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#1202166 - 02/07/2013 22:39 Re: Observations of climate variation [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2070
Loc: Manilla, near Tamworth NSW
A Model of Seasonal Rainfall for Manilla, NSW
At 31 degrees south latitude, Manilla lies between the winter rainfall regime of the westerly belt and the summer regime of the monsoon. Much more rain falls at Manilla in summer than in winter.
On this graph, the rainfall distribution by calendar months is shown by the black line and numbers (mm) . This is the average curve for the 125-year period from the first observations in 1883 up to 2007. For any shorter period the curve is not smooth. This record is scarcely long enough to yield a stable estimate of the seasonal pattern.

Curve fitting
I have fitted a model of two gaussian (or normal distribution) curves to these observations. [See Note below.]
Because the summer rainfall looks like a bell-shaped curve, I first plotted on the graph a gaussian curve fitted to that.
Noting that the tails of the summer gaussian curve extend for more than twelve months, I graphed three successive years of monthly average data, with three fitted summer curves. Where these curves overlapped, I summed their values.
I then plotted the residual: the monthly data less the summer gaussian curves. This represented the winter rainfall component of the total. Although monthly rainfall is almost constant from April to September, this residual amount was roughly bell-shaped, as I expected. To make the shape of the residual curve more like a gaussian curve I had to adjust the summer curve. In particular I had to make it narrower, so that some part of the rainfall in spring and autumn months could be allocated to a winter curve. I then fitted a second gaussian curve to the residual that represented the winter rainfall. I made a total model curve by summing the summer and winter curves. By further adjusting each of the two seasonal curves, I was able to make the residual values from the total model very small. The net residual value for the whole year was less than 0.5 mm in an annual total rainfall of 652 mm.
Monthly discrepancies of actual rainfall from the gaussian model are plotted at the bottom of the graph. Only two months cannot be made to fit the model well: October has 6.2 mm more rain than expected, and December has 10.0 mm less.

The Nature of the Bi-modal Gaussian Model
The two fitted Gaussian curves peak exactly six months apart, about the 27th of June and 27th of December. That is only six days after the winter and summer solstices. The peaks come much earlier than the dates of temperature extremes at Manilla: thirteen days earlier than the date of annual minimum temperature (10th of July) and twenty-nine days earlier than the date of annual maximum temperature (25th of January).

The peak value of the summer curve, 83.8 mm per month is nearly twice as high as that of the winter curve, which is 42.2 mm per month. The winter curve is 11% wider, with a width at half height of 5.1 months versus 4.6 months for the summer curve. Taking areas under the two (wrapped) curves, the summer rainfall curve accounts for 64% (420 mm) of the total annual rainfall (652 mm), while the winter curve accounts for 36% (232 mm).

Implications
As this simple, bimodal gaussian model fits the actual rainfall distribution so well, it is likely that two distinct sets of processes produce rain at Manilla. In the broadest terms these relate to the westerlies and the monsoon, as is well known. Further study should recognise that the mechanisms, in detail, produce effects concentrated very close to the solstices, and spread randomly around those dates. The spread of the effects due to "summer" processes is wide enough to occur sometimes in mid-winter, and vice-versa.
The model implies that there is no need to seek a mechanism that would produce uniform rainfall from April to September: the uniformity arises from the overlap of two gaussian models.
The large discrepancies that remain, excess rainfall in October, and deficient rainfall in December, perhaps deserve special study.

I will post showing how the rainfall anomalies of calendar months differed from time to time.


Note.
The spreadsheet application Microsoft Excel has a function "NORMDIST" which gives the normal or gaussian distribution curve. It has an input called "cumulative" which must be set to "FALSE" to give the bell-shaped normal density function curve. I experiment with different constants on both axes of the curve to achieve a fit.
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#1202436 - 04/07/2013 19:43 Re: Observations of climate variation [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2070
Loc: Manilla, near Tamworth NSW
A Model of Seasonal Rainfall for Manilla, NSW
II. Tri-Decadal Monthly Rainfall Anomalies

In post #1202166 (above) I modelled the seasonal distribution of rainfall at Manilla, NSW, as a bi-modal gaussian distribution with a higher gaussian peak very close to the summer solstice and a lower one very close to the winter solstice.
Monthly discrepancies of the 125-year average from the model are small. They are plotted in black on each of the two graphs below. Only two months could not be made to fit the model well: October has 6.2 mm more rain than expected, and December has 10.0 mm less.

