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Axisymmetric theory of atmospheric circulation is extended for the case of concentrated equatorial cooling and annually averaged heating. The solutions are derived in a 1.5-layer shallow water model on the spherical Earth, which includes vertical mixing with diagnostic surface momentum. The axisymmetric solutions capture the sensitivity of the largescale circulation to equatorial cooling seen in observations and in eddy-permitting models, namely, (i) weakening and widening of the meridional overturning circulation (MOC) and (ii) weakening and poleward shift of the subtropical jet. For sufficiently large equatorial cooling, a tropical anti-Hadley cell emerges that transports energy equatorward, balancing the equatorial energetic sink. The analytic solutions predict the critical cooling required for the emergence of the anti-Hadley cell and provide a simple mechanism for the response of the MOC to equatorial cooling. Specifically, equatorial cooling reduces net tropical heating, which weakens the circulation and shifts the edge of the rising branch poleward. This in turn reduces upper-level momentum which is set by surface momentum in the rising branch. The subtropical meridional temperature gradient decreases with upper-level momentum, requiring a widening of the circulation to close the energy budget. The subtropical jet therefore shifts poleward with the edge of the MOC and weakens due to the reduced upper-level angular momentum. The strong sensitivity to equatorial cooling seen in the axisymmetric system suggests that the above mechanism may have an important role in the sensitivity of the MOC to equatorial temperature anomalies on seasonal or longer time scales.

The tropical zonal-mean precipitation distribution varies between having single or double peaks, which are associated with intertropical convergence zones (ITCZs). Here, the effect of this meridional modality on the sensitivity of the ITCZ to hemispherically asymmetric heating is studied using an idealized GCM with parameterized Ekman ocean energy transport (OET). In the idealized GCM, transitions from unimodal to bimodal distributions are driven by equatorial ocean upwelling and cooling, which inhibits equatorial precipitation. For sufficiently strong equatorial cooling, the tropical circulation bifurcates to anti-Hadley circulation in the deep tropics, with a descending branch near the equator and off-equatorial double ITCZs. The intensity and extent of the anti-Hadley circulation is limited by a negative feedback:westerly geostrophic surface wind tendency in its poleward-flowing lower branches balances the easterly stress (and hence equatorial upwelling) required for its maintenance. For weak ocean stratification, which goes along with unimodal or weak bimodal tropical precipitation distribution, OET damps shifts of the tropical precipitation centroid but amplifies shifts of precipitation peaks. For strong ocean stratification, which goes along with pronounced double ITCZs, asymmetric heating leads to relative intensification of the precipitation peak in the warming hemisphere, but negligible meridional shifts. The dynamic feedbacks of the coupled system weaken the gradient of the atmospheric energy transport (AET) near the equator. This suggests that over a wide range of climates, the ITCZ position is proportional to the cubic root of the cross-equatorial AET, as opposed to the commonly used linear relation.

Current climate models represent the zonal- and annual-mean intertropical convergence zone (ITCZ) position in a biased way, with an unrealistic double precipitation peak straddling the equator in the ensemble mean over the models. This bias is seasonally and regionally localized. It results primarily from two regions: the eastern Pacific and Atlantic (EPA), where the ITCZ in boreal winter and spring is displaced farther south than is observed; and the western Pacific (WP), where a more pronounced and wider than observed double ITCZ straddles the equator year-round. Additionally, the precipitation associated with the ascending branches of the zonal overturning circulations (e.g., Walker circulation) in the Pacific and Atlantic sectors is shifted westward. We interpret these biases in light of recent theories that relate the ITCZ position to the atmospheric energy budget. WP biases are associated with the well known Pacific cold tongue bias, which, in turn, is linked to atmospheric net energy input biases near the equator. In contrast, EPA biases are shown to be associated with a positive bias in the cross-equatorial divergent atmospheric energy transport during boreal winter and spring, with two potential sources: tropical biases associated with equatorial sea surface temperatures (SSTs) and tropical low clouds, and extratropical biases associated with Southern Ocean clouds and north Atlantic SST. The distinct seasonal and regional characteristics of WP and EPA biases and the differences in their associated energy budget biases suggest that the biases in the two sectors involve different mechanisms and potentially different sources.

The ITCZ lies at the ascending branch of the tropical meridional overturning circulation, where near-surface meridional mass fluxes vanish. Near the ITCZ, column-integrated energy fluxes vanish, forming an atmospheric energy flux equator (EFE). This paper extends existing approximations relating the ITCZ position and EFE to the atmospheric energy budget by allowing for zonal variations. The resulting relations are tested using reanalysis data for 1979–2014. The zonally varying EFE is found as the latitude where the meridional component of the divergent atmospheric energy transport (AET) vanishes. A Taylor expansion of the AET around the equator relates the ITCZ position to derivatives of the AET. To a first order, the ITCZ position is proportional to the divergent AET across the equator; it is inversely proportional to the local atmospheric net energy input (NEI) that consists of the net energy fluxes at the surface, at the top of the atmosphere, and zonally across longitudes. The first-order approximation captures the seasonal migrations of the ITCZ in the African, Asian, and Atlantic sectors. In the eastern Pacific, a third-order approximation captures the bifurcation from single- to double-ITCZ states that occurs during boreal spring. In contrast to linear EFE theory, during boreal winter in the eastern Pacific, northward cross-equatorial AET goes along with an ITCZ north of the equator. EFE and ITCZ variations driven by ENSO are characterized by an equatorward (poleward) shift in the Pacific during El Niño (La Niña) episodes, which are associated with variations in equatorial ocean energy uptake.

