The dynamics of slow‐moving coherent cyclonic potential vorticity anomalies and their links to heavy rainfall over the eastern seaboard of Australia

Heavy rainfall occurs frequently on the subtropical eastern seaboard of Australia (ESB). Many rainfall events are associated with slow‐moving, upper‐level low‐pressure systems. Combined with moisture‐rich easterly winds associated with a surface anticyclone, these systems can produce heavy rainfall, leading to flooding events. Although the general meteorology of these events has been documented, much of the focus has been on surface processes, with limited attention paid previously to the dynamics aloft. Here, we investigate the upper‐level dynamics associated with heavy rainfall events over the ESB with the use of a coherent potential vorticity (PV) minimum climatology on the 330‐K isentropic level. Slow‐moving coherent cyclonic PV anomalies produce more rainfall than fast‐moving anomalies over the ESB. Rossby‐wave breaking is responsible for the development of a slow‐moving coherent cyclonic PV anomaly as well as the commonly observed surface patterns that are necessary for heavy rainfall over the ESB. Slow cyclonic coherent PV anomalies are either transported equatorwards into the Tropics, where they may influence tropical weather systems, or removed from the region by the restoration of the subtropical jet over continental Australia.

coupled with moist easterly flow from the Tasman and Coral Seas, rainfall in the region is enhanced by orographic uplift (Rakich et al., 2008).
The variety of tropical, subtropical, and extratropical influences in the ESB results in substantial rainfall interannual variability. The northernmost (southernmost) reaches show the most (least) variability (Speer et al., 2011) owing to their lesser (greater) extratropical influence. More rain falls along the ESB during La Niña phases of the El Niño Southern Oscillation, especially during austral summer, with the greatest increase in the northern parts of the ESB (Rakich et al., 2008;Risbey et al., 2009;Speer et al., 2011). Positive phases of the Southern Annular Mode, where the flow is anomalously easterly, result in greater rainfall, especially in the southernmost parts of the ESB (Hendon et al., 2007;Rakich et al., 2008). Owing to the greater extratropical influence, the southern parts of the ESB rainfall, and in particular heavy rainfall, are highly correlated with east-coast lows, especially during the cooler seasons (Pepler et al., 2014).
The surface synoptic patterns that result in heavy rainfall in the ESB have recently received significant attention. The moisture required for rainfall is transported onto the ESB from the Tasman and Coral Seas by low-level easterlies (Gimeno et al., 2010;Black and Lane, 2015). The moist low-level easterlies are often associated with a slow-moving anticyclone in the Tasman Sea. Additionally, the anticyclone often coincides with a surface trough extending from the north or an east-coast low, which acts to enhance easterlies onto the ESB. An example of these low-level patterns was reported by Reid et al. (2021), who highlighted the role of a surface anticyclone in the Tasman Sea (or blocking high) in providing a zone of high moisture flux (or atmospheric river) into the ESB. Moreover, the easterlies are to some extent lifted orographically as they encounter the Great Dividing Range, which runs parallel to the coastline of the ESB (Speer et al., 2011). Although orography plays a role in the vertical motion required for rainfall in the ESB, dynamically driven ascent and the associated lifting are essential for heavy precipitation and convection (Taschetto and England, 2009;Warren et al., 2021;White et al., 2022).
Although persistent zones of moisture transport and surface weather systems have both been shown to be part of high-precipitation events, there is still uncertainty as to how these zones of moisture transport and the known high-precipitation surface synoptic weather systems codevelop (Reid et al., 2021). Few studies have considered in detail the upper-tropospheric dynamics associated with the surface processes, despite global studies showing that zones of moisture transport and Rossby-wave breaking (RWB) often co-occur (de Vries, 2021). Upper-level cyclones have been studied extensively in the region.
However, the focus of these studies has largely been on their links to surface cyclogenesis and the associated heavy rainfall over the region (e.g. Dowdy et al., 2013;Pepler and Dowdy, 2020;Pepler and Dowdy, 2021). Others have reported that COLs co-occur with an anticyclone in the Tasman Sea and provide the upward vertical motion required for rainfall (Risbey et al., 2009;Pook et al., 2013). The codevelopment of these components during heavy rainfall in the ESB has not yet been discussed or analysed in detail.
Following the seminal work of Hoskins et al. (1985), dynamical analyses of weather systems are commonly based on potential vorticity (PV). The PV perspective has proved to be a powerful method to explain the growth, circulation, and movement of synoptic weather systems. Upper-level cyclones (such as COLs), for example, are associated with the isentropic, equatorward transport of stratospheric (large magnitude, highly cyclonic PV) air into the troposphere as a result of RWB (e.g. Ndarana and Waugh, 2011;Barnes et al., 2021). In the Southern Hemisphere, stratospheric PV is large and negative, and hence cyclonic motion is associated with anomalously negative PV values. The cyclonic circulation associated with the intrusion of stratospheric air penetrates surfacewards (Hoskins et al., 1985) with large intrusions, associated with a deeper penetration of cyclonic vorticity, sometimes reaching the surface (Barnes et al., 2021). In a baroclinic atmosphere, warm-air advection is induced ahead of the upper-level PV intrusion by the resultant surface cyclonic circulation. As discussed by Bretherton (1966), a warm surface potential temperature anomaly is mathematically equivalent to a low-level cyclonic PV anomaly, which will induce its own cyclonic circulation. The cyclonic motion around the warm surface potential temperature anomaly has an imprint in the upper levels, slightly ahead of the PV intrusion. The additional cyclonic motion in the upper levels acts to enhance the upper-level cyclonic motion induced by the upper-level PV anomaly. Upper-level and surface processes are thus mutually beneficial and, when in phase, act to amplify one another (see Hoskins et al. 1985). Berry et al. (2012) constructed a climatology of coherent cyclonic PV extrema (which are negative in the Southern Hemisphere) for the Australian region using ERA-Interim data for the warm season (November-March) for the period 1989-2009. Coherent cyclonic PV centres were most commonly found in the northern and eastern parts of Australia, with a secondary maximum of coherent cyclonic PV along the extratropical storm track in the extreme southern parts of the country. On average, cyclonic PV centres circulated the country in an anticyclonic gyre, moving especially quickly in the westerlies to the south of the continent. The transport of coherent cyclonic PV centres equatorward from the midlatitudes affects tropical Australia, where they are associated with enhanced rainfall (Berry et al., 2012) and monsoon bursts (Berry and Reeder, 2016;Narsey et al., 2017).
