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.