In the polar regions, more energy is emitted to space via longwave (terrestrial) radiation than is supplied by the absorption of solar radiation. This energy deficit is balanced by a radiation energy surplus at the Equator and poleward heat transport by the ocean and the atmosphere. The radiation energy deficit is smaller in the Antarctic region than in the Arctic region. The base model setup (Fig. a) and observations (Fig. b) show a pronounced Arctic–Antarctic asymmetry in the magnitude of the outgoing terrestrial radiation flux, which is in line with the higher average surface temperature (and lower average surface elevation) in the Arctic and also with a larger meridional heat flux from lower latitudes toward the Arctic.

Conversely, when Antarctica was assumed to be flat, the asymmetry in the simulated radiation budget decreased markedly (Fig. a). In the flat AA run, Antarctica was similar to the Arctic in terms of the zonal mean radiation budget, which implies that the overall poleward heat transport was also more symmetric in the flat AA run. Atmospheric and oceanic meridional heat transport will be further analyzed in Sect. .

The slight increase in absorbed shortwave radiation over the Antarctic continent in the flat AA run (Fig. a) is consistent with increased atmospheric absorption and also includes a minor contribution from an increase in snow albedo as the melting temperature is occasionally approached in the flat AA base run. The latter contribution is non-zero in spite of the fact that the entire Antarctic continent remains covered by snow year round (not shown). This is because the snow albedo in the CESM decreases with temperature whenever the melting temperature is approached.

Doubling CO2 in the base model setup led to the well-known pattern of a strong polar amplification in the Arctic region and a weaker polar amplification in the Antarctic region (Fig. , based on the RAD reruns) that is also found in certain transient climate change experiments. Conversely, in the flat AA run, the polar amplification was increased in the Antarctic region, while it decreased over time in the Arctic region (the temporal evolution in the original coupled runs will be discussed in Sect. ).

This decrease in asymmetry is also reflected in Table  (based on the original coupled runs), in which the polar warming due to doubling CO2 was analyzed for three consecutive 25-year time slices starting in year 51 and ending in year 126. In the base run, the Arctic region warmed on average 1.40 ± 0.29 K (mean of three time slices ± 1 standard deviation) more than the Antarctic region. Conversely, in the flat AA run, the difference between the Arctic and the Antarctic warming was reduced to 0.59 ± 0.32 K. Thus, on average, about 56 ± 30 % of the difference in warming between the Arctic and the Antarctic region (i.e., 0.81 ± 0.46 of 1.40 ± 0.29 K) was explained by the Antarctic surface height for the three time slices. However, as evidenced by the large standard deviation, this ratio was not constant in time.

In the first time slice, only 24 % of the difference was explained by Antarctic surface height, while 64 % was explained in the second, and 80 % was explained in the third time slice. When only Antarctic temperature change was taken into account (i.e., the Arctic temperature increase was taken from the base setup, while the Antarctic temperature increase was taken from the flat AA setup), 73, 26, and 42 % was explained by Antarctic surface height. The differences are explained by a pronounced Arctic warming toward the beginning of the flat AA 2 × CO2 run compared to the flat AA control run and a weaker subsequent Arctic warming (i.e., a cooling relative to the initial warming). This result is based on the original coupled runs and differs from the corresponding result of the RAD reruns since the temporal evolution of the surface temperature differs, although the finding that polar amplification asymmetry decreases markedly in the flat AA model setup holds in the RAD reruns as well. Because the original coupled runs reflect the standard configuration of the model, and also because the RAD reruns are only available for the years 76 to 125, the original coupled runs were chosen for this analysis.

Before discussing the underlying temporal evolution of the zonal mean temperature in the original coupled runs in detail in Sect. , the reasons for the decreased polar amplification asymmetry in the flat AA model setup (Fig. ) will be analyzed in some detail based on the RAD reruns, which generally yield sufficiently similar results to the original runs for this analysis to be useful.

In this section, the zonal mean AHT (Fig. ) and OHT (Fig. ) for the years 80–109 are compared between the base and the flat AA model setup, and their changes in the corresponding CO2-doubling runs are analyzed based on the RAD reruns. As expected, based on Fig. a, AHT and OHT were more symmetric in the flat AA model setup than in the base setup (although they cannot be expected to become completely symmetric because the overall land mass distribution differs between the Northern and Southern hemispheres). In the control runs, the poleward AHT increased in the flat AA model setup compared to the base setup mainly in the Southern Hemisphere. Poleward OHT across the polar circles increased in the Southern Hemisphere and also slightly increased in the Northern Hemisphere. Conversely, in the original coupled runs, poleward OHT across the polar circle in the Northern Hemisphere slightly decreased during this period (Fig. ). Other findings in this section were not affected by this difference.