Previous work has focused on the surface processes and synoptics during heavy rainfall. In this study we investigate the dynamics of heavy rainfall over the ESB, focusing on the upper-level dynamical processes. The analysis mostly follows a PV perspective. Hence, the role of upper-level coherent cyclonic PV anomalies during heavy rainfall over eastern Australia is investigated. The work is motivated by a case study of recent heavy rainfall over the ESB (during early 2022) and aims to further our understanding of the full tropospheric synoptic evolution of the atmosphere over the ESB. This article is structured as follows: in Section 2, the data and methods are described. The results, including the motivating case study, are reported in Section 3 and discussed in Section 4. Finally, our concluding remarks are made in Section 5.

DATA AND METHODS
In the Southern Hemisphere, stratospheric air is commonly characterised by large negative PV, with the dynamical tropopause defined by the −2 PVU (1 PVU = 10 −6 km 2 kg s −1 ) surface (Hoskins et al., 1985). Southern Hemispheric cyclonic (anticyclonic) PV anomalies are associated with anomalously lower (higher) PV. Cyclonic PV anomalies in the Southern Hemisphere can therefore be detected as minima in the raw PV field (as shown by the cyan crosses in Figure 1a). Using a method similar to that of Berry et al. (2012), PV minima are tracked using the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis product (Hersbach et al., 2020). The PV minima are tracked on the 330-K isentropic surface at six-hourly intervals. The 330-K isentropic surface is chosen as this level is close to the subtropical jet and is readily comparable with the results of Berry et al. (2012). Choosing a lower isentropic level may capture more low-level generated PV minima (such as those associated with diabatic heating processes), while a higher isentropic level may capture too many weaker, shallower intrusions of high-magnitude PV air (Barnes et al., 2021). The PV fields are first smoothed using two passes of a 13-point two-dimensional averaging operator. PV minima more negative than −0.01 PVU relative to the surrounding values are retained. Those PV minima found within 3 • of an adjacent PV minimum are deemed to be part of the same coherent PV minimum and the most negative of these are retained. The PV minima are then joined at subsequent timesteps to form tracks. Smoothed velocity fields on the 330-K level are used to predict the location of F I G U R E 1 Synoptic patterns associated with heavy rainfall over the ESB valid for 23-02-2022 00h00 UTC. a) 330K PV (shaded); coherent cyclonic PV anomalies detected by the tracking algorithm valid for 23-02-2022 00h00 UTC (cyan crosses); coherent cyclonic PV anomaly track associated with the coherent cyclonic PV anomaly situated over eastern Australia at 23-02-2022 00h00 UTC (points) scaled in size by their instantaneous speed. The track begins on 19-02-2022 18h00 and ends on 28-02-2022 18h00. b) 500hPa geopotential height (contours), 330K PV anomalies (shaded) and mean vertical velocity anomalies between 400hPa and 700hPa less than −0.03 Pa.s −1 (stippled areas). c) MSLP (contours) and vertically integrated water vapour transport (quivers). [Colour figure can be viewed at wileyonlinelibrary.com] PV minimum centres at the following timestep and those that are within 5 • of the forecast location are joined to form part of the same coherent cyclonic PV track. Coherent cyclonic PV tracks that do not persist for at least 24 hours are discarded.
Finally, coherent cyclonic PV anomalies are limited to those associated with stratospheric air (large negative PV values). Stratospheric air is characterised by PV values less than −2 PVU, which is the definition of the dynamical tropopause (Hoskins et al., 1985). However, since the PV fields used in this study have been smoothed, the amplitudes of the troughs have been reduced. Therefore, for the purpose of this study, coherent cyclonic PV anomalies of large-magnitude PV (presumably forming from stratospheric intrusions) are associated with a value of less than −1.5 PVU in the smoothed isentropic PV fields. A coherent cyclonic PV anomaly track is retained if at least one point is more cyclonic than (PV less than) −1.5 PVU. An example tracked coherent cyclonic PV anomaly produced by the tracking algorithm is shown in Figure 1a. In the figure, all tracked coherent cyclonic PV anomalies at the given timestep are shown by cyan crosses and an example track of one of the anomalies is shown by green points.
ERA5 reanalysis data are used for all analysis in this study unless otherwise explicitly specified. All anomalies are calculated as deviations from a daily mean climatology from the period 1980-2020. Vertically integrated parameters are taken directly from archived ERA5 fields. These data are integrated through the entire atmospheric column, from the surface to the top of the atmosphere.
The rainfall data used in this study are provided by the Australian Bureau of Meteorology Australian Water Availability Project (AWAP: Jones et al., 2009). The present study uses the daily rainfall data at a resolution of 0.05 • × 0.05 • from AWAP between 1980 and 2020. These gridded observations have been used extensively in previous studies in Australia and on the ESB in particular (e.g. Risbey et al., 2013;Black and Lane, 2015). Daily rainfall accumulations are used throughout the study. Each rainfall day is valid at 0900 Australian Standard Time for the preceding 24-hour period. The various composites of rainfall days are calculated relative to the end of the rainfall day. Heavy rainfall days are defined as the 100 highest mean rainfall days over a region on Australia's east coast, as outlined in Section 3.2.

A motivating case study: February 23, 2022
A series of heavy rainfall and flooding events were observed during the late summer and early autumn of 2022 along the ESB (Bureau of Meteorology, 2022). One such example is shown in Figure 1. The event took place on February 23, 2022 and was characterised by heavy rainfall and flooding that affected southern Queensland and northern New South Wales. The 330-K PV fields and the track of the coherent cyclonic PV anomaly are shown in Figure 1a. The coherent cyclonic PV anomaly track over eastern Australia is shown at six-hourly timesteps and the size of each point is scaled by the speed of the anomaly. Mid-to upper-level features, shown in Figure 1b, are characterised by 500-hPa geopotential heights, 330-K PV anomalies, and midlevel upward vertical motion. The surface-level features, shown in Figure 1c, are characterised by the mean sea-level pressure (MSLP) and vertically integrated water-vapour transport (IVT).
