Tropical influence on heat-generating atmospheric circulation over 1 Australia strengthens through spring 2

10 Extreme maximum temperatures during Australian spring can have deleterious impacts on a 11 range of sectors from health to wine grapes to planning for wildfires but are relatively 12 understudied compared to spring rainfall. Spring maximum temperatures in Australia have 13 been rising over recent decades and it is important to understand how Australian spring 14 maximum temperatures develop in the present and warming climate . Australia’s climate is 15 influenced by variability in the tropics and extratropics, but some of this influence impacts 16 Australia differently from winter to summer, and, consequently, may have different impacts 17 on Australia as spring evolves. Using linear regression analysis, this paper explores the 18 atmospheric dynamics and remote drivers of high maximum temperatures over the 19 individual months of spring. We find that the drivers of early spring maximum temperatures 20 in Australia are more closely related to low-level wind changes, which in turn are more 21 related to the Southern Annular Mode than variability in the tropics. By late spring, 22 Australia’s maximum temperatures are proportionally more related to warming through 23 subsidence than low-level wind changes, and more closely related to tropical variability. This 24 increased relationship with the tropical variability is linked with the breakdown of the 25 subtropical jet through spring and an associated change in tropically-forced Rossby wave 26 teleconnections. An improved understanding of how the extratropics and tropics project 27 onto the mechanisms that drive high maximum temperatures through spring may lead to 28 improved sub-seasonal prediction of high temperatures in the future. 29


