The relationship between P_Cent and AHT_EQ in the observations is coplotted with the slab ocean aquaplanet simulations in Fig. 8. The slope found in the observations is very close to that of the dos4-m depth run while the seasonal amplitude of P_Penny and AHT_EQ in the observations falls somewhere between that in the 6-m local hookup and 12-m runs. We will return to a discussion of these points in section 4.

The seasonal amplitude of ?SST increases with decreasing slab ocean depth, from 0.9 K in the 50-m run to 9.6 K in the 2.4-m run. Seasonal variations in ?SST are significantly correlated with those in P_Penny in all runs but the correlations are weaker than those between P_Cent and AHT_EQ and decrease to an R 2 of 0.67 in the 50-m run. The latter is a consequence of a phase lead of ?SST relative to P_Cent that increases with increasing mixed layer depth to 36 days for the 50-m run. In contrast, P_Cent and AHT_EQ are nearly antiphased in all runs with an average phase difference magnitude of 11 days. The regression coefficient between P_Cent and ?SST varies nonmonotonically with slab depth and reaches a maximum of 2.9° K ?1 in the 24-m run and a minimum of 1.4° K ?1 in the 50-m run with an ensemble average of 2.1° K ?1 .

The previous section demonstrated that there is a robust and consistent relationship between the P_Cent and AHT_EQ and between P_Cent and ?SST over the seasonal cycle in both observations and coupled climate models. We now analyze the relationship between annual mean shifts in ITCZ location and change in AHT_EQ and ?SST due to anthropogenic and paleoclimatic forcing. We argue that the same quantitative relationships found in the seasonal cycle also apply to the climate change problem across a myriad of different forcings.

1) Carbon dioxide increasing studies

We analyze the CMIP3 1% CO₂ increase to doubling experiments (Meehl et al. 2007). Each model is initialized from the equilibrated preindustrial (PI) or in some cases [CCSM, the Meteorological Research Institute (MRI) model, and ECHAM] the present-day (PD) simulations. Atmospheric carbon dioxide increases at a rate of 1% per year until it has doubled (at year 70) and is then held fixed for an additional 150 years of simulations. We calculate the climatology of each model over the last 20 years of simulations and then take differences relative to the climatology in the PI (or PD) run. We will refer to these runs as the 2XCO₂ runs. Fifteen different models are analyzed.

2) Past Glacial Restrict simulations

We utilize model output from phase 2 of the Paleoclimate Modeling Intercomparison Project (PMIP2), an ensemble of state-of-the-art coupled (ocean–atmosphere–cryosphere) model simulations run under prescribed forcing and boundary condition scenarios that represent different paleoclimatic epochs. The Last Glacial Maximum (LGM) simulations are forced by insolation from 21 000 years before present, with greenhouse gas and aerosol concentrations deduced from ice core data (CO₂ is set to 185 ppm), which amounts to a radiative forcing of approximately ?2.8 W m ?2 (Braconnot et al. 2007a), coastlines consistent with a 120-m decrease in sea level, and the prescribed land ice topography of Peltier (2004), which includes the expansive Laurentide ice sheet over North America. We use the LGM simulations with fixed vegetation (PMIP2 OA runs). All comparisons are made to the preindustrial simulations in the same model and resolution (many of which are lower resolution than the PI simulations analyzed in section 2b). Seven different model simulations are analyzed.