the extensive LGM ice sheets (Fig. ) combined with the increase in the spatial extent of sea ice into the mid latitudes (see Sect. ) increases the surface albedo (see Fig. f) which allows more multiple scattering and therefore also contributes to the increase in the surface SWin. In all high latitude regions showing enhanced surface SWin, SWnet (Fig. d) is reduced due to overcompensation from higher surface albedo (Fig. f).

The surface incoming longwave radiation (LWin; Fig. e) is reduced at all latitudes and times of the year with respect to the PI with the largest anomalies corresponding to the areas of largest cooling over the ice sheets (Fig. a)and expanded sea ice cover. The temporal and latitudinal pattern of surface net longwave radiation (LWnet; Fig. f) shows both positive and negative anomalies (positive corresponds to net radiation gain by the surface), with net radiation loss over the Northern Hemisphere ice sheets during the summer and, in the tropics, all year long. The magnitude of this summer reduction in LWnet over the ice sheets is smaller than for SWnet.

We continue our analysis of atmospheric change by examining changes in the atmospheric circulation (asymmetrical component of the geopotential height) and their connections with cloud change (Fig. ). Around the NAISC, two circulation anomalies appear (Fig. a and b). On the western coast of North America across the CIS, the PI winter ridge is intensified and extends further towards Asia. The winds associated with this ridge transport warm and moist air from the Pacific to Alaska. Across the east coast of North America and the LIS, a negative response occurs, due to the strengthening and southward elongation of the Greenland climatological low, extending the persistent inflow of Arctic air towards the North Atlantic margin. This response strengthens the geopotential gradient between the Atlantic and LIS, suggesting higher wind speeds of the polar jet.

The winter climatological ridge (Fig. a) which brings warmer and moister air from the North Atlantic towards Europe is weakened along its northern flank, which results in drier and colder Arctic air over northern Europe. On the Asian side, the Aleutian low is weakened. The summer circulation responses (Fig. b) are weaker than in winter. There is a negative response over the LIS, which represents a narrowing of the Rocky Mountain ridge and a strengthening and enlarged Greenland low. This change in summer circulation results in a reduction in temperature across the LIS during the LGM (Fig. a). There is a positive response in the North Atlantic which extends across the BIIS. As both these responses strengthen the PI climatological features, they sharpen the geopotential gradients and give rise to higher wind speeds, which is indicative of increased synoptic eddy activity. The circulation anomalies in LG-26 ka are very similar which suggests they are not strongly influenced by the changes in orbital forcing.

To investigate further the influence of clouds on the radiation fluxes, we examined the change in cloud liquid and ice content (Fig. d and e). Clouds with a higher liquid content will block incoming solar radiation, whereas ice is nearly transparent to incoming solar radiation. During the summer, there is very little cloud liquid water across the ice sheets (Fig. c), a significant reduction compared with the PI (Fig. d). This is caused by the increase in elevation, a relatively high cloud liquid water in the PI, as well as the negative circulation anomalies (Fig. b) making these areas receive more dry and cold Arctic air. Therefore, the positive anomalies in the SWin (Fig. a) are in part due to a reduction in cloud liquid. Conversely, there is a small increase in cloud ice water (Fig. e and f), a feature that is common over current ice sheets, due to the colder temperatures and higher elevation .

In summary, we see large differences in circulation, clouds, temperature, and precipitation between the LG-21 ka and PI climates, some of them largely connected with the presence of large ice sheets in the Northern Hemisphere. The circulation in LG-21 ka suggests more advection of Pacific air towards Alaska, bringing more moisture which increases precipitation and thickens clouds. In the interior of the NAISC (across the Laurentide ice sheet) there is an anomalous trough, which likely brings in drier Arctic air, leading to thinning of clouds, less precipitation, and much lower air temperatures than in the PI. In LG-21 ka the temperatures are lower around Greenland, particularly in the west where the PI low gets strengthened. The Eurasian ice sheets experience similar responses to those of the Laurentide: wetter in the south and drier in the interior and north.

