# Annual Rainfall Extremes at Manilla NSW: III

## III. When extreme values were more or less extreme

#### 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.

Forward to Extremes Part V.

[In later work, I use kurtosis as a measure of extremes. For example, in “Rainfall Kurtosis vs. HadCRUT4 revised”.]

### 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. See the post “Moments of Manilla’s 12-monthly Rainfall”.

I have more to say on this topic.

[In later work, I use kurtosis as a measure of extremes. For example, in “Rainfall Kurtosis vs. HadCRUT4 revised”.]

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: I

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

### 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.

Forward to Extremes Part V.

### 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.)

#### 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.

# Manilla’s Yearly Rainfall History

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

I have taken this topic very much further in posts such as “Relations Among Rainfall Moments” 29 May 2018.]

### 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.

### 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

### Part 3 of 3: A growth and collapse model for summer rainfall

(See Notes below for data and plotting details.)

I have put this October 2014  post up on the front page as a “sticky” (5/1/15) because I have just found a relevant scientific article. See “Note added January 2015” below.

#### A linear trend

In Part II, I showed that a linear trend fits well (R-squared = 0.54) to smoothed summer rainfall at Manilla, NSW from 1897 to 1976. This trend-line rises extremely steeply: 156 mm per century.

#### Implications of the extreme trend

Such an extreme trend cannot extend more than a short time into the past or the future without reaching physical limits. Extremely high values must be followed by lower values and vice versa. The oscillation between higher and lower values in nature is often modeled as a smooth harmonic curve. That does not fit well here. Not only does the rise from 1897 to 1976 fail to curve down approaching the final peak, the falls from 1892 to 1900 and from 1975 to 1987 are extremely sharp. They are collapses.
It seems to me that a model of steady growth followed by sudden collapse may perhaps reflect the processes involved. On the graph I have added speculative trend lines of the same rising slope as that observed for 1897 to 1976. The constant for the first speculative trend line is 130 mm higher and leads to a 130 mm collapse from 1896 to 1899. A 90 mm collapse from 1978 to 1981 then leads to a renewed rising trend that is 90 mm lower.

The sudden collapse in summer rainfall here at the beginning of the twentieth century was studied sixty years ago by E.B. Kraus (Snowy Mountains Authority!): “Secular changes of east-coast rainfall regimes” (1955).
“The mean rainfall along the east coasts of North America and Australia is shown to have decreased abruptly at the end of the 19th century… A simultaneous decrease of the rainfall in the Continue reading

### Part 2 of 3: The record restricted to 1891-1982 (92 years)

(See Notes below for data and plotting details.)

No climatic record is ever long enough to demonstrate apparent cycles, trends or extremes beyond doubt. In Part 1, a linear trend of summer rainfall rising at 24.7 mm per century was fitted to the whole 130-year record. Although this is a very high (perhaps unsustainable) rate of increase, the trend line explains hardly any of the variation. The R-squared value is 0.03! However, there does seem to be a steeper quasi-linear trend prevailing for most of the period of record. The graphs I have posted here show a restricted record beginning in 1891 and ending in 1982. This simulates an analysis done in 1983 (which could not have used more recent data) and supposes that records earlier than 1891 were unavailable for some reason.

I have chosen these dates so that
(i) the near-record smoothed summer rainfall maximum of 1891 is excluded but the record smoothed summer rainfall minimum of 1900 is included;
(ii) the record smoothed summer rainfall maximum of 1975 is included but the very low smoothed summer rainfall minimum of 1987 is excluded.
(Due to the smoothing window extending six years before and after a specified date, smoothed rainfall values can be calculated only from 1897 to 1976.)

#### Linear trends

For this restricted data set of 92 years, all four linear trends are very much steeper than for the whole 130-year record. The R-squared values are also much higher, indicating that the Continue reading