Introduction
Anomalously high Australian spring (September-October-November) maximum temperatures can be highly impactful.High temperatures may negatively impact health due to a lack of acclimatisation (e.g.Nairn and Fawcett, 2014), and agriculture by changing growing season length and crop yields (Cullen et al., 2009;Jarvis et al., 2019;Taylor et al., 2018).Hotter and drier spring conditions have been linked to an earlier start to (Dowdy, 2018) and preconditioning of (Abram et al., 2021) the summer fire season.Several recent springs exceeded historic temperature records, with some spring months breaking records set only the previous year (Arblaster et al., 2014;Gallant and Lewis, 2016;Hope et al., 2015;McKay et al., 2021).Much of this observed anomalous heat has been attributed to the background global warming trend (Arblaster et al., 2014;Gallant and Lewis, 2016;Hope et al., 2015;Hope et al., 2016).However, gaps remain in our understanding of the atmospheric mechanisms driving anomalous high maximum temperatures in Australia during spring, and particularly on the monthly timescale that some of these heat events occurred over.
High spring temperatures have been linked with several remote modes of variability in the tropics and extratropics.The negative phase of the Southern Annular Mode (SAM), and its associated equatorward shift of the eddy-driven jet, the positive phases of El Niño Southern Oscillation (ENSO) in the tropical Pacific and the Indian Ocean Dipole (IOD) in the tropical Indian Oceans are the strongest drivers of high spring maximum temperatures in centralsouthern Australia (Power et al., 1998;Jones and Trewin, 2000;Saji et al., 2005;Hendon et al., 2007;2014;Min et al., 2013;White et al., 2014;Fogt and Marshall, 2020).Many more studies focus on the relationships between remote drivers of Australian spring rainfall variability (e.g.Nicholls et al., 1989;Meyers et al., 2007;Ummenhofer et al., 2009;Risbey et al., 2009a;Watterson, 2010;2020;Cai et al., 2011;Min et al., 2013;Pepler et al., 2014;McIntosh and Hendon, 2018) or extreme spring fire weather (Harris and Lucas, 2019;Marshall et al., 2021).Other climate drivers may also promote anomalous high spring maximum temperatures in Australia, including the Madden-Julian Oscillation (MJO; e.g.Wheeler and Hendon, 2004;Wheeler et al., 2009;Marshall et al., 2014).Further, ENSO and the IOD co-vary strongly in austral spring (e.g.Meyers et al., 2007).As such, it can be useful to look at a single index that combines tropical SST variability, such as the tropical tripole index (TPI; Timbal and Hendon, 2011).Here, we use the SAM and tropical TPI to represent the extratropical and tropical influences on Australian heat respectively.
The drivers of anomalous maximum temperatures may vary on a sub-seasonal timescale through spring.The IOD's influence on Australia's temperature peaks around SON (Saji et al., 2005) compared to around NDJ (November-December-January) for ENSO (Jones and Trewin, 2000).The influence of SAM on maximum temperature changes from winter to spring, with the positive phase of SAM associated with warmer conditions across much of Australia during winter and cooler in spring (Hendon et al., 2007;Marshall et al., 2012;Min et al., 2013;Fogt et al., 2020).The climatological westerly winds over extratropical Australia shift poleward between winter to summer (e.g.Hendon et al., 2007).Further, the relationship between anomalously high geopotential height (or, synonymously, anticyclonic vorticity) over southern Australia and high spring maximum temperatures (Hope et al., 2015;Gallant and Lewis, 2016) is strongest later in spring (McKay et al., 2021).An ENSO-IOD induced Rossby wave train from the tropical Indian Ocean promotes anomalous high geopotential height south of Australia but follows different pathways from winter to spring (Cai et al., 2011;McIntosh & Hendon, 2018).These season-scale differences suggest that heat may form differently as spring evolves.As SAM, ENSO, and the IOD can only nudge spring conditions toward hotter temperatures (e.g.Hurrell et al., 2009) there is a gap in understanding spring heat, particularly on a monthly timescale.
The Indo-Pacific region subtropical jet (STJ) in the Southern Hemisphere may contribute to sub-seasonal atmospheric circulation changes through spring.The STJ is linked with SAM climate-impacts (e.g.Hendon et al., 2014) and with influencing and preventing Rossby wave propagation from the tropical Indian Ocean toward Australia (e.g.Hoskins and Ambrizzi, 1993;Simpkins et al., 2014;Li et al., 2014;2015a,b;McIntosh & Hendon, 2018;Gillet et al., in review).As the STJ decays through austral spring from its winter peak (Bals-Elsholz et al., 2001;Koch et al., 2006;Ceppi and Hartmann, 2013;Gillett et al., 2021), it may alter the teleconnection pathways from the extratropics and tropics to Australia, influencing local atmospheric circulation and maximum temperature formation as a result.
Atmospheric circulation can enhance spring heat through several mechanisms.Warmer and drier conditions can occur as a result of deflected cooling rain-bearing systems (e.g.Jones and Trewin 2000;Hendon et al., 2007;Pepler et al., 2014;van Rensch et al., 2019) away from Australia (Cai et al., 2011;Risbey et al., 2009b;McIntosh and Hendon, 2018;Hauser et al., 2020).Low rainfall correlates with high maximum temperatures (Simmonds, 1998;Jones and Trewin, 2000;Timbal et al., 2002;Hope and Watterson, 2018), and antecedent dry conditions have been found to contribute to anomalous spring heat (Arblaster et al., 2014) or heat waves (e.g.Fischer et al., 2007;Hirsch et al., 2019;Loughran et al., 2019;Hirsch & King, 2020).Anomalous heat is also associated with increased subsidence and insolation (Hendon et al., 2014;Lim et al., 2019b;Pfahl et al., 2015;Quinting and Reeder, 2017;Suarez-Gutierrez et al., 2020) or heat advection (Jones and Trewin, 2000;Boschat et al., 2015;Gibson et al., 2017).While land-surface feedbacks are important for heat formation we focus on the dynamical mechanisms that generate high spring maximum temperatures.This study will address the influence of atmospheric processes on how extreme maximum temperatures develop in Australia through spring.In particular, the relative influence of the extratropical and tropical drivers on a monthly timescale through spring will be explored.
Filling the gap between weather and seasonal time-scales is an ongoing area of research that can lead to improved sub-seasonal forecasting (Meehl et al., 2021).Given the increasing likelihood of future extreme heat events occurring through spring, it is imperative to understand how they develop now.
The remainder of the paper is structured as follows: The reanalysis datasets, Rossby wave and statistical analysis methods are described in Section 2. An overview of how Australian spring maximum temperatures are related to circulation and large-scale variability is in Section 3. How these relationships vary on a monthly timescale is assessed in Section 4 and how that relates to the subtropical jet is explored in Section 5. Section 6 describes how the drivers influence the mechanisms that promote high monthly maximum temperature.
Discussion and conclusions are provided in Section 7. Our focus is on understanding the atmospheric drivers of heat, although we include some discussion of land-surface feedbacks in Section 7.

