Downstream development associated with two types of ridging South Atlantic Ocean anticyclones over South Africa

There are at least two types of ridging South Atlantic Ocean high pressure systems in the South African domain. Type-N events occur north of 40°S and Type-S occur south of this latitude line. This study shows that there is no evidence of surface downstream development in terms of the evolution of eddy kinetic energy and associated ageostrophic geopotential fluxes for both types of ridging high events. Rather, for these systems downstream development is an upper level process. The baroclinic waves associated with the ridging develop from baroclinic instability, by converting eddy available potential energy 15 to eddy kinetic energy. The bulk of the conversion is located at the upstream end of the waves. The downstream trough, which is the part of the wave that influences upward motion over South Africa, develops from the transport of eddy kinetic energy across the trough axis by means of ageostrophic geopotential fluxes. These fluxes are stronger for Type-S events. The absence of downstream development at the surface and the presence of it aloft demonstrates that there are differences in the underlying dynamics in the evolutions of these systems in the vertical. The evolution of eddy kinetic energy associated with baroclinic 20 waves that occur during the ridging events is different from what has been observed for cut-off low pressure systems in the South African domain.


Introduction
The subtropical South Atlantic Ocean is characterised by a quasi-stationary anticyclonic circulation that exhibits pronounced variability in intensity and position at intra-annual and inter-annual (Sun et al., 2017) and multi-decadal (Reason, 2000) time 25 scales. It has also been shown that it might be impacted by future climate change (Engelbrecht et al., 2009;Reboita et al., induces the closed cyclonic circulation of the COL, together with the effect of the high potential vorticity anomaly that does the same (Hoskins et al., 1985). It is well known from forecasting experience in southern Africa that COLs are often accompanied by ridging highs at the surface, and that not all ridging highs have a COL aloft associated with them (Engelbrecht et al., 2015). There are many instances when a ridging high occurs with an ordinary trough aloft. Whilst these complex relations still need to be quantified; the fact that COLs exhibit particular downstream development characteristics (Ndarana et al. 2021b;70 Pinheiro et al. 2021) means that the ridging highs associated with them may be characterised by the same type or structure of the evolution of the eddy kinetic energy. However, it is still an open question whether for the general case, that is, the case when a general trough is associated with the ridging high would behave as the COL or not. Moreover, the differences in the behaviour of the baroclinic waves that were identified in Ndarana et al. (2022) have not been extended to the associated dynamical processes as yet. Using the local energetics framework (Orlanski and Katzfey 1991), this study aims to 75 perturbation velocity field. The fourth term is the Reynold's stress term, which is the conversion of to mean kinetic energy and the "Residual" is obtained by subtracting the terms just described from . The advection term, ⋅ ∇ , plays a dominant role in this eddy kinetic energy budget equation and various processes are embedded in it (Orlanski and Katzfey 100 1991). These processes are most clearly seen when it is decomposed in the following manner, Here = − and the rest of the symbols have already been defined. Once decomposed, it becomes clear that − ⋅ ∇ 105 is a dominant term in Eq. (1) because it embodies all the generation processes. The first term on the right-hand side − is the baroclinic conversion from eddy available potential to eddy kinetic energy. There clearly needs to be vertical motion and it is essentially a vertical heat flux (Li., 2021). The second term is the convergence of ageostrophic geopotential flux of , which is a horizontal process and the fluxes themselves, ( ) , as represented by the red curved arrows in Fig. 1, serve to radiate energy in the direction of the ageostrophic flow, across a ridge axis, so that a downstream may then develop at the 110 inflection point immediately east of the ridge axis. Across a trough axis, the downstream directed ageostrophic flux is caused by the fact that the flow is subgeostrophic (with a ageostrophic flow directed upstream) and < 0. The term ( ) is the vertical geopotential flux convergence.
