Winter Subtropical Highs, the Hadley Circulation and Baroclinic Instability

Subtropical highs have a profound influence on the weather and climate of adjacent continents. In this study, we use reanalysis data to investigate the interannual variability and trends in winter subtropical highs from 1979 to 2021. We find dynamical relationships between subtropical high intensity, the Hadley and Ferrel Circulation intensity, and the Eady Growth Rate (EGR). A poleward shift of the maximum in EGR is associated with a strengthening of the descending branches of the Ferrel and Hadley Cells, with subtropical troposphere adiabatic warming and an increased intensity and poleward movement of the subtropical highs. Shifts in the poleward EGR are dominated by changes in vertical wind shear which, in turn, are in thermal wind balance with variations and trends in temperature. The mechanism for the intensification of the subtropical highs involves feedbacks from high‐frequency transient eddies. Strong North Pacific and South Pacific Subtropical highs are associated with La‐Niña conditions. We also show that the mechanisms for interannual variations are similar to those for trends in the highs.

Plain Language Summary Wintertime subtropical highs have large climatic impacts but the dynamical explanation for their interannual variability and trends is incomplete.Here we find that wintertime subtropical high intensity is related to overturning cell intensities and the Eady Growth Rate (EGR), which is a measurement of baroclinic instability, in both interannual variability and long-term trends.The northward (southward) shift of the northern (southern) hemisphere EGR is associated with an increasing intensity of the Ferrel Cell and Hadley Cell.The enhancement of their descending branches strengthens the intensity of subtropical highs.The EGR change is dominated by the vertical wind shear change.The North Pacific Subtropical High and South Pacific Subtropical high are intensified by cold anomalies of sea surface temperature in the Central and Eastern Pacific but are also trending stronger and moving polewards.
concluded that there has likely been a poleward shift of the extratropical storm tracks and jet streams since the 1980s (Masson-Delmotte et al., 2021) and both the Pacific and Atlantic storm tracks have significantly intensified between the 1950s and 2010s (Chang & Yau, 2016) with a concurrent increase in the Arctic Oscillation (Blackport & Fyfe, 2022).
The Hadley Cell (HC) is a large-scale zonal-mean atmospheric circulation.It transports angular momentum and energy from tropical to subtropical regions and its descending branch in the subtropics plays an important role in driving the subtropical highs and the transition from tropical to subtropical climate (Hu et al., 2018;Kang & Lu, 2012;Rodwell & Hoskins, 2001).The HC width is thought to be determined by the latitude where baroclinic eddies begin to occur (Frierson et al., 2007;Held & Soden, 2000) and the recent expansion of the HC is thought to be caused by an increase in the subtropical static stability (Lu et al., 2007;Schneider, 2006) with an accompanying weakening from the flattening of meridional temperature gradients (Seo et al., 2014).The interannual variability of the HC is partly due to ENSO (Oort & Yienger, 1996).It strengthens and narrows in response to El-Niño and because of tropical warming there is an equatorward shift of the tropospheric subtropical jets (Lu et al., 2008;Nguyen et al., 2013).In contrast, observations and simulations show that the HC widened and weakened over recent decades (Hu & Fu, 2007;Johanson & Fu, 2009;Seidel & Randel, 2007).
Since both subtropical highs and storm tracks have tight connections with the Hadley Circulation and mid latitude baroclinic instability, we investigate these relationships and ask whether the long-term trend can be explained in terms of the mechanisms that drive interannual variability.

