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The Detailed Dynamics of the Hadley Cell. Part II: December–February

a,b a,c B. J. HOSKINS AND G.-Y. YANG a Department of Meteorology, University of Reading, Reading, United Kingdom b Grantham Institute for Climate Change, Imperial College, London, United Kingdom c Climate Directorate, National Centre for Atmospheric Science, University of Reading, Reading, United Kingdom

(Manuscript received 7 July 2020, in final form 15 October 2020)

ABSTRACT: This paper complements an earlier paper on the June–August Hadley cell by giving a detailed analysis of the December–February Hadley cell as seen in a 30-yr climatology of ERA-Interim data. The focus is on the dynamics of the upper branch of the Hadley cell. There are significant differences between the Hadley cells in the two solsticial seasons. These are particularly associated with the ITCZs staying north of the equator and with mean westerlies in the equatorial regions of the east Pacific and Atlantic in December–February. The latter enables westward-moving mixed Rossby–gravity waves to be slow moving in those regions and therefore respond strongly to upstream off-equatorial active convection. However, the main result is that in both seasons it is the regions and times of active convection that predominantly lead to upper-tropospheric outflows and structures that average to give the mean flow toward the winter pole, and the steady and transient fluxes of momentum and vorticity that balance the Coriolis terms. The response to active convection in preferred regions is shown by means of regressions on the data from the climatology and by synoptic examples from one season. Eddies with tropical origin are seen to be important in their own right and also in their interaction with higher-latitude systems. There is support for the relevance of a new conceptual model of the Hadley cell based on the sporadic nature of active tropical convection in time and space. KEYWORDS: Convection; Hadley circulation; Potential vorticity; Waves, atmospheric; Vortices

1. Introduction decades been seen as a limiter on the latitudinal extent of the Hadley cell. In their axisymmetric simulations using a dy- The concept of the Hadley cell (HC) in the zonally averaged namical core, Davis and Birner (2019) found that the Hadley view of the atmosphere is at the core of the traditional view of cell only extended through the depth of the atmosphere to the the general circulation of the atmosphere as discussed, for lower boundary if they included significant viscosity or pre- example, in Lorenz (1967). As reviewed by Held (2018), there scribed eddy driving. Schneider (2006), stressed the impor- have been contrasting views about the relative importance of tance for the Hadley cells of the extratropical eddies, and in tropical and midlatitude phenomena and processes for the subsequent years the emphasis has often been on their strong, existence, strength, and extent of Earth’s Hadley cells and the and even controlling, influence on the HC. strength of the upper-tropospheric subtropical jets on their However, from the tropical perspective, the improvement of poleward flank. From the midlatitude perspective, Jeffreys data availability permitted Starr et al. (1970) to calculate mo- (1926) raised the importance for the maintenance of the sur- mentum transport for the whole Northern Hemisphere and for face westerlies in midlatitudes of angular momentum transfers the four seasons. In winter the upper-tropospheric poleward from the subtropics by midlatitude eddies. The early datasets momentum flux by transient eddies occurred started from the for computation of momentum fluxes (e.g., Starr 1948) were deep tropics, but there were indications of a reversal of the only for the extratropical region. Eady (1950) saw that main- direction of transport by both standing and transient eddies in tenance of thermal wind balance would require that the mid- the lowest latitudes. Rosen and Salstein (1980) also saw these latitude eddy-induced poleward momentum transfer in the features in their improved datasets, and they were discussed by upper troposphere must be accompanied by a Hadley cell, Dima and Wallace (2003). Dima et al. (2005) associated the though this cell is weak, as was shown for the life cycle of a reversed tropical momentum transports with Rossby waves baroclinic wave by Simmons and Hoskins (1978). As was forced in the tropics, and in particular the horizontal tilts of quoted by Held (2018), baroclinic instability has also for many waves generated as a response to the regions of tropical heat- ing. However, Hartley and Black (1995) found that in their Denotes content that is immediately available upon publica- climate model the momentum fluxes on the equator that are tion as open access. equatorward in the Northern Hemisphere winter were asso- ciated with convective outflow rather than Rossby wave propagation and tilted troughs. Also, Zurita-Gotor (2019) Supplemental information related to this paper is available at found that the near equatorial momentum transfers were the Journals Online website: https://doi.org/10.1175/JCLI-D-20- dominated by the correlation of the divergent meridional wind 0504.s1. and the rotational zonal wind. A zonally symmetric and temporally uniform atmosphere Corresponding author: Gui-Ying Yang, [email protected] and angular momentum conservation in the tropical upper