The graphs show anomalies from the model for each of five "epochs" of three decades (or less). They are:
1883 to 1900 - "19th Century" (19thC)
1901 to 1930 - "World War I" (WW I)
1931 to 1960 - "World War II" (WW II)
1961 to 1990 - "BoM Normal Period" (BoM)
1991 to 2012 - "21st Century" (21stC)


First, there is some persistence of the whole-record anomalies in the various epochs. The December deficit is greater in 19thC and WW II than in the whole record. It is almost the same in WW I and BoM, and becomes an excess in 21stC. The October excess persists in all epochs except WW I, where there is no anomaly. The excess is greater in WW II.

The higher or lower anomalies of total annual rainfall in each epoch (noted in the legend to the graphs) accord with the curve of long-duration drought and deluge graphed in a post in another thread.

Taking each epoch in order:

1883 to 1900
This was the wettest epoch, with 36 mm more rain per year than the model. The Standard Deviation of its anomalies, 9.67 mm, is near the mean for the epochs. There are large excesses on the season breaks in March and September, and large deficits near the gaussian peaks in July and December. That is to say, the bi-modal summer-winter model of rainfall distribution is not expressed strongly in this earliest epoch.

1901 to 1930
This was the driest epoch, with 32 mm less rain per year than the model. Anomalies were the least variable, with a Standard Deviation of only 7.70 mm. Relative to the model, rainfall declined from a peak excess in June to a peak deficit in February. In this epoch, a different model may fit better, with an enhanced winter peak and a summer peak reduced and moved towards spring.

1931 to 1960
Annual rainfall was only 11 mm below the model, and the Standard Deviation of monthly anomalies (9.27 mm) was near the mean. This epoch had the greatest enhancement of the October and December anomalies. Anomalies in winter were small, and the greatest excess was in February.

1961 to 1990
This epoch, the one adopted by the Bureau of Meteorology to generate its reference climate normal, is not typical of the 125-year record at this site. Monthly anomalies have the largest Standard Deviation of any epoch (11.40 mm), and the annual rainfall is 23 mm above the model. Both measures relate to the fact that the January rainfall (114 mm) is nearly 31 mm above that in the model. Anomalies in October and December are close to those in the 125-year record, but anomalies are also quite large in May (+) and June (-).

1991 to 2012
The mean annual rainfall since 1990 is practically the same as that for the 125-year record (2 mm less). Total anomalies are small, with a Standard Deviation of only 7.96 mm. The greatest excess is in November, and there are large deficits in January, March, April, and May.

Notes on data from 1999
Citing data from 1999 to date, I mentioned in this post large monthly anomalies in the same sense as those graphed for the 1991-2012 epoch in the months of January, February, May, and November.

In posts in the present thread, I have plotted 14-year logs of anomalies of climate variables, including rainfall, for each calendar month. [See note below.]
The actual anomaly values, and the fitted cubic trend lines, show anomalies in the 1991-2012 sense:
January: Trend about 20 mm low; nearly all values low (but two very high).
May: Trend steady at minus 20; nearly all values low.
November: Trend about 20 mm high; all above zero, and very high at the ends.


Note.
In these graphs, the y-axis is marked only in degrees. As implied by the legend, the value of monthly rainfall anomaly in millimetres is 20 times the y-axis value in degrees.


Edited by Surly Bond (04/07/2013 19:51)
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#1206136 - 03/08/2013 23:09 Re: Observations of climate variation [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2070
Loc: Manilla, near Tamworth NSW
Manilla Smoothed Monthly Anomalies of Climate Variables
Parametric Plots
Update for July 2013
"Very warm days and nights"



Raw values for July showed a big jump towards hot and dry for most variables, but dew point anomaly fell only to zero. Minimum temperature and subsoil temperature fell back a little from extremely high anomaly values in June.

The fully-smoothed data point for January 2013 continues a drift towards normal from the mild drought of October.

