Annual Rainfall Extremes at Manilla NSW: II

II. Platykurtic, Bimodal Annual Rainfall

Histogram annual rainfall frequency Manilla NSW

Manilla’s 135 years of rainfall readings yield the graph above. There are several features to notice.

A ragged pattern

Despite having as many as 135 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

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

Continue reading

June 2017 not as wet as in 2016

Close-up Australian magpie

Thieving Magpie

The month began cool, but became warm in the second half. The only unusual daily temperature was the early morning reading of 12.0° on the 29th, 10.0° above normal. There were ten frosts, when there are normally thirteen. On several mornings there was fog in the valley.
Seven days (normally six) registered rain over 0.2 mm. Significant falls came around the 12th and the 29th. On the 29th, the reading was 23.4 mm, but the rain extended over more than one day, totalling 39 mm. It was neither steady nor heavy, but unusually persistent. At Tamworth, rain fell in 27 hours out of 30.

Weather log for June 2017

Comparing June months

June of 2016 had been the wettest and most cloudy of the new century, with warm nights and cold days to match. This June, while moist, was close to normal. It was very like June 2015 and June 2014.
The month’s total rainfall of 62.8 mm was at the 75th percentile, well above the June average of 44 mm. There are no shortages of rainfall for groups of months to this date.

Climate for June months


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. Since that gauge records “0.2 mm” on many rainless days, I cannot call those days rain days if the monthly count of rain days is not to show a sudden jump to record-breaking numbers.

All other data, including subsoil at 750 mm, are from 3 Monash Street, Manilla.

3-year trends to June 2017

Parametric plots of smoothed climate variables at Manilla
A 13-month “Mackellar cycle”

3-year climate trends to June 2017

June raw anomaly data (orange)

In June 2017 the daily maximum temperature was normal. Moisture variables were low on the graphs, showing rather high moisture. Both daily minimum temperature and subsoil temperature were high. For each variable, the raw value was close to the smoothed value of June 2016, just twelve months earlier.

 Fully smoothed data (red)

The latest available fully-smoothed data point, December 2016, showed warming and drying. Only the dew point anomaly had just passed a “dry” peak. Smoothed subsoil temperature anomaly, which had reached a record low value in November, began to rise, like both of the air temperature anomalies.

The Mackellar cycle

Manilla’s climate variables often move in the cycle of “droughts and flooding rains” from Dorothea Mackellar’s poem “My Country”.*

In that cycle, temperature and moisture move together: hot with dry, cold with wet. On my graphs, hot is to the right. The top four graphs have dry at the top. (I count daily temperature range anomaly as a moisture indicator: high values show dryness.)

The “Mackellar cycle” drives the anomaly values up and down the blue trend lines that skew from cold-and-wet at the lower left to hot-and-dry at the upper right. The path is seldom straight, as any lead or lag of moisture will curve it into an ellipse.

Ellipses on the graphs show the cycle has been strong for two years since the winter of 2015. Its period has been very short: only twelve or thirteen months. Daily maximum air temperature anomaly reached a peak in February of both 2016 and 2017 (hot in late summer-autumn), and reached a trough in August-September 2016 (cold in late winter-spring).

On the top four graphs the cycle advances around an ellipse clockwise. A peak of dryness (up) comes several months before the related peak of daily maximum temperature anomaly (right). Similarly, wetness (down) comes before low temperature (left). I have posted already about the way this cycle skewed the seasons in 2016.

The two graphs at the bottom contain only temperatures. Circles on those graphs show that both the daily minimum temperature anomaly and the subsoil temperature anomaly have been lagging the daily maximum temperature anomaly by several months during these last two years (and not before).


In a post to a “weatherzone” forum, I have annotated (in green) the graph for Dew Point Anomaly versus Daily Max Temp Anomaly. It is the one that shows most clearly the elliptical trace caused by the cycles. That forum thread: “Climate Driver Discussion 2017 (Enso, IOD, PDO, SAM etc.)” has almost no reports of climate cycles observed in Australia.


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.


*By arrangement with the Licensor, The Dorothea Mackellar Estate, c/- Curtis Brown (Aust) Pty Ltd.

House June warmth profiles: II

Part II: Daily temperature cycles, west wing

Graph of temperatures in the house west wing in mid-winter

I report here on the thermal performance of a solar-passive house in Manilla, NSW, during five days at the winter solstice of 2016. The house is described briefly in a Note below.
This post is about the 2-storied west wing of the house, which is less successful. The more successful east wing will be considered later. An earlier post showed that average temperatures decreased with height. Go to Part I.

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.

Observations

View of the house from the street

House From the Street

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

Subsoil in the garden near the house;
On the downstairs floor slab;
On the downstairs wall;
On the upstairs wall;
OUTDOORS, on the wall of the upstairs veranda.

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 west wing temperaturesThis 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

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.

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

House June warmth profiles: I

Graph of house temperatures versus height

Where is the warmth in a house?

People are building houses that should keep warm in winter with little heating.
Some parts of the house will stay warmer than other parts. Which parts? How warm?
Answers are not easily found. I hope this temperature record from a house with only personal heating may be useful. This was a time when the house was under extreme stress due to cold weather.

Over a five-day period in winter 2016, I read thermometers frequently at a number of stations around the house. I have selected those stations that form profiles from top to bottom of two wings of the house: the two-storied west wing, and the east wing that is one-storied with a clearstory.
To find how my house differs from yours, see the note below: “Key features of the house”.

Selected thermometer stations

In the West Wing (two-storied)

OUTDOORS, upstairs veranda (+4.7 metres);
Wall upstairs at head height (+4.2 metres);
Wall downstairs at head height (+1.5 metres);
Floor slab surface downstairs (0.0 metres);
Garden subsoil at -0.75 metres.

In the East Wing (single-storied)

Clearstory space at +3.5 metres;
Wall in the hallway at head height (+1.5 metres);
OUTDOORS, in a Gill Screen (+1.5 metres);
Floor slab surface in the en-suite (0.0 metres);
Solid “heat bank” beneath the floor slab (-0.75 metres).

Part I: Average temperature values

SUMMARY RESULT
In the ground under the floor slab the temperature would be just warm enough for winter comfort. Above the floor slab, the higher you go, the colder it gets.

Results

The graph above plots mean temperature against height above the floor slab. (The mean temperature is the time-average over the five days.)

Comparing east wing, west wing, and outdoors

The single-storied east wing was several degrees warmer at all heights than the two-storied west wing. The east wing has advantages: thermal mass, perimeter insulation in the footings, less shading, and a more compact shape.
Continue reading