Based on Orlanski and Sheldon (1995) for baroclinic waves in general and for the COL case in the South Atlantic Ocean/southern African sector (Ndarana et al., 2021b) and Southern Hemisphere in general (Pinheiro et al., 2021), downstream 115 development is a three stage process. During the first stage a centre I is generated by means of baroclinic conversion (− > 0), as represented by the red hatched oval shape. At the bottom of the wave, across the ridge axis, the supergeostrophic flow, as represented by the downstream directed ageostrophic flow, combined with > 0 , combine to produce the ageostrophic geopotential fluxes that begin to transport downstream. As I decreases in strength from state 1 to stage 2, II increases in strength to reach a maximum during the latter. This is largely informed by the increase in positive perturbation 120 geopotential in the ridge and the ageostrophic flow; thus increasing transport of energy downstream via the ageostrophic geopotential fluxes, which are particularly strong in COLs. This strength is caused by anticyclonically breaking waves which induce deep geopotential anomalies and a strong supergeostrophic flow ahead of the closed circulation (Ndarana and Waugh, 2021;Reyers and Shao, 2019;Ndarana et al. 2021b). The negative perturbation field across the trough axis (downstream of energy centre II) begins to appear and the upstream ageostrophic flow lead to energy transfer toward the inflection point 125 beyond the trough axis to cause III to develop. As was the case with the strengthening ridge, as the trough deepens, the flux increases; thus increasing centre III.

Data 130
We use the ridging high cases that were identified objectively in Ndarana et al. (2022). As in that study, to identify ridging South Atlantic Ocean high pressure systems, we use the Fifth Generation European Centre for Medium-Range Weather Forecasts Reanalysis (ERA5, Hersbach et al., 2020) products from 1979 to 2020. The horizontal grid spacing of each dataset is 2.5° at 6-hourly time intervals. Even though these products are available at finer mesh grids than this, we deem the chosen grid spacing sufficient because ridging high pressure systems are synoptic scale processes, the horizontal scale of which is 135 ~10 6 m (Holton and Hakim, 2014). The variables used are mean sea level pressure (MSLP), the zonal and meridional wind components and geopotential heights to calculate the geostrophic( + ) and ageostrophic ( + ) wind fields. In this study we assumed a variable geostrophic flow (Blackburn 1985) so that it is not non-divergent (Cook 1999).

Methods
Ridging highs are identified using a simple algorithm consisting of three steps. Its details are provided in Ndarana et al. (2018) 140 and only a brief description is provided here. In the first step, closed contours in the 6-hourly MSLP fields are identified within a domain bounded by 40°W and 60°E. We then group these closed contours so that concentric contours in the South Atlantic Ocean represent the South Atlantic Ocean High ( SAOH). This is the second step. In the third and final step, if the outermost contour extends east of the 25°E longitude line, we record such instances as the ridging process having occurred. If this condition is met on consecutive time steps, without any breaks in between, then this constitutes a single ridging event and is 145 the basis on which the duration of the events is determined.
To establish the climatological behaviour of the ridging events and associated fields, composite calculations are used. Only the duration and location of events, relative to the 40°S latitude line are taken into consideration and assumed. That is, we composite together events of durations 24 hours or longer, that occur north or south of this latitude line. No other assumption is made about the fields. This means that their average structures appear in a natural fashion, signalling their climatological 150 presence during the evolution of ridging events. The basic state (all the variables with subscript m) is calculated by the taking a 31-day mean centred on time step at which the South Atlantic Ocean high pressure system begins to extend east, to ridge across South Africa. What this implies is that the basic state variables are constant right through evolution of the ridging high.
The perturbation variables are then obtained by subtracting the basic state variables from the total variables.