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.
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#1207596 - 18/08/2013 22:15 Re: Observations of climate variation [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2070
Loc: Manilla, near Tamworth NSW
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#1256775 - 11/04/2014 13:25 Re: Observations of climate variation [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2070
Loc: Manilla, near Tamworth NSW
Manilla Smoothed Monthly Anomalies of Climate Variables
Parametric Plots
Update for August 2013
"Very warm days and nights"

The raw value of max temp anomaly for August was lower than for July. Other variables were typical of "drought", except for min temp, which was normal.

The fully-smoothed data point for February 2013 completes a summer season that moved away from drought.
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.


Continuing this series of posts
You see this post is in series with the one two posts up the page. However, it is not up to date.
Because discussion of this topic is now restricted under "weatherzone" rules, I have transferred my material to another place. My latest post in this format (March 2014) shows how drought at Manilla was developing through winter 2013, and may now be declining.
I am grateful to "weatherzone" and those posting on it for helping me to learn a great deal about climate in the course of the last decade.
"Surly Bond"
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#1258919 - 12/04/2014 21:34 Re: Observations of climate variation [Re: Surly Bond]
crikey Offline
Weatherzone Addict

Registered: 01/02/2011
Posts: 2586
Loc: Tweed Heads
HA. Awewsome surly. your back! been along time since the climate discussions got the boot.
Look forward to your updates on Manilla. NSW
Drought declining ?/ awesome. THat should be an eye opener for the El Nino forecasters. Can you elaborate?
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#1259770 - 13/04/2014 22:35 Re: Observations of climate variation [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2070
Loc: Manilla, near Tamworth NSW
Hi, Crikey. Good to hear from you.
My latest Manilla parametric plot, for March 2014 is here.
Only the fully-smoothed points, in red, accurately reflect the swings of climate. The last one, for September 2013, shows a rather severe drought, which had been deepening steadily since April. Points since September (uncoloured) are more and more affected by random variations from month to month. Points for February and March suggest we are out of the drought: provisional points for April agree.
By early May I will have the April parametric plot ready.
I think the smoothed daily maximum temperature anomaly may peak in October, but the extremes of rainfall and dew point will come a month or two later. Peak values for daily minimum temperature and for subsoil temperature came already in July 2013.


Edited by Surly Bond (13/04/2014 22:43)
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#1270027 - 16/07/2014 22:57 Re: Observations of climate variation [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2070
Loc: Manilla, near Tamworth NSW
Images on this thread

Until recently, images I have posted in this thread were hosted by "Photobucket".
It you click on an image, one of four things can happen:
1. You get a full screen view of the image.
2. You get an enormously enlarged view of part of the image. It is difficult to restore this to the proper size.
3. You get a small image surrounded by clutter on the "Photobucket" page.
4. You will be attacked by various kinds of hideous animated spam within "Photobucket". The experience is extremely unpleasant. I apologise if it has happened to you.
I don't know why any of this happens. I am now hosting images on my own website.
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#1330296 - 28/05/2015 16:48 Re: Observations of climate variation [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2070
Loc: Manilla, near Tamworth NSW
In case there are still any readers who suspect that the climate does not always stay the same, I have found a relationship in the rainfall record at Manilla, NSW that may interest them.
For nearly a century, droughts and flooding rains were related in a way that is remarkable and unexpected.
I have put a series of three posts on my blog, titled "More droughts after heavier rains".
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#1365156 - 09/02/2016 19:01 Re: Observations of climate variation [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2070
Loc: Manilla, near Tamworth NSW

I posted these graphs earlier in this thread ( Post #1135614 )

That post refers to three similar graphs that I posted earlier.
For those interested in these Chip Knappenberger-type graphs, I intend to post later ones on my blog. I have begun with a re-posting of this pair as a sample.
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#1375639 - 13/05/2016 13:27 Re: Observations of climate variation [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2070
Loc: Manilla, near Tamworth NSW
Two contrasting droughts

This graph shows that two of the catastrophic droughts of the past, in 1902 and 1912, were very different. The differences could be important for studying the generation of droughts in general.
In 1902, the short-duration and long-duration elements of the drought all ended in 1903, with the the long-duration elements having necessarily commenced up to eight years earlier (1895). In 1912, the reverse was the case: long-duration and short-duration elements of the drought must have all commenced near the same date in 1911, and the long-duration elements ended (i.e. the drought broke) up to six years later (as plotted on the graph).
Unfortunately, as ruled in the second Topic in this weatherzone "General Weather" forum, no such matters of climate history can be discussed here. I present this post simply as an "Observation", in line with the topic of the thread.
I have posted this graph and information about it on my blog. Discussion is permitted there, indeed welcomed!
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#1378152 - 04/06/2016 20:00 Re: Observations of climate variation [Re: Surly Bond]
Seira Offline
Meteorological Motor Mouth

