4.1. COL– RWB relationship
As discussed in the Introduction, the major focus of this study is to establish whether COLs can be linked to RWB in the SH. Thus, we first determine what percentage of the COLs can be linked to a RWB event. To find the link we proceed as follows. For every COL, we search for a RWB event that occurs 60° longitude upstream and 10° downstream of the COL centre, and occurs between four days prior to and four days after the day of the COL formation. We further require that the RWB event be within 15° latitude from the centre of the low.
Figure 4 shows an example of a COL pressure system (thin solid contours) with the cold core represented by the closed thickness (dotted) contour. The system began developing in the South Atlantic on 15 April 1985 and the closed circulation formed on 17 April 1985 with its centre at 40°S, 5°E. The closest RWB event to this particular COL that the search method identified occurred on 16 April 1985. Its position is represented by the westernmost point such that ∂yPV < 0 (section 2.3) on PV = – 2 PVU (bold solid) contour on the 330 K surface at 50°S, 25°W. Note that in some cases a COL might have multiple RWB associations. In such situations the code chooses the RWB event closest to the COL in both space and time.
Figure 4. Evolution of 250 hPa geopotential height (thin solid contours with interval 200 gpm), 250– 500 hPa thickness (dashed contours with interval 50 gpm) and PV = – 2 PVU contour (bold solid) on the 330 K surface at 0000 UTC on (a) 15, (b) 16 and (c) 17 April 1985.
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When applied to the 250 hPa COLs, the above procedure linked 2162 of 2430 (around 89%) COLs to a RWB event. In other words, the majority of the COLs are associated with RWB. The remaining 11% not linked to RWB are examined in the next section, however we note here that these COLs are actually linked to the equatorward advection of high-PV air but this advection of high-PV air does not meet the criteria for RWB described in the previous section.
We focus in the remainder of this section on the 89% of COLs that can be linked to a RWB event. These COLs can be divided into three groups according to isentropic surfaces on which their associated RWB occur: 34%, 48% and 5% of the lows are associated with 350, 330 and 310 K RWB events, respectively. Hereafter, we will name the COLs according to their RWB associations; for example, COLs that are linked to RWB on the 350 K surface will be called ‘350 K COLs’.
The relative timing of COLs and RWB is shown in Figure 5(a), which shows the distribution of COLs as a function of time lag (τ = tCOL − tRWB, in days), with each group plotted separately. For nearly all of the COLs, the RWB events occur on or before the day the COLs form, with frequencies decreasing with increasing time lag (the vast majority of the lows form within two days of the breaking). Furthermore, almost all the RWB events occur upstream of the COLs with a large percentage of them occurring 0– 20° west of the COLs (Figure 5(b)). This time lag and the position of RWB events relative to the COLs is consistent with the expectation that COLs are induced by high-PV anomalies (Hoskins et al., 1985), and that the advection of high PV, and therefore RWB, precedes the formation of the COL.
Figure 5. The distribution of COLs as a function of (a) time lag (days) between the occurrence of RWB and COLs (τ = tCOL − tRWB), (b) the difference between the longitudes of the COLs and those of the associated RWB events (Δλ = λCOL − λRWB) and (c) latitude. The solid, dashed and dash-dotted curves represent frequency of occurrence of COL formation that are associated with RWB on the 350, 330 and 310 K isentropic surfaces, respectively.
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This grouping of COLs by isentrope of accompanying RWB also tends to organize them latitudinally, with the COLs with a higher isentrope generally further north (Figure 5(c)). About 88% (70%) of 350 K (330 K) COLs occur north (south) of 35°S and are subtropical (midlatitude) systems. Therefore, there is overlap in the distributions across the demarcation latitude and so the categorising of the COLs in terms of the isentropic surface on which the associated RWB events occur is not the same as the subtropical versus midlatudinal classification. The reason for the spread of latitudes of the 330 and 350 K COLs is that the position of the dynamical tropopause changes with season (Liniger and Davies, 2004). This northward migration of the tropopause is most pronounced in the Australian region where the majority of the COLs form (Figure 2), just north of the split jet flow (Bals-Elsholtz et al., 2001). Therefore some of the lows that are classified as subtropical in the usual sense are associated with RWB on the 330 K isentropic surface, when the dynamical tropopause has migrated north in winter. Similarly, some midlatitudinal systems are associated with 350 K RWB, particularly during the warmer months when the subtropical dynamical tropopause is at the southernmost position. Nonetheless this way of categorizing COLs is considered more reliable because the variability and other characteristics of these systems are better explained in its context.
