The seasonal relationship between P_{Penny} and AHT_{EQ} was found to depend on how far off the equator the ITCZ moves in a series of aquaplanet simulations with varying mixed layer depth. We argue that the asymmetry between the winter and summer Hadley cells is critical to this result due to two processes: 1) AHT_{EQ} changes more than would be expected from simply translating the annual mean Hadley cell off the equator due to the intensification of the streamfunction in the winter cell as the Hadley cell moves off the equator, and dos) the ITCZ remains equatorward of the zero streamfunction because the maximum meridional divergence of the streamfunction and upward motion gets pushed into the winter cell due to the asymmetry between the winter and summer Hadley cells. As a consequence, the AHT_{EQ} change required per degree shift in the ITCZ increases as the ITCZ moves farther off the equator. We note that, in the annual average, the ITCZ is relatively close to the equator and the two branches of the Hadley cell are nearly symmetric as compared to the seasonal extremes. This might lead one to believe that the AHT_{EQ} change required to move the ITCZ 1° would be comparable to that expected from simply translating the Hadley cell meridionally without the concurrent intensification of the winter cell (on the order of 0.1 PW; see red asterisks in Fig. 5) and less than that found over the seasonal cycle (on the order of 0.3 PW; see upper panel of Fig. 3). _{Penny} and AHT_{EQ} over the observed seasonal cycle is statistically indistinguishable from the relationship found for the annual mean changes across the ensemble of climate change perturbation experiments. We argue below that the seasonal relationships between P_{Cent} and AHT_{EQ} is dictated by the seasonal cycle because the annual average is seldom realized and is better thought of as the average of the seasonal extremes (and the amount of time spent in the extreme) as illustrated in Fig. 7.

The top panel of Fig. 11 shows smoothed histograms (Eilers and Goeman 2004) of monthly mean P_{Penny} and AHT_{EQ} for https://datingranking.net/nl/casualdates-overzicht/ 200 years of the PI simulation in the IPSL model. The annual mean (black cross) is seldom realized and the system rapidly migrates between seasonal extremes of P_{Penny} in the Northern Hemisphere and southward AHT_{EQ} in the boreal summer and P_{Cent} in the Southern Hemisphere and northward AHT_{EQ} in the austral summer. The linear best fit (dashed black line) connects the seasonal extremes with a slope equal to the regression coefficient between P_{Penny} and AHT_{EQ} and nearly passes through the origin. By statistical construction, the annual mean lies on the linear best fit line. In short, the annual mean reflects the average of the two seasonal extremes. 4

(top) Smoothed histogram (colors) in the AHT_{EQ}–P_{Penny} plane taken from a 200-yr-long PI simulation in the L’Institut Pierre-Simon Laplace (IPSL) model. The dashed line is the linear best fit to the monthly data for all years of the simulation and the cross is the annual average. (middle) As at top, but the probability density function is contoured [contour interval of 0.75% (° PW) ?1 ] with black contours showing the PI values and red values showing the 2XCO_{2} values. The red and black crosses and dashed lines represent the annual average and linear best fits in the 2XCO_{2} and PI simulations respectively. (bottom) As in the middle panel except only the 2.5% (° PW) ?1 contour is shown. The PI simulation is shown in black, 2XCO_{2} in red, LGM in blue, and the 6Kyr simulation in green.

Logo of spatial structure off winds (grey arrows), meridional size overturning streamfunction (solid and you will dashed grey lines for the negative and positive streamfunction beliefs, respectively), precipitation (blue contours), and you will vertically provided atmospheric temperature transport (yellow arrows) on the Hadley mobile to have (top) boreal june and you can (bottom) austral june. The brand new equator ‘s the dashed eco-friendly range.

(left) The worldwide, annual-averaged atmospheric opportunity budget and (middle),(right) new interhemispheric compare of your time budget regularly get brand new cross-equatorial atmospheric temperatures transport. The fresh new position mounts imply the newest SH integrated without any NH inbuilt divided by dos and you may OHT + S is the cross-equatorial ocean temperatures transportation without shops within the for every hemisphere.

## (ii) Exotic SST gradient

(top) Scatterplot of one’s seasonal cycle out-of exotic rain centroid versus cross-equatorial atmospheric temperature transport. Each cross are centered on the new month-to-month average together with duration of the mix on every axis represents the newest 95% believe period assessed from the interannual variability. The filled field ‘s the yearly average. The new dashed range is the linear finest fit with the monthly averages. (bottom) Since at greatest, however for the newest exotic precipitation centroid vs the fresh interhemispheric difference in tropical SST.

Seasonal cycle of hemispheric contrast in energy fluxes defined as half the difference in spatial integral of fluxes in the SH minus that in the NH. The solid lines are the observations and the shaded region represents ±1 standard deviation about the CMIP3 PI ensemble average. The terms are defined in the legend and discussed in the text in reference to Eq. (5). The first four terms in the legend sum to yield AHT_{EQ}.

## The latest expected relationships between ?

(top) Scatterplot of AHT_{EQ} vs the mass overturning streamfunction at 500 hPa over the equator over the seasonal cycle in the observations. Each asterisk is a monthly average and the dashed line is the linear best fit. (bottom) Scatterplot of the location of the 0 mass overturning streamfunction ?_{?=0} at 500 hPa vs AHT_{EQ} (red asterisk and linear best fit dashed line) and P_{Cent} vs AHT_{EQ} (blue asterisk and linear best fit dashed line). _{?=0} and AHT_{EQ} from Eq. (9) is shown by the dashed black line.

(top) Seasonal range of precipitation centroid vs atmospheric heat transport at the equator (AHT_{EQ}) in individual CMIP preindustrial models (dashed colored lines with filled dots on each end), the model ensemble mean (thick purple line and filled dots), and the observations (thick black line and filled dots). The seasonal range is twice the amplitude of the annual harmonic of each variable and the slope of the line is the regression coefficient of the monthly data. The models are color coded by their annual average P_{Penny} with the color scale given by the color bar to the right. (bottom) As at top, but for precipitation centroid vs interhemispheric contrast of tropical SST.

Histograms of P_{Penny} in the CMIP3 PI models and observations. The shaded region is the normalized histogram of monthly mean P_{Penny} and the seasonal range (defined as twice the amplitude of the annual harmonic) of P_{Cent} is given by the dashed lines attaching the filled dots (representing the climatological northernmost and southernmost extent). The annual average for each model is also shown with the shaded diamond. The models are organized on the y axis and color coded by annual average P_{Cent} with the same color bar used in Fig. 6. Observations are given by the thick magenta line and the CMIP3 ensemble average is shown in the thick black lines. The vertical dashed black lines are the ensemble average annual mean, northernmost, and southernmost extent P_{Penny}.