The Hadley circulation (HC) has widened in recent decades, and it widens as the climate warms in simulations. But the mechanisms responsible for the widening remain unclear, and the widening in simulations is generally smaller than observed. To identify mechanisms responsible for the HC widening and for model–observation discrepancies, this study analyzes how interannual variations of tropical-mean temperatures and meridional temperature gradients influence the HC width. Changes in mean temperatures are part of any global warming signal, whereas changes in temperature gradients are primarily associated with ENSO. Within this study, 6 reanalysis datasets, 22 Atmospheric Modeling Intercomparison Project (AMIP) simulations, and 11 historical simulations from phase 5 of the Climate Modeling Intercomparison Project (CMIP5) are analyzed, covering the years 1979–2012. It is found that the HC widens as mean temperatures increase or as temperature gradients weaken in most reanalyses and climate models. On average, climate models exhibit a smaller sensitivity of HC width to changes in mean temperatures and temperature gradients than do reanalyses. However, the sensitivities differ substantially among reanalyses, rendering the HC response to mean temperatures in climate models not statistically different from that in reanalyses. While global-mean temperatures did not increase substantially between 1997 and 2012, the HC continued to widen in most reanalyses. The analysis here suggests that the HC widening from 1979 to 1997 is primarily the result of global warming, whereas the widening of the HC from 1997 to 2012 is associated with increased midlatitude temperatures and hence reduced temperature gradients during this period.

In the zonal mean, the ITCZ lies at the foot of the ascending branch of the tropical mean meridional circulation, close to where the near-surface meridional mass flux vanishes. The ITCZ also lies near the energy flux equator (EFE), where the column-integrated meridional energy flux vanishes. This latter observation makes it possible to relate the ITCZ position to the energy balance, specifically the atmospheric net energy input near the equator and the cross-equatorial energy flux. Here the validity of the resulting relations between the ITCZ position and energetic quantities is examined with reanalysis data for the years 1979–2014. In the reanalysis data, the EFE and ITCZ position indeed covary on time scales of seasons and longer. Consistent with theory, the ITCZ position is proportional to the cross-equatorial atmospheric energy flux and inversely proportional to atmospheric net energy input at the equator. Variations of the cross-equatorial energy flux dominate seasonal variations of the ITCZ position. By contrast, variations of the equatorial net energy input, driven by ocean energy uptake variations, dominate interannual variations of the ITCZ position (e.g., those associated with ENSO).

Energetic constraints on the time-dependent response of the intertropical convergence zone (ITCZ) to volcanic eruptions are analyzed using the Community Earth System Model Last Millennium Ensemble project. The energetic constraints are found to vary during the first few years, governed by conjoined variations of the energy budgets of the stratosphere, troposphere, and oceans. Specifically, following eruptions, sulfate aerosols heat the stratosphere by longwave absorption and cool the surface by shortwave reflection, leading to contrasting energy transport anomalies in the stratosphere and troposphere, which are of comparable strength during the first year. Similar contrasting responses are also seen by the mean and eddy components of atmospheric energy transport (AET). Consequently, ocean energy transport (OET) dominates the anomalous total interhemispheric energy transport during the first year. However, wind-driven OET, generally assumed to constrain shifts of the ITCZ, has a negligible role in the transient ocean response. Consistent with theory, anomalous cross-equatorial tropospheric energy transport, dominated by the anomalous Hadley circulation, is strongly negatively correlated with ITCZ shifts. However, due to the strong anomalous stratospheric energy fluxes, the commonly used energy flux equator (derived from net AET) is a poor predictor of transient ITCZ shifts following eruptions. El Niño–like conditions typically appear during the second year after eruptions, and La Niña–like conditions appear after the third year. These variations modulate ITCZ shifts in a complex manner, via changes in surface conditions and in associated energy transport variations in the atmosphere and oceans.

