We use the EBM to calculate and downscale the SMB from the coarse-resolution atmospheric model grid of MPI-ESM onto high-resolution ice-sheet topographies. The main challenge in downscaling the SMB is to realistically capture the small-scale features of both melt and accumulation. Melt and accumulation are highly dependent on the topographic height; e.g., at a given time, low elevations might experience melt, while higher elevations remain frozen. Projecting melt and accumulation on a topography with better-resolved vertical gradients has therefore a significant impact on the SMB. Hence, differences between the original and downscaled SMBs are mainly a result of differences in the elevation rather than the horizontal grid refinement. To account for this, we employ a 3-D EBM scheme that is forced with high-frequency atmospheric data. The EBM scheme is an enhanced version of the energy and mass balance code that has been used to couple the ice-sheet model SICOPOLIS to a previous version of MPI-ESM . The main improvements are (1) an advanced broadband albedo scheme considering aging, snow depth dependency, and the influence of the cloud coverage on the thermal radiation, (2) the consideration of snow compaction and the vertical advection of snow and ice properties, (3) rain-induced change in the heat content of the snow layers, and (4) an enhanced refreezing scheme. We further adapted the scheme by introducing elevation classes, following . Calculating the SMB on fixed elevation levels has the advantage that the model becomes computationally cheaper and that the obtained 3-D fields can be interpolated onto different ice-sheet topographies (see Sect. ). Note that an elevation dependence of the SMB components is a simplified assumption and valid mainly for present-day Greenland. Atmospheric dynamics also significantly contribute to variations in the SMB components, specifically over present-day Antarctica. In the following, we present the basic structure of the EBM, including its improvements compared to the scheme used in .

The simulations in this study are performed with the Max Planck Institute for Meteorology Earth System Model MPI-ESM, version 1.2; see, consisting of the spectral atmosphere general circulation model ECHAM6.3 , the land surface vegetation model JSBACH3.2 , and the primitive equation ocean model MPIOM1.6 . Two different resolutions are used for the simulations. (1) For calculating the SMB over the last deglaciation, MPI-ESM is used in its coarse-resolution (CR) setup, hereafter referred to as MPI-ESM-CR. In this setup, ECHAM6.3 has a T31 horizontal resolution (approx. 3.75∘) with 31 vertical hybrid σ levels which resolve the atmosphere up to 0.01 hPa , and MPIOM1.6 has a nominal resolution of 3∘ with two poles located over Greenland and Antarctica . The selected setup is a compromise between computational feasibility and model resolution. (2) We additionally use a simulation with the low-resolution version of MPI-ESM1.2, hereafter referred to as MPI-ESM-LR, in which ECHAM6.3 has a T63 spectral grid (approx. 1.88∘) with 47 vertical levels, and MPIOM features a 1.5∘ nominal resolution. For model details, see .

We performed different simulations with the MPI-ESM-CR setup: (1) simulations to investigate the SMB throughout the last deglaciation, starting at 26 ka until the present (here, defined as 1950), and (2) simulations to evaluate the SMB for historical climate conditions (see Table ). For the deglaciation experiment, the model was started from a spun-up glacial steady state and integrated from 26 ka until the year 1950 with prescribed atmospheric greenhouse gases and insolation . The ice sheets and surface topographies were prescribed from the GLAC-1D reconstructions see standardized PMIP4 experiments. We focus our analysis on the last 21 kyr of the simulation. Hereafter, this simulation is referred to as MPI-ESM-CR deglaciation experiment. All forcing fields are prescribed every 10 years and initiate changes in the topography and glacier mask, as well as modifications of river pathways, the ocean bathymetry, and the land–sea mask . Freshwater from changing ice sheets is calculated from the thickness changes in the ice-sheet reconstructions for each grid point. For grid cells over land, meltwater is distributed through the hydrological discharge model, and over ocean it is discharged into the adjacent ocean grid cells. Ocean cells that become land due to changes in the sea level are initialized with the same vegetation form as the adjacent grid cells, while land cells that are deglaciated are covered with bare soil. After this initialization, the vegetation of the grid cells evolves interactively with JSBACH. Anthropogenic forcing, such as land use, is turned off in this simulation. For calculating the SMB, relevant variables of the atmospheric component of MPI-ESM1.2 are written out hourly throughout the simulation. Using the obtained atmospheric fields within the EBM (see Sect. ) results in 3-D SMB fields which are then interpolated onto the GLAC-1D topography and ice mask . Computing a 3-D SMB also allows us to calculate the equilibrium line altitude (ELA), the elevation at which the SMB equals zero. At heights above the ELA, it is thermodynamically possible to accumulate snow throughout the year and form an ice sheet or glacier. At elevations below the ELA, melt dominates accumulation, and no ice sheet can form. Here, the ELA is calculated in each grid point, hence, resembling a potential ELA. It is a proxy for climate changes affecting the ice sheets. As the ELA estimate is calculated on the native model grid, it is more consistent with the model physics and boundary conditions used in the simulations than the downscaled SMB. Hence, integrated values of the ELA are less sensitive to changes in the ice-sheet mask than those of the SMB.

