Interdecadal Variations in the Seasonal Cycle of Explosive Growth of Southern Hemisphere Storms with Impacts on Southern Australian Rainfall

Abstract

Interdecadal variations, since the middle of the 20th century, in the seasonal cycle of Southern Hemisphere extratropical synoptic scale weather systems, are studied and related to associated anomalies in Southern Australian rainfall over south-west Western Australia (SWWA) and southeast Australia (SEA). A data-driven method is employed in which atmospheric fluctuations, specified from 6-hourly lower-tropospheric reanalysis data, are spectrally analysed in space and time to determine the statistics of the intensity and growth rates of growing and decaying eddies. Extratropical storms, blocking and north-west cloud band weather types are investigated in two frequency bands, with periods less than 4 days and between 4 and 8 days, and in three growth rate and three decay rate bins. Southern Australian rainfall variability is found to be most related to changes in explosive storms particularly in autumn and winter. During the first 10 years of the Australian Millennium Drought (AMD), from 1997 to 2006, dramatic changes in rainfall and storminess occurred. Rainfall declines ensued over SEA in all seasons, associated with corresponding reductions in the intensity of fast-growing storms with periods less than 4 days. These changes, compared with the 20-year timespans of 1949 to 1968 and 1975 to 1994, also took place for the longer duration of 1997 to 2016, apart from summer. Over SWWA, autumn and winter rainfall totals have decreased systematically with time for each of the 10-year and 20-year timespans analysed. Southern Australian rainfall variability is also found to be closely related to the local, hemispheric or global features of the circulation of the atmosphere and oceans that we characterise by indices. Local circulation indices of sea level pressure and 700 hPa zonal winds are good predictors of SWWA and SEA annual rainfall variability particularly in autumn and winter with vertical velocity generally less so. The new Subtropical Atmospheric Jet (SAJ) and the Southern Ocean Regional Dipole (SORD) indices are found to be the most skilful non-local predictors of cool season SWWA rainfall variability on annual and decadal timescales. The Indian Ocean Dipole (IOD) and Southern Oscillation Index (SOI) are the strongest non-local predictors of SEA annual rainfall variability from autumn through to late spring, while on the decadal timescale, different indices dominate for different 3-month periods.

1. Introduction

Australian climate and extremes are highly variable with both quasi-cyclical and systematic, or secular, changes evident and documented since the early 1900s and accelerating over the last seventy years as reviewed in Refs. [1,2,3,4,5,6]. Much of the literature describing the important changes in rainfall and associated synoptic scale disturbances and SH circulation shifts since the mid-20th century is reviewed by Osbrough and Frederiksen [5] and O’Kane et al. [6]. As well, mean and extreme rainfall and temperature changes in the Australian region and the associated literature were reviewed by Frederiksen and Osbrough [4]. They examined the time series of cool season rainfall and extreme rainfall and annual temperatures and extreme temperatures and determined regime changes in these variables. This variability in SH climate is driven both by internal changes in the large-scale circulation of the atmosphere and oceans [5,7,8,9,10,11,12,13,14,15,16,17,18] and by global warming [5,6,19,20,21,22,23,24,25,26,27].

1.1. Decline of SWWA Rainfall and Circulation and Storm Changes

Perhaps the most dramatic regional change in the SH since the mid-20th century has been the systematic decline in southern wet season (April to November) rainfall and extremes in SWWA that has been accompanied by an even more notable reduction in annual streamflow into Perth dams [28,29,30,31,32,33,34,35,36,37,38,39,40]. Compared with the average from the beginning of the 20th century to 1958, southern wet season SWWA rainfall has decreased by 21%, the percentage area experiencing extreme, decile 10, rainfall has reduced from about 15% to 0.2%, and annual Perth stream flow has reduced to just 21% in the ten-year timespan 2009 to 2018 [4] (Table 1).

Frederiksen and Frederiksen [41] reasoned that the cause of the drying of SWWA was reductions in the strength of the subtropical atmospheric jet, and baroclinicity, with accompanying reductions in the thermal gradient and increases in the Antarctic Oscillation or Southern Annular Mode (SAM). These changes in turn would lead to a decrease in extratropical storminess across SWWA. This was confirmed by studies of the observed differences in the National Centers for Environmental Prediction (NCEP) and the National Center for Atmospheric Research (NCAR) reanalyses [42] (hereafter referred to as NNR) between two 20-year timespans of 1949 to 1968 and 1975 to 1994 and shorter periods on either side of 1970. Moreover, they performed comprehensive instability calculations of the respective three-dimensional basic states in a primitive equation model and found reductions of as much as 30% in the leading explosive storm modes and a poleward shift of some cyclogenesis modes. This was carried out for both the NNR and European Centre for Medium-Range Weather Forecasting (ECWMF) Reanalysis (ERA40) [43] data with very close agreement for leading storm modes with pattern correlations between 0.94 and 0.99 and a growth rate difference of less than 4%. These instability changes were also confirmed for other months of the year [19,21].

Joseph and Sabin [44] (Figure 4) also noted the similar weakening of the SH winter subtropical jet in the 1990s compared with the 1950s and 1960s in the NNR and ERA40 data. Bromwich and Fogt [45] and Hertzog et al. [46], however, note the superiority of the NNR reanalysis in the pre-satellite period, as further discussed by O’Kane et al. [6]. The 20th-century changes in baroclinicity were also examined with several reanalysis datasets including NNR, ERA40 and the Twentieth Century Reanalysis (20CR) [47] by Frederiksen et al. [19]. The trends in baroclinicity over the second half of the 20th century were found to be reasonably similar for these datasets. This is in agreement with the work of Freitas et al. [26] and the subsequent study by Rikus [48], with high correlations of 20CR flow fields with NNR and ERA40 that decrease with height. O’Kane et al. [49] and Harries and O’Kane [50] also found that the performance of NNR and the Japanese 55-year Reanalysis (JRA55) [51] is quite similar.

1.2. Australian Millennium Drought and Weather System Changes

The Australian Millennium Drought (AMD) of 1997 to 2009 is arguably the most impactful drought of the 20th century [14,52,53,54,55,56,57,58,59,60,61,62,63]. The largest effect was on Southeast Australia (SEA) with 11% declines in rainfall between 1997 and 2009 [64] while for Melbourne, the reduction was 20% between 1997 and 2006 [65].

The AMD was shown to be associated with large-scale atmospheric circulation anomalies with substantial decreases in the tropospheric subtropical jet and baroclinicity in winter [66]. Frederiksen and Frederiksen [66] performed detailed calculations of the instability of three-dimensional basic states for 1997 to 2006 and compared them with the earlier periods of 1949 to 1968 and 1975 to 1994 in a primitive equation model. Substantial reductions during the AMD in the growth rates of explosive storms and blocking modes were deduced but with increased growth rates of north-west cloud band (NWCB) modes [67,68] and intraseasonal oscillations. The observational study of frontal storms and cut-off lows during the AMD by Risbey et al. [56] also found that the fact that there were fewer intense and fast-growing systems of these weather types caused the decrease in rainfall consistent with the theoretical results.

1.3. Rainfall Variability and Changes in Atmospheric and Oceanic Circulation

The changes in rainfall and synoptic scale weather systems are in turn related to variability and shifts in the large-scale circulation of the atmosphere and oceans. It has been customary and convenient to characterise many of the aspects of these large-scale drivers by circulation indices. The climate of Australia lurches from droughts to floods with the cycle of the El-Niño Southern Oscillation (ENSO), encapsulated by the Southern Oscillation Index (SOI) [69]. The Indian Ocean Dipole (IOD) index [70,71], like the SOI, also covaries notably with rainfall variability particularly in SEA. As well, the Antarctic Oscillation, or the Southern Annular Mode (SAM) [72,73,74,75], is significantly correlated with Australian rainfall, particularly in SWWA. These indices and others have frequently been used as drivers of climate and rainfall variability [1,13,14,27,34,49,53,56,61,76,77,78,79,80,81]. In an interesting study, Franzke et al. [23] found a cross-over, in the mid- to late-1970s, between the prevalence of the increasing positive phase of SAM and the decreasing wavenumber 3 SH teleconnection pattern [82] related to blocking. This agrees with the results of Frederiksen and Frederiksen [41,66] on the increasing polar jet and decreasing subtropical jet and the reduction in growth rates of blocks, as well as extratropical storms, after the mid-1970s. The applicability of circulation indices for interpreting Australian climate variability and trends are further reviewed in Refs. [5,83,84].