Doubling CO2 led to an increased poleward AHT in the base and flat AA model setups. The increase in the southward AHT across the polar circle in the 2 × CO2 runs was larger in the flat AA model setup than in the base model setup, but poleward of 60∘ S ΔAHT changed sign. At the same time, the increase in southward OHT reached a maximum around this latitude. This indicates that AHT and OHT are closely linked and that they should not be considered in isolation. Both AHT and OHT contributed to decreasing the asymmetry in the flat AA run compared to the base run, and changes of OHT are not confined to the Southern Hemisphere, especially in the tropics. In summary, for the CO2-doubling experiments, AHT and OHT both contributed to an increased southward heat transport in the flat AA model setup, with OHT changes being more important in the Southern Ocean and AHT taking over above the continent.

In addition to AHT and OHT, local radiative feedbacks and increased CO2 forcing over Antarctica contributed to the decreased polar amplification asymmetry in the flat AA run. Figure  shows the CO2 radiative forcing as well as various radiative feedbacks for the base and flat AA model setups for years 80–109 from the PRP computations. The residual (RES) represents the difference between the radiative perturbation from runs in which all variables, including the CO2 concentration, are replaced simultaneously and the sum of the individual contributions from the feedbacks, including the PL feedback and the CO2 forcing. For an identical 3 h sampling interval, replacing all variables yielded the same radiative perturbation as the corresponding 2 × CO2 coupled RAD rerun. The SUM and the RES terms in Fig.  are expected to balance the contributions from changes in AHT convergence, OHT convergence, and heat storage. The corresponding individual contributions were diagnosed separately as explained in Sect. 2 and they were found to be of the same order of magnitude as the SUM term, which is much smaller than the individual contributions of the major feedbacks, except for CL (not shown). Unfortunately, however, as explained in Sect. 2, the diagnosed contributions do not add up to the SUM + RES term as expected.

The difference between Fig. a and b is shown in Fig. . Maps of the feedbacks in the base model run are provided in Fig. . Figure  shows maps of the differences between the feedbacks in the flat AA and the base model setup.

Red bars that are shorter than blue bars in Fig.  indicate that the difference of the local radiative feedbacks between the Arctic and Antarctic regions has decreased in the flat AA run. The polar asymmetry for FSU (that is, the sum of all feedbacks except for PL) has roughly halved. The main contribution was the LR feedback, which will be further analyzed in Sect. . In addition, the WV feedback increased in the Antarctic region, as expected for a deeper atmospheric column. The ALB feedback changed only slightly and the overall contribution of the CL feedback was small, in general agreement with results from other coupled models .

The most pronounced ALB feedback in the Southern Ocean was found north of the Antarctic Circle (Fig. ). The more positive feedback in this region in the flat AA run (Fig. ) contributed to the overall decreased polar amplification asymmetry. The Antarctic region as defined here was not directly affected by the sea ice changes north of the Antarctic Circle (since it was defined as the region south of the Antarctic Circle), but rather indirectly via meridional heat transports. This indicates that the values in the bar charts should not be overinterpreted. Furthermore, the small tropical LR feedback in Fig.  is noteworthy, which together with the large positive high-latitude LR feedback, led to a positive global LR feedback during years 80–109 of this particular run. The (model-dependent) net cloud feedback over the Pacific warm pool was dominated by a negative shortwave feedback rather than the predominantly positive longwave feedback.

In the next section, the large contribution from the LR feedback to the decrease in polar amplification asymmetry is analyzed in some detail. Then the results are combined with the results from the previous sections.

The LR feedback was defined as LR = TA - PL, where PL depends only on the change in surface temperature (which is applied at each height level throughout the atmospheric column), while for TA changes in surface as well as the atmospheric temperatures were taken into account. In the tropics, the atmospheric lapse rate is coupled to the surface temperature via deep convection and via the dependence of the slope of the moist adiabat on surface temperature. In the polar regions, where subsidence takes place and deep convection is absent, atmospheric temperatures are less strongly coupled to surface temperatures, and the LR feedback is less well understood.

