Short Droughts are Worst

The shorter the drought, the less rainfall there is in it. The longer the drought, the more rainfall. News reports give the false impression that hardly any rain falls during a drought, even if the drought lasts a long time. That is not true.

To prove the point, I have made graphs and a table showing the very worst droughts that Manilla ever had: the very worst short droughts, year-long droughts and 30-year droughts.

Lowest ever rainfalls

Graphs of the driest times

The first graph shows how the driest two month drought had only one millimetre of rain, while the driest longer periods had very much more, up to over 5000 mm of rain in 120 months (10 years). That may seem obvious. So long as there is a little rain in most months, the longer the period, the bigger the rainfall total. But there is more to it than that.

The second graph shows the average rate of rainfall during each worst drought: the rainfall per month. The rate is not steady as you might expect. It too becomes higher as longer droughts are measured. Through the worst two-month drought, only half a millimetre of rain fell per month. Through the worst 12-month drought no less than 24 mm fell per month. The worst 120-month drought had 47 mm per month on average. That is not far below the normal average monthly rainfall of 54.3 mm per month.

The third graph builds on this comparison. Each drought rainfall rate is shown as a percentage of the normal rainfall rate. While those worst droughts that were shorter than than five months had less than 10% of normal rainfall, no droughts that were longer than five months ever had so little. Droughts lasting for 12 months never had rainfall lower than 44% of normal. As for the decade-long droughts mentioned in the news, the driest decades in history had rainfall rates more than 85% of normal. Such record dry times are hard to see in rainfall figures, although they surely deplete surface and underground water storages.

[These graphs show clearly why droughts are not well defined by the percentage of normal rainfall. Percentile values are more satisfactory, but they too have problems.]

Manilla’s list of driest times

Table of lowest rainfallsThe table shows all the figures mentioned for each of the driest times on record in 134 years at Manilla.
Records can be broken, but it seldom happens. These records have stood for a very long time – at least the forty-six years since 1971.

Many of these record-setting droughts had dates of onset or breaking that were members of a rather small set. In particular, the year 1911 saw the onset of nearly half of them.


[This table was amended on 14/8/2018. The original table had two errors, now corrected.
1. The lowest 30-month total was not 1082 mm (36.1 mm/month; 66.5%) set March 1911 to August 1913. It was 1078 mm (35.9 mm/month; 66.2%) set May 1964 to October 1966.
2. There were not 14 rainless months, but 15. The month missed was April 1971.]

A new record set in 2018

The record for 15-month low rainfall of 404 mm, set in 1912, was broken when the 15 months to September 2018 reached only 400 mm.
See the post “Record 15-month Drought in 2018”.

There is a video interview on the topic here:

More Droughts After Heavier Rains III.

Graphical log of errors when droughts are predicted from rains

Droughts and flooding rains at Manilla NSW were related in a way that is remarkable and unexpected.

Part III. Predicting drought from heavy rain

[Back to Part II: Scatter-plots]

The graph above is derived from the first graph in this series (copied here) by using the blue regression trend-line from the scatter plot of selected data (also copied here). (For data details, sLog of 1-year droughts and 5-year lagged heavy rainfallsee Note 1, below.)

The equation of the trend line, y = 0.030x is used AS IF to use the daily rainfall excesses to predict the drought frequency five years later. The graph shows the “error” of this “prediction”. (In Note 2, below, I concede that this data set could not support such prediction.)
As expected from the previous graphs, the “prediction” is accurate at most data points to 1975. It is correct to the nearest percentage whole number at nine of the eighteen points. From 1940 to 1955, droughts are uniformly more frequent than predicted. After 1975, the error curve swings wildly up and down.

Could droughts have been predicted from heavy rainfalls?

Scatter-plot 1890 to 1975

By about 1915, it is conceivable that this relationship could have been discovered, either by analysis of such data, or by modelling of the climate system. Then, the data for the next 20 years, up to 1935, would seem to confirm it. Data from 1940 to 1955 would cause doubts, but data from 1960 to 1975 would restore confidence. Then the utter failure of the model in the following four decades would have led to its abandonment, at least for the time being.