1.4. Simulations and Projections of Southern Hemisphere Circulation Changes

The declines in Southern Australian rainfall, reductions in subtropical jet strength, and baroclinicity, summarised in the previous subsections, led to examinations of how well CMIP3 and CMIP5 climate models reproduce the broad changes in the second half of the 20th century [19,21,24]. It was found that around a third of the models were able to capture the essence of the changes. However, when forced with increasing CO₂, particularly in high-emission scenarios, many of the less skilful models also responded with reduced baroclinicity in the 30° S latitude belt and increases near 55° S. Frederiksen et al. [19] found that for their multi-model ensemble of skilful CMIP5 models, both the 20th- and 21st-century baroclinicity and rainfall trends had high correlations over the SH with their external trend mode corresponding to radiative forcing, suggesting their cause is due largely to increasing anthropogenic greenhouse gases. This conclusion agrees with the model simulation findings of Freitas et al. [26], the attribution study analyses of Franzke et al. [23] and the studies of the relationship between increasing positive SAM and mid-latitude SH rainfall changes [85,86,87].

1.5. Weather Systems Influencing the Seasonal Cycle of Southern Australian Rainfall

Southern Australian cool season rainfall reductions since the mid-20th century are largely due to changes in low-pressure systems and fronts [56,57] with cut-off lows accounting for approximately two-thirds of rainfall in SEA and one-third in SWWA and fronts for most of the remainder. In the warm season, thunderstorms are particularly important, and throughout the year, combinations of weather systems may lead to particularly heavy downpours [88,89]. For example, Reid et al. [68] (Figure 12) show quite different rainfall distributions over Australia depending on whether north-west cloud bands (NWCBs) occur together with fronts or whether these weather systems occur by themselves.

In this study, we consider analyses of disturbances with periods up to 8 days, with separate results for high-pass (less than 4 days) and band-pass (between 4 and 8 days) filtered reanalysis data. As discussed by Osbrough and Frederiksen [5], it is known that the growth rate of extratropical storms, their speed of development and rainfall intensity are closely related, and for this reason, we focus our attention on the fastest-growing disturbances that have the potential for resulting in heavy rainfall. As in Osbrough and Frederiksen [5], the extratropical storm tracks are defined as the regions of large standard deviation of fluctuations in 850 hPa streamfunction with periods less than 8 days. The band-pass filtered disturbances are also shown to have structures that influence rainfall including Tasman blocking highs and associated east coast lows, as well as some NWCBs.

Longer-period disturbances also affect southern Australian rainfall. This includes NWCBs for which the period may extend from less than 8 days [66] to 14 days [67] and intraseasonal oscillations like the MJO with periods between 25 and 70 plus days [15,90]. In particular, Whelan and Frederiksen [15] found that the major 1974 and 2011 floodings of southeastern Queensland were due to the constructive interference of Kelvin waves and the MJO. Furthermore, tropical–extra-tropical interactions associated with the MJO resulted in flooding as far south as Victoria.

1.6. Aims and Structure

In this article, our aim is to examine relationships between growing weather systems and southern Australian rainfall for the whole seasonal cycle and how this has changed over the decades since the middle of the 20th century. It is to explore the links between SWWA and SEA rainfall and indices describing local, hemispheric and global circulation variability. This work builds on the study of Osbrough and Frederiksen [5] where these phenomena were explored for the mid-winter month of July. As well, we examine how the seasonal cycle of rainfall, weather systems and SH circulation have changed over decades since the middle of the 20th century. We also draw on the results of Osbrough and Frederiksen [91] where the structures, intensities and growth rates of synoptic-scale weather systems were examined over the seasonal cycle for the 20-year timespan 1997 to 2016.

A particular focus is to determine how the STDs of 850 hPa streamfunction anomalies for weather systems have changed in the early 21st century, in the 20-year timespan 1997 to 2016, and during the first 10 years of the AMD (1997 to 2006), compared with both of the earlier timespans of 1949 to 1968 and 1975 to 1994. We analyse the shifts from both earlier periods for several reasons. Hertzog et al. [46] (Figures 5, 6 and 8) note the reasonably good performance of the NNR data in the pre-satellite period. However, the NNR data for the period 1975 to 1994 is based on a larger number of observations with the inclusion of the satellite data starting in 1975. The changes in weather systems since the period 1949 to 1968 are also of considerable interest since the systematic rainfall decline in SWWA started occurring immediately following this period as discussed in Frederiksen and Osbrough [4]. In contrast, the SEA systematic rainfall reductions occurred later [4].

The plan of this chapter is as follows. In Section 2, we describe the NNR reanalysis dataset used for determining the properties of the large-scale circulation, particularly the zonal wind, and the weather systems. As well, the Australian Bureau of Meteorology rainfall dataset is described in this section. The methodology for filtering the atmospheric fluctuations into high-pass and band-pass contributions and for determining their growth rates and intensities and assigning them to three growth rate and three decay rate bins is described in Section 3. Section 4 describes the seasonal and decadal changes in southern Australian rainfall compared with the early period 1949 to 1968. Section 5 examines the interannual and decadal variability of rainfall and local circulation indices, as well as the interannual and decadal variability of rainfall and non-local large-scale circulation indices. The changes in early 21st century upper and lower tropospheric zonal winds and the 850 hPa storm tracks are examined in Section 6, with a focus on the storm tracks based on separate growing and decaying disturbances in different growth rate bins. In Section 7, we examine the changes in growing weather systems for the period associated with the Australian Millennium Drought compared to the 20-year baselines of 1949 to 1968 and 1975 to 1994. In Section 8, we discuss the weather system changes for the filtered disturbances and relate them to the changes in seasonal area averaged rainfall as described in our earlier Section 4 for both SEA and SWWA. In Section 9, we summarise our findings and present our conclusions. In Appendix A, we describe the methodology for calculating the growth and decay of weather systems. In Appendix B, we discuss the sensitivity of regional rainfall totals to sampling and our reasoning behind our choice of timespans.The heading Abbreviations contains a list of abbreviations used throughout the manuscript.

2. Datasets

2.1. Rainfall Dataset

Up-to-date total monthly Australian rainfall data beginning in 1900 are available from the Australian Bureau of Meteorology. We focus on seasonal and decadal changes in southern Australian total rainfall for the regions of SWWA [92] and SEA [93], as shown on the map in Figure 1 of Osbrough and Frederiksen [5]. These two distinct climatological regions are well represented spatially and temporally as seen from the rainfall network diagram on the Bureau of Meteorology [94] website. A complete analysis of the construction of this historical and ongoing real-time dataset of climate variables is described by Jones et al. [95].

2.2. Reanalysis Dataset

To investigate the properties of large-scale circulation impacting Australian rainfall, we employ the 2.5° gridded observational reanalysis dataset produced by the National Centers for Environmental Prediction (NCEP) and the National Centre for Atmospheric Research (NCAR) [42], herein referred to as NNR. The 20-year baseline periods used for comparison include the pre-satellite era 1949 to 1968, and the later 1975 to 1994 period, against the more recent periods of 1997 to 2006 of the AMD and 1997 to 2016. The seasonal changes in upper and lower tropospheric zonal wind across these timespans are examined at 300 hPa and 700 hPa. As well, we use the wind, temperature and humidity fields at 850 hPa taken every six hours (at 0 UTC, 6 UTC, 12 UTC and 18 UTC) to calculate streamfunctions and to determine the southern hemisphere storm tracks across all seasons.

3. Methodology

The methodology developed by Osbrough and Frederiksen [5] is used to determine the separate growing and decaying components of the weather system fluctuations. To begin with, the streamfunction, $\Psi$, as a function of longitude $(\lambda$), the sine of the latitude ($\mu =sin\varphi$) and time ($t)$ can be expanded in the following spherical harmonic series:

$$\Psi \left(\lambda ,\mu ,t\right)=\sum _m\sum _n{\Psi }_{mn}\left(t\right)P_n^m\left(\mu \right)e^{im\lambda },$$

(1)

where $m$ and $n$ are the zonal and total wavenumbers, and $P_n^m\left(\mu \right)$ are the Legendre functions. The spectral coefficients satisfy the complex conjugate property ${\Psi }_{-mn}\left(t\right)={\Psi }_{mn}^{*}\left(t\right)$ so that the physical space fields are confirmed real. A rhomboidal truncation is employed with a spectral resolution of 31 (R31). This equates to a longitude x latitude resolution of 375 km by 250 km at 30° S as described in Section 5 in Osbrough and Frederiksen [5].