Indices and datasets
All circulation variables for September, October, November monthly-averaged data are taken from the ECMWF's Reanalysis 5 (ERA5) (Hersbach et al., 2020) available from the Copernicus Climate Change Service (C3S, 2017) on a 0.25° grid.Here, we use data from 1979 to 2019.Low-level circulation is diagnosed using 850 hPa horizontal wind and mean sea level pressure (MSLP).Mid-tropospheric vertical motion is represented by 500 hPa velocity.
Upper-level circulation is represented by 200 hPa geopotential height (200Z).200 hPa horizontal winds are used for Rossby wave analysis.Similar results were found using ERA-Interim reanalysis (Dee et al, 2011) and the JRA-55 from the Japan Meteorological Agency (2013) (not shown).
Australian monthly-averaged daily maximum temperature data for 1979 to 2019 is taken from the Australian Water Availability Project (AWAP; Jones et al., 2009) analyses, available on a 0.05° resolution grid.
Monthly sea surface temperature (SST) is taken from NOAA Extended Reconstructed Sea Surface Temperature (ERRSST V5; Huang et al., 2017) The impact of SAM on Australia's climate shows some sensitivity to the method used to calculate the SAM index (e.g.Risbey et al., 2009a).To ensure consistency between the other indices and circulation variables, we calculate SAM as the difference between the standardized zonal means of ERA5 MSLP anomalies at 60°S and 40°S (Gong and Wang, 1999).
The tropical TPI (Timbal and Hendon, 2011) is defined as the difference in SST averaged over a parallelogram located over the Maritime Continent (0°-20S, 90°-140E at the equator shifted to 110°-160°E at 20°S) from SST averaged and summed over two regions in the tropical Indian Ocean (10°N to 20°S, 55° to 90°E) and tropical Pacific Ocean (a trapezium that extends from 15°N to 15°S, 150°E to 140°W in the north and 180°E to 140°W in the south).ENSO is described using the Niño3.4index (averaged SST anomalies over 5°N-5°S, 170°E-120°W) and the IOD using the dipole mode index (DMI; the difference between the SST anomalies averaged over 10°S-10°N, 50°-70°E and 10°S-0°, 90°-110°E; Saji et al., 1999).
To highlight the influence of interannual variability, the 1981-2010 climatological mean is removed from each month All data are linearly detrended before analysis.

Rossby wave analysis
We use wave activity flux (WAF) at 200 hPa to trace Rossby wave group propagation and to identify source and decay regions that influence the atmospheric circulation patterns.
Following Takaya and Nakamura (2001), we calculate WAF as: where  is the pressure (200 hPa) scaled against 1000 hPa,  and  are the climatological zonal and meridional wind speed magnitudes,  is the radius of the Earth, (, ) are latitude and longitude,  ′ =  ′ / is the quasi-geostrophic perturbation streamfunction,  ′ is the 200 hPa geopotential height anomaly obtained through regression onto maximum temperature or climate driver indices,  = 2 is the Coriolis parameter with the Earth's rotation .WAF is not plotted within 10° of the equator.
WAF is parallel to the direction of quasi-stationary Rossby wave group velocity, and regions of divergence or convergence of WAF correspond to zones of Rossby wave sources or sinks respectively.
Total stationary Rossby wave wavenumber (e.g., Hoskins and Karoly, 1981) is defined as: where  −   is the meridional gradient of mean-state absolute vorticity at 200 hPa.WAF should refract toward regions of higher KS and either reflect or evanesce on regions of KS<0, such as in the STJ where the curvature of the flow (  ) can become larger than the planetary vorticity gradient () (e.g Barnes and Hartmann, 2012;Li et al., 2015 a,b)

Statistical analysis
Linear, partial, and multi-linear regression and Spearman's ranked correlation are used to assess the relationships between Australian maximum temperature, atmospheric circulation and the tropics and extratropics.Due to the large decorrelation length scales, Australianaverage maximum temperature variability is representative of all but far north Australia's spring and spring-monthly maximum temperatures (Sup.Fig. 1).Statistical significance is calculated at the 95% confidence level using Student's (1908) t-test using 39 (41 years -2) degrees of freedom.Pattern correlation is used to compare regression patterns.