The upper levels over eastern Australia are dominated by an upper tropospheric cyclone or COL as defined by the closed 500-hPa geopotential height contours ( Figure 1b). The development of the COL is associated with RWB and the surfaceward isentropic transport of stratospheric air (Ndarana and Waugh, 2010). The COL is coincident with an anomalously negative (cyclonic) PV anomaly ( Figure 1a). The track shows that the coherent PV anomaly originates in the extratropical stratosphere. As the coherent cyclonic PV anomaly moves eastward over eastern Australia, it slows and remains over eastern Australia for several days. The coherent cyclonic PV anomaly is accompanied by a ridge in the isentropic PV field (Figure 1a Flow on the eastern edge of the COL is almost meridional (i.e., the zonal wind component is close to zero), while in the low levels the flow is easterly (i.e., the zonal wind component is negative) around the surface anticyclone in the Tasman Sea. Thus, in the region to the east of the COL, the easterly flow decreases with height. Given this configuration, quasigeostrophic theory (Holton and Hakim, 2013) predicts that midlevel upward vertical motion ( Figure 1b) is induced over the ESB. The persistence of the midlevel upward vertical motion provided by the slow-moving upper-level cyclonic PV anomaly and associated COL, together with persistent onshore moisture transport around the surface anticyclone in the Tasman Sea, was presumeably responsible for persistent, heavy rainfall over the seaboard of southern Queensland and northern New South Wales (Bureau of Meteorology, 2022).
A surface anticyclone centred over the Tasman Sea dominates the surface synoptic pattern. The resulting flow advects moist air from the Tasman and Coral Seas onto the ESB (Figure 1c). The synoptic pattern for this case is very similar to several heavy rainfall and flooding events over the ESB during March and April 2022 and to an event documented in March 2021 (Reid et al., 2021). The similar synoptic characteristics include upward vertical motion to the east of a cyclonic PV anomaly (COL) and easterly moisture transport around a surface anticyclone in the Tasman Sea. During some of these events, an east-coast low is also present. In this case, the east-coast low acts to enhance and focus the low-level easterly flow in areas of the ESB.

Composites of heavy rainfall over Eastern Australia
The case study reported in Section 3.1 indicates that heavy rainfall over the eastern parts of Australia can be associated with a cyclonic PV anomaly. In order to assess whether this association exists more generally, we composite the 100 highest daily mean rainfalls over a region on Australia's east coast ( Figure 2). The rainfall averaging region is defined as the landmass area enclosed by the green box depicted in Figure 2. Many of the 100 highest rainfall days are parts of multiday events. Of the selected heavy rainfall days, there were 13 events of 2 consecutive days, 1 event of 3 consecutive days, and 71 individual nonconsecutive days.
The composite MSLP and IVT fields ( Figure 2a) show striking similarities to the case study ( Figure 1) and are also consistent with previous studies (e.g. Black and Lane, 2015;Reid et al., 2021). Similarly to the case study, the composite synoptic pattern is characterised by a surface anticyclone in the Tasman Sea, which establishes a zone of easterly moisture transport over the heavy rainfall region. In contrast to the single case, the composite moisture transport into the region has a greater northerly component. The greater northerly component of the moist-air advection is part of a vertically integrated cyclonic flow over eastern Australia (centred on 27.5 • S, 147.5 • E), which contributes to the trough in the composite MSLP fields over eastern Australia. Figure 2b shows several important upper-level synoptic features associated with heavy rainfall days in the 500-hPa geopotential height, midlevel upward vertical motion, and 330-K PV anomaly fields. There is a steep upper-level trough in the 500-hPa geopotential height field (black contours) over eastern Australia. The upper-level trough is coincident with a cyclonic (negative) PV anomaly (shading). An anticyclonic (positive) PV anomaly lies to the south and southeast of the continent, and is associated with a ridge in the isentropic fields. Consistent with the upper-level patterns, there is a zone of midlevel upward motion (grey stippling) over the heavy rainfall region as well as the adjacent ocean to the east, as found in previous work (e.g. Black and Lane, 2015). Time-lagged composites (not shown) show both the cyclonic and anticyclonic PV anomalies two days prior to and two days after the daily rainfall maximum, indicating that heavy rainfall days are associated with a stalled or slow-moving cyclonic PV anomaly that affects the region for several days. This finding motivates us to investigate the synoptic environments under which cyclonic PV anomalies in eastern Australia are slow and fast.

Climatology of coherent cyclonic PV anomalies over Australia
Composites of heavy rainfall days indicate that cyclonic PV anomalies, particularly slow-moving cyclonic PV anomalies, are an important synoptic feature of heavy rainfall and flooding over eastern Australia. We therefore apply the coherent cyclonic PV anomaly detection and F I G U R E 2 Composites of the 100 highest mean rainfall days over the ESB (indicated by the box). a) MSLP (contours) and vertically integrated water vapour transport (quivers). b) Black contours are geopotential height (between 5000-6000m at 25m intervals), 330K PV anomalies (shaded) and mean vertical velocity anomalies between 400hPa and 700hPa less than −0.03 Pa.s −1 (stippled areas). [Colour figure can be viewed at wileyonlinelibrary.com] tracking algorithm described in Section 2 to construct a climatology of coherent cyclonic PV anomalies. We first describe the main features of the coherent cyclonic PV anomaly climatology for the entire Australian region and then focus on systems over eastern Australia to analyse their potential influence on heavy rainfall.
The densities of all coherent cyclonic PV anomalies on the 330-K isentropic surface over a 41-year period , their initial locations, and their propagation speeds are shown in Figure 3 for both austral summer and winter. In both seasons, the maximum number of coherent cyclonic PV anomalies is found to the southeast of Australia, with more found during the (extended) winter months than the (extended) summer months. A key difference between the cooler and warmer months is an increased occurrence of coherent cyclonic PV anomalies in tropical and subtropical Australia during summer. Local maxima in coherent cyclonic PV anomalies lie over tropical northwest Australia and along the subtropical east coast during summer ( Figure 3a).
The initial position climatology (Figure 3b,e) shows that coherent cyclonic PV anomalies form almost exclusively in the midlatitudes (Figure 3b,e), independent of the season, although this is affected by choosing PV minima more cyclonic than (more negative than) −1.5 PVU (see Section 2). The choice of large-magnitude PV anomalies on the 330-K isentropic level isolates coherent cyclonic PV anomalies that result from RWB and intrusions of stratospheric air into the troposphere, which are the focus of this study.
Coherent cyclonic PV anomalies generally travel from west to east with the extratropical jet (Figure 3c,f). As a result, they travel fastest over southern Australia. During the winter months, when the jet is generally stronger over the majority of the continent, coherent cyclonic PV anomalies move quickly eastward throughout the region. However, in the extended summer, coherent cyclonic PV anomalies move more slowly zonally and can be transported equatorward over subtropical eastern Australia. North of about 20 • S, coherent cyclonic PV anomalies tend to progress westward with the easterly trade-wind regime (Figure 3c). The equatorward flux of coherent cyclonic PV anomalies has been reported before by Berry et al. (2012) and Hoang et al. (2017). We note, however, that the equatorward flux is less pronounced in our results, as these earlier studies focused on the lower levels (i.e., 315 K).
