Abstract
Stateoftheart climate models predict the zonal mean midlatitude circulation will undergo a poleward shift and seasonally and hemispherically dependent intensity changes in the future. Here I review the mechanisms put forward to explain the zonal mean midlatitude circulation response to increased carbon dioxide (CO_{2}) concentration. The mechanisms are grouped according to their thermodynamic starting point, which are thought to arise from processes independent of the zonal mean midlatitude circulation response. There are 24 mechanisms and 8 thermodynamic starting points: (i) increased latent heat release aloft in the tropics, (ii) increased dry static stability and tropopause height outside the tropics, (iii) radiative cooling of the stratosphere, (iv) Hadley cell expansion, (v) increased specific humidity following the ClausiusClapeyron relation, (vi) cloud radiative effect changes, (vii) turbulent surface heat flux changes, and (viii) decreased surface meridional temperature gradient. I argue progress can be made by testing the thermodynamic starting points. I review recent tests of the increased latent heat release aloft in the tropics starting point, i.e., prescribing diabatic perturbations, quantifying the transient response to an abrupt CO_{2} increase and imposing latitudinally dependent CO_{2} concentration. Finally, I provide a future outlook for improving our understanding of predicted changes in the zonal mean midlatitude circulation.
Introduction
The zonal mean midlatitude circulation on Earth encompasses surface westerlies, upper level jet streams, storm tracks, eddies or Rossby waves, and the Ferrel circulation. Decades of research has established that the midlatitudes is an eddydominated regime. More specifically, eddies dominate (1) the surface westerlies via eddy momentum flux convergence [50], (2) the thermally indirect Ferrel circulation via eddy heat fluxes [28, 48], and (3) the transport of moist static energy (MSE, i.e., the sum of dry static and latent energy) between the equator and the pole [62].
For over four decades stateoftheart climate models have predicted zonal mean midlatitude circulation changes in response to increased greenhouse gas (GHG) concentrations, primarily increased carbon dioxide (CO_{2}) concentration. The earliest prediction comes from Manabe and Wetherald [37] who showed zonal mean eddy kinetic energy (EKE) in the upper troposphere shifts poleward in response to a doubling of CO_{2} (see their Fig. 11). Hall et al. [18] showed a poleward shift also occurs for other storm track metrics, including lowlevel eddy temperature and moisture fluxes. The poleward shift of the zonal mean storm tracks has been reproduced in more recent climate model intercomparisons and is largest in the Southern Hemisphere (SH) [1, 2, 8]. In addition, storm track intensity increases in response to increased CO_{2} in the SH [47]. However, in the Northern Hemisphere (NH), the intensity changes are seasonally dependent: intensity increases during winter but decreases during summer [47].
The zonal mean storm track response to increased CO_{2} coincides with a poleward shift of the zonal mean midlatitude westerlies and eddy momentum flux convergence maximum, and a strengthening of the eddydriven jet [1, 56]. The poleward shift is largest in the SH and is robust across the seasonal cycle [56]. Overall, the storm track and eddydriven jet changes in the SH are more robust than those in the NH because of the presence of opposing thermodynamic influences in the NH [20, 51], e.g., the meridional temperature gradient response at the surface and in the upper troposphere are opposite (Fig. 1, top). Thus, the emergent robust multimodel mean response of the zonal mean midlatitude circulation to increased CO_{2} includes (1) a poleward shift, (2) an intensity increase in the SH and during NH winter, and (3) an intensity decrease during NH summer.
The predicted zonal mean midlatitude circulation response is important because it is connected to changes in the hydrological cycle, individual storms, and extreme events [51]. To date, there is some observational evidence for the poleward shift of the zonal mean midlatitude circulation [3, 15] and the weakening of the NH storm track during summer [12]. However, in the SH, the observed poleward shift during SH summer most likely reflects the circulation response to ozone depletion [30].
Simulation does not equal understanding [21]. Confidence in the emergent zonal mean midlatitude circulation response to increased CO_{2} predicted by stateoftheart climate models requires a physically based explanation of the underlying mechanisms. Physically based explanations can be achieved using analytical models (equations), scaling arguments, or a hierarchy of numerical models of varying physical complexity. A success of climate theory has been the physically based explanation of several emergent zonal mean thermodynamic responses to increased CO_{2} predicted by stateoftheart climate models (Fig. 1, top), e.g., amplified warming aloft in the tropics, amplified warming at the surface in the Arctic, rising of the tropopause [13, 20, 64], and the wetgetwetter and drygetdrier response of the hydrological cycle [22]. Unfortunately, similar success does not exist for the response of the zonal mean midlatitude circulation to increased CO_{2} (Fig. 1, bottom). Instead, multiple mechanisms have been proposed, which have not been sufficiently tested.
