Regime transitions of Australian climate and climate extremes

Systematic changes, since the beginning of the 20th century, in average and extreme Australian rainfall and temperatures indicate that Southern Australian climate has undergone regime transitions into a drier and warmer state. Southwest Western Australia (SWWA) experienced the most dramatic drying trend with average streamflow into Perth dams, in the last decade, just 20% of that before the 1960s and extreme, decile 10, rainfall reduced to near zero. In south-eastern Australia (SEA) systematic decreases in average and extreme cool season rainfall became evident in the late 1990s with a halving of the 10 area experiencing average decile 10 rainfall in the early 21st century compared with that for the 20th century. The shift in annual surface temperatures over SWWA and SEA, and indeed for Australia as a whole, has occurred primarily over the last 20 years with the percentage area experiencing extreme maximum temperatures in decile 10 increasing to an average of more than 45% since the start of the 21st century compared with less than 3% for the 20th century mean. Average maximum temperatures have also increased by circa 1oC for SWWA and SEA over the last 20 years. The climate changes are associated with atmospheric 15 circulation shifts and are indicative of second order regime transitions, apart from extreme temperatures for which the dramatic increases are suggestive of first order transitions.

Some of those changes have been quasi-cyclical due, for example, to variability associated with the El Niño-Southern 25 Oscillation or the Indian Ocean Dipole (Cai et al., 2009;L'Heureux et al., 2017;Whelan and Frederiksen, 2017;Frederiksen and Francey, 2018; OF21 review the literature). On the other hand, there is also compelling evidence for systematic climate shifts in both hemispheres due to global warming (Corti et al., 1999;Frederiksen et al., 2010;O'Kane et al., 2013;CSIRO and Bureau of Meteorology, 2015;Franzke et al., 2015;Frederiksen and Grainger, 2015;Freitas et al., 2015;Grose et al., 2019;Bureau of Meteorology and CSIRO, 2020;OF21). 30 Our particular interest in this article is whether the changes that have occurred in Australian climate and climate extremes over the last seventy years are indicative of regime transitions in a noisy environment. There has been a long history of studies examining the possibility of regime transitions in various aspects of the climate system. The early simple energy balance models (EBMs) of the earth's climate (Budyko, 1969;Sellers, 1969;Faegre, 1972;Schneider and Gal-Chen, 1973;Frederiksen, 1976;Ghil, 1976) exhibited thermodynamical regime transitions in the mean temperature between several states as the order 35 parameter, the solar constant, is varied. Indeed, as shown in Figures 1 and 3 of Frederiksen (1976), the number of stable states and the number of bifurcation points (or critical or tipping points) may vary depending on the form of the thermodynamical functions, such as the effective albedo, and lead to the possibility of closely spaced tipping points. Charney and Devore (1979) and Wiin-Nielsen (1979) studied low order dynamical models of the atmospheric circulation and found multiple equilibrium states dominated by either strong zonal flow and weak wave structure or weak zonal flow and 40 strong wave structure that they interpreted as a blocking state. Charney and Devore (1979) found that regime transitions between the zonal and blocking states occurred as the order parameter, the height of the topography, varied through the bifurcation point. Similar regime transitions were also found in baroclinic models by Charney and Straus (1980). Frederiksen and Frederiksen (1989) reviewed subsequent developments in the theory of multiple equilibria and the role of topographic instability in regime transitions. 45 Frederiksen (1985Frederiksen ( , 1991 examined regime transitions of inviscid barotropic and baroclinic zonal flows over topography in high dimensional systems using methods of equilibrium statistical mechanics. The critical points for barotropic flow and critical lines and triple points for baroclinic flows were determined and the similarities and differences with magnetic phase transitions (Patashinski and Pokrovskii, 1979;Thompson, 1979) were examined. Zidikheri et al. (2007) studied the interaction of barotropic zonal flows with topography in high resolution forced dissipative numerical simulations and established the phase 50 diagram (their Figure 2) for regime transitions. They found hysteresis effects in transitions between strong and weak zonal flow states with qualitative similarities to those for magnetic phase transitions (e.g., Figure 3 of Saghayezhian et al. (2019) and references therein). The regime transitions between strong zonal states and blocking found in simple models have also been found in comprehensive weather prediction models (e.g., Frederiksen et al. (2004)) and associated with observed climate shifts (O'Kane et al., 2013). 