The intrusion of high-magnitude PV (large negative values), stratospheric air into the troposphere has long been associated with RWB. Perhaps not surprisingly, our climatology of coherent cyclonic PV anomalies (Figure 3) shows similarities to previously published RWB (e.g. Ndarana and Waugh, 2011) and PV streamer (e.g. de Vries, 2021) climatologies. Coherent cyclonic PV anomalies are most prevalent to the south of Australia, and specifically over southeastern Australia during the winter months (Figure 3d), where RWB is also most prevalent. Sections 3.1 and 3.2 show that slow-moving upper-level cyclonic PV anomalies are an important ingredient for heavy rainfall over eastern Australia. We therefore divide our climatology of tracked coherent cyclonic PV anomalies based on their propagation velocities over the eastern Australian region. To do so, we analyse systems located between 140 • E and 155 • E and 20 • S and 35 • S (see Figure 4). This region is chosen to exclude both the strong westerly zone south of 35 • S, where coherent cyclonic PV anomalies frequently develop, and the tropical monsoon zone north of 20 • S. The upper and lower quartiles of the instantaneous zonal velocities of all 19,710 points from the 5786 coherent cyclonic PV anomaly tracks that pass through this region are calculated. Coherent cyclonic PV anomalies with zonal velocities in the lower quartile (approximately less than 4 m s −1 ) are classified as slow systems, while those in the upper quartile (approximately greater than 16 m s −1 ) are deemed to be fast-moving. Figure 4 shows the total track density of coherent cyclonic PV anomalies in eastern Australia for both the slow and fast velocity categories. Slow coherent cyclonic PV anomalies during the austral summer ( Figure 4a) are scattered throughout the domain. The origin of these anomalies is presumably extratropical RWB and the subsequent isentropic transport of large-magnitude PV stratospheric air. Slow coherent cyclonic PV anomalies are less frequent during winter and are more restricted to the southern parts of the domain (Figure 4c). With the subtropical jet generally less prominent during the summer months, the climatology suggests that coherent cyclonic PV anomalies move into eastern Australia slowly (zonally), since they are removed from the fast-moving basic-state westerly flow. Conversely, during the winter months, when the subtropical jet is stronger, slow coherent cyclonic PV anomalies are less frequent over continental Australia and are generally concentrated in the southern parts, between the climatological subtropical and polar-front jetstreams in weaker zonal flow.
Fast coherent cyclonic PV anomalies (Figure 4b,d) are found in the most southern parts of the region, poleward of the climatological jet axis. Consistent with upper-level low climatologies (e.g. Pepler and Dowdy, 2020), higher frequencies of faster coherent cyclonic PV anomalies occur during the winter seasons when the subtropical jet is stronger. Note that this is not necessarily the case for lower-level coherent cyclonic PV anomalies (for example on the 315-K surface) as seen in other previous studies, which focus on coherent PV anomalies in tropical Australia (Berry et al., 2012;Hoang et al., 2017).
Having established the climatology of slow-moving coherent cyclonic PV anomalies in the eastern Australian region, we investigate the synoptic conditions in which they occur and contrast these conditions with those for fast-moving systems in the next subsection.

Synoptic characteristics of slow coherent cyclonic PV anomalies over eastern Australia
The synoptic environment associated with slow coherent cyclonic PV anomalies is investigated by composite analysis. Coherent cyclonic PV anomalies in the extratropics are embedded in the westerly jet and hence move more quickly (Figure 3), while low-level (i.e., 315-K) PV anomalies are common in the Tropics (e.g. Berry et al., 2012). Hence, a subregion of the eastern Australian region (as depicted in Figure 5) is chosen, in which fast-moving coherent anomalies do not dominate the climate (north of 30 • ) and tropically induced circulations are likely excluded (south of 25 • S). Also, as seen in Figure 2b, the coherent cyclonic PV anomaly during heavy rain events occurs inland of the ESB, with upward vertical motion to the east. Therefore, we focus the subregion for compositing the PV anomalies inland between longitudes of 145 • E and 150 • E. The resulting subregion is shown by a green box in the composite plots (Figures 5, 6, and 7). All coherent cyclonic PV anomalies that pass through this region are used in the analysis. Day 0 is defined as the first coherent cyclonic PV anomaly point in each track that moves through the region. Lag composites are calculated relative to day 0 and are named by their days relative to day 0 (i.e., day 2 refers to two days after day 0 and day −2 refers to a composite two days before day 0).
Composites of the isentropic PV on the 330-K surface for both slow and fast coherent cyclonic PV anomalies for day 0 are shown in Figure 5. Perhaps the most striking feature of the figure is that the slow-moving coherent cyclonic PV anomalies are detached from the stratospheric (high-magnitude) PV reservoir to the south of Australia, while those that move fast are strongly connected to it. Moreover, PV contours associated with slow-moving coherent cyclonic PV anomalies exhibit well-defined overturning. This pattern is, by definition, RWB (Mcintyre and Palmer, 1983;Esler and Haynes, 1999). The northwest-southeast tilt of the overturning indicates that the wave breaking is anticyclonic (Thorncroft et al., 1993).
The intrusion of stratospheric air (large negative PV values) into the upper troposphere in the slow-moving cases is reflected in the increase in the amplitude of the trough at 500 hPa days prior to day 0 (compare Figure 6a-c) and RWB. The high-amplitude trough and associated cyclonic PV anomaly persist for several days (Figure 6a,c,e). In the slow-moving cases, there is a strong anticyclonic PV anomaly and an associated upper-level geopotential height ridge to the south of mainland Australia, which are largely absent in the fast-moving cases. Cyclonic-anticyclonic PV anomaly dipoles are often the result of anticyclonic RWB and are often associated with atmospheric blocking (Coughlan, 1983;Hoskins et al., 1985).
The difference in speed between the two categories of coherent cyclonic PV anomalies is evident in Figure 6. For fast coherent cyclonic PV anomalies (Figure 6b,d,f), there is a strong cyclonic PV anomaly over eastern Australia on day 0 as is expected. In addition, the PV contours tilt slightly northwest-southeast; however, the amplitude of the perturbation is weak (Figure 5b). As overturning is weak, only a small and weak anticyclonic PV anomaly is generated south of the coherent cyclonic PV anomaly. This anticyclonic PV anomaly is short-lived and only present on day 0 (Figure 6d).