Here I review the mechanisms that have been proposed to explain the predicted zonal mean midlatitude circulation response to increased CO_{2}. There are many possible ways to define and organize the mechanisms. I choose to define a mechanism broadly, i.e., I include all idealized modeling results that demonstrate a midlatitude circulation response by changing some factor even if the detailed chain of causality is not clear. I choose to organize the mechanisms according to their thermodynamic starting point, which are thought to arise from processes independent of the zonal mean midlatitude circulation response, e.g., tropical convective adjustment or stratospheric radiative adjustment. Before reviewing the mechanisms, I briefly review some relevant frameworks. I then review the mechanisms proposed to explain the (1) poleward shift, (2) intensity increase, and (3) intensity decrease response of the zonal mean midlatitude circulation to increased CO_{2}. I argue progress can be made by testing the thermodynamic starting points. I review recent tests of the thermodynamic starting point tied to tropical convective adjustment. Finally, I provide a future outlook for understanding the zonal mean midlatitude circulation response to increased CO_{2}.
Background on Relevant Frameworks
Before reviewing the mechanisms that have been proposed to explain the zonal mean midlatitude circulation response to increased CO_{2}, it is useful to review some relevant dynamical frameworks.
Barotropic Rossby Wave Dynamics
Assuming eddies can be usefully described as plane waves with perturbation streamfunction \(\psi ^{\prime } = Re [A \exp i(kx+\ell y \omega t)]\) where A is the wave amplitude, k is the zonal wavenumber, ℓ is the meridional wavenumber, and ω is the frequency then they are governed by the Rossby wave dispersion relation:
or
where c is the eddy phase speed, \(\overline {u}\) is the background zonal mean zonal wind, \(\beta ^{*} = \beta \partial ^{2} \overline {u}/\partial y^{2}\) is the meridional gradient of the absolute vorticity, and
[63]. The sign convention of the meridional wave number is such that poleward propagation (ℓ > 0 in NH and ℓ < 0 in SH) occurs poleward of the wave source (poleward side of the jet) and equatorward propagation (ℓ < 0 in NH and ℓ > 0 in SH) occurs equatorward of the wave source (equatorward side of the jet). Linear theory predicts eddies propagate away from their source region and dissipate (break) at the critical latitude where \(\overline {u} = c\) (\(\ell \rightarrow \infty \)) or reflect at the turning latitude where ℓ = 0.
An equation for the eddy momentum flux can be derived using the relationship between the velocity components and the stream function, i.e., \(v^{\prime }=\partial \psi ^{\prime }/\partial x\) and \(u^{\prime }=\partial \psi ^{\prime }/\partial y\):
Consistent with the sign convention discussed above, poleward of the source the eddy momentum flux is equatorward (\(\overline {u^{\prime }v^{\prime }} < 0\) in NH and \(\overline {u^{\prime }v^{\prime }} > 0\) in SH) and equatorward of the source the eddy momentum flux is poleward (\(\overline {u^{\prime }v^{\prime }} > 0\) in the NH and \(\overline {u^{\prime }v^{\prime }} < 0\) in the SH). Thus, eddies propagate away from the source region converging momentum flux into that region and drive surface westerlies [50], i.e., \(\overline {\tau _{u}} \approx  \partial (\langle \overline {u^{\prime }v^{\prime }} \rangle )/\partial y > 0\) where τ_{u} is the zonal surface wind stress and 〈⋅〉 is a massweighted vertical integral. Hereafter, the eddydriven jet is referred to as the jet.
Simpson et al. [56] showed that the response of the zonal mean midlatitude westerlies to increased CO_{2} is dominated by eddy momentum flux convergence changes, i.e.,
According to barotropic dynamics, a change in eddy momentum flux can be decomposed as follows:
where
and
Three possible scenarios of the eddy momentum flux response to increased CO_{2} that lead to a poleward shift of the eddy momentum flux convergence maximum, i.e., the surface westerlies, are illustrated schematically in Fig. 2. Since the meridional wave number and wave propagation are hemisphere dependent, we illustrate the scenarios for the SH. In the first scenario, there is increased poleward momentum flux (equatorward wave propagation, Fig. 2a, red line) around the jet position (Fig. 2a, vertical black line), which leads to a dipole response of the eddy momentum flux convergence (Fig. 2b, red line) that shifts the jet poleward (Fig. 2b, vertical red line). In the second scenario, there is increased equatorward momentum flux (poleward wave propagation, Fig. 2a, blue line) equatorward of the jet position, which decreases the eddy momentum flux convergence on the equatoward side (Fig. 2c, blue line) and shifts the jet poleward (Fig. 2c, vertical blue line). Finally, in the third scenario, there is an eddy momentum flux dipole (Fig. 2a, green line), which shifts the latitude of maximum value of the eddy momentum flux poleward. This leads to a tripole response of the eddy momentum flux convergence (Fig. 2d, green line) that shifts the jet poleward (Fig. 2d, vertical green line). Clearly, there are multiple ways barotropic dynamics can explain a poleward jet shift as discussed in more detail in the section “Mechanisms Explaining the Poleward Shift of the Zonal Mean MidLatitude Circulation” below.