Spring-season maximum temperatures -circulation patterns and associations with drivers
We start by giving an overview of the spring-seasonal relationships between average Australian austral spring maximum temperature and lower-and upper-level atmospheric circulation (Fig. 1a,b).Barotropic cyclones appear southwest and southeast of Australia, occurring in both the lower-and upper-level circulation regressions (Fig. 1a-b), as noted during recent extreme spring heat events (Gallant and Lewis, 2016;Hope et al., 2016;McKay et al., 2021).Weak anomalous anticyclonic low-level winds are found over Australia, as well as sinking motion across the eastern half of the continent.An upper-level anticyclone sits over southern Australia, with the wave activity flux indicating Rossby wave propagation predominantly from the subtropical Indian Ocean, through the anticyclone, and into the subtropical Pacific Ocean.
We now compare the atmospheric patterns associated with spring maximum temperature to those calculated via linear regression onto each standardised climate driver index.Note that the TPI and SAM indices have been multiplied by negative one to present positive associations with high temperatures.The pattern for SAM (x-1) shows elongated barotropic low and high anomalies lie in the middle and high latitudes respectively (Fig. 1c-d), with upper-level cyclonic nodes to the southeast and southwest of Australia.Negative SAM is associated with high maximum temperatures through much of subtropical, and particularly eastern, Australia (Fig. 1e).Low-level circulation is represented by anomalous mean sea level pressure (hPa) (black and filled contours), 850 hPa wind vectors (ms -1 ) and 500 hPa omega (hPas -1 ) contours from -0.02 to 0.02 hPas -1 in steps of 0.01 hPas -1 (magenta contours are positive; downward motion) and cyan contours are negative; upward motion, and the zero contour is not plotted).Upper-level circulation is represented by 200 hPa geopotential height (black and filled contours and wave activity flux vectors (m 2 s -2 ).Filled contours, bold wind vectors, cross-hatching, and all vertical motion contours are significant at the 95% confidence level using a Student's t-test with 39 independent samples.Hendon, 2018).The tropical TPI (x-1) is a blend of both Niño3.4 and DMI circulation patterns and has a strong relationship with Australian spring maximum temperatures across all but northern Australia.Each tropical regression also shares anomalous high surface pressure over Australia, sinking motion in the east, cyclonic nodes to the southwest and east of Australia, and elongated upper-level cyclones in the subtropical Indian Ocean.These similarities are likely the result of the strong co-variability between the IOD and ENSO (e.g.Meyers et al., 2007;Risbey et al., 2009a).However, the IOD has a stronger low-level cyclone to the southeast and a poleward extension of the subtropical Indian Ocean cyclone that sets a subtly different wave train from around 50°S, 60°E that is poleward of that generated by ENSO.The positive IOD is also associated with high maximum temperatures across a broader region of southern and western Australian than is El Niño.
Given the similarities and connections between ENSO and IOD teleconnections, we use the tropical TPI to represent the large-scale influence of the tropics.SAM is used to represent the influence of the extratropics.Statistical models of Australian weighted area-averaged spring maximum temperatures reconstructed through multilinear regression using either Niño3.4,DMI and, SAM or the tropical TPI and SAM as the predictors explain similar levels of maximum temperature variability (32% and 34% respectively; Sup.Fig. 2).
We next compare the atmospheric circulation associated with spring monthly high maximum temperatures to that with the large-scale modes of variability.To ensure that we are assessing the influence of the tropics and extratropics separately, we use multi-linear regression onto the monthly circulation variables.

Monthly circulation patterns and associations with drivers
The regression of monthly Australian maximum temperature onto the lower-and upperlevel atmospheric circulation is displayed in Figures 2a-c 2c) also contributes to the anomalous northerly flow over eastern Australia in November in particular (Fig. 2c).Tasman Sea anticyclonic blocking patterns have previously been linked to anomalously warm conditions (Marshall et al., 2014), but here appear to only contribute to high maximum temperatures in November.The SWC and SEC vary in geographic shape and strength through the months.The SWC dominates in September but weakens through October and November, whereas the SEC is temperatures.However, the SAM and TPI (x-1) anticyclones are weaker and too far east relative to that associated with high maximum temperatures, such that they may not contribute strongly to the SAA formation.We explore this idea further in section 6.
While the southern Australian anticyclone is not well explained by SAM or TPI (x-1) through spring, much of the statistically significant 500 hPa vertical motion associated high maximum temperatures (green and magenta contours, Fig. 2a-c) matches that associated with TPI (Fig. 2h-j) and to a lesser extent SAM (Fig. 2d-f).In September, sinking motion over subtropical Australia and rising motion over the southern coasts is associated with high maximum temperatures.By November, the rising motion has largely vanished, and the sinking motion has shifted to be over eastern Australia.It was expected that the SAA would generate some of the sinking motion associated with high maximum temperature, however, this vertical motion does not correlate strongly with any of the key circulation features examined here (Sup.Table1).
Changes in wave activity flux help explain some of the changes in the broad scale circulation changes through spring.In September, WAF predominantly diverges from the southwest cyclone toward the southern Australian anticyclone.In October, a component of WAF also diverges from the eastern tropical Indian Ocean region.By November, the tropical- with the TPI, it does not appear to generate WAF that diverges into the extratropics.It is not until November that WAF associated with the TPI (x-1), and weakly with SAM (x-1), appears to diverge directly from the cyclone in the eastern subtropical Indian Ocean, indicating a wave that joins the anticyclone over southeastern Australia.
Overall, the circulation associated with maximum temperature appears to shift from extratropical to tropical forcing as spring progresses.SAM projects onto the atmospheric circulation associated with maximum temperatures in September, while the TPI projects more strongly later in spring.The change in WAF associated suggests that there may be a blocking mechanism between the tropics and extratropics generating this change.
We find qualitatively similar results if we perform the linear regressions using maximum temperature averaged over sub-regions of Australia, for example southwest or southeast Australia (Sup.Fig. S3).