The surface synoptic features for slow and fast coherent cyclonic PV anomalies are shown in Figure 7. The MSLP for slow-moving coherent cyclonic PV anomalies shows an anticyclone in the Tasman Sea at day 0. The anticyclone builds from day −2 and reaches its maximum at day 0, before weakening slowly. The surface anticyclone translates slowly to the east, particularly after day 0. There is strong easterly moisture transport across the east coast in the slow-moving cases. The integrated vapour-transport vectors turn from an alongshore southeasterly to an onshore easterly by day 0, which persists through day 2. There is midlevel upward motion (Figure 6a,c,e) above the zone of onshore moisture transport and east of the coherent cyclonic PV anomaly. In the fast-moving case, an anticyclone does not develop in the Tasman Sea (Figure 7b,d,f). Critically, the integrated moisture transport is westerly, and hence offshore, transporting dry continental air across the east coast. This difference in the direction of moisture transport presumably limits the production of rainfall associated with fast-moving coherent cyclonic PV anomalies.
The seasonality of slow and fast coherent cyclonic anomalies, as shown in Figure 4, is strongly imprinted the eastern sub region (indicated by the box). 500hPa geopotential height (contours), 330K PV anomalies (shaded) and mean vertical motion anomalies between 400hPa and 700hPa less than −0.03 Pa.s −1 (stippled areas). Fields are composited on the first detected point in each coherent cyclonic PV anomaly track passing through the eastern sub region (c, d). Also plotted are the lag composites 2 days prior (a, b) and 2 days after (e, f) the first detected point in each coherent cyclonic PV anomaly track passing through the eastern sub region. [Colour figure can be viewed at wileyonlinelibrary.com] on the composites of these features in Figure 5,6, and 7. Composites of fast coherent cyclonic PV anomalies resemble a wintertime atmosphere in which the subtropical surface ridge and the upper-level jet are situated further equatorward. In order to investigate this further, we perform the same analysis for both the extended summer and winter periods (Figure 8). Notably, as the climatology ( Figure 4) suggests, there are few slow winter (28 cases, compared with 225 fast winter cases) and fast summer (78 cases, compared with 144 slow summer cases) coherent cyclonic PV anomalies in the composites. Nonetheless, the large-scale synoptic features of slow and fast coherent cyclonic PV anomalies remain similar in both summer and winter. Slow coherent cyclonic PV anomalies F I G U R E 7 Near surface synoptic composites for slow (left) and fast (right) coherent cyclonic PV anomalies through the eastern sub region (indicated by the box). MSLP (black contours), potential temperature anomalies at 900hPa (shaded) and vertically integrated water vapour transport (quivers). Fields are composited on the first detected point in each coherent cyclonic PV anomaly track passing through the eastern sub region (c, d). Also plotted, lag composites for 2 days prior (a, b) and 2 days after (e, f) the first detected point in each coherent cyclonic PV anomaly track passing through the eastern sub region. [Colour figure can be viewed at wileyonlinelibrary.com] during winter still occur in combination with a poleward anticyclonic PV anomaly, surface anticyclone, and associated easterly moisture transport. In the slow-moving cases, the magnitudes of both the cyclonic and anticyclonic PV anomalies during winter are greater than those in summer. The fast coherent cyclonic PV anomalies during summer and winter are relatively similar, both with predominant offshore, westerly moisture transport, and no surface anticyclone over the Tasman Sea. Summertime fast anomalies, however, appear to be connected to a larger cyclonic PV streamer emanating from the extratropics, whereas those in winter show a weak anticyclonic PV anomaly over the southeast of the continent.

Dynamics of slow-moving PV anomalies over eastern Australia
Having identified the main characteristics of slow-moving cyclonic PV anomalies, the aim of this section is to analyse their motion from a PV-vortex perspective. From this perspective, the movement of an upper-level coherent cyclonic PV anomaly is determined by the advection of PV by the basic-state flow, vortex retrogression resulting from the basic state gradient of PV, vertical interactions with surface-level PV-like anomalies, and lateral interactions with PV anomalies on the same isentropic level (e.g. Hoskins et al., 1985;Hakim et al., 1996;Huo et al., 1999). Following Hakim et al. (1996), each of these interactions in the Southern Hemisphere is depicted conceptually in Figure 9.
First, the coherent cyclonic PV anomaly can simply be advected by the basic-state flow. The schematic in Figure 9a illustrates the movement of the coherent cyclonic PV anomaly in a strong westerly jet. Second, the movement can be affected by the basic-state quasigeostrophic potential vorticity (QGPV) gradient. In a north-south directed QGPV gradient (as in Figure 9b) the coherent cyclonic PV anomaly is directed westward, against the basic-state westerly jet (Hoskins et al., 1985;Hakim et al., 1996). Dynamically, this process is the same as that responsible for the propagation of Rossby waves. In the subtropics, away from the westerly jet, the QGPV gradient is weak and thus this effect is also weak.
Third, coherent cyclonic PV anomalies can also be advanced by interactions with surrounding anomalies (Figure 9c). A coherent cyclonic PV anomaly induces cyclonic motion around it. Thus, a coherent cyclonic PV anomaly to the south of another coherent cyclonic PV anomaly will advect the northern coherent cyclonic PV anomaly eastward, while the northern coherent cyclonic PV anomaly will advect the southern PV anomaly westward. Similar arguments can be made for laterally located coherent cyclonic PV anomalies in an east-west configuration.
Fourth, a coherent cyclonic PV anomaly can be advected by anomalies at lower levels ( Figure 9d). A warm surface potential temperature anomaly acts dynamically like a cyclonic PV anomaly (Bretherton, 1966;Hoskins et al., 1985). The cyclonic motion induced by the warm surface anomaly and associated geopotential height fall is mirrored in the upper levels and results in the advection of the coherent cyclonic PV anomaly towards the surface warm anomaly. Conversely, a cold surface anomaly, associated with anticyclonic motion and geopotential height increases, directs the coherent cyclonic PV anomaly away from it.
With the conceptual interactions in Figure 9 in mind, we analyse composites of all fast and slow coherent cyclonic PV anomalies. Figure 10 shows composites of the zonal wind anomalies at 250 and 500 hPa, potential temperature anomalies at 900 hPa, and isentropic PV at 330 K centred on the coherent cyclonic PV anomaly in eastern Australia for slow-and fast-moving systems.