For the evaluation of the derived SMBs under historical climate conditions, we branched off a last millennium simulation at 950 years BP (years before present) from the deglaciation experiment. Within PMIP, last millennium simulations are used to provide a seamless transition between the last deglaciation and the historical period . For the simulation, topography, land–sea and glacier masks, river pathways, and the ocean bathymetry are taken from the deglaciation experiment and kept constant at 950 years BP. Other forcing fields are adopted according to the PMIP3 standard protocol for the last millennium simulations and updated every year. The forcing fields for the years 1850 to 2010 are taken from the CMIP6 simulations see. For the years beyond 2010, the forcing fields in the desired resolution were not available at the time of the analysis. Overall, the applied forcing allows for a more realistic treatment of atmospheric processes associated with changes in, e.g., ozone, aerosols, CO2 concentrations, and land use, and it accounts for their climatic impacts for present-day climate conditions. Specifically, we apply time-varying greenhouse gases (CO2, N2O, CH4), volcanic forcing, ozone, tropospheric aerosols, and land-cover changes see. For the evaluation, only the years 1980–2010 are used, which allows for a sufficient adjustment of the model to changes in the forcing. We hereafter refer to this simulation as the MPI-ESM-CR historical experiment. Note that changes in the topography due to ice sheets are small between 950 years BP and 2010. Hence, we expect only a minor impact on the obtained SMBs.

Additionally, we performed a deglacial, last millennium, and historical simulation in which ice sheets and topographies are prescribed from ICE-6G reconstructions , an alternative reconstruction often used as boundary forcing in deglacial simulations . Results from these simulations, hereafter referred to as MPI-ESM-CRIce6G experiments, are shown in Appendix 1 and emphasize differences in the SMB and relevant fields due to different ice-sheet boundary conditions. While the SMB response to the climate forcing in these simulations is qualitatively similar to the MPI-ESM-CR simulations forced with GLAC-1D reconstructions, differences in the freshwater runoff between the reconstructions lead to a different climate response in the model simulations.

For a thorough evaluation of the EBM and in order to investigate the effect of model resolution on the historical SMB, we additionally calculate the 3-D SMB fields from a CMIP6 historical simulation with the MPI-ESM-LR setup see Sect. ;. The simulation allows us to further evaluate the EBM and to investigate differences in SMBs in regards to the spatial model resolution, as well as differences due to the underlying topographies. This simulation is hereafter referred to as MPI-ESM-LR historical experiment.

The 3-D fields derived for all historical control simulations are 3-dimensionally interpolated onto the ISMIP6 topography and masked with the ISMIP6 ice mask see Sect. ;.

To evaluate the EBM with respect to the atmospheric forcing data and its resolution, we additionally force the EBM with ERA-Interim reanalysis data from the European Center for Medium-Range Weather Forecasts ECMWF;. ERA-Interim was chosen as it is used as boundary forcing in the RCM simulations, which are used for a more thorough evaluation and are introduced at the end of this section. For comparison, we interpolate the ERA-Interim derived 3-D SMB fields onto the ISMIP6 topography and mask it with the ISMIP6 ice mask (see Sect. ). ERA-Interim is available as 6-hourly data at a 0.75∘ × 0.75∘ horizontal resolution. ERA-Interim assimilates a great fraction of in situ and remote sensing observations, making it one of the best reanalysis products available . However, as reanalysis data sets are model products, they exhibit biases specifically for variables associated with small-scale processes and areas where in situ observations are sparse e.g., precipitation, clouds;. These biases are not unique to ERA-Interim but can be found in other reanalyses . Relevant biases for this study are discussed in Sect. .

