Corresponding author: T. J. Parker, Monash Weather and Climate, School of Mathematical Sciences, Monash University, Clayton, Victoria 3800, Australia. (Tess.Parker@monash.edu)
 Heat waves in southeastern Australia in summer are commonly associated with slow-moving surface high-pressure systems, which result in warm northerly flow from the continental interior. The underlying dynamical pattern of heat waves in this region is associated with propagating Rossby waves, which grow in amplitude and eventually overturn, forming an upper level anticyclonic potential vorticity anomaly. The influence of tropical cyclones on the development of these anomalies is investigated here. Tropical cyclones may affect heat waves in this region indirectly, as the divergent outflow at upper levels perturbs the Rossby wave guide, leading to downstream development. However, the effect may also be direct, through the advection of anomalously anticyclonic potential vorticity from regions of deep convection in the vicinity of tropical cyclones into the upper level anticyclone. Our research shows that this direct reinforcement of the anticyclone is likely to be more important in the formation of severe heat waves in southeastern Australia.
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 Heat waves in southeastern Australia in summer are associated with strong, slow-moving transient surface anticyclones: the dry flow on the western flank of these high-pressure systems directs warm air from the interior of the continent in a northerly or northwesterly flow over the region. This pattern of a strong, slow-moving anticyclone is well known and is also evident on days of high fire danger in the region; less well understood are the fundamental dynamical atmospheric processes that cause this pattern.
 In the study presented here, the link between tropical cyclones (TCs) and the strength of the anticyclones that are responsible for heat waves in southeastern Australia is investigated. One way in which TCs may interact with the midlatitude flow is remotely and indirectly, by perturbing the waveguide and producing a Rossby wave, which subsequently propagates downstream. A study by Riemer et al.  of the interaction between a TC undergoing extratropical transition and a straight jet showed that the formation of an upper level ridge-trough couplet was due to the excitation of a Rossby wave train. In this case the strong potential vorticity (PV) gradient associated with the jet acts as a wave guide for Rossby waves [Schwierz et al., 2004]. The interaction of a TC during extratropical transition with a developing baroclinic wave [Riemer and Jones, 2010] similarly produces a ridge-trough couplet, together with enhanced downstream ridge building. Archambault et al.  examined the extratropical flow response to TC recurvature in the western North Pacific, finding that the tendency for amplified flow to develop is sensitive to the relative phasing of the TC and the large scale flow, but relatively insensitive to both the size and intensity of the TC.
 A second way in which TCs interact with the midlatitude flow is locally and directly through the advection of diabatically generated PV. TC convection generates cyclonic PV at low and midlevels and anticyclonic PV at upper levels [Hoskins et al., 1985]. A number of studies propose that the reduction of upper tropospheric PV as a result of latent heat release in regions of convection can enhance downstream ridging [Davis et al., 1993; Stoelinga, 1996; Dickinson et al., 1997; Thorncroft and Jones, 2000; Massacand et al., 2001; Jones et al., 2003]. In addition to the perturbation of the wave guide and subsequent downstream development described in previous studies of the Northern Hemisphere, our research shows material advection of anomalously low PV air from a region of deep convection associated with a TC into the upper level anticyclonic PV anomaly. This PV advection directly reinforces the upper level ridge, and thereby enhances the conditions necessary for the formation of heat waves over southeastern Australia. Furthermore, the upper level anticyclone associated with heat waves in this region is immediately downstream of the site of the TC-extratropical flow interaction, in contrast to many Northern Hemisphere cases where the weather impact over continental areas tends to be several wavelengths downstream.
 The aim of this paper is to determine the dynamical link between TCs and the transient, slow-moving anticyclone located to the south of the Australian continent during heat waves in this region. The paper is organized so that section 2 describes the analysis methodology and data sources. The main results are discussed in section 3, and our conclusions are presented in section 4.
2 Methodology and Data Sets
 Data for the December to February (DJF) summer season are extracted from the European Center for Medium Range Weather Forecasting (ECMWF) ERA-Interim (ERAI) reanalysis for the 21 year period from January 1989 to December 2009. These data are available at 6-hourly intervals at 1.5° horizontal resolution. Anomalies are defined as the deviation from the seasonal mean for DJF 1989–2009. The position of named tropical cyclones is taken from the International Best Track Archive for Climate Stewardship (IBTrACS) data set [Knapp et al., 2010].