The zonal wind composites (Figure 10a,b,e,f) for slow and fast coherent cyclonic PV anomalies show anomalous cyclonic rotation around the coherent cyclonic PV anomaly, as is expected around an intrusion of stratospheric air. Notably, however, slow coherent cyclonic PV anomalies show a pronounced easterly anomaly at and south of the coherent cyclonic PV anomaly centre. Conversely, fast coherent cyclonic PV anomalies are associated with a larger magnitude anomalous westerly to the north of the coherent cyclonic PV anomaly. The large easterly anomaly flow suggests that slow coherent cyclonic PV anomalies are embedded in a weaker westerly zonal jet compared with that of fast coherent cyclonic PV anomalies. Presumably, the juxtaposition with the westerly jet is one reason why the faster coherent cyclonic PV anomalies propagate quickly eastward. The differences in the zonal wind surrounding the coherent cyclonic PV anomalies also help us understand the spatial and seasonal (Figure 4) distribution of slow-and fast-moving coherent cyclonic PV anomalies. The subtropical jet is more prominent and situated over the Australian continent during the winter months (Figure 3c and f). Therefore, coherent cyclonic PV anomalies that develop during the winter months are more likely to be embedded in the fast-moving westerly jet, explaining the prevalence of fast systems during the extended winter season.
Vertical interactions are investigated using composites of potential temperature at 900 hPa (Figure 10c and g). Slow coherent cyclonic PV anomalies over eastern Australia are associated with a warm anomaly to the southwest of the coherent cyclonic PV anomaly and a cold anomaly to the north and east. There are similar horizontal F I G U R E 10 Slow (top) and fast (bottom) coherent cyclonic PV anomaly composites of (a,e) zonal (Earth-relative) wind anomalies at 250 hPa in m s −1 , (b,f) zonal (Earth-relative) wind anomalies at 500 hPa in m s −1 , (c,g) potential temperature anomalies at 900 hPa in K, and (d,h) isentropic PV at 330 K in PVU in eastern Australia. Composites are centred on the coherent PV minima at (0,0) and indicated by bold grid lines. [Colour figure can be viewed at wileyonlinelibrary.com] temperature structures in the synoptic composites of slow coherent cyclonic PV anomalies in Figure 7. As the coherent cyclonic PV anomaly moves into the eastern parts of Australia, a warm potential temperature anomaly develops and strengthens from the west (Figure 7a and c). Consistent with Figure 9d, the low-level temperature anomalies result in southwestward advection of the coherent cyclonic PV anomaly, opposing the flow of the westerly jet to the south. This contributes to it stalling over eastern Australia.
In contrast, fast coherent cyclonic PV anomalies are associated with a cold anomaly near the surface and no warm anomaly close to the centre of the coherent cyclonic PV anomaly (Figure 10g). The position of the cold potential temperature anomaly to the south and west of the coherent cyclonic PV anomaly is associated with a geopotential height increase in the upper levels and therefore advects the coherent cyclonic PV anomaly eastward, with the zonal jet. It should be noted, however, that the cold surface potential temperature anomaly in the fast case is weaker than that associated with the slow coherent cyclonic PV anomaly. As a result, the effect of advection on the motion of the coherent cyclonic PV anomaly by its interaction with low-level temperature anomalies is likely to be relatively weak. The motion of the fast coherent cyclonic PV anomaly toward the east is therefore likely to be dominated by its interaction with the zonal basic-state flow.
Finally, we analyse the coherent cyclonic PV anomaly's lateral interaction with surrounding PV anomalies on the 330-K surface (Figure 10d,h). By construction, the coherent cyclonic PV anomaly lies at the centre of the composite for both slow-and fast-moving anomalies. The major difference between the two composites is the anticyclonic PV anomaly (or local PV maximum) to the south of the coherent cyclonic PV anomaly for slow-moving systems. Similar anomalies can be seen in the synoptic composites in Figure 6a and c. The anticyclonic PV anomaly is associated with anticyclonic motion, which advects the coherent cyclonic PV anomaly westward. During winter the subtropical jet reduces the number of slow-moving coherent cyclonic PV anomalies. For an anomaly to move slowly, a westward advection is necessary to counteract the intense westerly basic-state flow. According to Figure 8c, the anticyclonic PV anomaly that forms poleward of the coherent cyclonic PV anomaly is more intense during winter than in summer. This intensity is important for the anomaly to advect the coherent cyclonic PV anomaly towards the west effectively, against the strong westerly basic-state flow, resulting in its relatively slow eastward motion.
In contrast, there is no equivalent anticyclonic PV anomaly associated with the fast coherent cyclonic PV anomaly composite. In fact, a weak cyclonic PV anomaly lies poleward of fast coherent cyclonic PV anomalies. The absence of any lateral PV anomalies associated with fast coherent cyclonic PV anomalies suggests that its motion is presumably dominated by the basic-state flow and therefore by its location in the subtropical jet. During winter, the easterly advection by the weak anticyclonic PV anomaly (Figure 8d) is overwhelmed by the intense westerly of the subtropical jet. In summer, however, the eastward motion of fast-moving coherent cyclonic PV anomalies is enhanced by a poleward-located weak cyclonic PV (Figure 8b).

Transport of slow coherent cyclonic PV anomalies away from eastern Australia
The climatology of coherent cyclonic PV anomalies over eastern Australia (Figure 3c) suggests that some coherent cyclonic PV anomalies move northwestwards into tropical northern Australia. Previous work has shown that, at times, cyclonic PV debris from the midlatitudes is transported into the Tropics, initiating and organising tropical rainfall (e.g. Berry et al., 2012;Hoang et al., 2017;Narsey et al., 2017). Figure 1 and the subsequent heavy rainfall during February-April 2022 (not shown) indicate that this is not always the case, with coherent cyclonic PV anomalies exiting the east coast eastwards during this period. The eastward exit of a coherent cyclonic PV anomaly away from the continent removes an important ingredient (midlevel vertical motion) for enhanced rainfall over the ESB. The processes associated with the exit of slow coherent cyclonic PV anomalies from eastern Australia are therefore investigated here. Slow-moving coherent cyclonic PV anomalies that move eastwards of 160 • E are separated from those that stall over Australia and remain west of 150 • E. These categories are based on the last detected point in each track. 86 slow-moving coherent cyclonic PV anomalies are classified as exiting mainland Australia eastwards, while 63 are found to stall over the continent.
