1. Introduction
The general circulation of the atmosphere is expected to change in a variety of ways as climate warms in response to CO2-induced radiative forcing. Projected circulation responses include a widening of the Hadley circulation (Lu et al. 2007), a narrowing of the intertropical convergence zone (ITCZ) (Byrne and Schneider 2016b), a slowdown in the Walker circulation (Vecchi and Soden 2007), and a poleward shift of the midlatitude storm tracks (Yin 2005; Schneider et al. 2010). Regional climate change, including projected changes in the water cycle, is strongly dependent on these circulation responses (e.g., Seager et al. 2010; Scheff and Frierson 2012; Shepherd 2014; Byrne and O’Gorman 2015). Not only does the circulation affect regional climate, but it has also been suggested that global climate change may be amplified or dampened by the atmospheric circulation response via its effect on the planetary radiation budget (e.g., Pierrehumbert 1995); we refer to this effect as the “atmospheric dynamics feedback.”
Studies of how atmospheric circulation responses to global warming affect top-of-the-atmosphere (TOA) radiation and climate have largely focused on interactions between the tropical circulation and clouds (Lindzen et al. 2001; Bony et al. 2004; Wyant et al. 2006; Mauritsen and Stevens 2015; Bony et al. 2016). The “iris” hypothesis of Lindzen et al. (2001) argued that a decrease in the portion of the tropics covered by high clouds and a concurrent increase in low-cloud area under global warming is an important negative feedback on climate change. Pierrehumbert (1995) put forward a similar mechanism as a potential means of regulating tropical sea surface temperatures in warm climates of the past (e.g., the Eocene). The physics of this proposed negative feedback are intuitive and rely on differences in cloud-radiative effect between low-cloud and high-cloud regions. The shortwave and longwave cloud-radiative effects are defined conventionally as the differences between the clear-sky outgoing shortwave or longwave fluxes at TOA and the all-sky outgoing fluxes (Allan 2011). Specifically, the shortwave cloud-radiative effect is 
Although the validity of the original iris hypothesis proposed by Lindzen et al. (2001) has been strongly challenged (e.g., Fu et al. 2002), recent studies have revived interest in iris-type phenomena as potentially important feedbacks on climate change (Mauritsen and Stevens 2015; Bony et al. 2016; Cronin and Wing 2017). The suggestion that tropical convection will become more aggregated as sea surface temperatures increase (e.g., Wing and Emanuel 2014) has formed the conceptual basis for these so-called iris 2.0 studies. Convective aggregation is not typically simulated by global climate models, in which convection is parameterized out of necessity, but it has been put forward as a negative iris-type atmospheric dynamics feedback (Bony et al. 2016; Wing et al. 2017; Cronin and Wing 2017). Perhaps related to convective aggregation, a narrowing of tropical high-cloud regions (i.e., the ITCZ) relative to neighboring low-cloud regions under global warming has been observed over recent decades (Wodzicki and Rapp 2016) and further narrowing is expected as the climate continues to warm (Lau and Kim 2015; Byrne and Schneider 2016b). This ITCZ narrowing represents another potential iris effect. At higher latitudes, cloud feedbacks associated with shifts in the extratropical circulation have received considerable attention in recent years (Grise et al. 2013; Kay et al. 2014; Wall and Hartmann 2015), although climate models disagree on the magnitude and importance of these feedbacks (Ceppi et al. 2017).
The studies mentioned above focus on cloud feedbacks, but it is plausible that a reorganization of the atmospheric circulation could also affect the water vapor feedback by changing the spatial pattern and intensities of moisture convergence and divergence zones. More generally, atmospheric circulation changes can conceivably influence both the cloud-radiative effect and all-sky TOA radiative fluxes at all latitudes, but the magnitudes of these atmospheric dynamics feedbacks and their dependences on latitude are unknown. Are there latitudes at which climate feedbacks are dominated by large-scale circulation changes? How do these circulation changes contribute to global climate change? Can our emerging understanding of atmospheric dynamics in a changing climate be used to better constrain global climate sensitivity? Are low-latitude or high-latitude circulation changes more effective at changing global-mean surface temperature? Related to this latter question, a number of studies have shown that the spatial pattern of ocean heat uptake strongly affects the global temperature response (Armour et al. 2013; Rose et al. 2014; Rugenstein et al. 2016); that is, heat absorbed by the ocean at high latitudes has a stronger effect on global temperature than the same quantity of heat absorbed at low latitudes. Should such a latitudinal dependence also exist for the atmospheric dynamics feedback, it would have important implications for the ability of tropical iris-type mechanisms to regulate past and future climate change.
Here we use coupled climate models together with idealized simulations to assess how large-scale atmospheric circulation changes contribute to TOA radiative feedbacks and global climate change. We begin by outlining the method used to decompose dynamic versus thermodynamic influences on TOA radiation (section 2) before analyzing the atmospheric dynamics feedback in simulations with coupled models (section 3). Idealized simulations with stylized TOA radiative forcings are also performed to understand how circulation changes at different latitudes could influence global climate (section 4). We conclude by summarizing our results and discussing directions for future research (section 5).