Additionally, we compare the obtained SMB data sets from the MPI-ESM historical experiments to SMBs derived with MAR (version 3.9.6). For a detailed description of MAR and its setup, see . The MAR simulation used in this study was run at a 15 km horizontal resolution with ERA-Interim boundary forcing and interpolated onto the ISMIP6 topography , as described in .

Accumulation patterns in MAR and the three EBM simulations are similar. However, they show some differences in the low-elevation areas in the southeast of the ice sheet and the northern plateau (Fig. ). Integrated over the ice sheet, EBMERAI, EBMMPI-ESM-CR, and EBMMPI-ESM-LR simulate lower accumulation than MAR, as well as the Regional Atmospheric Climate Model RACMO; Table ;. This difference is associated with less snowfall and more rainfall in ERA-Interim and the two MPI-ESM simulations than in the regional models, specifically in the low-elevation areas along the coastal areas of Greenland (Fig. ). The underestimation of ERA-Interim's snowfall that extends into the high-elevation areas of the ice sheet is likely associated with an unrealistic representation of clouds and a low cloud bias, as well as shortcomings in modeling seasonal changes in surface temperatures see Sect. ;. In the higher-elevation areas of most of the central parts of Greenland, MPI-ESM-CR and MPI-ESM-LR overestimate snowfall, which is tightly linked to topographic differences underlying the models, as well as model biases in the atmospheric circulation patterns affecting precipitation Fig. ;. Areas that are lower in MPI-ESM-CR and MPI-ESM-LR than MAR, mainly due to the spectral smoothing in MPI-ESM, generally show more snowfall in the MPI-ESM simulations (Fig. ). Comparing the accumulation derived from EBMMPI-ESM-CR with EBMMPI-ESM-LR shows that accumulation patterns in the southeast of the ice sheet are more confined towards the east coast, but EBMMPI-ESM-LR still presents a significant underestimation of accumulation in the low-elevation areas. Hence, even the higher resolution of MPI-ESM-LR is not sufficient to represent the regionally confined processes that determine the accumulation in these regions. The overestimation of accumulation in the north of the ice sheet is reduced in EBMMPI-ESM-LR compared to EBMMPI-ESM-CR. The reduction is likely associated with a better representation of the topographic gradients in the MPI-ESM-LR version of the model and an associated shift in precipitation patterns reducing precipitation at higher elevation. The comparison between EBMMPI-ESM-LR and EBMMPI-ESM-CR indicates that an increase in resolution should not always resolve all biases. This is in line with findings by showing that a regional grid refinement in simulations with the Community Earth System Model (CESM) did not improve all SMB components. Model biases, e.g., in the large-scale circulation, clouds, and precipitation patterns , as well as uncertainties due to internal variability, are exhibited in all ESMs and explain part of the differences seen in the presented comparison.

Note that the EBM calculates snowfall as precipitation at temperatures below 0 ∘C and partly compensates for these differences in snowfall and rainfall specifically along the coastal areas in the west and southeast of the ice sheet (not shown). The seasonal differences are larger. In summer, ERA-Interim simulates less snowfall and more rainfall but shows slightly less total precipitation than MAR, which impacts the melt patterns (not shown).

Integrated over the ice sheet, EBMERAI, EBMMPI-ESM-CR, and EBMMPI-ESM-LR simulate less melt than MAR and RACMO (Table ), but the sign of the differences varies significantly depending on the region (Fig. ). EBMMPI-ESM-CR shows significantly more surface melt along the western margins of the ice sheet than MAR (Fig. ). These areas are topographically higher in MPI-ESM-CR than the ISMIP6 topography (Fig. ). One problem of downscaling melt in these regions is that temperatures are always at the freezing point during melting. By projecting the temperatures onto lower elevations, the height-corrected temperatures depart significantly from the freezing point towards higher temperatures. Hence, the vertical downscaling from higher elevations to low elevations overestimates melting. In contrast, the area in the south that is significantly higher than the ISMIP6 topography shows less melt. It indicates that most of the differences are closely related to differences in the topography. Comparisons with EBMMPI-ESM-LR, which shows less melt in the north and west of the ice sheet compared to EBMMPI-ESM-CR (Figs.  and ), confirm that differences in the melt patterns are linked to the underlying topographies of the model versions. MPI-ESM-LR is slightly higher than MPI-ESM-CR and thereby closer to MAR on the northern and western flanks of the ice sheet; hence, EBMMPI-ESM-LR shows less melt than EBMMPI-ESM-CR in these areas. EBMERAI shows less melt in the southern and western parts of the ice sheets than MAR. These low melt rates are partly a result of the model tuning towards a similar integrated Greenland SMB value (see Table ).