Composites of the two classes of slow-moving coherent PV anomalies based on their final positions are shown in Figure 11. Green contours describe the area covered by the coherent anomaly positions of slow coherent PV anomalies at the relevant time. Coherent cyclonic PV anomalies that remain over Australia move northwestward, tracing the Australian coastline (Figure 11b,c). Its northwestward movement into the Tropics is consistent with the PV climatology (Figure 3), and in particular the extended summer climatology in Figure 3c. A major difference between the coherent cyclonic PV anomalies that exit Australia and those that do not is the re-establishment of the subtropical jet (as shown by grey quivers in Figure 11e,f). Slow-moving coherent cyclonic PV anomalies that exit Australia, moving eastwards into the Tasman or Coral Seas, are associated with stronger upper-level zonal winds by day 2 (Figure 11e). Conversely, when the subtropical jet remains F I G U R E 11 Composites of stalled coherent cyclonic PV anomalies (those that remain permanently over the Australian mainland) weak over the eastern parts of Australia (Figure 11b,c), the coherent cyclonic PV anomaly moves into tropical Australia. The increase in upper-level westerlies is likely the result of the eastward progression of the upper-level trough that lies to the west of Australia (Figure 6c,e), while the coherent cyclonic PV anomaly is present over eastern Australia.

4.3
Vertically coupled, synoptic evolution of slow coherent cyclonic PV anomalies over eastern Australia The circulation induced by upper-level PV anomalies can extend to the surface. Given a low-level thermal gradient, the induced low-level flow will result in low-level thermal advection (Hoskins et al., 1985). In this case in the Southern Hemisphere, the induced anticyclonic low-level flow will result in cold-air advection ahead (east) of the upper-level anticyclonic PV anomaly. Cold potential temperature anomalies at the surface induce anticyclonic motion, leading to the development of a surface anticyclone ahead of the upper-level anticyclonic PV anomaly. Surface anticyclones are often the response to upper-level anticyclonic PV anomalies (e.g. Ivanciu et al., 2022;Ndarana et al., 2022), including those associated with heatwaves (e.g. Parker et al., 2014).
Returning to the case of slow-moving cyclonic anomalies, the upper-level anticyclonic PV anomaly poleward of the slow-moving coherent cyclonic PV anomaly ( Figure 6) induces a surface anticyclone (Figure 7). This surface anticyclone in the Tasman Sea strengthens towards day 0 (Figure 7c), and eventually weakens slowly and moves eastwards towards day 2 ( Figure 7e). The changes in both strength and motion of the surface anticyclone are mirrored by those of the upper-level anticyclonic PV anomaly (Figure 6a,c,e), indicating their interconnectedness. Despite the various synoptic features associated with heavy rainfall in the ESB occurring at various levels of the troposphere, the codevelopment of the key synoptic processes that lead to heavy rainfall in the ESB highlights that these various processes are vertically coupled and occur in unison through the same process, that is, anticyclonic RWB.

4.4
Links between slow coherent cyclonic PV anomalies and heavy rainfall synoptics over the ESB Synoptic composites of heavy rainfall in the ESB (Figure 2) and slow coherent cyclonic PV anomalies (Figures 5a;  6a,c,e; 7a,c,e) exhibit many similar features. A surface anticyclone is present over the Tasman Sea, transporting moisture-rich air from the Tasman and Coral Seas into the ESB in both cases. Likewise, both composites are associated with midlevel upward vertical motion associated with a steep upper-level trough and an associated cyclonic PV anomaly over eastern Australia. Moreover, both composites are associated with an anticyclonic PV anomaly to the south of mainland Australia. The development of both anticyclonic and cyclonic PV anomalies results from anticyclonic RWB, which transports high-magnitude, stratospheric PV air isentropically into the upper troposphere. Figure 12 shows the composite mean daily rainfall on all days for which a slow or fast coherent cyclonic PV anomaly moves through the eastern subregion (as indicated in Figure 12 and used throughout the study). The results show that the rainfall on days with slow-moving anomalies far exceeds that on days with fast-moving cyclonic PV anomalies. The results in Section 3 show that this difference is as a result of the persistence of the slow-moving coherent cyclonic PV anomaly, the associated vertical motion on its eastern edge, and the surrounding meteorology that develops coincident with the slow-moving coherent cyclonic PV anomaly through anticyclonic RWB. Moreover, Figure 8 shows that, compared with those days associated with a fast-moving PV anomaly, more rainfall occurs for slow-moving PV Although fast-moving coherent cyclonic PV anomalies produce rain (Figure 12b), the pattern of rainfall is similar to that for fronts with larger accumulations over the west coast of Tasmania. The synoptic patterns are similar because fast-moving PV anomalies (Figures 5b;6b,d,f;7b,d,f) are associated with PV streamers (Figure 5b), which are essentially upper troughs, and westerly moisture transport (Figure 7b,d,f).
Slow coherent cyclonic PV anomalies are strongly linked with heavy rainfall over the ESB. Figure 13 categorises the slowest coherent cyclonic PV anomaly detected in the region spanning 140 • S-155 • S and 20 • S-40 • S on each day of heavy rainfall and the preceding day. This region is expanded 5 • further south than the region shown in Figure 4 to ensure that coherent cyclonic PV anomalies that may be associated with rainfall in the southern reaches of the ESB are captured. Slow and fast categories retain the previous lower and upper quartile F I G U R E 13 Category (colours) of the slowest coherent cyclonic PV anomaly located in the region spanning 140 • S-155 • S and 20 • S-40 • S of the highest 100 rainfall days in the ESB. Each grid cell represents a heavy rainfall day, ordered from highest (top left) to lowest (bottom right) daily rainfall. Slow (red cells, first quartile), medium-slow (orange cells, second quartile), medium-fast (green cells, third quartile), and fast (blue cells, fourth quartile) categories are shown. White cells indicate days in which no coherent cyclonic PV anomaly on the 330-K surface is located on a heavy rainfall day.
[Colour figure can be viewed at wileyonlinelibrary.com] definition as used previously. Additional medium-slow (second quartile) and medium-fast (third quartile) catergories are added. 72% of heavy rainfall days coincided with at least one detected slow-moving coherent cyclonic PV anomaly during the two-day period. An additional 14% of heavy rainfall days occurred with medium-slow coherent cyclonic PV anomalies, while only 6% occurred with medium-fast or fast anomalies. For the 8% of heavy rainfall days that remain uncategorised, analysis highlights the arbitrary nature of region and level selection for coherent cyclonic PV anomaly analysis. Of these uncategorised days, 2% were associated with a monsoon low over northern Australia, while the rest had a PV streamer. Of the 6% of uncategorised cases in which a PV streamer is present, half occurred with a PV streamer (and possibly therefore a coherent cyclonic PV anomaly) situated above the 330-K surface (i.e., on the 350-K surface). The remaining half occurred with an elongated PV streamer on the 330-K surface that reached into eastern Australia from the midlatitudes, but where a coherent cyclonic PV anomaly identified by the tracking algorithm occured out of the region used in this analysis. These findings underscore the importance of upper-level PV features and, more importantly, slow-moving coherent cyclonic PV anomalies and the processes producing them, which result in heavy rainfall over the ESB.