2. Estimating the atmospheric dynamics feedback
a. CMIP5 simulations
We will investigate the role of the atmospheric circulation in controlling radiative feedbacks using simulations from phase 5 of the Coupled Model Intercomparison Project (CMIP5; Taylor et al. 2012). In particular, we analyze changes in TOA radiative fluxes for 27 models1 between preindustrial control runs (piControl) and runs in which the CO2 concentration is instantaneously quadrupled relative to preindustrial levels (abrupt4xCO2). For both the piControl and abrupt4xCO2 runs, we analyze 100 years of monthly-mean data. All-sky and clear-sky TOA radiative fluxes are defined as positive downward.
b. Dependence of top-of-the-atmosphere radiation on the atmospheric circulation
To estimate the radiative feedbacks associated with changes in the large-scale atmospheric circulation, we first decompose TOA radiative anomalies (e.g., due to changes in greenhouse gas concentrations) into dynamic, thermodynamic, and nonlinear components (where “nonlinear” here means the combined influence of changes in dynamic and thermodynamic processes on TOA radiation). To perform this decomposition, we follow Bony et al. (2004) in using the midtropospheric vertical velocity ω as an admittedly imperfect proxy for dynamical effects. That is, we decompose changes in TOA fluxes into those that are, and are not, associated with vertical velocity changes.
The dependence of tropical cloud-radiative effect on vertical velocity (Fig. 1a) and the area PDF of vertical velocity (Fig. 1d) in one coupled climate model are similar to the observed functions [cf. Fig. 2 in Bony et al. (2004)]. Note that in Fig. 1, each quantity has been averaged from 
The annual-mean TOA tropical (averaged from 
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
The annual-mean TOA tropical (averaged from
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
The annual-mean TOA tropical (averaged from
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
Although we would not necessarily expect the dependence of clear-sky radiative fluxes on vertical velocity to be as strong as that found for the cloud-radiative effect, it is plausible that regions of low-level convergence would be moister than regions of divergence, which would have a signature in the clear-sky radiative flux and contribute to an all-sky flux dependence on vertical velocity. Indeed, tropical ascending regions are observed to have smaller clear-sky longwave cooling relative to descending regions (Bony et al. 1997); this clear-sky flux dependence on vertical velocity is at least qualitatively captured by climate models (Fig. 1b). There is also a simulated dependence of clear-sky shortwave radiation on vertical velocity (Fig. 1b), with regions of descent generally having a larger outgoing shortwave flux and a stronger longwave radiative cooling (presumably because the atmosphere in these descending regions is dry and consequently absorbs less shortwave radiation, e.g., above deserts such as the Sahara). The influences of vertical velocity on clear-sky fluxes and on the cloud-radiative effect combine to produce a strong dependence of all-sky fluxes on vertical velocity, particularly the longwave fluxes (Fig. 1c). Figure 1 shows the relationships of cloud-radiative effect, clear-sky fluxes, and all-sky fluxes to vertical velocity for one climate model, but these relationships are qualitatively similar for the other 26 models analyzed (not shown).
The area PDF of vertical velocity in a climate model shows a skewed distribution in the tropics (Fig. 1d), with a large area covered by slow-moving descending air masses—the so-called radiator fin regions where longwave cooling is strong (Pierrehumbert 1995). The area PDF has a relatively small ascent region with a larger variance in vertical velocity compared to the descent region (Fig. 1d) and is qualitatively similar to a PDF calculated using reanalysis data (Bony et al. 2004).
c. Dynamic/thermodynamic decomposition of changes in top-of-the-atmosphere radiation
In general, the dynamic components of (4) and (5) could be due to changes in the areas occupied by ascending versus descending air (e.g., a narrowing of the ITCZ), strengthening/weakening of the circulations within the ascending and descending regimes (e.g., a slowdown of the Walker circulation), or spatial shifts in circulation features (e.g., a poleward movement of the storm track). It should be noted that dynamic processes, for example lower-tropospheric mixing or convective mass fluxes, that might be decoupled from midtropospheric vertical velocity or that are not explicitly resolved by global climate models, do not form part of what we define as the (large scale) dynamic components and are instead included in the thermodynamic components (Wyant et al. 2006). The thermodynamic components represent the portion of the all-sky radiative response or the change in cloud-radiative effect that would occur if the atmospheric circulation did not change [i.e., for fixed 
Our method of evaluating (4) and (5) differs from that of Bony et al. (2004) in a number of respects. First, we perform the decomposition over the whole globe, not only for tropical regions, and construct the 
When performing the decompositions (4) and (5), the vertical-velocity limits of 
d. Feedback calculation
3. Atmospheric dynamics feedback in coupled climate models
a. Feedbacks versus latitude
The multimodel-mean all-sky and cloud feedbacks in the abrupt4xCO2 simulations are plotted in Fig. 2, along with the thermodynamic, dynamic, and nonlinear components of these feedbacks. The nonlinear component is substantially smaller than the dynamic component so for simplicity we will mostly show the sum of the dynamic and nonlinear components rather than each individually (a discussion of the factors controlling the magnitude of the nonlinear component is provided later in this section).