Connection between subtropical jet and atmospheric circulation
We next explore how the subtropical jet (STJ) may be influencing the WAF through the spring months.
The STJ should effectively block direct propagation of Rossby waves from the tropical Indian Ocean into the extratropics (e.g.Simpkins et al., 2014;Li et al., 2014;2015a,b).However, the gradual decay of the jet through spring (e.g.see figure 9, Ceppi and Hartmann, 2013) may reduce its effectiveness as a Rossby wave block (e.g.Wirth, 2020), allowing more direct propagation into the extratropics by November.The STJ decay coincides with a decrease in the area with total stationary wavenumber (Ks) less than zero over southern Australia (Fig. 4).
The wave activity flux vectors from the maximum temperature, TPI and SAM (x-1) regressions in Fig. 3  As the jet weakens in October (Fig. 4b) a portion of WAF also diverges from the tropical Indian Ocean to dissipate on the jet's equatorward flank, but mostly propagates from west to east along the STJ waveguide.WAF in November (Fig. 4c) is even more distinctive in showing Rossby waves that propagate along the jet waveguide from a region near Africa, The STJ acts as a waveguide (Hoskins and Ambrizzi, 1993), with the majority of WAF associated with Australian maximum temperature, and with the tropics and extratropics We now look more closely into how the drivers, circulation features, and heat mechanisms relate to each other and how that results in higher Australian maximum temperatures.

Mechanisms and drivers of monthly maximum temperatures through spring
As with the atmospheric circulation regressions, the relationships between Australian maximum temperature and SAM and TPI (x-1) evolve through the spring months.In September, negative SAM (Fig. 5a) is associated with a broad area of high maximum temperature over subtropical Australia, that contracts in October and November (Figs. 5 bc).Conversely, the relationship with negative TPI and maximum temperature is weaker early in spring, with statistically significant high temperatures confined to the west and east, and cool temperatures in the far north in September (Fig. 5d).The TPI's relationship with high southwest Australia, or if using Niño3.4 or DMI as predictors instead of the tropical TPI (Sup. Fig. 4).
To explore how the atmospheric circulation relates to some of the mechanisms that develop heat through spring, we first compose indices of the key circulation features discussed in temperatures from these circulation features (Fig. 6a-c) explains consistently higher maximum temperature variance (around 60%) than did the model from the indices of tropical and extratropical large-scale modes of variability.Further, despite the changes in the features' geographic shape, strength, and position across the spring months in Fig .2, the majority of maximum temperature across Australia is well explained by at least one of these features at all times through spring (Sup.Fig. 5).We next explore how these MSLP or 200 hPa geopotential height features relate to the anomalous low-level westerly or northerly winds and vertical motion and how that relates to high maximum temperature development.
Figure 6.As in figure 4 (g-i), but using time series of key circulation features (south-west low, south-east low and southern Australian anticyclone) identified in figures 1 and 2 as predictors in the top row (a-c) and area-averaged dynamical heat mechanism components (850 hPa zonal wind and meridional wind (multiplied by -1) and 500 hPa vertical motion; see text for region averaged over) as predictors in the bottom row (d-e) for September, October, and November.
Following van Rensch et al (2019), indices of three dynamical heat mechanisms were created by weighted area-averaging of westerly and northerly wind (meridional wind multiplied by -1) anomalies over a region around southern Australia (25°S-45°S, 105°-155°E), and 500 hPa vertical motion anomalies (omega; positive is sinking motion) averaged over subtropical Australia (15°S-25°S, 120°-155°E).Regions were selected based on the areas of highest statistical significance between atmospheric circulation and Australian maximum temperature in Fig. 2a-c.A statistical model of Australian-averaged maximum temperatures that uses these mechanisms as the predictors explains a higher proportion of maximum temperature variance through spring than does the model using SAM or the tropical TPI (Fig. 6 d-e).The percent variance explained is higher in September (about 80%), before dropping to around 55% in October-November.This decrease appears to be primarily associated with how strongly the anomalous westerly winds correlate with maximum temperature over southern Australia; strong positive relationship with anomalous westerly wind in September changes to insignificant or negative in October and November (Sup.Fig

