Added February 27, 2022. The same data, i.e. annual South Australia (Victoria) rainfall have been used in form of anomaly (base 1961-90) in order to analyze the whole series and, separately, both positive and negative anomalies.
Here I also use histograms to represent datasets and LOMB spectra (instead of MEM as in the first part). Again, I use now the complete datasets (total, positive and negative anomalies) without looking for separate slopes before and after a fixed date, because I'm interested in "lunar" 18.6 yr cycle (as e.g. in https://astroclimatelink.wordpress.com/).
The above line-of-nodes (or Draconic) cycle depends on the tilt of about 5° between Earth and Moon orbital planes. Such a cycle has been found in several rain gauges around the world (see e.g. https://www.zafzaf.it/clima/lunar/lunarhome.html for a list of observed cases where the cycle is present) and also in other series, in some a way linked to water.
With respect to the "old" cases, here I use the updated version of the datasets (1900-2021).
Fig.1: South Australia (Victoria) annual rain as anomaly with respect 1961-90 base. The bottom plot is the Lomb spectrum: please note the 19.5 yr period, perhaps to be linked to Draconic cycle of 18.6 yr.

Fig.2: South Australia (Victoria) annual rain positive anomalies. The bottom plot is the Lomb spectrum: please note the 19 yr period, derived from the following periods and powers:
    Period (yr)             Power
  19.032258064516121   3.5725263331771089
  18.437499999999993   3.5482619688480086
so, the 18.6 yr peak is really present.

Fig.3: South Australia (Victoria) annual rain negative anomalies. The bottom plot is the Lomb spectrum: please note the 19.8 yr period, within the 18-20 yr range I use for "lunar" periods.
So, I can confirm that a "lunar" period (18-20 yr) exists in the anomaly of South Australia (Victoria) rain and also in the separate positive & negative anomaly series.
Also if I'm not focused on this aspect, I must notice that no evident and progressive grow or fall appears from such annual data (i.e. something depending on the CO2 continous rise from pre-industrial period).
Looking at single (pos. or neg.) series, a general grow through 1970 can be noted, followed by a drop in positive anomaly. The negative anomaly shows a grow through 1940, a decrease through 1970 and again a grow up to present. Both grows and falls are widely indicative, mainly if we consider the spectral peaks at lunar periods which give the rain pace (at least following an active research line): so, e.g., the last maximum for positive anomaly (stronger rain) happened in 2010-11 and the next one should appear in 2029-30, while the next date for negative anomaly should be 2038-39.
Page written: Feb. 27, 2022. Updated: Feb. 27, 2022