The kurtosis of annual rainfall at Manilla NSW forms a time-series that matches the time-series of global surface temperature when detrended.
Earlier posts were based on rainfall data sets that were too small. Estimates of kurtosis and skewness were unstable. For details please read “Rainfall kurtosis matches HadCRUT4” and “Rainfall kurtosis vs. HadCRUT4: scatterplots”.]
These two climate variables have little in common. Manilla, NSW, is a single station that has a 134-year record of daily rainfall only. That yields estimates of rainfall kurtosis, an indicator of the relative frequency of extreme values.
HadCRUT4 is one of several century-long estimates of near-surface temperature for the whole world. [See Note below: “Data Sources”.]
The visual match of the patterns
The first graph (a dual-axis line chart) shows that these two variables have similar patterns of variation over time.
I found the best visual match by:
* scaling 0.5 units of Manilla rainfall kurtosis to 0.1° of detrended HadCRUT4 temperature;
* aligning the kurtosis value of -0.3 units with the zero of detrended temperature;
* lagging the rainfall by two years.
Features that the two patterns have in common are:
* matching main peaks at 1897, 1942 and 2005, each higher than the one before;
* persistent low values in the 1910’s, 1920’s, 1950’s, 1960’s, 1970’s and early 1980’s;
*some matching minor peaks and troughs.
The correlation chart
The second graph is a correlation chart. The linear regression of kurtosis on detrended temperature has the reasonable R-squared value of 0.67.
As I have made it a connected scatterplot, you can see how the relation has changed through time. From the first data point in 1898 (in red) both variables decreased together to the lowest temperature in 1910. Both peaked in 1942, having risen since 1920, later falling until 1955-56. The final rise to the highest peak (2005) was continuous from 1984 for temperature, but the rise in kurtosis was not. It fell slightly in 1990, then remained static until 1998.
All rainfall figures actually came two years earlier. [See note below: “Manilla’s 2-year lead”.] The assigned two-year lag not only makes peaks match on the first graph. It sharpens the reversals on the second graph. On a trial connected scatterplot without lag, these reversals had been smooth clockwise curves.
What it means
As evidence of extreme behaviour in climate
It is said that more extremes in climate will occur as the world becomes warmer. The evidence is not strong. Most data sets are overwhelmed by noise, and “extreme” is seldom defined with rigor.
In the present case, I believe that the definition of “extreme” that I use is sound: that is, the kurtosis of a frequency-distribution. The instability of kurtosis when based on my small samples had been an issue. In this revision I have increased the sample population size from 21 to 125.
My rainfall data set that displays more and less extreme behaviour is not general but local. It can merely suggest that data elsewhere may reveal functional relationships.