DOI: 10.1175/JCLI-D-20-0504.1 Ó 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 10/04/21 03:27 AM UTC 806 JOURNAL OF CLIMATE VOLUME 34 troposphere formed the basis of the simple model of the longitudinal variation of the convection and meridional motion equinoctial HC given by Held and Hou (1980) in their seminal was seen to be fundamental in the dynamics of the HC. paper, which followed the study of Schneider (1977). In this In this paper the dynamics of the December–February model the HCs exist to reduce the midtropospheric tempera- (DJF) HC are analyzed in a manner similar to that used in ture gradient, and therefore to reduce the upper-tropospheric HC1 for the other solsticial season. The aims of the study are winds implied by thermal wind balance to those which are at- the following: tainable by angular momentum (AM) conservation from zero d to investigate the similarities and differences between the zonal wind at the equator. The latitudinal extent of the HC is two seasons, determined by the latitudinal range over which the reduction d to determine to what extent this further study reinforces the of the latitudinal temperature gradient is needed, along with picture given in HC1 that longitudinal and temporal varia- energy conservation. In this model, the subtropical jet (STJ) is tions are of order one importance for the HC, and at the latitude of the edge of the HC and its magnitude is that d to explore the interaction of the tropics with higher latitudes given by angular momentum conservation. The role of eddies is that is initiated by flaring in regional tropical convection. restricted to removing the discontinuity between this STJ wind and the zero wind in latitudes outside the HC and to reducing Section 2 gives a summary of the equations on which the the speed of the STJ. A factor of about 3 would be required to analysis is based and of the reanalysis dataset that is employed. give the observed values. The Held and Hou model for an Further details of both are given in HC1. An analysis from a equinoctial HC was extended to include the solsticial seasons conventional time and zonally averaged perspective is pre- by Lindzen and Hou (1988). sented in section 3.Theninsection 4 the time-mean 3D A fundamental issue associated with the dynamics of the behavior is analyzed. Section 5 produces a view of the upper branch of the HC was raised with one of us by John temporal behavior in terms of spectra and of regressions on Sawyer in the 1970s (J. Sawyer, personal communication). In a OLR in a number of tropical regions. In section 6 the be- solsticial season, as the air in the upper branch of the HC moves havior through one season is looked at in detail in order to from the tropics of the summer hemisphere to near 308 in the illustrate the synoptic behavior and to investigate the rele- winter hemisphere the change in its potential vorticity (PV) vance for it of the regressions in the previous section. A can be expected to be small. Therefore, this air will carry PV of discussion of the results for the HC in DJF is given in the opposite sign to that of the air in the rest of this winter section 7 and conclusions from this study and that in HC1 for hemisphere. There is then the possibility of instabilities or a JJA are drawn. 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 2. Data and diagnostics study of the low-level inflow to the Indian summer monsoon. The basis for the analysis is ECMWF interim reanalysis However, in this contribution to the lower branch of the HC, (ERA-Interim) horizontal winds (u, y), and vorticity fields for surface processes were usually found to be able to produce the the 30-yr period from 1981 to 2010. The fields are available 6- PV modification that enabled a steady monsoon inflow from hourly with horizontal resolution of about 0.78 and at 37 the southern Indian Ocean. pressure levels from 1000 to 1 hPa. When fields for a day are In the first part of this study (Hoskins et al. 2020, hereafter shown, the data are averaged over the four periods in the day. HC1) the dynamics of the HC in June–August (JJA), partic- In addition, potential vorticity is available on a limited number ularly its upper-tropospheric branch, were studied in detail. of isentropic levels, including 350 and 370 K. Detailed infor- Zonally averaged momentum and vorticity budgets showed the mation on the data can be found in Dee et al. (2011). As a proxy importance of both steady and transient eddy fluxes. These for convection, use is made of NOAA interpolated daily out- fluxes had a similar structure to each other in the HC latitudes, going longwave radiation (OLR) on a 2.5832.58 grid with an equatorial maximum and reversal in sign near 128 in the (Liebmann and Smith 1996). For part of the analysis and for winter (southern) hemisphere. The longitudinal behavior of case studies the single season DJF 2007/08 is used. This season the steady and transient fluxes was also found to be similar, and was chosen at random to be the first one to analyze. It is a La further analysis suggested that they were both associated with Niña year, which will influence the distribution and magnitude motion at the outflow level from a flaring of tropical convec- of tropical convection, and other years can be expected to show tion, particularly in the Indian Ocean and west Pacific sectors somewhat different detailed behavior. of the Northern Hemisphere (NH). From the top of these It is convenient to use m 5 sinf as latitudinal coordinate, convective regions, filaments of tropical air from the NH where f is the latitude, and also U 5 ucosf and V 5 ycosf as moved southwestward in the upper troposphere across the velocity variables. The axial component of the specific absolute equator. Some of these filaments returned to the NH and some angular momentum is were mixed in with the ambient air in the southern tropics. 8 However, in strong convective events near 12 S the filaments A 5 a2V(1 2 m2) 1 aU , (1) turned to move southeastward and phase in ahead of a trough in the Southern Hemisphere (SH) subtropical jet. The air with where a is the radius of Earth, and V its rotation rate. its tropical PV values caused a strengthening of the down- Denoting a zonal average by [ ], the zonally averaged equations stream ridge and the local STJ. In HC1, the temporal and for A and U may be written in flux form:

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›[A] ›[U] › › Use will also be made of the potential vorticity (PV or P): 5 a 52 [UV] 2 a [vU] 1 af [V] 1 [F], (2) ›t ›t ›m ›p 1 P 5 z =u, (10) where F is the frictional force in the longitudinal direction. The r derivation of this equation and all the others in this section are discussed in HC1 (section 2 and the appendix). As the pressure where z is the 3D absolute vorticity. On large length scales, the r z ›u › gradient force impacts on the local rate of change of angular term (1/ ) ( / z), involving the vertical component of abso- momentum, it is generally more convenient to consider vorticity lute vorticity, dominates. In the large-scale tropics, variation in than angular momentum for analysis of the dynamics in other the absolute vorticity dominates this term so that PV behavior than a zonally averaged domain. The vertical components of is mimicked by that of the vertical component of absolute absolute vorticity z and relative vorticity j are defined by vorticity. Since PV is conserved moving with the atmosphere in the absence of frictional and diabatic processes, away from con- 1 ›V 1 ›U vective regions it can generally act as a tracer over time scales of a z 5 2Vm 1 j and j 5 2 : (3) a(1 2 m2) ›l a ›m few days. The inversion properties of PV also mean that impli- cations can be drawn from its distribution for the dynamic and z In the zonal average, A and are simply related: thermodynamic state of the atmosphere (Hoskins et al. 1985). In section 5, power spectra of OLR are shown. These are 1 ›[A] 52a[z]: (4) computed over a 120-day time window for each DJF (centered a ›m on DJF). A 120-day window is used because a 10% taper In particular, if [A] is uniform with latitude, then [z] is identi- (12 days) is applied at the two ends of the data record and to cally zero, a result used by Plumb and Hou (1992) in their include the intraseasonal (30–60 days) signal. Also in section 5, discussion of the zonally averaged HC. regressions are performed on DJF seasonal data. The seasonal The poleward flux of absolute vorticity is trend was not removed as its impact was considered to be negligible for the fields shown. [Vz] 5 f[V] 1 [Vj], (5) and the poleward flux of relative vorticity is related to the 3. Zonal average perspective momentum flux: The zonally averaged, time-mean DJF Hadley cell is shown   in Fig. 1, with m 5 sinf as the abscissa. In each panel, the 1 › ›v [Vj] 52 [UV] 2 U . (6) meridional circulation is indicated by arrows, representing (V, a ›m ›p v), and the dark blue contours are for the zonal flow U. The Therefore, the angular momentum equation, Eq. (2), can be field shown with block color contours is angular momentum rewritten using the absolute vorticity flux: (Fig.1a), absolute vorticity (Fig.1b), and potential vorticity   (Fig.1c). This figure can be compared with the equivalent for ›[A] ›[U] ›U JJA, shown as Fig. 1 in HC1. The overturning circulation is to a 5 a 5 a[Vz] 2 a v 1 [F]. (7) ›t ›t ›p first approximation the mirror image of that in JJA, with the winter STJ near latitude 308 at the extratropical edge of the In a long-term average the tendency (local time rate of change) HC. However, there are significant departures from this mirror terms in Eqs. (2) and (7) will be very small. The terms involving image picture. Whereas the midtropospheric ascent region in v are also likely to be small. Away from the boundary layer, the JJA is concentrated in a peak in the 108 band from 58 to 158N, frictional term may be significant in regions of convection, due that in DJF is more evenly distributed in a band 208 wide in the to convective momentum flux convergence, but is likely to be summer hemisphere from 58Nto158S. However, the descent small elsewhere. Equation (2) emphasizes that there must be occupies a similar range of latitudes in the two winter hemi- near balance between the meridional momentum flux conver- spheres. The Hadley cell in DJF is distorted in the lower tro- gence and the Coriolis force (terms 1 and 3 in the right-hand posphere with the ascent remaining in the NH. As might be expression), and Eq. (7) shows that the poleward absolute vor- expected, this is mainly due to the ITCZs remaining north of ticity flux must be small compared with its constituent terms. the equator in the NH winter. It will prove useful to make a decomposition of the meridi- Zhang et al. (2004), in their discussion of shallow meridional j onal flux of both U and based on a time average (below this circulations in the tropical atmosphere, showed that both will be for the DJF 30-yr period), denoted by an overbar, and 0 shallow and deep Hadley cell modes exist in the two ITCZ deviations from it by () . Then regions. In DJF, the low-level flow into the NH, ascent there and the return flow from 800 hPa upward in the ITCZ regions [UV] 5 [U V] 1 [U0V0], (8) leave their imprint on the zonal average. If the average me- [Vz] 5 f [V] 1 [V j] 1 [V0j0]. (9) ridional circulation is calculated for the longitudes other than those of the ITCZs, the picture (not shown) is closer to the In each case, the term involving only products of time averages mirror image of the zonal mean in JJA, with low-level flow into will be referred to as the steady flux, and the final term will be the summer hemisphere (here, the Southern Hemisphere) and referred to as the transient flux. more concentrated midtropospheric ascent.

