The existence of the subtropical jet (STJ) is generally attributed to angular momentum transport within the Hadley Cell (HC) [Kim and Lee, 2004], and axisymmetric theory predicts the location of a STJ at the poleward edge of the HC [Held and Hou, 1980]. A STJ at the HC edge is indeed found in reanalyses and climate models. However, several recent studies have shown that, even though there is strong relationship between the variability of locations of the HC edge and eddy-driven jet (EDJ), there is little relationship between variability in the edge of the HC and the latitude of STJ [Solomon et al., 2016;Davis and Birner, 2017;Waugh et al., 2018]. Specifically, even though their climatological latitudes are similar, there are very weak interannual correlations between the latitude of the HC edge and STJ, over both hemispheres and for all seasons. Furthermore, while the HC expands in simulations with increasing CO 2 , there is no consistent change in the STJ latitude [Davis and Birner, 2017;Waugh et al., 2018;Wang et al., 2018].
This disconnect between movement of the STJ and HC edge is surprising, and suggests a gap in our understanding of the dynamics of the STJ. Understanding the variability and trends of the STJ is important, as its location has been used as a metric for tropical width [Fu and Lin, 2011;Archer and Caldeira, 2008;Manney and Hegglin, 2018]. Moreover, the STJ is a key component of the global atmospheric circulation and influences numerous atmospheric processes including subtropical cyclogenesis [Otkin and Martin, 2004], atmospheric rivers and other extreme events [Ryoo et al., 2013;Zhang and Villarini, 2018;Winters and Martin, 2014], and wave propagation between the tropics and extratrop--2-Confidential manuscript submitted to Geophysical Research Letters ics [Matthews and Kiladis, 1999], between hemispheres [Webster and Holton, 1982], and into the stratosphere [Shepherd and McLandress, 2011].
In this study we further examine the HC-STJ relationship by considering the intensities of the HC and STJ, in addition to the latitudes of the STJ and HC edge. We examine both the natural variability and forced response of the HC and STJ in a large number of climate models, and investigate the mechanisms causing variability and trends in the two features. We find that the HC edge and STJ strength relationship reverses sign between interannual variability and the response to increased atmospheric CO 2 . It is suggested that this is due to the differing sensitivities of the HC edge and STJ strength to shifts in latitude of the peak eddy momentum flux, which would be consistent with previous work showing the HC edge's response to increased CO 2 is closely connected to changes in the midlatitudes [Chemke and Polvani, 2019;Shaw and Tan, 2018], while the STJ is more influenced by the tropics [Shaw and Tan, 2018].
Our analysis is performed using monthly-mean model output from 23 climate models that participated in the Coupled Model Intercomparison Project, Phase 5 (CMIP5) [Taylor et al., 2012]. These are the same models as those considered in Grise and Polvani [2017] and Waugh et al. [2018] (see Supporting Information, Table S1). As in these studies, we analyze the first ensemble member ("r1i1p1") from the preindustrial control (pi-Control) and the instantaneous quadrupling of atmospheric CO 2 (4xCO 2 ) simulations. The analysis of the control simulations gives insight into the system's natural variability (Sect.
3) whereas the changes in the 4xCO 2 simulations relative to the control allow us to evaluate the response of the HC and STJ to increased radiative forcing (see Sect. 4).
To quantify the characteristics of the HC and STJ, we use metrics calculated using the Tropical-width Diagnostics (TropD) code [Adam et al., 2018]. The zonal-mean fields used to define these metrics are presented in Figure 1 which shows the DJF climatology. For all calculations, the basic fields are zonally and temporally averaged (i.e. over a season) before calculation of the metrics. The edge of the HC (φHC) is defined as the latitude at which the mean meridional streamfunction at 500 hPa ( 500 ) crosses zero poleward of its tropical extremum (Fig. 1a), and is calculated using the "Psi_500" method in TropD_Metric_PSI. -4-Confidential manuscript submitted to Geophysical Research Letters
The latitude of the STJ (φST J) is the latitude of maximum ∆u, where ∆u subtracts the near-surface zonal-mean wind at 850 hPa from the column integrated zonal-mean upper tropospheric wind between 100-400 hPa (Fig. 1c). Defining the STJ based on ∆u (referred to as the "adjusted method" [Adam et al., 2018]) enables a better distinction of the STJ from the eddy-driven jet (EDJ) [Davis and Birner, 2016] than by simply finding the latitude of maximum column integrated zonal-mean tropospheric wind between 100-400 hPa (referred to as the "core method" [Adam et al., 2018]). In seasons where the STJ is well separated from the EDJ (e.g., during winter [Lachmy and Harnik, 2014;Eichelberger and Hartmann, 2007;Lee and Kim, 2003]), the two methods detect the STJ at a similar latitude around 30 • , sufficiently distinct from the EDJ (see Supporting Information, Figure S1). However, in the seasons that have a relatively weak subtropical jet (such as summer), the core method produces a STJ that is noticeably poleward from the adjusted STJ and located next to the EDJ (see Supporting Information, Figure S1). In this case, the core method is mistaking the EDJ for the STJ. For this reason, the adjusted method is a more accurate tool for locating the STJ, even though the STJ is not entirely isolated from the impact of eddies [Lee and Kim, 2003]. In Waugh et al. [2018], φST J was calculated using the "adjusted_max" method in TropD_Metric_STJ, but here we use a quadratic "fit" method to find the latitude of the maximum value, making it easier to determine the strength of the STJ (see below).