Data and Methods
Monthly winds, geopotential height, temperature and surface pressure data are taken from ERA5 (0.25° × 0.25°, Hersbach et al., 2020) and JRA55 (1.25° × 1.25°, Kobayashi et al., 2015).We investigate the northern hemisphere winter (December to February, DJF) and the southern hemisphere winter (June to August, JJA) during the satellite era of 1979-2021.We checked the calculation of the diagnostics using both ERA5 and JRA55 and found no significant differences.Both reanalyzes are interpolated onto a 2.5° × 2.5° latitude-longitude grid and the average of the two is used for the analysis.200 hPa zonal wind and meridional wind for eddy flux calculations are derived from ERA5 6-hr daily data and they are interpolated onto a 1° × 1° horizontal resolution.
The intensity of the Hadley Cell (HC index) is here defined as the difference between the vertically averaged value of ψ between 900 and 200 hPa on the poleward and equatorward sides of the HC descending branch.The definitions of poleward and equatorward sides of the HC are the maximum anomaly of stream-function positions (Table 1, Figure 5, shading).The edge of the HC is defined as the zero isoline of ψ on the poleward side of the HC between 400 and 700 hPa, estimated using linear interpolation.We define the distance between edges of the two cells as the HC width.
The Eady model is the simplest and most elegant model that satisfies the necessary conditions for atmospheric baroclinic instability in a continuous atmosphere (Eady, 1949;Holton, 1973).The maximum Eady Growth Rate (EGR, σ, units: day −1 ), is defined as: where f is the Coriolis parameter (units: s −1 ), N the Brunt-Väisälä frequency (units: s −1 ), V the horizontal wind vector (units: ms −1 ), z the vertical height (units: m) and 86,400 is to change the unit to day −1 .In our analysis, we calculate the zonal mean anomaly of EGR on the poleward side and on the equatorward side of the HC, based on the patterns between subtropical high strong years and climatology (Figure 5, contour) and the long-term trend (Table 1), average over 250-850 hPa, to demonstrate the latitudinal shifts of the EGR (EGR index).
In both hemispheres, the HC descending branch is associated with the baroclinic instability zone, which is in turn related to higher latitudes via the meridional temperature gradient.This temperature gradient results in westerlies that strengthen with height because of thermal wind balance: where u is zonal wind (units: ms −1 ), T is temperature (units: K), R is the specific gas constant for dry air (units: JK −1 kg −1 ), f is the Coriolis parameter (units: s −1 ), p is pressure (units: hPa), and φ is latitudinal distance (units: m).
To test whether the zonal wind obeys thermal wind balance, we integrate the thermal wind balance equation in every level: Table 1 The Choices of Poleward and Equatorward Sides of Hadley Cell and Eady Growth Rate where p0 is lower level and p is upper level and compare the results to the full wind in the reanalysis.
Zonal and meridional winds are used to calculate streamfunction and relative vorticity.The transient eddy on the time scale of 2-8 days is extracted by a Lanczos bandpass filter onto the daily data with 41 weights.Low frequency variability is defined as the monthly mean anomaly (DJF for the Northern Hemisphere and JJA for the Southern Hemisphere).The streamfunction tendency (ψ t , units: m 2 s −2 ) induced by anomalous eddy vorticity fluxes can be expressed in terms of eddy vorticity forcing to measure the eddy feedback.The monthly mean horizontal eddy vorticity forcing (χ vort , units: m 2 s −2 ) and eddy vorticity flux (F vort , units: ms −1 ) are represented, respectively: where u′, v′, ψ′ and ξ′ denote the synoptic (2-8 days) zonal wind, meridional wind, streamfunction and vorticity;  ( ) denotes the monthly mean anomaly derived by subtracting the climatology of the reanalysis; ∇ • ( ) and ∆ −1 ( ) are the horizontal divergence and the Laplacian inversion operators, respectively; and ( ) ed indicates the tendency induced by transient eddies (Zhou & Ren, 2017).In the Northern Hemisphere, a positive streamfunction tendency is associated with a strengthening of the subtropical high whereas in the Southern Hemisphere, a negative tendency is associated with a strengthening.
In this study, interannual variability is calculated after removing trends computed using least-squares regression, and statistical significance is assessed at the 95% confidence level (p < 0.05) according to a two-tailed t-test.Trends are expressed using least-squares regression coefficients, and statistical significance is assessed at the 95% confidence level (p < 0.05) according to a two-tailed t-test.
The average of the northern (southern) hemisphere subtropical high intensities are defined as a subtropical high intensity index.All the indices are divided by their standard deviations after removing their mean (i.e., they are standardized).Multiple regression is used to build the equation among subtropical high intensity index (y), the HC index (ψ) and the EGR index (σ) after standardization: The partial regression coefficients are assessed at the 95% confidence level (p < 0.05) according to an F test.