Multimodel-mean total (a) all-sky and (b) cloud feedbacks vs latitude (black lines) in the abrupt4xCO2 simulations. The thermodynamic (blue lines) and the dynamic components (red solid lines) of the feedbacks are also plotted, along with the nonlinear components (red dashed lines). Each total feedback and component has been estimated using least squares regression over the first 100 years of the abrupt4xCO2 simulations. In this figure and in all subsequent figures in which quantities are plotted as a function of latitude, each term has been multiplied by a factor of 
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
Multimodel-mean total (a) all-sky and (b) cloud feedbacks vs latitude (black lines) in the abrupt4xCO2 simulations. The thermodynamic (blue lines) and the dynamic components (red solid lines) of the feedbacks are also plotted, along with the nonlinear components (red dashed lines). Each total feedback and component has been estimated using least squares regression over the first 100 years of the abrupt4xCO2 simulations. In this figure and in all subsequent figures in which quantities are plotted as a function of latitude, each term has been multiplied by a factor of
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
Multimodel-mean total (a) all-sky and (b) cloud feedbacks vs latitude (black lines) in the abrupt4xCO2 simulations. The thermodynamic (blue lines) and the dynamic components (red solid lines) of the feedbacks are also plotted, along with the nonlinear components (red dashed lines). Each total feedback and component has been estimated using least squares regression over the first 100 years of the abrupt4xCO2 simulations. In this figure and in all subsequent figures in which quantities are plotted as a function of latitude, each term has been multiplied by a factor of
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
1) All-sky and cloud feedbacks
As expected, the total all-sky feedback is negative (i.e., decreasing net downward radiation at TOA as climate warms) at all latitudes (Fig. 2a). The thermodynamic component typically dominates the all-sky feedback but the dynamic component is substantial in the tropics, where its magnitude is up to half of the magnitude of the thermodynamics feedback. Changes in large-scale circulation produce a positive dynamics feedback close to the equator (the opposite of a negative iris feedback) and contribute +0.5 W m−2 K−1 global warming to the TOA imbalance in that region. The positive all-sky dynamics feedback in the deep tropics is a result of cloud (Fig. 2b) and clear-sky feedbacks (not shown) and extends into the Southern Hemisphere subtropics, although the magnitude is smaller than in the deep tropics. In the Northern Hemisphere subtropics, the dynamics feedback is more complex, with a positive–negative dipole between 10° and 30°N (Fig. 2a).
The latitudinal structure of the dynamics feedback broadly reflects changes in midtropospheric vertical velocity (Fig. 3): A strengthening of ascent in the core of the ITCZ under global warming intensifies moisture convergence in that region, which increases atmospheric water vapor and enhances the longwave greenhouse effect (Figs. 4a,b). These positive longwave all-sky and cloud feedbacks in the ITCZ are caused by strengthening ascent and moisture convergence in the middle of the ITCZ with warming (Byrne and Schneider 2016b) and an upward shift in the altitude of high clouds (Zelinka et al. 2012), which together produce a large and positive dynamics feedback on the equator (Fig. 2a). The extent to which this dynamical longwave cloud feedback is consistent with the fixed anvil temperature (FAT) hypothesis of Hartmann and Larson (2002) is a topic for future work. The all-sky longwave feedback in the core of the ITCZ is counteracted somewhat by a smaller negative shortwave feedback (Fig. 4a). This shortwave feedback is predominantly associated with cloud processes (Fig. 4b) and points to increases in cloud fraction, thickness, and albedo in the core of the ITCZ because of the strengthening and narrowing of the ascent in that region; this pattern of tropical circulation changes has been termed the “deep-tropics squeeze” (Lau and Kim 2015).
Multimodel-mean change in (minus) the midtropospheric vertical velocity (averaged from 400 to 500 hPa) between the piControl and abrupt4xCO2 runs (black line) along with (minus) the multimodel-mean vertical velocity from piControl (red line), which has been rescaled by a factor of 0.15. For both the climatological vertical velocity and the change in vertical velocity, 100-yr averages are computed from the piControl and abrupt4xCO2 runs. The vertical red dotted lines indicate the edges of the climatological ITCZ in piControl, where the ITCZ edges are defined as the latitudes closest to the equator at which the zonal-mean midtropospheric vertical velocity passes through zero (Byrne and Schneider 2016a).