In the present climate, tropical rain bands exhibit a bifurcated pattern, continuously forming along single intertropical convergence zones (ITCZs) in some regions, and along double ITCZs that straddle the equator in other regions. This bifurcated ITCZ pattern is studied in a Matsuno‐Gill‐type model forced by relaxation to zonally asymmetric surface pressure. The model includes an idealized Bjerknes feedback which couples surface winds and sea surface temperatures (SSTs) via oceanic Ekman balance. Consistent with observations, solutions in the limit of strong damping are explored. Two ITCZ bifurcation mechanisms are identified. First, in the viscous limit, ITCZs form along negative anomalies of the local Rossby number, which tend to occur near the equator for equatorial low pressure and off the equator for equatorial high pressure; this leads to a single ITCZ in the rising branch of zonal‐overturning circulations and a double ITCZ that straddles the equator in the descending branch. Second, ocean upwelling produces an equatorial cold tongue with increased surface pressure, which reduces vertical winds and can lead to precipitation peaks that straddle the equator in regions of near‐equator ascent. Consistent with observations, the cold tongue intensifies with increasing zonal SST gradients, and its base widens with weakened poleward SST gradients, modulating the zonal orientation of the ITCZs on either side of the cold tongue. Analytic approximate solutions in the viscous limit capture the emergence of the bifurcated ITCZ pattern, as well as the dependence of the bifurcated ITCZ pattern on zonal and poleward SST gradients Plain Language Summary Tropical rain bands lie along near‐surface convergence zones where the lower branches of the meridional overturning circulation intersect. In the present climate, tropical rain bands exhibit a bifurcated pattern, continuously forming along single intertropical convergence zones (ITCZs) in some regions, and along double ITCZs that straddle the equator in other regions. Since the tropical overturning circulations in regions dominated by single and double ITCZs are inextricably linked, a theory of the zonally varying tropical rain belt requires consideration of the bifurcated ITCZ pattern (i.e., concurrent single and double ITCZs) as a whole. In this paper, a classical simple model of the tropical circulation is used to gain a conceptual understanding of the bifurcated ITCZ pattern. It is found that the bifurcated ITCZ pattern emerges in the limit of strong mechanical damping. In addition, when surface winds are coupled to ocean heat transport, an equatorial cold tongue emerges which modulates the intensity and regional characteristics of the bifurcated ITCZ pattern in a manner consistent with observations. Key Points Concurrent single and double ITCZs emerge in the limit of strong mechanical damping An idealized Bjerknes feedback produces an equatorial cold tongue The zonal orientation of the double ITCZs varies with the width of the equatorial cold tongue

The tropical rain belt varies between unimodal and bimodal meridional precipitation distributions, both regionally and on seasonal to geological time scales. Here we show that this variation is largely driven by equatorial precipitation inhibition, and quantify it using an equatorial modality index (EMI) that varies continuously between 1 and 2 for purely unimodal and bimodal distributions. We show that tropical modality is a fundamental characteristic of tropical climate, which we define as annual-mean EMI. We examine large-scale aspects of tropical modality across 73 climate models from phases 5 and 6 of the Coupled Model Intercomparison Project, 45 paleo simulations (~300 million years ago to present), and observations. We find increased tropical modality to be strongly related to increased width of the tropical rain belt, wider and weaker meridional overturning circulation, colder equatorial cold tongues, and more severe double intertropical convergence zone bias in modern climate models. Tropical sectors (or global zonal means) with low tropical modality are characterized by monsoonal seasonal variations (i.e., seasonal migrations of rainbands following the sun). In sectors with high tropical modality we identify three important seasonal modes: (i) migration of the precipitation distribution toward the warmer hemisphere, (ii) variation in the latitudinal separation between hemispheric rainbands, and (iii) seesaw variation in the intensity of the hemispheric rainbands. In high tropical modality sectors, due to contrasting shifts of the migration and separation modes, counter to general wisdom, seasonal migrations of tropical rainbands cannot be generally assumed to follow the sun.

In recent decades, the subtropical edges of Earth’s Hadley circulation have shifted poleward. Some studies have concluded that this observed tropical expansion is occurring more rapidly than predicted by global climate models. However, recent modeling studies have shown that internal variability can account for a large fraction of the observed circulation trends, at least in an annual-mean, zonal-mean framework. This study extends these previous results by examining the seasonal and regional characteristics of the recent poleward expansion of the Hadley circulation using seven reanalysis datasets, sea level pressure observations, and surface wind observations. The circulation has expanded the most poleward during summer and fall in both hemispheres, with more zonally asymmetric circulation trends occurring in the Northern Hemisphere (NH). The seasonal and regional characteristics of these observed trends generally fall within the range of trends predicted by climate models for the late twentieth and early twenty-first centuries, and in most cases, the magnitude of the observed trends does not exceed the range of interdecadal trends in the models’ control runs, which arise exclusively from internal variability. One exception occurs during NH fall when large observed poleward shifts in the atmospheric circulation over the North Atlantic sector exceed nearly all trends projected by models. While most recent NH circulation trends are consistent with a change in phase of the Pacific decadal oscillation (PDO), the observed circulation trends over the North Atlantic instead reflect 1) large natural variability unrelated to the PDO and/or 2) a climate forcing (or the circulation response to that forcing) that is not properly captured by models.