Drought Fifth Month: July 2018

Rainfall status June and July 2018

Rainfall shortages at June and July 2018.[Note 13/8/18. The large graph above is an  amended graph. Values in mm are unchanged, but percentile values have been recalculated. The 4-month and 5-month percentile values now plot as less extreme than before. The original graph is on the right.]

Graph of Rainfall Shortages

This graph shows all the present rainfall shortages at Manilla, short term and long term, in terms of percentile values. The latest values, as at the end of July, are shown by a black line with black circles. Those from one month earlier, at the end of June, are shown by a thinner line with smaller white circles.
The classes of rainfall shortage are:
• Serious shortage: below the 10th percentile;
• Severe shortage: below the 5th percentile;
• Extreme shortage: below the 1st percentile. [See note below on my usage “Extreme shortage”.]

Extreme shortages

At Manilla, the drought is now extreme by several measures.
At the end of July 2018, rainfall shortages are extreme for 3 months (15 mm), 4 months (33 mm) and 5 months (58 mm). “Extreme shortage” means that Manilla has seen such shortages less than 1% of the time since 1883.
Since the end of June, rainfall totals have fallen lower for periods of 3, 4, 5, 6, and 9 months. The 5-month total fell most remarkably. It had been 121 mm, not even a “severe” shortage (below the 5th percentile), but merely a “serious” shortage (below the 10th percentile). It has now fallen to only 58 mm, which is an “extreme” shortage (below the 1st percentile). It is not much higher than the lowest ever 5-month rainfall total of 29 mm, a record set 130 years ago in 1888.

The graph makes it clear that we are now in the fifth month of an extreme drought.

Long-term shortages

At this date, there are no extreme rainfall shortages measured over periods longer than five months. However, there are some severe shortages below the fifth percentile rank. Should rainfall continue to be below average, these shortages could also become extreme. The current twelve-month total of 346 mm needs to fall only 19 mm (to 327 mm) to become an extreme shortage. The 6-year rainfall total (3234 mm) is a severe shortage lower than any since 1962. Rainfall shortages measured over periods of a year or more will not maintain groundwater levels or river flows.


Note: The term “Extreme shortage”

I have adopted classes of rainfall shortage from the classes of “Rainfall deficiency” defined by the Bureau of Meteorology in their Climate Glossary as follows:

“Serious rainfall deficiency: rainfall lies above the lowest five per cent of recorded rainfall but below the lowest ten per cent (decile range 1) for the period in question,
“Severe rainfall deficiency: rainfall is among the lowest five per cent for the period in question.
“Areas where the rainfall is lowest on record for the given time period are also shown.”

Since the Manilla rainfall record extends back 134 years, so that I calculate percentile ranks from more than 1200 cumulative monthly values, I can identify percentile ranks lower than the 0.1th percentile.
To the Bureau’s two classes of deficiency I would add a third:

“Extreme deficiency (or extreme shortage): rainfall lies below the lowest one percent for the period in question.”

 

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.]

Rainfall Shortages up to June 2018

Rainfall shortage Manilla, June 2018

Since the twelve-month drought of 2002, Manilla has been free from extreme rainfall shortage until now. Such a long gap between extreme droughts has not been seen here before. [See Note below: Dry May 2006.]

Rainfall shortages now

On this graph the black line with black squares shows Manilla rainfall shortages at the end of June 2018. Shortages are shown for short terms down to one month, and for long terms up to 360 months (30 years). [Shortages at the end of May are shown in a previous post.]

Extreme shortages

Three extreme rainfall shortages have now developed, all below the 1st percentile rank:
Total for two months (May and June): 6 mm;
Total for three months (April, May and June): 24 mm;
Total for four months (March, April, May and June): 50 mm.

Severe shortages

There were five severe shortages in rainfall totals as follows:
Total for six months: 141 mm, at the 4th percentile;
Total for twelve months: 350 mm, at the 2nd percentile;
Total for fifteen months: 492 mm, at the 3rd percentile;
Total for sixty months: 2672 mm, at the 4th percentile;
Total for seventy-two months: 3317 mm, at the 4th percentile.

Serious shortages

Some other rainfall shortages were not severe, but serious:
Total for one month: 5.2 mm, at the 7th percentile;
Total for five months: 120 mm, at the 6th percentile;
Total for nine months: 464 mm, at the 10th percentile;
Total for eighteen months: 658 mm, at the 6th percentile.

Comparing June 2018 with the month before

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Rainfall Shortages up to May 2018

Rainfall shortage Manilla May 2018

Rainfall shortages now

On this graph the black line with black squares shows Manilla rainfall shortages at the end of May 2018. Shortages are shown for short terms down to one month, and for long terms up to 360 months (30 years).

Extreme shortages

There were no extreme rainfall shortages at this date.

Severe shortages

There were severe shortages in rainfall totals as follows:
Total for one month (May): 1.2 mm, at the 2nd percentile;
Total for two months (April and May): 19 mm, at the 3rd percentile;
Total for three months (March, April and May): 45 mm, at the 4th percentile.

Serious shortages

Some other rainfall shortages were not severe, but serious:
Total for five months: 136 mm, at the 9th percentile;
Total for twelve months: 408 mm, at the 6th percentile;
Total for sixty months: 2765 mm, at the 8th percentile;
Total for seventy-two months: 3358 mm, at the 6th percentile.