4.2. Spatial structure
We now examine the spatial structure of different fields during the evolution of the linked COLs and RWB. To do this, composite mean fields of all relevant fields are formed in the manner described in section 2.4. We show primarily composites that correspond to 330 K RWB and COLs with lag – 1, but qualitatively similar results are found for all time lags and isentropic surfaces. The choice of presenting lag – 1 instead of lag 0 is motivated by the desire to illustrate how RWB precedes COL formation as suggested above.
Figure 6 shows the evolution of 330 K PV, 250 hPa geopotential heights, and ‘jet streaks’ from day – 3 (3 d before the formation of the COLs) to day + 2 (2 d after they have formed). On day – 3, the composites suggest that on average the Rossby waves propagate along the jet stream with a jet streak just southwest of where the PV contours appear to be undulating. The small amplitudes during the undulations suggest that nonlinear processes have not begun to take effect. As the jet streak moves eastward on day – 2, the amplitude of the waves grows substantially and the undulations appear to have ceased because of the extensive deformation of the material contours, suggesting that nonlinearity is setting in.
Figure 6. The evolution of composite mean fields from (a) three days before the formation of the COLs (day – 3) to (f) two days after (day + 2). The mean fields shown are geopotential heights at 250 hPa (thin contours with 100 gpm intervals), PV = – 1.5, – 2 and – 2.5 PVU (bold contours), and jet streaks with wind speeds greater than 25 m s−1 (shading). White contours are isotachs beginning at 30 m s−1. The composite mean fields were formed using COLs and RWB events that occur on the 330 K isentropic surface for τ = – 1 day. The x- and y-axes represent the longitude and latitude axes relative to the centre of the COL pressure system.
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By day – 2 another important development is observed – the formation of the split jet flow (Holland et al., 1987; Campetella and Possia, 2007). It appears that the formation of this flow regime is a result of the reduction in wind speeds where the PV contour deformation is most pronounced. The split flow structure consists of a larger, broader jet streak located southwest to southeast of the composite low and breaking event, and a smaller-scale jet streak north of the low pressure system. On day – 1, the split jet is fully developed, the deformation of the PV contours is much more pronounced and there is now a region of reversed meridional PV gradients. This is the day on which the RWB actually occurs according to the definition used in this paper. As the Rossby waves break, high-PV air is advected onto the region of weak winds exactly where the COLs are anticipated to form.
The COLs form, by definition, on day 0. The closed isohypse characteristic of COLs is evident. At this time, the high-PV air has pinched off forming a closed high-PV anomaly. The anomaly persists until the next day and on day + 2 it disappears. On day + 1 the large jet streak continues to move eastward, and beyond day + 2 (not shown) the split jet structure is destroyed. All the while, the northern component of the split jet has been somewhat stagnant and starts dissipating from day + 2.
This analysis involves all COLs and does not take their duration into consideration. For this reason, the COL signal disappears completely on day + 1 because most of the systems are short-lived (e.g. Fuenzalida et al., 2005; Nieto et al., 2005; Reboita et al., 2009) with 58%, 25% and 10% lasting 1, 2 and 3 d respectively. However, if the longevity of the systems is considered, then the signal becomes evident beyond day 0. For example, for COLs that persist for 3 and 5 d, it can be observed on day + 1 (Figure 7(c) and (d)) and day + 3 (Figure 7(e) and (f)), respectively. The longer-lived COLs are maintained by the persistent high-PV anomaly (Hoskins et al., 1985).