The spectrally analysed six-hourly NNR reanalysis data with its annual cycle removed are filtered into two bands. The first, high-pass band, consists of small, fast-propagating disturbances with periods less than 4 days, while the second band consists of larger disturbances with periods occurring between 4 and 8 days. The growth rates of disturbances in each band are calculated as described in Appendix A and then dispensed into separate bins. A number of growth rate bins are chosen for this study as described in Section 6. The standard deviations (STDs) of the fluctuations in each bin are subsequently analysed to determine the decadal changes in weather systems across the three 20-year periods and the AMD, as described above in Section 2.

4. Seasonal and Decadal Changes in Southern Australian Rainfall

Table 1. SWWA rainfall totals (mm month⁻¹) for overlapping 3-month seasons (first letter of each month is used in three-letter identifiers, beginning with JFM describing January, February and March, etc.) during multi-decadal timespans and their percentage differences to the baseline period 1949 to 1968.

SWWA	Season
Years	JFM	FMA	MAM	AMJ	MJJ	JJA	JAS	ASO	SON	OND	NDJ	DJF
1949 to 1968	17.61	27.95	51.55	88.41	115.18	115.98	91.30	67.35	45.13	32.05	18.89	16.71
% diff	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
1975 to 1994	19.22	25.38	45.79	73.48	96.26	97.78	84.51	63.44	45.74	30.10	22.22	18.00
% diff	9.13	−9.17	−11.18	−16.89	−16.43	−15.69	−7.44	−5.80	1.35	−6.07	17.66	7.76
1997 to 2006	19.64	25.07	46.09	68.68	87.09	95.90	86.77	69.07	43.53	26.27	20.12	15.84
% diff	11.53	−10.29	−10.59	−22.31	−24.39	−17.32	−4.96	2.55	−3.55	−18.04	6.55	−5.17
1997 to 2016	18.87	24.98	45.55	66.35	85.84	92.03	86.23	66.34	45.31	28.64	22.93	17.20
% diff	7.17	−10.61	−11.64	−24.95	−25.47	−20.65	−5.55	−1.50	0.40	−10.65	21.42	2.94
2001 to 2020	18.82	24.77	42.45	62.51	82.24	89.85	84.52	64.67	44.25	28.78	22.95	18.09
% diff	6.89	−11.37	−17.66	−29.29	−28.60	−22.53	−7.43	−3.98	−1.94	−10.20	21.53	8.26

and

Table 2. SEA rainfall totals (mm month⁻¹) for overlapping 3-month seasons (first letter of each month is used in three-letter identifiers, beginning with JFM describing January, February and March, etc.) during multi-decadal timespans and their percentage differences to the baseline period 1949 to 1968.

SEA	Season
Years	JFM	FMA	MAM	AMJ	MJJ	JJA	JAS	ASO	SON	OND	NDJ	DJF
1949 to 1968	41.34	44.79	53.36	59.42	65.02	64.50	62.42	62.82	58.31	55.17	45.71	42.17
% diff	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
1975 to 1994	40.03	40.62	49.24	54.08	60.77	63.07	63.82	62.48	57.14	52.75	46.82	41.24
% diff	−3.16	−9.31	−7.72	−8.99	−6.53	−2.22	2.25	−0.55	−2.02	−4.39	2.41	−2.21
1997 to 2006	35.68	35.58	36.35	45.44	51.86	57.70	57.62	57.81	53.82	47.73	41.22	38.60
% diff	−13.68	−20.56	−31.88	−23.53	−20.23	−10.55	−7.69	−7.98	−7.71	−13.49	−9.84	−8.47
1997 to 2016	41.76	41.36	42.28	49.12	55.43	59.96	58.41	55.53	52.66	49.43	46.41	43.82
% diff	1.02	−7.66	−20.76	−17.33	−14.75	−7.03	−6.41	−11.62	−9.70	−10.41	1.52	3.90
2001 to 2020	41.66	42.13	42.90	48.59	54.16	59.03	56.51	52.77	49.15	48.19	45.90	43.87
% diff	0.77	−5.95	−19.61	−18.23	−16.70	−8.47	−9.46	−16.01	−15.72	−12.65	0.40	4.03

show the three-monthly average rainfall in successive periods between JFM and DJF, for SWWA and SEA, respectively. The data have been averaged over 20-year timespans between the middle of the 20th century and early 21st century and for the first 10 years of the AMD. As well, the tables show the percentage changes in each timespan compared with that for 1949 to 1968.

The timespans used in Table 1 and Table 2 were suggested in Refs. [5,41,65] with the new addition of the timespan 2001 to 2020. The first 20-year period 1949 to 1968 corresponds to the start of the NNR data and 1975 to 1994 was chosen as the next 20-year period with a gap of several years from the end of the first so that they are largely independent. The second period is also a time of significant reduction in SWWA rainfall [5,41,65]. The third period is the first 10 years of the AMD, 1979–2006, with the longer 20-year fourth period 1997–2016 chosen for comparison with the AMD and to test sensitivity to the length of the timespans. Rainfall results for the final period 2001 to 2020 are included to give insight into the sensitivity of the statistics to slight shifts in the start of the 20-year periods. This issue of possible sensitivity to the chosen 20-year periods is discussed in more detail in Appendix B. The central issue is that annual rainfall in SWWA and SEA has been reducing essentially consistently on 20-year timescales, and the results in Table 1 and Table 2 reflect this fact at least for the cooler seasons.

For SWWA, there is a systematic decrease with time in rainfall totals in AMJ, MJJ and JJA (compared with both the baselines of 1949 to 1968 and 1975 to 1994) in Table 1. For each timespan of 10 or 20 years shown, there is also a decrease compared with 1949 to 1968 in the 3-month averages between FMA and JAS. In the other 3-month averages, the changes are more variable with a tendency towards increasing rainfall in the summer periods.

For SEA, rainfall totals also decrease for each 20-year timespan, shown in Table 2, in AMJ, MJJ and JJA compared with 1949 to 1968, but the biggest decreases occur during the 10-year period of the AMD. The effect of the AMD is remarkable in that SEA rainfall decreased compared with 1949 to 1968 and with 1975 to 1994 in all 3-month averages between JFM and DJF. During the 20-year timespan 1997 to 2016, SEA rainfall also decreased compared with 1949 to 1968 and with 1975 to 1994, apart from slight increases in some summer periods and timespans.

5. Indices of Atmospheric and Oceanic Processes Affecting Rainfall

Relationships between southern Australian rainfall and indices characterising large-scale circulation variability and change are considered in this section. We consider a number of indices that describe regional circulation variability and indices that encapsulate hemispheric and global processes.

5.1. Interannual Variability of Rainfall and Local Circulation Indices

The local circulation indices we consider are sea level pressure (SLP), ${\omega }^{850}$, the 850 hPa vertical velocity in pressure coordinates, and $u^{700}$, the zonal wind at 700 hPa. We use the regions defining these indices, shown in

Table 3. Definition of indices used for local, hemispheric and global regions.

Index	Regions and Variables Defining Indices
SWWA SLP	27.5° S–35° S, 115° E–125° E
SWWA ${\omega }^{850}$ hPa	25° S–35° S, 115° E–117.5° E
SWWA $u^{700}$ hPa	20° S–35° S, 110° E–132.5° E
SEA SLP	30° S–40° S, 137.5° E–155° E
SEA ${\omega }^{850}$ hPa	32.5° S–40° S, 137.5° E–155° E
SEA $u^{700}$ hPa	20° S–35° S, 132.5° E–155° E
SAJ	Zonally averaged 20° S–35° S zonal wind u at 700 hPa
SAM	Zonally averaged 40° S SLP — 65° S SLP
SOI	Standardised Tahiti—Darwin SLP
IPO	50° S–50° N, 100° E–100° W SST
IOD	(10° N–10° S, 50° E–70° E)—(0°–10° S, 90° E–110° E) SST
SORD	(52.5° S–60° S, 60° E–110° E)—(20° S–35° S, 90° E–110° E) SST

for SWWA and SEA, respectively, that were also used by Osbrough and Frederiksen [5] to describe July rainfall correlations. There it was found that they gave high and significant correlations with mid-winter rainfall, and we expect that will also be the case in a large proportion of the rest of the cool season.