Baroclinic Rossby Wave Dynamics
Assuming eddies can be usefully described as plane waves in the zonal direction then their meridional and vertical structure is determined by solving the quasigeostrophic potential vorticity (PV) equation (a wave equation), which includes a meanstate quasigeostrophic index of refraction, i.e.,
where \(\overline {P}\) is the time and zonal mean PV, f is the Coriolis parameter, N is the buoyancy frequency, and H is the densityscale height [38]. Assuming WKB conditions and linearity, Rossby waves are refracted by gradients of n^{2}: they propagate toward regions of large n^{2} [24]. Thus, a change in the index of refraction affects wave propagation and is often dominated by changes in the mean PV gradient and eddy phase speed, i.e.,
Potential Vorticity Dynamics
The steadystate response of the zonal mean midlatitude westerlies can be connected to the response of the eddy PV flux (\(\overline {v^{\prime }P^{\prime }}\)) and the thermal forcing (Q) following [36]:
where F is the frictional damping of the zonal mean zonal wind and 𝜃 is potential temperature. If the eddy PV flux is assumed to be downgradient, then a change in the eddy PV flux can be decomposed as follows:
where K_{eff} is the effective diffusivity, which can be quantified using the finite amplitude wave activity budget [44, 45].
Mean Available Potential Energy
According to the Lorenz energy cycle, EKE is driven by Mean Available Potential Energy (MAPE). MAPE scales linearly with EKE in idealized simulations and reanalysis data [40, 46, 47]. O’Gorman and Schneider [46] derived the following scaling estimate for MAPE:
where {⋅} is an average over the baroclinic zone, [⋅]_{v} is a vertical average over model sigma levels from \(\sigma _{t}^{\max \limits }\) (model top) to σ_{s} = 0.9, L_{Z} is the width of the baroclinic zone, \({\varGamma } =  \kappa \{\partial \overline {\theta }/\partial p\}^{1}/\{ \overline {p}\}\) is an inverse measure of the dry static stability, and the other symbols have their usual meaning. MAPE is proportional to the square of the Eady growth rate. Changes in MAPE affect the storm track position and intensity and are typically dominated by changes in the inverse dry static stability and meridional temperature gradient, i.e.,
Energy Budget
The dominant components of eddy energy transport are dry static and latent energy, which combine to form MSE. Since the eddy energy flux maximizes in the lower troposphere and is downgradient [29], it is often closed diffusively, i.e.,
where 〈⋅〉 denotes a massweighted vertical integration, m = c_{p}T + gZ + L_{v}q is the MSE, s = c_{p}T + gZ is the dry static energy (DSE). The mean meridional gradient (\(\partial \overline {m}/\partial y\), \(\partial \overline {s}/\partial y\) or \(\partial \overline {T}/\partial y\)) is taken to be near the surface consistent with energy balance models (EBMs). A change in the eddy energy flux can be decomposed as follows:
Held and Soden [22] showed the latent energy flux (\(\langle \overline {Lv^{\prime }q^{\prime }} \rangle \)) in midlatitudes increases following the ClausiusClapeyron relation in response to increased CO_{2} in coupled climate models, i.e., \({\varDelta } \langle \overline {L v^{\prime }q^{\prime }} \rangle \approx \alpha {\varDelta } T \langle \overline {Lv^{\prime }q^{\prime }} \rangle \) where ΔT is the change in global mean surface temperature and α ≈ 7%/K.
Recently, Barpanda and Shaw [2] and Shaw et al. [53] derived a MSE framework that connects changes in storm track position and intensity to (1) changes in energy input to the atmosphere (shortwave absorption, surface heat fluxes and outgoing longwave radiation or OLR) and (2) changes in the MSE flux by the stationary circulation (mean meridional circulation and stationary eddies). More specifically, a change in storm track intensity can be written as follows:
where ϕ_{s} is the storm track position (latitude of maximum value of the eddy MSE flux), ΔF_{SWABS}, ΔF_{SHF}, and ΔF_{OLR} are the change in shortwave absorption, surface heat fluxes and OLR respectively, and \({\varDelta } \langle \overline {v}~\overline {m} \rangle \) is the change in the MSE flux by the stationary circulation.
Mechanisms Explaining the Poleward Shift of the Zonal Mean MidLatitude Circulation
Here I review the mechanisms that have been proposed to explain the poleward shift of the zonal mean midlatitude circulation in response to increased CO_{2}. The mechanisms are grouped according to their thermodynamic starting point.
Increased Latent Heat Release Aloft in the Tropics
Increased CO_{2} increases latent heat release aloft in the tropics due to warmer and moister surface air parcels and assuming moist adiabatic adjustment [20, 64]. The enhanced latent heat release aloft increases the dry static stability of the tropics and strengthens the subtropical meridional temperature gradient in the upper troposphere, which accelerates the subtropical jet via thermal wind balance. The following mechanisms are connected to increased tropical latent heat release aloft:
Butler et al. [4] showed a prescribed diabatic heating in the tropical upper troposphere shifts the storm track and jet poleward in dry dynamical core simulations. Butler et al. [5] argued the prescribed diabatic heating results in a poleward shift of the mean PV gradient, which enhances the eddy PV flux, i.e., \( {\varDelta } \overline {v^{\prime }P^{\prime }} \approx  K_{\text {eff}} \partial {\varDelta }\overline {P}/\partial y\) assuming ΔK_{eff} ≈ 0 (see Eq. 12), on the poleward side of the jet shifting the eddies and circulation poleward. Figure 8 in [5] is a schematic of their mechanism.
