1. Introduction

The concept of the Hadley cell (HC) in the zonally averaged view of the atmosphere is at the core of the traditional view of the general circulation of the atmosphere as discussed, for example, in Lorenz (1967). As reviewed by Held (2018), there have been contrasting views about the relative importance of tropical and midlatitude phenomena and processes for the existence, strength, and extent of Earth’s Hadley cells and the strength of the upper-tropospheric subtropical jets on their poleward flank. From the midlatitude perspective, Jeffreys (1926) raised the importance for the maintenance of the surface westerlies in midlatitudes of angular momentum transfers from the subtropics by midlatitude eddies. The early datasets for computation of momentum fluxes (e.g., Starr 1948) were only for the extratropical region. Eady (1950) saw that maintenance of thermal wind balance would require that the midlatitude eddy-induced poleward momentum transfer in the upper troposphere must be accompanied by a Hadley cell, though this cell is weak, as was shown for the life cycle of a baroclinic wave by Simmons and Hoskins (1978). As was quoted by Held (2018), baroclinic instability has also for many decades been seen as a limiter on the latitudinal extent of the Hadley cell. In their axisymmetric simulations using a dynamical core, Davis and Birner (2019) found that the Hadley cell only extended through the depth of the atmosphere to the lower boundary if they included significant viscosity or prescribed eddy driving. Schneider (2006), stressed the importance for the Hadley cells of the extratropical eddies, and in subsequent years the emphasis has often been on their strong, and even controlling, influence on the HC.

However, from the tropical perspective, the improvement of data availability permitted Starr et al. (1970) to calculate momentum transport for the whole Northern Hemisphere and for the four seasons. In winter the upper-tropospheric poleward momentum flux by transient eddies occurred started from the deep tropics, but there were indications of a reversal of the direction of transport by both standing and transient eddies in the lowest latitudes. Rosen and Salstein (1980) also saw these features in their improved datasets, and they were discussed by Dima and Wallace (2003). Dima et al. (2005) associated the reversed tropical momentum transports with Rossby waves forced in the tropics, and in particular the horizontal tilts of waves generated as a response to the regions of tropical heating. However, Hartley and Black (1995) found that in their climate model the momentum fluxes on the equator that are equatorward in the Northern Hemisphere winter were associated with convective outflow rather than Rossby wave propagation and tilted troughs. Also, Zurita-Gotor (2019) found that the near equatorial momentum transfers were dominated by the correlation of the divergent meridional wind and the rotational zonal wind.

A zonally symmetric and temporally uniform atmosphere and angular momentum conservation in the tropical upper troposphere formed the basis of the simple model of the equinoctial HC given by Held and Hou (1980) in their seminal paper, which followed the study of Schneider (1977). In this model the HCs exist to reduce the midtropospheric temperature gradient, and therefore to reduce the upper-tropospheric winds implied by thermal wind balance to those which are attainable by angular momentum (AM) conservation from zero zonal wind at the equator. The latitudinal extent of the HC is determined by the latitudinal range over which the reduction of the latitudinal temperature gradient is needed, along with energy conservation. In this model, the subtropical jet (STJ) is at the latitude of the edge of the HC and its magnitude is that given by angular momentum conservation. The role of eddies is restricted to removing the discontinuity between this STJ wind and the zero wind in latitudes outside the HC and to reducing the speed of the STJ. A factor of about 3 would be required to give the observed values. The Held and Hou model for an equinoctial HC was extended to include the solsticial seasons by Lindzen and Hou (1988).

A fundamental issue associated with the dynamics of the upper branch of the HC was raised with one of us by John Sawyer in the 1970s (J. Sawyer, personal communication). In a solsticial season, as the air in the upper branch of the HC moves from the tropics of the summer hemisphere to near 30° in the winter hemisphere the change in its potential vorticity (PV) can be expected to be small. Therefore, this air will carry PV of the opposite sign to that of the air in the rest of this winter hemisphere. There is then the possibility of instabilities or a return to the summer hemisphere much as described in the inertial motion discussed by Paldor and Killworth (1988). Rodwell and Hoskins (1995) found both such behaviors in their study of the low-level inflow to the Indian summer monsoon. However, in this contribution to the lower branch of the HC, surface processes were usually found to be able to produce the PV modification that enabled a steady monsoon inflow from the southern Indian Ocean.

In the first part of this study (Hoskins et al. 2020, hereafter HC1) the dynamics of the HC in June–August (JJA), particularly its upper-tropospheric branch, were studied in detail. Zonally averaged momentum and vorticity budgets showed the importance of both steady and transient eddy fluxes. These fluxes had a similar structure to each other in the HC latitudes, with an equatorial maximum and reversal in sign near 12° in the winter (southern) hemisphere. The longitudinal behavior of the steady and transient fluxes was also found to be similar, and further analysis suggested that they were both associated with motion at the outflow level from a flaring of tropical convection, particularly in the Indian Ocean and west Pacific sectors of the Northern Hemisphere (NH). From the top of these convective regions, filaments of tropical air from the NH moved southwestward in the upper troposphere across the equator. Some of these filaments returned to the NH and some were mixed in with the ambient air in the southern tropics. However, in strong convective events near 12°S the filaments turned to move southeastward and phase in ahead of a trough in the Southern Hemisphere (SH) subtropical jet. The air with its tropical PV values caused a strengthening of the downstream ridge and the local STJ. In HC1, the temporal and longitudinal variation of the convection and meridional motion was seen to be fundamental in the dynamics of the HC.

In this paper the dynamics of the December–February (DJF) HC are analyzed in a manner similar to that used in HC1 for the other solsticial season. The aims of the study are the following:

• to investigate the similarities and differences between the two seasons,

• to determine to what extent this further study reinforces the picture given in HC1 that longitudinal and temporal variations are of order one importance for the HC, and

• to explore the interaction of the tropics with higher latitudes that is initiated by flaring in regional tropical convection.

2. Data and diagnostics

The basis for the analysis is ECMWF interim reanalysis (ERA-Interim) horizontal winds (u, υ), and vorticity fields for the 30-yr period from 1981 to 2010. The fields are available 6-hourly with horizontal resolution of about 0.7° and at 37 pressure levels from 1000 to 1 hPa. When fields for a day are shown, the data are averaged over the four periods in the day. In addition, potential vorticity is available on a limited number of isentropic levels, including 350 and 370 K. Detailed information on the data can be found in Dee et al. (2011). As a proxy for convection, use is made of NOAA interpolated daily outgoing longwave radiation (OLR) on a 2.5° × 2.5° grid (Liebmann and Smith 1996). For part of the analysis and for case studies the single season DJF 2007/08 is used. This season was chosen at random to be the first one to analyze. It is a La Niña year, which will influence the distribution and magnitude of tropical convection, and other years can be expected to show somewhat different detailed behavior.

In section 5, power spectra of OLR are shown. These are computed over a 120-day time window for each DJF (centered on DJF). A 120-day window is used because a 10% taper (12 days) is applied at the two ends of the data record and to include the intraseasonal (30–60 days) signal. Also in section 5, regressions are performed on DJF seasonal data. The seasonal trend was not removed as its impact was considered to be negligible for the fields shown.