Figure 1 shows the average correlation, for the timespan 1948 to 2018, of the three local indices with rainfall for SWWA and SEA. The bar graphs show results for twelve successive (overlapping) 3-month periods between January–February–March (JFM) and December–January–February (DJF). Both correlations between the total data, including trends, and the detrended data for SWWA (Figure 1a and detrended in Figure 1b) and SEA (Figure 1c and detrended in Figure 1d) are depicted. For both SWWA and SEA and for both correlations and detrended correlations of rainfall with $-$SLP and $u^{700}$, the correlations are greater than 0.5 and they are highly significant with confidence levels $C_L>0.99\%$ for the cool season periods between AMJ and ASO. The correlations for $u^{700}$ and $-$SLP are generally very similar with peak values in the early to middle winter 3-month periods of MJJ and JJA. The sea level pressure of course measures the strength of the lows and unsurprisingly is closely related to cool season rainfall. The relationship between $u^{700}$, as a measure of lower atmosphere baroclinicity, and rainfall is more complex since it is a measure of the growth of storms and their role in rainfall. The fact that $u^{700}$ performs nearly as well as SLP, and on occasions slightly surpasses it, is quite remarkable. The correlations between rainfall and ${-\omega }^{850}$ are also generally higher in the cool season between AMJ and ASO but smaller than for $-$SLP and $u^{700}$. This was also noted in Ref. [5] for July.

Interestingly, in the MAM transition season, ${-\omega }^{850}$ has higher correlation with SEA rainfall than $-$SLP and $u^{700}$. For both SWWA and SEA in the MAM and SON transition seasons, $-$SLP and $u^{700}$ are still reasonable descriptors of rainfall variability.

In the warm seasons between OND and FMA, the skill of the local indices generally falls away, although $-$SLP and $u^{700}$ still perform reasonably in OND with correlations near 0.5 for $-$SLP and $u^{700}$ with SWWA rainfall. Correlations of SEA rainfall with ${-\omega }^{850}$, in the warm seasons, are higher than for the other two indices but still less than or near 0.5.

5.2. Interannual Variability of Rainfall and Large-Scale Circulation Indices

Southern Australian rainfall is also related to large-scale circulation features and teleconnection patterns associated with the Southern Oscillation Index (SOI), the Indian Ocean Dipole (IOD), the Southern Annular Mode (SAM) and two indices introduced in Ref. [5], the Subtropical Atmospheric Jet (SAJ) index and the Southern Ocean Regional Dipole (SORD) index. The regions defining these indices are listed in Table 3. The British Antarctic Survey data for SAM starts in 1957 [75]. We therefore calculated correlations of the indices including SAM from 1957 to 2018 and from 1948 to 2018 for the remaining indices. However, in the following, we focus on 1957 to 2018 since the differences with the longer timespan are generally small.

Figure 2 shows the average correlations for 1957 to 2018 of the five hemispheric and global circulation indices with SWWA and SEA rainfall for the 3-month periods from JFM to DJF. In broad terms, the correlations for the total data (Figure 2a for SWWA and Figure 2c for SEA) and the detrended correlations (Figure 2b for SWWA and Figure 2d for SEA) have similar seasonal variability. We note, however, that including the trends makes some difference.

Between AMJ and JJA, total rainfall correlations in SWWA with SORD are largest, with SAJ equal in JJA, and second largest in AMJ and MJJ. Total SWWA rainfall correlations with $-$SAM are third largest between MJJ and JJA and largest in JAS. The detrended correlations are generally lower with SAJ and $–$SAM, yielding equal strongest correlations in JJA. In JAS, $-$SAM is dominant for both total and detrended SWWA rainfall correlations. The influence of the $-$IOD on SWWA rainfall is seen primarily in SON where both correlations are largest but still less than 0.4. In the other 3-month periods, the index correlations are generally small and with confidence levels $C_L<95\%$.

Both total and detrended SEA rainfall correlations with SOI and $-$IOD are dominant and significant with confidence levels $C_L>99\%$ between MJJ and OND with SOI correlations also 0.5 in NDJ. For the other indices (SORD, SAJ and $-$SAM), the correlations are generally small and with confidence levels $C_L<95\%$. Interestingly, the significant SOI and $-$IOD correlations are largely unaffected by the trends.

In broad terms, SORD, and the jet stream index characterised by SAJ and SAM, are most important for SWWA rainfall between AMJ and JAS. In contrast, SEA interannual variability is most related to SOI and IOD between MJJ and OND with SOI also significant in NDJ.

5.3. Decadal Variability of Rainfall and Local Circulation Indices

Next, we examine how decadal changes in local atmospheric indices affect southern Australian rainfall. Figure 3 shows total and detrended correlations for 3-month periods between JFM and DJF of 10-year running mean data, based on 1948 to 2018, for local indices of $-$SLP, ${-\omega }^{850}$ and $u^{700}$ and SWWA and SEA rainfall. The local indices are again defined in Table 3 for SWWA and SEA.

We note the high correlations between SWWA rainfall and $-$SLP and $u^{700}$ also occur on decadal timescales, particularly between MJJ and JAS with confidence levels $C_L>90\%$. Indeed, SLP is a reasonably good predictor between AMJ and JAS based on both total and detrended rainfall correlations. In the remainder of the 3-month periods, SLP and $u^{700}$ correlations are generally smaller and less significant with confidence levels $C_L<90\%$. The uplift index ${-\omega }^{850}$ in general does not perform well on decadal timescales as a descriptor of SWWA rainfall. For SEA, rainfall total correlations with $-$SLP and $u^{700}$ on decadal timescales are greater than or equal to 0.45 between MAM and OND. Detrended correlations tend to be smaller. Interestingly, the uplift index ${-\omega }^{850}$ gives the highest SEA rainfall correlations in the warmer periods of NDJ, DJF, JFM and FMA, as well as MAM to MJJ, and this is the case for both the total and detrended results (with $u^{700}$ equal highest in MAM for detrended correlations).

5.4. Decadal Variability of Rainfall and Large-Scale Circulation Indices

Decadal changes in indices characterising hemispheric and global atmospheric and oceanic large-scale processes are also useful descriptors and predictors of associated changes in Southern Australian July rainfall as noted and reviewed by Osbrough and Frederiksen [5]. Total and detrended correlations of 10-year running means of the large-scale circulation indices in Table 3 with SWWA and SEA rainfall are shown in Figure 4 for JFM to DJF.

Decadal variability in SWWA rainfall is highly correlated with both the SAJ and SORD indices, introduced in Ref. [5], on this timescale, in MJJ and JJA whether detrended or not. This is also the case for SORD in AMJ and MAM. The total correlations between $-$SAM and SWWA rainfall are also high and significant ($C_L>90\%$) between MAM and JJA, but much of this correlation is due to similar trends of $-$SAM and rainfall with the detrended correlations being much smaller. The $-$IOD and SWWA rainfall also have quite large total correlations for AMJ to JJA, but apart from MJJ, this is largely due to similar trends. In other 3-month periods and for the other indices shown, the correlations are generally small or reversed.

On decadal timescales, the importance of the large-scale indices for describing SEA rainfall variability is quite complex for the different 3-month periods as shown in Figure 4c,d. Overall, the highest correlations are with the $-$IOD in ASO and SON for detrended and total data; the $-$IOD also yields large negative correlations in NDJ, DJF and JFM. In JAS, the SAJ index dominates for both correlations, reflecting the July results of Ref. [5], while in MAM and AMJ, the $-$SAM index has the highest correlations, and in MJJ and JJA, the IPO plays an important role.

6. Circulation and Storm Track Changes in the Early Twenty-First Century

Osbrough and Frederiksen [91] examined the seasonal variability of the large-scale SH circulation, characterised primarily by the 300 hPa and 700 hPa zonal winds, and the storm tracks for the 20-year period 1997 to 2016. The standard storm tracks defined by the regions of large standard deviations of 850 hPa streamfunction anomalies were considered in two frequency bands corresponding to high-pass data with periods $T_r<4$ days and band-pass data with $4\le T_r<8$ days.

As well, the storm tracks associated with separate growing and decaying disturbances in three growth rate bins and three bins for decaying disturbances over 6 h timespans were studied. The growth rate bins are shown in Table 1 of Ref. [91] and reproduced below in

Table 4. Growth rate ranges of six growth rate bins.