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
Multimodel-mean change in (minus) the midtropospheric vertical velocity (averaged from 400 to 500 hPa) between the piControl and abrupt4xCO2 runs (black line) along with (minus) the multimodel-mean vertical velocity from piControl (red line), which has been rescaled by a factor of 0.15. For both the climatological vertical velocity and the change in vertical velocity, 100-yr averages are computed from the piControl and abrupt4xCO2 runs. The vertical red dotted lines indicate the edges of the climatological ITCZ in piControl, where the ITCZ edges are defined as the latitudes closest to the equator at which the zonal-mean midtropospheric vertical velocity passes through zero (Byrne and Schneider 2016a).
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
Multimodel-mean change in (minus) the midtropospheric vertical velocity (averaged from 400 to 500 hPa) between the piControl and abrupt4xCO2 runs (black line) along with (minus) the multimodel-mean vertical velocity from piControl (red line), which has been rescaled by a factor of 0.15. For both the climatological vertical velocity and the change in vertical velocity, 100-yr averages are computed from the piControl and abrupt4xCO2 runs. The vertical red dotted lines indicate the edges of the climatological ITCZ in piControl, where the ITCZ edges are defined as the latitudes closest to the equator at which the zonal-mean midtropospheric vertical velocity passes through zero (Byrne and Schneider 2016a).
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
As in Fig. 2, but here showing the dynamic components only (black lines) of the (a) all-sky and (b) cloud feedbacks. The shortwave (red lines) and longwave contributions (blue lines) to these dynamics feedbacks are also shown.
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
As in Fig. 2, but here showing the dynamic components only (black lines) of the (a) all-sky and (b) cloud feedbacks. The shortwave (red lines) and longwave contributions (blue lines) to these dynamics feedbacks are also shown.
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
As in Fig. 2, but here showing the dynamic components only (black lines) of the (a) all-sky and (b) cloud feedbacks. The shortwave (red lines) and longwave contributions (blue lines) to these dynamics feedbacks are also shown.
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
Moving from the core of the ITCZ to its equatorward flanks and into the subtropics, the longwave and shortwave components of the dynamics feedback change signs and tend to largely cancel one another (Fig. 4). The weakening of ascending motion on the equatorward flanks of the climatological ITCZ following CO2 quadrupling (Fig. 3) causes reduced moisture convergence in those regions and negative longwave clear-sky and cloud feedbacks; changes in free-tropospheric clouds associated with a narrowing of the ITCZ are also likely to contribute to this negative longwave feedback. The longwave feedbacks are mostly cancelled by positive shortwave feedbacks at the edges of the ITCZ and in the subtropics, and these shortwave components are also dominated by cloud feedbacks (Fig. 4b). The positive shortwave cloud feedback in this region reflects a decrease in the amount of shallow marine cloud with global warming (Bony and Dufresne 2005), although the physical processes driving these changes in low-cloud amount are neither well understood nor well represented in global climate models (Ceppi et al. 2017). Because of the strong cancellation between longwave and shortwave feedbacks on the equatorward flanks of the ITCZ and in the subtropics, the overall all-sky dynamics feedback in this region is smaller than in the core of the ITCZ (Fig. 4a).
2) Fast versus slow dynamic responses
Cloud-radiative feedbacks are typically divided into “cloud adjustments,” which emerge rapidly in response to a radiative forcing, and surface temperature-mediated changes, which evolve slowly as the climate warms (Andrews et al. 2012; Kamae et al. 2015). The dynamic components of 
Multimodel-mean dynamic plus nonlinear components of the (a) all-sky radiative response and (c) changes in cloud-radiative effect, along with (b),(d) the respective thermodynamic components, between piControl and year 1 (red lines) and the averages over years 91–100 (black lines) of the abrupt4xCO2 runs.
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
Multimodel-mean dynamic plus nonlinear components of the (a) all-sky radiative response and (c) changes in cloud-radiative effect, along with (b),(d) the respective thermodynamic components, between piControl and year 1 (red lines) and the averages over years 91–100 (black lines) of the abrupt4xCO2 runs.
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
Multimodel-mean dynamic plus nonlinear components of the (a) all-sky radiative response and (c) changes in cloud-radiative effect, along with (b),(d) the respective thermodynamic components, between piControl and year 1 (red lines) and the averages over years 91–100 (black lines) of the abrupt4xCO2 runs.
