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.

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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.


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

Continue reading

Annual Rainfall Extremes at Manilla NSW: III

III. When extreme values were more or less extreme

Graph of history of extremes of 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.)


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


Making the graph

For each year, I have identified the highest and lowest values of annual rainfall in its 21-year sample. I already know the long-term mean annual rainfall at Manilla: 652 mm. From those values I have plotted the height of the maximum value above the mean (red) and the depth of the lowest value below the mean (green). Both may be called “Extreme Values”.
The difference between the maximum value and the minimum value in each 21-year sample is the Total Range. That also is a measure of Extreme Value, which I graphed in an earlier post.
The Total Range is equal to the sum of the two Extreme Values that are plotted. To make it easy to compare the three measures, I have divided the Total Range by two. I have  plotted that value in blue.

Two discordant results

All three measures agree well except at two dates: 1897 and 1980. On both occasions the Minimum Value (green) was not extreme at all, being only about 200 mm below the long-term mean. The Maximum Value in 1980 was rather extreme (about 330 mm above the mean). The Maximum Value in 1897 was the most extreme value that appears on this graph: 475 mm above the mean!
The pattern of this graph is dominated by this single feature. It is due to just one data item: the annual rainfall reading of 1129 mm in the year 1890, which was the highest ever.

The pattern

For extreme annual rainfalls at Manilla, this graph suggests the following:

They were more extreme than usual at the end of the 19th century and in the 1940’s.
They were less extreme than usual from the 1900’s through to the 1930’s.
They have been no more or less extreme than one should expect through all of the last five decades.

Comment

This graph depends on very simple statistics: the maximum, the minimum and the mean. Such a sparse data set is subject to the effect of chance. Also, although this is not obvious, this graph assumes that other features of the distribution of annual rainfall have not been changing, which is not true.

I have more to say on this topic.


Note about Sampling

I chose a 21-year sampling window to be wide enough to contain enough points for analysis, without losing time-resolution, or losing too many years at each end of the record from 1883 to 2016.
The first mid-year of a sampling window was 1893 and the last, 2006.
To remove jumps in the trace on the graph, I then applied a nine-point Gaussian smoothing function. That further reduced the years that could be plotted to those from 1897 to 2002.

Annual Rainfall Extremes at Manilla NSW: II

II. Platykurtic, Bimodal Annual Rainfall

Histogram annual rainfall frequency Manilla NSW

Manilla’s 134 years of rainfall readings yield the graph above. There are several features to notice.


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


A ragged pattern

Despite having as many as 134 annual rainfall values, the graph is still ragged. Some of the 20 mm “bins” near the middle have less than 2% of the observations, while others have over 5%. The pattern has not yet become smooth.

It is not near a normal distribution

Rainfall is thought of as a random process, likely to match a curve of normal distribution. On the first two graphs I have drawn the curve of normal distribution that best fits the data.

Smoothed annual rainfall frequency Manilla NSW

In this second graph, I have smoothed out the ragged shape of the plotted data, using a 9-point Gaussian smoothing. You can see more clearly where the actual curve (black) and the normal curve (magenta) differ. The dotted red line shows the differences directly:

The peak is low;
The shoulders, each side of the “peak”, are high;
Both of the tails are thin.

These three features describe a platykurtic curve: one with low kurtosis. This fact makes the highest and lowest annual rainfalls at Manilla less extreme than would be expected in a normal distribution.

Another departure from normality is that the curve is skewed: the tail on the left is shorter than the one on the right. That is a positive skew, but it is small. (By contrast, most of the rainfall distributions for individual months at Manilla have large positive skew. In them, the peak is well below the mean, and a tail extends to rare high values.)

In summary, four of the leading features of the shape of Manilla’s annual rainfall distribution are:

Mean or average: 652 mm per year.
Standard Deviation (measuring spread or scatter): 156 mm.
Skewness: 0.268 (slightly positive).
Kurtosis: -0.427 (strongly platykurtic).


A platykurtic curve matches the Manilla annual rainfall frequency curve to some extent.

The sum of two Gaussian curves gives a much better match.


Fitting a platykurtic near-normal curve

Much of the poor fit of a normal curve to the data is due to the data having a platykurtic distribution. Being platykurtic produces a reduced peak, high shoulders, and thin tails, as was noted.

Smoothed rainfall frequency and a platykurtic curve

In the third graph, I have drawn (in magenta) a new model distribution that is platykurtic. It is a transform of the normal distribution with a weighted sinusoidal correction. The new curve fits much better up both flanks of the data curve. It cannot be made to fit in the peak area between 500 mm and 820 mm.