Additionally, we define metrics to quantify the strength of the HC and STJ. The strength of the HC (maxHC) is calculated as the maximum value of 500 inside the HC (between the equator and φHC), while the STJ strength (maxST J) is the magnitude of ∆u at φST J, the maximum value of the quadratic fit.
The latitude of the EDJ (φE DJ) is the latitude of maximum zonal-mean 850 hPa zonal winds (u 850 , Fig. 1c), and is calculated in TropD_Metric_EDJ using the same quadratic fit method as φST J.
We first examine the interannual variability of the HC and STJ in the control runs of the models. Before considering the correlations between different metrics, we examine how the zonal-mean meridional circulation, zonal wind, and temperature vary with a change in the width of the HC (Fig. 2a-c). The left hand plots in Figure 2 show the multi- model, annual-mean difference between composites of an expanded and contracted HC for each of these fields. We consider the HC to be expanded or contracted when φHC is poleward or equatorward of its climatological mean value by more than two standard deviations, respectively, corresponding to about 0.9 • latitude. When the HC is expanded, it is weaker by up to 0.5x10 10 kg s -1 (Fig. 2a), and there is a strengthening of surface winds on poleward side of the mid-latitude jet, consistent with the well documented poleward shift of the EDJ when there is a broader HC (Fig. 2b). In the upper troposphere there is a weakening of the zonal winds in the subtropics by ⇠ 20-30% and a narrow tropical cooling (Fig. 2c). Altogether, Fig. 2a-c demonstrate that a weakening of the HC, poleward shift of the EDJ, a narrow tropical cooling and a weakening of the STJ are related to a HC expansion. The changes in the HC, EDJ and tropical temperatures shown in Fig. 2ac are very similar to the difference between La Niña and El Niño events [e.g., Lu et al., 2008].
To better quantify the relationships shown in Fig. 2a-c, we use the metrics described in Section 2 to statistically evaluate the natural co-variability of the HC with the STJ. As shown in previous studies, Figure 3 shows there are almost no significant correlations between the HC edge and the STJ location (Fig. 3, row 1), a surprising result that contrasts the well known strong, positive correlation between the HC edge and latitude of the EDJ during most seasons (Fig. 3, row 7) [Kang and Polvani, 2011;Davis and Birner, 2017;Waugh et al., 2018;Solomon et al., 2016]. Not only are most of the correlations not significant, the sign of relationship changes from negative to positive depending on the season. Note that the strength of the HC is also poorly correlated with the STJ latitude and the sign of correlation is inconsistent over seasons. (Fig. 3, row 4).
In contrast, the STJ strength has a consistently weak to moderate negative correlation with the HC edge (Fig. 3, row 2) for all seasons and both hemispheres. This relationship is strongest in the Northern Hemisphere (NH). Likewise, the correlation between the strength of the HC and the strength of the STJ is weakly positive (Fig. 3, row 3), which is true for all seasons except the near-zero negative value of NH's summer (JJA). These results suggest that a weaker, more poleward HC is associated with a weaker STJ. Such a conclusion is also consistent with the patterns shown in Fig. 2b-c where for the Southern Hemisphere (SH), a poleward expansion of the HC edge by ⇡ 1.2 • is associated with a weakening of the HC by about 0.5x10 10 kg s -1 and a weakening of the STJ by 0.8 m s -1 .
The fifth and sixth rows of Fig. 3 show the correlations between strength and location for the STJ and for the HC, and in both cases there are moderate negative correlations except during summer in both hemispheres and fall in the NH. Thus during winter and spring the STJ is weaker when it is further poleward and the HC is weaker when expanded.
Although not examined in detail, we note that there is a similar weak relationship between the STJ and EDJ, where the STJ and EDJ latitudes are not correlated and there is a small negative correlation between the EDJ latitude and STJ strength in the NH. The lack of correlations between the latitudes of the STJ and EDJ has been shown previously -8-Confidential manuscript submitted to Geophysical Research Letters [Solomon et al., 2016;Davis and Birner, 2017;Waugh et al., 2018], and correlations between metrics of the jets are shown in Figure S2 of the Supporting Information.