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FIG. 1. The 30-yr mean DJF Hadley cell. In each panel the meridional circulation (V, v) is shown by vectors, with 2 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: a2V), (b) the vertical component of absolute vorticity (unit: V), and (c) potential vorticity (PV) (unit: PVU).

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0 0 FIG. 2. Northward fluxes of angular momentum in 30-yr DJF by (a) the steady [U V] and (b) the transient [U V ] motions, as defined in Eq. (8). The contour interval is shown on the color bar and is not uniform, and contours at 2 negative values are dotted. The unit is m2 s 2.

Specific absolute angular momentum A, as defined in Eq. (1) are some contours of potential temperature. The 350-K isen- and shown in Fig. 1a by block contours, has values near the tropic surface, near 175 hPa, is seen to be close to the maximum surface close to that given by Earth’s rotation alone, given the flow in the upper branch of the HC, and the 370-K surface, near small values of U. There the meridional circulation crosses 100 hPa, toward the upper side of it. The winds and PV on these the contours of A and the frictional term is important in the surfaces will be used for diagnosis in case studies in section 6. balance in the momentum/A equation, Eq. (2). In the upper The steady and transient momentum fluxes for DJF are troposphere there is a maximum in A, just north of the equator. shown in Fig. 2, which can be compared with the JJA versions There is a sense that the northward motion in the upper branch (HC1, Fig. 2).The steady flux in the NH is the largest. All these of the Hadley cell appears to carry its value of A with it, but there near-surface fluxes are associated with the trade winds blowing is motion across the contours both in the band from 88Stothe into the ITCZs, in the east Pacific, Atlantic, and east Indian equator and from 58 to 258N. Here friction is in general not Oceans. In JJA, the general picture of these near-surface fluxes important and the balance in the momentum equation will be was similar, but the steady flux in the SH was slightly larger discussed below. than that in the NH and the zero-flux line was at about 38N. The From Eq. (4), the zero absolute vorticity (z) contour in DJF fluxes are consistent with the ITCZs staying near and Fig. 1b marks the maximum in A. In Fig. 1a it is seen that it north of the equator in that season. In the band 08–108N, the remains close to the equator, being slightly north of it in the flux convergence is comparable with the Coriolis term in upper troposphere. The region of small positive z extends Eq. (2), and their sum is balanced by friction. northward from the equator toward 108N, consistent with the In the upper troposphere, the near-equatorial maxima in weak gradient in A there. Potential vorticity (Fig. 1c) shows southward momentum fluxes are the equivalent of the rather similar features but also emphasizes the high-amplitude PV in stronger northward (toward the winter pole) momentum the stratosphere acting as a lid on the HC. Also shown in Fig. 1c fluxes in JJA (Fig. 2 in HC1). In both seasons, in the tropics the

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FIG. 3. The northward flux of absolute vorticity at 200 hPa for DJF 2007/08, and its com- ponent 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, 2 2 and trans, respectively. The unit is 1 3 10 4 ms 2. The ordinate is linear in latitude.