3. Zonal average perspective

The zonally averaged, time-mean DJF Hadley cell is shown in Fig. 1, with μ = sinϕ as the abscissa. In each panel, the meridional circulation is indicated by arrows, representing (V, ω), and the dark blue contours are for the zonal flow U. The field shown with block color contours is angular momentum (Fig.1a), absolute vorticity (Fig.1b), and potential vorticity (Fig.1c). This figure can be compared with the equivalent for JJA, shown as Fig. 1 in HC1. The overturning circulation is to a first approximation the mirror image of that in JJA, with the winter STJ near latitude 30° at the extratropical edge of the HC. However, there are significant departures from this mirror image picture. Whereas the midtropospheric ascent region in JJA is concentrated in a peak in the 10° band from 5° to 15°N, that in DJF is more evenly distributed in a band 20° wide in the summer hemisphere from 5°N to 15°S. However, the descent occupies a similar range of latitudes in the two winter hemispheres. The Hadley cell in DJF is distorted in the lower troposphere with the ascent remaining in the NH. As might be expected, this is mainly due to the ITCZs remaining north of the equator in the NH winter.

The 30-yr mean DJF Hadley cell. In each panel the meridional circulation (V, ω) is shown by vectors, with the scale at the top right. (a),(b) U is shown by dark blue contours with interval 10 m s⁻¹, and with the zero contour dotted. (c) The dark blue contours are for the isentropes, with interval 20 K. The abscissa is the sine of the latitude. The fields shown with block contours are (a) angular momentum (unit: a²Ω), (b) the vertical component of absolute vorticity (unit: Ω), and (c) potential vorticity (PV) (unit: PVU).

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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The 30-yr mean DJF Hadley cell. In each panel the meridional circulation (V, ω) is shown by vectors, with the scale at the top right. (a),(b) U is shown by dark blue contours with interval 10 m s⁻¹, and with the zero contour dotted. (c) The dark blue contours are for the isentropes, with interval 20 K. The abscissa is the sine of the latitude. The fields shown with block contours are (a) angular momentum (unit: a²Ω), (b) the vertical component of absolute vorticity (unit: Ω), and (c) potential vorticity (PV) (unit: PVU).

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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The 30-yr mean DJF Hadley cell. In each panel the meridional circulation (V, ω) is shown by vectors, with the scale at the top right. (a),(b) U is shown by dark blue contours with interval 10 m s⁻¹, and with the zero contour dotted. (c) The dark blue contours are for the isentropes, with interval 20 K. The abscissa is the sine of the latitude. The fields shown with block contours are (a) angular momentum (unit: a²Ω), (b) the vertical component of absolute vorticity (unit: Ω), and (c) potential vorticity (PV) (unit: PVU).

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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Zhang et al. (2004), in their discussion of shallow meridional circulations in the tropical atmosphere, showed that both shallow and deep Hadley cell modes exist in the two ITCZ regions. In DJF, the low-level flow into the NH, ascent there and the return flow from 800 hPa upward in the ITCZ regions leave their imprint on the zonal average. If the average meridional circulation is calculated for the longitudes other than those of the ITCZs, the picture (not shown) is closer to the mirror image of the zonal mean in JJA, with low-level flow into the summer hemisphere (here, the Southern Hemisphere) and more concentrated midtropospheric ascent.

Specific absolute angular momentum A, as defined in Eq. (1) and shown in Fig. 1a by block contours, has values near the surface close to that given by Earth’s rotation alone, given the small values of U. There the meridional circulation crosses the contours of A and the frictional term is important in the balance in the momentum/A equation, Eq. (2). In the upper troposphere there is a maximum in A, just north of the equator. There is a sense that the northward motion in the upper branch of the Hadley cell appears to carry its value of A with it, but there is motion across the contours both in the band from 8°S to the equator and from 5° to 25°N. Here friction is in general not important and the balance in the momentum equation will be discussed below.

From Eq. (4), the zero absolute vorticity (ζ) contour in Fig. 1b marks the maximum in A. In Fig. 1a it is seen that it remains close to the equator, being slightly north of it in the upper troposphere. The region of small positive ζ extends northward from the equator toward 10°N, consistent with the weak gradient in A there. Potential vorticity (Fig. 1c) shows similar features but also emphasizes the high-amplitude PV in the stratosphere acting as a lid on the HC. Also shown in Fig. 1c are some contours of potential temperature. The 350-K isentropic surface, near 175 hPa, is seen to be close to the maximum flow in the upper branch of the HC, and the 370-K surface, near 100 hPa, toward the upper side of it. The winds and PV on these surfaces will be used for diagnosis in case studies in section 6.

The steady and transient momentum fluxes for DJF are shown in Fig. 2, which can be compared with the JJA versions (HC1, Fig. 2).The steady flux in the NH is the largest. All these near-surface fluxes are associated with the trade winds blowing into the ITCZs, in the east Pacific, Atlantic, and east Indian Oceans. In JJA, the general picture of these near-surface fluxes was similar, but the steady flux in the SH was slightly larger than that in the NH and the zero-flux line was at about 3°N. The DJF fluxes are consistent with the ITCZs staying near and north of the equator in that season. In the band 0°–10°N, the flux convergence is comparable with the Coriolis term in Eq. (2), and their sum is balanced by friction.

Northward fluxes of angular momentum in 30-yr DJF by (a) the steady $\left[\overline{U}\overline{V}\right]$ and (b) the transient $\overline{\left[U^{\prime }{V}^{\prime }\right]}$ motions, as defined in Eq. (8). The contour interval is shown on the color bar and is not uniform, and contours at negative values are dotted. The unit is m² s⁻².

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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Northward fluxes of angular momentum in 30-yr DJF by (a) the steady $\left[\overline{U}\overline{V}\right]$ and (b) the transient $\overline{\left[U^{\prime }{V}^{\prime }\right]}$ motions, as defined in Eq. (8). The contour interval is shown on the color bar and is not uniform, and contours at negative values are dotted. The unit is m² s⁻².

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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Northward fluxes of angular momentum in 30-yr DJF by (a) the steady $\left[\overline{U}\overline{V}\right]$ and (b) the transient $\overline{\left[U^{\prime }{V}^{\prime }\right]}$ motions, as defined in Eq. (8). The contour interval is shown on the color bar and is not uniform, and contours at negative values are dotted. The unit is m² s⁻².

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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In the upper troposphere, the near-equatorial maxima in southward momentum fluxes are the equivalent of the rather stronger northward (toward the winter pole) momentum fluxes in JJA (Fig. 2 in HC1). In both seasons, in the tropics the upper-tropospheric transient fluxes have a very similar structure in the latitudes of the winter Hadley cell, although their magnitudes are smaller by a factor of about 2. The steady fluxes were highlighted by Dima and Wallace (2003) and associated by Dima et al. (2005) with the tilted troughs of the steady response to tropical heating. However, Zurita-Gotor (2019) stressed the importance of the divergent meridional wind. The smaller transient fluxes appear to have not been discussed explicitly though they were in the figures given by Starr et al. (1970), Rosen and Salstein (1980), and Dima et al. (2005).

As expected, there is a large difference in the winter hemisphere fluxes between the two solsticial seasons in the region poleward of the equatorial extremum. In DJF there is a poleward (northward) steady flux maximum of more than 50 m² s⁻² centered at 22°N and a transient maximum of more than 30 m² s⁻² centered at 30°N. However, in JJA the poleward (southward) fluxes in the equivalent region were all associated with the transients, with a maximum of more than 50 m² s⁻².