Heat fluxes towards the surface control predominately surface temperatures and melting. , who compared surface energy fluxes over Greenland from different reanalyses with surface observations, found that ERA-Interim largely underestimates downward longwave and shortwave radiation, which is likely associated with an unrealistic representation of cloud optical properties. Low surface albedos in ERA-Interim and an associated underestimation of outgoing shortwave radiation partially compensate for the downward longwave radiation deficit. Further, seasonal biases in the latent heat fluxes dampen the seasonal changes in surface temperatures. Such biases are not unique to ERA-Interim but can also be found in other reanalyses for details see and models, such as MAR . We find similar biases in the EBMMPI-ESM-LR simulation which are likely associated with the simulated cloud cover.

As the SMB is highly dependent on the prescribed ice-sheet geometry, it is challenging to interpret SMB changes for ice sheets that undergo substantial geometry changes throughout the deglaciation. As all Northern Hemisphere ice sheets except Greenland disappear entirely, we investigate the SMB evolution mainly for Greenland, where changes in the geometry were relatively small (Fig. , gray line in the top panel). Values for the SMB, ELA, accumulation, and melt integrated over Greenland are shown in Fig. . The SMB and ELA for six time slices of the deglaciation are shown in Fig.  in order to indicate the most drastic changes in the Northern Hemisphere ice-sheet configuration.

Cold Northern Hemisphere temperatures during the Last Glacial Maximum (LGM; approx. 21 to 19 ka) are associated with a positive Greenland-wide integrated SMB of about 380 Gt a-1. This SMB is dominated by accumulation, while melt is close to zero (Figs.  and ). This result is consistent with the Greenland ice sheet being close to its maximum extent during this period . Due to the increase in temperatures following an increase in Northern Hemisphere summer insolation by approximately 7 % of the LGM value and a simultaneous increase in the global CO2 concentrations from 187 ppmv (parts per million by volume) at 19 ka to 228 ppmv at 15 ka, both accumulation and melt increase. The total accumulation over Greenland increases from about 420 Gt a-1 at 19 ka to about 670 Gt a-1 at 15 ka (more than 35 %). The largest accumulation increase is evident over the southwestern part of the ice sheets, which is associated with more precipitation (Fig. ). Intriguingly, the increase in precipitation is not a uniform signal for the entire Northern Hemisphere but shows regional patterns, such as a decrease over parts of the North Atlantic and south of the Laurentide ice sheet edge. These patterns indicate that precipitation changes are not entirely thermodynamically driven (the atmosphere being able to hold more water with increasing temperatures) but points towards changes in the atmospheric dynamics. Melt increases from about 0 to 25 Gt a-1 between the LGM and 15 ka. The growing melt is small and limited to the low-elevation areas along the coast of Greenland. This growth is a consequence of increasing summer temperatures that exceed the freezing point in these areas and lead to enhanced melt during summer. In the other areas over Greenland, temperatures are, despite warmer summers, still too cold to trigger melt. As the increase in accumulation dominates enhanced melting, the SMB time series increases until about 15 ka (Figs.  and ). Interestingly, the ELA increases despite an SMB increase. Per definition, the ELA depends directly on shifts in areas of net melt and accumulation. Hence, it closely follows the increase in the ablation area. From the LGM to 15 ka, the area of net ablation increases from 0 to about 58 400 km2.

A simultaneous increase in SMB and ELA seems to be counterintuitive at first given that in a present-day climate, a decrease in SMB over Greenland is associated with an increase in the ELA and vice versa e.g.,. As the climate warms, the area of net ablation expands, while the area of net accumulation recedes, which moves the ELA upward. As melt is close to zero in the glacial climate, the SMB is dominated by the significant growth of accumulation due to warmer atmospheric temperatures and the associated increase in precipitation. The dominance of the accumulation in controlling the SMB explains the counterintuitive behavior of the SMB and ELA in the glacial climate. Further, it suggests that changes in the ELA cannot be taken as a proxy for changes in the SMB.