Figure 7. Composites of PV = – 1.5, – 2.0, – 2.5 PVU (bold) contours and 250 hPa geopotential heights (thin contours) for 330 K COLs with 1-day duration and τ = 0, showing the COL development (a) one day (day + 1) and (b) three days (day + 3) after their formation. (c, d) and (e, f) are as (a, b), but for COLs with 3- and 5-day durations, respectively.
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The evolution and structure of the PV and geopotential height fields is very similar for the composites of COLs with other time lags between RWB and the COL, and for RWB on the 350 K surface. This is illustrated in Figure 8 showing the composite fields at day 0 for different time lags and isentropic surfaces. The geopotential height fields show that the 330 K COLs are larger and deeper than their 350 K counterparts. A comparison of the evolution of the associated 350 K and 330 K PV suggests that the 330 K PV anomaly is more persistent and therefore 330 K COLs are longer-lived (Hoskins et al., 1985). This is consistent with the findings of Kentarchos and Davies (1998) in the NH.
Figure 8. Composites of PV = – 1.5, – 2.0, – 2.5 PVU (bold) contours and 250 hPa geopotential heights (thin contours with 100 gpm contour intervals) on day 0 on (a) 350 K and (b) 330 K COLs with τ = – 2 days. (c, d) and (e, f) are as (a, b), but for τ = – 1 day and τ = 0 days, respectively. The x- and y-axes represent the longitude and latitude axes relative to the centre of the COL pressure system.
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Note also that the distortion of the PV contours occurs on the equatorward side of the jet and is therefore influenced by anticyclonic shear. The waves consequently break in an anticyclonic fashion, as shown in Peters and Waugh (2003) using simple barotropic shear arguments. The deformed PV contours have a northwest– southeast tilt (Thorncroft et al., 1993; Lee and Feldstein, 1996), signalling this anticyclonic breaking which is confirmed by the equatorward direction of the meridional fluxes of wave activity that have been shown in previous studies to be associated with anticyclonic RWB, as shown in Figure 9(a) (e.g. Esler and Haynes, 1999; Gabriel and Peters, 2008).
Figure 9. Composites for 330 K COLs corresponding to τ = – 1 day on day 0: (a) meridional component of wave activity flux vector (thin solid and dashed contours with interval 15 m2s−1) with PV = – 2 PVU (bold) contour; (b) static stability, − ∂pθ (thin contours with interval 0.3 × 10−3K Pa−1); (c) absolute vorticity (thin contours with interval – 2 × 10−5s−1); (d) conversion from shear to curvature vorticity (contours with interval 0.5 × 10−4s−2, solid for positive and dashed for negative); (e) geopotential heights at 850 hPa (solid) and 250 hPa (dashed) with interval 20 gpm; (f) cold advection at 850 hPa (solid contours with interval – 6 × 10−6K m s−1), with geopotential heights at 250 hPa (dashed). In (c) and (d), wind speeds > 25 m s−1 are shaded with superimposed white isotachs at 5 m s−1 intervals.
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The above composite analysis confirms that COL formation in the SH is strongly associated with anticyclonic RWB and the equatorward advection of high PV occurring on the equatorward lobe of the RWB. It is also of interest to examine the evolution of other fields during the RWB and formation of COLs. As described in Hoskins et al. (1985), PV anomalies appear as a combination of anomalies of absolute vorticity and static stability. Next, we examine the composite fields of these two fields.