Interannual Variability
The composite analysis of interannual variability, shows that the subtropical highs move poleward when they are strong (Figure 2).It also shows relationships among the subtropical highs.When the NASH is strong, the NPSH tends to be weak (Table 2).Note that there is both significant interannual variability and a significant trend in the intensity of the winter subtropical highs (Figure 2).It is also notable that the NPSH and SPSH strong years are associated with a cold sea surface temperature (SST) anomaly in the eastern Pacific (correlation coefficients are −0.61 and −0.67, p < 0.01, with Niño3.4 respectively, Figures 4a and 4c).The NASH is linked with a triple SST pattern in north Atlantic, marked by a warm anomaly on the east of Gulf Stream and two cold anomalies on the tropical Atlantic and west of northern Europe (Figure 4b).The SASH is related to the warm anomaly of SST in eastern tropical Pacific and south Atlantic subtropical dipole (Figure 4d).
The greatest eddy forcing appears in the winter and the smallest in the summer (Zhou & Ren, 2017).From Figure 3, we find that the streamfunction tendency is entirely positive in the NPSH area (Figure 3a) and shows a dipole pattern in the NASH area which is negative in east America and positive in the northeast Atlantic (Figure 3b).In the southern hemisphere, it is negative in the SPSH area (Figure 3c) and in the southern flank of the SASH (Figure 3d).The eddy feedback is consistent with the subtropical high strengthening and the positive (negative) streamfunction tendency in the Northern Hemisphere (Southern Hemisphere) acts to enhance the anticyclonic circulation.
We further examine the cross-section of zonal mean atmospheric circulation anomalies between subtropical high strong years and the climatology of the recent four decades (Figure 5).For the northern hemisphere, the results show that the maximum of the EGR moves poleward and the HC and Ferrel Cell both strengthen when the subtropical highs are strong (Figures 5b and 5d, Table 3).The thermally indirect Ferrel Cell is a good indicator of the location and strength of baroclinic eddies in midlatitudes (James, 1995).For the southern hemisphere, the HC strengthened when the subtropical highs are strong, especially for SPSH (Figure 5a, Table 3).
We next investigate the variability of northern hemisphere baroclinic instability and its relationship with subtropical high strength.When the subtropical high is strong, the EGR is weak on the equatorward side of the baroclinic instability zone, but it is strong on the poleward side (contour, Figure 5).We note that the relationship between the EGR and winter subtropical high intensity is stronger than between HC intensity and winter subtropical high intensity in the northern hemisphere (Table 3).However, the SPSH has stronger relationship with HC intensity than with EGR (Table 3).
The poleward shift of baroclinicity is associated with the energy transport of the Ferrel Cell (Trenberth & Stepaniak, 2003;Yin, 2005).The Ferrel Cell, and by implication baroclinic eddy activity, is strengthened when the subtropical highs are strong and EGR maximum shifts poleward, especially for NPSH and NASH (contour, Figures 5b and 5d).The HC intensity is also significantly correlated with the strength of the subtropical highs in the northern hemisphere (Table 3, shading in Figures 5b and 5d).The poleward movement of the EGR maximum shows a significant relationship with subtropical high strength in the northern hemisphere (Table 3) but not in the southern hemisphere (Table 3).
The temperature in mid-latitudes is anomalously high when the subtropical highs are strong.The troposphere warming around 30°N (S) is associated with the adiabatic warming in the descending branches of HC and Ferrel Cell (shading, Figure 6).EGR variations could, in principle arise, from variations in static stability, variations in vertical wind shear, or both.Figure 6 (contour) show that the EGR anomalies are dominated by the vertical shear component (the change of zonal wind speed with height), which is consistent with Ren et al. (2010).Furthermore, the anomalies in the growth rate are well approximated by the change in vertical shear calculated from the meridional gradient of temperature, via the thermal-wind relationship (cf.contours in Figures 5 and 6).
To quantify the relationship between the subtropical highs, the HC and the mid latitude baroclinicity in the boreal winter, we fit a multiple linear regression equation between the subtropical high intensity (y), HC intensity (φ) and the EGR shift (σ) for every subtropical highs (see Section 2):  The transient eddy tendency is not included as an explanatory variable as we view this as a feedback due to the change in baroclinicity capture by the EGR.The northern hemisphere subtropical highs can be better explained by these two factors than the southern hemisphere.The partial regression coefficients are 0.17 (p = 0.31) and 0.36 (p = 0.04) and the correlation coefficient is 0.47 (p < 0.01) for NPSH, so 22% of the variance of NPSH intensity can be explained by these two factors.Similarly, the partial regression coefficients are 0.30 (p = 0.037) and 0.37 (p = 0.011) and the correlation coefficient is also 0.47 (p < 0.01) for NASH and 22% of the variance of NASH intensity can be explained by these two factors.For the southern hemisphere, the partial regression coefficients are 0.47 (p = 0.005) and −0.19 (p = 0.24) and the correlation coefficient is 0.43 (p < 0.01) for SPSH.Although an equation has been proposed for SASH, it is not statistically significant and only accounts for 3.5% of the variance of SASH intensity.
The relationships in austral winter are weaker than boreal winter (Table 3).The troposphere temperature in the southern hemisphere also warms within the descending areas (shading, Figures 6a and 6c) and the variability of EGR is also dominated by the shear term (contour, Figures 6a and 6c).The Southern Hemisphere westerly jet has moved poleward over the past few decades and this is caused by ozone depletion (Kang et al., 2011).In addition, the anthropogenic greenhouse gases or aerosols forcings may also play a different role in affecting circulation patterns in both hemispheres.