Figure  shows that the actual mid- and upper-tropospheric temperature change in response to doubling CO2 in the Antarctic region was similar in the base and flat AA model setups, even though assuming a flat Antarctica affected atmospheric dynamics in various ways. This indicates that the large difference in the LR feedback between the flat AA and the base model setup might not only depend on changes in the mid- and upper-tropospheric temperature profile. Instead, they could have been influenced by different surface temperatures in the base and flat AA control runs. The apparent mismatch between the dots and crosses and the profiles at the lowest atmospheric levels in Fig. b and d is explained by the condition that all pressure levels where more than 20 % of the grid points are above ground are shown in the profiles. Consequently, only a limited number of grid points entered the average temperature for the lowest atmospheric levels, while the average surface temperature was computed as an average over all grid points.

In order to find out whether the difference of the LR feedback between the flat AA and the base run can be attributed to differences in atmospheric temperatures or in surface temperatures, a number of PRP sensitivity computations were conducted in which variables from flat AA model runs were substituted into results of runs from the base setup (see Sect.  and Table  for details). The results from these runs are shown in Fig. .

In the first sensitivity experiment (LRPLsens) surface air and atmospheric temperature were taken from the flat AA setup to perform the PRP computations. The LR feedback in this sensitivity computation is similar to the LR feedback in the flat AA standard PRP computation. This indicates that the depth of the atmospheric column was not the main reason for the difference in the LR feedback between the flat AA and base model setups.

In the second sensitivity computation (LRSens), only the atmospheric temperatures were taken from the flat AA setup, and in the third computation (PLSens) only the surface temperatures were taken from the flat AA setup. When only atmospheric temperatures were replaced, the LR feedback was similarly strong to the one in the base setup. Applying only the surface temperatures from the flat AA model setup in the base model setup, however, explained the stronger Antarctic LR feedback in the flat AA model setup, even though the actual atmospheric lapse rate above the lowest atmospheric model layer did not change in the PRP computations.

In other words, the difference of LR = TA - PL between the flat AA and base runs appeared to be dominated by a change of PL and not by a change of TA, and it is therefore difficult to interpret the changes in the LR feedback in terms of atmospheric lapse rate changes

Consequently, the LR and PL feedbacks will be considered together in the next section. The rationale for this is that in the present study setup the sum LR + PL in the Antarctic region is mainly sensitive to changes in surface temperature and not to changes in the atmospheric lapse rate above the surface layer. Note that by definition, LR + PL corresponds to total temperature feedback TA, i.e., the perturbation that is obtained by substituting the surface as well as the atmospheric temperatures. The definition of the TA feedback is identical to the definition of the longwave feedback in a study by and to the definition of the temperature feedback in a study by .

The usual decomposition of the total temperature feedback into PL and LR feedbacks is nevertheless useful for understanding polar climate change. As explained above, the PL feedback is defined as the hypothetical feedback that would be expected if the atmosphere would warm at the same rate as the surface. However, the polar atmosphere generally warms less than the surface due to a lack of vertical mixing (e.g., Manabe and Wetherald, 1975). Conversely, the tropical atmosphere warms more than the surface. Therefore, in order to radiate away a given amount of energy, a larger surface warming is required in the polar regions compared to the tropics (Pithan and Mauritsen, 2014). The lack of atmospheric warming in the polar atmosphere relative to the surface is reflected in the large positive polar LR feedback.

In Sect.  it was argued that the partitioning between the atmospheric and oceanic heat transport toward Antarctica strongly depends on the exact latitude that is used to define the Antarctic region. Furthermore, in Sect.  it was argued that the ALB feedback outside the Antarctic region as defined by the grid points poleward of the Antarctic Circle almost certainly acts to decrease the polar amplification asymmetry in contrast to the ALB feedback inside the region. Furthermore, in Sect.  it was explained that closing the energy budgets turned out to be more problematic than anticipated, especially for the Arctic. In spite of these caveats, a comparison between local forcings, feedbacks, changes of heat transport convergence, and heat storage terms is attempted here.

Figure  essentially shows the difference between the blue and red bars in Fig. , where PL and LR have been combined into a single temperature feedback based on the arguments in Sect. , and FSUP is defined as the sum of all feedbacks, including the Planck feedback. In addition, the heat transport convergence differences and the heat storage terms are shown. On the whole, it appears as if the changes in local feedbacks have increased the asymmetry, although this finding depends on whether or not one chooses to follow the arguments in the previous section and to include the Planck feedback here. Apart from the LR feedback (see Sect. ), which was here combined with the Planck feedback into a single temperature feedback, only the CO2 forcing and the WV feedback acted to decrease the polar amplification asymmetry.