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
The vertically integrated atmospheric moist static energy (MSE) budget can be used diagnostically to understand the physical processes influencing tropical vertical velocity (Byrne and Schneider 2016a). Changes in the net energy input to the atmosphere (e.g., through TOA radiative anomalies) influence the MSE budget and consequently vertical velocity, and can be a fast response to CO2 forcing. On the other hand, poleward transport of MSE by large-scale mean advection and transient eddies also affects tropical vertical velocity and depends fundamentally on meridional MSE gradients (Byrne and Schneider 2016a); these gradients would be expected to evolve slowly in response to CO2 forcing as sea surface temperatures increase. It is unclear why the dynamic components of changes in cloud-radiative effect 
Finally, there is only a weak correlation across CMIP5 models between the globally averaged fast and slow dynamic components of the all-sky radiative response 
3) “Area” and “mix” components of the dynamics feedback
In an influential paper on the energetics of tropical climate, Pierrehumbert (1995) used a simple two-box model to argue that “the warm pool sea surface temperature is very sensitive to […] the relative area of the dry versus convective regions.” Expressed in an equivalent way, Pierrehumbert (1995) was suggesting that the ratio of the areas of tropical ascent versus descent regions is an important controller of tropical climate. A widening of the Hadley circulation and a narrowing of the ITCZ are expected to occur as climate warms, resulting in a decrease in the area of tropical ascent relative to the area of tropical descent (Byrne and Schneider 2016b). We have calculated the total dynamics feedback, but it is also of interest to isolate the portion of this feedback that is due to a change in the up/down area ratio (e.g., due to ITCZ narrowing) and the portion that is due to strengthening/weakening of the circulation within the distinct ascent and descent regimes (e.g., due to a slowdown of the Walker circulation).
Multimodel-mean dynamic plus nonlinear components of the (a) all-sky and (b) cloud feedbacks in the abrupt4xCO2 simulations (black lines). The “area” (red lines) and “mix” contributions (blue lines) to these dynamic plus nonlinear components [as defined by (8)] are also shown.
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
Multimodel-mean dynamic plus nonlinear components of the (a) all-sky and (b) cloud feedbacks in the abrupt4xCO2 simulations (black lines). The “area” (red lines) and “mix” contributions (blue lines) to these dynamic plus nonlinear components [as defined by (8)] are also shown.
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
Multimodel-mean dynamic plus nonlinear components of the (a) all-sky and (b) cloud feedbacks in the abrupt4xCO2 simulations (black lines). The “area” (red lines) and “mix” contributions (blue lines) to these dynamic plus nonlinear components [as defined by (8)] are also shown.
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
Overall, the influence of changes in the tropical up/down area ratio on climate feedbacks is weak compared to the influence of thermodynamic processes (cf. Fig. 2). This result contrasts with the findings of Pierrehumbert (1995) based on a simple two-box model of the tropical climate, and casts doubt on the ability of changes in the widths of the ITCZ or Hadley circulation to strongly influence global climates of the past or the future.
4) Size of the nonlinear component
We found that the nonlinear components of the radiative feedbacks are small relative to the dynamic and thermodynamic components (Fig. 2). However, it is interesting to consider the factors controlling the magnitudes of these nonlinear terms. To gain insight into the nonlinear components of the all-sky and cloud feedbacks [(6) and (7)], it is instructive to assume the relationship between TOA radiation and vertical velocity is linear, namely 
b. Global atmospheric dynamics feedback
Averaged over all latitudes, TOA radiative anomalies induced by CO2 quadrupling are mostly a result of thermodynamic processes (see the results for one representative climate model in Fig. 7). Although the atmospheric dynamics feedback is relatively important at low latitudes (Fig. 2a), there is a large degree of cancellation between positive and negative dynamics feedbacks when the global average is calculated. In what follows, we explain why the atmospheric dynamics feedback is small when averaged over large regions.
Global-mean TOA all-sky radiative anomalies for the CCSM4 model (black crosses) as a function of annual global-mean near-surface temperature changes for the first 100 years in the abrupt4xCO2 simulation. The thermodynamic (blue dots) and dynamic plus nonlinear components (red dots) of the anomalies are also shown (the diagnosed radiative forcing has been added to the thermodynamic component), along with ordinary least squares fits to the total anomalies (black solid line) and to the thermodynamic component of the anomalies (blue dashed line). The estimated equilibrium climate responses, based on the least squares fits, are also indicated.
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
Global-mean TOA all-sky radiative anomalies for the CCSM4 model (black crosses) as a function of annual global-mean near-surface temperature changes for the first 100 years in the abrupt4xCO2 simulation. The thermodynamic (blue dots) and dynamic plus nonlinear components (red dots) of the anomalies are also shown (the diagnosed radiative forcing has been added to the thermodynamic component), along with ordinary least squares fits to the total anomalies (black solid line) and to the thermodynamic component of the anomalies (blue dashed line). The estimated equilibrium climate responses, based on the least squares fits, are also indicated.
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
Global-mean TOA all-sky radiative anomalies for the CCSM4 model (black crosses) as a function of annual global-mean near-surface temperature changes for the first 100 years in the abrupt4xCO2 simulation. The thermodynamic (blue dots) and dynamic plus nonlinear components (red dots) of the anomalies are also shown (the diagnosed radiative forcing has been added to the thermodynamic component), along with ordinary least squares fits to the total anomalies (black solid line) and to the thermodynamic component of the anomalies (blue dashed line). The estimated equilibrium climate responses, based on the least squares fits, are also indicated.
