Abstract

Although heat waves account for more premature deaths in the Australian region than any other natural disaster, an understanding of their dynamics is still incomplete. The present study identifies the dynamical mechanisms responsible for heat waves in southeastern Australia using 10-day backward trajectories computed from the ERA-Interim reanalyses. Prior to the formation of a heat wave, trajectories located over the south Indian Ocean and over Australia in the lower and midtroposphere ascend diabatically ahead of an upper-level trough and over a baroclinic zone to the south of the continent. These trajectories account for 44% of all trajectories forming the anticyclonic upper-level potential vorticity anomalies that characterize heat waves in the region. At the same time, trajectories located over the south Indian Ocean in the lower part of the troposphere descend and aggregate over the Tasman Sea. This descent is accompanied by a strong adiabatic warming. A key finding is that the temperatures are raised further through diabatic heating in the boundary layer over eastern Australia but not over the inner Australian continent. From eastern Australia, the air parcels are advected southward as they become incorporated into the near-surface anticyclone that defines the heat wave. In contrast to past studies, the importance of cloud-diabatic processes in the evolution of the midlatitude large-scale flow and the role of adiabatic compression in elevating the near-surface temperatures is emphasized. Likewise, the role of the local surface sensible heat fluxes is deemphasized.

1. Introduction

Summer heat waves in Australia have a major effect on many sectors of the community, economy, and natural environment. Since the middle of the nineteenth century, heat waves in Australia have killed more than 5000 people, making these extreme weather situations the deadliest natural hazard of the continent (Coates et al. 2014). And future projections suggest an increase in the intensity, frequency, and duration of heat waves in a warmer climate (e.g., Alexander and Arblaster 2009; Cowan et al. 2014), including southeastern Australia. Although statistical investigations of the links between subseasonal and seasonal modes of climate variability and southeastern Australian heat waves have received much attention, few studies have focused on the dynamical mechanisms acting on shorter time scales. Thus, a comprehensive physical picture of how the processes on various time scales interact is still missing. This picture, however, is an essential part of understanding the mechanisms controlling the location and strength of heat waves, including the changes anticipated in a warmer world.

Numerous studies have investigated how heat waves in southeastern Australia relate to sea surface temperature anomalies and to the dominant intraseasonal-to-interannual modes of climate variability such as the southern annular mode (SAM; Rogers and van Loon 1982), the Madden–Julian oscillation (MJO; Madden and Julian 1972), and El Niño–Southern Oscillation (ENSO; Bjerknes 1969). Heat waves in southeastern Australia occur more frequently during episodes of enhanced convection over the Maritime Continent and over northern Australia; for example, during La Niña phases of ENSO, during MJO phases 3–6 of the Wheeler and Hendon (2004) Real-time Multivariate MJO (RMM) index, or during active periods of the Australian monsoon (e.g., Parker et al. 2014b; Perkins et al. 2015). During positive phases of SAM (i.e., when the Southern Hemisphere midlatitude jet is shifted poleward), heat waves over southeastern Australia tend to occur more frequently and tend to last longer (Perkins et al. 2015). Although the climate modes provide some information on the amplitude and frequency of southeastern Australian heat waves, the statistical link to climate modes is weaker than for other regions of Australia. Also, southeastern Australian heat waves occur on much shorter time scales than the intraseasonal-to-interannual modes of climate variability. Thus, processes on shorter synoptic time scales are expected to be of major importance in determining the timing and amplitude of heat waves.

Globally occurring heat waves are typically linked to anomalous anticyclonic flow conditions (e.g., Meehl and Tebaldi 2004; Cassou et al. 2005; Matsueda 2011; Pfahl and Wernli 2012; Stefanon et al. 2012) that can evolve into persistent blocking patterns. Likewise, heat wave conditions in southeastern Australia are generally associated with tropospheric-deep anticyclonic flow anomalies over the Tasman Sea (e.g., Hudson et al. 2011; Parker et al. 2014a). These anomalies are characterized by positive geopotential height or anticyclonic PV anomalies (i.e., positive anomalies on the Southern Hemisphere) that remain quasi stationary during the heat wave and roughly centered over the southeast of Australia (e.g., Pezza et al. 2012; Parker et al. 2014a; Purich et al. 2014). The anticyclonic flow anomalies evolve as part of midlatitude Rossby wave packets, which have their origin in far upstream regions several days prior to the onset of the heat wave (Parker et al. 2014a). These Rossby wave packets grow in amplitude, start to extend poleward, and eventually break anticyclonically over southeastern Australia.

Several dynamical processes have been identified to be conducive to the amplification of the anticyclonic flow anomalies. An investigation of heat waves over southeastern Australia during DJF 1989–2009 reveals the importance of tropical cyclones (TCs) for the intensification of the upper-level anticyclone (Parker et al. 2013). Their analysis suggests that the poleward advection of anticyclonic PV air by diabatically enhanced irrotational flow contributes likely indirectly to a poleward extension of the midlatitude anticyclone southeast of the TC. This is in line with recent studies that show the importance of diabatically enhanced irrotational flow for midlatitude flow amplifications on the synoptic time scale (e.g., Riemer et al. 2008; Archambault et al. 2015; Teubler and Riemer 2016; Quinting and Jones 2016; Grams and Archambault 2016; Bosart et al. 2017).

In addition, the direct injection of diabatically processed anticyclonic PV air from the upper-level TC outflow contributes to a further strengthening of the upper-level anticyclone (e.g., Parker et al. 2013; Grams et al. 2011; Grams and Archambault 2016). Likewise, the direct injection of diabatically processed anticyclonic PV air from midlatitudes could enhance the anticyclone. In midlatitudes, the direct diabatic PV modifications occurring on synoptic time scales are usually associated with rapidly ascending and coherent airstreams, so-called warm conveyor belts (WCBs; e.g., Harrold 1973; Carlson 1980). Diabatic processes during the WCB ascent lead to a net cross-isentropic transport of low-PV air into regions that are climatologically located in the lower stratosphere (Madonna et al. 2014), producing intense anticyclonic PV anomalies. Although several studies in midlatitude dynamics have highlighted this process for the formation of upper-level anticyclones (e.g., Pomroy and Thorpe 2000; Massacand et al. 2001; Croci-Maspoli and Davies 2009; Grams et al. 2011), Pfahl et al. (2015) was the first to use a Lagrangian approach to systematically quantify the importance of diabatically processed air masses in the formation of midlatitude-blocking anticyclones. Their analysis reveals that diabatically processed air masses are of the same importance for blocking formation as adiabatically advected air masses.