55 Further developments in the role of regime transitions and tipping points in various aspects of the climate system, including under global warming, have been considered by Franzke et al. (2015); Freitas et al. (2015); Jones and Ricketts (2017); Dijkstra (2019); Lenton (2019); Kypke et al. (2020); Yan et al. (2020);Fabiano et al. (2021); and Australian Academy of Science (2021). It is clear from all the studies mentioned in this Introduction that there are dynamical and thermodynamical processes of the climate system that can result in regime transitions. However, the methodologies for analysing components and 60 simplifications of the climate system are not easily applied to the full system given its complex equations and interactions over vast scales. This is clearly the case for the analytical and semi-analytical bifurcation methods, including singularity theory (Ball, 2007), for analysing low order systems (Dijkstra, 2013) and for the equilibrium statistical mechanics methods (Frederiksen, 1985(Frederiksen, , 1991. Renormalization group methods (Wilson and Kogut, 1974;Wilson, 1979;McComb, 2004reviews https://doi.org/10.5194/wcd-2021  the literature) and renormalized perturbation theory (McComb, 2004; review the literature) are more 65 generally applicable to the statistical dynamics of phase transitions but the complex equations and interactions of the climate system again make these approaches unfeasible. In this study we therefore take an approach based on the general characteristics of phase transitions which involve a discontinuity in the dependent variable (first order phase transition) or its derivative (second order phase transition) as the order parameter transits through a critical point (Harter et al., 2017;Saghayezhian et al., 2019 and references therein). 70 The paper is structured as follows. The mean and extreme rainfall, streamflow into Perth dams, the mean and extreme surface temperature data sets, and the reanalysis data determining atmospheric flow fields, are described in Section 2. Section 3 examines changes in SWWA mean and extreme rainfall and streamflow since the beginning of the 20 th century and relates the changes to those of the atmospheric circulation in the surrounding regions. There, systematic shifts in these variables and their trends or gradients over different time periods are examined and are related to regime transitions. In Section 4, a corresponding 75 analysis is performed for mean and extreme rainfall for SEA and in Section 5 results for northern Australia are presented. The changing nature of SWWA average and extreme maximum surface temperatures are examined in Section 6 and the shifts in temperatures and trends again related to transitions between regimes. Section 7 presents an analysis of temperature trends in SEA, and for states and regions fully or partially within this area, while Section 8 summarizes corresponding results for Australia as a whole. The implications of our findings and our conclusions are discussed in Section 9. 80 2 Data sets

Rainfall, temperature and streamflow data sets
The average and extreme rainfall and temperature data used in this paper have been obtained from the Bureau of Meteorology (2020) website. In this study we focus on various regions such as SWWA, SEA, northern Australia, and Australian states, shown in Fig. 1. The construction of the rainfall data set is described by (Jones et al., 2009) and the temperature data set by 85 (Trewin, 2013). The data for streamflow into Pert dams has been obtained from the Water Corporation (2020) of Western Australia.

Reanalysis data sets
The analysis of the changes in atmospheric circulation in our study uses the reanalysis data set of the National Centers for Environmental Prediction (NCEP) and the National Centre for Atmospheric Research (NCAR), (Kalnay et al., 1996). It will 90 be referred to as the NNR data set.