There are, however, some key differences between the composite synoptic patterns for heavy rainfall days and the composite synoptic patterns for slow coherent cyclonic PV anomalies. On heavy rainfall days, an anticyclonic PV anomaly extends east of the ESB into the Tasman Sea ( Figure 2b). This additional anticyclonic anomaly in the Tasman Sea has two major consequences. First, the anticyclonic upper-level flow induced around the anomaly acts to advect the coherent cyclonic PV anomaly westwards. This adds to the westward advection of the coherent cyclonic PV anomaly induced by the anticyclonic PV anomaly to the south of Australia, and assists in stalling the anomaly. Second, the anticyclonic PV anomaly promotes anticyclonic development at the surface. Surface anticyclonic building in the Tasman Sea enhances easterly flow and hence moisture transport over the ESB.
Another key difference between the composites of heavy rainfall days and slow coherent cyclonic PV anomalies is strong northerly moisture transport parallel to the coastline in the heavy rainfall composite (shown by IVT vectors in Figure 2a). The northerly moisture transport develops through a well-defined vertically integrated cyclonic circulation over eastern Australia. Analysis of geopotential height composites (not shown) reveals an extended, closed circulation from the upper levels to the surface. Deep cyclonic circulations are associated with deeper stratospheric intrusions of high-magnitude PV air (Barnes et al., 2021). Moreover, the surfaceward cyclonic development of the upper-level cyclonic circulation in composites of heavy rainfall days presumably explains the along-shore MSLP trough reported by Black and Lane (2015) and highlights the role that deep cyclones (that extend from the surface into the midlevels) play in heavy rainfall in the ESB, as previously reported by Dowdy (2020, 2021). The effect of the deep cyclonic circulation on the ESB is to provide poleward transport of moisture from the Tropics. The input of tropical, moisture-rich air likely enhances rainfall over the ESB further.

SUMMARY AND CONCLUSION
Motivated by multiple flooding events in early 2022 (Figure 1), this study investigates meteorology of heavy rainfall over the ESB. Previous studies have linked heavy rainfall over the ESB to a surface anticyclone and the resulting transport of moisture on its northern flank from the Tasman and Coral Seas to the east of Australia. In addition to these known surface processes, we show that a slow-moving cyclonic PV anomaly over eastern Australia is an important ingredient of almost all heavy rainfall over the ESB, as it provides the necessary upward motion. Importantly, a large proportion (72%) of heavy rainfall events over the ESB occur coincident with a slow-moving coherent cyclonic PV anomaly. Slow-moving cyclonic PV anomalies, which are most frequent in summer, are produced and subsequently transported from the midlatitudes into eastern Australia through anticyclonic RWB. Such RWB produces an upper-level PV dipole with a slow-moving coherent cyclonic PV anomaly over eastern Australia and an anticyclonic PV anomaly to the south and east of the continent. This dipole is crucial to the development of the synoptic patterns associated with heavy rainfall. Both slow-moving cyclonic and anticyclonic upper-level PV anomalies have an imprint at low levels. The anticyclonic PV anomaly generates and strengthens a surface anticyclone in the Tasman Sea. Easterlies on the northern flank of this anticyclone transport the moisture required for rainfall from the Coral and Tasman Seas onto the ESB. A deep intrusion of stratospheric air associated with the slow-moving coherent cyclonic PV anomaly is associated with a deep cyclonic circulation. Consequently this deep cyclonic circulation promotes a more meridional transport of moisture-rich air from the Tropics. The vertical coupling of the slow-moving coherent cyclonic PV anomaly to the surface may additionally deepen a surface trough or produce a closed surface low (or east-coast low), focusing low-level easterly flow in areas of the ESB. Coupled with vertical motion on the eastern flank of the coherent cyclonic PV anomaly (or COL), the large influx of moisture onto the ESB results in heavy rainfall in the region. This study thus highlights the important role that RWB plays in producing the synoptic components throughout the troposphere required for rainfall over the ESB.
The zonal movement of coherent cyclonic PV anomalies in eastern Australia depends on the basic-state flow and its interaction with surrounding PV anomalies. Fast-moving coherent cyclonic PV anomalies are more prevalent during winter and are generally embedded in the fast-flowing basic-state westerly jet. These anomalies move more slowly when they occur in an anomalously easterly basic-state flow. Their eastward advection is additionally slowed through anticyclonic RWB through their interaction with an anticyclonic PV anomaly to the south and a warm (cold) surface potential temperature anomaly to the southwest (east).
Some coherent cyclonic PV anomalies remain stalled over the Australian continent, while others exit the continent to the east. These stalled coherent cyclonic PV anomalies are most prevalent during summer, when the subtropical jet is weak and strong westerlies lie poleward of the Australian continent. Their exit from eastern Australia is controlled by the subtropical jet. Stalled coherent cyclonic PV anomalies exit mainland Australia by an upper-level trough approaching from the west, re-establishing the strong zonal upper-level westerlies. In the absence of a strong zonal basic-state flow, coherent cyclonic anomalies often move into tropical, northern Australia.
The present study is limited by its strong reliance on a qualitative use of PV thinking. These arguments could be strengthened using a more quantitative approach in future work. The results presented are also limited by the tracking algorithm. The algorithm tracks coherent cyclonic PV anomalies by tracking PV minima, linking these cyclonic PV anomalies in time by geographic location. Coherent cyclonic PV anomalies that split into two or more anomalies are deemed to be distinct. This may result in missing coherent cyclonic PV anomalies that originate in the extratropics or high latitudes. Coherent cyclonic PV anomalies are assumed to have extratropical and stratospheric origins based on their central PV magnitude. It is, however, possible for circulations with a tropical or low-level origin to attain large PV magnitudes in the mid to upper levels, although Figure 3 indicates that these are relatively rare. Finally, this study only examines the synoptic-scale processes associated with heavy rainfall over the ESB. There is, however, little doubt that other processes affect the amount of rain from a particular event, including mesoscale processes (such as diabatic heating) and interactions with the Tropics (such as high sea-surface temperatures). Future work should investigate these processes further in order to advance our understanding and ability to predict heavy rainfall events in the ESB.