S6 a-c).
There is also an increase in negative correlation between maximum temperatures and anomalous northerly winds in north-eastern Australia (Sup.Fig S6 d-e) that will partly offset the increasing positive relationship further poleward.These changing relationships between dynamical mechanisms and maximum temperature through spring are linked with the changing relationships with the circulation features (Sup.Table 1).Overall, the three dynamical heat mechanisms explain much of Australia's monthly spring maximum temperature variability.

Discussion and conclusions
The sources of the atmospheric circulation patterns associated with high monthly-maximum temperatures in Australia appear to change from primarily extratropical in early spring to tropical in late spring.Examination of three dynamical heat mechanisms (anomalous lowlevel winds broken into westerly and northerly components, and anomalous midtropospheric sinking motion) indicates that this shift may be due to a change in how heat develops.In early spring, the low-level wind plays a greater role in maximum temperatures, advecting relatively warmer air from the oceans over the cold landmass.This wind correlates strongly with the extratropics (here, SAM), as SAM projects strongly onto the southwest and southeast cyclones that direct a lot of the low-level flow around Australia.
Conversely, the atmospheric circulation associated with the TPI (x-1) acts to counter the low-level flow that drives higher temperatures.Thus, in early spring we have a closer association with heat production and the extratropics.By late spring, the circulation patterns associated with high temperature have changed and the wind does not correlate as strongly.As such adiabatic sinking over subtropical Australia has a proportionally stronger correlation with high temperatures.Both SAM and TPI (x-1) regressions show sinking motion in the subtropics through spring.While El Niño can promote negative SAM from late spring (L'Heureux and Thompson, 2006;Hendon et al., 2007;Lim et al., 2016;Lim et al., 2019a), the TPI that better matches the sinking motion over eastern Australia in November.Hence, the apparent change from extratropical to tropical forcing in the circulation pattern is likely because the tropics promotes more of the heat developing mechanisms later in spring.
However, much of the atmospheric patterns associated with heat through spring are explained by neither the tropical TPI nor SAM.
The subtropical jet appears to play a greater role in Australian spring heat by acting as a wave guide (Hoskins and Ambrizzi, 1993) that directs quasi-stationary Rossby waves toward Australia, rather than as a block that limits direct propagation of Rossby waves from the tropical Indian Ocean to the southern hemisphere extratropics (e.g.Simpkins et al., 2014;Li et al., 2015 a,b).While wave activity flux appears to indicate wave propagation occurs directly out of the tropical Indian Ocean later in spring, the upper-level atmospheric anomalies are broadly consistent with IOD-forced wave trains identified in the literature (Cai et al., 2011;McIntosh and Hendon, 2018;Wang et al., 2019).As such, the secondary wave source in the high latitudes of the Indian Ocean proposed by McIntosh and Hendon (2018) may be key for promoting the TPI-forced atmospheric circulation in early spring.Overall, the STJ decay appears to be a lesser factor than the dynamical heat mechanisms in the apparent change from extratropical to tropical forcing of maximum temperatures through spring.
Consistent with this idea, wave activity flux calculated by first regressing 200Z onto the three dynamical heat mechanisms (Sup.Fig. 7) also indicates waves change extratropical or tropical forcing through spring, that then propagates along the jet wave guide toward Australia.
Area-averaged anomalous low-level wind and vertical motion were used to understand how the atmospheric circulation relates to Australia-wide maximum temperatures and explain much of the spring maximum temperature variability.However, it was not always clear how the atmospheric circulation features influenced those heat mechanisms.The southern Australian anticyclone and 500 hPa subtropical-Australian sinking motion, while important for heat, appear to be largely uncorrelated with the other circulation features and mechanisms.Greater insight into how remote forcing of the atmospheric circulation results in high Australian temperatures could be gained by including other heat mechanisms in future analyses, including: insolation (Lim et al., 2019b), changes to synoptic weather systems (Cai et al., 2011;Hauser et al., 2020), and land-surface feedbacks linked to antecedent moisture (e.g Seneviratne et al., 2010;Arblaster et al., 2014;Hirsch and King, 2020).Including the preceding month's Australian-averaged rainfall anomaly as an additional predictor of Australian monthly maximum temperatures did increase the percent variance explained by the statistical model (Sup.Fig. 8), but only in later spring.Dry conditions have been noted as an important factor in Australian summer heat waves (Hirsch et al., 2019;Loughran et al., 2019;Hirsch & King, 2020), and may be important for extreme heat in late spring.