South west Western Australian rainfall, rainfall extremes and atmospheric circulation
In this section, we analyse rainfall over SWWA and streamflow into Perth dams since the early 1900s. There was a notable deficit in Southern Wet Season (SWS), April to November, rainfall in SWWA and an even larger relative reduction in annual streamflow into Perth dams between the mid-1970s and early 1980s. This has been documented in numerous studies, starting 95 with the articles by Pittock (1988) and Sadler et al. (1988), and further analysed and reviewed by Hope (2006); Bates et al. (2008) and OF21. Frederiksen and Frederiksen (2005;2007 -hereafter FF05, FF07) noted that there was an associated 17% reduction in the peak upper troposphere winter jet-stream and a 20% drop in the 300 − 700 hPa baroclinicity in the region of SWWA between 1949SWWA between -1968SWWA between and 1975SWWA between -1994. They showed through instability model calculations, with the respective observed climate states for the above two 20-year periods, that there was a circa 30% reduction in the growth rate of leading storm track 100 modes crossing SWWA and a poleward deflection of some storms. OF21 have recently confirmed, through a detailed data driven study, that the cause of the SWWA winter rainfall decrease over the last 50 years is in fact the reduction in the intensity of the fast-growing storms associated with changes in the basic state.
Our aim here is to present evidence that both SWS rainfall over SSWA and Perth annual streamflow have undergone regime transitions with qualitative similarities to the phase transitions discussed in the Introduction. 105

SWWA rainfall, rainfall extremes and streamflow
We start by examining the time series of SWS rainfall over SWWA rainfall and annual streamflow into Perth dams between January to December. The SWWA region is shown in Fig. 1 which also displays other regions of Australia that we consider in this study. Figure 2 shows the time series of (a) SWWA rainfall in SWS from 1900 to 2019, (b) the Percentage Area with Rainfall in Decile 10 (PARD10) for SWWA in SWS and (c) the January to December Perth streamflow from 1911 to 2018. We 110 note that the three graphs show a general decline with time. This is perhaps most easily seen from Table 1 where averages of these quantities are displayed for different time spans. For each time interval shown the rainfall, streamflow and PARD10 decrease systematically apart from a slight recovery of PARD10 in the last period. The reductions shown there are quite profound for streamflow and extreme rainfall. We note that Perth streamflow decreased from an annual average of 414 giga litres for 1911-1958 to 389 giga litres for 1959-1978 to 183 giga litres for 1979-2018 and to as little as 88 giga litres for 2009-2018. 115 Thus, in the last decade Perth streamflow has reduced to just 21% of the historical annual average inflow into dams. Extreme rainfall, represented by PARD10 in Table 1, followed a similar dramatic decrease. By these two measures the climate of SWWA has transited into a completely different regime. Somewhat lesser declines in streamflow have also occurred in other drainage divisions across southern and eastern Australia (Bureau of Meteorology and CSIRO, 2020). For SWWA rainfall (Fig. 1a) the broad decreases with time follow a similar pattern to streamflow ( Fig. 1c) but with the magnitudes of the reductions being 120 considerably less, at circa 20%, since the 1970s. with the rainfall squared and with a quadratic fit of rainfall with streamflow. Annual streamflow into Perth dams is particularly well predicted or described by the quadratic fit with correlation = 0.88 (detrended = 0.86 ). 125 Next, we consider decadal variability of rainfall, streamflow and PARD10. Figure 3 shows time series of 10 year running means of these variables that make the systematic decrease since the mid 1970s more evident than the noisier annual data in Fig. 2.
The close covariability of the low-pass filtered SWWA rainfall and Perth streamflow is evident and the correlations are even larger ( = 0.94 and detrended = 0.83) than for interannual variability ( = 0.84 and detrended = 0.81). Perhaps most dramatic is the drop in PARD10 displayed in Fig. 3b from before the 1970s to after. This illustrates an important point that how 130 evident a regime transition is depends on the variable of interest and its sensitivity to the changes in the forcings or external environment (order parameters). Clearly extreme rainfall is more sensitive to changes in the circulation that in turn affect the extratropical storms and rainfall (FF07; OF21).
The nature of the regime transition can be further elucidated by examining the average trend or gradient of the rainfall and streamflow data over relevant time spans. This is summarized in Table 3 which show the trends up to 1958, between 1959 and 135 1978 and since 1979. For each of the data sets there is a considerable decreasing trend in the twenty years between 1959-1978 compared with in the periods before and after. Again, these results support the proposition that SWWA rainfall and streamflow into Perth dams underwent a regime transition from a relatively high rainfall state to a lower much drier state and that this occurred over a period of about twenty years. The broad findings detailed for SWS over SWWA apply equally to winter rainfall and Cool Season (April to October) rainfall (not shown). 140