Figure  shows a comparison of the spatially averaged SMB and its components across the six major Northern Hemisphere ice sheets with the corresponding values for the present-day ice sheets of Greenland and Antarctica . Average values have been chosen to compare different ice sheets regardless of their different areas.

The averaged SMB of the IcIS, SIS, GrIS, and BKIS is positive, with the latter two results of similar value to present-day Greenland and Antarctica (around 200 mm yr-1). The similarity in the simulated mean GrIS SMB is the result of the almost zero melt rate (Fig. e) at the LGM combined with the ∼50 % reduction in the snowfall rate (200 mm yr-1 at the LGM versus 400 mm yr-1 for present day; Fig. b). These differences in the SMB components are associated with the lower temperature and drier LGM climate (Fig. ).

The LG-21 ka GrIS excluding the wetter southeast margin (Fig. b) and BKIS have similar mean SMB and components: low snowfall rates, zero rainfall and melt (except for a narrow band in southwest Greenland), and interiors with low net snow deposition (Fig. b) contrasting with low sublimation-dominated margins (Fig. f). All other ice sheets have large areas of melt which largely correspond with the relatively wide ablation areas (Fig. a and e). The SIS has a mean SMB that is half of the BKIS, regardless of more than double the snowfall rates (Fig. b), with a value very similar to that of present-day Greenland. This is due to relatively large melt rates (almost double than for present-day Greenland). The SMB of the IcIS is the largest of all the six ice sheets, due to a very high snowfall rate (Fig. b) that is only partially compensated by melt rates of a similar magnitude to those of present-day Greenland.

Two ice sheets have an extremely negative SMB across the ablation area: NAISC and BIIS. The CIS, which is part of the NAISC, has a wide ablation area along the southern and western (Pacific) margins, with the latter corresponding to the high snow accumulation rates over the high elevation of the Sierra Nevada mountain range (Fig. b). For the LIS, the high ablation and melt area extends along the entire southern margin, even over the relative high elevation of the southern (Atlantic) margin, due to the relatively high summer temperatures (Fig. ). High refreezing rates are simulated along the equilibrium line altitude, at the transition between the accumulation and ablation zone along the southern margin (Fig. d). Both these ice sheets (CIS and LIS) have high rainfall rates and inverse sublimation (or snow deposition) along the marine terminating margins not bordered by sea ice (see Fig. a), with mean values more than double present-day Greenland and Antarctica, respectively (Fig. c and f). The BIIS has the lowest mean SMB of the six ice sheets, despite having the second largest snow accumulation. The simulated ablation areas cover most of the ice sheet except for a minimal accumulation area in the interior, across the higher elevation of Scotland (Fig. a). The entire ice sheet surface melts seasonally (Fig. e), with average melting rates almost an order of magnitude larger than for present-day Greenland.

If the simulated SMB, including the very wide and negative ablation area of the NAISC and BIIS, was applied to a dynamic ice sheet model (for example, CISM2.1; ), it would be highly unlikely/challenging that the spatial extent of the southern margin in either ice sheet would be maintained; rapid retreat would likely occur. However, as outlined in Sect. 1, the timing of the LGM for both these ice sheets was earlier than the historical 21 ka BP definition (25 ka BP for NAISC and 23 ka BP for BIIS). Therefore, an earlier time step in this 6 ka period may be more appropriate to simulate the glacial maximum for these ice sheets. For this reason, in Sect. 4.3, we compare the LG-21 ka simulation with LG-26 ka.

Here we will examine the components for the summer (JJA) energy budget over all Northern Hemisphere ice sheets (Fig. ). Melt is simulated across all margins of the major six continental ice sheets (Fig. a) apart from those bordered by sea ice (Fig. ), for example, the BKIS, the eastern margins of GrIS, and the arctic sea margin of the LIS.