Table 2
The Correlation Coefficients Between the North Pacific Subtropical High, the North Atlantic Subtropical High, the South Pacific Subtropical High, and the South Atlantic Subtropical High

Trends
The intensities of NPSH (standardized, reg = 0.026 ± 0.024, p < 0.05, Table 4) and SPSH (reg = 0.023 ± 0.024, p < 0.05, Table 4) are significantly increasing.The Atlantic subtropical highs trends are, however, not significant.Figures 7a and 7b show the trend of zonal mean meridional stream-function and EGR over the period 1979-2021.The EGR moves poleward in the northern hemisphere (reg: 0.028 ± 0.024, p < 0.05) and southern hemisphere (reg = 0.023 ± 0.024, p < 0.05).The intensity of the dominant cell of the Hadley circulation is strengthening (reg = 0.029 ± 0.024, p < 0.05) and widening (reg = 0.021 ± 0.025, p < 0.05) through the troposphere in the northern hemisphere.The intensity of the Ferrel cell is also increasing.However, the whole trend pattern is more confined in latitudinal width in comparison to the interannual variability.
The EGR trends show a similar pattern to the interannual cases in both hemispheres.There is a tripole pattern (−, +, −) from tropical to polar areas in the northern hemisphere (contour, Figure 7d).The EGR in low and high latitude regions is decreasing while in the mid-latitude areas it is increasing (contour, Figures 7c and 7d).This suggests that the EGR is migrating poleward in the region of the edge of the Hadley Circulation and the subtropical highs.Both the interannual variability and the trends of the EGR are again dominated by the vertical wind shear rather than changes in stability (contour, Figures 7c and 7d).
The tropospheric temperatures are increasing in the subtropical area of the northern hemisphere (shading, Figure 7d) coincident with adiabatic warming associated with the increased downward branches of the Ferrel Cell and HC and poleward eddy heat transport.This is similar to the change associated with the interannual variability case (shading, Figure 7d).The easterlies increased in the tropical areas and the westerlies increased in the midlatitudes but the region of westerly wind is latitudinally narrower compared with the interannual case.Multiple data sets confirm that the tropospheric jets have shifted poleward after the 1970s and wind speed has increased in winter in both hemispheres (Davis & Rosenlof, 2012;Lee et al., 2019;Manney & Hegglin, 2018).
In the previous section, we found an equation relating the subtropical high strength, HC intensity and EGR.We can use this relationship to infer and estimate the trend of wintertime subtropical high intensity.The trend of estimated NPSH intensity using the trends in the Hadley Circulation and Eady Growth Rate is 0.015 ± 0.009 (p < 0.01) and agrees with the observed change (0.026 ± 0.024) within the estimated uncertainty (variables are standardized).The trend of estimated NASH intensity is 0.019 ± 0.011 (p < 0.01).For the southern hemisphere, the estimated trends are −0.005± 0.013(p = 0.41) and 0.004 ± 0.006 (p = 0.20) for SPSH and SASH, respectively.The northern hemisphere wintertime subtropical high trends are therefore well reproduced by the trends in HC intensity and EGR.Again, the EGR is more important than the HC for the trends of subtropical high intensity in the northern hemisphere.
The trends in austral winter are weaker than boreal winter (Table 4).Nevertheless, the HC is strengthened and the EGR moves poleward over the last four decades (Figure 7a).The temperature distribution shows similar warming in the troposphere (shading, Figure 7c).The trend of EGR is again dominated by the shear component (contour, Figures 7a and 7c).Both inferred and observed trends are small in the southern hemisphere.
The change of streamfunction tendency in the recent four decades is also consistent with the trend of geopotential height (Figure 8).In the Northern Hemisphere, it has strengthened in the northern part of the NPSH and the NASH areas.In the Southern Hemisphere, the trend of streamfunction tendency show a dipole pattern, which strengthened in the west and weakened in the east in the SPSH areas.The eddies show a monopole decreasing anticyclonic circulation in the South Atlantic.These trends are with the strong role of baroclinicity changes in explaining the trends in subtropical highs.