SH atmospheric circulation
As noted in FF07 and further analysed and reviewed by OF21, the July rainfall reduction in SWWA after the 1970s was accompanied by significant decreases in the July upper tropospheric subtropical jet near 30 o S over Australia. Here, we examine the time series of the SH jet stream changes since the mid-20 th century in more detail focusing on the SWS of April to November. Figure 4 shows a latitude cross section of the (1975-1994) minus (1949-1968)  which is necessary for baroclinic instability. The superscripts denote the winds at appropriate upper and lower levels of the atmosphere and the critical value, , depends on the vertical temperature gradient and the Coriolis parameter. In spherical geometry the expression for is given, for example, by Frederiksen (1978, Eq (3.9)) and in Eq.
(1) of OF21 155 (and references therein). FF07 and Frederiksen and Frederiksen (2011 -hereafter FF11) found that the primary determinant of changes in the SH baroclinicity during the 20 th century were changes in the zonal wind shear with changes in the vertical temperature gradient, and thus in , being relatively minor.  Table 4 show the systematic decrease in 150 hPa zonal wind and 300 − 700 hPa tropospheric baroclinicity for the time spans 1948-1958, 1959-1978 and 1979-2018. The corresponding trends or gradients of these field for 1959-1978 and 1979-2018 are given in Table 5. The gradients decrease rather steeply between 1959-1978 and thereafter 165 the trend is near zero. In these respects, the results in Table 5 mirror those for SWWA rainfall and stream flow into Perth dams shown in Table 3 Table 6 shows correlations between mid-tropospheric baroclinicity and characteristics of SWWA rainfall for SWS and annual streamflow into Perth dams for the time span 1959-2018; similar results are obtained for 1948-2018 (not shown). Correlations with the 300 − 700 hPa zonal wind are as high as 0.58 except with PARD10 where they are lower. We note however that somewhat larger correlations between baroclinicity and rainfall may be obtained by optimizing the region and levels of the 175 flow fields (OF21). This is done in the right-hand column of Table 6 where correlations (as high as 0.66) with the 700 hPa zonal wind in the region 20S-35S 100E-132.5E are shown for SWS. As noted in OF21 the strong correlations of SWWA rainfall with the low-level flow suggests that surface cyclogenesis is a major contributor to the rainfall and the variability of the 700 hPa zonal wind is a primary determinant of variability in low-level baroclinicity. Their results for July are confirmed here for the time span of April to November. 180

