Decadal and Inter-decadal changes in rainfall: III.

Summer rainfall anomalies and trends

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

Decadal and Inter-decadal changes in rainfall: II.

Log of smoothed summer and winter rainfall anomalies.

Part 2 of 3: The record restricted to 1891-1982 (92 years)

(See Notes below for data and plotting details.)

No climatic record is ever long enough to demonstrate apparent cycles, trends or extremes beyond doubt. In Part 1, a linear trend of summer rainfall rising at 24.7 mm per century was fitted to the whole 130-year record. Although this is a very high (perhaps unsustainable) rate of increase, the trend line explains hardly any of the variation. The R-squared value is 0.03! However, there does seem to be a steeper quasi-linear trend prevailing for most of the period of record. The graphs I have posted here show a restricted record beginning in 1891 and ending in 1982. This simulates an analysis done in 1983 (which could not have used more recent data) and supposes that records earlier than 1891 were unavailable for some reason.

I have chosen these dates so that
(i) the near-record smoothed summer rainfall maximum of 1891 is excluded but the record smoothed summer rainfall minimum of 1900 is included;
(ii) the record smoothed summer rainfall maximum of 1975 is included but the very low smoothed summer rainfall minimum of 1987 is excluded.
(Due to the smoothing window extending six years before and after a specified date, smoothed rainfall values can be calculated only from 1897 to 1976.)

Log of smoothed sum and difference of summer and winter rainfall anomalies.

Linear trends

For this restricted data set of 92 years, all four linear trends are very much steeper than for the whole 130-year record. The R-squared values are also much higher, indicating that the Continue reading