Bin	Slow	Moderate	Fast
Decaying systems	$-0.5\le {\varpi }_i<0\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$	$-1\le {\varpi }_i<-0.5\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$	${\varpi }_i<-1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$
Growing systems	$0\le {\varpi }_i<0.5\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$	$0.5\le {\varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$	${\varpi }_i\ge 1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$

. The storm tracks of growing and decaying disturbances were again analysed in the high-pass and band-pass frequency bands. In this article, we combine the results in the slow and moderate bins since they have similar behaviour to the bins shown in

Table 5. Growth rate ranges of four growth rate bins.

Bin	Slow and Moderate	Fast
Decaying systems	$-1\le {\varpi }_i<0\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$	${\varpi }_i<-1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$
Growing systems	$0\le {\varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$	${\varpi }_i\ge 1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$

.

In this section, we examine how the 300 hPa and 700 hPa zonal winds and 850 hPa storm tracks have changed in the early 21st century (1997 to 2016) compared with two twenty-year timespans in the 20th century (1949 to 1968 and 1975 to 1994). Our focus is on changes in the storm tracks based on separate growing and decaying disturbances in several growth rate bins.

6.1. Decadal Circulation and Storm Track Changes Between 1949 to 1968 and 1997 to 2016

The development of extratropical storms has a strong connection with the structure of the jet streams as discussed by Osbrough and Frederiksen [91]. The Phillips [96] criterion for the onset of baroclinic instability is an approximate diagnostic for storm formation. In spherical geometry, it is given by

$$u^{upper}-u^{lower}-{\displaystyle \frac{\sigma b_{\kappa }{c}_{p}cos\varphi }{a\mathsf{\Omega }{sin}^2\varphi }}$$

(2)

where $u^{upper}$ and $u^{lower}$ are the zonal winds at suitable upper and lower pressure levels. The static stability, $\sigma$, is a measure of the potential temperature shear between these levels; it may include the effects of moisture. In Equation (2), the earth’s radius is $a=6.371\times {10}^6$ m, and the angular rotation speed is $\mathsf{\Omega }=7.292\times {10}^{-5}$ rad s⁻¹. The specific heat of air at constant pressure is $c_p=1004$ JK⁻¹kg⁻¹, and the nondimensional constant$b_{\kappa }=0.124$. Instability occurs whenever the Phillips criterion is positive. To a large extent, the wind shear provides a good measure of the changes in instability because the static stability has changed considerably less over the decades [41,91].

6.1.1. Changes in Zonal Winds

Next, we examine the seasonal variability of the changes in 300 hPa and 700 hPa SH zonal winds between 1949 to 1968 and 1997 to 2016. Figure 5 shows the 1997 to 2016 minus 1949 to 1968 SH zonal wind differences for the standard seasons JJA, SON, DJF and MAM and at 300 hPa (Figure 5a) and 700 hPa (Figure 5b). In broad terms, we see increases in the strength of the polar jet in each season and at both levels, particularly on the polar flank near 60° S, with the maxima occurring nearer 45° S to 50° S over the South Pacific Ocean.

There are also regions of significant reductions in the zonal jets in Figure 5 both equatorward and poleward of the polar jet locations. At 300 hPa, in Figure 5a, we see that there is a decrease in jet strength between 0° and 120° E, particularly between 30° S and 40° S. Primarily over the South Pacific Ocean, the reductions occur at lower latitudes mainly between 20° S and 30° S. In the regions around South America and over the South Atlantic Ocean, the deficit in jet strength is centred near 40° S. There are also decreases in the 300 hPa zonal wind to the south of the polar jet stream. At 700 hPa, the zonal wind differences in general follow those in the upper troposphere with lower magnitudes although there are some notable differences. Over the Indian Ocean, the reductions are centred on 20° S in JJA and SON, and this is also the case over the eastern part of the South Pacific, particularly in SON, DJF and MAM.

6.1.2. Changes in Standard Deviations of Weather Systems with Periods $T_r<4$ Days

In the study of Osbrough and Frederiksen [5], it was found that examining changes in storm tracks in the separate bins of growing and decaying disturbances was most informative. We found that this is the case not just for the month of July considered in Ref. [5] but for the whole seasonal cycle. For this reason, we focus in this subsection on the separate bins rather than also documenting changes in the storm tracks based on all fluctuations in a given frequency band. We also found that there is generally some commonality between the changes in the growth rate bins with $0\le {\varpi }_i<0.5\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ and $0.5\le {\varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ and those with $-0.5\le {\varpi }_i<0\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ and $-1\le {\varpi }_i<-0.5\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$. For the sake of brevity, we therefore reduce the number of bins by combining corresponding growth and decay rates such that $0\le {\varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ and $-1\le {\varpi }_i<0\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$. We maintain the separate growth rate bins for both rapid growth and decay with ${\varpi }_i>1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ and ${\varpi }_i<-1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$, respectively.

Figure 6 shows the changes in SH 850 hPa high-pass filtered ($T_r<4$) streamfunction anomalies between 1949 to 1968 and 1997 to 2016 for the four growth rate bins shown in Table 5 and for the standard seasons JJA (Figure 6a), SON (Figure 6b), DJF (Figure 6c) and MAM (Figure 6d).

Throughout the seasonal cycle and for both the growing and decaying disturbances, there are increases in the STDs of the fluctuations in the regions of the polar jets as might be expected on the basis of baroclinic instability theory and the increases in these jets seen in Figure 5. The increased storminess in the bin $0\le {\varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ in Figure 6 has a generally larger contribution from disturbances with growth rates $0\le {\varpi }_i<0.5\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ than those with $0.5\le {\varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ in each season. Similarly, the bin $-0.5\le {\varpi }_i<-1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ is the dominant contributor to the bin $-1\le {\varpi }_i<0\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$.

In most seasons, but less so in MAM, there is some reduction in the STDs, in Figure 6, over and near the continents of southern Africa, Australia and South America in the bin of fast-decaying disturbances with ${\varpi }_i<-1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$. The most notable reductions, however, are in the bin of fast-growing weather systems with ${\varpi }_i\ge 1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$. These deficits again mainly occur over and near the continents of southern Africa and South America and in the Australian–New Zealand region. The regions with lower STDs are broadly consistent with the reduced zonal winds in Figure 5 near 30° S to 40° S in the eastern hemisphere. However, there is little reduction in storminess over the South Indian Ocean. It is possible that this could be related to the lower data quality away from the continents in the pre-satellite era [4,6,97]. Over and near South America, the reduced storminess extends further poleward in broad agreement with the reductions in zonal winds in Figure 5. Over the Pacific Ocean, the storminess has increased, and the reason for this may have several ingredients. Firstly, the equatorward flanks of the polar jets in Figure 5 have extended to lower latitudes over the Pacific Ocean and increased in strength. Secondly, the reductions in jet strengths that occur over the Pacific Ocean at still lower latitudes are likely to have less influence on baroclinic instability because of the $si{n}^2\left(\varphi \right)$ in the denominator of the Phillips criterion in Equation (2) that stabilises the flow nearer the equator. Thirdly, lower data quality over the Pacific Ocean during the pre-satellite era could play a role as discussed further in Section 8.

6.1.3. Changes in Standard Deviations of Weather Systems with Periods $4\le T_r<8$ Days

As noted in Ref. [5] for July, the slower-propagating larger-scale weather systems with periods $4\le T_r<8$ days in general grow and decay less rapidly than those in the high-pass band. This is reflected in the lower magnitudes in the STD differences of 850 hPa streamfunction fluctuation between 1949 to 1968 and 1997 to 2016 in the bins with ${\varpi }_i\ge 1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ and with ${\varpi }_i<-1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ in Figure 7 throughout the four seasons. In the bins with $0{\le \varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ and $-1{\le \varpi }_i<0\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$, the STDs of weather system fluctuations broadly increased in the timespan 1997 to 2016 compared with 1949 to 1968 south of 30° S. The main exceptions are near and over SEA and the Tasman Sea, extending to New Zealand to some extent. The reductions are largest in the transition seasons of MAM, and particularly SON, where there are also reduced STDs over the Indian Ocean at 20° S and to the east of New Zealand.