Climate shifts of 1975

Continue reading

More Droughts After Heavier Rains II.

Scatter-plot 1890 to 1975

Droughts and flooding rains at Manilla NSW were related in a way that is remarkable and unexpected.

Part II. Scatter-plots

[Back to Part I: Graphical logs]

I have made scatter plots to see how much correlation there is between the two data sets: the frequency % of severe 12-month drought and the total decadal daily rainfall excesses over 50 mm, when lagged five years. (For data details, see Note 1, below.)

A. The first 70% of the data

The first scatter-plot includes only the first 70% of the data, from 1890 to 1975, which showed matching patterns on the graphical log copied below. I have broken the data points into two groups: the aberrant group 1940 to 1955 (red) and the fourteen best-matched points (blue). The trend line that best fits those fourteen points is y = 0.028x + 0.407, with R-squared = 0.898. However, I have been able to fit the trend line y = 0.030x, that shows y proportional to x, without making R-squared worse than 0.892.
Similarly, the four decades centred on 1940, 1945, 1950 and 1955, had y = 0.050x, with R-squared equal to 0.902.

Expressed in words: for fourteen of the first eighteen data points, the frequency % of severe 12-month droughts remained close to 0.03 times the decade total of daily rainfall (>50 mm/day) measured five years earlier. For the other group of four adjacent points, the number was not 0.03, but 0.05.

B. All the data

Scatter-plot 1890 to 2010

The second scatter plot shows data for all 25 (five-year overlapped) decades. There is a “shot-gun” pattern, as expected. Continue reading

More Droughts After Heavier Rains I.

Log of 1-year droughts and 5-year lagged heavy rainfalls

Droughts and flooding rains at Manilla NSW were related in a way that is remarkable and unexpected.

Part 1. Graphical logs

As the first graph shows, for most of the 130-year record year-long droughts came in direct proportion to very heavy daily rainfall five years earlier. (For data details, see Note 1, below.)
The match between these two variables is astonishing. Both are based on rainfall readings, but they are scarcely related. Excessive daily rainfalls are transient extreme weather events; 12-month droughts are an aspect of climate.

Mackellar’s “Droughts and flooding rains”

Dorothea Mackellar’s famous line * is more apt for this graph than for other graphs where I use “flooding rains” to mean periods unlike drought. (See Note 2. below.) The rains and droughts that I plot here both bring hardship. Severe droughts lasting one year are among the worst of droughts: long enough to use up reserves, and not so long as to be eased by periods of rain. The daily rainfall events plotted are the ones that cause damaging floods.

Features of the graphical log

Log of 1-year droughts and heavy rainfalls

This second graph shows the data at the actual dates. Although the data points for the decade excess of heavy daily rainfall and those for frequency % of 12-month droughts have a matching pattern for much of the record, the pattern is offset. Heavy rainfall points come five years earlier than corresponding drought points. Notice that the heavy rainfalls do not (except in 1980) come squarely in gaps between droughts.
Lagging the rainfall points by five years (as in the first graph) makes some matches almost exact. Such matches occur at all data points from 1890 to 1975, except those from 1940 to 1955, where drought frequencies are relatively higher. Both variables show a two-decade-long, slow decline from 1905 to 1925. At the chosen scales, the amplitude of corresponding rises and falls are usually similar as well.
After 1975, daily rainfall oscillates through a wide amplitude with a twenty-year period, while the frequency % of drought varies Continue reading

Southern Oscillation Index: CUSUM plot


This graph is a log of cumulative values of the monthly Southern Oscillation Index for the last 139 years. (See Note added 25th August 2014 below.)

(See also Note Added 19 December 2015 regarding the mis-match between this SOI record and the climate record at Manilla.)

(See Note added 27/3/2016 below, for a prior construction of this graph.)