Riviere [49] showed that when the meridional temperature gradient in the upper troposphere is increased in a threelevel quasigeostrophic model, long waves become more unstable, and the increased eddy length scale favors anticyclonic wave breaking and a poleward shift of the jet.
Kidston and Vallis [27] and Lorenz [33] used barotropic models to show that the acceleration of the zonal wind aloft reduces the meridional gradient of the absolute vorticity on the flanks of the jet (\({\varDelta } \beta ^{*}= \partial ^{2} {\varDelta } \overline {u}/\partial y^{2}<0\), see Eq. 8), which affects the turning latitude (where ℓ = 0) on the poleward side of the jet. There is increased wave reflection from the poleward side of the jet, equatorward wave propagation (\({\varDelta } \ell \approx {\varDelta } \beta ^{*}/ 2\ell (\overline {u}c) > 0\) in the SH, see Eq. 7), a poleward momentum flux response (\({\varDelta } \overline {u^{\prime }v^{\prime }} \approx A^{2}k {\varDelta } \ell /2 < 0\) in the SH, see Eq. 6), and a poleward shift of the jet. This is analogous to scenario 1 in Fig. 2.
Lu et al. [36] showed that the eddy PV flux response to prescribed diabatic heating in the tropical upper troposphere in a dry dynamical core model leads to a poleward shift of the jet due to a change in effective diffusivity (\({\varDelta } \overline {v^{\prime }P^{\prime }} \approx  {\varDelta } K_{\text {eff}} \partial \overline {P}/\partial y\), see Eq. 12) rather than due to a change in the mean PV gradient, which was argued to be the important factor by [5] (see above). Their results were based on the finite amplitude wave activity budget. Figure 10 in [36] is a schematic of their mechanism.
Increased Dry Static Stability and Tropopause Height Outside the Tropics
Increased CO_{2} increases the dry static stability and tropopause height outside the tropics in stateoftheart climate models [64]. While the cause of the stability and tropopause height responses may not be independent of the circulation response, the following mechanisms rely on vertical temperature changes outside the tropics:
Lorenz and DeWeaver [32] showed that artificially raising the tropopause poleward of the climatological jet shifts the jet poleward in dry dynamical core simulations. Interestingly, raising the tropopause equatorward of the climatological jet shifts the jet equatorward.
Frierson [14] argued increased subtropical dry static stability reduces eddy generation on the equatorward side of the jet (ΔA < 0 where ℓ > 0 in the SH), leading to an equatorward momentum flux response (\({\varDelta } \overline {u^{\prime }v^{\prime }} \approx Ak\ell {\varDelta } A > 0\) in the SH, see Eq. 6) and a poleward jet shift. This is analogous to scenario 2 in Fig. 2.
Chen et al. [10] and Lu et al. [35] argued that the increased extratropical tropopause height increases the meridional temperature gradient and zonal wind, and leads to faster eddy phase speeds (\({\varDelta } (\overline {u}  c) < 0\)), a poleward shift of the critical latitude (where \(\overline {u}=c\)) on the equatorward side of the jet, equatorward wave propagation (\({\varDelta } \ell \approx \beta ^{*}{\varDelta } (\overline {u}c)/(2\ell (\overline {u}c)^{2}>0\) in the SH, see Eq. 7), a poleward shift of the latitude of maximum absolute value of the eddy momentum flux, and a poleward shift of the jet. This is analogous to scenario 3 in Fig. 2.
Kidston et al. [25, 26] argued that increased dry static stability causes an increase in the eddy length scale, i.e., Rossby radius of deformation L_{R} = NH/f, thus Δk < 0, a decrease in the eddy phase speed relative to the background mean wind, a poleward shift of the critical line (where \(\overline {u}=c\)) on the poleward side of the jet, a poleward momentum flux response (\({\varDelta } \overline {u^{\prime }v^{\prime }} \approx A\ell {\varDelta } k < 0\) in the SH, see Eq. 6), leading eddies to dissipate further poleward, and shifting the jet poleward. This is analogous to scenario 1 in Fig. 2.
Radiative Cooling of the Stratosphere
Increased CO_{2} cools the stratosphere via radiative adjustment [20, 64]. The following mechanisms rely on the stratospheric response:
Sigmond et al. [55] showed that doubling CO_{2} only in the middle atmosphere (above the climatological tropopause) shifts the jet poleward in a prescribed sea surface temperature (SST) atmospheric general circulation model (AGCM).
Butler et al. [4] showed that a prescribed diabatic cooling in the polar lower stratosphere shifts the storm track and jet poleward in dry dynamical core simulations.