6.2. Decadal Circulation and Storm Track Changes Between 1975 to 1994 and 1997 to 2016

6.2.1. Changes in Zonal Winds

The general increases in the 300 hPa and 700 hPa SH zonal winds shown in Figure 5 around 60° S near the polar jet and decreases around 30° S near the subtropical jet between 1949 to 1968 and 1997 to 2016 also occur to some extent between 1975 to 1994 and 1997 to 2016. However, as shown in Figure 8, the changes in most regions are smaller and geographically more variable. Nevertheless, for JJA, DJF and MAM, there are increases in the polar jet near 60° S in the eastern hemisphere, and these increases are shifted slightly equatorward in the western hemisphere. In SON, the largest increases in jet strength occur over the South Pacific Ocean near 45° S. At 300 hPa, there are also decreases in jet strength in all seasons over the South Pacific Ocean at lower latitudes. At 700 hPa, the reductions in zonal wind occur over the eastern South Pacific Ocean off the coast of South America with strongest signals near 15° S. In the eastern hemisphere equatorward of 50° S, the response in the zonal wind is more variable geographically. At 700 hPa, there are significant areas of zonal wind decrease upstream of Australia, over the Indian Ocean, particularly between 15° S and 30° S in JJA and SON with weaker but more expansive areas in DJF and MAM. At 300 hPa, the zonal wind changes in the eastern hemisphere between 20° S and 50° S have some local areas of increase in a broad domain of decrease.

6.2.2. Changes in Standard Deviations of Weather Systems with Periods $T_r<4$ Days

Differences in SH 850 hPa high-pass filtered ($T_r<4$ days) streamfunction fluctuations between 1975 to 1994 and 1997 to 2016 are shown in Figure 9 for the same four bins as in Table 5. They consist of two bins of decaying disturbances with ${\varpi }_i<-1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ and ${-1\le \varpi }_i<0 \mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ and two bins of growing disturbances with ${0\le \varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ and ${\varpi }_i>1 \mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ as in Table 5.

Throughout the seasonal cycle, there are increases in weather system fluctuations with ${0\le \varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$, in the timespan 1997 to 2016 compared with 1975 to 1994, across the hemisphere in the polar storm track. In each season, the increases in STDs are located in much the same band as in Figure 6 but with somewhat reduced magnitudes. This is broadly consistent with the fact that polar jet differences in Figure 8 for 1997 to 2016 minus 1975 to 1994 are smaller than in Figure 5 for 1997 to 2016 minus 1949 to 1968.

In the bin with the fast-growing storms, ${\varpi }_i>1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$, autumn and winter STDs in Figure 9 have increased poleward of 60° S apart from in the vicinity of South America, but the increases are less than in Figure 6. In spring and summer, the changes in the STDs of fast-growing storms south of the polar jet are more variable depending on geographical location. The changes that have occurred in STDs in the mid-latitudes for the bin with fast-growing disturbances are particularly interesting. Again, with the reduction in the zonal winds in Figure 8, around 30° S in the vicinity of the subtropical jets, there have been reductions in the STDs of 850 hPa streamfunction fluctuations in what appears to be a wave number 4 pattern of large lows and smaller highs across the hemisphere. Three of the areas of reduction in storm activity are located over the land masses of southern Africa, Australia, extending to New Zealand, and particularly Southern America and surrounds. The fourth low centre is over the central South Pacific Ocean between the date line and 120° W. These regions broadly agree with the band of reduction in the zonal winds and associated low and mid-level baroclinicity that can be deduced from Figure 8.

Interpreting the magnitudes of the changes in Figure 9 and the wave number 4 structure, based on the changes in the zonal winds, is more difficult. Indeed, as noted in Frederiksen and Frederiksen [98], even in the case of linear instability theory, the structures of the storm tracks based on primitive equations may have considerable differences compared with simple criteria like the Phillips criterion [96]. In principle, one would need to know the complete flow and thermal structure of at least the troposphere together with boundary layer processes and the effective moist static stability over the domain [99]. Moreover, as discussed in Ref. [5], here, the weather mode instabilities see the instantaneous flow on which they are growing rather than the climatological basic states. As noted by Frederiksen and Bell [100] and Osbrough and Frederiksen [5], instantaneous basic states generally result in instabilities with larger growth rates than climatological basic states where the potential vorticity gradients are smoothed. Thus, taking the statistical average of instabilities growing on many snapshots of the flow fields yields more accurate information than calculating the instability of a statistically averaged flow or a simple criterion based on such a climatological flow.

6.2.3. Changes in Standard Deviations of Weather Systems with Periods $4\le T_r<8$ Days

The changes in band-pass filtered STDs of 850 hPa streamfunction anomalies between 1975 to 1994 and 1997 to 2016 are shown in Figure 10 for growing weather systems in the bins with $0{\le \varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$and ${\varpi }_i>1 \mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$. The differences are shown for each season with the band-pass filter again corresponding to periods $4\le T_r<8$days. There are again only small changes in STDs for fast-growing disturbances with ${\varpi }_i>1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ as in Figure 7.

In the bin with $0{\le \varpi }_i<1 \mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$, the STD differences for JJA in Figure 10a(iii) have broad similarities with those in Figure 7a(iii). In both cases, there are increases in the STDs generally south of 30° S, but they are smaller for 1997 to 2016 minus 1975 to 1994, consistent with the smaller reductions in the strengths of the polar jets between these timespans. We also note the localised centre of decrease in amplitude off the east coast of South Africa and the low values over eastern Australia and the Tasman Sea in Figure 10a(iii).

In the other three seasons, the increases in STDs in 1997 to 2016 are less extensive and less consistent across the hemisphere and generally restricted to areas nearer the polar jet. In DJF, we note negative centres in Figure 10c(iii) off the east coast of South Africa, near New Zealand and over the southern part of South America. The most extensive reductions in STDs occur in the transition seasons of MAM (Figure 10d(iii)) and particularly SON (Figure 10b(iii)). In MAM, there are low-amplitude centres across the eastern hemisphere in a band from eastern South Africa at 30° S across the Indian Ocean to more southern latitudes near Australia and New Zealand. As well, there is a localised area of low values over Southern America. The magnitudes of the reductions in MAM in Figure 10d(iii) are larger and more extensive than the differences with the earlier period in Figure 7d(iii). The most extensive reductions in the eastern hemisphere occur in SON in Figure 10b(iii) where they are largely located equatorward of 50° S. Over the central South Pacific Ocean, there is also a band of negative values between 20° S and 30° S. The reductions are particularly large near South Africa, over SEA and the Tasman Sea with another low-value centre over the southern part of South America.

7. Storm Track Changes During the Australian Millennium Drought

As reviewed in the Introduction, the AMD was perhaps the most significant drought in southern Australia during the 20th century and into the early 21st century. In this section, we focus on the first decade of the AMD between 1997 and 2006 with the drought breaking in late 2009. There is in fact much in common between the circulation and storm tracks and rainfall over southern Australian during the AMD and during the 20 yr period 1997 to 2016 that incorporates the AMD. For that reason, in this section, we do not go into the changes in circulation and the hemispheric changes in the STDs of weather systems, in the AMD, in the same detail as in the earlier sections. Rather, we focus mainly on the Australian New Zealand (ANZ) region and the shifts in the STDs of growing weather systems that occurred during the AMD.

7.1. Changes in Storm Tracks Between 1949 to 1968 and the AMD

7.1.1. Changes in STDs of Weather Systems with Periods $T_r<4$ Days

The differences between 1949 to 1968 and the AMD years of 1997 to 2006, in SH 850 hPa high-pass filtered ($T_r<4$ days) streamfunction disturbances, are shown in Figure 11 for the two growth rate bins of growing systems with $0{\le \varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ and ${\varpi }_i>1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$and for each of the standard seasons. The broad similarities with the corresponding differences between 1949 to 1968 and 1997 to 2016 in Figure 6 are very apparent. Throughout the seasonal cycle, there is increased activity in the growth rate bin $0{\le \varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$, particularly south of Australia over the Great Australian Bight and in the region of New Zealand as well as over South America, in both Figure 6 and Figure 11. The results for JJA are also very similar to those in Figure 7 of Osbrough and Frederiksen [5] for July. Again, in each season, the decreased STDs over Australia and New Zealand for the fast-growing disturbances with ${\varpi }_i>1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ are the striking features in Figure 6 and Figure 11. Most notable are the similar broad-scale features in a given season with some variability in magnitudes of changes. As expected, the July results in Figure 7 of Ref. [5] are largely replicated in Figure 11 in JJA but with a slightly smaller magnitude for the season.