South east Australian rainfall, rainfall extremes and atmospheric circulation
Next, we examine changes in SEA rainfall since the early 1900s with a particular emphasis on indications of regime transitions as in Section 3 for SWWA rainfall. We focus on the Cool Season (CS), April to October, SEA rainfall which is most affected by extra-tropical storms (OF21). Perhaps the most dramatic period of rainfall reduction during the 20 th and early 21 st century was the Australian Millennium Drought (AMD) of 1997 to 2009. SEA rainfall changes, particularly during the AMD, have 185 been the focus of numerous diagnostic studies including by Fawcett (2004); Gallant et al. (2007) and Watkins and Trewin (2007), and further investigated and reviewed by Risbey et al. (2013) the growth rates of leading extra-tropical storm track modes were reduced by more than 30% and onset-of blocking modes by around 20% although there was some increase in the growth rate of North-West Cloud Band modes (NWCBs) and intraseasonal oscillation modes. These theoretical analyses of the causes of the AMD were also supported by the observational study of Risbey et al. (2013), who found fewer fast growing and intense frontal storms and cut-off lows during the AMD and again attributed this to the reduction in baroclinicity in the Australian region. The data driven analysis in OF21 confirmed 195 these findings and established that changes in the intensity of explosive storms were primarily responsible for the reduced winter rainfall in Southern Australia during the AMD. They also found that while the El Niños played a significant role in the SEA rainfall reduction during the AMD the general drying of Southern Australia continued and is evident during the longer period 1997-2016. Figure 6 shows the annual and 10 year running mean time series of SEA rainfall and extreme rainfall characterized by PARD10 for the Cool Season (CS) of April to October; results based on April to November (SWS) are broadly similar (not shown). The reduction in SEA rainfall and PARD10 are most evident from the late 1990s as also see in from Table 7. The SEA reductions in rainfall of about 10% and a halving of PARD10 since the late 1990s are very significant as they affect the Murray Daring Basin (MDB; see Fig. 1) which is Australia's main food bowl. Nevertheless, they are not yet as dramatic as the larger reductions 205 experienced by SWWA since the late 1970s discussed in Section 3. As one would expect, many of the states and sub-regions making up, or overlapping with, SEA experienced very similar Cool Season changes as those depicted for SEA. This is the case for the states of Victoria (VIC) and New South Wales (NSW) and for the MDB region (Fig. 1). In fact, the variability of rainfall and PARD10 for VIC (the central part of SEA) is essentially the same as for SEA with CS rainfall (PARD10) correlation of 0.97 (0.94). Indeed, the relationships between explosive storms and SEA rainfall established in OF21 apply equally to VIC 210 rainfall.

SEA rainfall and streamflow 200
The Tasmanian variability of CS rainfall and PARD10 are less representative of SEA with correlations of 0.64 and 0.60 respectively. Interestingly, the changes in TAS rainfall and PARD10 have some similarities to those for SWWA in that the noteworthy reductions of total and extreme CS rainfall also commenced in the late 1970s as shown in Fig. 7 and in Table 7.
However, the Tasmanian rainfall reductions have been more typical of SEA than the larger deficits for SWWA. The reductions 215 in CS rainfall, and extreme rainfall, over the state of South Australia (SA) (not shown) have some similarities with those over SWWA (although not as large) and Tasmania in that they became evident in the late 1970s with further reductions at the start of the 21 st century.
For CS total and decile 10 rainfall averages over the Southern Australian (SNA) and Eastern Australian (EA) regions (Fig. 1) the reductions became most evident at the start of the 21 st century (not shown); this is also the case for the state of Queensland 220 (QLD) and to a lesser extent even for the Northern Australian (NA) region (not shown). In this study we shall not make an extensive analysis of the associated changes in streamflow that occurred in SEA or other regions. As might be expected from the relative changes in rainfall between SEA and SWWA the streamflow reductions into some drainage divisions across SEA have been notable but less impactful than those into Perth dams as discussed, for example, in Bureau of Meteorology and CSIRO (2020). 225

SH atmospheric circulation
The dynamical study of FF11 noted that the July rainfall reductions during 1997 to 2006, in the AMD, (compared with the baseline 1949-1968 period) were associated with reductions as large as 6 ms -1 in the strength of the SH upper tropospheric subtropical jet centred on 30S between the longitudes of 110E and 160E. Similar increases in peak jet strength near 55S were also noted. From Figure 2 of FF11, it is evident that there was also a noteworthy reduction in the baroclinicity of the SH mid-230 troposphere near 30S particularly in the Australian region. OF21 further discussed the changes in the SH circulation, as characterized by several local, hemispheric, and globally important predictors or indices. In particular, they found that July SEA rainfall variability was highly correlated with the 700 hPa zonal wind in the region 20S-35S, 132.5E-155E. Table 8 shows that average the correlations between SEA and Tasmanian rainfall and this 700 hPa regional zonal wind are even larger for the seven-month cool season of April to October that for July (OF21 , Table 4). 235