 Daily maximum and minimum temperatures are obtained from the high-quality daily temperature (HQDT) data set for Australia developed by Trewin . Corrected daily temperature records are available for 99 nonurban stations and four stations located at major cities. Eleven of these stations are in the state of Victoria and are reasonably uniformly located throughout the state. For the purposes of this study, the HQDT data set is used to determine the monthly 80th and 90th percentile (viz., the highest 20% and 10%) maximum and minimum daily temperatures for each of the 11 stations in Victoria for DJF 1989–2009. A hot event in Victoria is then defined as any period of at least 3 days for which the following two conditions are satisfied. First, the daily maximum temperature at one or more stations equals or exceeds the 80th percentile for that station for that month. Second, the daily minimum temperature for that station equals or exceeds the 80th percentile minimum on at least 2 of those 3 days. A heat wave is defined in the same way, but using the 90th percentile maximum and minimum temperatures. Although no formal definition of a heat wave exists, the use of a percentile-based threshold over at least 3 consecutive days aligns well with the methods described in Perkins and Alexander . This definition results in the identification of a total of 76 hot events of varying lengths in Victoria during the 21 year period under review, of which 32 satisfy the definition of a heat wave. One of the most severe heat waves in southeastern Australia, the “pre-Black Saturday heat wave,” occurred in Victoria between 27 January and 8 February 2009. Between 28 and 30 January, Melbourne recorded 3 days with temperatures between 43° and 45°C. This extreme heat wave is used as an illustration of the main results of this research.
3.1 PV Climatology of Heat Waves and Hot Events
 Heat waves in southeastern Australia in summer are associated with persistent upper level anticyclonic PV anomalies, which are thought to form as a result of Rossby wave overturning in the region. (Throughout this study, the PV field is multiplied by negative one so that a low or negative PV anomaly refers to an anticyclonic anomaly, and a high or positive PV anomaly to a cyclonic anomaly.) Although the exact mechanism responsible for the overturning remains unclear, and its investigation is beyond the scope of this study, the southwestern Pacific is a preferred region for Rossby wave overturning in DJF [Berrisford et al., 2007].
 A k-means cluster analysis is used to objectively group hot events on the basis of the structure of the upper level 350 K PV anomalies in a box from latitude 20 to 60°S, longitude 100 to 180°E (see box in Figure 1a). The k-means clustering algorithm is based on that of Forgy  and uses randomly generated seed points for each cluster from the data points to be analyzed, following McRae , with three clusters prescribed. (The number of clusters was varied, but a value of three was found to generate representative, unique and robust clusters.) The cluster analysis was performed on the two-dimensional 350 K PV anomaly on all days comprising the 76 hot events, and the results are shown in Figure 1. Cluster 1 (Figure 1a) shows a strong anticyclonic anomaly over the southeast of the continent, with a band of cyclonic PV wrapped around it. Of the three clusters, the anticyclonic anomaly in Cluster 1 extends farthest toward the equator and most closely resembles the pattern in Riemer and Jones [2010, Figure 3(a)]. In Cluster 2 (Figure 1b), the anticyclone is less extensive and less intense, and the cyclonic anomaly to the southwest is weaker while that to the northeast is stronger. Although both Clusters 1 and 2 are consistent with Rossby wave overturning, the pattern of anomalies in Cluster 3 (Figure 1c) more closely resembles two synoptic troughs separated by a weak ridge.
 Air parcel back trajectories are computed for 12 days using the horizontal and vertical components of the wind from the 6-hourly ERAI reanalysis. Trajectories are calculated for parcels that are initially located at reanalysis data grid points which lie within the upper level anticyclonic 350 K PV anomaly at 12 UTC on the second day of each hot event, and for which the magnitude of the anomaly is 2 PVU or greater (1PVU=1×10−6 K m2s−1kg−1). The 350 K isentropic surface is chosen since this is the approximate level of the maximum PV anomaly (not shown). The relative vorticity normal to the 350 K isentropic surface is calculated and then summed using an area-weighted average in order to approximate the total (relative) circulation for the anticyclonic anomaly at the initial time. The contribution to the total circulation of the 350 K anomaly from parcels that have trajectories within a 200 km, 500 km, or 1000 km radius from the center of a named TC is then determined.
