Downstream development during South African cut-off low pressure systems

. . Atmospheric Research 249 (2021) 105315. . Available online 17 October 2020 0169-8095/© 2020 Elsevier B.V. All rights reserved..

. . Atmospheric Research 249 (2021) 105315. 2. can be used to show how some COLs extend to the surface (Barnes, 2020). COLs in the South African domain have been extensively studied using reanalysis products (e.g. Singleton and Reason, 2007a; Favre et al., 2012, 2013) and using numerical models e.g. Singleton and Reason, 2006, 2007b; Omar and Abiodun, 2020; Muofhe et al., 2020), and have clearly been shown to bring rainfall to different parts of the country (Moelekwa et al., 2014; Engelbrecht et al., 2015; Omar and Abiodun, 2020a; Omar and Abiodun, 2020). The typically heavy rainfall associ- ated with COLs implies that east of the upper air trough axis substantial upward motion exists. This vertical uplift is a well known dynamical characteristic of a fully developed baroclinic weather system, with convergence at the surface and divergence aloft. Such a system dissi- pates when the upper level disturbance catches up with the one at the surface so that its vertical structure becomes equivalent barotropic. Therefore, when COLs reach South Africa as rainbearing systems; they are usually already matured synoptic weather systems, at least from a dynamic meteorology point of view. To support this notion, given the fact that the COLs are preceded by RWB (Ndarana and Waugh, 2010; Reyers and Shao, 2019), as already mentioned, Favre et al. (2013) and Omar and Abiodun (2020a) consistently note that they develop from unstable Rossby waves and, due to this instability, these waves even- tually evolve into non-linear regimes and break. This breaking is actu- ally a dissipative process (Methven et al., 2005) during baroclinic life cycles. When viewed in the context of an idealised experiments (e.g. Thorncroft et al., 1993; Kunz et al., 2009; Kunkel et al., 2016), irre- versible deformation of the PV contours that signals RWB occurs during the downturn of eddy kinetic energy (Ke), when the vertical propagation of wave activity has ceased and its meridional component dominates. This happens during the barotropic conversion stage and the Ke de- creases, as it is converted into mean kinetic energy. The connection between COL pressure systems and RWB then sug-.

. . Atmospheric Research 249 (2021) 105315. 3. 10s 10S (a) t = —36 hours relative mgitude (b) t = —24 hours (c) t = -12 hours (d) t O hours relabve (e) t hours relative longiWde ! los 10s (f) t = —36 hours relative (g) t z —24 hours itu& (h) t —12 hours itude O hours relative itude +12 hours relative longitude.

. . Atmospheric Research 249 (2021) 105315. 4. the subscript m represent the total and time mean variables, respec- tively. The lowercase symbols represent the perturbation fields and U = Ui + Vj + ωk is the three dimensional velocity flow and V = Ui + Vj is the horizontal flow on isobaric surfaces. The symbols Φ and Θ are the geopotential and potential temperature, respectively. The forms of available potential (Pe) and eddy kinetic energy (Ke) used in this study are.

. . Atmospheric Research 249 (2021) 105315. 5. e 10s 1 10S m2 day 500 x (a) t hours (b) t —24 hours (C) t z —12 hours (d) t O hours hours itu 10s los 10S (f) t hours relative Étude (g) t —24 hours relative itude (h) t z —12 hours relative itude (i) O hours relative itude (j) t +12 hours relative 10m itude.

. . Atmospheric Research 249 (2021) 105315. 6. (a) t = —36 hours relative (b) t = —24 (c) t = —12 hours relative W&itude (d) t = O hours 10s relative (e) t = +12 hours (f) t = -36 relative (g) t = -24 hours (h) t = —12 hours relative O hours re•Étjve (j) t = •12 hours.

. . Atmospheric Research 249 (2021) 105315. 7. e 10s ! los (a) t hours (b) t —24 hours (C) t z —12 hours (d) t = O hours reabve lomitude hours day 10s 10S (f) t hours relative Étude (g) t —24 hours relative itude (h) t z —12 hours relative itude (i) O hours relative 0m i tude (j) t +12 hours relative 10m itude.