Northern Australian rainfall and rainfall extremes
While Southern Australia has undergone noteworthy reductions in rainfall since the 1970s, due largely to a reduction in storminess and, particularly, in the intensity of fast-growing extratropical storms (FF05; FF07; FF11; Hope, 2006;Alexander et al., 2011;Risbey et al., 2013;OF21), Northern Australia ( Fig. 1) has seen increased precipitation (Frederiksen and Grainger, 2015;Dey et al., 2019; Bureau of Meteorology and CSIRO, 2020 and references therein). Table 6  240 shows the increases in total rainfall (of circa 15%) and in extreme precipitation measured by PARD10 (of a nearly three-fold increase) since the late 1960s. While these increases are of importance, they cannot make up for the decreases that have occurred in the population centres and food bowls of Southern Australia which are our primary concern in this study.

South west Western Australian temperature and temperature extremes
Next, we examine the changes in Australian temperatures that have occurred primarily in the latter part of the 20 th century and 245 in two decades of the 21 st century. Average Australian temperatures have increased by circa 0.  Table 9 we see that the increase in maximum temperatures since the early 1990s is circa 0.9 o C while the average area experiencing extreme maximum temperatures has increased from a negligible percentage to 46% of SWWA since the start of the 21 st century. The average trends, or gradients, of the 10-year running means of SWWA temperatures, shown in 255 Figs. 8c and d, are presented in Table 10 for the time spans relevant to the above regimes. We note that the gradient associated with the maximum temperature increases by a factor of nearly 5 between the early and late periods shown while the trend in maximum extreme temperatures (PATD10) changes from negligible  to 4.8% yr -1 (2002-2019). Indeed, the rate of increase of maximum temperatures and PATD10 for the period 2002-2019 is higher than for any of the other major geographical regions considered next for which corresponding results are also shown in Table 10. 260

South east Australian temperature and temperature extremes
We now turn to regime transitions of south east Australian temperatures that began near the start of the 21 st century with a focus on maximum temperatures including extreme temperatures. Figure 9a shows the annual anomaly in maximum temperatures over SEA with nearly identical results for VIC (correlation of 0.99) and quite similar results for New South Wales (NSW) and the Murray Darling Basin (MDB) (not shown). The MDB is Australia's main food bowl which stretches inland 265 between Victoria through NSW to southern Queensland (Fig. 1). We note from Fig. 9a that while there is considerable interannual variability in the graph it is evident that maximum temperatures have increased considerably in the early 21 st century compared with the 20 th century. This change between centuries is more dramatic when considering extreme temperatures. Figure 9b shows time series of the annual Percentage Area with Temperatures in Decile 10 (PATD10) for SEA maximum temperatures with again nearly identical results for VIC (correlation of 0.99). Again, Figs. 9c and 9d show the 270 corresponding 10-year running mean results corresponding to Figs. 9a and 9b respectively. It is clear from Fig. 9 that during the circa 20 years of the early 21 st century there were many occasions when extreme maximum temperatures in the decile 10 band covered large areas of SEA compared with earlier. Figure 10 shows corresponding results for changes in annual maximum temperatures over Tasmania. We note that the temperature increases started earlier than shown for the combined temperatures for SEA in Fig. 9. 275 The main deductions that can be made from the results in Figs. 9 and 10 are summarised in Table 9. We note that for the whole of the SEA region, and for NSW and MDB (and VIC -not shown), annual maximum temperature anomalies averaged between For annual average maximum temperatures and PATD10 for maximum temperatures averages over the Southern Australian 290 (SNA) and Eastern Australian (EA) regions (Fig. 1), and for the state of QLD, the notable increases again occurred at the start of the 21 st century (not shown). For the Northern Australian (NA) region the increases in maximum temperatures and PATD10 started in the 1990s and became more evident during the 21 st century (not shown).