It is not yet clear whether the direct injection of anticyclonic PV air from the tropics or midlatitudes is a general feature of southeastern Australian heat waves. In this study, we apply a Lagrangian approach to characterize air masses that are associated with heat waves in southeastern Australia. After introducing the dataset and methodology in section 2, we analyze in section 3 the characteristics of the air masses of which upper-level anticyclones are composed. Section 3 aims to answer the following questions:

  • What is a characteristic pathway of air masses that reach these upper-level anticyclones?

  • Is the cross-isentropic transport of anticyclonic PV through diabatic heating important for the formation of heat waves?

  • Where does the cross-isentropic transport occur?

Although the analysis in section 3 helps to explain the dynamics of upper-tropospheric anticyclones during southeastern Australian heat waves, it does not explain the processes that lead to anomalously warm air masses at the surface. Near-surface temperatures during heat waves have been linked to the advection of warm dry air to the affected regions (e.g., Miralles et al. 2014; Perkins 2015), adiabatic warming in sinking air masses (e.g., Black et al. 2004; Galarneau et al. 2012; Pfahl and Wernli 2012; Bieli et al. 2015), and to radiatively driven heating over anomalous dry soils (e.g., Fischer et al. 2007; Quesada et al. 2012; Miralles et al. 2014; Kala et al. 2015; Herold et al. 2016). Concerning the latter process, anomalously dry soils reduce evaporative cooling by latent heat fluxes and increase atmospheric heating due to enhanced sensible heat fluxes. All these processes may co-occur and reinforce each other culminating in mega–heat waves (Miralles et al. 2014; Fischer 2014) such as the European heat wave of 2003 and the Russian heat wave of 2010. A commonly accepted picture of southeastern Australian heat waves is that the advection of warm and dry air masses from the inner continent leads to the anomalously high temperatures (e.g., Reeder and Smith 1987; Hudson et al. 2011; Engel et al. 2013; Marshall et al. 2014; Parker et al. 2014a; Boschat et al. 2015; Perkins 2015). Anomalously low antecedent soil moisture also tends to favor the development of heat waves in this region (Mueller and Seneviratne 2012; Perkins et al. 2015; Herold et al. 2016), although the connection appears to be weaker than in other regions of the world (Perkins et al. 2015). To better understand the physical and dynamical processes leading to the anomalously high temperatures that define southeastern Australian heat waves, the pathway of the near-surface air masses is analyzed in section 4. The analysis addresses the following questions:

  • Is there a characteristic pathway of the near-surface air masses?

  • How important is adiabatic warming in sinking air masses compared to near-surface diabatic temperature increase in producing heat waves?

The study ends with the conclusions in section 5.

2. Dataset and methodology

All analyses presented in this paper are based on 6-hourly ERA-Interim (Dee et al. 2011) on a regular 0.75° latitude–longitude grid. Climatological means in this study always refer to averages over the 30-yr period 1981–2010.

a. Definition of southeastern Australian heat waves

The characteristics of trajectories during southeastern Australian heat waves for the period DJF 1989–2009 are investigated. The definition of these heat waves is based on daily maximum and minimum temperatures at 11 weather stations in southeastern Australia (Fig. 1) in the high-quality daily temperature dataset (Trewin 2001). Following the definition of Parker et al. (2013), a heat wave is defined as a period of at least three consecutive days for which

  1. the daily maximum temperature for at least one station exceeds the 90th percentile maximum for that station and month;

  2. the daily minimum temperature is above the 90th percentile of minimum temperatures for at least two of three days.

This definition yields 32 heat waves in Victoria for the period DJF 1989–2009 with a total of 132 heat wave days. A total of 39 heat wave days fall into December, 36 days fall into January, and 57 fall into February. The highest number of heat wave days within a single summer season (15 days) were recorded in 1994/95 and 1996/97, respectively. The most prolonged heat wave of 13 days occurred in January–February 2009. Mildura in northwestern Victoria experiences the highest temperatures with the 90th percentile of daily maximum temperature reaching 39.7°C in January (Fig. 1). The 90th percentile of the daily maximum temperature is generally lower in coastal regions than in northern Victoria. However, even in coastal regions the daily maximum temperature can reach 40°C (e.g., Cape Otway on 20 January 1997; Parker et al. 2014a). For a detailed discussion, the interested reader is referred to section 3 in Parker et al. (2014a).

Fig. 1.

Map of the 11 weather stations in southeastern Australia that are part of the high-quality daily temperature dataset (Trewin 2001). The numbers give the 90th percentile of maximum temperature (°C) for each station and month. Dashes indicate that a heat wave did not occur at that station and month during 1989–2009. Backward trajectories presented in section 4 are started from the four ERA-Interim grid points closest to each weather station.

Fig. 1.

Map of the 11 weather stations in southeastern Australia that are part of the high-quality daily temperature dataset (Trewin 2001). The numbers give the 90th percentile of maximum temperature (°C) for each station and month. Dashes indicate that a heat wave did not occur at that station and month during 1989–2009. Backward trajectories presented in section 4 are started from the four ERA-Interim grid points closest to each weather station.

b. Definition of anticyclonic upper-tropospheric potential vorticity anomalies

The identification of upper-tropospheric anticyclonic anomalies is motivated by the PV-based atmospheric blocking definition of Schwierz et al. (2004). It is based on the instantaneous 500–150-hPa vertically integrated PV anomaly relative to the monthly climatology of the vertically integrated PV. First, a two-dimensional mask is created that includes all longitude–latitude grid points at which the anomaly of vertically averaged PV is greater than 1 PVU (1 PVU = 10−6 K kg−1 m2 s−1). We then identify all grid points every 50 hPa between 500 and 150 hPa that lie within the mask. Finally, the instantaneous PV at the identified grid points must be more positive than −1 PVU to exclude grid points in the stratosphere from the analysis. Unlike Schwierz et al. (2004), we are interested in anticyclonic anomalies at all time scales. For this reason the data are not filtered in time, nor is their condition for continuity in time imposed (i.e., their condition that the anomalies calculated in consecutive 6-h times must at least partially overlap in space).