Changes in AHT and also changes in heat content (heat storage terms) appear to have contributed to the decreased asymmetry found in the previous sections. Part of the reason for the change in heat content being fairly important is that the ocean heat content south of the Antarctic Circle decreases in the flat AA base run and increases in the flat AA 2 × CO2 run.

This result should, however, not be over-interpreted since for example the albedo feedback would most likely contribute to the overall decrease in asymmetry if contributions from outside the region were also taken into account. Furthermore, in Sect. , it was argued that OHT also contributed to an overall decrease in asymmetry since it transports heat to the Southern Ocean, where the atmospheric heat transport then becomes more dominant. Finally, in Sect.  it was shown that small OHT changes in response to doubling CO2 across the Arctic Circle that contribute to the OHT difference in Fig.  depend on whether the original runs or the RAD reruns are analyzed.

In a more qualitative sense, Fig.  suggests that contributions from changes of heat transport convergence and from heat storage (which would be zero in equilibrium) were of roughly the same magnitude as contributions from local feedbacks, indicating that local feedbacks and changes in heat transport convergence both played a role.

Figure  shows the temporal evolution of the zonal mean surface temperature in the control runs and the 2 × CO2 runs for the original coupled runs. As expected, the largest surface temperature response to the assumption that Antarctica is flat occurred during the first decades of the flat AA control run (Fig. c). These decades were not taken onto account in the preceding analysis. After this, the surface temperatures remained fairly stable in the flat AA control run, although the deep ocean was still adjusting. Taking the difference between the flat AA 2 × CO2 run and the flat AA control run (as was done in the preceding sections) is expected to remove most of the latter effect.

Figure b and d show that Antarctic surface temperatures increased faster in the flat AA 2 × CO2 run than in the base 2 × CO2 run, as expected based on the previous sections. The Arctic temperatures varied strongly due to internal variability, which helps to explain the differences between the original coupled run and the coupled reruns with half-hourly radiation calls, which have been pointed out in the discussion of the ocean heat transport in Sect. .

The weaker Arctic warming in the middle of the 2 × CO2 base run (Fig. b) is an indication of a slowing of the ocean's meridional overturning circulation (MOC). Such a slowdown has often been found in CO2 perturbation experiments, and it tended to be stronger in low-resolution, low-complexity models compared to state-of-the-art high-resolution models. Since the CESM was run at a low resolution in this study, this finding should also not be overinterpreted. In the 2 × CO2 flat AA run, the MOC started to slow down earlier than in the 2 × CO2 base run (Fig. d), which might indicate that assuming a flat Antarctica did not only influence the Antarctic region but also the Arctic region. For a more reliable estimate of this effect, coupled runs at a higher resolution and an ensemble of model runs with slightly perturbed initial conditions would be required.

Figure a shows the evolution of the Arctic and Antarctic surface temperature for the base and flat AA model setups, and Fig. b shows ratios of the Arctic to the Antarctic amplification, which are computed as f=AArAAA=T^Ar,2xCO2-T^Ar,ControlT^AA,2xCO2-T^AA,Control, where T^ is a regional average 25-year running mean temperature.

It should be noted that Antarctic warming relative to the respective control run (Fig. a) was stronger in the flat AA than in the base model setup throughout almost the entire 600-year period. However, even though the temperature in the flat AA control run stabilized after a moderate initial warming and even though the temperature evolution from the control run was subtracted in this analysis, it cannot be completely ruled out that this moderate initial warming could have also played a role in the later development in the 2 × CO2 flat AA run. Therefore, in retrospect, starting the flat AA 2 × CO2 run from a separate long flat AA spinup run and prescribing a more realistic gradual increase of the CO2 concentration, which would allow the inspection of the first decades of the CO2 perturbation experiments, would have been better.

After 250 years, f was lower than unity in the base and the flat AA model setup, which indicates that the Antarctic temperature increase was stronger than the Arctic temperature increase in both model setups. This finding is related to a slowdown of the north Atlantic MOC in both of the 2 × CO2 runs, which could in part be a transient feature as the MOC recovery times are known to be extremely long. Again, in order to gain confidence in this result, additional ensemble model runs at higher resolution and ideally also a comparison with results from a multi-model ensemble would be necessary. Since the aim of the various model sensitivity runs has been to investigate the sensitivity of the polar amplification asymmetry to Antarctic surface height (and not to provide a future projection of Antarctic climate change under global warming), the runs were performed without an ice sheet model. In order to arrive at a more credible projection of Antarctic climate change, state-of-the-art high-resolution models that include state-of-the-art ice sheet dynamics models should be used.