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
1) Mass budget constraint
As in our discussion of the nonlinear component above, a useful starting point is to assume the dependence of TOA radiation (either the all-sky radiative response or the cloud-radiative effect) on midtropospheric vertical velocity is linear [i.e., 
2) Effect on global climate change
Although small in magnitude, the globally averaged atmospheric dynamics feedback nevertheless has an influence on the climate response to CO2 quadrupling (Figs. 7 and 8). For the equilibrium climate response (ECR), defined here as the equilibrium change in near-surface temperature following CO2 quadrupling calculated using the regression method of Gregory et al. (2004), the dynamics feedback marginally increases the surface warming (Figs. 7 and 8a)—the multimodel-mean ECR is approximately 0.5 K larger than that predicted by the thermodynamics feedback alone (0.5 K corresponds to 8% of the multimodel-mean ECR in these simulations). Interestingly, the global dynamics feedback is robustly positive across CMIP5 models (Fig. 8). This contrasts with the hypothesis that tropical circulation changes may be a negative iris-type feedback on climate change (e.g., Lindzen et al. 2001). Despite being a small and positive feedback on climate change, there is no correlation between the all-sky dynamics feedback (globally averaged) and ECR, indicating that differences in atmospheric circulation responses across models cannot be used to explain intermodel spread in ECR. In contrast, there is a strong correlation of 
(a) Equilibrium climate response and (b) global feedback parameter in the abrupt4xCO2 simulations for individual CMIP5 models (black open circles) and for the multimodel mean (red solid circles). Both quantities are calculated using the regression method of Gregory et al. (2004). The y axes show the two quantities calculated using the total TOA all-sky radiative responses (4), and the x axes show the quantities calculated using only the thermodynamic components of the responses for each model (i.e., assuming a fixed circulation). Hence, any departures from the one-to-one relationships (blue lines) in the x direction are due to changes in the atmospheric circulation [e.g., circulations changes increase the multimodel-mean ECR as shown in (a)].
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
(a) Equilibrium climate response and (b) global feedback parameter in the abrupt4xCO2 simulations for individual CMIP5 models (black open circles) and for the multimodel mean (red solid circles). Both quantities are calculated using the regression method of Gregory et al. (2004). The y axes show the two quantities calculated using the total TOA all-sky radiative responses (4), and the x axes show the quantities calculated using only the thermodynamic components of the responses for each model (i.e., assuming a fixed circulation). Hence, any departures from the one-to-one relationships (blue lines) in the x direction are due to changes in the atmospheric circulation [e.g., circulations changes increase the multimodel-mean ECR as shown in (a)].
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
(a) Equilibrium climate response and (b) global feedback parameter in the abrupt4xCO2 simulations for individual CMIP5 models (black open circles) and for the multimodel mean (red solid circles). Both quantities are calculated using the regression method of Gregory et al. (2004). The y axes show the two quantities calculated using the total TOA all-sky radiative responses (4), and the x axes show the quantities calculated using only the thermodynamic components of the responses for each model (i.e., assuming a fixed circulation). Hence, any departures from the one-to-one relationships (blue lines) in the x direction are due to changes in the atmospheric circulation [e.g., circulations changes increase the multimodel-mean ECR as shown in (a)].
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
The global feedback parameter, or the slope of the linear regression of the all-sky radiative response versus near-surface temperature anomalies, describes the efficiency with which the Earth system equilibrates a radiative forcing. The feedback parameter is the sum of all the individual feedback processes (e.g., water vapor, cloud, lapse rate) and is typically negative, meaning that the net downward flux of radiation at TOA decreases as the surface temperature increases during equilibration. The atmospheric dynamics feedback robustly makes the global feedback parameter less negative (Figs. 7 and 8b), implying that the Earth system is less efficient at eliminating a TOA forcing because of circulation changes. This reduction in the magnitude of the feedback parameter is consistent with the all-sky radiative response associated with circulation changes becoming less negative over time following CO2 quadrupling (Figs. 5a and 7).
The climate models examined here are unable to simulate processes such as convective aggregation that have been put forward as potentially important influencers of global climate (Bony et al. 2016). Furthermore, climate models struggle to accurately simulate clouds (Pincus et al. 2008), and it is plausible that important nonlinearities in the 
4. Effectiveness of high- versus low-latitude dynamics feedbacks
a. Idealized forcing simulations
We use a moist idealized GCM perturbed by stylized TOA longwave forcing profiles to investigate in a general way how the latitudinal structure of the atmospheric dynamics feedback could impact global climate. Simulations are performed using the slab-ocean aquaplanet GCM of O’Gorman and Schneider (2008), which is based upon the model of Frierson et al. (2006) and Frierson (2007). The GCM is run at a horizontal spectral resolution of T42 with 10 vertical levels and the surface heat capacity is equivalent to 1 m of liquid water. The model uses a simplified two-stream gray radiation scheme with a prescribed longwave optical thickness; shortwave fluxes are specified as a function of latitude and longitude [see O’Gorman and Schneider (2008) for full details of the radiation scheme]. It is important to note that this model does not simulate water vapor or cloud feedbacks.
