Drought Sixth Month: August 2018

Rainfall status, July and August 2018.

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 August, are shown by a black line with black circles. Those from one month earlier, at the end of July, 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”.]

Changes this month

Rain late in August raised the one month and two month rainfall totals out of the class of “serious shortage”. The total for August (28.2 mm) is at the 40th percentile for the month, and the total for July and August is at the 10th percentile. The three-month total, which had been an extreme shortage, fell to become only a severe shortage.

Extreme shortages

Extreme shortages, seen less than 1% of the time since 1883, are now seen for the durations of 4, 5, 6, and 15 months. Without last week’s rain, the 6 month total would have been one of the lowest ever recorded.
There is an extreme shortage at 15 months, due to low rainfall in mid-2017, in the months of July (13.2 mm), August (13.8 mm), and September (5.5 mm).

Long-term shortages

The 6-year rainfall total for August (3252 mm) is a severe shortage, only slightly above that of July (3234 mm). Both these values are lower than any 6-year rainfall totals since 1962. When rainfall shortages of such long duration persist, rainfall does not maintain the groundwater levels or river flows required for irrigation or town supply.

[A graph showing rainfall shortages to the end of September 2018 is in the later post: “Record 15-month Drought in 2018”.]


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.”

The Manilla rainfall record allows me to be more exact than the Bureau. Because the record extends back 134 years, it includes more than 1200 cumulative monthly rainfall values. I can identify percentile ranks even below the 0.1th percentile.
To the Bureau’s two classes of deficiency I add a third:

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

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”.]

[A graph showing shortages at the end of August is in a later post: “Drought Sixth Month; August 2018”.]

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.”

The Manilla rainfall record allows me to be more exact than the Bureau. Because the record extends back 134 years, it includes more than 1200 cumulative monthly rainfall values. I can identify percentile ranks even below the 0.1th percentile.
To the Bureau’s two classes of deficiency I add a third:

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

 

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.]

[A graph showing shortages at the end of July is in a later post: “Drought Fifth Month; July 2018”.]

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).

[Later data

The following graph in this series is in the post: “Rainfall Shortages up to June 2018”.]

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 graphs of rainfall moment relations

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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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

ALL 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”.

Annual Rainfall Extremes at Manilla NSW: IV

IV. Some distributions had heavy tails

Graph of history of heavy tails in Manilla annual rainfall

This graph is based on applying a 21-year sampling window to each year in the Manilla rainfall record, then adding smoothing. (See “Note about Sampling” below.)

“Heavy tails”

In the previous postI plotted only the most extreme high and low values of annual rainfall in each sampling window. Now, I choose two rainfall amounts (very high and very low) to define where the “Tails” of the frequency distribution begin. These Tails are the parts that I will call “extreme”. I count the number of values that qualify as extreme by being within the tails.
In this post, I recognise heavy tails, when before I recognised long tails.


Back to the prelude “Manilla’s Yearly Rainfall History”.
Back to Extremes Part I.
Back to Extremes Part II.
Back to Extremes Part III.

Forward to Extremes Part V.


Making the graph

The long-term Normal Distribution

The graph relies on the long-term Normal Distribution curve (“L-T Norm. Dist.” in the legend of the graph). That is, the curve that I fitted earlier to the 134-year record of annual rainfall values at Manilla NSW.
Histogram annual rainfall frequency Manilla NSWThe graph is copied here.

I defined as “Extreme Values” those either below the 5th percentile or above the 95th percentile of the fitted Normal Distribution. That is to say, those that were more than 1.645 times the Standard Deviation (SD = 156 mm) below or above the Mean (M = 652 mm). When expressed in millimetres of annual rainfall, that is less than 395 mm or more than 909 mm.
These ‘Tails’ of the Normal Distribution each totalled 5% of the modeled population, making 10% when added together.

The data

For each year’s 21-year sample, I counted those rainfall values that were lower than 395 mm (for the Low Tail) and those higher than 909 mm (for the High Tail). I added the two to give a count for Both Tails. To get a percentage value, I divided by 21.
I then found the ratio of this value to that of the fitted long-term Normal Distribution by dividing by 5% for each tail, and by 10% for both tails together. Ratios above 1.0 are Heavy Tails, and ratios below 1.0 are Light Tails.
That ratio, when smoothed, is plotted on the main graph at the head of the page.

Results

The resulting pattern of heavier and lighter tails, shown above, is similar to that found by using more and less extreme values, shown in the graph copied here.

Graph of history of extremes of annual rainfallAs before, there were less extremes in the 1900’s, 1910’s, 1920’s and 1930’s.
As before, there were more extremes in the 1940’s and 1950’s.
In the 1890’s, the “Tails” graph did not confirm the more extreme values that had been found earlier.

The 1990’s discrepancy

Extremes had been near normal through the last five decades in the earlier graph. By contrast, the “Tails” graph shows extremes in the most recent decade, the 1990’s, that were just as high as those in the 1950’s. Those two episodes differ, however: in the 1950’s only the high tail was heavy; in the 1990’s, only the low tail was heavy.
(For the 1990’s heavy low tail, see the Note below.)

The inadequacy of the data

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