Wu et al. [68] showed that the transient evolution of the poleward shift of the jet in response to CO_{2} doubling in an AGCM was dominated by changes in the stratosphere. More specifically, the subpolar lower stratospheric zonal wind response increased the index of refraction via the mean PV gradient (\({\varDelta } n^{2} \approx (\partial {\varDelta } \overline {P}/\partial y)/(\overline {u}c)/a>0\), see Eq. 9) on the poleward side of the jet such that eddies propagate further poleward and shift the jet poleward.
Hadley Cell Expansion
Increased CO_{2} leads to a poleward shift of the Hadley cell edge [34], and several theories have been proposed to explain its poleward shift [57]. Mbengue and Schneider [39, 40] showed the Hadley cell and storm track shifts were related in dry dynamical core simulations via MAPE changes that were dominated by the meridional temperature gradient response (\({\varDelta } \text {MAPE} \approx \frac {c_{p} p_{0}}{24g} (\sigma _{s}  \sigma _{t}^{\max \limits }) {L_{Z}^{2}} [ {\varGamma }]_{v} {\Delta }[ \{\partial _{y} \overline {T}\} ]^{2}_{v} \), see Eq. 14). Mbengue and Schenider [41] showed the expansion of the Hadley cell shifts the nearsurface meridional temperature gradient poleward, which shifts the latitude of maximum MAPE, and thus the storm track poleward in an EBM. An equation linking the storm track position to the Hadley cell edge and nearsurface meridional temperature gradient can be derived using the EBM (see equation 10 in [41]).
Increased Specific Humidity Following the ClausiusClapeyron Relation
Increased CO_{2} increases the saturation specific humidity and nearsurface specific humidity following the ClausiusClapeyron relation [22]. The following mechanisms rely on changes in specific humidity following the ClausiusClapeyron relation:
Held [23] argued that if the total MSE flux is constant in response to increased CO_{2} (\({\varDelta } \langle \overline {v^{\prime }m^{\prime }} \rangle = {\varDelta } \langle \overline {Lv^{\prime }q^{\prime }} \rangle + {\varDelta } \langle \overline {v's^{\prime }} \rangle \approx 0\)), then increased latent energy flux following the ClausiusClapeyron relation (\({\varDelta } \langle \overline {Lv^{\prime }q^{\prime }} \rangle \approx \alpha {\varDelta } T \langle \overline {Lv^{\prime }q^{\prime }} \rangle < 0\) in the SH) should result in decreased DSE flux (\({\varDelta } \langle \overline {v's^{\prime }} \rangle >0 \) in the SH). Since the increased latent energy flux occurs on the equatorward side of the latitude of the maximum absolute value of the DSE flux, the corresponding DSE flux decrease leads to a poleward shift of the latitude of maximum absolute value of the DSE flux, i.e., a poleward shift of the dry storm track.
Shaw and Voigt [52] showed that if the total MSE flux is constant in response to SST warming (\({\varDelta } \langle \overline {v^{\prime }m^{\prime }} \rangle \approx 0\)) and the nearsurface meridional MSE gradient response to increased CO_{2} follows the ClausiusClapeyron relation (\(\partial {\varDelta } \overline {m}/\partial y \approx \alpha ^{2} {\varDelta } T L q\partial \overline {T}/ \partial \phi /a \)), then the eddy diffusivity change [\({\varDelta } D_{m} \approx  D_{m} (\alpha ^{2} {\varDelta } T L q\partial \overline {T}/ \partial \phi /a) / (\partial \overline {m}/\partial y)\), see Eq. 17 with \({\varDelta } \langle \overline {v^{\prime }m^{\prime }} \rangle \approx 0\) and \(\partial {\varDelta } \partial \overline {m}/\partial y \approx \alpha ^{2} {\varDelta } T L q\partial \overline {T}/ \partial \phi /a \)] shifts the maximum diffusivity, i.e., the storm track, poleward in aquaplanet models.
Cloud Radiative Effect Changes
Increased CO_{2} leads to an upward shift of high clouds, which impacts the longwave cloud radiative effect (CRE). There is also an increase in cloudliquid water in midtohigh latitudes in response to warming, which primarily impacts the shortwave CRE [6]. While it is unclear how much of the CRE response to increased CO_{2} is shaped by the circulation, the following mechanisms rely on CRE changes.
Voigt and Shaw [65] showed that prescribing the cloud radiative response to warming in climatological prescribed SST aquaplanet simulations leads to a poleward jet shift. Voigt an Shaw [66] showed the poleward shift is dominated by the response of midlatitude (20–50^{∘}) high clouds.
Shaw and Voigt [52] showed the atmospheric CRE (ACRE) response (top of atmosphere minus surface CRE) to warming in prescribed SST aquaplanet simulations implies a change in atmospheric energy transport (\({\varDelta } \langle \overline {vm} \rangle =2\pi a^{2} {\int \limits }^{\phi }_{\pi /2} {\cos \limits } \phi {\varDelta } F_{\text {ACRE}} ~ d \phi \)) that shifts the latitude of the maximum absolute value of the MSE transport poleward.
Ceppi and Hartmann [7] showed that prescribing the shortwave cloud radiative response to increased CO_{2} in a climatological slabocean aquaplanet simulation dominates the poleward shift of the midlatitude circulation.