Although the climatological distribution of upper-tropospheric PV anomalies during DJF in the Southern Hemisphere is reasonably uniform in space, they generally occur between 40° and 60°S and on the poleward flank of the 500–150-hPa mean jet (Fig. 2a). Anomalies are climatologically least frequently downstream of South America and to the south of New Zealand.

Fig. 2.

(a) DJF climatological occurrence frequency of anticyclonic 500–150-hPa PV anomalies (shading in %) and 500–150-hPa mean wind speed (contours at 25 and 30 m s−1). (b) The 500–150-hPa mean PV (contours at 1, 2, and 3 PVU) and anomalous occurrence frequency of 500–150-hPa anticyclonic PV anomalies during southeastern Australian heat waves (shading in %).

Fig. 2.

(a) DJF climatological occurrence frequency of anticyclonic 500–150-hPa PV anomalies (shading in %) and 500–150-hPa mean wind speed (contours at 25 and 30 m s−1). (b) The 500–150-hPa mean PV (contours at 1, 2, and 3 PVU) and anomalous occurrence frequency of 500–150-hPa anticyclonic PV anomalies during southeastern Australian heat waves (shading in %).

As outlined in section 1, southeastern Australian heat waves are characterized by upper-level anticyclonic PV anomalies that evolve as part of a midlatitude Rossby wave packet (Parker et al. 2013, 2014a). Composites of vertically averaged PV for all heat wave days corroborate these findings. The vertically averaged PV reveals a midlatitude trough along 120°E (black contours in Fig. 2b) and a downstream ridge that breaks anticyclonically as indicated by the overturning 1-PVU contour. The upper-level ridge is collocated with a positive anomalous occurrence frequency of anticyclonic PV anomalies (shading in Fig. 2b). The location of the occurrence frequency anomaly reveals that the anticyclonic PV anomalies during heat waves occur farther equatorward compared to climatology (cf. shading in Figs. 2a,b).

c. Trajectory calculations

Two sets of 240-h (10 days) backward trajectories are computed with the Lagrangian analysis tool (LAGRANTO; Sprenger and Wernli 2015) using the ERA-Interim three-dimensional wind field at 60 model levels. Trajectories are started 6-hourly at each day of a heat wave from a regular 0.75° longitude–latitude grid. To account for the convergence of meridians toward the poles, all mean quantities presented later in the study are weighted by the square root of the cosine of the latitude. In this way backward trajectories starting close to the poles are weighted less than trajectories starting farther equatorward when computing statistical quantities of their physical properties. Physical properties that are traced along the trajectories include specific humidity, PV, potential temperature, temperature, anomalies of PV relative to the monthly climatology, cloud liquid water content, and cloud ice water content. Changes in potential temperature between two times along the trajectory are attributed to diabatic processes. Although PV is conserved in the absence of diabatic processes, the PV anomalies can change along the trajectories as the anomalies are calculated relative to the climatology (an example being the adiabatic advection of high-PV air into regions of climatologically low-PV air).

The first set of trajectories comprises about 3 000 000 trajectories and is designed to document air masses involved in the formation of upper-tropospheric anticyclones. Following the approach of Pfahl et al. (2015), three-dimensional Lagrangian backward trajectories are started from PV anomalies identified in section 2b between 120°E and the date line, and equatorward of 80°S. We choose this region as anticyclones that are associated with southeastern Australian heat waves typically occur in this longitude range (Fig. 2b). The starting time of the backward trajectories (i.e., the time when the trajectories are located in the upper-tropospheric PV anomalies) is referred to as t = 0 h.

The second set comprises about 14 000 trajectories and is designed to analyze the characteristics of air masses close to the surface. These 240-h backward trajectories are started from the four grid points closest to each of the weather stations that are incorporated in the definition of southeastern Australian heat waves (Fig. 1). We account for variations in the planetary boundary layer height by starting the trajectories 10, 30, and 50 hPa above the surface (Bieli et al. 2015). The starting time of the backward trajectories (i.e., the time when the trajectories are located at the respective weather station, is referred to as t = 0 h).

One important limitation in the computation of trajectories from reanalysis data is that the analyzed wind fields do not resolve convection explicitly. This limitation is of particular relevance in the tropics. Consequently the Lagrangian transports due to subgrid-scale convective cells are not fully represented in the 6-hourly wind fields. In addition, the 6-hourly analysis times might underestimate the vertical displacement of air parcels when convection occurs between two time steps or overestimate the vertical displacement when the vertical motion associated with short-lived convection is applied to the 6-h period. Nonetheless, case studies and climatological analyses (e.g., Ploeger et al. 2011; Martius and Wernli 2012) indicate that ERA-Interim reanalyses are suitable for trajectory analysis in tropical latitudes.

3. Air masses in upper-tropospheric anticyclones

This section focuses on the history of the air masses defined by the first trajectory set (i.e., those air masses that are located in upper-tropospheric anticyclones over the Australian region at t = 0 h). Every 6 h the longitudes and latitudes of all trajectories, their pressure, and their 6-hourly potential temperature change are regridded on a regular 1° latitude–longitude grid. The spatial distribution of the trajectories at different times is analyzed from these regridded data. The distributions are normalized by the spatial integral of the trajectory number so that the spatial integral over each distribution yields 100%.

a. Pathway of air masses

At t = −216 h, trajectories that end in anticyclonic anomalies during southeastern Australian heat waves (at t = 0 h) are nearly equally distributed between South America and Australia (black contours in Fig. 3a). Most trajectories are initially located in the subtropics and midlatitudes. East of South America, South Africa, and over Australia, the trajectories lie on average below 500 hPa (shading in Fig. 3a). Thereafter, these trajectories ascend, reaching the upper-tropospheric anticyclone, which is located by definition above 500 hPa.

Fig. 3.

Mean height (shading in hPa) and spatial density (black contours every % 10−6 km−2) of trajectories that are involved in the formation of upper-level anticyclones during southeastern Australian heat waves. The times prior to the arrival of the air parcels in anticyclonic anomalies at t = 0 h are given in subcaptions.

Fig. 3.