We also use composite means to analyse the synoptic climatological behaviour of these systems and the associated 155 variables. Unlike in the case of COLs where the systems and associated fields are brought together so that the centres of the closed circulation coincide, we composite the fields on the basis of duration only and do not make any attempt to shifte the events so that they coincide in space. This, of course, is influenced by the fact that the ridging of the SAOH is a quasi-stationary process that varies in position, mostly latitudinally (Ndarana et al. 2022). In this case the ridging highs that last longer than 24 hours are brought together such that the time of their inception coincide and then averaged. Details of the compositing procedure are provided in Ndarana et al. (2022). All the variables that have been calculated according to the diagnostics reviewed in Section 2 are then averaged 4. Results

Vertical profiles of the energetics diagnostics 165
Unlike previous studies on energetics of baroclinic waves (e.g. Orlanski and Katzfey, 1991;Orlanski and Sheldon, 1995;Lackmann et al., 1999;McLay and Martin, 2002;Decker and Martin, 2005;Danielson et al., 2006;Harr and Dea, 2009;Piva et al., 2010;Gan and Piva, 2013;2016;Ndarana et al., 2021b;Pinheiro et al., 2021) who integrated the diagnostics vertically, we consider vertical variations of the processes associated with ridging high eddy energy exchange. The reason for this is that 170 not only does the flow at the surface differ during the evolution of a ridge, there are also variations between types of ridges as shown in Ndarana et al. (2022). Moreover, there are substantial differences in flow between the surface and the middle to the upper troposphere. To address the differences between the characteristics of downstream development that is associated with the two types of ridging events, we make use of the eddy kinetic energy framework (see Eqs. (1) and (2)) and the perturbation fields as described in Section 2. 175 Fig. 2 shows all the diagnostics under consideration averaged for the composite mean fields from t = 0 to +48 hours in the domain bounded by 30°S, 60°S, 30°W and 60°E to the north, south, west and east, respectively. The red and black (green and blue) curves represent positive (negative) values for Type-N and Type-S ridging events, respectively. The vertical profiles of ( Fig. 2a) show that it increases as a function of pressure level until it attains a maximum at about 250 hPa. This vertical increase in is caused by the fact that | |; the magnitude of the perturbation flow, also increases in the vertical to become 180 strongest at that level as well (Figs 2b and c). The latter, of course, is caused by the thermal wind relation, which is valid for the perturbations fields. Furthermore, the associated with Type-S ridging events is stronger than that associated with Type-N events. Figs 2b and c show that the source of this difference is the zonal component of the perturbation flow being stronger for the former.
The tendency of is also a maximum aloft at levels slightly lower than 250 hPa (Fig. 2d). This may be influenced by 185 many factors, two of which are baroclinic conversion from eddy available potential energy and the convergence/divergence of the ageostrophic geopotential fluxes. The former is informed by the vertical circulation, which attains maximum values at about 600 hPa, as shown in Fig. 2e. Note that the upward vertical motion (i.e. < 0) that is associated with Type-S events is stronger. Fig. 2f shows that the vertical circulation maximises where ∇ ⋅ is a minimum. This is a well-known phenomenon.
Combined with specific volume profiles shown in Fig. 2g, this leads to baroclinic conversion from eddy available potential 190 energy to eddy kinetic energy that is a maximum at about 400 hPa ( Fig. 2 (h)). The ageostrophic geopotential flux has been shown in previous studies to transport energy downstream in a baroclinic wave so that downstream development occurs (Orlanski and Katzfey, 1991;Orlanski and Sheldon, 1995;Lackmann et al., 1999;McLay and Martin, 2002;Decker and Martin, 2005;Danielson et al., 2006;Harr and Dea, 2009;Piva et al., 2010;Gan and Piva, 2013;2016;Ndarana et al., 2021b; https://doi.org/10.5194/wcd-2022-2 Preprint. Discussion started: 19 January 2022 c Author(s) 2022. CC BY 4.0 License. Pinheiro et al. 2021). Fig. 2i clearly shows that downstream development that is associated with ridging highs in the South 195 Atlantic Ocean/South African sector is largely an upper level process, as the field |∇ ⋅ ( )| is a maximum at 250 hPa, where flow divergence is a maximum. In general, the vertical profiles of ∇ ⋅ ( ) are informed by those of flow convergence in suggests that there might be need to consider the energetics for the upper and lower levels, separately, as will be done in the 200 following sections.

The characteristics of lower level energy during ridging highs
We now consider the horizontal evolution of , first at the surface in this section and subsequently for the upper troposphere, 205 in order to characterise the downstream development associated with Type-N and Type-S events at these levels. To link the structure of the MSLP to the behaviour of and the differences in that behaviour between the two types of ridging events at the surface, we use the connection between the perturbation geopotential field, which is clearly induced by the ridging process (Ndarana et al., 2022), and the associated horizontal perturbation flow, in terms of which the is defined. Scaling arguments from standard texts on dynamic meteorology (e.g. Holton and Hakim 2014) have shown that in the mid-latitudes, the synoptic 210 scale flow is in approximate geostrophic balance (i.e. ≈ −1 × ∇ Φ). The mean flow may also be characterised in the same way, so that ≈ −1 × ∇ is , thus suggesting a direct link between the horizontal perturbation flow and the horizontal gradient of the perturbation geopotential field. Fig. 3 shows the 1000 hPa composite mean fields of (shaded), superimposed with a few selected MSLP (thick dashed black) contours, the perturbation geopotential field and associated horizontal perturbation geostrophic flow , represented by the grey arrows for DJF. It is clear from this figure that the surface 215 horizontal flow that is important during the evolution of ridging high pressure systems occur in the southern edge of the subtropical belt and the mid-latitudes, where the geostrophic approximation is valid because the Rossby number = / is small enough there. It follows then that ≈ , so that the differences in the strength of the flow that is associated with the two different types of ridging are influenced by the strength in the horizontal gradient of the geopotential (∇ ). The thin black contours in Fig. 3 show that these gradients are much stronger within the 30°S and 50°S latitudinal belt, than north and south 220 of it, during the ridging process, so that the geostrophic flow (and by approximation the flow) is strongest there, thus informing the location of (Fig. 3).