7.1.2. Changes in STDs of Weather Systems with Periods $4\le T_r<8$ Days

For the band-pass filtered weather systems, there is again little change in STDs between 1949 to 1968 and the AMD period in the bin with fast-growing disturbances. We therefore focus in this subsection on the 850 hPa STD difference in the bin with $0{\le \varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$with the results shown in Figure 12 for each season. Comparing the results in Figure 12 with those in Figure 7, the similarities are most notable. In the AMD, as in the 20 yr timespan 1997 to 2016, the STDs of weather systems have generally increased poleward of 30° S to 40° S. Again, there are reductions over the Tasman Sea in MAM and SON that are geographically more extensive, also influencing SEA and New Zealand in particular.

7.2. Changes in Storm Tracks Between 1975 to 1994 and the AMD

7.2.1. Changes in STDs of Weather Systems with Periods $T_r<4$ Days

Figure 13 shows the STD differences between 1975 to 1994 and the AMD years of 1997 to 2006 in SH 850 hPa high-pass filtered streamfunction disturbances in the two growth rate bins with $0{\le \varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$and ${\varpi }_i>1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$. In both growth rate bins and for a particular season, the similarities between the results in Figure 13 with those in Figure 9 are much more obvious than the minor geographical shifts. In the bin of fast-growing fluctuations, the patterns of decrease over the Australian and New Zealand regions are virtually identical with some slight changes in amplitude. Again, in the bin of slow- and moderately growing systems the dominant feature in the results is the increases in amplitudes south of 30° S to 40° S.

7.2.2. Changes in STDs of Weather Systems with Periods $4\le T_r<8$ Days

For the band-pass filtered weather systems, we again focus on the bin of slow- and moderately growing disturbances with $0{\le \varpi }_i<1 \mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ since the STDs of 850 hPa streamfunctions for fast-growing systems vary little between 1975 to 1994 and the 10 years of the AMD of 1997 to 2006. Figure 14 shows these results for the Southern Hemisphere. The characteristic structures of the differences between 1975 to 1994 and 1997 to 2016 in the STDs of slow and moderately growing disturbances shown in Figure 10 are again evident in Figure 14. Particularly in the transition months of MAM and SON, the reductions in STDs in the southern Australia and New Zealand regions are very evident in Figure 14 with magnitudes slightly larger than in Figure 10. There are also large reductions in MAM and particularly SON from southeast of Africa across the Indian Ocean and over South America.

8. Weather Systems and Southern Australian Rainfall Changes

In the previous two sections, we analysed the changes in weather systems between the modern timespan of 1997 to 2016 and the AMD of 1997 to 2006 and two earlier 20-year time periods in the 20th century, namely 1949 to 1968 and 1997 to 1994. The changes in the STDs of streamfunction anomalies at 850 hPa were considered for both growing and decaying systems with a focus on the growing disturbances. The decadal shifts were analysed for the seasonal cycle and thus extended considerably the study of Osbrough and Frederiksen [5] where related results were obtained for the mid-winter month of July. Osbrough and Frederiksen [5] found that there were broad connections between the reductions in southern Australia rainfall and those in the storm tracks of growing weather systems. The links were particularly strong for explosive weather systems with periods $T_r<4$ days. The storm tracks in the high-frequency range consist of baroclinic Rossby wavetrains of highs and lows with the low-pressure systems having the most impact on rainfall changes as noted in the studies of fronts and cut-off lows by Risbey et al. [56,57]. Indeed, it was found by Osbrough and Frederiksen [5] that there was general consistency between the data-driven results and the theoretical studies by Frederiksen and Frederiksen [41,66] and the synoptic studies of Risbey et al. [56,57].

In this section, we aim to make similar determinations to those of Osbrough and Frederiksen [5] between weather system changes and southern Australian rainfall decline but for the seasonal cycle. The high-pass ($T_r<4$ days) and band-pass ($4\le T_r<8$ days) frequencies that we consider mean that the extratropical weather systems are frontal systems, cyclones and anticyclones, blocks and cut-off lows, and shorter-period NWCB disturbances. Our results are essentially replicated by STDs of meridional winds as noted in Ref. [5]. The NNR data with 2.5° resolution in latitude and longitude largely excludes the resolution of thunderstorms which play an important role in determining Southern Australian rainfall, particularly in the warm season [88,89,101]. Most of the cool season rainfall in SEA between 1979 to 1996 and 1997 to 2015 has been found to be related to fewer rain-bearing fronts and cyclones [56,57,88]. Thunderstorm rainfall has also increased at the same time, primarily in the warm season. Combinations of weather systems can result in high-rainfall events. As noted in the Introduction, lower-frequency weather systems such as NWCBs and intraseasonal oscillations also contribute to rainfall. Given the diverse processes contributing to rainfall and the difficulty in uniquely describing some processes [68,88], our aim in this section is to draw interesting connections between changes in storm tracks and rainfall decline rather than make definitive attributions.

8.1. Weather Systems and SEA Rainfall Changes

We start our comparison of changes in the STDs of 850 hPa streamfunction anomalies and rainfall by considering SEA where the more recent shifts have been particularly dramatic. This is of course the case for the 10-year period 1997 to 2006 of the AMD as discussed in Section 4, and we consider this period next followed by the 20-year timespan 1997 to 2016.

8.1.1. Changes in Weather Systems and SEA Rainfall During the AMD

From Table 2, we note the consistent reduction in SEA rainfall between 1949 to 1968 and the first 10 years of the AMD. This occurs for all the twelve 3-month periods shown but with the largest reductions in MAM. We also note that the changes between the two 20-year periods 1949 to 1968 and 1975 to 1994 were relatively modest as discussed and reviewed by Frederiksen and Osbrough [4] and as also seen from Table 1. Thus, there are also consistent reductions in SEA rainfall between 1975 to 1994 and the AMD, and these again occur for all of the twelve 3-month periods. Generally, these reductions are slightly lower than from the earlier period (apart from JAS and NDJ). As we have noted in the Introduction and in this section, thunderstorms are expected to have contributed to the smaller reductions in rainfall in the warmer periods. The consistent reductions across all 3-month periods are, however, remarkable, and this occurs for both changes from 1949 to 1968 and from 1975 to 1994.

As detailed in Section 7, in each season, and for both baselines of 1949 to 1968 and 1975 to 1994, the STDs of high-pass filtered ($T_r<4$ days) streamfunction fluctuations for explosive storms (${\varpi }_i>1 \mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$), during the AMD, are reduced over and upstream of SEA (Figure 11 and Figure 13). For DJF, the reductions immediately over SEA are less extensive, however. Slower- and moderately growing storms ($0{\le \varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$) tend to counteract this reduction, but as discussed by Osbrough and Frederiksen [5] and in the Introduction, explosive storms are expected to have a high impact on rainfall.

Weather systems in the band-pass frequency band ($4\le T_r<8$ days) tend to grow more slowly with little change in the explosive systems with ${\varpi }_i\ge 1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$. The changes during the AMD compared with each of the two baseline periods of 1949 to 1968 (Figure 12) and 1975 to 1994 (Figure 14) in STDs occur mainly in the growth rate bin with $0{\le \varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$. In the transition seasons of MAM, and particularly SON, there are considerable reductions over the SEA region during the AMD and more so compared with the baseline of 1975 to 1994 than with 1949 to 1968. In JJA and to some extent in DJF, the change is an increase, particularly compared with 1949 to 1968.

8.1.2. Changes in Weather Systems and SEA Rainfall in 1997 to 2016

The SEA rainfall changes during the 20-year period 1997 to 2016 compared with each of the baselines 1949 to 1968 and 1975 to 1994 have much in common with those during the AMD. As shown in Table 2, there are consistent reductions between 1949 to 1968 and 1997 to 2016 in all 3-month periods apart from summer (NDJ, DJF and JFM). This is also the case between 1975 to 1994 and 1997 to 2016. The declines in SEA rainfall for 1997 to 2016 are, of course, generally smaller than for the AMD, although there are exceptions such as for ASO and SON.