Mean height (shading in hPa) and spatial density (black contours every % 10−6 km−2) of trajectories that are involved in the formation of upper-level anticyclones during southeastern Australian heat waves. The times prior to the arrival of the air parcels in anticyclonic anomalies at t = 0 h are given in subcaptions.

Relatively few trajectories reach the upper-tropospheric anticyclone from tropical latitudes, in particular from the eastern south Indian Ocean and northern Australia. At t = −216 h, the trajectories from the eastern south Indian Ocean between 90° and 110°E are located on average above 500 hPa and consequently do not necessarily ascend to reach the upper-level anticyclone.

At t = −144 h, the trajectory densities are highest over the western south Indian Ocean and over the Australian continent (Fig. 3b). The trajectory density in both regions increases from that at t = −216 h, indicating a local confluence of the trajectories. Since these trajectories are mostly located in the lower half of the troposphere they must ascend to reach the anticyclone.

Three days prior to reaching the location of the upper-tropospheric anticyclone at t = 0 h, the density of trajectories over the south Indian Ocean and over the Australian continent increases further as they head toward the PV anomaly (Fig. 3c). The trajectories over the Australian continent are on average located below 500 hPa, and subsequently ascend southward in the final 72 h to reach the upper-tropospheric anticyclone.

b. Role of diabatic processes

That a large fraction of the trajectories over the Australian continent ascends during the final 72 h raises the question: how important are diabatic processes for that ascent? In this section, we quantify the proportion of trajectories that are diabatically heated during the three days prior to reaching the upper-tropospheric anticyclone at t = 0 h and contrast their evolution with trajectories that are diabatically cooled. To do so, we integrate all 6-hourly changes in the potential temperature along the trajectories over the three days prior to reaching the location of the anticyclone at t = 0 h. This approach follows Pfahl et al. (2015), although they only considered positive potential temperature changes along the trajectories. We find nearly identical results with either approach.

We start by investigating the joint frequency distribution of the integrated potential temperature changes along the trajectories and of the PV anomaly relative to the monthly climatology at the location of the trajectories at t = −72 h. This bivariate joint frequency distribution is obtained by a nonparametric kernel-density estimate using Gaussian kernels (e.g., Wand and Jones 1993).

The distribution of the trajectories involved in the formation of the upper-level anticyclones has two branches (Fig. 4). Hereafter, the term “branch” always refers to the branch of a distribution and not to the branch of an atmospheric airstream. The first branch of the distribution comprises 56% of all trajectories (Table 1, Fig. 4). These trajectories are cooled diabatically between t = −72 and t = 0 h (i.e., ), while being transported into the upper-level anticyclone. The cooling, which is as much as 8 K in 72 h, is likely to be radiatively driven. The PV anomalies along this branch range from −0.7 to 1.5 PVU. We refer to this branch as horizontal branch. The second branch of the distribution comprises air masses with relatively small PV anomalies, ranging from −0.4 to 0.4 PVU, but with an integrated diabatic heating of up to 22 K. About 44% of the trajectories fall into the second branch (Table 1). We refer to this branch of the distribution as the vertical branch. Although more than half of the trajectories are cooled diabatically between t = −72 and t = 0 h, the net effect of all trajectories is a heating due to the strong diabatic heating along the trajectories on the vertical branch. Hence, the results show that, as for Northern Hemispheric blocking anticyclones investigated by Pfahl et al. (2015), the transport of diabatically heated air masses is a central part of the formation of anticyclones during southeastern Australian heat waves. As discussed in section 3c, none of the results are sensitive to the precise definition of the two branches.

Fig. 4.

Joint frequency distribution of PV anomalies at the location of the backward trajectories at t = −72 h and integrated change in potential temperature along the trajectories between t = −72 and t = 0 h. Shading shows densities of a kernel-density estimate using Gaussian kernels. We refer to the distribution below (above) the gray line as horizontal (vertical) branch of the distribution. The numbers give the fraction of trajectories in each branch.

Fig. 4.

Joint frequency distribution of PV anomalies at the location of the backward trajectories at t = −72 h and integrated change in potential temperature along the trajectories between t = −72 and t = 0 h. Shading shows densities of a kernel-density estimate using Gaussian kernels. We refer to the distribution below (above) the gray line as horizontal (vertical) branch of the distribution. The numbers give the fraction of trajectories in each branch.

Table 1.

Percentage of trajectories in the horizontal and vertical branches of the distribution relative to the total number of trajectories selected according to their potential temperature θ at t = 0 h.

Percentage of trajectories in the horizontal and vertical branches of the distribution relative to the total number of trajectories selected according to their potential temperature θ at t = 0 h.
Percentage of trajectories in the horizontal and vertical branches of the distribution relative to the total number of trajectories selected according to their potential temperature θ at t = 0 h.

In a case study of the Pre–Black Saturday heat wave, Parker et al. (2013) showed that air masses reached the 350-K isentropic level at t = 0 h from the tropics. To determine their pathway systematically, we partition each branch into a set of trajectories that were located below and a set located above the 350-K isentropic level at t = 0 h. It is 4% of all trajectories that reach at least 350 K (Table 1). The trajectories above 350 K have their starting points predominantly in the tropics over northern Australia and the Maritime Continent (shading in Figs. 5a and 5d). Most of these trajectories remain confined to this region until t = −144 h (shading in Figs. 5b and 5e), after which they head westward with the climatological upper-tropospheric easterly winds (gray lines in Figs. 6a and 6f denote height of the trajectories, winds are not shown). At t = −72 h, most of the trajectories are located over the central and eastern south Indian Ocean (shading in Figs. 5c,f). From there, they head poleward in the climatologically northerly winds before heading eastward in the midlatitude jet. Overall, the spatial distribution for this set of trajectories is similar for the horizontal and vertical branches. The described path of the trajectories matches the one in the Pre–Black Saturday heat wave case study by Parker et al. (2013, their Fig. 2a).

Fig. 5.

Spatial densities of trajectories on the (a)–(c) vertical and (d)–(f) horizontal branches at times given in subcaptions. Densities for trajectories above (below) the 350-K isentropic level at t = 0 h in shading (red contours) every % 10−6 km−2. The densities are normalized such that the spatial integral yields 100% for each set of trajectories.

Fig. 5.

