Here is the second major claim contained in van Ommen and Morgan from the abstract:

Here we report a significant inverse correlation between the records of precipitation at Law Dome, East Antarctica and southwest Western Australia over the instrumental period, including the most recent decades.

The actual figures quoted for correlation are as follows.

The results show significant negative correlation between seasonal June–August average values of the SWWA regional series and LawDome. The correlation r=−0.16 (P=0.05, effective sample size, Neff=105) increases in strength to r=−0.55 (P=0.05, N5eff=10) for 5-year smoothed data.

With the following regional pattern (of interest to Geoff).

For individual stations, a general pattern emerges with stronger correlations (reaching r=−0.69, N5eff =9, P=0.02, at Boyanup, five-year smoothed) for stations in the west and centre, diminishing to the east and far south.

I think aggregation is a much better approach than smoothing data, as smoothing adds a lot of autocorrelation that you then have to compensate for in your significant test. You can never be sure that you have compensated enough. In aggregation you slice the series into even sized pieces and take the mean. It produces fewer data points for coarser aggregations, but this is what you want to accurately reflect the actual information in the series. Smoothing is good for visualization, bad for estimating correlation.

In the figure below I show the adjusted R2 value (black) and the significance of the slope parameter (red) at a range of aggregations from one to 20.

For the raw data (aggregation=1) the R2 value is 0.016 and the correlation is non-significant at P=0.10. Taking the square root of my R2 value gives 0.1264911, which could be consistent with a Pearson coefficient R=-0.16. The P value is way off though, P is stated as a significant 0.05 while I get a non-significant P=0.10.

There are a number of significant correlations (below P=0.05) at coarser aggregations, particularly from 6 to 11 years. The 10 year aggregation has an R2=0.71 and a significant P=0.0007 corresponding to the stated values of r=−0.55 (P=0.05, N5eff=10) for 5-year smoothed data.

Notably these correlations are more pronounced at some scales, indicating important periodicity in the data that should be teased out. The strength of the correlation is subject to the specific scale the data is tested at.

In summary, there is a puzzling disagreement why I find no correlation between rainfall in SWWA and snowfall at LD on the raw data that should be reconciled.

However I agree within reason on the correlation of the aggregated (climate scale) data, and won’t pursue this avenue further.