Li et al. [31] showed that prescribing the highcloud radiative response in a dry dynamical core shifts the jet poleward.
Mechanisms Explaining the Intensification of the Zonal Mean MidLatitude Circulation
Here I review the mechanisms that have been proposed to explain the intensification of the zonal mean midlatitude circulation in response to increased CO_{2}. Once again, the mechanisms are grouped according to their thermodynamic starting point.
Increased Latent Heat Release Aloft in the Tropics

Held [20] argued that an increase in the meridional temperature gradient aloft should increase eddy energy (ΔA > 0), leading to an equatorward momentum flux response poleward of the source (\({\varDelta } \overline {u^{\prime }v^{\prime }} \approx Ak\ell {\varDelta } A > 0\) where ℓ < 0 in the SH, see Eq. 6), a poleward momentum flux response equatorward of the source (\({\varDelta } \overline {u^{\prime }v^{\prime }} \approx Ak\ell {\varDelta } A < 0\) where ℓ > 0 in the SH, see Eq. 6), convergence of eddy momentum flux into the source region and a strengthening of the jet.

O’Gorman [47] showed the EKE increase in response to increased CO_{2} in the SH and during NH winter follows an increase in MAPE. The MAPE increase in the SH was connected to the robust increase of the meridional temperature gradient in the upper troposphere (\({\varDelta } \text {MAPE} \approx \frac {c_{p} p_{0}}{24g} (\sigma _{s}  \sigma _{t}^{\max \limits }) {L_{Z}^{2}} [ {\varGamma }]_{v} {\Delta }[ \{ \partial _{y} \overline {T}\} ]^{2}_{v} > 0 \), see Eq. 14).
Turbulent Surface Heat Flux Changes
Shaw et al. [53] used the MSE framework for storm tracks to show that the SH storm track intensifies in response to SST warming in prescribed SST AGCM simulations following the increase in the equatortopole energy gradient induced by changes in surface heat fluxes, i.e., more evaporation in the tropics than at the South Pole (\({\varDelta } \langle \overline {v^{\prime }m^{\prime }} \rangle = 2\pi a^{2} {\int \limits }^{\pi /2}_{\phi _{s}} \cos \limits \phi {\varDelta } F_{\text {SHF}}~ d \phi > 0\), see Eq. 19).
Mechanisms Explaining the Weakening of the Zonal Mean MidLatitude Circulation
Here I review the mechanisms that have been proposed to explain the weakening of the zonal mean midlatitude circulation in response to increased CO_{2}. Recall that a weakening of the zonal mean midlatitude circulation occurs in response to increased CO_{2} during NH summer. Most of the mechanisms below were not proposed to explain the seasonality of the NH response to increased CO_{2}. Thus, it is not clear in all cases why the mechanisms below should apply only during NH summer. It is possible that different mechanisms operate in NH winter and summer and that more than one mechanism operates in a given season. Once again, the mechanisms are grouped according to their thermodynamic starting point.
Increased Specific Humidity Following the ClausiusClapeyron Relation
The following mechanisms rely on changes in specific humidity following the ClausiusClapeyron relation:
Held [23] argued that if the total MSE flux is constant in response to increased CO_{2} (\({\varDelta } \langle \overline {v^{\prime }m^{\prime }} \rangle \approx 0\)), then increased latent energy flux following the ClausiusClapeyron relation (\({\varDelta } \langle \overline {Lv^{\prime }q^{\prime }} \rangle \approx \alpha {\varDelta } T \langle \overline {Lv^{\prime }q^{\prime }} \rangle <0 \) in the SH) should result in decreased DSE flux (\({\varDelta } \langle \overline {v's^{\prime }} \rangle >0 \) in the SH), i.e., a weakening of the dry storm track.
Shaw and Voigt [52] showed that if one assumes the total MSE flux is constant in response to SST warming (\({\varDelta } \langle \overline {v^{\prime }m^{\prime }} \rangle \approx 0\)) and the nearsurface MSE gradient response to increased CO_{2} follows the ClausiusClapeyron relation (\(\partial {\varDelta } \overline {m}/\partial y \approx \alpha ^{2} {\varDelta } T L q\partial \overline {T} / \partial \phi /a < 0\)), then the eddy diffusivity decreases [ΔD_{m} ≈−D_{m}\((\alpha ^{2} {\varDelta } T L q\partial \overline {T} / \partial \phi /a) / (\partial \overline {m}/\partial y)<0\), see Eq. 17 with \({\varDelta } \langle \overline {v^{\prime }m^{\prime }} \rangle \approx 0\) and \(\partial {\varDelta } \overline {m}/\partial y \approx \alpha ^{2} {\varDelta } T L q\partial \overline {T} / \partial \phi /a < 0\)], i.e., the storm track weakens (see their Eq. 11) in aquaplanet models.