To identify the centre more easily, we label these in red in Figs 3b and f as centre I, II and III. Centres I and II occur west and east of the positive geopotential height anomaly that arrives in South African domain as a component of the wave packet that passes over the country as ridging occurs (see Ndarana et al., 2022). Energy centre labelled III occurs east of the 225 negative geopotential anomaly that in turn is located to the east of the positive geopotential anomaly. The magnitudes of the energy centres characterise the first difference between the two types of ridging. All three centres, in particular I and II are https://doi.org/10.5194/wcd-2022-2 Preprint. Discussion started: 19 January 2022 c Author(s) 2022. CC BY 4.0 License. stronger for Type-S events compared to Type-N ridging. This may be a consequence of ∇ ϕ induced by Type-S events being stronger, thus leading to a more intense perturbation flow field, as discussed above. The other key observation to be made in Fig. 3 is that, for both types of ridging events, energy centre I maximises at the inception of the ridging process, whilst energy 230 centre II attains its maximum values, as the ridging process matures, as indicated by the SAOH having extended across the South African domain. The latter is largely due to the fact that the ridging process induces progressively stronger ∇ ϕ so that the perturbation flow increases and, hence, . This also explains the seasonal variations in as shown in Fig. 4 values during the winter months. This comes from the fact that the ridging induces stronger low level geopotential anomalies from DJF to JJA (Ndarana et al., 2022).
through the evolution of the ridging process. This orientation of the ageostrophic flow relative to the perturbation geopotential height fields is the second clue that downstream development might not exist at the surface, as it appears to fail to comply with the patterns reviewed in Section 2. This applies to both types of ridging.
The above has profound implications for energy transport. Combining the behaviour and structure of the ageostrophic flow and the patterns of , as well as those of and its convergence/divergence that are very different from those expected for 265 downstream development emerge. For Type-N energy, growth that is associated with the first energy centre appears to first be influenced by cyclonic ageostrophic fluxes in the mid-latitudes that converge (i.e. where −∇ ⋅ ( ) > 0) near the Greenwich Meridian (Fig. 5e). These fluxes diverge from just south of 60°S, and between 30°W and the Greenwich Meridian. This pattern is very different from the one induced by Type-S ridging highs. In that case, the fluxes are oriented in a south-westerly direction (Figs 5f), just south of energy II. This pattern suggests that energy is transported from energy centre II towards I, which is 270 opposite to what is expected during downstream development. Energy centre III, located just west of the Indian Ocean high, also grows from ageostrophic geopotential fluxes that have a north-easterly configuration. They appear to originate from a flux divergence region with the positive MSLP anomaly that is induced by the ridging process, and not by the transfer of energy from energy centre II. All of the above is not indicative of energy transport across a trough (ridge) where the flow is subgeostrophic (supergeostrophic), so that the energy centre located downstream grows at the expense of the centre 275 immediately upstream of it. This confirms observation made in the previous section that there is no evidence of downstream development at the surface during the evolution of ridging highs.
Since is always positive, will clearly be oriented as the surface circulation, which is shown by the arrows in Figs 3 and 4. In a baroclinic wave, the effect of this energy flux is to distribute from the rear end of the energy centre to the front of it. In this case however, the surface circulation transport energy in south-easterly (southerly) direction during the 280 evolution of Type-N (Type-S) events, just west of the surface MSLP anomaly (i.e. in the rear end of the leading edge of the ridging high), within energy centre I. In the Southern Hemisphere, it is well known that the flow is directed towards the southeast ahead of the cold front but towards the northeast behind it, ahead of the ridging high. This means that the effect of the cold front is to grow energy centres II and III.

