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 Septemer 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”.

Australian climate Quasi-Biennial Oscillations.

Australian temperature and rainfall from 1950

[See the Note below: “2010 data re-posted.”]

The above graphs plot the time series of monthly data for the whole of Australia, smoothed with a Gaussian window of half-width 6 months.
The two independent series of (a) mean maximum monthly temperature anomaly in degrees celsius and (b) total monthly rainfall anomaly in mm are plotted on the same graphs, but the scale for temperature is inverted for easy comparison.
One degree on the left axis corresponds to 10 mm on the right axis, but the zero lines may differ.

There is an obvious sine-wave cycle with a wavelength of between one and three years. (This is the “quasi-biennial cycle” that A.B. Pittock identified in 1971.)
Most peaks and troughs on these independent time series almost coincide, and their relative heights and depths tend to agree. In fact. the correlation between values of temperature and rainfall is poor, but the shapes of the sinusoidal curves match extremely well.
Peaks and troughs on the rainfall curve tend to lead those on the (inverted) temperature curve by one, two, or three months. In these graphs, I have lagged rainfall values one month, to show that many of the peaks and troughs are aligned.

Taking the whole of Australia in the last 60 years, it is fairly clear that:
* points of lowest maximum temperature have generally lagged about one month behind points of highest rainfall;
* points of highest maximum temperature have generally lagged about one month behind points of lowest rainfall.

Given this lag effect, times of lowest rainfall cannot be caused by times of highest temperature, but it is possible that times of highest temperature may be caused by times of lowest rainfall.
I find it plausible that temperature swings would closely follow rainfall swings (but in the opposite sense) due to lack of cooling by evapotranspiration in times of drought and effective cooling by evapotranspiration in times of deluge.

[Note: 2010 data re-posted.
This material appeared originally in a “Weatherzone” forum “Observations of climate variation”, Post #810237 of 27 December 2009.
Since the graphs as posted are lost, due to the action of the “Photobucket” image-hosting web-site, I am re-posting the graphs from my records.]


Data source.
The data was sourced at the following web-page.
http://reg.bom.gov.au/silo/products/cli_chg/
That web-page no longer exists.


[Note posted to “weatherzone”.

I never did find Barrie Pittock’s 1971 article in which he referred (I believe) to a quasi-biennial oscillation in Australian surface climate.
However, here is a detailed discussion of that particular topic:

“Historical El Nino/Southern Oscillation variability in the Australasian region” by Neville Nicholls, Chapter 7 (p151-173) in “El Nino: Historical and Paleoclimatic Aspects of the Southern Oscillation”, Henry F.Diaz and Vera Markgraf (eds.), Cambridge U P, 1992, 476pp.

On p.158, Nicholls has a section headed “Biennial cycle” that refers to papers written in the 1970’s, 1980’s, and 1990’s. He says:

“The biennial cycle is observed over the equatorial Pacific and Indian Oceans and is tightly phase-locked with the annual cycle. It varies in amplitude from cycle to cycle and sometimes changes phase. It is not strictly a 2-year cycle so it may be characterised better as a quasi-biennial cycle…..Rainfall over much of Australia displays a quasi-biennial cycle (e.g.Kidson 1925).”]

Moments of Manilla’s Yearly Rainfall History

Manilla Annual rainfall history: Four moments

Comparing all four moments of the frequency-distributions

Annual rainfall for Manilla, NSW, has varied widely from decade to decade, but it is not only the mean amounts that have varied. Three others measures have varied, all in different ways.

I based the graph on 21-year sub-populations of the 134-year record, centred on consecutive years. I analysed each sub-population as a frequency-distribution, to give values of the four moments: mean (drawn in black), variance (drawn in red), skewness (drawn in blue) and kurtosis (drawn in magenta).

[For more about the moments of frequency-distributions, see the recent post: “Kurtosis, Fat Tails, and Extremes”. See also the Note below: “Instability in the third and fourth moments.”]

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.

The latest values are on the right. They show that the annual rainfall is now remarkable in all four respects. First, the mean rainfall (black) closely matches the long-term mean, which has seldom happened before. By contrast, the other three moments are now near historical extremes: variance (red) is very low, skewness (blue) very negative, and kurtosis (magenta) very positive.

To my knowledge, such a result has not been observed or predicted, or even suspected, anywhere.

[REVISION
A revised version of this post uses twelve times as much data. It is “Moments of Manilla’s 12-monthly Rainfall” posted on 15 May 2018.]

Manilla Annual rainfall history: Mean

The mean yearly rainfall (the first moment)

As I have shown before, the mean annual rainfall was low in the first half of the 20th century, and high in the 1890’s, 1960’s and 1970’s. Rainfall crashed in 1900 and again in 1980.

Manilla Annual rainfall history: Variance

Yearly rainfall variance (the second moment)

Continue reading

A drought has begun

A year ago, I showed that Manilla was far from being in a drought. That is not true now. There are severe shortages of rain.

Rainfall status at Manilla, September 2016 and September 2017.

The first graph has rainfall totals up the left margin. They are not expressed in millimetres but as percentile values, Along the bottom margin is the number of months included in calculating each rainfall total.

On the graph, I have compared the rainfall situation today, September 2017, plotted in red with that of September 2016, plotted in grey. Much has changed.

Take, for example, the 12-month (one-year) rainfall total. Rainfall totals for 12 month periods are directly above the value “12” at the bottom of the graph, near the label “Number of Months included”. In data for the month of September 2016 (grey), the 12-month total (actually 802 mm) had been at the 80th percentile, which was very high. In up-to-date data for the month of September 2017 (red), the 12-month total (actually 484 mm) is at the 17th percentile, which is very low.
Although rainfall totals for  periods longer than 12 months have not fallen so much, nearly all of them have fallen. Three that have not are those for 30 months, 36 months and 42 months. They were already low, due to including in them some months of low rainfall several years ago, in 2013 and 2014.

So far, real shortages have occurred mainly within the last 12 months. Beyond that, the two-year rainfall total of 1285 mm, for example, is still near normal, plotting at the 48th percentile.

The second graph shows in detail how shortages that are serious or severe have developed during the last six months. These were the monthly rainfall amounts, with the normal amounts in brackets:

April: 24.0 mm (39.3);
May: 55.6 mm (40.3);
June: 62.8 mm (44.3);
July: 13.2 mm (41.4);
August: 13.8 mm (39.5);
September: 5.5 mm (41.2).

As a result, the current situation is as shown below. There are already severe rainfall shortages, at the 2nd or 3rd percentile, in the two-month and three-month totals to date. There are also serious shortages, at the 8th and 9th percentiles, in the four-month and six-month totals to date.

Drought status at Manilla in September 2017

I will update these graphs each month to show how the situation changes.

[Serious rainfall shortages did not occur in any following months up to January 2018.]