Spatial densities of trajectories on the (a)–(c) vertical and (d)–(f) horizontal branches at times given in subcaptions. Densities for trajectories above (below) the 350-K isentropic level at t = 0 h in shading (red contours) every % 10−6 km−2. The densities are normalized such that the spatial integral yields 100% for each set of trajectories.

Fig. 6.

Temporal evolution of (a),(f) height; (b),(g) specific humidity; (c),(h) potential temperature; (d),(i) cloud fraction; and (e),(j) PV anomaly along trajectories on the (left) vertical and (right) horizontal branch. Evolution for trajectories above (below) the 350-K isentropic level at t = 0 h in gray (black). Whiskers give the 25th and 75th percentile, respectively.

Fig. 6.

Temporal evolution of (a),(f) height; (b),(g) specific humidity; (c),(h) potential temperature; (d),(i) cloud fraction; and (e),(j) PV anomaly along trajectories on the (left) vertical and (right) horizontal branch. Evolution for trajectories above (below) the 350-K isentropic level at t = 0 h in gray (black). Whiskers give the 25th and 75th percentile, respectively.

In contrast, trajectories lying on the vertical and horizontal branches, but not reaching the 350-K isentropic level at t = 0 h, reach the anticyclones over Australia along very different pathways. At t = −216 h, most trajectories on the vertical branch are located in the low- to midtroposphere (black in Fig. 6a) between South Africa and eastern Australia (red contours in Fig. 5a), whereas those on the horizontal branch are located in the mid- to upper troposphere (black in Fig. 6f) over the South Atlantic and the western south Indian Ocean (red contours in Fig. 5d). The trajectory density on the vertical branch is locally highest over the western half of Australia. This local maximum in the trajectory density increases considerably over the next three days such that the largest fraction of the trajectories on the vertical branch is located over Australia already 144 h prior to the arrival in the anticyclone (Fig. 5b). The trajectories on the horizontal branch are located between South Africa and Australia, too, although the locally highest density occurs over the western south Indian Ocean (Fig. 5e). Though the trajectories on the horizontal branch are cooled between t = −72 and t = 0 h by definition, an additional analysis reveals that between t = −144 and t = −72 h a large fraction of these trajectories are actually heated diabatically (not shown). The median trajectory of these diabatically heated trajectories ascends from 700 to 450 hPa, the potential temperature increases by more than 10 K, and the specific humidity decreases from 4 to 1 g kg−1. This clearly indicates that the ascent can at least be partially attributed to cloud-diabatic processes over the western south Indian Ocean.

At t = −72 h, the spatial distributions of the two branches form a strong dipole over the south Indian Ocean and Australia. Although the trajectories on the vertical branch lie mostly over western and central Australia (Fig. 5c), the horizontal branch trajectories are mainly located over the south Indian Ocean (Fig. 5f). That the trajectories on the horizontal branch are located farther upstream indicates a rapid eastward advection of these air parcels by the midlatitude jet during the final 72 h. By definition, the trajectories on the vertical branch ascend poleward into the upper-level anticyclone in the next 72 h (black in Fig. 6a).

In summary, three main trajectory pathways are identified. The trajectories on both branches reaching above the 350-K isentropic level at t = 0 h are initially located in the upper troposphere of the tropics. The trajectories on the vertical branch that do not reach the 350-K isentropic level start in the lower to midtroposphere over Australia and the south Indian Ocean. These trajectories aggregate over the Australian continent before ascending into the upper-level anticyclone. In contrast, the horizontal branch comprises trajectories from the mid- to upper troposphere over the South Atlantic and south Indian Ocean that are advected rapidly eastward with the midlatitude jet.

The differences between the vertical and horizontal branches are clearly reflected in the physical properties along the trajectories. The trajectories forming the vertical branch generally remain in the lower half of the troposphere prior to t = −72 h (black in Fig. 6a). About 50% percent of the trajectories are located in the 800–500-hPa layer. The median pressure along the trajectories indicates weak descent from t = −240 to t = −96 h. This descent, together with the spatial evolution depicted in Figs. 5a–c, suggests that the trajectories mainly descend over the Australian continent before they start ascending into the upper-tropospheric anticyclone. While descending, the median specific humidity along the trajectories increases from about 1.5 to 3 g kg−1 (black in Fig. 6b), implying that some of the air parcels are moistened by the environment. This moistening occurs mainly along those parcels that are located below 600 hPa (not shown).

That the vertical branch trajectories remain in the lower to midtroposphere for several days indicates that any forcing mechanisms for ascent are initially missing. During the final 96 h the median trajectory then ascends from about 600 to 400 hPa (black in Fig. 6a). The ascent is accompanied by a decrease in specific humidity to about 0.5 g kg−1 (black in Fig. 6b). The reduction in specific humidity, the simultaneous increase in potential temperature (black in Fig. 6c), and an increase of the percentage of trajectories inside clouds1 (black in Fig. 6d) imply diabatic heating through latent heat release. At t = −48 h, the region of heating is over southern Australia and the Great Australian Bight (Fig. 7a). Composites of the cloud liquid water path and cloud ice water path reveal anomalously high values in the same region (Figs. 7b,c), indicating that the latent heating may be due to both condensation and deposition. A detailed analysis of the cloud microphysical processes is beyond the scope of this study. The region of latent heating as well as the anomalously high cloud liquid- and cloud ice water paths coincide with enhanced rainfall in this region during and before southeastern Australian heat waves as documented in previous studies (see Fig. 6 in Parker et al. 2014a). The forcing for this ascent is potentially provided by an approaching midlatitude trough that typically occurs prior to heat waves over western Australia (black contours in Fig. 2b; Parker et al. 2014a). In addition, the heating occurs along a midlatitude baroclinic zone (black contours in Fig. 7b) indicating slantwise ascent and highlighting the importance of midlatitude synoptic-scale processes during the evolution of southeastern Australian heat waves.

Fig. 7.

(a) Spatial density (black contours every % 10−6 km−2) and mean potential temperature change [K (day)−1] of trajectories on the vertical branch at t = −24 h. Anomalies of (b) cloud liquid and (c) ice water path relative to climatology (shading in g m−2), composite mean of (b) cloud liquid and (c) ice water path (stippled where greater than 100 and 50 g m−2, respectively, and (b),(c) 850-hPa potential temperature (black contours every 5 K) at t = −24 h.

Fig. 7.