We perform a control simulation (without TOA longwave forcing) that has a climate roughly similar to that of present-day Earth, along with three perturbed simulations with prescribed longwave forcings (Fig. 9a): a tropical forcing from 
(a) Imposed longwave TOA forcings (positive downward) as a function of latitude for three idealized simulations perturbed from a control run, and (b) the surface-temperature responses for each perturbed simulation relative to the control run. The black lines correspond to the tropical forcing and induced response, the red lines to the extratropical forcing and response, and the blue lines to the global-wave forcing and response. Each forcing has a 
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
(a) Imposed longwave TOA forcings (positive downward) as a function of latitude for three idealized simulations perturbed from a control run, and (b) the surface-temperature responses for each perturbed simulation relative to the control run. The black lines correspond to the tropical forcing and induced response, the red lines to the extratropical forcing and response, and the blue lines to the global-wave forcing and response. Each forcing has a
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
(a) Imposed longwave TOA forcings (positive downward) as a function of latitude for three idealized simulations perturbed from a control run, and (b) the surface-temperature responses for each perturbed simulation relative to the control run. The black lines correspond to the tropical forcing and induced response, the red lines to the extratropical forcing and response, and the blue lines to the global-wave forcing and response. Each forcing has a
Citation: Journal of Climate 31, 8; 10.1175/JCLI-D-17-0470.1
b. Surface temperature responses
Although the tropical and extratropical forcings have equal magnitudes in the global mean, they induce strikingly different surface temperature responses (Fig. 9b). The global temperature response to extratropical forcing (1 K) is greater than twice the magnitude of the response to tropical forcing (0.4 K). This stronger sensitivity of climate to extratropical versus tropical forcing has also been shown for surface forcings (Rose et al. 2014; Rugenstein et al. 2016)—ocean heat uptake at high latitudes cools the climate more efficiently than the same heat uptake at low latitudes. The difference in temperature responses between low- and high-latitude forcings (a factor of approximately 2) found in our idealized simulations is somewhat smaller than for full-physics simulations forced by ocean heat uptake patterns (a factor of approximately 3–4; Rose et al. 2014). The enhanced contrast in global temperature responses for high- versus low-latitude forcings in full-physics simulations (Rose et al. 2014) relative to the idealized simulations is due to the full-physics simulations including water vapor and cloud feedbacks, which further strengthen differences in the forcing responses. To further emphasize how the latitudinal pattern of TOA forcing influences global temperature, the global-wave forcing has a global-mean magnitude of zero (Fig. 9a) and yet induces a surface temperature cooling of 0.2 K. That the global-mean temperature can change in response to a forcing with latitudinal structure but zero global mean has been shown in previous studies (e.g., Rose and Ferreira 2013; Rose and Rencurrel 2016).
The physical mechanisms leading to the enhanced global climate response to high-latitude versus low-latitude forcings have received considerable attention (e.g., Hansen et al. 1997; Langen and Alexeev 2007; Lu and Cai 2010; Pithan and Mauritsen 2014; Rose et al. 2014; Roe et al. 2015). Fundamentally, the contrasting temperature responses are driven by different sensitivities of poleward atmospheric energy transport to high- and low-latitude temperature perturbations, as well as latitudinal variations in local radiative feedbacks [see Rose et al. (2014) for an insightful discussion of this topic]. Consequently, although the idealized GCM used here omits a variety of processes which might be expected to change the magnitude of the climate response to TOA forcing (e.g., water vapor and ice albedo feedbacks), we believe the larger climate sensitivity to high-latitude forcing is a robust result that is grounded in well-established physical mechanisms. It should be noted that despite global surface temperature being more sensitive to a 
The idealized simulations discussed in this section have important implications for the atmospheric dynamics feedback. Although the influence of circulation changes on Earth’s global radiative balance is constrained to be weak as discussed above, the effect of circulation changes on the TOA radiative response at different latitudes is nonnegligible (Fig. 2a), and the global temperature response to circulation changes is likely to depend on this latitudinal structure. Furthermore, discussions of how the atmospheric circulation response might mitigate climate change have focused largely on tropical iris-type mechanisms (e.g., Pierrehumbert 1995; Lindzen et al. 2001; Mauritsen and Stevens 2015; Bony et al. 2016). However, based on the idealized simulations presented here, a 10 W m−2 tropical TOA forcing would be needed to change global temperature by 1 K (a more realistic model with water vapor and cloud feedbacks would be expected to require a smaller TOA forcing to change global temperature by 1 K, as discussed above). Our analysis of the influence of atmospheric dynamics on TOA radiation in CMIP5 models suggests a circulation-induced tropical TOA radiative anomaly of no greater than 1–2 W m−2under CO2 quadrupling (Fig. 5a), which would have only a minor influence on global temperature. Furthermore, an observational analysis shows that convective aggregation also has only a weak influence on TOA radiation (on the order of 1 W m−2; Tobin et al. 2012). Consequently, we argue that the relative insensitivity of global temperature to tropical TOA perturbations, combined with these perturbations due to changes in the atmospheric circulation being constrained to be small on large scales, means that tropical iris-type mechanisms are unlikely to exert a substantial influence on past or future climate change.