High values of the SOI (contrary to NINO3.4 values for the ENSO index) relate to deluges in Australia and low values relate to droughts.

This is the CUSUM technique, invented in 1954 by E.S.Page. Pay attention to the slopes on the graph.

I have identified major El Niño and La Niña events on the graph. La Niñas have extreme upward slopes and El Niños exteme downward slopes.
The main feature of the graph, which is obscure in graphs that do not use CUSUM, is that La Niñas dominated the 60-year period from 1917 to 1976, and El Niños dominated the 25-year period from 1976 to 2000. I have drawn linear trend lines to make this clear. The first trend line (La Niña dominant) begins at an SOI CUSUM value of -30 in May 1917 and ends at a value of +960 in February 1976, yielding a slope of +1.4 SOI units per month. The second trend line (El Niño dominant) ends at a value of -40 in December 1999, yielding a slope of -3.5 SOI units per month.
The tendency to El Niños in the second period was greater than the tendency to La Niñas in the first period by a factor of more than two.
Although the period since 2000 is very short, the trend seems to slope upward at about +1.0 SOI units per month.

These decadal changes in the short-term mean value of the SOI are graphed in a later post. That graph does not use the CUSUM concept, and the changes in the mean value are overwhelmed by month-to-month variation.

I posted discussion of an earlier version of this graph in “Weatherzone” Forums >> Weather >> Climate and Climate Change >> ENSO Discussion 2012 Post #1103736

Note added 25th August 2014

Another CUSUM SOI graph

By searching the net for “cusum soi” I find that a plot of the cumulative sum of values of the Southern Oscillation Index was published by Cordery and Yao in 1993: “Non stationarity of phenomena related to drought”.

Neither the data nor the approach of Cordery and Yao are the same as mine.


Cordery and Yao used monthly normalised SOI anomaly data supplied by the Bureau of Meteorology, as I did. They mention that “Prior to 1933 there are 7 gaps in the SOI sequence resulting from a total of 102 months of data missing from the Papeete pressure record.” I have not found any note of this with the Bureau’s current data table.
Apart from an (unexplained) reduction in the scale of CUSUM values by a factor of 500, there are important differences in detail. During the time of La Niña dominance, I find that the major CUSUM peaks (La Niña turning to El Niño) in 1918, 1939, and 1976 lie almost in one line. Cordery and Yao’s plot has the 1939 peak relatively much higher: the second highest on the record after the 1976 peak, and almost as high.


Cordery and Yao used CUSUM to show that the SOI series was not stationary for a part of the time. I used it to identify persistent shifts in the SOI mean value.

Note added 19 December 2015

The influence of the Southern Oscillation index on the climate of Manilla, NSW is cryptic at best.
In particular, the inter-decadal changes shown on this graph are not expressed at all in the episodes of drought at this station. Extreme droughts were concentrated in the period from 1900 to 1950 as shown here.

I have discussed the mis-match with the SOI in another post.

In that post, I also pointed out:
“The record for this site provides no support for any relation at all between global temperature and drought.”

Note added 22 March 2018, amended 21 May 2018.
I have since found a relation of that kind, described in the post “Rainfall kurtosis vs. HadCRUT4, revised”.
Patterns of rainfall kurtosis and global temperature.Leptokurtosis of Manilla 12-monthly rainfall totals, which indicates extremes of rainfall – both positive and negative – has a pattern that matches that of global temperature anomalies when detrended.

Note added 27 March 2016

Prior construction of this graph.
I constructed this CUSUM SOI graph in 2012 on my own initiative, without knowledge of a prior construction by David Archibald in 2010. His graph (yellow background colour) appears to have an identical trace. Without adding linear trend lines, Archibald identifies the same end points of the long period of La Nina dominance followed in 1976 by a period of El Nino dominance.
Archibald published his graph in a guest post in “Watt’s Up With That”:

My graph and Archibald’s can both by found in a search of images for “southern oscillation index”.