First consider the static stability (e.g. Trenberth, 1991) shown in Figure 9(b). The anomalies in this quantity are clearly caused by the advection of high static stability stratospheric air into the troposphere during the RWB process. Secondly, as the waves are breaking, absolute vorticity anomalies form on the area where the COLs form (Figure 9(c)). Absolute vorticity can be written in terms of curvature and shear vorticity (Holton, 2004). These two forms of vorticity play a crucial role in establishing absolute vorticity fields in COLs by converting from one form to the other (Bell and Keyser, 1993). In the NH, the conversions are facilitated by the presence of a jet streak that propagates along the periphery of the amplifying trough (Keyser and Shapiro, 1986; Bell and Keyser, 1993). However, the above composites seem to suggest that the evolution of wind fields differs from the NH. In the SH a split flow forms, and its quasi-stationary northern component appears to be the one that facilitates the conversions. This is confirmed by Figure 9(d), showing the conversion terms on day 0, calculated using the expressions in the appendix of Bell and Keyser (1993). Using the vorticity sign convention of the SH, positive values (solid) mean conversions from shear vorticity to curvature vorticity and the negative (dashed) ones mean the reverse conversion. Shear vorticity is converted to curvature vorticity at the right exit of the northern component of the split jet and curvature vorticity is converted to its shear counterpart at the jet streak right entrance. The static stability anomalies, the split jet, and hence the absolute vorticity anomalies, all form as the waves are breaking and not before, which suggests that the RWB plays a role in establishing conditions conducive for COL formation aloft. These arguments apply at the 350 K surface as confirmed by Figures 10(a) to (d).
Upper-level PV processes also affect surface development (Hoskins et al., 1985). We therefore investigate the surface conditions of COLs linked to RWB occurring on different surfaces. Figures 9(e) and 10(e) show 850 hPa (solid) and 250 hPa (dashed) geopotential heights, for composites for 330 K and 350 K COLs, respectively. Although the upper-level evolution is similar, the evolution of the 850 hPa geopotential heights differs between the 350 K and 330 K composites. 350 K COLs are associated with a north– south trough– ridge system, whereas the surface low for 330 K COLs develops between two high pressure systems located east and west of it. The different development patterns are similar with differences in case-studies for COLs over the land and ocean. Synoptic structures similar to the 350 K composites have been observed over South Africa (Taljaard, 1985) and were presented schematically by Holland et al. (1987) and Katzfey and McInnes (1996), whereas development similar to the 330 K composites have been observed for case-studies of ocean COLs (e.g. Taljaard, 1985; Figure 3 of Katzfey and McInnes, 1996).
It is expected that there will be cold advection associated with COL formation. The composite surface temperature advection , where v and T are horizontal velocity and temperature respectively, for the 330 K and 350 K COLs are shown in Figures 9(f) and 10(f), respectively. In the case of 350 K COLs, cold fronts usually precede the eastward ridging high pressure systems (Figure 10(e) solid contours), as seen for example south of South Africa (Taljaard, 1985). The cold advection caused by the cold fronts deepens the upper-level developing troughs and COLs form eventually. In both these scenarios, the cold advection is concentrated over the northwestern portion of the deepening upper-level trough. However, cold advection associated with 350 K COLs is weaker than that associated with 330 K systems, which is consistent with deeper 330 K COLs than their 350 K counterparts (Figure 8). This occurs because cold fronts associated with Figure 10(e) make their passage much earlier prior to the ridging of the high.
In summary, the evolution of the PV, geopotential height, static stability, vorticity and temperature advection fields for COL-based composites are consistent with theoretical expectations (e.g. Hoskins et al., 1985). The high-PV anomalies are established before the formation of COLs by RWB processes that precede them. The anomalies then induce the closed circulations. By the hypsometric relation, temperature advection at the surface reduces temperature in the column of air immediately above it, thereby creating the cold core.
4.3. Influence of RWB on COL variability
The above link between RWB and COLs provides a possible way of connecting the variability of COLs to that of jet streams in the SH. Several previous studies have linked RWB and jet variability in the SH (e.g. Postel and Hitchman, 1999; Berrisford et al., 2007), and can be used to understand variability in COLs which will be explained using Figure 11.
Figure 11. Frequency of RWB (dashed) and COLs (solid) as a function of month. The left and right y-axes represent the number of COLs and RWB events, respectively. (a) is for RWB on the 350 K isentropic surface and the COLs that are associated with them. (b) is as (a) but for RWB on the 330 K surface. (c) is the distribution of COLs associated with RWB on the 350 K isentropic surface as a function of longitude for DJF and MAM. (d) is as (c) but for COLs that are associated with RWB on the 330 K isentropic surface. (e, f) are as (c, d) but for JJA and SON.