upper-tropospheric transient fluxes have a very similar struc- times larger than the transient flux, and the latter is some 50% ture in the latitudes of the winter Hadley cell, although their larger than the residual. In JJA, the cancellation in the region magnitudes are smaller by a factor of about 2. The steady fluxes was even greater and the transient flux was slightly more im- were highlighted by Dima and Wallace (2003) and associated portant in the balance. Calculations suggest that the small re- by Dima et al. (2005) with the tilted troughs of the steady re- sidual flux is not cancelled by the vertical advection of sponse to tropical heating. However, Zurita-Gotor (2019) momentum and a small frictional term would be required for stressed the importance of the divergent meridional wind. balance even in this region. Alternatively, data assimilation The smaller transient fluxes appear to have not been discussed might lead to such a slight imbalance. In passing, we also note explicitly though they were in the figures given by Starr et al. the expected higher latitude balance of the Coriolis term, as- (1970), Rosen and Salstein (1980), and Dima et al. (2005). sociated with the Ferrel cell, with the transient flux conver- As expected, there is a large difference in the winter hemi- gence in the 308–508S band, and with the steady and transient sphere fluxes between the two solsticial seasons in the region fluxes in the 308–508N band. poleward of the equatorial extremum. In DJF there is a pole- In the transient fluxes in the tropics, the contribution from 2 ward (northward) steady flux maximum of more than 50 m2 s 2 the transient zonal mean terms (i.e., fluctuations in the zonal centered at 228N and a transient maximum of more than Hadley cell) are negligible, so that the fluxes are associated 2 30 m2 s 2 centered at 308N. However, in JJA the poleward almost entirely with the zonally asymmetric, transient eddies. (southward) fluxes in the equivalent region were all associated As was the case in JJA (HC1), in both the momentum and 2 with the transients, with a maximum of more than 50 m2 s 2. vorticity flux views the tropical steady and transient fluxes Referring to the momentum/A equation, Eq. (2), the flux have a structure that is similar to each other, with the transient divergence from 108S to the equator balances the Coriolis term flux being a factor of 2–3 smaller. The similarity of their associated with the SH portion of the upper branch of the HC, structures raises the question whether there is a common and the convergence from about 38 to 238N performs the bal- mechanism underlying the steady and transient fluxes. The ance for the NH (winter) portion. It is evident that the near- importance of the tropical fluxes in the momentum balance in equatorial flux extrema, highlighted previously by Dima and the upper branch of the winter Hadley cell contrasts with the Wallace (2003), play an important role in the momentum view of the complete dominance in it of poleward momentum budget of the upper branch of the HC in both solsticial seasons. fluxes associated with the equatorward extension of eddies on As discussed above, the form of the U/A equation in Eq. (7) and poleward of the winter STJ. requires that, in regions of small friction in the upper tropo- sphere, the time-averaged poleward flux of absolute vorticity, 4. 3D structure [Vz], must be small compared with its constituent terms. A similar conclusion would be reached by consideration of the A picture of the longitudinal structure of the time-mean vorticity equation at these levels. For DJF 2007/08 and at meridional flow that averages to give the Hadley cell is pro- 200 hPa, the flux and its component terms as in Eq. (9) are vided in Fig. 4. This presents in a longitude–pressure plane the shown in Fig. 3. From 158Sto58N there is little evidence of meridional wind averaged over the 158 latitude band from 58S cancellation in this region of significant deep convection. This to 108N. The picture is robust to the choice of the latitude band, is consistent with this being a belt where significant deep con- either making it more restricted to the equator or more ex- vection occurs and the inclusion in the ECMWF system of tended in either hemisphere, apart from in the longitudes of cumulus momentum transport and the associated friction. the two ITCZs. The comparable figure for the 108S–58N band However, in the region of the upper branch of the HC north of in JJA was given in Fig. 5 of HC1. Zhang et al. (2004) showed this, from 58 to 258N, both steady and transient fluxes of relative similar cross sections of meridional wind on the equator for vorticity act to balance the Coriolis term. The steady flux is 3–4 January and July.

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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 21 FIG. 4. 30-yr DJF time-mean meridional wind (m s ) averaged and 950 hPa, and the mean OLR and its standard deviation between 58S and 108N. Also shown are the isentropic levels 330, (SD), are shown in Fig. 5.InFig. 5b, the dominant regions of 350, and 370 K. 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 The basic expectation for the DJF picture is that it is the these add up to give most of the low-level branch of the HC. reverse of that in JJA, with flow into the winter hemisphere Also apparent are the east Pacific and Atlantic ITCZs, north of (NH) in the upper troposphere and a return in the surface the equator with the trade winds blowing into them. In the upper boundary layer. This is the case in the Eastern Hemisphere troposphere (Fig. 5a), in the EH there is a pair of anticyclones (EH), over Africa and over the Indian Ocean to the west either side of the equator with the strong STJ in the NH and a Pacific, and also over South America, near 3008E (608W). northward component in the winds from 58Sto258Ngivingmuch However, the upper troposphere in the equatorial region of the of the upper branch of the HC. There are discrete SH anticylonic Western Hemisphere (WH) is dominated by two wave trains, circulations over Africa and South America. Equatorial westerlies one over the Pacific from the date line to 2808E and the other are present in the east Pacific and Atlantic. The waves on them eastward from South America over the Atlantic to the spread from the SH through the equator, with the shorter wave- Greenwich meridian. The wavetrains appear to propagate length on the weaker westerlies in the Atlantic. eastward and upward, and in the case of the Pacific also The standard deviation of the OLR is given in Fig. 5c. The downward. The wavelike meridional wind in the equatorial Indian Ocean to west Pacific region is implied to have high region is the signature of westward-moving mixed Rossby– variability in the region of strong convection. The low-latitude gravity (WMRG) waves. The two regions with the waves are portion of the convection in Africa and South America appears to those with westerly winds in the upper-tropospheric equatorial be relatively steady, whereas south and east of these regions there region. As shown by, for example, Yang et al. (2007, their is high variability with moderate intensity convection in the mean. Fig. 7b) and Yang and Hoskins (2016, their Fig. 3a), in a The same also applies in the northern Australian region. westerly basic flow WMRG waves can be Doppler shifted to Because of their possibly different characteristics, the 12 have a phase speed that is a reduced westerly or even, for very boxes indicated in Fig. 5c have been defined for detailed diag- strong westerlies, zero or eastward . The group velocity is nosis. The details of the 12 regions are indicated in Table 1.The 2 eastward and typically about 20 m s 1 so that a wave pattern results from most of these will be discussed in the next section. could develop from 1508 to 608W in about 4 days. As discussed The final figure of this section, Fig. 6, shows the 200-hPa by Dunkerton and Baldwin (1995), the crest and trough lines longitudinal structure of the momentum fluxes that average tilt in the vertical westward from the upper-tropospheric zonally to give the fluxes shown in Fig. 2. In HC1 it was found source level as the waves propagate vertically away from the that both the steady and transient fluxes near the equator to- source level as well as eastward. The temporal, longitudinal, ward the summer pole and the fluxes in the opposite direction and vertical structures of the waves were shown and discussed in the winter tropics had major contributions from the EH with in Yang et al. (2011, their Figs. 13c,d) and Yang et al. (2012, more minor ones from the east Pacific and Atlantic sectors. In their Figs. 11b,e). The latter showed the WMRG structures for DJF the major contribution to the tropical fluxes that are im- the opposite phases of the QBO, these differing significantly portant in the winter Hadley cell, southward near the equator only above 70 hPa. Yang and Hoskins (2016, their Fig. 6) and northward north of this again come from the EH. showed that WMRG activity was present in the east Pacific and Referring to Fig. 5a, the steady fluxes are associated with the Atlantic in both phases of ENSO, though it was stronger in the generally southeasterly winds near the equator, turning to east Pacific in La Niña and the Atlantic in El Niño, consistent southwesterly in 108–158N. The transient fluxes also have a with the differing strength of the westerlies. In Yang and contribution from the east Pacific and Atlantic sectors, but the Hoskins (2016, their Figs. 10c,d and 12c) it was shown that the waves in the mean wind field in the equatorial east Pacific, and westward moving WMRGs in these regions were typically as- to a lesser extent the Atlantic, gives a signature that makes the sociated with an arching pattern originating in the Southern picture of the steady fluxes more complex. However, as in JJA Hemisphere. the major input to the important tropical steady and transient It is proposed here that the waves seen in the upper tropo- zonally averaged momentum fluxes have a similar structure in sphere can be associated with WMRG waves forced in the east longitude as well as latitude, consistent with the possibility of Pacific by convective heating in the South Pacific convergence them having a common underlying origin.