(a) Spatial density (black contours every % 10−6 km−2) and mean potential temperature change [K (day)−1] of trajectories on the vertical branch at t = −24 h. Anomalies of (b) cloud liquid and (c) ice water path relative to climatology (shading in g m−2), composite mean of (b) cloud liquid and (c) ice water path (stippled where greater than 100 and 50 g m−2, respectively, and (b),(c) 850-hPa potential temperature (black contours every 5 K) at t = −24 h.

The trajectories lying on the horizontal branch and residing below 350 K start typically at higher levels as indicated by the initially lower pressure (black in Fig. 6f), lower specific humidity (black in Fig. 6g), and higher potential temperature (black in Fig. 6j). Only minor changes in these quantities occur along the trajectories. A slight decrease in potential temperature during the final 96 h indicates diabatic cooling accompanied by relatively weak descent. A closer analysis of this potentially radiative cooling is beyond the scope of this study.

The height, specific humidity, and potential temperature evolution of the trajectories contributing either to the vertical or horizontal branch that reach above 350 K are very similar. The majority of trajectories are initially located in the upper troposphere as shown by an initial median pressure of 250 hPa (gray in Figs. 6a,f). A decrease of the median pressure to 150 hPa before t = −72 h is accompanied by a decrease in specific humidity (gray in Figs. 6b,g) and an increase in potential temperature (gray in Figs. 6c,h) indicating diabatic ascent. The trajectories that reach the 350-K isentropic level exhibit a much larger PV anomaly at t = 0 h than the rest of the trajectories (Figs. 6e,j). This larger PV anomaly is due to the predominantly adiabatic transport of relatively high-PV air into regions with climatologically much lower PV at this high isentropic level.

c. Sensitivity of results to the definition of the branches

The horizontal and vertical branches of the joint frequency distribution (Fig. 4) are defined, respectively, as the subset of trajectories for which is either negative or positive. Despite the physical association of the two branches with diabatic cooling and diabatic warming, splitting the distribution into two parts along the line = 0 is to some degree arbitrary and leaves open the possibility that the trajectories close to (in some undefined sense) = 0 should belong to a separate adiabatic subset. The sensitivity of the results to this choice is now investigated.

To test the sensitivity, the frequency distribution is partitioned into three subsets defined by , , and , which are the horizontal, adiabatic, and vertical branches, respectively; is allowed to vary between 0.5 and 3.0 K in 0.5-K increments. For a given the fraction of trajectories in each branch is listed in Table 2. The main point is that, although the fractions of trajectories in the horizontal and vertical branches decrease with increasing (as expected), the fractions remain substantial. For example, with K, 30% of the trajectories still lie on the vertical branch compared to 43.9% when K. Moreover, as shown in Fig. 8, the spatial distributions of the trajectories for the horizontal and vertical branches at t = −72 h for three different values of are almost identical to each other and Figs. 5c and 5e. Hence, the results reported here are insensitive to the details of how the frequency distribution is divided.

Table 2.

Percentage of trajectories in the horizontal and vertical branch of the distribution for different values of . The horizontal, adiabatic, and vertical branches are defined by , , and , respectively.

Percentage of trajectories in the horizontal and vertical branch of the distribution for different values of . The horizontal, adiabatic, and vertical branches are defined by , , and , respectively.
Percentage of trajectories in the horizontal and vertical branch of the distribution for different values of . The horizontal, adiabatic, and vertical branches are defined by , , and , respectively.
Fig. 8.

Spatial densities of trajectories on the (a)–(c) vertical and (d)–(f) horizontal branches at t = −72 h for different values of as given in subcaptions. Densities for trajectories above (below) the 350-K isentropic level at t = 0 h in shading (red contours) every % 10−6 km−2. The densities are normalized such that the spatial integral yields 100% for each set of trajectories.

Fig. 8.

Spatial densities of trajectories on the (a)–(c) vertical and (d)–(f) horizontal branches at t = −72 h for different values of as given in subcaptions. Densities for trajectories above (below) the 350-K isentropic level at t = 0 h in shading (red contours) every % 10−6 km−2. The densities are normalized such that the spatial integral yields 100% for each set of trajectories.

4. Air masses at the surface during heat waves

The Lagrangian analysis presented above shows that the transport of diabatically cooled air masses and cloud-diabatic processes along a baroclinic zone over the Great Australian Bight work in concert during the evolution of the upper-tropospheric anticyclone. A widely accepted paradigm is that the upper-level anticyclone induces a strong low-level northwesterly flow on its western flank that simply advects hot air masses from inner-continental Australia leading to anomalously high temperatures in southeastern Australia. However, there are multiple processes that may contribute to the anomalously high temperatures such as warming through adiabatic descent in the anticyclone or diabatic heating in and above the planetary boundary layer. To better understand the processes that lead to anomalously high temperatures at the surface, we analyze the history of the air masses close to the surface and contrast the roles of diabatic and adiabatic processes in producing the anomalously high temperatures. The analysis is based on a set of about 14 000 (in total) 240-h backward trajectories starting 10, 30, and 50 hPa above the surface during southeastern Australian heat waves (see section 2c).

a. Pathway of air masses

The key finding of this analysis is that the hot air masses during southeastern Australian heat waves do not usually originate from the inner Australian continent. Instead, air masses that arrive near the surface during southeastern Australian heat waves are initially located over the south Indian Ocean and the Tasman Sea (black contours in Fig. 9a). At t = −216 h, trajectories over the south Indian Ocean lie on average between 700 and 800 hPa (shading in Fig. 9a). Thus, they must descend by definition to reach the lowest 50 hPa of the troposphere at the time of the heat wave. Likewise, trajectories over the Tasman Sea must descend as they are located between 800 and 900 hPa at t = −216 h. The trajectory density increases over the Great Australian Bight and over the Tasman Sea until t = −144 h (Fig. 9b). The increase of the average pressure implies descent, particularly over the Tasman Sea where the average pressure increases to more than 900 hPa. At t = −72 h, the trajectories are mainly located over the Tasman Sea and over southeastern Australia (Fig. 9c), after which time the trajectories continue to descend over southeastern Australia until t = 0 h.

Fig. 9.

As in Fig. 3, but for trajectories that arrive close to the surface at t = 0 h. Note the different color spacing compared to Fig. 3. Contour levels are 4%, 8%, 12%, 16%, 20%, and 24% 10−6 km−2.