At around 14.6 ka, the SMB and ELA over Greenland decrease significantly for about 500 years, the SMB drops from about 630 to 380 Gt a-1, and the ELA decreases from more than 460 to 120 m (Fig. ). Regionally, differences are even larger (Fig. ). These drastic changes are associated with a significant reduction in the AMOC as a response to increased inflow of freshwater from melting ice sheets into the global ocean, as prescribed from the GLAC-1D ice-sheet reconstructions. The strong meltwater pulse leads to a near shutdown of the thermohaline circulation and a significant cooling of the North Atlantic and adjacent regions (Fig. ). Although the largest cooling is occurring over the North Atlantic, the annual cooling signal extends over large regions of the Northern Hemisphere, including the Arctic Ocean, the North Pacific, and large parts of Eurasia and North America (Fig. ). Over Greenland, this cooling diminishes surface melt during summer, which is similar to LGM conditions. Again, the largest response is evident over the low-elevation areas along the southern coasts of Greenland (see also Fig.  for similarities). Associated with the overall cooling is a decline in precipitation which reduces accumulation by more than 40 % over the ice sheet. Although melt and accumulation again partly compensate for each other, accumulation changes occur over a much larger area and dominate changes in melt so that the integrated SMB decreases for Greenland (Fig. ).

After the recovery of the AMOC at around 14 ka, the SMB declines, and the ELA continues to move upward. It thereby follows the overall warming signal as a response to increasing insolation and atmospheric greenhouse gases (Figs.  and ). The decline in the SMB is associated with an overcompensation of the accumulation by a significant increase in melting. Thus, ELA and SMB are anticorrelated from about 14 ka onward and continue to increase and decrease, respectively. Only at around 13.6 and 11.6 ka do the ELA and SMB decrease significantly again due to a second and third weakening of the AMOC. Similar to the first AMOC decline, the associated cooling of the North Atlantic and parts of Greenland leads to a decrease in accumulation, melt, and the ELA (Fig. ). The changes are regionally very similar to the first event (Fig. ). However, the Greenland integrated SMB shows a weaker signal in both cases than during the first freshwater event as the changes in accumulation and melt partly compensate for each other when integrated over the ice sheet (Fig. ).

After the two AMOC events, the retreat of the Greenland ice sheet towards its present-day state continues and is associated with a decrease in SMB and an increase in ELA. The minimum SMB (216 Gt a-1) is reached at 8.7 ka, and the maximum ELA (1556 m) occurs at 9.3 ka (Figs.  and ), corresponding to the Holocene Thermal Maximum for a recent review, see. Due to the continuing deglaciation, Greenland experiences its largest ice volume and extent changes between 10.8 and 9.1 ka (the ice-sheet geometry influences SMB values during this period). At around 11.1 ka, the Northern Hemisphere summer insolation reaches its maximum and decreases continuously thereafter until the present, while the CO2 concentration remains rather constant between 11.1 and 6 ka and slightly increases thereafter. Consequently, the ELA decreases, and the SMB begins to recover continuously after about 8.7 ka. Note that a series of smaller AMOC weakening events is evident at around 10.1, 8.4, and 7.1 ka, but their climate impact on the ELA and SMB does not manifest significantly in the time series for Greenland (Fig. ). The ELA decrease and SMB increase continue until 200 years BP despite a slight increase in the CO2 concentration. These continuing changes suggest that the decreasing summer insolation drives SMB and ELA changes between 9 ka and 200 years BP. It is not before 100 years BP that the ELA and SMB closely follow the CO2 signal again. The sharp drop in the SMB and the uplift of the ELA for the last 100 years of the simulation is similar to the warm period observed in the coastal temperatures of Greenland in the 1930s . At the end of the simulation, the ELA lies at about 1150 m, and the SMB reaches values of 550 Gt a-1. These values are similar to values observed during the 21st century, although they are slightly higher as no anthropogenic forcings are considered in the deglaciation simulation see Fig. , Sect.  and Table ;.