General shortage

The first comment and reply below notes the fact that no rainfall total for any period reaches the 50th percentile. This has not happened for seventy years (1947).

Comparing May 2018 with September 2017

The graph also has a grey line showing similar rainfall shortages at September 2017 (See the earlier post “A drought has begun”.). In the following month, October, there were no rainfall shortages, because the rainfall, 84 mm, was far above average. November, December and February also had rainfalls above average.
Since March 2018, shortages have appeared again. By comparing the black line (May 2018) with the grey line (September 2017), you can see that the rainfall totals are now lower for nearly all periods of time. Only four totals are now higher, including the 4-month total.

What are the classes of rainfall shortage?

We need to compare rainfall shortages. The best way is not by how far below normal the rainfall is, but by how rare it is. That is, not by the percentage of normal rainfall, but by the percentile value. As an example, when the rainfall is at the fifth percentile, that means that only five percent of all such rainfall measurements were lower than that.
Once the percentile values have been worked out for the rainfall record, each new reading can be given its percentile value. Percentile values of low rainfall are classed as extreme, severe, or serious.
For a rainfall shortage to be classed as extreme, its value must be at or below the 1st percentile.
A severe rainfall shortage is one that is below the 5th percentile.
A serious rainfall shortage is one that is below the 10th percentile.
A rainfall shortage that is above the 10th percentile is not counted as serious.

Long-lasting rainfall shortages

Rainfall shortages sometimes last a long time. The same classes of shortage are used for long periods, such as a year, as for short periods, such as a month. They depend on how rare such a shortage is on the average, and they all use the same percentile values to separate extreme, severe, and serious rainfall shortages.

Relations Among Rainfall Moments

Six thumbnail graphs of rainfall moment relationships

Twelve-monthly values of rainfall since 1883 at Manilla NSW yield the four moments of their frequency distributions: mean, variance, skewness, and kurtosis. I plotted the history of each moment (when smoothed) in an earlier post.
Here, I compare the moments in pairs. Connected scatterplots reveal the trajectory of each relationship with time.
Some linear and cyclic trends persist through decades, but none persists through the whole record.
The first image is an index to the suite of six graphs of pair-wise relationships that I present below.

Rainfall Variance vs. Mean

Trajectory of Variance versus Mean

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Moments of Manilla’s 12-monthly Rainfall

Manilla 12-monthly rainfall history: Four moments

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.]

Manilla 12-monthly rainfall history: Mean

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.

Manilla 12-monthly rainfall history: Variance

12-monthly rainfall variance (the second moment)

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Annual Rainfall Extremes at Manilla NSW: V

V. Extremes marked by high kurtosis

Manilla annual rainfall kurtosis

This graph shows how the extreme values of annual rainfall at Manilla, NSW have varied, becoming rarer or more frequent with passing time.
The graph quantifies the occurrence of extreme values by the kurtosis of 21-year samples centred on successive years.

The main features of the pattern are:
* Two highly leptokurtic peaks, showing times with strong extremes in annual rainfall values. One is very early (1897) and one very late (1998).
* One broad mesokurtic peak, in 1938, showing a time with somewhat weaker extremes.
* Broad platykurtic troughs through the 1910’s, 1920’s, 1950’s, 1960’s and 1970’s, decades in which extremes were rare.
All these features were evident in the cruder attempts to recognise times of more and less occurrence of extremes in Parts I, II, III and IV of this series of posts. This graph is more precise, both in quantity and in timing.

Superseded

The results shown in this post are based on sparse data. They are superseded by results based on much more detailed data in the post “Relations Among Rainfall Moments”.

However, kurtosis (the fourth moment of the distribution) does not distinguish extremes above normal from those below normal. It is known that some early dates at Manilla had extremes that were above normal, and some late dates had extremes that were below normal.

Use of skewness

Extremes above normal are distinguished from those below normal by the third moment of the distribution, that is, the skewness.
Manilla Annual rainfall history: SkewnessThe post “Moments of Manilla’s Yearly Rainfall History” shows graphs of the time sequence of each of the four moments, including the skewness (copied here) and the kurtosis ( the main graph, copied above). The skewness function, like the kurtosis function, relates to the most extreme values of the frequency distribution, but to a lesser extent (by the third power, not the fourth).

I have shown the combined effect of kurtosis and skewness on the occurrence of positive and negative extremes in this data set in the connected scatterplot below.

Manilla rain skew vs.kurt

The early and late times of strong extremes were times of strongly positive and strongly negative skewness respectively. As kurtosis fell rapidly from the initial peak (+0.9) in 1897 to slightly platykurtic (-0.4) in 1902, the skewness also fell rapidly, from +0.7 to +0.3.
Much later, in mirror image, values were almost the same in 1983 as in 1902, then kurtosis rapidly rose while skewness rapidly fell, until kurtosis reached +0.9 and skewness -0.3 by 1998.
Between 1902 and 1983, while kurtosis remained below -0.2, the pattern was complex. In the decades of strong platykurtosis (below -0.9) there were extremes of skewness: +0.7 in 1919 and -0.3 in 1968.
Note that the skewness range was as high in times of low kurtosis as in times of high kurtosis, and the same applies to kurtosis range in relation to skewness. Conversely, when either moment was near its mean, the range of the other was not high.


See also:
“Rainfall kurtosis matches HadCRUT4” and “Rainfall kurtosis vs. HadCRUT4 Scatterplots”.