Fig. 9.

As in Fig. 3, but for trajectories that arrive close to the surface at t = 0 h. Note the different color spacing compared to Fig. 3. Contour levels are 4%, 8%, 12%, 16%, 20%, and 24% 10−6 km−2.

b. Contrasting the role of diabatic and adiabatic processes

Physically, the near-surface air masses can warm either through adiabatic compression as they descend in the anticyclone or diabatically, through sensible, condensational, and radiative heating. In this section, we estimate the diabatic and adiabatic contribution to the temperature change by tracking the potential temperature and temperature along the trajectories.

Air masses that arrive close to the surface during heat waves descend considerably (Fig. 10a). The median pressure increases from about 780 to 940 hPa between t = −240 and t = −72 h. This descent warms the air mass adiabatically as indicated by constant potential temperature (Fig. 10b) and an increase in temperature (Fig. 10c). The median temperature along the trajectories increases from 273 to 288 K between t = −240 and t = −72 h. The nearly constant potential temperature implies that diabatic processes play a negligible role until t = −72 h.

Fig. 10.

Temporal evolution of (a) height, (b) potential temperature, and (c) temperature along trajectories that arrive close to the surface at t = 0 h. Whiskers give the 25th and 75th percentile, respectively.

Fig. 10.

Temporal evolution of (a) height, (b) potential temperature, and (c) temperature along trajectories that arrive close to the surface at t = 0 h. Whiskers give the 25th and 75th percentile, respectively.

During the final 72 h, the median temperature along the trajectories increases rapidly to nearly 303 K (Fig. 10c). This temperature increase is mainly due to diabatic processes as indicated by a rapid increase of potential temperature by about 10 K (Fig. 10b). The rapid diabatic heating occurs when the majority of trajectories are no longer over the Tasman Sea, but over southeastern Australia. Composites of ERA-Interim surface sensible heat fluxes reveal that the fluxes are directed upward over the entire continent (i.e., they heat the atmosphere) during the final 48 h (green contours in Fig. 11a). At t = −48 h, the trajectories are located over eastern Australia (black contours in Fig. 11a) in a region of anomalous upward surface sensible heat flux (shading in Fig. 11a), suggesting that the diabatic heating along the trajectories can be linked to upward surface sensible heat fluxes over eastern Australia. The anomalous surface sensible heat flux in that region intensifies until t = 0 h (Fig. 11b). It is likely, however, that the increase has only a minor effect on the near-surface trajectories since most of them reach southeastern Australia where the surface sensible heat flux is anomalously low. The region of anomalously low surface sensible heat flux extends from Western Australia toward Tasmania and, hence, is aligned with the positive anomalies in cloud ice and liquid water content. Presumably the clouds related to the ascent along the baroclinic zone reduce the solar insolation at the surface and weaken the heating of the overlying atmosphere compared to climatology. Of course, the net surface sensible heat fluxes are still directed upward leading to a heating of the overlying air mass. Another possibility is that the anomalously low sensible heat fluxes may be due to a lower contrast between the skin temperature and the temperature of the overlying air mass during southeastern Australian heat waves. This possibility is unlikely as the composite difference between skin temperature and the 2-m air temperature during heat waves differs by less than 0.5 K from the climatological mean (not shown).

Fig. 11.

Spatial density of trajectories that arrive close to the surface at t = 0 h (black contours at 10%, 30%, 50%, 70%, 90%, and 120% 10−6 km−2), anomalies of surface sensible heat flux (shading in W m−2), and average surface sensible heat flux during southeastern Australian heat waves (green contours in W m−2) at times given in subcaptions.

Fig. 11.

Spatial density of trajectories that arrive close to the surface at t = 0 h (black contours at 10%, 30%, 50%, 70%, 90%, and 120% 10−6 km−2), anomalies of surface sensible heat flux (shading in W m−2), and average surface sensible heat flux during southeastern Australian heat waves (green contours in W m−2) at times given in subcaptions.

5. Conclusions and outlook

This study is the first to systematically analyze the pathway of air masses involved in 32 southeastern Australian heat waves in the period DJF 1989–2009. First, we analyzed 10-day backward trajectories that ended in upper-tropospheric anticyclones between 120°E and 180° during heat waves.

The analysis identifies the subtropics and midlatitudes between South America to Australia as source regions of air masses 10 days prior to the heat wave. About 44% of all trajectories in the upper-tropospheric anticyclone are heated diabatically during the final 72 h. These trajectories ascend ahead of an upper-level trough and over a midlatitude baroclinic zone (green contours in Fig. 12) to the south of the Australian continent (label 1 in Fig. 12). This highlights the importance of midlatitude cloud-diabatic processes for the evolution of the upper-level anticyclone. South of Australia and over the south Indian Ocean, trajectories aggregate in the lower troposphere over several days before they start ascending into the upper-tropospheric anticyclone. This trajectory aggregation is accompanied by weak descent suggesting that air is being circulated in anticyclones over the Indian Ocean and over Australia. The simultaneous increase in specific humidity implies that some of the parcels are moistened by the environment. This moistening, primarily along trajectories in the lower troposphere, indicates shallow convection or surface evaporation as potential sources of moisture. Hence, positive sea surface temperature anomalies or enhanced soil moisture may cause an additional moistening of the air parcels before they ascend diabatically into the upper-level anticyclone during the final 72 h. Since these trajectories comprise 44% of all trajectories in the upper-level anticyclone, the enhanced initial moisture may lead to stronger upper-level anticyclones due to enhanced latent heat release. This would corroborate the findings of Kala et al. (2015) who found that increased soil moisture over the Australian continent lead to a strengthened midtropospheric anticyclone over the Great Australian Bight and Tasmania. Interestingly, this stands in contrast to the central European heat wave in 2003 where anomalously dry soils amplified the upper-level anticyclone (Fischer et al. 2007). A future study could use the trajectories of this study to identify regions of moistening and perform sensitivity experiments with changed soil moisture conditions or changed sea surface temperature in the regions of moistening. This physical approach could help to assess the poorly understood causality between regional sea surface temperature anomalies and southeastern Australian heat waves (Purich et al. 2014; Boschat et al. 2016).

Fig. 12.