Referring to the momentum/A equation, Eq. (2), the flux divergence from 10°S to the equator balances the Coriolis term associated with the SH portion of the upper branch of the HC, and the convergence from about 3° to 23°N performs the balance for the NH (winter) portion. It is evident that the near-equatorial flux extrema, highlighted previously by Dima and Wallace (2003), play an important role in the momentum budget of the upper branch of the HC in both solsticial seasons.

As discussed above, the form of the U/A equation in Eq. (7) requires that, in regions of small friction in the upper troposphere, the time-averaged poleward flux of absolute vorticity, $\left[\overline{V\zeta }\right]$, must be small compared with its constituent terms. A similar conclusion would be reached by consideration of the vorticity equation at these levels. For DJF 2007/08 and at 200 hPa, the flux and its component terms as in Eq. (9) are shown in Fig. 3. From 15°S to 5°N there is little evidence of cancellation in this region of significant deep convection. This is consistent with this being a belt where significant deep convection occurs and the inclusion in the ECMWF system of cumulus momentum transport and the associated friction. However, in the region of the upper branch of the HC north of this, from 5° to 25°N, both steady and transient fluxes of relative vorticity act to balance the Coriolis term. The steady flux is 3–4 times larger than the transient flux, and the latter is some 50% larger than the residual. In JJA, the cancellation in the region was even greater and the transient flux was slightly more important in the balance. Calculations suggest that the small residual flux is not cancelled by the vertical advection of momentum and a small frictional term would be required for balance even in this region. Alternatively, data assimilation might lead to such a slight imbalance. In passing, we also note the expected higher latitude balance of the Coriolis term, associated with the Ferrel cell, with the transient flux convergence in the 30°–50°S band, and with the steady and transient fluxes in the 30°–50°N band.

The northward flux of absolute vorticity at 200 hPa for DJF 2007/08, and its component split as in Eq. (9). The total flux is denoted as tot. The three components, the Coriolis torque, the steady flux of relative vorticity, and the transient flux are denoted as Cor, steady, and trans, respectively. The unit is 1 × 10⁻⁴ m s⁻². The ordinate is linear in latitude.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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The northward flux of absolute vorticity at 200 hPa for DJF 2007/08, and its component split as in Eq. (9). The total flux is denoted as tot. The three components, the Coriolis torque, the steady flux of relative vorticity, and the transient flux are denoted as Cor, steady, and trans, respectively. The unit is 1 × 10⁻⁴ m s⁻². The ordinate is linear in latitude.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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The northward flux of absolute vorticity at 200 hPa for DJF 2007/08, and its component split as in Eq. (9). The total flux is denoted as tot. The three components, the Coriolis torque, the steady flux of relative vorticity, and the transient flux are denoted as Cor, steady, and trans, respectively. The unit is 1 × 10⁻⁴ m s⁻². The ordinate is linear in latitude.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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In the transient fluxes in the tropics, the contribution from the transient zonal mean terms (i.e., fluctuations in the zonal Hadley cell) are negligible, so that the fluxes are associated almost entirely with the zonally asymmetric, transient eddies. As was the case in JJA (HC1), in both the momentum and vorticity flux views the tropical steady and transient fluxes have a structure that is similar to each other, with the transient flux being a factor of 2–3 smaller. The similarity of their structures raises the question whether there is a common mechanism underlying the steady and transient fluxes. The importance of the tropical fluxes in the momentum balance in the upper branch of the winter Hadley cell contrasts with the view of the complete dominance in it of poleward momentum fluxes associated with the equatorward extension of eddies on and poleward of the winter STJ.

4. 3D structure

A picture of the longitudinal structure of the time-mean meridional flow that averages to give the Hadley cell is provided in Fig. 4. This presents in a longitude–pressure plane the meridional wind averaged over the 15° latitude band from 5°S to 10°N. The picture is robust to the choice of the latitude band, either making it more restricted to the equator or more extended in either hemisphere, apart from in the longitudes of the two ITCZs. The comparable figure for the 10°S–5°N band in JJA was given in Fig. 5 of HC1. Zhang et al. (2004) showed similar cross sections of meridional wind on the equator for January and July.

30-yr DJF time-mean meridional wind (m s⁻¹) averaged between 5°S and 10°N. Also shown are the isentropic levels 330, 350, and 370 K.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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30-yr DJF time-mean meridional wind (m s⁻¹) averaged between 5°S and 10°N. Also shown are the isentropic levels 330, 350, and 370 K.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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30-yr DJF time-mean meridional wind (m s⁻¹) averaged between 5°S and 10°N. Also shown are the isentropic levels 330, 350, and 370 K.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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The basic expectation for the DJF picture is that it is the reverse of that in JJA, with flow into the winter hemisphere (NH) in the upper troposphere and a return in the surface boundary layer. This is the case in the Eastern Hemisphere (EH), over Africa and over the Indian Ocean to the west Pacific, and also over South America, near 300°E (60°W). However, the upper troposphere in the equatorial region of the Western Hemisphere (WH) is dominated by two wave trains, one over the Pacific from the date line to 280°E and the other eastward from South America over the Atlantic to the Greenwich meridian. The wavetrains appear to propagate eastward and upward, and in the case of the Pacific also downward. The wavelike meridional wind in the equatorial region is the signature of westward-moving mixed Rossby–gravity (WMRG) waves. The two regions with the waves are those with westerly winds in the upper-tropospheric equatorial region. As shown by, for example, Yang et al. (2007, their Fig. 7b) and Yang and Hoskins (2016, their Fig. 3a), in a westerly basic flow WMRG waves can be Doppler shifted to have a phase speed that is a reduced westerly or even, for very strong westerlies, zero or eastward . The group velocity is eastward and typically about 20 m s⁻¹ so that a wave pattern could develop from 150° to 60°W in about 4 days. As discussed by Dunkerton and Baldwin (1995), the crest and trough lines tilt in the vertical westward from the upper-tropospheric source level as the waves propagate vertically away from the source level as well as eastward. The temporal, longitudinal, and vertical structures of the waves were shown and discussed in Yang et al. (2011, their Figs. 13c,d) and Yang et al. (2012, their Figs. 11b,e). The latter showed the WMRG structures for the opposite phases of the QBO, these differing significantly only above 70 hPa. Yang and Hoskins (2016, their Fig. 6) showed that WMRG activity was present in the east Pacific and Atlantic in both phases of ENSO, though it was stronger in the east Pacific in La Niña and the Atlantic in El Niño, consistent with the differing strength of the westerlies. In Yang and Hoskins (2016, their Figs. 10c,d and 12c) it was shown that the westward moving WMRGs in these regions were typically associated with an arching pattern originating in the Southern Hemisphere.

It is proposed here that the waves seen in the upper troposphere can be associated with WMRG waves forced in the east Pacific by convective heating in the South Pacific convergence zone (SPCZ) and in the Atlantic by convective heating in South America, south of the equator. The shorter wavelength of the stationary waves in the Atlantic is consistent with the weaker westerlies there. In JJA, no comparable regions of westerlies are found on the equator, and WMRG waves in the EH are rapidly westward-moving synoptic features that are important in triggering convection but leave no signature in the time-averaged meridional wind. Further discussion of this is given below.