Section 6 and Section 7 contain analyses of the close similarities between weather system changes during 1997 to 2016 and the AMD compared with each of the baseline periods of 1949 to 1968 and 1975 to 1994. In particular, the reductions in STDs over and upstream of SEA of explosive storms (${\varpi }_i>1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$) in the high-pass band ($T_r<4$ days) in each season is the outstanding feature of both the 10-year (Figure 11 and Figure 13) and 20-year (Figure 6 and Figure 9) recent periods. There are, however, only subtle variations in the magnitudes of the changes.

Again, the statistics of weather systems with periods $4\le T_r<8$ days are very similar during 1997 to 2016 and the AMD. The reductions in STDs in the growth rate bin $0{\le \varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ over SEA are slightly larger during the AMD than for the 20-year period 1997 to 2016.

8.2. Weather System and SWWA Rainfall Changes

Next, we consider associations between changes in STDs of 850 hPa streamfunction fluctuations and SWWA rainfall and for the AMD, followed by the 20-year period 1997 to 2016.

8.2.1. Changes in Weather Systems and SWWA Rainfall During the AMD

Table 1 shows that the SWWA rainfall declined in the AMD 10-year period of 1997 to 2006 compared with 1949 to 1968 between FMA and JAS. In the 3-month periods between ASO and JFM, the changes in rainfall were more variable. Changes between the AMD and the baseline of 1975 to 1994 are generally smaller and less consistent even in the cool season. In the cool season, the largest-percentage declines between 1975 to 1994 and the AMD occurred in AMJ and MJJ with reductions between SON and DJF coming from a much lower base.

As seen from Figure 11 and Figure 13, throughout the seasonal cycle, there are reductions in the STDs of streamfunction fluctuations at 850 hPa over SWWA in the high-pass band ($T_r<4$ days) and the bin with ${\varpi }_i\ge 1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$during the AMD compared with either 1949 to 1968 or 1975 to 1994. Notably, declines with respect to 1975 to 1994 extend further upstream over the Indian Ocean.

The most notable changes in longer-period weather systems ($4\le T_r<8$ days) between the AMD and the two earlier baselines is in the transition seasons of MAM and SON where reductions compared with 1975 to 1994 (Figure 14) in the bin with $0{\le \varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$are evident over and upstream of SWWA.

8.2.2. Changes in Weather Systems and SWWA Rainfall in 1997 to 2016

Rainfall changes in 1997 to 2016 (Table 1) broadly follow the same pattern as in the AMD. Most evident are again the declines between FMA and JAS compared with the baseline of 1949 to 1968 and with more variability in differences in the warmer 3-month periods. Compared with the baseline of 1975 to 1994, the main reductions are in AMJ to JJA with smaller differences in the other 3-month timespans.

Figure 6 and Figure 9 again depict the declines in storminess over SWWA in the high-pass frequency band ($T_r<4$ days) of explosive storms (${\varpi }_i\ge 1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$) in each season for 1997 to 2016 compared with both baseline periods. Once more, the reductions with respect to 1975 to 1994 (Figure 9) are larger and more extensive upstream of SWWA over the Indian Ocean than compared with 1949 to 1968 (Figure 6).

As is the case for the AMD, reductions during 1997 to 2016 in the STDs of band-pass filtered weather systems, over and upstream of SWWA, in the growth rate bin with $0{\le \varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$stand out in MAM and SON when compared with 1975 to 1994 (Figure 10).

8.3. Observations of Weather Systems Upstream and over SWWA and SEA

Hertzog et al. [46] note that the NNR datasets perform reasonably well in the pre-satellite era in the Southern Hemisphere, including capturing the weather systems as shown in their Figure 8. There is particularly good agreement between the NNR data and observations over Australia and New Zealand where the reanalysis standard deviations from observations are significantly smaller than over the oceans. The reanalysis standard deviations are low from the west coast of Australia and even lower towards the east, including and over New Zealand, as shown in their Figure 8. This is a reflection of the large radiosonde network over Australia extending to New Zealand as reviewed by O’Kane et al. [6]. This may partly explain why changes in cool season storminess and rainfall over SEA between both the AMD and the 1997 to 2016 period and the two baseline periods of 1949 to 1968 and 1975 to 1994 are slightly more consistent than is the case for SWWA.

9. Discussion and Conclusions

The aim of this article has been primarily to examine decadal changes in the seasonal cycle of extratropical storminess in the Southern Hemisphere over the last circa 70 years. We have also documented and analysed the decadal and seasonal variability in southern Australian rainfall over SWWA and SEA during the same period. As well, we have studied the extent to which changes in extratropical-synoptic-scale weather systems can be linked to changes in SWWA and SEA rainfall.

As noted in the Introduction and Section 8, there are many processes that contribute to southern Australian rainfall, and they vary over the seasonal cycle. This means that although we find strong associations of reductions in storminess, particularly due to explosive storms in the high-pass frequency band and during the cool seasons, definite attribution is more difficult. This is compounded by the fact that the NNR reanalysis data during the third quarter of the 20th century, after which SWWA rainfall declined significantly, is less reliable, particularly over the oceans, including upstream of SWWA, than is the subsequent timespans.

Despite these caveats, there have been some very dramatic changes in rainfall and storminess with the clearest signals occurring in SEA during the first 10 years of the Australian Millennium Drought (AMD, 1997 to 2006). Compared with both of the baselines of 1949 to 1968 and 1975 to 1994, SEA experienced consistent declines in rainfall during the AMD throughout the annual cycle. The decreases were largest in the cooler season between FMA and MJJ. However, they persisted even into summer when thunderstorm rainfall has been increasing [88]. In this study, we have noted the associated reductions over SEA throughout the seasonal cycle of the intensity of explosive storms (growth rates ${\varpi }_i\ge 1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$) with periods $T_r<4$ days. This is also the case, particularly in spring and autumn, for weather systems with periods $4\le T_r<8$ day that grow more slowly ($0{\le \varpi }_i<1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$).

The changes in rainfall and storminess over SEA during the 20-year period 1997 to 2016, with respect to both baselines, are very similar to those during the AMD. The main exceptions are slight increases in summer rainfall.

Rainfall totals for SWWA in the cool periods of AMJ, MJJ and JJA have decreased systematically for each of the 10- or 20-year timespans we have considered, and this is the case compared with both of the baselines of 1949 to 1968 and 1975 to 1994. During the AMD and in the 20-year timespan 1997 to 2016, there have also been decreases in the intensity of cool-season explosive storms in the high-pass frequency band ($T_r<4$ days) over SWWA.

We have focused in this article on storm track differences between two recent periods (1997 to 2016 and the AMD for 1997 to 2006) and the two baselines of 1975 to 1994 and 1948 to 1968. The reasons for this have been detailed in Section 1 and Section 8 and are related to the poorer data quality for the earliest period. We have, however, also compared the changes in the STDs of 850 hPa streamfunction anomalies in both high-pass and band-pass bands between 1975 to 1994 and 1949 to 1968. Briefly, our findings for the late autumn and winter months of May and June are broadly similar to those described in [5] for July. This is particularly so for the bin with fast-growing (${\varpi }_i\ge 1\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$) high-pass filtered storm track disturbances with significant reductions in the Australian–New Zealand region similar to those in Figure 7(iv) of Ref. [5].

We have found that indices characterising regional, hemispheric and global atmosphere and ocean circulation features have stronger correlations with SWWA and SEA rainfall in the cooler seasons. Many of these indices that we have considered also have close relationships with frontal and extratropical cyclone formation. This would suggest consistent links between circulation changes on the larger scales and fronts and lows, and in turn rainfall in the cooler months. The smaller-scale processes involved in thunderstorms and associated rainfall in the warmer months are less successfully described by our indices. Interestingly, in the cooler seasons, we find that regional averages of the 700 hPa zonal wind are nearly as good a descriptor of SWWA and SEA rainfall variability as sea level pressure on both annual and decadal timescales. As well, the new indices of the Southern Ocean Regional Dipole (SORD) and hemispheric Subtropical Atmospheric Jet (SAJ) introduced in Ref. [5] are the most important predictors of cool-season SWWA rainfall variability on both annual and decadal timescales. This is also the case in SEA for the 3-month period of JAS on decadal timescales. On annual timescales, the Indian Ocean Dipole (IOD) and Southern Oscillation Index (SOI) play the strongest role between MJJ and OND in SEA. On decadal timescales, the situation in SEA is quite complex with different indices playing the stronger role in different 3-month periods. In addition to SAJ, they include the IOD, Interdecadal Pacific Oscillation (IPO) and the Southern Annular Mode (SAM).