. . Atmospheric Research 249 (2021) 105315. 8. produces composite patterns that are similar to those of − ∇ ⋅ (VPe), that are shown in Fig. 2(a) to (e). This means that the Pe flux divergence is the more dominant forcing between the two, and effects the eastward propagation of the energy centre in Fig. 1. The fluxes (represented by the arrows in the left panels of Fig. 2) show that the energy is transported from the rear end of the potential energy centre (where there is flux divergence) to the front end of the structure (where there is flux convergence). The strength and direction of the fluxes is influenced by two factors. The first is the magnitude of Pe in the jet streak, and the strength of zonal flow of the jet streak itself. The second factor is the direction of the meridional flow, which is poleward (equatorward) at the jet entrance (exit) region, but also weaker than the zonal jet streak flow (Ndarana et al., 2020). This causes the fluxes to be strong in the Pe and weaker everywhere else, and further highlights the reason why the Pe structure follows the jet streak. The process that links Pe to Ke is baroclinic conversion (Orlanski and Katzfey, 1991; Orlanski and Sheldon, 1993; McLay and Martin, 2002; Decker and Martin, 2005; Harr and Dea, 2009). In Eqs. (6) and (7), this process is represented by the term ωα. When ωα < 0, then a conversion from Pe to Ke takes place. Composites of ωα shown in Fig. 2(f) to (j) demonstrate that baroclinic conversion during the evolution of South African COLs dominates during the six hourly time steps leading up to the time step at which the systems form at t = 0 h. These composites also show that it occurs in the rear end of the Pe centre, represented in Fig. 2 by the thick solid contour and is associated with increasing midlatitude baroclinicity as demonstrated by the increasing strength of the jet streak (Ndarana et al., 2020). Note that the relative location of ωα < 0 and − ∇ ⋅ (VPe) < 0 means that ∂tPe < 0 found in the rear end of the Pe centre is caused by both baroclinic conversion and Pe flux divergence, with the former ceasing earlier and the latter continuing beyond the day of COL formation..

. . Atmospheric Research 249 (2021) 105315. 9. (a) t —36 hours —24 hours IOS 500 x 8-2 SOOX •.06 m' reabve (c) t • —12 hours los • reabve (d) t O hours reab-ve (e) t z +12 hours reab-ve (f) t —36 hours re•tjve Jon (g) t —24 hcNrs e Jon (h) t —12 hours retive Jon (i) t O hours e Jon (j) t = +12 hours r"tjve On *ude.

. . Atmospheric Research 249 (2021) 105315. 10. end of the subtropical energy centre (eastern energy centre). This phe- nomenon is most clearly seen from about t = −24 to 0 h in Fig. 4(g) to (i). The fact that the energy flux is stronger in the western half of this Ke centre explains why it is oriented as it is. Its rear (or upstream) end moves further northward as compared to the eastern part. The orien- tation of the fluxes in the PV overturning region is caused by the fact that the zonal flow is significantly decelerated there to values close to zero and is, in some cases, slightly negative (Ndarana et al., 2020). The di- rection of the fluxes is consistent with the flux divergence (convergence) that is found on the south (north) end of the subtropical Ke centre..

. . Atmospheric Research 249 (2021) 105315. 11. Region B and it is stronger. The energy transfer occurs as the midlatitude jet streak propagates eastward and increases in strength, thus bringing with it increasing anticyclonic barotropic shear, and increasing strain rate (Nakamura and Plumb, 1994) that leads to wave breaking on the 330 K dynamical tropopause in the case of Region A COLs. The wave breaking induces the ageostrophic geopotential fluxes, as shown in Subsection 3.4. Simple experimentation shows that for Region B COLs, the wave breaking that influences the fluxes is most clearly seen on the.