The geographical distributions of the mean motion at 200 and 950 hPa, and the mean OLR and its standard deviation (SD), are shown in Fig. 5. In Fig. 5b, the dominant regions of convection as indicated are Africa, the Maritime Continent, and South America. The low-level northeasterly wind flows into each of these from the neighboring oceanic regions, and these add up to give most of the low-level branch of the HC. Also apparent are the east Pacific and Atlantic ITCZs, north of the equator with the trade winds blowing into them. In the upper troposphere (Fig. 5a), in the EH there is a pair of anticyclones either side of the equator with the strong STJ in the NH and a northward component in the winds from 5°S to 25°N giving much of the upper branch of the HC. There are discrete SH anticylonic circulations over Africa and South America. Equatorial westerlies are present in the east Pacific and Atlantic. The waves on them spread from the SH through the equator, with the shorter wavelength on the weaker westerlies in the Atlantic.

30-yr DJF time-mean horizontal winds and OLR statistics. (a) 200-hPa vector winds (scale arrow at top right). (b) 950-hPa vector winds (scale arrow at top right) and time-mean OLR (W m⁻²). (c) Time-mean of the seasonal standard deviation of OLR. The boxes shown in (c) are the 12 regions defined in Table 1.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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30-yr DJF time-mean horizontal winds and OLR statistics. (a) 200-hPa vector winds (scale arrow at top right). (b) 950-hPa vector winds (scale arrow at top right) and time-mean OLR (W m⁻²). (c) Time-mean of the seasonal standard deviation of OLR. The boxes shown in (c) are the 12 regions defined in Table 1.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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30-yr DJF time-mean horizontal winds and OLR statistics. (a) 200-hPa vector winds (scale arrow at top right). (b) 950-hPa vector winds (scale arrow at top right) and time-mean OLR (W m⁻²). (c) Time-mean of the seasonal standard deviation of OLR. The boxes shown in (c) are the 12 regions defined in Table 1.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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The standard deviation of the OLR is given in Fig. 5c. The Indian Ocean to west Pacific region is implied to have high variability in the region of strong convection. The low-latitude portion of the convection in Africa and South America appears to be relatively steady, whereas south and east of these regions there is high variability with moderate intensity convection in the mean. The same also applies in the northern Australian region.

Because of their possibly different characteristics, the 12 boxes indicated in Fig. 5c have been defined for detailed diagnosis. The details of the 12 regions are indicated in Table 1. The results from most of these will be discussed in the next section.

Table 1.

Geographical regions analyzed.

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The final figure of this section, Fig. 6, shows the 200-hPa longitudinal structure of the momentum fluxes that average zonally to give the fluxes shown in Fig. 2. In HC1 it was found that both the steady and transient fluxes near the equator toward the summer pole and the fluxes in the opposite direction in the winter tropics had major contributions from the EH with more minor ones from the east Pacific and Atlantic sectors. In DJF the major contribution to the tropical fluxes that are important in the winter Hadley cell, southward near the equator and northward north of this again come from the EH. Referring to Fig. 5a, the steady fluxes are associated with the generally southeasterly winds near the equator, turning to southwesterly in 10°–15°N. The transient fluxes also have a contribution from the east Pacific and Atlantic sectors, but the waves in the mean wind field in the equatorial east Pacific, and to a lesser extent the Atlantic, gives a signature that makes the picture of the steady fluxes more complex. However, as in JJA the major input to the important tropical steady and transient zonally averaged momentum fluxes have a similar structure in longitude as well as latitude, consistent with the possibility of them having a common underlying origin.

30-yr DJF time-mean northward flux of angular momentum at 200 hPa. (a) Steady $\left(\overline{U}\overline{V}\right)$ and (b) transient $\overline{\left(U^{\prime }{V}^{\prime }\right)}$. The unit is m² s⁻².

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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30-yr DJF time-mean northward flux of angular momentum at 200 hPa. (a) Steady $\left(\overline{U}\overline{V}\right)$ and (b) transient $\overline{\left(U^{\prime }{V}^{\prime }\right)}$. The unit is m² s⁻².

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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30-yr DJF time-mean northward flux of angular momentum at 200 hPa. (a) Steady $\left(\overline{U}\overline{V}\right)$ and (b) transient $\overline{\left(U^{\prime }{V}^{\prime }\right)}$. The unit is m² s⁻².

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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5. Temporal behavior

The first view of the temporal behavior is provided by Fig. 7, which gives the spectral information for OLR in the 12 boxes shown in Fig. 5c and defined in Table 1. The order of the boxes in Table 1 and Fig. 7 is from Africa eastward to the Atlantic, with SH boxes directly after their near-equatorial counterparts. The period is indicated on the ordinate. In Fig. 7a, the spectral power in each region is given. This highlights the low-frequency power, particularly in the EH. To examine the important frequency peaks in each region, Fig. 7b presents the ratio of the spectral power to that associated with a red noise spectrum, with 1 indicating significance at the 95% level. The intraseasonal time scale dominates in the near-equatorial region from Africa to the Maritime Continent (MC; boxes 1 and 3–5), consistent with the importance there of the MJO. The 1–2-week period is prominent in SAf (box 2), and in the off-equatorial boxes for NAus (box 6) and the 2–3-week period is prominent in the SPCZ (box 8), as it is also in the MC (box 7). There are peaks in the 4–7-day time scale in all regions except the MC.

(a) Raw spectra for 30 years of DJF OLR averaged over each of the 12 regions and (b) spectral power divided by a red-noise power specified with a significance level of 95%, so that values greater than 1 indicate the power exceeding the 95% significance level. The power unit in (a) is W² m⁻⁴. The regions are as defined in Table 1.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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(a) Raw spectra for 30 years of DJF OLR averaged over each of the 12 regions and (b) spectral power divided by a red-noise power specified with a significance level of 95%, so that values greater than 1 indicate the power exceeding the 95% significance level. The power unit in (a) is W² m⁻⁴. The regions are as defined in Table 1.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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(a) Raw spectra for 30 years of DJF OLR averaged over each of the 12 regions and (b) spectral power divided by a red-noise power specified with a significance level of 95%, so that values greater than 1 indicate the power exceeding the 95% significance level. The power unit in (a) is W² m⁻⁴. The regions are as defined in Table 1.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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To exhibit the fluctuations in the OLR and in the 200- and 950-hPa flow and their contribution to the Hadley cell that are typically associated with variability in OLR in the boxes, two approaches have been taken. In the first, the winds and OLR have been regressed against OLR in each box and the anomalies and full fields for OLR with ±1.5 standard deviations (SD) have been considered. In the second approach, fields have been composited for the days with the anomaly of OLR averaged over each box exceeding ±1.5 SD. The results are very similar and only some of the regression results with OLR set as −1.5 SD will be presented in this paper. In the online supplemental material, as a good summary of anomalies associated with convection in a range of tropical regions, the differences in OLR and 200-hPa wind between the −1.5 SD and +1.5 SD composites are presented for each of the 12 boxes defined in Table 1. The pictures for the regressions with OLR set to +1.5 SD and for the composites for this value of OLR have been used to check the motions when the implied convection in a region is a minimum but will not be commented on explicitly.