 Back trajectories are computed for all Victorian hot events (not shown), and the minimum distance from a TC center is then calculated for each individual trajectory. For 11 of the 32 heat waves, more than 50% of the calculated circulation of the upper level anticyclone is attributable to parcels with trajectories passing within 1000 km of a TC center; this includes the pre-Black Saturday heat wave, for which the percentage is 99%. For six of these heat waves, more than 70% of the circulation is attributable to such parcels. For trajectories within 500 km of a named TC center, four events have more than 50% and 13 events more than 20% of the circulation associated with such parcels; again, the pre-Black Saturday heat wave is included at 66%. For a distance of 200 km, four events have more than 20% and eight events more than 10% of the circulation associated with such trajectories.
 Figure 1d shows the percentage of hot event days which fall within each of the three clusters of 350 K PV anomalies. The days are divided into heat wave days (denoted “90th p”) and hot event days excluding heat wave days (denoted “80th p”), and further subdivided based on the percentage of the relative 350 K PV anomaly circulation attributable to parcels with trajectories passing within 1000 km of a TC center. Heat wave days for which more than 50% of the circulation is associated with such trajectories fall mostly within Cluster 1, with the remainder in Cluster 2; when this percentage is less than 50%, the majority of days are in Clusters 2 and 3. For hot event days (i.e., not heat wave days), those above the 50% circulation threshold are mostly within Cluster 2, and those below are in Cluster 3. These results show that the upper level anticyclonic anomaly is stronger and more extensive for hot events where a larger percentage of the circulation is associated with air parcel trajectories which pass closer to a TC center.
3.2 Pre-Black Saturday Heat Wave
 To further illustrate the relationship between heat waves and TCs, we now consider the most severe event in Victoria, the pre-Black Saturday heat wave. Figure 2a shows the air parcel back trajectories from 12 UTC on 28 January 2009 (the second day of the heat wave), color-coded according to the pressure levels at each time step, together with the anticyclonic 350 K PV anomalies at the initial time. The majority of trajectories originate at tropical latitudes where climatologically the PV is low, with over 95% originating equatorward of 30°S. Some, however, originate in the midlatitudes on the western side of the Indian Ocean. Importantly, all trajectories converge in a relatively narrow band over southwestern Australia; satellite images at this time (not shown) indicate a band of cloud in this region extending from northwest to southeast in association with the upper level outflow of TC Dominic.
 In order to show the advection of low PV air from the TC outflow region, forward trajectories are calculated from 00 UTC on 26 January 2009 for a 9×9° grid at 200 hPa, centered on the IBTrACS position of TC Dominic. These calculations are shown in Figure 2b, together with the trajectory point positions and the 350 K PV anomalies at 00 UTC on 31 January 2009. Since the trajectories originate at 200 hPa and remain at about this level throughout the analysis period, the trajectories are colored according to the average of the 500 hPa diabatic heating (in general, the level of maximum heating) at consecutive time steps. The generation of PV is approximately proportional to the product of the absolute vorticity and the vertical gradient of diabatic heating. Together with the contours of 500 hPa diabatic heating at 00 UTC on 28 January 2009, the forward trajectories show that air parcels pass at higher levels directly above the region of maximum diabatic heating, and thus in the region of anticyclonic PV generation at upper levels. Figure 2b shows that low PV air is both advected from the outflow region of the TC, and generated at upper levels as a result of the vertical gradient of diabatic heating.
 Figure 3 shows three plots each for 06 UTC on 27 and 28 January 2009, illustrating the physical ideas behind the direct and indirect effects of TC convection on the upper level anticyclonic anomaly. Figures 3a and 3b show the diabatic heating at 500 hPa in the cloud band associated with the TC outflow, which extends from TC Dominic toward the upper level anomaly and coincident with the region of ascent at this level shown in Figures 3e and 3f. The physical ideas behind the direct effect are illustrated in Figures 3c and 3d. The 250–150 hPa layer averaged advection of PV by the total wind field demonstrates that material is advected from the TC outflow region into the region of the upper level anticyclone to the southeast. The large advection of low PV on the southwestern side of the 2 PVU contour in these plots is presumably connected to the amplification of the trough and ridge. Also shown in these two panels is the 250–150 hPa layer averaged specific humidity. A plume of moist air produced by the convection extends from the TC well into the interior of the anticyclonic anomaly, supporting our contention that material is transported directly from the area of convection into the anticyclonic anomaly.