Australian temperature and temperature extremes
The regime transitions of SWWA and SEA maximum temperatures and particularly extreme maximum temperatures in fact 295 apply to extreme temperatures averaged more generally across the whole of Australia, as might be expected from the results in the previous sections. For both mean and maximum temperatures extremes characterized by PATD10 increase dramatically in the first two decades of the 21 st century; PATD10 increases from just a few percent to 44% for mean and 47% for maximum temperatures for 2002-2019 as show in Table 9. Again, Table 10 shows that there is a considerable change in the averaged gradient around 2002 based on 10-year running means of PATD10 for both mean and maximum temperatures. The distinct 300 increases in trends in the early 21 st century again support the concept of a regime transition in Australian temperatures.

Discussion and conclusions
The main purpose of this study has been to present evidence of regime transitions during the 20 th and early 21 st century in important aspects of Australian climate. We have focussed on the changes over Southern Australia in rainfall, temperatures and extremes, and associated circulation features since the early 20 th century. We have also examined some particularly 305 dramatic shifts in streamflow into Perth dams.
We have found very clear signals that the climate of south-west Western Australia (SWWA) has transited into a drier and warmer state with some of these changes in rainfall, rainfall extremes and streamflow into Perth dams starting as early as the 1960s. Annual streamflow into Perth dams over the last decade has reduced to just 20% of the pre-1960s average. We have determined that the gradient of the 10-year running mean (RM) of streamflow is negligible for the period 1911-1958 followed 310 by a steep decline between 1959 and 1978 and a lesser decline between 1979 and 2018 (circa 40% of that for 1959-1978). SWWA has seen the earliest and most dramatic systematic shifts in climate to a drier state with South-Eastern Australia (SEA) impacted towards the end of the 20 th century. Cool Season (CS) rainfall over SEA reduced by an average of 12% between the 335 two periods 1900-1998 and 1999-2019 while PARD10 reduced from 11% to 5%. For Victoria (VIC), which is the central region of SEA, the relative changes are virtually identical, and they are also very similar for New South Wales (NSW) and the Murray Darling Basin (MDB). In Tasmania (TAS), the southern part of SEA, rainfall reductions, particular for extreme rainfall, occurred earlier with PARD10 reducing from 12.5% to 5% between the period 1910-1978 and 1979-2019. Again, the changes in rainfall in SEA is associated with changes in the circulation over and around this region. The regime transitions of SWWA and SEA temperatures are in fact mirrored by shifts over Australia, as a whole. This is seen particularly in extremes, with PATD10 increasing from very low values to 44% for mean and 47% for maximum temperatures for 2002-2019.
We note that there is considerable interannual variability in average and extreme rainfall and temperatures and in streamflow 350 into Perth dams. For that reason, we have also examined 10-year running means to see the systematic changes in the climate variables and their gradients. We have noted discontinuities in the average gradients of the smoothed data typical of second order regime transitions. However, the large and sudden shifts in the temperature extremes are suggestive of first order regime transitions.

355
Code availability. Reasonable requests for access to code used to generate the results in the paper will be considered by contacting the authors.            Table 9: The annual mean of maximum temperatures and percentage areas with maximum temperatures in decile 10 (PATD10) for SWWA, SEA, NSW, MDB and TAS and Australian PATD10 for mean and maximum temperatures, for different time periods.  Table 9 for the gradients or trends of 10-year RM of the temperatures and PATD10.     (1975-1994) minus (1949-1968). Contour intervals are 1 ms -1 . 560