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FIG. 5. 30-yr DJF time-mean horizontal winds and OLR statistics. (a) 200-hPa vector winds (scale arrow at top 2 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.

5. Temporal behavior in Table 1 and Fig. 7 is from Africa eastward to the Atlantic, The first view of the temporal behavior is provided by Fig. 7, with SH boxes directly after their near-equatorial counter- which gives the spectral information for OLR in the 12 boxes parts. The period is indicated on the ordinate. In Fig. 7a, the shown in Fig. 5c and defined in Table 1. The order of the boxes spectral power in each region is given. This highlights the

TABLE 1. Geographical regions analyzed.

Geographical region Name Longitude range Latitude range 1 Central Africa CAf 128–408E58N–158S 2 Southern Africa SAf 128–408E158–228S 3 Western Indian Ocean WIO 408–808E08–208S 4 Eastern Indian Ocean EIO 808–1008E108N–108S 5 Maritime Continent MC 1008–1508E108N–58S 6 Northern Australia and Java NAus 1008–1508E58–208S 7 Western Pacific WP 1508–1808E08–208S 8 South Pacific convergence zone SPCZ 1808–1308W58–258S 9 Eastern Pacific ITCZ EP-I 1458–1158W128–58N 10 Near-equatorial South America EqSAm 758–508W58N–158S 11 Subtropical South America SAm 658–308W158–308S 12 Atlantic ITCZ Atl-I 458–158W108N–08

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FIG. 6. 30-yr DJF time-mean northward flux of angular momentum at 200 hPa. (a) Steady (U V) and (b) transient 2 (U0V0). The unit is m2 s 2.

low-frequency power, particularly in the EH. To examine the associated with convection in a range of tropical regions, the important frequency peaks in each region, Fig. 7b presents the differences in OLR and 200-hPa wind between the 21.5 SD ratio of the spectral power to that associated with a red noise and 11.5 SD composites are presented for each of the 12 boxes spectrum, with 1 indicating significance at the 95% level. The defined in Table 1. The pictures for the regressions with OLR intraseasonal time scale dominates in the near-equatorial re- set to 11.5 SD and for the composites for this value of OLR gion from Africa to the Maritime Continent (MC; boxes 1 and have been used to check the motions when the implied con- 3–5), consistent with the importance there of the MJO. The 1– vection in a region is a minimum but will not be commented on 2-week period is prominent in SAf (box 2), and in the off- explicitly. equatorial boxes for NAus (box 6) and the 2–3-week period is The regressions for low OLR, indicating strong convection, prominent in the SPCZ (box 8), as it is also in the MC (box 7). in WIO (box 3) and MC (box 5) are summarized in Fig. 8.In There are peaks in the 4–7-day time scale in all regions ex- each panel the block contours show the OLR anomalies and cept the MC. the vectors indicate the full 200-hPa winds. This choice of fields To exhibit the fluctuations in the OLR and in the 200- and enables the regions of enhanced/reduced convection and the 950-hPa flow and their contribution to the Hadley cell that are full wind field that accompanies them to be seen. The two re- typically associated with variability in OLR in the boxes, two gions are chosen to illustrate the MJO behavior that dominates approaches have been taken. In the first, the winds and OLR in the equatorial EH. The OLR anomaly exhibits the antiphase have been regressed against OLR in each box and the anom- behavior between the two regions, with a further antiphase alies and full fields for OLR with 61.5 standard deviations slightly east of the date line. The winds in Fig. 8 can be com- (SD) have been considered. In the second approach, fields pared with each other and with the 30-yr climate in Fig. 5a, and have been composited for the days with the anomaly of OLR use can be made of the differences in composites shown in averaged over each box exceeding 61.5 SD. The results are Figs. S1c and S2a in the online supplemental material . From very similar and only some of the regression results with the region of enhanced convection there is a strong south- OLR set as 21.5 SD will be presented in this paper. In the easterly flow across the equator. The direction turns near 108N online supplemental material, as a good summary of anomalies to become a strong southwesterly at 208N and then into the