Conclusion and Discussion
In this study, we use observational reanalysis data to find relationships between winter Subtropical highs, the Hadley and Ferrel Cells and the EGR in both hemispheres over the last four decades.We find that the northern hemisphere EGR moves polewards when the subtropical high is strong.The poleward shift of baroclinicity is linked with the strengthening Ferrel Cell and HC.The strengthening of the descending branches in subtropical areas in both hemispheres are associated with higher troposphere temperatures and adiabatic warming.The EGR is dominated by the vertical wind shear term and it can be reproduced by using the meridional temperature gradient to calculate the shear component that is in thermal-wind balance.The transient eddy forcings also act to strengthen the background anticyclonic circulation and contribute to the trends in subtropical highs, consistent with the important role of changing baroclinicity.These relationships are consistent for both interannual variability and the long-term trends.
Despite its simplicity, the EGR, determined by vertical shear, has a tight connection with subtropical high intensity (Hoskins & Valdes, 1990;Kawasaki et al., 2021).From the relation between subtropical high intensity, HC intensity and the EGR shift on interannual timescales, we find that the trend in subtropical high intensity can be explained by these two factors, especially in the Northern Hemisphere.We also note that these results agree with recent studies arguing for a stronger role of the midlatitudes than the deep tropics in determining the trends in the subtropical circulation (Freisen et al., 2022).
We also consider transient eddy feedback in our study.This is the process by which synoptic scale transient eddies amplify large-scale quasi-stationary climate anomalies in the mid-latitudes (e.g.,: Hardiman et al., 2022;Kug et al., 2010;Lau & Nath, 1991).These midlatitude transient eddy feedbacks play an important role in generating and maintaining the planetary-scale flow anomalies (Lau & Nath, 1991).The midlatitude eddy feedback is also involved in the expansion of the HC (Sun et al., 2013) and the anomalous subsidence in the subtropics (Choi et al., 2016).Kang et al. (2011) and Chu et al. (2020) diagnose the dynamical role of midlatitude transient eddy feedbacks to the ENSO related wintertime teleconnection patterns.
Finally, we note that observed trends show that the tropics have been following the midlatitude meridional temperature gradient and expanding polewards since the late 1970s (Yang et al., 2020).Consistent with the role of eddy feedback, our findings suggest stronger relationships between subtropical highs and the EGR than the HC strength.This is consistent with the tropical width being more sensitive to extratropical than tropical influences (Freisen et al., 2022).In future work we will examine the effect of the extratropical process on the subtropical highs in climate models to test whether the relationships found here in reanalysis also occur in climate model simulations of historical climate and whether they continue in future climate projections.

Figure 1 .
Figure 1.Trends over the period 1979-2021 in 850 hPa geopotential height (m), indicating the regions of the winter subtropical highs studied here.The blue boxes represent the selected subtropical high index regions for the North Pacific Subtropical High, the North Atlantic Subtropical High, the South Pacific Subtropical High, and the South Atlantic Subtropical High.The zonal mean trend has been removed.The Northern Hemisphere and Southern Hemisphere trends are for DJF and JJA respectively.

