Interdecadal changes, over the last seventy years, in winter synoptic weather systems that grow and decay in the extratropical storm tracks of the Southern Hemisphere are investigated. The statistics of the intensity of growing and decaying eddies, and their preferred structures and growth rates, are determined from 6-hourly lower-tropospheric reanalysis data for high-pass filtered (period less than 4 days) and band-pass filtered (period between 4 and 8 days) disturbances. A new data-driven methodology is used in which the perturbations are spectrally analysed in both space and time, their growth rates are calculated and statistics are accumulated for growing and decaying instabilities. Rainfall variability in Southern Australia is found to be closely related to the changing statistics of weather system intensity and to interannual and decadal variability in indices or predictors that characterize local, hemispheric or global aspects of the atmospheric circulation. In investigations into the mid-1970s drying of southwestern Western Australia, the Australian Millennium Drought and Southern Australian rainfall anomalies of the early twenty-first century it is found that decadal changes in rainfall are most related to the intensity of the fast growing weather systems. Two new indices, the Subtropical Atmospheric Jet (SAJ) index and the Southern Ocean Regional Dipole (SORD) index, are introduced and shown to have some skill in characterizing aspects of Southern Australian winter rainfall variability particularly on decadal timescales.