Part 3 of 3: A growth and collapse model for summer rainfall

(See Notes below for data and plotting details.)

I have put this October 2014  post up on the front page as a “sticky” (5/1/15) because I have just found a relevant scientific article. See “Note added January 2015” below.

A linear trend

In Part II, I showed that a linear trend fits well (R-squared = 0.54) to smoothed summer rainfall at Manilla, NSW from 1897 to 1976. This trend-line rises extremely steeply: 156 mm per century.
(See also the Duodecadal Means graph below.)

Implications of the extreme trend

Such an extreme trend cannot extend more than a short time into the past or the future without reaching physical limits. Extremely high values must be followed by lower values and vice versa. The oscillation between higher and lower values in nature is often modeled as a smooth harmonic curve. That does not fit well here. Not only does the rise from 1897 to 1976 fail to curve down approaching the final peak, the falls from 1892 to 1900 and from 1975 to 1987 are extremely sharp. They are collapses.
It seems to me that a model of steady growth followed by sudden collapse may perhaps reflect the processes involved. On the graph I have added speculative trend lines of the same rising slope as that observed for 1897 to 1976. The constant for the first speculative trend line is 130 mm higher and leads to a 130 mm collapse from 1896 to 1899. A 90 mm collapse from 1978 to 1981 then leads to a renewed rising trend that is 90 mm lower.

Note added January 2015.

The sudden collapse in summer rainfall here at the beginning of the twentieth century was studied sixty years ago by E.B. Kraus (Snowy Mountains Authority!): “Secular changes of east-coast rainfall regimes” (1955).
“The mean rainfall along the east coasts of North America and Australia is shown to have decreased abruptly at the end of the 19th century… A simultaneous decrease of the rainfall in the Continue reading →