Next, we examine the response of the HC and STJ to an instantaneous quadrupling of atmospheric CO 2 . The multi-model annual-mean response of the zonal-mean meridional circulation, zonal wind, and temperature are shown in the right hand plots of Figure 2. Here, the response was calculated by averaging the fields over years 100-150 of the 4xCO 2 simulation and subtracting the climatological annual-mean values taken from the piControl simulation. As shown previously [e.g., Held and Soden, 2006;Lu et al., 2007;Frierson et al., 2007], there is an expansion and weakening of HC in response to the increase in CO 2 (in the SH, the multi-model mean φHC moves poleward by 1.7 • and maxHC decreases by up to 1.1x10 10 kg s -1 ). There is also a slight poleward shift of the Ferrel cells (Fig. 2d), and in the SH, this shift of the Ferrel cell is accompanied by a 1.6 m s -1 strengthening and 2.9 • poleward shift of the EDJ (Fig. 2e), again consistent with previous studies [e.g., Kushner et al., 2001;Barnes and Polvani, 2013;Simpson et al., 2014;Collins et al., 2013]. There is additionally a strong increase in zonal winds in the subtropical upper troposphere, resulting in a strengthening of the STJ in both hemispheres (4.6 m s -1 in the SH, 1.6 m s -1 in the NH). Finally, Fig. 2f shows the well-known warming of the entire troposphere, with amplified warming in the tropical upper troposphere and polar lower troposphere.
Comparison of the left and right hand side of Figure 2 shows the same general relationship between the HC and EDJ for the cases of natural variability and 4xCO 2 , that is a more poleward EDJ occurs with an expanded and weaker HC. There is, however, a change in relationship between the HC and tropical upper tropospheric fields, such that a weaker STJ and colder tropical upper troposphere is associated with an expanded HC interannually but the opposite occurs for 4xCO 2 . This change of relationship is consistent with the well documented difference in the HC and EDJ response to ENSO forcing and global warming: the HC widens and EDJ moves poleward under global warming but during ENSO warming, the HC contracts and EDJ moves equatorward [Lu et al., 2008].
Figure 2 shows that the differing response between ENSO and global warming does not occur for the STJ as it strengthens both interannually (i.e., in response to ENSO warming), and under global warming. Shaw and Tan [2018] present these same broad conclusions, -9-Confidential manuscript submitted to Geophysical Research Letters explaining that the STJ responds to forcing that occurs in the tropics whereas the HC and EDJ responses are dominated by subtropical forcing.
Figure 2 shows the multi-model responses to 4xCO 2 , but it is also of interest to consider the response of individual models. There is a poleward expansion of the HC and increase in the STJ strength for all models and both hemispheres, but the sign of change in the STJ latitude varies between models, especially in the NH where STJ moves equatorward in a similar number of models as it does poleward (see Supporting Information, Figure S3). However, although there is consistent sign change in φHC and maxSTJ, there is an insignificant correlation across models in the magnitude of the change (r ⇡ 0.2). This indicates that the models with a larger change in φHC do not necessarily have a larger change in maxSTJ, which is inconsistent with the interannual correlation. Also, while there is no consistency across the models in direction of change in φSTJ, there is a positive correlation between the changes in φHC and φSTJ across models (r ⇡ 0.4 -0.5), so models with large poleward shift in φHC tend to have a larger shift in φSTJ.
The inconsistency in sign of the response or weak correlations across models between STJ metrics and φHC suggests that different processes are responsible for the changes in the STJ and HC (see further discussion below). Note, this contrasts the consistencies between the HC edge and EDJ latitude responses. In all models there is a poleward movement of φHC and φEDJ in response to 4xCO 2 , there is a high correlation in the φHC and φEDJ response across models, and the slope of the linear fit between change across models is close to the multi-model mean regression coefficient for interannual variations in the piControl runs (see Figure 8 of Waugh et al. [2018]). This consistency occurs interannually and in response to forcing, strongly suggesting that the latitudes of the HC edge and EDJ are governed by the same physical processes.
Previous studies have demonstrated that examining the transient response in the 4xCO 2 simulations provides insight into the processes involved [Grise and Polvani, 2017;Chemke and Polvani, 2019]. Following these studies we show in Figure 4a the evolution of the multi-model annual-mean time series of the metrics in the SH (shading represents the 95th percentile between models). Consistent with Fig. 2d-f, the HC weakens slightly (orange) and shifts poleward ⇡ 1.7 • (red), while the STJ strengthens by 4.6 m s -1 (blue) and shifts minimally (green). Interestingly, the shift of the HC and strengthening of the STJ occur on different timescales. Following Grise and Polvani [2017], we calculate a quan-tity's response time as the time it takes to reach 90% of its steady state value (averaged over years 140-150). The HC edge responds in 7 years while the STJ does so in 40 years.
