REVISED, WITH MORE PRECISE DATA
Supersedes the post “Moments of Manilla’s Annual Rainfall Frequency” (15 November 2017). This post includes twelve times as much data.[See Note below: “Data handling”]
Comparing all four moments of the frequency-distributions
Yearly rainfall for Manilla, NSW, has varied widely from decade to decade, but it is not only the mean amounts that have varied. Three other measures have varied, all in different ways.
I based the graph on 125-month (decadal) sub-populations of the 134-year record. I plotted data for every month, at the middle month of each sub-population.
I analysed each sub-population as a frequency-distribution, to give values of the four moments: mean (drawn in indigo), variance (drawn in orange), skewness (drawn in green) and kurtosis (drawn in blue).
[For more about the moments of frequency-distributions, see the post: “Kurtosis, Fat Tails, and Extremes”.]
Each trace of a moment measure seems to have a pattern: they are not like random “noise”. Yet each trace is quite unlike the others.
Twenty-first century values are on the right. They are remarkable in three of the four moments. First, the mean rainfall (indigo) stays near the long-term mean, which has seldom happened before. By contrast, two moments are now near historical extremes: variance (orange) is very low and kurtosis (blue) very positive. Skewness (green) is rather negative.
To my knowledge, such a result has not been observed or predicted, or even suspected, anywhere.
[Note. The main difference from the earlier 4-moment graph based on more sparse data is that skewness does not trend downward.]
The mean 12-monthly rainfall (the first moment)
The first moment of the frequency-distribution of 12-monthly rainfall is the mean, or average. It measures of the amount of rain.
As I have shown before, the rainfall was low in the first half of the 20th century, and high in the 1890’s, 1950’s and 1970’s. Rainfall crashed in 1900 and again in 1980.
12-monthly rainfall variance (the second moment)