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

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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.

Courtyard wicket gates

Courtyard wicket gate half open

View East Through Wicket Gate

This small courtyard has been described on its own page: “A Heat-control Courtyard”.

Built to help control the indoor climate, it is enclosed by solid walls and solid gates made of a sandwich of fibre and polystyrene.
At times when free circulation of air is wanted, the gates can be latched open. That has the disadvantage that dogs and small children can pass in and out.
I have now made the control of air separate from the control of traffic by adding a wicket gate in each gateway.

The first photo (above) is a view of the courtyard as one would enter it from the west. Both main gates are open. The west wicket gate stands partly open, and the east wicket gate is closed.

Courtyard wicket gate bolted open.

West solid gate closed and wicket gate bolted open.

The second photo, taken from just inside the courtyard, shows the west main gate closed to prevent the flow of air. The wicket gate is fully open, as it would be in that case, secured there by its drop bolt.

Courtyard seen through the east wicket gate

Courtyard through east wicket gate

 

 

 

 

In the third photo, the courtyard is seen through the open east main gate and the bars of the closed east wicket gate.

These photos were taken on the 1st of August 2017 at 10:30 am. They show the courtyard receiving sunshine that passes over the roof of the house, as it does during winter mornings. Some sunshine is direct, some reflecting diffusely off the wall, and some reflecting brightly off mirrors of aluminium foil.

Two thermometer screens can be seen in the third photo. I am monitoring temperatures to find if the courtyard is affecting the indoor climate. As an experiment, I keep the main gates open or closed in alternate months. When gates were open in a particular month of the first year, they are closed in that month of the next year.


The wicket gates are made of welded, pre-galvanised steel tube in the style “Pool’nPlay Flattop”, powder-coated in white. They were supplied and installed in July 2017 by Bluedog Fences for $1793.

July 2017 fine with cold nights

July morning photo of Manilla from the lookout

Manilla Prospect in July

Through most of the month, days were fine and sunny, but some days, mainly in the middle, were cloudy and some had a little rain. The highest reading, on the 16th, was only 7.4 mm.
No days were remarkable except the 28th which, at 23.7°, equalled the record for July set 31/07/14. It was 6.1° above normal.
Frosts (below +2.2° in the screen) happened on 23 mornings, 6 more than normal. However, the coldest morning, at -2.6°, was not nearly as cold as the record of -5.1° set in 2002.

Weather log

Comparing July months

Unlike July 2016, which had been cloudy with warm nights, this July was fine with cold nights. Days, at 18.1°, were not quite as warm as in July 2013 (18.9°), the warmest in the new century.
Moisture was scarce, as in the record-making July of 2002. Readings that reflected low moisture were:

Daily minimum temperature very low: +1.2° (2002: 0.9°);
Very many frosts: 23 (2002: 27);
Very low percentage of cloudy mornings: 29% (2002: 23%);
Very low early morning dew point: -1.4° (2002: -1.4°);
Very wide daily temperature range: 16.9° (2002: 18.5°);
Very low rainfall: 13.2 mm (2002: 1.0 mm).

Relative humidity in the early mornings, normally 90% in July, was 74%. That was the lowest July value in my 13-year record.
Despite the total rainfall of 13.2 mm (16th percentile) being far below the July average (41 mm), there are still no shortages of rainfall for groups of months. The most recent serious shortage was nearly two years ago. In October 2015, the 30-month total to that date (1216 mm) was still down at the 6th percentile. That shortage was carried over from an earlier extreme event: the 85 mm summer rainfall of 2013-14 that was 142 mm below average.

Climate graph for July


Data. A Bureau of Meteorology automatic rain gauge operates in the museum yard. From 17 March 2017, 9 am daily readings are published as Manilla Museum, Station 55312.  These reports use that rainfall data when it is available. All other data, including subsoil at 750 mm, are from 3 Monash Street, Manilla.

3-year trends to July 2017

Fine with a wide daily temperature range

3-year climate trends to July 2017

July raw anomaly data (orange)

In July 2017 the largest anomaly was the very wide daily temperature range (middle right graph). This was linked to the daily minimum temperature anomaly (lower left graph) falling suddenly very low.
All moisture indicators pointed to aridity (upwards), and the anomalies of both daily maximum temperature and subsoil temperature were high.

 Fully smoothed data (red)

The latest available fully-smoothed data point, January 2017, showed continued warming in the anomalies of maximum, minimum and subsoil temperatures. These were coming to a peak: the maximum and minimum perhaps in February, but subsoil not for several months.
Moisture anomaly variables were near a peak of aridity. Dew point had peaked (low) in November, cloudiness (low) and daily temperature range (high) in January, with rainfall (low) likely in February.


Note:

Fully smoothed data – Gaussian smoothing with half-width 6 months – are plotted in red, partly smoothed data uncoloured, and raw data for the last data point in orange. January data points are marked by squares.
Blue diamonds and the dashed blue rectangle show the extreme values in the fully smoothed data record since September 1999.

Normal values are based on averages for the decade from March 1999.* They appear on these graphs as a turquoise (turquoise) circle at the origin (0,0). A range of anomalies called “normal” is shown by a dashed rectangle in aqua (aqua). For values in degrees, the assigned normal range is +/-0.7°; for cloudiness, +/-7%; for monthly rainfall, +/-14 mm.

 * Normal values for rainfall are based on averages for the 125 years beginning 1883.

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

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House June warmth profiles: III

Part III: Daily temperature cycles, east wing

Graph showing the daily temperature cycles for five days at mid-winter

This five-day period was a testing time for the unheated solar-passive house. Days were at their shortest, some nights were frosty, and overcast persisted for two days. It fell within a cold, wet, and cloudy winter.

This post is about the single-storied east wing of the house. It is the main part of the house, with most of the clearstory windows.

Back to Part I: Average temperature values.

Back to Part II: Daily temperature cycles, west wing

Observations

View of the house from the street

House From the Street

In this wing, seen on the left in the photo, five thermometer stations define a profile in height. They are:

Subsoil in the heat bank beneath the house;
On the floor slab;
On the room wall;
In the clearstory space;
OUTDOORS, in a Gill Screen, 1.5 metres above the ground and eight metres from the house.

During the five days I made 84 observations at each station at intervals as shown. They define the daily temperature cycles. I observed the amount of cloud in Octas (eighths of the sky) at the same intervals.

Table of east wing temperatures.This table lists for each thermometer station the five-day values of the average, maximum, and minimum temperatures, and the temperature range.

The daily cycles

Subsoil

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