Fitting a bimodal model made of two normal curves

The shoulders of the smoothed rainfall distribution curve (black) are not simply high; they are higher than the  zone in the middle where the peak would normally be. There is a major mode (peaking at 5.1%) on the left, a minor mode (3.9%) on the right, and an antimode (3.7%) between them.

Smoothed rainfall frequency and a bimodal curve

Continue reading

Annual Rainfall Extremes at Manilla NSW: I

I. Better graphs of Manilla’s annual rainfall and its scatter

Manilla 21-year rainfall medians

Background

The first two graphs  are new versions of graphs in an earlier post, published also as an article in “The Manilla Express” (28/2/17) and in the “North West Magazine” (20/3/17).

In that article, I said:
“This Manilla rainfall record is one counter-example to the snow-balling catalogue of reported extreme climatic events.”
My claim was not well supported. While the two graphs showed that recent annual rainfalls have been normal, with little scatter, they do not show whether there were any extreme events.

However, Manilla’s annual rainfall record can be analysed to show extreme events. This post considers the Total Range within a 21-year sampling window as a measure of extremes. Using that measure, extremes were at their highest in the 19th century, before anthropogenic global warming began.

A following post discusses kurtosis as another measure, with a different result.


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


The two improved graphs

The re-drawn graphs of historical records in this post use a 21-year sampling window, as before. They now have an improved smoothing procedure: a 9-point Gaussian curve. (The weights are stated below.)

1. Yearly Rainfall Totals

The first graph (above) represents the normal rainfall as it changes. The earlier version showed the arithmetic mean. The new version uses the median value (the middle, or 50th percentile value) instead.
The new version is less “jumpy” due to better smoothing. The median varies much more than the mean does. All the same, most features of the shape are unchanged: very low annual rainfall from 1915 to 1950; very high rainfall from 1955 to 1982; normal rainfall since 1983. There are some shape changes: rainfall before 1900 does not plot so high; from 1911 to 1913 there is a respite from drought; the highest rainfall by far now appears from 1970 to 1980.

As before, one can say:
“Present rainfall will seem low to those who remember the 1970’s, but the 1970’s were wet times and now is normal. Few alive now will remember that Manilla’s rainfall really was much lower in the 1930’s.”

In addition, this new version makes the pattern of growth and sudden collapse obvious. Collapses amounting to 100 mm came within a few years after both 1900 and 1978. Growth in the 58 years from 1920 to 1978 came at the phenomenal and unsustainable rate of 33 mm per decade. By the 1970’s, elderly residents of Manilla would have seen rainfall increase decade by decade throughout their lives.
(I noted this pattern of growth and collapse in an earlier post about Manilla’s summer rainfall.)

Manilla 21-year rainfall Inter-quartile Range

2. Yearly Near-Mean Rainfall Scatters

The plot on this second graph is changed only by better smoothing. However, the titles are changed. I realised that the Inter-quartile Range is not a good general indicator of spread or, in this case, of reliability of rainfall (as I had assumed). Inter-quartile Range measures the scatter of values that are close the middle: just the middle 50%. My new title refers to “near-mean” scatter. Any values that could be called “extreme” fall very far beyond the Inter-quartile Range.

Two more measures of scatter

An alternative measure of scatter in data is the Standard Deviation. In normally distributed data, the Standard Deviation extends 34% each side of the median (and mean). The “Standard Deviation Range” then extends from the 16th percentile to the 84th percentile. It includes a much larger proportion (68%) of a population than the Inter-quartile Range (50%) does. However, it also says nothing about extremes, which will lie far out in the residual 32% “tails” of the data.

The broadest measure of scatter is the Total Range from the lowest to the highest value. This measure does include any extreme values that exist in the data.
In the present case, each calculation uses a sample that includes only 21 points. The lowest data point is close to the 5th percentile and the highest data point is close to the 95th percentile of a similar continuous curve.

All three measures of scatter graphed

Manilla 21-year rainfall Total Range, Standard Deviation Range and Inter-quartile Range

Continue reading

Manilla’s Yearly Rainfall History

Lately, Manilla’s rainfall is normal, and more reliable
than it ever was.

Manilla yearly rainfall record, 21-yr smoothed

Yearly rainfall totals

The first graph helps to make sense of the history of Manilla’s rainfall, using the totals for each year. The actual figures make little sense, jumping up or down from one year to the next. The figures here have been calmed down. First, I replaced each yearly figure by an average of twenty-one years, ten years before and ten years after the date. Then I smoothed that figure some more.
The pattern is plain. There were periods in the past when there was much more or less rain than usual.
In four decades the rainfall was some 30 mm higher than normal: the 1890’s, 1950’s, 1960’s and 1970’s. In four other decades, the rainfall was some 30 mm lower than normal: the 1900’s, 1910’s, 1920’s and 1930’s.
Rainfall here collapsed about 1900. The collapse was was widespread, as was recognised half a century ago.