While simplifying heat mechanisms into three separate indices was useful, geographic differences across Australia and interactions between mechanisms should also be considered.The combination of poleward advection of adiabatically warmed air after it descends anticyclonically over the Tasman Sea has been identified as a key mechanism for summer heatwaves in southeast Australia (e.g.Quinting and Reeder, 2017).This combination of mechanisms may generate heat through spring, particularly in the east and in November.The rising motion over southern Australia requires further investigation as it may be another factor in the combination of heat-mechanisms.Air diabatically warmed in association with storminess just to Australia's south may then be advected and descend toward Australia.
We used the tropical TPI to represent tropical variability relevant to Australia's maximum temperature, but other indices or drivers may highlight different Rossby wave pathways or heat mechanisms.Reconstructing Australian maximum temperature time series with more commonly used indices for the IOD and ENSO did not change the effectiveness of the statistical models overall (Sup.Fig. 4).However, this model did show a stronger relationship between temperature and the IOD in early spring andENSO in later spring, consistent with earlier studies (Jones and Trewin, 2000;Saji et al., 2005).As such, monthly IOD regressions onto atmospheric circulation may produce different wave trains earlier in spring than found with the tropical TPI.The MJO may also influence the atmospheric circulation associated with monthly maximum temperature development.MJO-initiated Rossby wave trains from the western Pacific promote low winter minimum temperatures in Australia (Wang and Hendon, 2020), and from the tropical Indian Ocean to promote high spring maximum temperatures in Australia (personal communication: Wang and Hendon, 2021).The positive phase of the IOD suppresses MJO activity across the Indian Ocean (Wilson et al., 2013), possibly restricting the MJO's influence on Australia's maximum temperature.However, MJO activity in the tropical Indian Ocean has recently been found to counter the wetting influence of La Niña during spring (Lim et al., 2021b).As such the MJO may be an important factor for spring maximum temperatures, particularly when the tropical SSTs are not otherwise conducive for high temperatures.
As the trend toward higher Australian spring temperatures is projected to continue into the future, a better understanding of what drives maximum temperatures over the months of spring is critical.A combination of extreme values in remote tropical and extratropical drivers of variability, exacerbated already dry and hot conditions in spring 2019 to promote one of Australia's deadliest fire seasons (Watterson, 2020;Lim et al., 2021a;Abram et al., 2021, Marshall et al., 2021).Further, projected trends toward positive IOD (Cai et al., 2014;Abram et al., 2020) may contribute to higher maximum temperatures in the future, particularly in later spring when the tropics exert greater influence on Australia's dynamical heat mechanisms.As we have shown just how different the atmospheric circulation and heat mechanisms can be through a season in Australia, other regions and seasons could also benefit from similar analysis, particular as the world continues to warm (e.g.Collins et al., 2013).
Figure1.Linear regressions of spring standardised weighted area-averaged Australian maximum temperature (a-b), SAMx-1 (c-e), tropical TPIx-1 (f-h), Niño3.4 (i-j) and DMI (jn) onto low-level circulation (left column), upper-level circulation (middle column) and Australian maximum temperatures (right column).Low-level circulation is represented by anomalous mean sea level pressure (hPa) (black and filled contours), 850 hPa wind vectors (ms -1 ) and 500 hPa omega (hPas -1 ) contours from -0.02 to 0.02 hPas -1 in steps of 0.01 hPas -1 (magenta contours are positive; downward motion) and cyan contours are negative; upward motion, and the zero contour is not plotted).Upper-level circulation is represented by 200 hPa geopotential height (black and filled contours and wave activity flux vectors (m 2 s -2 ).Filled contours, bold wind vectors, cross-hatching, and all vertical motion contours are significant at the 95% confidence level using a Student's t-test with 39 independent samples.
and 3a-c respectively for September, October and November.The multi-linear regression onto the standardised monthly indices of SAM (x-1) and tropical TPI (x-1) are in Figures 2d-j and 3d-j.At first glance, these monthly circulation patterns are similar to the spring-average regression patterns.However, the details of the circulation patterns change as the months progress.The most obvious change in atmospheric circulation through the months is in the low-level flow across Australia, particularly generated by the barotropic cyclones southwest (SWC) or southeast (SEC) of Australia (boxes in Fig 2a-b).Weak anomalous low-level anticyclonic flow around the Tasman Sea (box in Fig.