Sketch of Lagrangian pathways of air masses that are typically involved in the formation of southeastern Australian heat waves. Trajectories are colored by pressure where reddish colors indicate low levels. Green contours show the low-level potential temperature field and the blue (red) cone denotes upper-level negative (positive) PV anomaly. See section 5 for details.

Fig. 12.

Sketch of Lagrangian pathways of air masses that are typically involved in the formation of southeastern Australian heat waves. Trajectories are colored by pressure where reddish colors indicate low levels. Green contours show the low-level potential temperature field and the blue (red) cone denotes upper-level negative (positive) PV anomaly. See section 5 for details.

That 44% of the trajectories are processed diabatically during the 72 h prior to reaching the location of the upper-level anticyclone at t = 0 h corroborates the findings of Pfahl et al. (2015) who found similar results for the formation of atmospheric blocking anticyclones in the Northern Hemisphere. The importance of diabatic processes reveals that climate models with a coarse resolution may not adequately represent the structure of upper-level anticyclones during heat waves. Hence, future studies could investigate the effect of numerical model resolution and the role of convective parameterizations on the representation of the heat waves over Australia.

The remaining 56% of all trajectories are cooled diabatically during the final 72 h. Although the majority of the trajectories are cooled diabatically between t = −72 and t = 0 h, the net effect of all trajectories is a heating. This is due to the strong diabatic heating along the trajectories on the vertical branch. Prior to being cooled, a large fraction of the trajectories on the horizontal branch are actually heated diabatically while ascending over the western south Indian Ocean (label 2 in Fig. 12). This region is climatologically characterized by high frequencies of WCBs [Figs. 4 and 5 in Madonna et al. (2014)]. Although we do not quantify the fraction of WCB trajectories in our dataset, the results suggest that WCBs in remote regions contribute to the formation of upper-level anticyclonic PV anomalies that are then advected with the midlatitude jet (label 3 in Fig. 12) into the anticyclones in the Australian region. Parker et al. (2013) showed this advection of air masses from the western south Indian Ocean into an anticyclone over Australia in a case study of the Pre–Black Saturday heat wave (their Fig. 2a). A detailed analysis of the relation between WCBs over the western south Indian Ocean and Australian heat waves is left for future work. Trajectories that are located above the 350-K isentropic level at t = 0 h stem from tropical latitudes (label 4 in Fig. 12). These trajectories exhibit the strongest PV anomalies at t = 0 h, as they end up in regions of climatologically low-PV air.

A widely accepted paradigm is that the upper-level anticyclone induces a strong low-level northerly flow on its western flank, which simply advects hot air masses from inner-continental Australia into southeastern Australia. The pathway of these near-surface air masses (i.e., those air masses that actually produce the heat wave) is analyzed with a second set of trajectories. The key finding of the near-surface trajectory analysis is that southeastern Australian heat waves do not result from the transport of air masses from the inner continent into the affected region. This is a marked contrast to the widely accepted view derived from Eulerian fields that low-level northerly winds induced by the upper-level anticyclone simply advect hot inner-continental air to southeastern Australia. Instead, and this is consistent with an analysis of 14 selected heat waves by Boschat et al. (2015), the trajectories reaching southeastern Australia during heat waves are initially located over the midlatitude south Indian Ocean and the Tasman Sea (label 5 in Fig. 12). Until 72 h prior to the heat wave the trajectories descend adiabatically and aggregate in the anticyclone over the Tasman Sea (label 6 in Fig. 12). The adiabatic descent is associated with a temperature increase of more than 15 K. A large fraction of trajectories that lead to the anomalously high temperatures reach eastern Australia at about t = −72 h. Although the spatial distribution of the trajectories during the final 72 h indicates a northeasterly flow (Fig. 11), the most extreme temperatures still occur in a northwesterly flow, which is consistent with previous studies (e.g., Engel et al. 2013; Parker et al. 2014a). For example, 70% of the trajectories during the upper-decile heat waves in Melbourne are located northwest of Melbourne at t = −12 h (not shown).

The adiabatic warming until t = −72 h does not by itself explain the anomalous near-surface temperatures. Once the trajectories reach the Australian continent, air parcels are heated diabatically. The temperature along the trajectories increases rapidly by about 10 K in a region of upward directed surface sensible heat fluxes. These are anomalously high over eastern Australia (label 7 in Fig. 12). The anomalous surface sensible heat fluxes may be due to reduced soil moisture that typically reduces evaporative cooling through latent heat fluxes and increases atmospheric heating from sensible heat fluxes (e.g., Mueller and Seneviratne 2012). Since the diabatic heating occurs mainly over eastern and southeastern Australia the direct effect of soil moisture conditions on the near-surface air parcels is potentially limited to this region. That low-level diabatic heating increases the likelihood for heat wave conditions corroborates findings of previous studies (e.g., Fischer et al. 2007; Quesada et al. 2012; Miralles et al. 2014; Perkins et al. 2015). However, the combination of anomalously low fluxes in southeastern Australia and anomalously high fluxes in remote regions indicates that the local soil moisture may not be so important for heat wave conditions. Rather, it may be the transport of air masses heated over anomalously dry soils in remote regions into southeastern Australia that causes the high temperatures. Sensitivity experiments would further elucidate the effect of local and remote soil moisture anomalies on southeastern Australian heat waves. Overall, the analysis of the near-surface trajectories during southeastern Australian heat waves highlights the importance of adiabatic and diabatic processes working in concert to produce anomalously high temperatures.

Although this study sheds light on the dynamics of southeastern Australian heat waves, future studies could investigate how often the identified features exist and a heat wave does not occur. This might be particularly helpful to operational forecasters in southeastern Australia. Also, it would be intriguing to see how the dynamics of extremely hot days that are not part of a heat wave differ from those investigated in this study.

Acknowledgments

JFQ has been supported by the Australian Research Council Centre of Excellence for Climate System Science (CE110001028). We thank Australia’s National Computational Infrastructure and ECMWF for providing access to the ERA-Interim data. Inspiring discussions with Christian Grams and the helpful comments of three reviewers are gratefully acknowledged.

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Footnotes

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1

The percentage of trajectories inside clouds is based on the traced cloud ice and liquid water content. Whenever the cloud ice or liquid water content is positive, we assume that the considered air mass is inside clouds.