 Following Archambault et al. [2013, Figure 5], Figures 3e and 3f illustrate the indirect effect. A region of ascent and associated divergent outflow can be seen in the vicinity of the outflow from TC Dominic over southwestern Australia, together with strong negative PV advection by the divergent wind along the wave guide. Presumably, this perturbation of the wave guide amplifies the Rossby wave to some degree. The reversal of the meridional PV gradient associated with Rossby wave overturning is also visible in these panels.
3.3 Composite Structure of Tropical Cyclones
 Figure 4 shows a storm relative composite for DJF from 1989 to 2009 of all named storms within a box over northwestern Australia (latitude 0–30°S, longitude 90–140°E), at 72 h from first appearance as a named TC (a total of 79 storms). Figure 4a shows the mean 330 K PV anomaly, with the cyclonic anomaly evident in the region of the storm center. The mean 350 K PV anomaly (Figure 4b) shows the plume of anomalously anticyclonic PV which extends from the storm center toward the southeast, with the cyclonic filament wrapping around it. As well as the expected region of strong diabatic heating near the composite TC center, Figure 4c shows a band of anomalous diabatic heating extending toward the southeast, in the region of convection associated with the TC. The mean 250 hPa specific humidity anomaly (Figure 4d) shows increased upper level moisture to the southeast of the composite TC center, indicating that, even in the mean, material is transported from the region of convection toward the upper level anticyclonic PV anomaly. Composites for 1–5 days from first appearance of a TC (not shown) exhibit similar features.
 These composites indicate that, for TCs to the northwest of Australia in DJF, the upper level outflow region extending to the southeast, with accompanying advection of anomalously low PV air and moisture, is a robust feature of the climatology. This result supports our hypothesis that the direct advection of anticyclonic PV from the TC outflow to the upper level anomaly over the southeast of Australia reinforces the anticyclone which forms as a result of Rossby wave overturning and leads to persistence of the synoptic pattern associated with heat waves in this region.
 Heat waves in Victoria, Australia have been defined by applying a percentile-based threshold to daily maximum and minimum temperature data. A simple cluster analysis of the two-dimensional 350 K potential vorticity anomalies showed that heat waves are generally associated with stronger anomalies than hot events. Air parcel trajectories revealed that the proximity of tropical cyclones was an important contributing factor to the strength of the upper level anomalies. The interaction between tropical cyclones and the extratropical flow was investigated. In addition to the indirect effect on the upper level anticyclone of wave propagation and downstream development, it has been shown that the direct effect of the advection of anomalously anticyclonic PV from the upper level tropical cyclone outflow appears to constitute an important contribution to the strength of the upper level anomalies for strong heat waves in this region. This interaction is clearly evident in the lead up to the most severe heat wave in January–February 2009. The relative role of the direct and indirect effects may vary from case to case, and further modeling studies are required in order to determine the importance of these mechanisms.
 This study provides the first analysis of the dynamics of heat waves in Victoria, revealing the importance of favorable phasing between tropical cyclones and the upper level wave guide in the intensification of the upper level anticyclone. The advection of anomalously low potential vorticity from the cyclone outflow region into the upper level anomaly is an important additional mechanism for the maintenance of the circulation in some cases. An understanding of the dynamics of heat waves in this region is necessary not only for improved forecasting of these events but will better inform the evaluation of changes in the number or severity of heat waves in Victoria as a result of future climate change.
 TJP has been supported in part by the Australian Research Council Centre of Excellence for Climate System Science. GJB has been supported by Australian Research Council grant FS100100081. Data were provided by the European Centre for Medium-Range Weather Forecasts (ECMWF), the National Oceanic and Atmospheric Administration of the National Climatic Data Center (NOAA-NCDC), and the Australian Bureau of Meteorology (BoM). The authors thank Thomas Spengler and one anonymous reviewer for their input and improvements in the manuscript.
 The Editor thanks an anonymous reviewer and Thomas Spengler for their assistance in evaluating this paper.