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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 128S and becoming northwesterly and then turning anti- cyclonically 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 con- vection 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 1508Wandthen northwesterlies near 1108W and weak southerlies near 858W. 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 1608W gives an almost iden- tical wave pattern to the east and an OLR anomaly in the FIG. 7. (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 SPCZ region. Figure 9d showsasimilarbehaviortothatofthe power specified with a significance level of 95%, so that values SPCZ for strong convection in the South American region. greater than 1 indicate the power exceeding the 95% significance The major difference, as noted before, is the shorter scale of 2 level. The power unit in (a) is W2 m 4. The regions are as defined in the wave pattern over the Atlantic in the 200-hPa flow. The Table 1. wave patterns in both regions are clearly seen in the com- posite differences given in Figs. S2d and S3c. The east Pacific and Atlantic ITCZ regions (EP-I and Atl-I, equatorial flank of an enhanced STJ. In the region of supressed boxes 9 and 12) both give evidence at 200 hPa (see Figs. S3a,d) convection this flow is much weaker. The tilts and strength of for the triggering of convection by southeastward Rossby wave the outflows are consistent with the momentum fluxes (Figs. 2 propagation from the extratropics. In both cases, the enhanced and 6), southward near the equator and northward near 208N, ITCZ convection is on the equatorial flank of a 200-hPa and are significant contributors to them. southwesterly flow anomaly, which is part of the wave train. Figure 9 give the corresponding results for low OLR (active This wave train is present through the troposphere (not shown) convection) in the off-equatorial regions of SAf (box 2) and but tilts slightly backward (northwestward) with height, sug- NAus (box 6), and for SPCZ (box 8) and SAm (box 11). gesting some baroclinic growth. Referring first to NAus (Fig. 9b), the anomalous active con- In HC1, some regressions were shown for 63-day lags with vection is centered there, but is present in a larger area, in- OLR. However, in DJF the general dominance of time scales cluding the MC. The 200-hPa flow is quite similar to that for the of 1–2 weeks or longer (except in the ITCZ regions) and, MC (Fig. 8b). However, the equatorward flow on the eastern consistent with this, little difference is found if the regressions side of the anticyclone over Australia that is associated with are lagged by a few days. the convection over NAus links with the southeasterly flow north of the MC to give the possibility of advection from deep 6. Examples from 2007/08 in the SH into the enhanced flow into the NH there. Summer seasons with enhanced convection in northern Australia have To answer the question to what extent the regressions for the recently been investigated by Sekizawa et al. (2018). They 30-yr climate are relevant for the fields seen in specific periods, noted a teleconnection from there to the region of Japan. the daily OLR and 350-K PV and winds have been looked at This teleconnection is particularly noticeable in Fig. S2b. for the 2007/08 DJF season. A Hovmöller plot for 200-hPa Anomalies in OLR and flow anomalies are weaker in SAf y averaged between 58S and 108N is given in Fig. 10 (colors). In (Fig. 9a). However, again a link is seen with the flow crossing the the EH slow eastward movement, likely related to the MJO, is equator, this flow being associated with the convection over CAf seen, together with fast westward-moving synoptic systems. In (box 1). Figures S1a and S1b also show these features. The 150-hPa the WH slow-moving large-scale waves are present much of the composite flow difference for CAf (not shown) gives a stronger time with varying amplitude. Further evidence that that these outflow and cross-equatorial flow near 308E than that at 200 hPa. are dominated by WMRG waves will be given below. The patterns of upper-tropospheric flow from the two re- For discussion here, four days have been selected to repre- gions of off-equatorial convection seen in Figs. 9a and 9b are sent the behavior seen in the whole season. All show inter- reminiscent of those found in HC1 for JJA, although not as esting features associated with enhanced tropical convective

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FIG. 8. 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 21.5 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. 2 The scale for the wind vectors is shown at the top right. The OLR unit is W m 2.

activity in one or more of the regions defined in Table 1, and On 1 January and 22 January, convective activity is en- diminished activity in others. The discussion will be organized hanced over western central Africa and southern Africa, with around these features, rather than on the time development this spreading into the west Indian Ocean on 22 January. On through the period. The days chosen are all from January 2008, both days there is flow from the south Indian Ocean around the apart from 15 February 2008. According to Sekizawa et al. anticyclone over southern Africa, with a southeasterly flow (2018, Fig. 2a), 2007/08 was a weak year for the northern across the equator and into a strong anticyclonic perturbation Australian summer monsoon, and consistent with this there of and strengthening of the NH STJ in the Middle Eastern were no good examples of strong OLR minima there. The region. On 22 January, consistent with the convective activity February date was added to give another example for active in the WIO, there is southeasterly flow across the equator from convection in the tropical Australian region. there. On 25 January (not shown) the active convection region For the 4 days, Fig. 11 gives the OLR averages for the has spread to 808E and the cross-equatorial southeasterlies are specified day and the previous 2 days. The 3-day average for found from Africa to there. On 16 January and 15 February, OLR is used to produce a slightly smoother OLR field and, as the convection is generally not enhanced over the CAf, SAf, seen in HC1, to take account of the fact that there may be a lag and WIO regions, and the flow features noted above are absent of a day or so before the wind field response away from the or much weaker. active convective region reaches its maximum. Figure 12 shows On 1 January there is enhanced convective activity in the the PV and winds on the 350-K isentropic surface (about MC region. Associated with this is a strong anticyclone north of 180 hPa). These will be used to indicate the upper-tropospheric it and again a local perturbation and strengthening of the motion associated with the variety of convective activity indi- STJ. On 15 February the active convection region extends 2 cated by the OLR. It is worth noting that a 10 m s 1 meridional farther into Australia and to the east of it. There is now more wind would enable an air parcel to move from near the equator indication of southeasterly flow from near 208S and across the to 258N in about 3 days. equator into the strong NH anticyclone. On 16 and 22 January,

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FIG. 9. 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 21.5 SD: (a) SAf, (b) NAus, (c) SPCZ, and (d) SAm. The conventions are as in Fig. 8.