Figure 2 .
Figure 2. Composite difference analysis between subtropical high strong years and the climatology (m) for 850 hPa geopotential height.The blue boxes represent the selected subtropical high index regions for the North Pacific Subtropical High in DJF (a), the North Atlantic Subtropical High in DJF (b), the South Pacific Subtropical High in JJA (c), and the South Atlantic Subtropical High in June to August, JJA (d).The zonal mean has been removed in each figure.

Figure 3 .
Figure 3. Composite analysis of transient eddy streamfunction tendency between subtropical high strong years and the climatology (m 2 s −2 ).The blue boxes represent the selected subtropical high index regions for the North Pacific Subtropical High in DJF (a), the North Atlantic Subtropical High in DJF(b), the South Pacific Subtropical High in JJA(c), and the South Atlantic Subtropical High in JJA(d).

Figure 4 .
Figure 4.The correlation map of SST and subtropical high intensities.(a)-(b) show the correlation coefficients between D(-1)JF(0) average SST and the North Pacific Subtropical High (a) and the North Atlantic Subtropical High (b) intensities.(c)-(d) show the correlation coefficients between JJA average SST and the South Pacific Subtropical High (c) and the South Atlantic Subtropical High (d) intensities, respectively.Stippling indicates correlation coefficients are significant above the 95% level.

Figure 5 .
Figure 5. Atmospheric zonal anomalies during strong subtropical high years.The changes of overturning circulation (shading,  10 −11 kgs −1 ) and Eady Growth Rate (EGR) (contour, day −1 ) are calculated for the winter South Pacific subtropical high (a), the North Pacific Subtropical High (b), the South Atlantic Subtropical High (c) and the North Atlantic Subtropical High (d) respectively.The purple lines indicate the zero isoline of anomalous meridional stream-function.Stippling indicates stream-function anomalies (a), (b) are significant above the 95% level.Hatching indicates anomalous EGR values that are significant above the 95% level.Solid lines indicate positive values and negative values are indicated as dashed lines.

Figure 7 .
Figure 7. Trends in atmospheric zonal circulation in JJA (a), (c) and DJF (b), (d) over the period 1979-2021.The trends of overturning circulation (shading,  10 −11 ⋅ kgs −1 ) and Eady Growth Rate (EGR) (contour, day −1 ) are shown in (a) and (b).The trends of temperature (shading, K) and EGR derived from thermal wind balance with climatological N (contour, day −1 ) is shown in (c) and (d).Stippling indicates stream-function anomalies (a), (b) and temperature (c), (d) that are significant above the 95% level.Hatching indicates that the contoured values are significant above the 95% level.Solid lines indicate positive values and negative values are indicated as dashed lines.

Figure 8 .
Figure8.The trend of streamfunction tendency in the recent four decades (m 2 s −2 ).The blue boxes represent the selected subtropical high index regions for the North Pacific Subtropical High, the North Atlantic Subtropical High, the South Pacific Subtropical High, and the South Atlantic Subtropical High.The Northern Hemisphere and Southern Hemisphere trends are for DJF and JJA respectively.
Acknowledgments M.C. and A.A.S were supported by NERC project EMERGENCE (NE/ S005242/1).AAS was supported by the UK-China Research & Innovation Partnership Fund through the Met Office Climate Science for Service Partnership (CSSP) China as part of the Newton Fund and the Met Office Hadley Centre Climate Programme funded by BEIS and Defra.W.T.Q. was supported by the joint scholarship from University of Exeter and China Scholarship Council (no.202106040023).

Table 3
Correlation Coefficients Between STH Index, HC Index, Hadley Cell Width and Eady Growth Rate Index Figure 6.Temperature and Eady Growth Rate (EGR) zonal anomalies during strong subtropical high years.The anomaly of temperature (shading, K) and EGR derived from thermal wind balance with climatological static stability, N, (contour, day −1 ) is calculated from the winter South Pacific Subtropical High (a), the North Pacific Subtropical High (b), the South Atlantic Subtropical High (c) and the North Atlantic Subtropical High (d) strong years, respectively.Stippling indicates temperature anomalies (shadings) are significant above the 95% level.Hatching indicates anomalous EGR values (contours) that are significant above the 95% level.

Table 4
Standardized Trends for Subtropical Highs, Hadley Cell Intensity, Hadley Cell Width and Eady Growth Rate