. . Atmospheric Research 249 (2021) 105315. 12. associated with them. As noted in the Introduction, Tennant and Reason (2005) found that wet South African seasons are associated with two branches of the baroclinic kinetic energy. Fig. 7 shows this split (thin black contours). This figure also shows that COLs that develop in the western half of South Africa are associated with a large scale baroclinic kinetic energy structure that is located over the subtropical South Atlantic, South Af- rican mainland and South West Indian Ocean, and oriented in a north- west/southeast slant. It is quasi-stationary relative to the one observed to appear to be moving with the midlatitude jet streak..

. . Atmospheric Research 249 (2021) 105315. 13. 0 discussed in Subsection 3.4) causes the fluxes to be orientated north- eastward, into the eastern half of the subtropical baroclinic kinetic en- ergy branch. In this study, we thus propose that the branches of baroclinic kinetic energy of Tennant and Reason (2005) are connected. The transfer of eddy kinetic energy from the midlatitudes into the eastern parts of the South African domain is facilitated by wave breaking on the 340 K and 330 K dynamical tropopause for Region C and D COLs, respectively. Note that the RWB processes associated with these COLs occur downstream from those shown in Fig. 8 and discussed above. The Ke density associated with Region C COLs is much weaker than its Re- gion D COL counterpart. This is caused by the much weaker ageo- strophic geopotential fluxes out of the midlatitudes, as informed by the depth of the tropopause fold associated with them. Observe the behav- iour of the PV = −1.5 PVU (thick red contour), which is much more deformed in the case of Region D COLs than in that of Region C COLs. When the deformation of this contour is compared across all categories of COLs (Figs. 7(d), (i), 8(d) and (i)), it becomes apparent that the depth of the PV anomaly might be playing a role in the strength of the Ke and might related to the extension of the COLs to the surface (see Barnes et al., 2020b). This will be a subject of further analysis because it is beyond the scope of the current study. The weak nature of the Region C COL Ke density and orientation of the associated fluxes means that the COLs that occur in this area have little connections to the midlatitudes, except the fact that the PV anomalies that induce them are a results of wave breaking that is caused by the midlatitude jet. In stark contrast to Fig. 7, inspection of Fig. 8 indicates that the subtropical baroclinic kinetic energy is located in the Indian Ocean for COLs that develop over the eastern half of the country. For Region D COLs it is more further east than for Region C COLs. Therefore, if there is any connection between the subtropical branch of baroclinic kinetic.

. . Atmospheric Research 249 (2021) 105315. 14. closed COL circulation forms and appears to cease thereafter as the jet streaks passes south of the COLs. The movement of the Ke is caused by energy fluxes by the total flow within the energy centre and they distribute the energy from the rear to front end of the centre (represented by the thick black arrows, at the minus and plus signs in Fig. 9). The strength and direction of the fluxes are influenced by the flow of the jet streak in the case of the midlatitude Ke centre. 3. The propagation of the jet streak and its increasing zonal flow, coupled with the smaller scale jet streak north of the COL region, constitute a split jet found in previous studies (Ndarana and Waugh, 2010; Reyers and Shao, 2019), which in turn, increases anticyclonic barotropic shear and shearing strain (Nakamura and Plumb, 1994) leading to anticyclonic RWB (Peters and Waugh, 2003), signalled by PV overturning. The wave breaking processes create a ridge south- west of the COL circulation but on the equatorward side the jet and this ridge deepens as wave breaking evolves. As a result, the flow becomes increasingly supergeostrophic and the positive geopotential anomalies deepen, thus inducing ageostrophic geopotential fluxes (blue curves arrows in Fig. 9), and with time, increasing their magnitude. The supergeostrophic flow that is associated with the wave breaking is directed anticyclonically, which in turn informs the direction of the fluxes towards the COL regions because the geo- potential perturbations are positive. 4. These ageostrophic geopotential fluxes are responsible for trans-.

. . Atmospheric Research 249 (2021) 105315. 15. Moelekwa, S., Engelbrecht, C.J., deW Rautenbach, C.J., 2014. Attributes of cut-off low induced rainfall over the Eastern Cape Province of South Africa. Theor. Appl. Climatol. 118 (1–2), 307–318..