The regressions for low OLR, indicating strong convection, in WIO (box 3) and MC (box 5) are summarized in Fig. 8. In each panel the block contours show the OLR anomalies and the vectors indicate the full 200-hPa winds. This choice of fields enables the regions of enhanced/reduced convection and the full wind field that accompanies them to be seen. The two regions are chosen to illustrate the MJO behavior that dominates in the equatorial EH. The OLR anomaly exhibits the antiphase behavior between the two regions, with a further antiphase slightly east of the date line. The winds in Fig. 8 can be compared with each other and with the 30-yr climate in Fig. 5a, and use can be made of the differences in composites shown in Figs. S1c and S2a in the online supplemental material . From the region of enhanced convection there is a strong southeasterly flow across the equator. The direction turns near 10°N to become a strong southwesterly at 20°N and then into the equatorial flank of an enhanced STJ. In the region of supressed convection this flow is much weaker. The tilts and strength of the outflows are consistent with the momentum fluxes (Figs. 2 and 6), southward near the equator and northward near 20°N, and are significant contributors to them.

200-hPa horizontal winds (vector) and OLR anomalies (color) obtained by regressions on OLR averaged over the geographical regions and shown for OLR anomalies in those regions of −1.5 SD. (a) the West Indian Ocean (WIO) and (b) Maritime Continent (MC). The daily data for the regressions are from the 30 years of DJF. The scale for the wind vectors is shown at the top right. The OLR unit is W m⁻².

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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200-hPa horizontal winds (vector) and OLR anomalies (color) obtained by regressions on OLR averaged over the geographical regions and shown for OLR anomalies in those regions of −1.5 SD. (a) the West Indian Ocean (WIO) and (b) Maritime Continent (MC). The daily data for the regressions are from the 30 years of DJF. The scale for the wind vectors is shown at the top right. The OLR unit is W m⁻².

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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200-hPa horizontal winds (vector) and OLR anomalies (color) obtained by regressions on OLR averaged over the geographical regions and shown for OLR anomalies in those regions of −1.5 SD. (a) the West Indian Ocean (WIO) and (b) Maritime Continent (MC). The daily data for the regressions are from the 30 years of DJF. The scale for the wind vectors is shown at the top right. The OLR unit is W m⁻².

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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Figure 9 give the corresponding results for low OLR (active convection) in the off-equatorial regions of SAf (box 2) and NAus (box 6), and for SPCZ (box 8) and SAm (box 11). Referring first to NAus (Fig. 9b), the anomalous active convection is centered there, but is present in a larger area, including the MC. The 200-hPa flow is quite similar to that for the MC (Fig. 8b). However, the equatorward flow on the eastern side of the anticyclone over Australia that is associated with the convection over NAus links with the southeasterly flow north of the MC to give the possibility of advection from deep in the SH into the enhanced flow into the NH there. Summer seasons with enhanced convection in northern Australia have recently been investigated by Sekizawa et al. (2018). They noted a teleconnection from there to the region of Japan. This teleconnection is particularly noticeable in Fig. S2b. Anomalies in OLR and flow anomalies are weaker in SAf (Fig. 9a). However, again a link is seen with the flow crossing the equator, this flow being associated with the convection over CAf (box 1). Figures S1a and S1b also show these features. The 150-hPa composite flow difference for CAf (not shown) gives a stronger outflow and cross-equatorial flow near 30°E than that at 200 hPa.

200-hPa horizontal winds (vector) and OLR anomalies (color) obtained by regressions on OLR averaged over the geographical regions and shown for OLR anomalies in those regions of −1.5 SD: (a) SAf, (b) NAus, (c) SPCZ, and (d) SAm. The conventions are as in Fig. 8.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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200-hPa horizontal winds (vector) and OLR anomalies (color) obtained by regressions on OLR averaged over the geographical regions and shown for OLR anomalies in those regions of −1.5 SD: (a) SAf, (b) NAus, (c) SPCZ, and (d) SAm. The conventions are as in Fig. 8.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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200-hPa horizontal winds (vector) and OLR anomalies (color) obtained by regressions on OLR averaged over the geographical regions and shown for OLR anomalies in those regions of −1.5 SD: (a) SAf, (b) NAus, (c) SPCZ, and (d) SAm. The conventions are as in Fig. 8.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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The patterns of upper-tropospheric flow from the two regions of off-equatorial convection seen in Figs. 9a and 9b are reminiscent of those found in HC1 for JJA, although not as strong as these. In JJA, from active convection in the Indian Ocean/Bay of Bengal and west Pacific/Philippines regions there were northeasterly winds across the equator, turning near 12°S and becoming northwesterly and then turning anticyclonically to merge with the flank of the STJ.

Figures 9c and 9d give the regression pictures for active convection in the two other main off-equatorial regions of variable active convection, SPCZ and SAm. In the regression, active convection in SPCZ is accompanied by weakened convection in the MC (though the reverse link is not seen in Fig. 8b). The 950-hPa motion (not shown) is strongly westerly/northwesterly along the SPCZ, with southwesterlies turning into it on its southern flank. There is evidence of enhanced cross-equatorial flow over the west and central Pacific. The 200-hPa flow turns anticyclonically over the SPCZ to give strong near-equatorial southerlies near 150°W and then northwesterlies near 110°W and weak southerlies near 85°W. This is an enhanced version of the wave pattern seen in the 30-yr average in Fig. 5a, and also in the longitude–pressure cross section in Fig. 4a. Regression of OLR and winds on the equatorial meridional wind near 160°W gives an almost identical wave pattern to the east and an OLR anomaly in the SPCZ region. Figure 9d shows a similar behavior to that of the SPCZ for strong convection in the South American region. The major difference, as noted before, is the shorter scale of the wave pattern over the Atlantic in the 200-hPa flow. The wave patterns in both regions are clearly seen in the composite differences given in Figs. S2d and S3c.

The east Pacific and Atlantic ITCZ regions (EP-I and Atl-I, boxes 9 and 12) both give evidence at 200 hPa (see Figs. S3a,d) for the triggering of convection by southeastward Rossby wave propagation from the extratropics. In both cases, the enhanced ITCZ convection is on the equatorial flank of a 200-hPa southwesterly flow anomaly, which is part of the wave train. This wave train is present through the troposphere (not shown) but tilts slightly backward (northwestward) with height, suggesting some baroclinic growth.

In HC1, some regressions were shown for ±3-day lags with OLR. However, in DJF the general dominance of time scales of 1–2 weeks or longer (except in the ITCZ regions) and, consistent with this, little difference is found if the regressions are lagged by a few days.

6. Examples from 2007/08

To answer the question to what extent the regressions for the 30-yr climate are relevant for the fields seen in specific periods, the daily OLR and 350-K PV and winds have been looked at for the 2007/08 DJF season. A Hovmöller plot for 200-hPa υ averaged between 5°S and 10°N is given in Fig. 10 (colors). In the EH slow eastward movement, likely related to the MJO, is seen, together with fast westward-moving synoptic systems. In the WH slow-moving large-scale waves are present much of the time with varying amplitude. Further evidence that that these are dominated by WMRG waves will be given below.

