In each experiment, the change in annual mean PCent and AHTEQ changes are significantly negatively correlated among the ensemble members with an average correlation coefficient of ?0.81 and a correlation coefficient of ?0.85 when considering all experiments collectively. The regression coefficient between PCent and AHTEQ ranges from ?4.dos° PW ?1 in the 2XCO2 ensemble to ?3.2° PW ?1 in the LGM and 6Kyr ensembles (Table 3) and 
the regression coefficient of all simulations considered simultaneously is ?3.2° PW ?1 . Cent and AHTEQ of ?2.7° PW ?1 found in the observations. These results collectively suggest that the relationship between PPenny and AHTEQ is robust across time scales (seasonal vs annual mean) and across different climate states. We return to this point in the discussion section.
The intermodel spread in annual mean PPenny and ?SST changes are significantly positively correlated in all three perturbation experiments with an average correlation coefficient of 0.86 and a slope that ranges from +1.5° K ?1 in the LGM simulations to +2.4° K ?1 in the 6Kyr experiments (Table 3). These slopes are significantly shallower but of similar magnitude to that found in the seasonal cycle in the observations (+3.3° K ?1 ).
1) 2XCO2 tests
The ITCZ response to CO2 doubling in the CMIP3 slab ocean simulations was analyzed thoroughly by Frierson and Hwang (2012), who concluded that there are large intermodel differences in the annual mean ITCZ shift due to differences in the AHTEQ change that primary reflect intermodel differences in extratropical feedbacks. We find a similar relationship between PPenny and AHTEQ in the coupled 1% CO2 increase runs. The ensemble average 0.02 PW increase AHTEQ in the 2XCO2 simulations analyzed in this study is decomposed into a nearly compensating 0.22 PW increase in ?SWNet,TOA? [associated with increased cloudiness in the Northern Hemisphere midlatitudes as assessed by the method of Donohoe and Battisti (2011)] and a 0.29 PW increase in ?OLR? (associated primarily with the Planck feedback and larger temperature increases in the Northern Hemisphere as compared to those in the Southern Hemisphere). Additionally, there is a 0.09 PW decrease in ?OHT + S?, which implies either more southward ocean heat transport or more transient heat storage in the Northern Hemisphere as compared to the Southern Hemisphere. We emphasize that the ensemble average change in the hemispheric contrast of the energy budget due to CO2 doubling is small compared to the intermodel spread as pointed out by Zelinka and Hartmann (2012) and Frierson and Hwang (2012). Furthermore the ITCZ shift due to anthropogenic climate forcing varies in sign between models and depends critically on extratropical climate feedbacks.
2) LGM experiments
The most pronounced change in the interhemispheric energy budget in the LGM is the presence of the Laurentide ice sheet in the Northern Hemisphere; the cryosphere expanded drastically in the Northern Hemisphere and only modestly in the Southern Hemisphere during the LGM. The ensemble average spatially and solar weighted surface albedo of the Northern Hemisphere increased by 0.029 relative to that in the Southern Hemisphere (with an ensemble standard deviation of 0.018 due to differences in the albedo of the Laurentide ice sheet), which translates to an increase in ?SWWebsites,TOA? of +1.30 PW if the same surface albedo change was found in the planetary albedo. However, the shortwave atmospheric opacity limits the surface albedo’s impact on the TOA radiative budget while decreased cloudiness over the ice sheet compensates for the increased surface reflection and the ensemble average change in ?SWWebsites,TOA? is +0.43 PW (and ranges from +0.03 to +0.84 PW in the ensemble members). Using the method of Donohoe and Battisti (2011) to partition the planetary albedo into contributions from surface albedo and cloud reflection, we find that the ensemble average change in ?SWWeb,TOA? is due to a +0.60 PW contribution from changes in surface albedo and a ?0.17 PW contribution from changes in atmospheric reflection (fewer clouds over the ice sheet).