Increased Dry Static Stability Outside the Tropics
O’Gorman [47] showed the weakening of the zonal mean midlatitude EKE during NH summer in response to increased CO_{2} follows the decrease in MAPE, which is partly related to increased dry static stability (\({\varDelta } \text {MAPE} \approx \frac {c_{p} p_{0}}{24g} (\sigma _{s}  \sigma _{t}^{\max \limits }) {L_{Z}^{2}} {\varDelta } [ {\varGamma }]_{v} [ \{ \partial _{y} \overline {T}\} ]^{2}_{v} < 0 \), see Eq. 14).
Decreased Surface Meridional Temperature Gradient
In addition to the stability changes discussed above, Gertler and O’Gorman [16] showed that the weakening of the surface meridional temperature gradient in midlatitudes around NH land also contributes to the decrease of nonconvective MAPE (\({\varDelta } \text {MAPE} \approx \frac {c_{p} p_{0}}{24g} (\sigma _{s}  \sigma _{t}^{\max \limits }) {L_{Z}^{2}} [ {\varGamma }]_{v} {\Delta }[ \{ \partial _{y} \overline {T}\} ]^{2}_{v} < 0 \), see Eq. 14).
Turbulent Surface Heat Flux Changes
Shaw et al. [53] used the MSE framework for storm tracks to show that the storm track weakens in response to increased CO_{2} over land during NH summer following the decreased equatortopole energy gradient induced by changes in surface heat fluxes over land, i.e., land warms more than the atmosphere and ocean (\({\varDelta } \langle \overline {v^{\prime }m^{\prime }} \rangle = {\int \limits }^{\pi /2}_{\phi _{s}} a \cos \limits \phi {\varDelta } F_{\text {SHF}}~ d \phi < 0\), see Eq. 19).
Testing Mechanisms
There are 24 mechanisms and 8 thermodynamic starting points:
 1.
Increased latent heat release aloft in the tropics
 2.
Increased dry static stability and tropopause height outside the tropics
 3.
Radiative cooling of the stratosphere
 4.
Hadley cell expansion
 5.
Increased specific humidity following the ClausiusClapeyron relation
 6.
Cloud radiative effect changes
 7.
Turbulent surface heat flux changes
 8.
Decreased surface meridional temperature gradient
that have been proposed to explain the zonal mean midlatitude circulation response to increased CO_{2}. While the mechanisms are not necessarily distinct, it is very unlikely that so many are needed to explain the response of the zonal mean midlatitude circulation to increased CO_{2}. Since there are fewer thermodynamic starting points than mechanisms, it is useful to test the thermodynamic starting points. If a thermodynamic starting point is falsified, then all the mechanisms tied to it are falsified. If a thermodynamic starting point is confirmed, then more work is needed to determine which mechanism tied to that starting point is correct.
To date, there exist several different tests of thermodynamic starting points explaining the zonal mean midlatitude circulation response to increased CO_{2}: (1) prescribing diabatic perturbations, (2) quantifying the transient response to an abrupt CO_{2} increase, and (3) imposing latitudinally dependent CO_{2} concentration. In what follows, I review how these approaches have been used to test whether the increased latent heat release aloft in the tropics starting point (see section “Increased Latent Heat Release Aloft in the Tropics”), hereafter referred to as the tropical starting point, can explain the annual mean poleward shift of the zonal mean midlatitude circulation response to increased CO_{2} in the SH.
For the prescribed diabatic perturbation approach, the test of the tropical starting point is conducted by prescribing a diabatic pertubation in the tropical upper troposphere, which mimics the tropical temperature response in CMIP5 models (Fig. 1, top), in a dry dynamical core model. If there is no poleward shift then the tropical starting point is falsified. The results of these tests show (1) raising the tropopause equatorward of the climatological jet shifts the jet equatorward [32] and (2) prescribing diabatic heating in the tropical upper troposphere leads to a poleward shift of the midlatitude circulation only if the heating extends into the subtropics [4, 36, 59, 61].
It is difficult to interpret the results of tests that prescribe diabatic perturbations (e.g., prescribing diabatic heating in dry dynamical core simulations or prescribing the cloud radiative response to increased CO_{2} in aquaplanet simulations) for several reasons. Prescribed diabatic perturbations require knowledge of the equilibrium response to increased CO_{2}, which is shaped by the circulation. The perturbations, including their meridional and vertical extent, have not been shown to occur in the absence of the circulation response, i.e., in radiativeconvective equilibrium either without [60] or with the climatological circulation. Thus, it is possible the meridional extension of the prescribed diabatic heating into the subtropics is shaped by the circulation and encodes the circulation response. In order for tests involving prescribed diabatic perturbations to be useful the perturbations must be shown to occur in response to increased CO_{2} in radiativeconvective equilibrium either without [60] or with the climatological circulation.