Hovmöller plots of 200-hPa υ averaged from 5°S to 10°N for DJF 2007/08. The raw data are shown in block colors. The black line contours show the same field but for the projection of the winds and geopotential onto the horizontal structure of the WMRG wave as in Yang et al. (2003), but filtered to leave zonal wavenumbers 2–40 and with no time filter. The line contours are at the same values as the change in colors and contours at negative values are dotted.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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Hovmöller plots of 200-hPa υ averaged from 5°S to 10°N for DJF 2007/08. The raw data are shown in block colors. The black line contours show the same field but for the projection of the winds and geopotential onto the horizontal structure of the WMRG wave as in Yang et al. (2003), but filtered to leave zonal wavenumbers 2–40 and with no time filter. The line contours are at the same values as the change in colors and contours at negative values are dotted.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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Hovmöller plots of 200-hPa υ averaged from 5°S to 10°N for DJF 2007/08. The raw data are shown in block colors. The black line contours show the same field but for the projection of the winds and geopotential onto the horizontal structure of the WMRG wave as in Yang et al. (2003), but filtered to leave zonal wavenumbers 2–40 and with no time filter. The line contours are at the same values as the change in colors and contours at negative values are dotted.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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For discussion here, four days have been selected to represent the behavior seen in the whole season. All show interesting features associated with enhanced tropical convective activity in one or more of the regions defined in Table 1, and diminished activity in others. The discussion will be organized around these features, rather than on the time development through the period. The days chosen are all from January 2008, apart from 15 February 2008. According to Sekizawa et al. (2018, Fig. 2a), 2007/08 was a weak year for the northern Australian summer monsoon, and consistent with this there were no good examples of strong OLR minima there. The February date was added to give another example for active convection in the tropical Australian region.

For the 4 days, Fig. 11 gives the OLR averages for the specified day and the previous 2 days. The 3-day average for OLR is used to produce a slightly smoother OLR field and, as seen in HC1, to take account of the fact that there may be a lag of a day or so before the wind field response away from the active convective region reaches its maximum. Figure 12 shows the PV and winds on the 350-K isentropic surface (about 180 hPa). These will be used to indicate the upper-tropospheric motion associated with the variety of convective activity indicated by the OLR. It is worth noting that a 10 m s⁻¹ meridional wind would enable an air parcel to move from near the equator to 25°N in about 3 days.

OLR for 4 days in DJF 2007/08. The OLR is averaged over the specified day and the previous 2 days. The unit for the 3-day OLR average is W m⁻².

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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OLR for 4 days in DJF 2007/08. The OLR is averaged over the specified day and the previous 2 days. The unit for the 3-day OLR average is W m⁻².

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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OLR for 4 days in DJF 2007/08. The OLR is averaged over the specified day and the previous 2 days. The unit for the 3-day OLR average is W m⁻².

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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PV (color) and vector winds on the 350-K isentropic surface for the same 4 days in the DJF season in 2007/08 as in Fig. 11. The color bar gives the scale for PV (unit: PVU), and the scale for the winds is shown at the top right.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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PV (color) and vector winds on the 350-K isentropic surface for the same 4 days in the DJF season in 2007/08 as in Fig. 11. The color bar gives the scale for PV (unit: PVU), and the scale for the winds is shown at the top right.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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PV (color) and vector winds on the 350-K isentropic surface for the same 4 days in the DJF season in 2007/08 as in Fig. 11. The color bar gives the scale for PV (unit: PVU), and the scale for the winds is shown at the top right.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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On 1 January and 22 January, convective activity is enhanced over western central Africa and southern Africa, with this spreading into the west Indian Ocean on 22 January. On both days there is flow from the south Indian Ocean around the anticyclone over southern Africa, with a southeasterly flow across the equator and into a strong anticyclonic perturbation of and strengthening of the NH STJ in the Middle Eastern region. On 22 January, consistent with the convective activity in the WIO, there is southeasterly flow across the equator from there. On 25 January (not shown) the active convection region has spread to 80°E and the cross-equatorial southeasterlies are found from Africa to there. On 16 January and 15 February, the convection is generally not enhanced over the CAf, SAf, and WIO regions, and the flow features noted above are absent or much weaker.

On 1 January there is enhanced convective activity in the MC region. Associated with this is a strong anticyclone north of it and again a local perturbation and strengthening of the STJ. On 15 February the active convection region extends farther into Australia and to the east of it. There is now more indication of southeasterly flow from near 20°S and across the equator into the strong NH anticyclone. On 16 and 22 January, consistent with the eastward movement of the MJO, convective activity is much weaker than normal, first in the EIO and then in the MC. There is almost zero cross-equatorial flow in the IO and MC regions and the NH anticyclone is weaker, particularly on 22 January.

On 16 and 22 January there is enhanced convective activity in the SPCZ region, with an eastward shift between the two days. On 16 January there is strong southerly flow across the equator near 170°W. 1 January had a weaker but similar OLR signature in the region and a similar but weaker flow associated with it. On 22 January the cross-equatorial motion is shifted eastward to nearer 150°W and is southeasterly. In each case, there are northerlies to the east. The wave pattern moving eastward along the equator is particularly striking on 16 January, with signs of a wave breaking near South America as the equatorial westerlies weaken.

The Hovmöller plot for 2007/08 of 200-hPa υ averaged between 5°S and 10°N given in Fig. 10 also shows in black line contours υ obtained by projection of the horizontal structure on to that of the MRG wave, following the methodology of Yang et al. (2003). The similarity with the raw data (Fig. 10, block colors) strongly supports the interpretation in terms of WMRG waves. There are slow-moving waves in the east Pacific through much of the season, with periods of westward, stationary, and eastward phase speed. For much of the time there is evidence of an eastward group velocity of 20 m s⁻¹ or more.

The NH anticyclone associated with South American convection is apparent on all four days. The variable convection in the region of South America seen in Fig. 5c and which is partly identified by the SAm box is particularly notable on 22 January. In this case there is southeasterly flow around the SH anticyclone and across the equator in the region of enhanced convection and a pronounced anticyclone with northerly flow on its eastward flank.

The four examples shown in Fig. 12 are consistent with the more general patterns of the regressions in Figs. 8 and 9, though often stronger than them, as would be expected for individual events. Examples are seen in the 4 days of the MJO enhancement of convection in the WIO to WP summarized in Fig. 8, and also of the diminishment in the opposite phase implied by the regression. The behaviors seen for off-equatorial convection in SAf and NAus seen in these examples are similar to those given in Figs. 9a and 9b, although as remarked above 2007/08 was a year of generally weak convection in the NAus region. Finally, the triggering of cross-equatorial flow and an eastward wave pattern by SPCZ and SAm as in Figs. 9c and 9d was seen in the examples, particularly the SPCZ on 16 January. Despite the convection and anomalous flow seen on a daily basis being more localized and flexible in location than the large fixed boxes used in the regressions, it is clear that the flavor of the regression figures is highly relevant to the large-scale behavior seen on a daily basis.

The strong anticyclones in the NH between the equator and the subtropics are seen to be variable in space and time. In the EH they can occur at any longitude, dependent on the phase of the MJO, but are enhanced in the African and MC regions, and in the WH they occur over or to the east of South America. 1 January gives good examples of the ones associated with African and MC convection. PV contours show the northward movement of near-equatorial or SH PV on its western flank and the southward movement of extratropical PV, and their wrapping up, which will lead to irreversible mixing. The signature of this is seen in the southward vorticity and PV flux by the stationary and transient eddies in the NH tropics that was seen to be crucial in the upper branch of the HC (Fig. 3), and its tropical origins are clear. The homogenization of PV in the regions of the anticyclones is the main contributor to the weak gradients seen in the zonal average in Figs. 1b and 1c. Equally, the southeasterly flows across the equator, turning to southwesterlies near 12°N, are consistent with the momentum fluxes highlighted in the discussion of Fig. 2.