Evidence of downstream development at the upper levels
As a first step to presenting evidence of downstream development aloft during the evolution of baroclinic waves that are associated with ridging high pressure systems, we show graphs of composite maximum as functions of time-lag in hours in Fig. 6. Therefore the green, blue and red curves in Fig. 6 respectively represent the evolution of the maximum of the 290 composite eddy kinetic for centres I, II and III, labelled from west to east as schematically represented and highlighted by the thick oval shapes in Stage 2 in Fig. 1 We first recall that t = 0 hour on the x-axes of Fig. 6 is the composite time at which the riding process is initiated and this is used as reference point for the discussion. The top panels of Fig. 6 show that in the case of Type-N ridging events the growth of energy centre II saturates during the 24 hours leading up to the initiation of the ridging process, whereas energy centre III reaches its largest values during the first 24 hours after the ridging process has begun. Centre III enters the South African 300 domain first as it is located downstream. The dots on the red curves show that associated with this centre reaches a maximum and dissipates when that component of the wave is over the Indian Ocean; meaning that it grows whilst it is in the South African domain. This is indicated by the red dots being located on the increasing side of the red curve. The dots on the blue curves similarly show that centre II dissipates in the South African domain. It grows whilst it is over the South Atlantic Ocean and peaks just before it crosses the western boundary of the domain, marked by the 10 °E longitude line. Energy centre 305 I enters the South African domain substantially later, and only briefly beyond t = +48 hours, when the ridging process has completed in most cases. These features are common to all seasons. The variations between seasons are observed for the relative maximum values that centres II and III attain. During DJF the associated with centre II is lower than that associated with centre III downstream, they are of comparable magnitude during MAM and during the winter months centre III attains the largest value.. Changes that lead to the summer structures start occurring in spring. 310 The evolution of the associated with the most important components of the Type-N baroclinic wave is reminiscent of Life Cycle 1 (LC1; Thorncroft et al., 1993;Hartmann and Zuercher, 1998). In contrast, the of the waves associated with Type-S events (shown on the bottom panels of Fig. 6) taper off in a similar fashion to Life Cycle 2 (LC2; Thorncroft et al., 1993;Hartmann and Zuercher, 1998). These latter baroclinic waves have longer life spans (Ndarana et al., 2022), which is consistent with the behaviour of the discussed here. The structure of Type-S energy centre II, in particular, starts off in an 315 LC2-like manner (cf. Fig.4 in Thorncroft et al. 1993) during the summer to become more like LC1 during the winter months. This is consistent with the fact that an upstream and southwest jet streak develops during the winter (Ndarana et al., 2022), thus introducing anticyclonic barotropic shear, so that the waves that might have been breaking cyclonically, as a result of being located on the poleward side of the upstream jet, now break anticyclonically. To support this argument about the change in structure, Hartmann and Zuercher (1998) showed by introducing cyclonic shear, LC1 becomes LC2, and even though to 320 the best of our knowledge, no study has shown the opposite, it is plausible that an addition of anticyclonic barotropic shear may change LC2 to LC1. Note that Type-S energy II starts growing in the South Atlantic Ocean but reaches its maximum values in the South African domain. The structure of Type-S energy III is also very different from that of Type-N. During DJF and MAM it tapers off, in LC2 like fashion as energy centre II but becomes flat and lacks growth in winter. Note however that the long lived nature energy centre III is the result of a completely different process from that influencing centre II. This will 325 be further explored below. In spring energy centre III grows in the South African domain, and saturates over the South West Indian Ocean, where it subsequently dissipates. https://doi.org/10.5194/wcd-2022-2 Preprint. Discussion started: 19 January 2022 c Author(s) 2022. CC BY 4.0 License.