The remaining approaches for testing the tropical starting point (quantifying the transient response to an abrupt CO_{2} increase and imposing latitudinally dependent CO_{2} concentration) do not suffer from the issues associated with prescribing diabatic perturbations because the diabatic response emerges as part of the model solution. For the transient response approach, the test of the tropical starting point is conducted by quantifying the timescale of the response of the tropical starting point and the zonal mean midlatitude circulation shift to an abrupt CO_{2} increase. If the timescale of the tropical response and midlatitude shift are different, then the tropical starting point is falsified. Recent tests of the transient response to abrupt 4 × CO_{2} in the SH in CMIP5 models shows the eddy momentum flux and eddydriven jet evolve on a faster timescale than the maximum absolute value of the upper tropospheric meridional temperature gradient from 0 to 45^{∘} S and the subtropical jet strength (compare the orange and purple lines to the blue and pink lines in Fig. 3), which are connected to the tropical starting point [42]. Using similar CMIP5 experiments, Chemke and Polvani [9] showed the eddy momentum flux also responds faster than the surface meridional temperature gradient in the subtropics. The fast timescale response of the eddy momentum flux and eddydriven jet to an abrupt CO_{2} increase is similar to that of subtropical dry static stability and the Hadley cell edge (compare the orange and purple lines to the red line in Fig. 3). The slow timescale response of the subtropical jet and maximum absolute value of the meridional temperature gradient to an abrupt CO_{2} increase follows the evolution of global mean surface temperature, which is dominated by tropical adjustment. Interestingly, the eddydriven jet also exhibits a distinct evolution in response to uniform sea surface temperature warming compared to the subtropical jet [11].
Finally, for the latitudinally dependent CO_{2} concentration approach, the test of the tropical starting point is conducted by increasing CO_{2} concentration only in the tropics (20^{∘} S to 20^{∘} N). The CO_{2} concentration can be easily prescribed as a constant value in each latitudinal grid box for all longitudes in most climate models. If there is no poleward shift in response to the tropical CO_{2} increase, then the tropical starting point is falsified, assuming the response to increased CO_{2} is linear. The response is linear if the sum of the response to increased CO_{2} in the tropics and outside the tropics is close to the response when CO_{2} increases everywhere. Shaw and Tan [54] showed quadrupling CO_{2} concentration in the tropics in aquaplanet models does not produce a significant circulation shift (Fig. 4) even though it does produce a large response of the subtropical meridional temperature gradient in the upper troposphere and subtropical jet strength. Similar results are obtained for the SH circulation when quadrupling CO_{2} in the tropics of a slabocean AGCM with climatological qflux (Fig. 5). The SH response in the aquaplanet and AGCM are close to linear for a number of shift metrics (compare sum of red, blue, and green crosses to black cross in Fig. 6). The latitudinal decomposition shows quadrupling CO_{2} in the subtropics dominates the poleward shift of the SH circulation in the aquaplanet and slabocean AGCM (Fig. 6).
Overall, the recent tests discussed above do not support the tropical starting point and its underlying mechanisms (see section “Increased Latent Heat Release Aloft in the Tropics”) as an explanation for the poleward shift of the SH midlatitude circulation in response to increased CO_{2}. More specifically, (1) the meridional temperature gradient and subtropical jet strength evolve on a different timescale than the midlatitude circulation shift in response to an abrupt CO_{2} increase and (2) increased CO_{2} in the tropics does not produce a significant poleward shift. Instead, the tests lend support to the increased dry static stability and tropopause height outside the tropics starting point (see section “??”). However, more tests are needed, including with climate models across the model hierarchy, before falsifying the tropical starting point. The results above demonstrate the importance of using climate models in novel ways to test mechanisms.
Future Outlook
Future progress in understanding the zonal mean midlatitude circulation response to increased CO_{2} relies on (1) carefully designed climate model experiments that attempt to falsify the thermodynamic starting points and assumptions underlying the proposed mechanisms and (2) subsequently using the remaining mechanisms to create emergent constraints. Several approaches can be used to test mechanisms, for example, (1) imposing diabatic perturbations based on the response to increased CO_{2} in radiativeconvective equilibrium either in the absence [60] or presence of the climatological circulation, (2) quantifying the transient evolution of the circulation response to an abrupt CO_{2} increase [9, 11, 17, 36, 42, 67, 68], (3) imposing latitudinally dependent CO_{2} concentration [54], (4) quantifying the seasonality of the mechanisms, and (5) nudging parameters to their climatological value, e.g., turning off wind induced surface heat exchange [43]. Emergent constraints (see [19]) are needed in order to quantify and compare the modeled mechanisms to those in the real atmosphere. Finally, in addition to recommending more be done to falsify existing mechanisms, I would also recommend any new mechanism proposed in the future should (1) be simple, (2) be able to predict the circulation response without running a model, (3) involve an equation (to ensure transparency), and (4) be falsifiable.
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Acknowledgments
TAS thanks the section editor Isla Simpson and two anonymous reviewers for their comments and Molly Menzel for providing Fig. 3.
Funding
TAS acknowledges support from the National Science Foundation (AGS1742944) and the David and Lucile Packard Foundation.
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Shaw, T.A. Mechanisms of Future Predicted Changes in the Zonal Mean MidLatitude Circulation. Curr Clim Change Rep 5, 345–357 (2019). https://doi.org/10.1007/s40641019001458
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Keywords
 Circulation
 Climate change