The direct interaction of tropical air flows induced by maxima in regional tropical convective activity with individual midlatitude weather systems seen in JJA (HC1) has not been seen in our analysis of DJF. However, the direct impact on the behavior of the NH STJ is clear, and this implies that there will be an impact on the NH extratropical weather systems.

Associated with each of the near-equatorial active convective events, the enhanced anticyclone in the NH tropics produced a ridge in the NH STJ, an enhancement of its strength and a downstream trough in it. These features are clear, for example, in the region of the Red Sea north of the African convection on 1 January (Fig. 12a). They are also seen in the South China region on that day. Three days earlier, on 29 December, the Pacific jet was very short and finished near 140°E. During the next 6 days, the jet exit on the eastern side of the anticyclone extended eastward as the center of gravity of the region of tropical convection shifted eastward until the jet exit reached 150°W on 4 January (not shown).

Perhaps the most spectacular extratropical interaction seen in 2007/08 was associated with the SPCZ and equatorial east Pacific wave event seen in the 350-K PV and flow for 16 January (Fig. 12b). This occurred during a 1–2-week period of minimum OLR in the SPCZ box. On 13 January (not shown) only the strong cross-equatorial flow near 170°W and the ridge to the east is present. By 16 January (Fig. 12b) the wave pattern has developed to the east. This is consistent with the eastward group velocity expected for a nearly stationary WMRG wave on a westerly equatorial flow. According to Fig. 4, the time mean flow suggests propagation upward as well as eastward, and such vertical propagation is also expected on theoretical grounds. To investigate this possibility, the PV and winds on the 370-K isentropic surface (near 100 hPa) have been looked at during this period, and the fields for 20 January are given in Fig. 13a. By 15 January wind field anomalies in the east Pacific have started to produce southward and northward perturbations of the near-equatorial PV contours. By 18 January these features are developing significantly and by 20 January (Fig. 13a) filaments of opposite hemisphere air are found deep in each hemisphere. The strong southwesterly flow over Florida and the associated anticyclone over the Caribbean are particularly interesting as they are suggestive of interaction with the middle latitudes. On maps of potential temperature on the PV2 surface (the dynamical tropopause; see, e.g., Hoskins 2015) it is evident that from 20 to 23 January a sharp tropopause gradient progresses from the Florida region to the eastern North Atlantic. These are not shown here, but the resultant change in the North Atlantic regime from a jet only near North America to one across the whole North Atlantic is illustrated by the 250-hPa winds for the two periods 18–20 and 21–23 January (Figs. 13b,c).

(a) PV (color) and vector winds on the 370-K isentropic surface on 20 Jan 2008; the color bar gives the scale for PV (unit: PVU), and the scale for the winds is shown at the top right. (b),(c) North Atlantic 250-hPa winds for the periods 18–20 and 21–23 Jan 2008; color shading indicates the magnitude (m s⁻¹) of the wind, and the vectors its direction.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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(a) PV (color) and vector winds on the 370-K isentropic surface on 20 Jan 2008; the color bar gives the scale for PV (unit: PVU), and the scale for the winds is shown at the top right. (b),(c) North Atlantic 250-hPa winds for the periods 18–20 and 21–23 Jan 2008; color shading indicates the magnitude (m s⁻¹) of the wind, and the vectors its direction.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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(a) PV (color) and vector winds on the 370-K isentropic surface on 20 Jan 2008; the color bar gives the scale for PV (unit: PVU), and the scale for the winds is shown at the top right. (b),(c) North Atlantic 250-hPa winds for the periods 18–20 and 21–23 Jan 2008; color shading indicates the magnitude (m s⁻¹) of the wind, and the vectors its direction.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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As a final comment in this section, we note that in this season, daily OLR minima in the east Pacific and Atlantic regions are, as expected, found to be associated with the southwesterly motion ahead of the tips of midlatitude troughs as evidenced by the winds and PV. Examples of this for the Pacific are near 15°N, 155°W on 1 January and 135°W on 15 February and for the Atlantic near 5°N, 30°W on the latter day (Figs. 11 and 12).

7. Discussion

Many aspects of the Hadley cell in DJF have been seen to be the mirror image of those for JJA previously presented in HC1. However, the Pacific and Atlantic ITCZs stay north of the equator in DJF and the vertical circulations associated with them are somewhat shallower in DJF. These ITCZs act to distort the simple zonally averaged HC reversal picture in the lower troposphere. The upper-tropospheric branches of the HC in DJF and JJA are very similar. Angular momentum decreases more slowly toward the winter pole than implied by Earth’s rotation but is closer to this than it is to a uniform value. Related to this, the magnitude of the absolute vorticity is below that of f, but closer to this than to zero.

In both DJF and JJA, centered close to the equator in the winter hemisphere there is a maximum in the steady and transient fluxes of momentum out of the winter hemisphere, with the steady fluxes being stronger by a factor close to 2. In the two solsticial seasons, the steady and transient fluxes both change sign near 10°–12° in the winter hemisphere. As expected, there are differences at higher latitudes. In DJF the steady poleward fluxes become dominant and have a maximum near 22°N while the transient fluxes becoming larger near 30°N, whereas in the SH winter subtropics and extratropics the transient fluxes are completely dominant. The constraint that in the upper branch of the HC the poleward flux of absolute vorticity must be small compared with its component terms is achieved in both seasons by the flux of f being largely balanced by the steady and transient fluxes of relative vorticity. Again, both fluxes have a similar structure moving vorticity from the winter tropics to the subtropics, with the steady flux being the larger.

In JJA the longitudinal structure of the motions that average to give the HC was quite simple, with a dominance in the Indian Ocean to west Pacific region in both the lower and upper branches. This region is again important in DJF, but the African and American signatures are clearer. In the upper troposphere in both the east Pacific and Atlantic regions there is clear evidence of a steady near-equatorial wave. The evidence given in this paper suggests that these are WMRG waves, as will be discussed further below. In contrast, in the JJA season, with no such equatorial westerlies, mobile WMRG waves were seen to be important in the triggering of tropical convection (HC1).

As in JJA, the most coherent contribution to the zonally averaged momentum flux were from the Eastern Hemisphere, and again the two fluxes have a similar spatial pattern in this region.

The mean OLR generally emphasizes regions closer to the equator than in JJA when the convective maxima are over southern Asia and the west Pacific near the Philippines. However, the northern Australian and SPCZ regions have large temporal variability as well as a significant signature in the mean. This is the case, though to a lesser extent, for southern Africa, and South America. The temporal variability in the sector from Africa to the Maritime Continent is more dominated by the intraseasonal signature of the MJO than in JJA. Periods of 1–2-weeks dominate in southern Africa and northern Australia, and 2–3 weeks dominate in the SPCZ and are important in the MC.