Baroclinic conversion and upper-level downstream development 330
We now consider the processes that underpin the evolution of aloft during the evolution of the two types of ridging highs that was discussed in the previous subsection. A convenient point of departure for the discussion of this section is the growth and decay of energy centre II (blue curves in Fig. 6). As this energy centre is located at the inflection point that is situated between the upstream ridge and trough immediately downstream, there is strong upper level convergence (Ndarana et al. 2022), 335 and hence downward motion (i.e. > 0) associated with it. Recall also that decreases as a function of height from the ridge to the trough axis, implying that = − < 0, so that − > 0. This, according to Eqs (1) and (2), represents the conversion from eddy available potential energy to . Most of the growth observed for energy centre II is caused by this conversion as shown by the Hovmöller diagram in Fig. 7. For Type-N events during all seasons, as well as during the summer and spring in the case of Type-S, baroclinic growth is confined within the region, where the meridional component of the 340 perturbation flow, , is positive within energy centre II. The top panels of Fig. 7 show that the baroclinic conversion increases whilst the energy component is propagating over the South Atlantic Ocean and maximises before energy II enters the South African domain. Therefore this explains the > 0 of the blue curve in Fig. 6. This baroclinic conversion also increases from DJF to JJA, which explains the progressively higher values of as clearly shown in Fig. 6. It also explains the higher values associated with Type-S during JJA and SON. Note also that during the winter months substantial amounts of 345 baroclinic conversion occur for energy centre I during Type-S evolution (Fig. 7g), hence the higher values during this season compared to Type-N (compare the green curves in Figs 6c and g). Regardless of season and type of ridging associated with the baroclinic waves, the growth from baroclinic conversion occurs upstream as discussed in the recent review of Rossby wave packets (Wirth et al., 2018). However, this conversion coincides with downward motion as it is located east of an upper ridge axis so that latent heat release would not be expected, and thus no divergent amplification (Wirth et al. 2018). 350 in a baroclinic wave grows in one of two ways and by means of two processes, namely baroclinic conversion from eddy available potential energy and downstream development (Orlanski and Katzfey, 1991). Fig. 7 shows that there is no baroclinic contribution to the growth of energy centre III. Therefore it can only grow at the expense of energy centre II, by means of latter process which is presented in the first instance as Hovmöller diagrams of −∇ ⋅ ( a ) shown in Fig. 8 (see Eq. 2). As illustrated by this graph, there are large differences between Type-N and Type-S events and large seasonal variations, in keeping with 355 other SAOH metrics (Sun et al. 2017). By comparing the top panels of Figs 7 and 8, and also taking Fig. 6 (1) and (2) as shown in Fig. 6. The ageostrophic geopotential flux convergence is a maximum during MAM (Fig. 8b), so that saturates at higher values during this season compared to the others (Fig. 6b).
The bottom panels of Fig. 8 show that the situation is different for Type-S events. For one thing, during DJF (Fig. 8a), the 365 strongest ageostrophic geopotential flux energy sinks and sources are located downstream from the South African domain.
The weaker but elongated −∇ ⋅ ( a ) > 0 structure is in agreement with the fact that the red curve in Fig. 6b is not as steep as its Type-N counterpart in Fig. 6a, and also explains why energy centre III is longer lived for Type-S events. Similar arguments apply to MAM, whilst growth of energy III in Fig. 8f is not clearly defined as indicated also in Fig. 6. The structure of these sources and sinks in Fig. 8h are very similar to those associated with Type-N and there is evidence of this similarity 370 in the structure of the evolution of the in Fig. 6h.
Finally, to explain the processes that underlie the structures of the energy sources and sinks shown in Fig. 8 we make use composite fields (Fig. 9), shown only for the time lag t = 0 hours because they are similar for the other time steps as the ridging process evolves. The top panels (Figs 9a and b) show (shaded) and (hatched), middle panels (Figs 9c and d) show the ageostrophic flow and its divergence/convergence and in the bottom panels (Figs 9e and f) the ageostrophic geopotential 375 fluxes and their divergence/convergence are presented. All the fields are at 250 hPa. The patterns of shown in the top panels are contributed to, amongst other processes, by −∇ ⋅ ( ) that acts to translate the energy centres eastward (Orlanski and Sheldon 1995) and −∇ ⋅ ( a ) which, as previously discussed, describes the growth of energy by means of the downstream development process. We focus on the latter. The middle panels (Figs 9c and d) show that there is supergeostrophic and subgeostrophic flow across the ridge (red curve marked R in Fig. 9c) and trough (black curve marked 380 T), respectively. This means that across ridge (trough) axis the ageostrophic flow is directed downstream (upstream). A brief review of the flow involved in baroclinic waves is provided in Ndarana et al. (2022). The direction of the ageostrophic flow just described, combined with the sign of the across the ridge (where > 0) and trough (where < 0) axes lead to a radiation of energy from an upstream energy centre to one immediately downstream. For the two types of ridging highs considered in this study, this flux is strongest across the trough axis (see bottom panels of Fig. 9), so that the most significant 385 downstream development occurs from energy II to energy III. This is true for the baroclinic waves that are associated with both types of ridging, but more so for Type-N, as shown by the discussion of Fig. 8 above. This is quite different from what was found for COLs in the South African domain (Ndarana et al. 2021b) and for strong COLs in the Southern Hemisphere (Pinheiro et al., 2021) A more detailed comparison of these two downstream development regions is presented in the next section. 390