Using the average line drawn across the graph (at 652 mm), you can see that rainfall was below average from 1902 to 1951: almost exactly the first half of the twentieth century. After 1951, rainfall was above average for the 44 years to 1995. Since then, the annual rainfall (as plotted) has been remarkably close to the 132-year average.
Present rainfall will seem low to those who remember the 1970’s, but the 1970’s were wet times and now is normal. Few alive now will remember that Manilla’s rainfall really was much lower in the 1930’s.

The pattern in Manilla’s history of annual rainfalls is better shown in a graph in a later post. The new graph, using 21-year median values, has a clear pattern of collapse, growth and collapse.

Manilla yearly rainfall scatters.

Yearly rainfall scatter

The second graph also groups the data twenty-one years at a time. It shows the scatter of yearly rainfalls in each group. More scatter or spread means the rainfall was less reliable. Comparing the graphs, times of high scatter (very unreliable rainfall) were not times of low rainfall, as one might think. Annual rainfall scatter and rainfall amount were not related.
Times of very unreliable rainfall came in 1919 (dry), 1949 (normal) and 1958 (wet). Times of reliable rainfall came in 1908 and 1936 (both dry). However, by far the most reliable rainfall came since 1992, extending to 2004 and likely up to this year.

Global warming

It has been argued that human-induced climate change will cause climatic extremes to happen more often in future. Already, when any extreme climate event is reported, someone will say that climate change has caused it.

The present steady rise in global temperature began about 1975. Does this Manilla rainfall record show more extreme events since that date? Definitely not! Quite the contrary. Continue reading

Is There Any Drought Now?

No. In Manilla just now, there is no drought of any kind: not a short drought, a medium-length drought, or a long drought; not an extreme drought, a severe drought, or even just a serious drought.

A new comprehensive graph of the severity of drought at one site.

In this graph, each line of data points is for one particular month. The middle line, joining the red squares, shows the whole rainfall drought situation for last month: September 2016.
This is a new kind of graph. (See Note 1 below.) It can show how severe a drought is, not only during the last month or two, but during the last year, and during the last many years. That is a lot of information.

How to read the graph

A month of extreme drought would have data points very low down on the graph. The scale on the left side is amount of rainfall. It must be a “percentile” value. For example: if the amount of rain that fell is just more than has been seen in the driest 5% of all months, it has a value in the 5th percentile. (See Note 2 below.)

Along the top and bottom of the graph I have plotted a number of months.
The number does not show time passing. It shows the number of months I included in a calculation. For each month on record I did many calculations. I added up the total rainfall for:
* the month itself;
* two months including the previous month;
* three months including the month before that;
* … and so on.
I found the totals for larger groups of months extending back as far as 360 months (30 years).
Using all these rainfall totals, I calculated percentile values to plot on the graph. For example, for groups of 12 months, all groups of 12 consecutive months are compared with each other, to find the percentile value of the 12-month period ending in a given month. (See Note 3 below.)

Which months had the most drought and least drought?

The worst drought there could ever have been would be one with data points along the bottom line of the graph. In such a disastrous month, all the rainfall totals would be the lowest on record, not just the one-month total, but also the two-month total and so on up to the 360-month total. Every one of them would be the lowest total on record. It has never been as bad as that.
The “best” time, in terms of being free of drought, would be a month with all its data points along the top edge of the graph. For that month, every rainfall total, for a short period or a long period, would be the wettest on record.
From the Manilla rainfall record, I have chosen to display the most drought and the least drought that actually occurred.

The most drought: August 1946

The month of August 1946 had no rain. Of course, that was the lowest rainfall for any August month (One among 13 months on record that had no rain.). As a result, the percentile rank for that month’s rainfall is zero. Most totals for groups of any number of months ending in August 1946 are also on the “zero-th” percentile, that is, the lowest on record. Thus, it was an extreme drought in the short term, medium term and long term.
For this month, percentile values that are above the third percentile occur in the totals for 48, 60, and 72 months, as shown. These figures, while not extremely low, were still well below normal (Normal is the 50th percentile.). They occur because these totals include some wet months in 1940, 1941, and 1942.

The least drought: March 1894

March 1894, with 295 mm of rain, was one of the the wettest months ever, ensuring a 100th percentile value. The rainfall totals for groups of months ending in that month included six other “wettest ever” values, and all other groups of months were also very wet. No group of months was below the 95th percentile. (See Note 4 below.)

Current drought situation (September 2016)

This month’s rainfall total of 122.4 mm puts it in the 92nd percentile of all monthly rainfall values, far above the median value marked as “normal” on the graph. The 2-month rainfall total (203 mm), and the 4-month rainfall total (350 mm) are almost as high, each in the 90th percentile.
Continue reading