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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 en- hanced convection and a pronounced anticyclone with north- erly 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 exam- ples are similar to those given in Figs. 9a and 9b, although as remarked above 2007/08 was a year of generally weak con- vection 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 anoma- lous flow seen on a daily basis being more localized and flexible FIG. 10. Hovmöller plots of 200-hPa y averaged from 58Sto108N in location than the large fixed boxes used in the regressions, it 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 is clear that the flavor of the regression figures is highly relevant and geopotential onto the horizontal structure of the WMRG wave to the large-scale behavior seen on a daily basis. as in Yang et al. (2003), but filtered to leave zonal wavenumbers 2– The strong anticyclones in the NH between the equator and 40 and with no time filter. The line contours are at the same values the subtropics are seen to be variable in space and time. In the as the change in colors and contours at negative values are dotted. 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. consistent with the eastward movement of the MJO, convec- 1 January gives good examples of the ones associated with tive activity is much weaker than normal, first in the EIO and African and MC convection. PV contours show the northward then in the MC. There is almost zero cross-equatorial flow in movement of near-equatorial or SH PV on its western flank the IO and MC regions and the NH anticyclone is weaker, and the southward movement of extratropical PV, and their particularly on 22 January. wrapping up, which will lead to irreversible mixing. The sig- On 16 and 22 January there is enhanced convective activity nature of this is seen in the southward vorticity and PV flux by in the SPCZ region, with an eastward shift between the two the stationary and transient eddies in the NH tropics that was days. On 16 January there is strong southerly flow across the seen to be crucial in the upper branch of the HC (Fig. 3), and its equator near 1708W. 1 January had a weaker but similar OLR tropical origins are clear. The homogenization of PV in the signature in the region and a similar but weaker flow associated regions of the anticyclones is the main contributor to the weak with it. On 22 January the cross-equatorial motion is shifted gradients seen in the zonal average in Figs. 1b and 1c. Equally, eastward to nearer 1508W and is southeasterly. In each case, the southeasterly flows across the equator, turning to south- there are northerlies to the east. The wave pattern moving westerlies near 128N, are consistent with the momentum fluxes eastward along the equator is particularly striking on highlighted in the discussion of Fig. 2. 16 January, with signs of a wave breaking near South The direct interaction of tropical air flows induced by max- America as the equatorial westerlies weaken. ima in regional tropical convective activity with individual The Hovmöller plot for 2007/08 of 200-hPa y averaged be- midlatitude weather systems seen in JJA (HC1) has not been tween 58S and 108N given in Fig. 10 also shows in black line seen in our analysis of DJF. However, the direct impact on the contours y obtained by projection of the horizontal structure behavior of the NH STJ is clear, and this implies that there will on to that of the MRG wave, following the methodology of be an impact on the NH extratropical weather systems. Yang et al. (2003). The similarity with the raw data (Fig. 10, Associated with each of the near-equatorial active convec- block colors) strongly supports the interpretation in terms of tive events, the enhanced anticyclone in the NH tropics WMRG waves. There are slow-moving waves in the east produced a ridge in the NH STJ, an enhancement of its Pacific through much of the season, with periods of westward, strength and a downstream trough in it. These features are stationary, and eastward phase speed. For much of the time clear, for example, in the region of the Red Sea north of the 2 there is evidence of an eastward group velocity of 20 m s 1 African convection on 1 January (Fig. 12a). They are also seen or more. in the South China region on that day. Three days earlier, on The NH anticyclone associated with South American con- 29 December, the Pacific jet was very short and finished near vection is apparent on all four days. The variable convection in 1408E. During the next 6 days, the jet exit on the eastern side of

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FIG. 11. OLR for 4 days in DJF 2007/08. The OLR is averaged over the specified day and the previous 2 days. The 2 unit for the 3-day OLR average is W m 2.

the anticyclone extended eastward as the center of gravity of group velocity expected for a nearly stationary WMRG wave the region of tropical convection shifted eastward until the jet on a westerly equatorial flow. According to Fig. 4, the time exit reached 1508W on 4 January (not shown). mean flow suggests propagation upward as well as eastward, Perhaps the most spectacular extratropical interaction seen and such vertical propagation is also expected on theoretical in 2007/08 was associated with the SPCZ and equatorial east grounds. To investigate this possibility, the PV and winds on Pacific wave event seen in the 350-K PV and flow for the 370-K isentropic surface (near 100 hPa) have been looked 16 January (Fig. 12b). This occurred during a 1–2-week period at during this period, and the fields for 20 January are given in of minimum OLR in the SPCZ box. On 13 January (not shown) Fig. 13a. By 15 January wind field anomalies in the east Pacific only the strong cross-equatorial flow near 1708W and the ridge have started to produce southward and northward pertur- to the east is present. By 16 January (Fig. 12b) the wave pattern bations of the near-equatorial PV contours. By 18 January has developed to the east. This is consistent with the eastward these features are developing significantly and by 20 January

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FIG. 12. 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.

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FIG. 13. (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 2 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.

(Fig. 13a) filaments of opposite hemisphere air are found deep However, the Pacific and Atlantic ITCZs stay north of the in each hemisphere. The strong southwesterly flow over equator in DJF and the vertical circulations associated with Florida and the associated anticyclone over the Caribbean are them are somewhat shallower in DJF. These ITCZs act to particularly interesting as they are suggestive of interaction with distort the simple zonally averaged HC reversal picture in the the middle latitudes. On maps of potential temperature on the lower troposphere. The upper-tropospheric branches of the PV2 surface (the dynamical tropopause; see, e.g., Hoskins 2015) HC in DJF and JJA are very similar. Angular momentum it is evident that from 20 to 23 January a sharp tropopause decreases more slowly toward the winter pole than implied by gradient progresses from the Florida region to the eastern North Earth’s rotation but is closer to this than it is to a uniform value. Atlantic. These are not shown here, but the resultant change in Related to this, the magnitude of the absolute vorticity is below the North Atlantic regime from a jet only near North America to that of f, but closer to this than to zero. one across the whole North Atlantic is illustrated by the 250-hPa In both DJF and JJA, centered close to the equator in the winds for the two periods 18–20 and 21–23 January (Figs. 13b,c). winter hemisphere there is a maximum in the steady and As a final comment in this section, we note that in this sea- transient fluxes of momentum out of the winter hemisphere, son, daily OLR minima in the east Pacific and Atlantic regions with the steady fluxes being stronger by a factor close to 2. In are, as expected, found to be associated with the southwesterly the two solsticial seasons, the steady and transient fluxes both motion ahead of the tips of midlatitude troughs as evidenced by change sign near 108–128 in the winter hemisphere. As ex- the winds and PV. Examples of this for the Pacific are near pected, there are differences at higher latitudes. In DJF the 158N, 1558W on 1 January and 1358W on 15 February and for steady poleward fluxes become dominant and have a maximum the Atlantic near 58N, 308W on the latter day (Figs. 11 and 12). near 228N while the transient fluxes becoming larger near 308N, whereas in the SH winter subtropics and extratropics the transient fluxes are completely dominant. The constraint that 7. Discussion in the upper branch of the HC the poleward flux of absolute Many aspects of the Hadley cell in DJF have been seen to be vorticity must be small compared with its component terms is the mirror image of those for JJA previously presented in HC1. achieved in both seasons by the flux of f being largely balanced