Regressions and composites using 30-yr climate data and examples from one season have shown that, associated with active near-equatorial convection from Africa to the west Pacific and also South America, the upper-tropospheric winds that emanate from the convective regions are southeasterlies in the belt from 0°–10°N and turn southwesterly north of this. This is consistent with the equatorward momentum flux south of 10°N and poleward flux north of this. It is also consistent with these signatures being seen in both the steady and transient fluxes. The southerly winds form the western flanks of anticyclones, particularly in the African, East Asian, and South American regions. The anticyclonic motions bring higher-latitude air equatorward on their eastern flanks leading to equatorward vorticity fluxes. After active convection, the anticyclones will mix air from different latitudes, and therefore act in the sense of local homogenization of PV and absolute vorticity.

Active off-equatorial convection in the NH in JJA led to filaments of air from the convective regions deep in the summer hemisphere moving across the equator toward the subtropics of the winter hemisphere. This occurs to a lesser extent also in DJF from southern Africa, northern Australia, the SPCZ, and South America. A big difference in DJF is that in this season the latter two are to the west of equatorial westerlies. The flaring of convection in these regions is found to have an associated wave pattern in the equatorial regions of the east Pacific and Atlantic, respectively. It is proposed that these large-amplitude waves can be associated with WMRG waves that in a westerly mean flow can be nearly stationary, as well as having large eastward group velocity. The vertical propagation and smaller wavelength in the Atlantic with its weaker westerlies are consistent with the theory of WMRG waves.

The constraint on the dynamics that the time and zonal mean meridional vorticity flux, $\left[\overline{V\zeta }\right]$, is small is trivially satisfied in the upper branch of a simple angular momentum–conserving HC as ζ is identically zero there. The picture seen here for DJF and in HC1 for JJA is that where and when there is active convection, the strong, confined outflow of air into the winter hemisphere tends to have absolute vorticity more characteristic of equatorial values than the local value of the Coriolis parameter. An assumption of a zero absolute vorticity limit at the tropopause in convective regions in the tropics was used by Emanuel (1995) to derive thermodynamic constraints in the tropics. At other places and times, the contribution to the upper branch of the HC and to $\left[\overline{V\zeta }\right]$ is likely to be small. The extreme version of this is the idealized conceptual model that was given in HC1: convection typically occurs on a proportion α_λ of the longitudes and a proportion α_t of the time; when and where there is active convection the meridional flow and the absolute vorticity are, respectively, V and 0, and they are, respectively, 0 and f otherwise. Then $\left[\overline{V\zeta }\right]=0$ so that the dynamical constraint is satisfied. The meridional wind and absolute vorticity in the zonally averaged HC would be αV and f(1 − α), where α = α_λα_t is the frequency of occurrence of active convection in space and time. The magnitude of the STJ would be αu_AM, where u_AM is the angular momentum–conserving speed. So, for a Hadley cell extending to 30° the actual STJ speed would be reduced from 132 m s⁻¹ to the observed value of about 40 m s⁻¹ if the value of α is about 0.3.

This conceptual model for Hadley cells is certainly very idealized. However, it is proposed here that, with α in the lower part of the interval 0 to 1, it has advantages as a conceptual model for the HC compared with that based on zonally and temporally uniform overturning with angular momentum conservation (i.e., α = 1). An axisymmetric perspective is retained as useful for analysis, but it is considered that a conceptual model with active convection that is sporadic in space and time may prove to be more useful than one with axisymmetric motion and angular momentum conservation.

As an indication of the relevance of the conceptual model, for one season, DJF 2007/08, Fig. 14 shows the joint pdf at 150 hPa of meridional wind and absolute vorticity in a 10° × 4° box centered on 10°N, 125°E in the outflow region north of the MC. There are indeed signs of a bimodal distribution, with strong meridional wind (5–11 m s⁻¹) tending to be associated with weak absolute vorticity (0–1 × 10⁻⁵ s⁻¹), and of weak meridional wind (0–2 m s⁻¹) associated with larger absolute vorticity (1–2 × 10⁻⁵ s⁻¹). For comparison, in the box f is in the range 2–3 × 10⁻⁵ s⁻¹. In future work it is intended to further explore the relevance and usefulness of the conceptual model.

Joint pdf of meridional wind υ (abscissa) and absolute vorticity ζ (ordinate) for DJF 2007/08 at 150 hPa in a box covering 8°–12°N, 120°–130°E. The eight contours are at equal intervals.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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Joint pdf of meridional wind υ (abscissa) and absolute vorticity ζ (ordinate) for DJF 2007/08 at 150 hPa in a box covering 8°–12°N, 120°–130°E. The eight contours are at equal intervals.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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Joint pdf of meridional wind υ (abscissa) and absolute vorticity ζ (ordinate) for DJF 2007/08 at 150 hPa in a box covering 8°–12°N, 120°–130°E. The eight contours are at equal intervals.

Citation: Journal of Climate 34, 2; 10.1175/JCLI-D-20-0504.1

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• Download figure as PowerPoint slide

One aspect discussed in HC1, with possibly far-reaching implications, was the evidence for a direct interaction between some filaments of near-equatorial air triggered by events with active convection in the Indian Ocean and west Pacific sectors and mobile waves on the southern winter STJ. The filaments moved in ahead of a trough in the STJ and appeared to amplify the downstream ridge and the local strength of the STJ. There was also a suggestion that the contribution to the poleward transient eddy momentum flux by these extratropical weather systems was enhanced. In DJF the two NH oceanic storm tracks develop on the STJs that are enhanced by the major upstream convection in the Maritime Continent and South American regions, so that direct interaction of filaments of air from convective outflow with individual weather systems is not likely. However, there is strong evidence for direct effects of motions triggered by tropical convection on the NH STJ and, therefore, an expected indirect effect on NH weather systems. Many examples have been given that show that the strong anticyclones north of active convection in the African, East Indian Ocean/west Pacific, or South American regions lead to a buckling of the STJ and a local strengthening of it. For 2007/08, an example is also discussed in which the North Pacific STJ lengthened by 70° as the tropical convection moved eastward as part of an MJO event. Also in this year, an SPCZ triggered equatorial wave broke near the end of the westerlies in the east Pacific and there was a suggestion that a filament of SH or near-equatorial air moved into the North Atlantic and triggered a change of regime from a short to a long jet.

If the conceptual model of the Hadley cell is adopted, a major question is what determines that α, the frequency in space and time of active convection, is about 0.3 for Earth’s atmosphere. This is the case for both observed solsticial HCs and also for aquaplanet models. Energetic constraints in the tropics, the dynamics and physics of the extratropics, in particular the poleward momentum transports, and tropical–extratropical interaction like that discussed above are all likely to be important in determining the most realistic value of α.

As in HC1, it is important to question to what extent the ECMWF reanalysis system is able to correctly represent the details in the upper-tropospheric response to the flaring of tropical convection, and the shallow filaments of air moving from the tropics of the summer hemisphere to the tropics and subtropics of the winter hemisphere. However, it seems unlikely that the data will overemphasize such behavior.

From the analysis here and in HC1, it is clear that, for a good representation of the tropics in weather and climate models, the systems leading to regional flaring of convection, the level of their outflow, and the representation of shallow filaments of air moving into higher latitudes and interacting with STJ and waves on it would all need to be well represented—a challenge to any weather or climate model. Also, it is likely that any complete theory of the width of the HC and the strength of the STJs and the regional realization of these will have to take account of the nature of the tropical systems that average to give the HC, and of their rich interactions with the STJ and the extratropics.