The SMB and ELA derived from the MPI-ESM-CR simulation with the prescribed ICE-6G ice sheets are qualitatively similar to the presented results based on the GLAC-1D ice-sheet reconstructions (see Figs.  to ). The overall trends of both variables, as well as the relationships between accumulation and melt (e.g., accumulation dominating melting until about 15 ka), are similar, but the timing of the weakening of the AMOC, as well as the magnitude, differs. These deviations are due to a different timing, magnitude, and location of meltwater release in the GLAC-1D and ICE-6G reconstructions, which are currently being investigated in a separate study .

As discussed earlier, the North American (Laurentide and Cordilleran) and Eurasian (Fennoscandian, British Isles, and Barents–Kara Sea) ice sheets experienced substantial changes in their glacial extent throughout the last deglaciation (Fig. ). Reconstructions suggest a steady retreat of the Eurasian ice sheets starting from the LGM until about 8.7 ka when the ice sheets converged to present-day conditions e.g.,. The decline is highly discontinuous and shows an acceleration at around 17.8 ka. Similarly, the extent of the North American ice sheet started to decrease shortly after the LGM and continued until about 6.8 ka with only a little ice left at present e.g.,. As the SMB is highly dependent on the ice-sheet geometry, it is difficult to fully interpret SMB changes for the North American and Eurasian ice sheets. Hence, we only briefly point out the similarities between the climate responses of the ELAs over the North American, Eurasian, and Greenland ice sheets (see Figs. , , and ) while keeping in mind that the interpretation is limited due to the extensive changes in the ice-sheet geometries throughout the deglaciation. To account for the massive ice-sheet changes in the time series, we split the ice sheets into different subregions and investigate their dependence on the ice-sheet geometry. Fig.  shows the ELA time series for Eurasia, subdivided into a southern (<60∘ N), central (60–70∘ N), and northern (>70∘ N) ice sheet, and North America, split into a northern and southern Laurentide ice sheet (east of 120∘ W and north of 60∘ N and south of 60∘ N, respectively) and a Cordilleran ice sheet (west of 120∘ W).

During the LGM, the average ELAs over Eurasia and North America are significantly higher than the ELA over Greenland for the same period except for the northeastern Laurentide and northern Eurasian ice sheets (see Figs.  and ). Similar to the Greenland ice sheet, the ELA increases continuously until about 15 ka for the Eurasian and North American ice sheets. At around 14.5 ka, the southern and central Eurasian ice sheets both show a slight decrease in the ELA. This is likely associated with the AMOC slowdown (see Sect. ); other AMOC events at around 19.6, 18.2, and 15.2 ka also result in a decrease in ELA for the southern and central Eurasian ice sheet. However, the signal in the ELA is relatively weak and regionally confined compared to the response over Greenland. Around 14.5 ka, the Eurasian ice sheet exhibits decreased ELAs on its western boundaries and the Laurentide ice sheet on its eastern boundaries since both melt and accumulation decrease in response to reduced North Atlantic temperatures (Fig. ). This result suggests that the AMOC slowdown at 14.5 ka affected all ice sheets, at least regionally. Another possible contributing factor to the pronounced SMB and ELA variability over the Northern Hemisphere ice sheets during this time period are changes in the atmospheric circulation. found that elevation changes in the North American ice sheets around the saddle collapse, defined by the separation of the Laurentide and Cordilleran ice sheets, caused significant changes in the stationary wave patterns. An amplifying factor for atmospheric circulation changes is the southward-extending sea-ice cover due to the AMOC slowdown and reduced North Atlantic sea-surface temperatures. Such changes have a significant influence on downstream precipitation and temperature patterns over the North Atlantic and adjacent areas.

After about 14 ka, the ELA continues to increase for nearly all ice sheets, following the overall warming signal. However, specifically for the southern ice sheets over Eurasia and North America, the changes in the ice-sheet extent have a large effect on the ELA. The signal in the ELA due to the changes in the ice-sheet mask exceeds the signal due to the natural climate variability in the ELA at around 20.6 ka for the southern Eurasian ice sheet, at about 18.9 ka for the northern Eurasian and southeast Laurentide ice sheets, at about 15.3 ka for the northern and central Eurasian ice sheets, and at 13.3 ka for the Cordilleran ice sheet (Fig. ). Hence, the second and third AMOC slowdowns are only poorly reflected in the ELA time series, although similar regional responses are evident in Fig. . By 9.7 ka, Eurasia is completely ice free, while North America has only small ice sheets left (see Fig. ).