5. Summary and discussion
The response of the atmospheric circulation to radiative forcing, via its influence on clouds and water vapor, has been put forward as a potentially important negative feedback on climate change (Lindzen et al. 2001). Here, using a method based on that of Bony et al. (2004), we have calculated for the first time the atmospheric dynamics feedback at each latitude in a range of climate models subjected to an abrupt CO2 quadrupling. For the all-sky feedback, the dynamic component is generally smaller than the thermodynamic component, although it is not entirely negligible, particularly in the tropics, where it is positive with a magnitude of approximately 0.5 W m−2 K−1. For the cloud feedback, the dynamic component is comparable to the thermodynamic component close to the equator. The latitudinal pattern of the dynamics feedback reflects previously identified changes in the tropical circulation under global warming including enhanced ascent in the core of the ITCZ and a narrowing of this convergence zone. This coupling between radiation and circulation emphasizes the necessity of understanding the sensitivity of large-scale atmospheric dynamics to climate change in order to fully understand climate feedbacks at low latitudes.
At individual latitudes in the tropics, the atmospheric dynamics feedback is comparable to the thermodynamics feedback. However, a large degree of cancellation between positive and negative dynamics feedbacks at different latitudes results in the thermodynamic component dominating the global climate response. That the global-mean atmospheric dynamics feedback is small is shown to be a consequence of 1) the steady-state atmospheric mass budget and 2) approximately linear relationships between midtropospheric vertical velocity and the cloud-radiative effect and all-sky fluxes, although these relationships between vertical velocity and radiation require further investigation in high-resolution simulations that permit clouds and explicitly simulate convection. This atmospheric mass constraint on the dynamics feedback raises doubts regarding the ability of iris-type mechanisms (e.g., convective aggregation) to limit future climate change.
Although the global radiative anomalies induced by circulation changes are small relative to anomalies induced by thermodynamic processes (e.g., temperature-driven changes in water vapor), they do affect the climate response to CO2 quadrupling. Circulation changes are a positive feedback on global climate change (in contrast to iris-type negative feedbacks) and make the Earth system less efficient at equilibrating an imposed radiative forcing. Specifically, the dynamics feedback increases the multimodel-mean ECR by 0.5 K (or approximately 8% of the total warming) relative to a calculation of ECR using the thermodynamics feedback alone.
We performed idealized simulations to assess how hypothetical circulation-induced TOA anomalies at low and high latitudes, such as those due to unresolved dynamical processes including convective aggregation, could affect global climate. We showed that a high-latitude forcing is twice as effective as a low-latitude forcing in changing global surface temperature (interestingly and in agreement with previous studies, we also found that a forcing with a global average of zero can induce a nonzero temperature response). These results further strengthen our argument that low-latitude dynamical responses to climate change—such as convective aggregation or ITCZ narrowing—are unlikely to greatly influence global climate unless they are capable of inducing very large TOA anomalies. On the other hand, circulation changes that create TOA anomalies at higher latitudes (e.g., poleward shifts in the storm tracks or deflections of the midlatitude jet by large continental ice sheets in cold climates) are expected to be more than twice as effective at changing global temperature and consequently should be a priority to understand and quantify.
Our findings suggest a number of avenues for future research. Decades of satellite measurements now enable observational estimates of the atmospheric dynamics feedback; such estimates would be a useful benchmark with which to assess our climate model results. These observations could also be examined in detail to assess whether nonlinearities in observed 
Acknowledgments
We thank Paulo Ceppi, Reto Knutti, Paul O’Gorman, Brian Rose, Maria Rugenstein, and the editor for helpful comments, suggestions, and discussion. M.P.B. acknowledges support from the Imperial College London Research Fellowship Scheme.
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The models analyzed in this study are ACCESS1.0, ACCESS1.3, BCC-CSM1.1, BCC-CSM1.1-M, CanESM2, CCSM4, CNRM-CM5, CNRM-CM5.2, CSIRO-Mk3.6.0, FGOALS-g2, FGOALS-s2, GFDL-CM3, GFDL-ESM2G, GFDL-ESM2M, GISS-E2-H, GISS-E2-R, HadGEM2-ES, INMCM4, IPSL-CM5A-LR, IPSL-CM5B-LR, MIROC5, MIROC-ESM, MPI-ESM-LR, MPI-ESM-MR, MPI-ESM-P, MRI-CGCM3, and NorESM1-M; expansions of acronyms are available online at http://www.ametsoc.org/PubsAcronymList.