For comparison, the global-mean surface temperature increases even more slowly, taking around 65 years to reach 90% of its value at 150 years [Grise and Polvani, 2017;Chemke and Polvani, 2019;Seviour et al., 2018].
These broad conclusions, that 4xCO 2 induces a rapid poleward shift of the HC edge and slower strengthening of the STJ, also hold in the NH (see Supporting Information, Fig. S4). The major difference between hemispheres is that in the NH, the STJ initially shifts poleward and then returns to its original latitude by the end of the first century [Shaw and Voigt, 2015]. Additionally, the metrics' behavior is generally consistent across all seasons where the HC shifts poleward and weakens slightly, and the STJ strengthens and shifts minimally.
We now consider the physical processes associated with these changes in the HC and STJ. Chemke and Polvani [2019] showed that the rapid expansion of the HC occurs with increases in the subtropical static stability and a poleward shift in the subtropical eddy momentum fluxes. This connection is presented in Fig. 4b which shows the evolution of φHC (red) and the latitude of the maximum eddy momentum fluxes (purple) for the subset of models that archived the necessary daily fields (indicated in Supporting Information, Table S1) to calculate the eddy momentum fluxes (see Chemke and Polvani [2019] for details of the calculation). Both fields in Fig. 4b increase at a similar rapid time scale. Further, they have similar year-to-year variations with a model-mean correlation of about 0.6 for both hemispheres in the piControl time series.
As the strength of the STJ (maxST J) increases much more slowly than the shift in φHC or eddy momentum fluxes, it must be dynamically related to other processes. One possibility is that meridional temperature gradients, and thus thermal wind balance, sets maxST J [Davis and Birner, 2017]. To test this we examine the evolution of the maximum meridional temperature gradient calculated at each latitude between 0-45 • S (Fig. 4c, yellow). There is good agreement in the evolution of maxST J and the meridional temperature gradient, as both increase on the same time scale, which is slower than φHC but quicker than the global mean surface temperature. Furthermore, there is not a significant change in the latitude of maximum meridional temperature gradient, consistent with the limited movement of the STJ (not shown).
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The close connections between φHC and the latitude of the maximum eddy momentum fluxes and between maxST J and maximum meridional temperature gradient are also found for the spread among models: Models with larger shift in latitude of the maximum eddy momentum fluxes in response to 4xCO 2 tend to have a larger shift in φHC (correlation of 0.97 in the SH) and models with larger increase in meridional temperature gradient tend to have larger increase in maxST J (correlation of 0.91 in the SH). This further indicates that while the movement of the HC edge is connected to the shifts in latitude of maximum eddy momentum flux, a strengthening of the STJ is accompanied by changes in the meridional temperature gradient.
Although the STJ latitude does not co-vary interannually with the HC edge [Davis and Birner, 2016;Solomon et al., 2016;Waugh et al., 2018], we have shown that the HC edge is weakly to moderately correlated to the STJ strength. However, this correlation does not hold when the two features respond to 4xCO 2 . On interannual time scales the STJ tends to be weaker with a wider HC, whereas the STJ strengthens and the HC widens under increased CO 2 .
The distinct time scales of response to increased CO 2 by the HC width and STJ strength indicate that the two features are influenced by different physical processes. As shown in Section 4, the rapid expansion of the HC is associated with a poleward shift in the subtropical eddy momentum fluxes. Both the edge of the HC and the subtropical eddy fields are strongly impacted by subtropical baroclinicity and shift poleward given an increase in static stability (see Chemke and Polvani [2019] for details). However, the strength of the STJ shows no connection to the eddy momentum fluxes, and the slower time scale of the STJ's strengthening is instead associated with increases in the meridional temperature gradient in the subtropical upper troposphere. This is in agreement with the suggestion by Davis and Birner [2017] that the differences between movement of the HC edge and the STJ are due to the meridional stream function (used to define the HC edge) being physically linked to the distribution of eddy momentum fluxes via subtropical baroclinicity, whereas the upper tropospheric winds (used to define the STJ) are related to the latitudinal distribution of temperature. in the may 2010 nashville flood, Weather and Forecasting, 29(4), 954-974. Zhang, W., and G. Villarini (2018), Uncovering the role of the east asian jet stream and heterogeneities in atmospheric rivers affecting the western united states, Proceedings of the National Academy of Sciences,115(5),[891][892][893][894][895][896]