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 trends explain much more of the variation. The R-squared values of 0.54 for summer rainfall anomaly (red)  and 0.58 for the seasonal difference anomaly (orange) are quite respectably high.
Gradients of the four trend lines are:
Smoothed summer rainfall anomaly (red) : +156 mm per century;
Smoothed winter rainfall anomaly (blue) : -53 mm per century;
Smoothed seasonal difference rainfall anomaly (orange) : +209 mm per century;
Smoothed (summer+winter) rainfall anomaly (purple) : +104 mm per century.

Average rainfall values

I showed in an earlier post that mean rainfall values were:
Summer rainfall: 420 mm (64%);
Winter rainfall: 232 mm (36%);
Summer minus winter: 188 mm;
Summer plus winter 652 mm (100%).
From the intersection of trend lines with the zero line on the graphs, these mean rainfall values were experienced about 1935.

Historic and future summer rainfall at Manilla, NSW

The linear trends imply extreme rainfall climates in the past and in the future. Extrapolating the summer linear trend at 156 mm per century gives amazing results. The summer season rainfall at Manilla would have been zero in 1666, the year of the Great Plague of London. Before that, summer rainfall would have been negative!
By the year 2200, summer rainfall can be expected to double to 840 mm , a value now mainly found in the tropical north. The imbalance between summer and winter rainfalls changes even faster than summer season rainfall.
So far, this exercise seems to show mainly the danger of linear extrapolation, as demonstrated in 1883 by Mark Twain in the case of the shortening of the Mississippi River.

Posts on this topic

This post is one of three on “Decadal and Inter-decadal changes in rainfall” based on the 130-year rainfall record at Manilla, NSW, Australia:
I: The whole 130-year record.
II: The record restricted to 1891-1982 (92 years). (This post.)
III: A growth and collapse model for summer rainfall.


Rainfall at Manilla, NSW, has been observed since 1883. As I posted earlier, there are two distinct rainfall modes, centred on the summer and winter solstices. The summer (monsoon) mode has nearly twice the rainfall of the winter (westerly) mode.

Here, I have assigned to the winter mode the monthly data from April to September, and assigned to the summer mode the monthly data from October, extending to March in the following year.
Each data value has been expressed as an anomaly from the 130-year mean. I found the anomalies not only for the “summer” and “winter” totals, but also for their sum (April to March) and their difference (summer minus winter). To remove high-frequency noise and the effect of ENSO from the plotting, I applied a Gaussian filter of half-width 6 years.

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