Unauthenticated | Downloaded 10/04/21 03:27 AM UTC 15 JANUARY 2021 H O S K I N S A N D Y A N G 821 by the steady and transient fluxes of relative vorticity. Again, east Pacific and Atlantic, respectively. It is proposed that these both fluxes have a similar structure moving vorticity from the large-amplitude waves can be associated with WMRG waves winter tropics to the subtropics, with the steady flux being that in a westerly mean flow can be nearly stationary, as well as the larger. having large eastward group velocity. The vertical propagation In JJA the longitudinal structure of the motions that average and smaller wavelength in the Atlantic with its weaker west- to give the HC was quite simple, with a dominance in the erlies are consistent with the theory of WMRG waves. Indian Ocean to west Pacific region in both the lower and The constraint on the dynamics that the time and zonal mean upper branches. This region is again important in DJF, but the meridional vorticity flux, [Vz], is small is trivially satisfied in African and American signatures are clearer. In the upper the upper branch of a simple angular momentum–conserving troposphere in both the east Pacific and Atlantic regions there HC as z is identically zero there. The picture seen here for DJF is clear evidence of a steady near-equatorial wave. The evi- and in HC1 for JJA is that where and when there is active dence given in this paper suggests that these are WMRG convection, the strong, confined outflow of air into the winter waves, as will be discussed further below. In contrast, in the hemisphere tends to have absolute vorticity more character- JJA season, with no such equatorial westerlies, mobile WMRG istic of equatorial values than the local value of the Coriolis waves were seen to be important in the triggering of tropical parameter. An assumption of a zero absolute vorticity limit at convection (HC1). the tropopause in convective regions in the tropics was used by As in JJA, the most coherent contribution to the zonally Emanuel (1995) to derive thermodynamic constraints in the averaged momentum flux were from the Eastern Hemisphere, tropics. At other places and times, the contribution to the up- and again the two fluxes have a similar spatial pattern in per branch of the HC and to [Vz] is likely to be small. The this region. extreme version of this is the idealized conceptual model that The mean OLR generally emphasizes regions closer to the was given in HC1: convection typically occurs on a proportion equator than in JJA when the convective maxima are over al of the longitudes and a proportion at of the time; when and southern Asia and the west Pacific near the Philippines. where there is active convection the meridional flow and the However, the northern Australian and SPCZ regions have absolute vorticity are, respectively, V and 0, and they are, re- large temporal variability as well as a significant signature in spectively, 0 and f otherwise. Then [Vz] 5 0 so that the dy- the mean. This is the case, though to a lesser extent, for namical constraint is satisfied. The meridional wind and southern Africa, and South America. The temporal variability absolute vorticity in the zonally averaged HC would be aV and in the sector from Africa to the Maritime Continent is more f(1 2 a), where a 5 alat is the frequency of occurrence of dominated by the intraseasonal signature of the MJO than in active convection in space and time. The magnitude of the STJ

JJA. Periods of 1–2-weeks dominate in southern Africa and would be auAM, where uAM is the angular momentum– northern Australia, and 2–3 weeks dominate in the SPCZ and conserving speed. So, for a Hadley cell extending to 308 the 2 are important in the MC. actual STJ speed would be reduced from 132 m s 1 to the ob- 2 Regressions and composites using 30-yr climate data and served value of about 40 m s 1 if the value of a is about 0.3. examples from one season have shown that, associated with This conceptual model for Hadley cells is certainly very active near-equatorial convection from Africa to the west idealized. However, it is proposed here that, with a in the lower Pacific and also South America, the upper-tropospheric winds part of the interval 0 to 1, it has advantages as a conceptual that emanate from the convective regions are southeasterlies in model for the HC compared with that based on zonally and the belt from 08–108N and turn southwesterly north of this. This temporally uniform overturning with angular momentum is consistent with the equatorward momentum flux south of conservation (i.e., a 5 1). An axisymmetric perspective is re- 108N and poleward flux north of this. It is also consistent with tained as useful for analysis, but it is considered that a con- these signatures being seen in both the steady and transient ceptual model with active convection that is sporadic in space fluxes. The southerly winds form the western flanks of anticy- and time may prove to be more useful than one with axisym- clones, particularly in the African, East Asian, and South metric motion and angular momentum conservation. American regions. The anticyclonic motions bring higher- As an indication of the relevance of the conceptual model, latitude air equatorward on their eastern flanks leading to for one season, DJF 2007/08, Fig. 14 shows the joint pdf at equatorward vorticity fluxes. After active convection, the an- 150 hPa of meridional wind and absolute vorticity in a 108348 ticyclones will mix air from different latitudes, and therefore box centered on 108N, 1258E in the outflow region north of the act in the sense of local homogenization of PV and absolute MC. There are indeed signs of a bimodal distribution, with 2 vorticity. strong meridional wind (5–11 m s 1) tending to be associated 2 2 Active off-equatorial convection in the NH in JJA led to with weak absolute vorticity (0–1 3 10 5 s 1), and of weak 2 filaments of air from the convective regions deep in the sum- meridional wind (0–2 m s 1) associated with larger absolute 2 2 mer hemisphere moving across the equator toward the sub- vorticity (1–2 3 10 5 s 1). For comparison, in the box f is in the 2 2 tropics of the winter hemisphere. This occurs to a lesser extent range 2–3 3 10 5 s 1. In future work it is intended to further also in DJF from southern Africa, northern Australia, the explore the relevance and usefulness of the conceptual model. SPCZ, and South America. A big difference in DJF is that in One aspect discussed in HC1, with possibly far-reaching this season the latter two are to the west of equatorial west- implications, was the evidence for a direct interaction between erlies. The flaring of convection in these regions is found to some filaments of near-equatorial air triggered by events with have an associated wave pattern in the equatorial regions of the active convection in the Indian Ocean and west Pacific sectors

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from the tropics of the summer hemisphere to the tropics and subtropics of the winter hemisphere. However, it seems un- likely 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. FIG. 14. Joint pdf of meridional wind y (abscissa) and absolute vorticity z (ordinate) for DJF 2007/08 at 150 hPa in a box covering 88–128N, 1208–1308E. The eight contours are at equal intervals. Acknowledgments. We would like to acknowledge the very helpful reviews we received, and in particular that by Thomas Birner. GYY acknowledges the long-term support of the and mobile waves on the southern winter STJ. The filaments National Centre for Atmospheric Science (NCAS). The re- moved in ahead of a trough in the STJ and appeared to amplify search was conducted as part of the NERC project (NE/ the downstream ridge and the local strength of the STJ. There I012419/1). was also a suggestion that the contribution to the poleward transient eddy momentum flux by these extratropical weather REFERENCES systems was enhanced. In DJF the two NH oceanic storm Davis, N. A., and T. Birner, 2019: Eddy influences on the Hadley tracks develop on the STJs that are enhanced by the major circulation. J. Adv. Model. 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