Figure 2 .
Figure 2. Regressions onto low-level circulation, as in Fig. 1, except for September (left column), October (middle column) and November (right column).Standardised areaaveraged Australian maximum temperature is linearly regressed onto low-level circulation (ta-c) and SAMx-1 (d-f) and tropical TPIx-1 (g-i) are multi-linear regressions onto low-level circulation.Pattern correlation between the maximum temperature MSLP regressions and the SAM and tropical TPI regressions calculated over 5°S-70°S; 70°E-170°E are written in the top right of each SAM or tropical TPI regression.The boxes (a-c) show key low-level circulation features identified as being important for maximum temperature development: The southwest cyclone (SWC) 35°S-55°S; 70°-120°E; southeast cyclone (SEC) 45°S-60°S; 160°-200°E and Tasman Sea high (TSH) 20°S-40°S; 150°-170°E

Figure 3 .
Figure 3.As with figure 2, but for upper-level circulation.The Australian-region pattern correlation between the maximum temperature Z200 regressions and SAMx-1 and TPIx-1 are in the top right of each figure.Boxed area (a-c) highlights the southern Australian anticyclone (SAA; 30°-40°S, 120°-150°E) that is linked with high maximum temperatures.
are overlaid in Fig.4on the monthly climatological Ks associated with the zonal winds.In September, the WAF associated with high maximum temperature indicates waves propagate through a region of low Ks over southwest Australia and are then directed along the STJ waveguide (e.g.Ambrizzi et al., 1995) (i.e. from high to low latitudes).
Figure 4. Total wave number (Ks) calculated September, October and November.Vectors are the wave activity flux repeated from figure 3.
indicating wave trains divert to propagate along the jet.Limits around linear Rossby wave theory (e.g.Liu & Alexander, 2007) may explain why some wave activity flux cross the region of imaginary wavenumber associated with the STJ.While the breakdown of the STJ through spring may help explain the change in teleconnection pathways of the TPI toward Australia it may not directly explain the change in atmospheric circulation associated with maximum temperature.
Figure 5. Multilinear regression coefficients (°C) of Australian maximum temperature regressed onto standardised timeseries of the SAMx-1 (a -c ) and the tropical TPI x-1 (d -f) for September, October and November over the years 1979 to 2019.Reconstructions (blue bars) of September, October and November (i-k) Australian areaaveraged maximum temperature from standardised time series of SAM and tropical TPI indices.Observed values are shown as red bars.The dashed line shows the 95% prediction interval computed as +/-1.96standard error and the variance explained (r 2 ) of the model is in the top right of each figure.

section 4 .
Weighted area-averages of mean-sea level pressure (multiplied by negative one) over the southwest and southeast cyclones (SWC and SEC) and 200 hPa geopotential height over the southern Australian anticyclone (SAA) for each spring month.See Figs.2a,b and 3ac for regions.Creating a statistical model of Australian-averaged monthly spring maximum

Figure 7
Figure 7 summarises the relationship between Australian maximum temperatures, circulation features, dynamical heat mechanisms and climate drivers through the spring months.The correlation between the SEC and Australian maximum temperature is strongest in September and rapidly decreases through October and November, and simultaneously the correlations with the SWC and particularly the SAA increase.As expected from Fig. 2, the SEC and SWC are more closely linked with the extratropics.Linearly regressing out the SAM component from time series of the SWC and SEC reduces the correlation strength with Australian maximum temperature (Fig. 7a), particularly in September.Conversely, linearly removing the tropical TPI slightly increases the correlation between the cyclones and temperature, with the partial-correlation only weakening in