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Figures 11(a) and (b), for the 350 and 330 K isentropic surfaces respectively, show the variation of RWB events (dashed) on the right y-axis. The left y-axis shows the variability of COLs (solid) that are associated with RWB events on the respective isentropic surfaces. Figures 11(c) and (e) show the longitudinal variation of 350 K COLs; Figures 11(d) and (f) are similar but for 330 K COLs.
The subtropical and polar front jets (STJ and PFJ), as waveguides (e.g. Hoskins and Ambrizzi, 1993; Ambrizzi et al., 1995), restrict the meridional growth of wave amplitude and therefore inhibit the RWB process. The waves break more often when they propagate in reduced zonal wind speeds (Peters and Waugh, 1996; Swanson et al., 1997). Because COLs are linked to RWB, it is then plausible that the seasonal march of the jets will influence the interseasonal variability of COLs on both isobaric surfaces, by first influencing that of RWB. Indeed, the similarities between seasonal profiles (Figures 11(a) and (b)) of these processes support this notion.
To understand this further, the COLs are broken down into seasonal longitudinal variations according to their RWB links on various surfaces. As was the case with subtropical lows (Figure 3(c)), the Australian/New Zealand sector plays the most significant role in influencing 350 K COL occurrence around 30°S or so (Figures 11(c) and (e)), as the reduction of these COLs from DJF to JJA is clear. The reason for this is that 350 K RWB is inhibited by the STJ during JJA because this jet is a waveguide for these waves during this season and so RWB events induce fewer COLs. There are changes in other subtropical regions but they are not as significant because the STJ is not strong there (Hurrell et al., 1998).
The hemispheric-wide increases in 330 K COLs from DJF to MAM (Figure 11(d)) are caused by the fact that the PFJ ceases being a waveguide as RWB activity and the dynamic tropopause migrates equatorward (Figures 2(a) and (b)). These increases are also evident in Figure 11. Moreover, 330 K COLs break in the reduced zonal flow of the split jet structure (Bals-Eslholz et al., 2001). Figures 11(d) and (f) show that away from the STJ region there are increases in COL counts from MAM to JJA, however modest, whilst there are reductions in the Australian sector. The latter is caused by the fact that the 330 K dynamical tropopause has migrated into the STJ (Figure 2), north of the weak flow of the split jet, which tends to reduce 330 K RWB events and hence 330 K COLs there. Increases in COL occurrence from JJA to SON is associated with the southward migration of the dynamical tropopause and the dissipation of the STJ. Therefore the variability of the jet streams in the SH regulates the seasonal occurrence of COLs at 250 hPa, by first influencing the interseasonal variations in RWB occurrence. Note that the STJ reduces COLs more significantly than the PFJ at this level.
The variability of the jet streams and of RWB can be used to understand the differences in the interseasonal variability of COLs at 250 hPa and 500 hPa. 81% of the 500 hPa COLs are linked to RWB. Therefore arguments similar to those above apply, but note that Figure 12(a) shows that RWB at 310 and 330 K make a larger contribution to COLs at 500 hPa. Consequently these RWB events will play a more significant role in inducing COLs at 500 hPa than 350 K RWB events. This is particularly true in JJA as shown in Figure 12(b). On this basis, the PFJ reduces 500 hPa COLs more effectively during DJF than those at 250 hPa and the STJ does not affect the COLs at 500 hPa as much as at the higher level, as discussed above.
Figure 12. (a) The relative frequency of 500 hPa (black) and 250 hPa (grey) COLs as a function of isentropic surface on which the RWB occurs with which they are associated. (b) Frequency of COLs at 500 hPa that are associated with RWB on the 350 K (solid), 330 K (dashed) and 310 K (dash-dotted) isentropic surfaces, as a function of month.
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