Comparison with COL downstream development
We now update Fig. 1, in a geographical  the findings of the current study, for both Type-N and Type-S ridging events. For both downstream development regimes, II is located between two jets streaks, one that is located upstream relative to it, which we call the upstream jet (UJ), with the 400 other situated downstream; the downstream jet (DJ). Only Type-N events have a clearly defined UJ. Note that, whilst there are large differences between the fields associated with Type-N and Types-S ridging events, in as far as intensity and seasonality are concerned, the general characteristics associated with downstream development associated with them are similar but differ significantly from that associated with COLs. We list these differences as bullet points for clarity: 405 1. The COL UJ propagates in a south-easterly direction by the distribution of zonal momentum from the entrance to the exit of the jet streaks (Ndarana et al., 2020) for the COLs case (see left panels of Fig. 10). This causes the deformation of the geopotential heights so that the trough approaching South Africa has a pronounced northwest/southeast orientation tilt. This deformation is more clearly seen when viewed from a potential vorticity perspective (Ndarana et 410 al. 2021b), in terms of which anticyclonic Rossby wave breaking (RWB) is defined (Thorncroft et al., 1993). What contributes to this is that the COL trough appears quasi-stationary, relative to the mid-latitude jet streak, so that I eventually catches up with II. The UJ observed during ridging highs does not propagate, in contrast to its COL counterpart. What this leads to is that the ageostrophic geopotential fluxes across the ridge axis (black line in Fig. 10) associated with COLs are stronger than those in the upper level baroclinic wave that is associated with ridging high 415 pressure systems.
2. The DJ associated with ridging highs is much stronger and much larger in spatial extent than that associated with COLs. It's thermally direct transverse circulation at its entrance therefore makes a more significant contribution to the downward motion west of the trough axis, thus leading to higher baroclinic conversion. 420 3. Points 1 and 2 have profound implications for the differences in the evolution of that is associated with COLs from that associated with baroclinic waves that have been observed aloft during ridging high pressure systems. The COL eddy energy centre I grows from baroclinic conversion from eddy available potential energy. In the case of ridging high baroclinic waves, the bulk of the baroclinic conversion is located downstream of the ridge axis. Because the 425 supergeostrophic flow is weaker than it is for COLs, the ridging high energy centre II grows from this conversion, rather than from downstream development from energy centre I, as it is the case for COLs. This is a direct effect of the fact that the UJ is quasi-stationary for ridging high upper air waves, relative to the one observed for COLs. https://doi.org/10.5194/wcd-2022-2 Preprint. Discussion started: 19 January 2022 c Author(s) 2022. CC BY 4.0 License.
The baroclinic wave dynamics findings in the study may then be summarised in this manner: Baroclinic waves that are associated with ridging high pressure systems develop from baroclinic instability in the mid-latitudes over the South Atlantic Ocean, as they propagate east. The development of the trough that eventually induces vertical motion over South Africa occurs 465 via downstream development. This downstream baroclinic wave development is different from that which is associated with COLs both in terms of orientation and also terms of which aspect of the wave develops from baroclinic conversion. Precisely why these differences exist remains an open question and a subject of further study. It is also apparent that characteristics of downstream development in the South African domain and surrounding oceans is greatly influenced by the dynamics of the jet streaks. In particular the movement of the upstream jet streak. As such, another open question is why does this jet propagate 470 so much faster during the evolution of COLs compared to that of upper air baroclinic waves that are associated with ridging highs in general? Also, contrasts between the jet streak configurations associated with the two types of ridging events suggest that barotropic shear influences the evolution of the energy centre that develops from downstream development. This hypothesis is based on classic idealised studies of baroclinic life studies (e.g. Thorncroft et al., 1993; Hartmann and Zuercher,  Orlanski and Sheldon (1995). It also draws from the findings of Ndarana et al.