Incoming solar radiation is high in the interior of the NAISC, GrIS, and SIS with much lower rates at the margins (Fig. b). Minimum incoming solar radiation is simulated over the southern and Atlantic margins of the NAISC and over the BIIS, due to higher amounts of cloud water over those ablation areas. An increase in shortwave radiation towards the higher elevation in the interior of ice sheets is also a feature of the present-day GrIS and is simulated by regional and global climate models . Conversely, maximum incoming longwave radiation is simulated over the margins which have higher temperatures, except for northern North America, GrIS, and BKIS (Fig. c). Compared with the PI simulation, across the ice sheets there is an increase in cloud fraction (i.e. gets cloudier), but the clouds are thinner. These two specific changes in the nature of the clouds can be related to the earlier responses in the radiation fluxes (see Sect. 3.3). Thinner clouds act to increase the incoming solar radiation at the surface (Fig. a). Conversely, in cloudier areas, the clouds increase the incoming longwave radiation, although the clouds are thinner (Fig. g and h).

Summer surface albedo (Fig. f) is minimum (between 0.5 and 0.55) over the ablation areas corresponding to bare ice exposure. The highest albedo values (>0.80) correspond to dry snow areas extending from northern Canada, where the LIS and Innuitian ice sheet (IIS) coalesce, into central and southeastern Greenland, the interior of IcIS, and most of the BKIS. The combination of this spatial albedo pattern and the reduction in incoming solar radiation over the ablation areas (Fig. b) results in maximum net solar radiation over the southern regions of the NAISC and SIS ice sheet margins (Fig. d). The sensible heat flux (SHF) provides energy for the surface over most of the ablation areas and all over Greenland. The largest flux towards the atmosphere is simulated at intermediate elevations, just above the equilibrium line altitude of the southern half of the NAISC. The latent heat flux (LHF) is positive (directed towards the surface) over a somewhat narrower band than the sensible heat flux along the lowest part of the ablation areas and is negative over the rest of the ice sheets. The positive LHF anomaly along the southern margin of the ice sheets is due to prolonged bare-ice exposure, whereas when relatively warm and moist air is advected over this region condensation occurs . The ground heat flux (GHF) provides energy to the surface along the areas with maximum refreezing (cf. Figs. d and i), due to the heat released in the refreezing process.

The LG-26 ka simulation results in an SMB increase with respect to LG-21 ka for the NAISC, BIIS, and SIS (Figs.  and a), with the largest absolute difference for the BIIS. However, for the NAISC and BIIS this does not reverse the SMB sign, which if applied to an offline ice sheet dynamical model would likely initiate retreat. This increase in the SMB is primarily caused by a reduction in the melt rates (Figs. e and e). Over the BIIS, a small increase in snowfall contributes secondarily to higher SMB and is related to a cooling-related reduced fraction of precipitation falling as rainfall (Figs. c and b). concluded that a warming of the climate after 26 ka, and the resultant reduction in SMB, was in fact required to initiate the retreat of the BIIS at 21 ka. Therefore, the 1.5 ∘C warming between LG-26 ka and LG-21 ka due to the change in orbital parameters may be one factor that led to the retreat of the BIIS, due to the increase in melt rate (Fig. e).

Over the other five ice sheets, snowfall rates are lower in the LG-26 ka simulation compared with LG-21 ka. Mean rainfall rates decrease over all ice sheets, apart from the two driest (GrIS and BKIS) where it remains almost zero. The largest reduction is over the ice sheets with a prominent North Atlantic climate (BIIS and cIS).

The SMB is lower in LG-26 ka with respect to LG-21 ka for the two ice sheets with almost zero melt (GrIS and BKIS) and the IcIS, which has relatively low average melt rates. This decrease is due to reduced snowfall (Fig. b). A fall in melt rates at LG-26 ka results in a refreezing reduction over all ice sheets except for the BIIS, where the combination of a large reduction in melt and rainfall and a minor increase in precipitation results in an increase in refreezing (Figs. d and d). Spatially (Fig. a), the SMB increases over the ablation areas and decreases in the accumulation areas, the latter being due to reductions in snowfall (Fig. b). Snowfall increases and rainfall decreases along the western margin of the NAISC in connection with colder temperatures (Fig. b). Refreezing increases over the ablation areas in connection with a cooling-induced increase in the refreezing capacity, and decreases over the percolation areas, as a result of the reduction in melt (Fig. d and e).