Registered: 27/08/2003
Posts: 7213
Loc: Adelaide Hills.
Originally Posted By: Surly Bond
Unfortunately, as ruled in the second Topic in this weatherzone "General Weather" forum, no such matters of climate history can be discussed here. I present this post simply as an "Observation", in line with the topic of the thread.

Because observations are factual smile .
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#1409708 - 27/02/2017 00:45 Re: Observations of climate variation [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2070
Loc: Manilla, near Tamworth NSW
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#1410900 - 05/03/2017 12:40 Re: Observations of climate variation [Re: Surly Bond]
Seira Offline
Meteorological Motor Mouth

Registered: 27/08/2003
Posts: 7213
Loc: Adelaide Hills.
Keep going Surly... smile .
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#1411037 - 06/03/2017 00:48 Re: Observations of climate variation [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2070
Loc: Manilla, near Tamworth NSW


Encouraged by "Naz", I present a graph of very hot days and nights through the last eighteen summers. I am not game to give an opinion on the pattern until after next summer.
Before this summer's data came in, I used seventeen years of hot day data in a light-hearted discussion of changing prospects for thermal soaring in gliders.
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#1424536 - 29/05/2017 00:36 Re: Observations of climate variation [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2070
Loc: Manilla, near Tamworth NSW

When is the first frost at Manilla?



https://climatebysurly.com/
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#1424806 - 31/05/2017 09:56 Re: Observations of climate variation [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2070
Loc: Manilla, near Tamworth NSW
Setting up your own Normals

When you have collected weather data for a decade or more, you will want to see how the climate is changing at your place. It will be particularly interesting if you are not near a Bureau of Meteorology weather station.
You need to set up "climate normals".
At the world scale, the World Meteorological Organisation administers "Climatological Standard Normals". The most recent standard period is 1961 to 1990.
This standard period is so long, and began so long ago, that there must be hardly any amateur observers that can use it for their own data. For amateurs, a decade may be quite long enough. There is nothing to stop you setting up your own normal period, and beginning it as soon as you have got over teething troubles at your station.
This is what I have done, using as a normal period the decade commencing in March 1999.
I have written a few paragraphs about climate normals as Notes to my blog post about the date of first frost:
https://climatebysurly.com/2017/05/28/when-is-the-first-frost/


Edited by Surly Bond (31/05/2017 09:58)
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#1426294 - 19/06/2017 18:23 Re: Observations of climate variation [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2070
Loc: Manilla, near Tamworth NSW



Explained in my blog.
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#1428558 - 20/07/2017 22:00 Re: Observations of climate variation [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2070
Loc: Manilla, near Tamworth NSW
Missing Images

I noticed that someone visiting my blog "Climate By Surly" had clicked a link to this thread, specifically to Item #863801 of 18 May, 2010. (That was about the quasi-biennial oscillation of about 30 months between cool-wet and hot-dry times in Australian climates.)
Looking at my posts here, I see that all my images have been erased up to 11 April 2014.
I had expected to see that. I had been using the photo-sharing website "photobucket". Photobucket has now advised me, in a "no-reply" e-mail, that they are closing public access to images, except for subscribers to paid accounts. They proposed that I should become one.
I didn't want to do that, as I am now able to host images on my blog.
Some time ago, in Post #1270027 of 16 July 2014, I warned readers that linking to any of my photobucket images could lay them open to "shock-and-awe" level spam. At least that will not happen any more.
If you are curious about any one of the missing images, you will most likely find that I have copied it to my blog. As they are not indexed in any way, it will be a treasure hunt for you.
https://climatebysurly.com/

This episode is a reminder that there is nothing permanent about the internet. This may be the technology with the shortest life-span of any in history.
Make paper copies of everything that you value.


Edited by Surly Bond (20/07/2017 22:06)
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#1428561 - 20/07/2017 22:17 Re: Observations of climate variation [Re: Surly Bond]
Seira Offline
Meteorological Motor Mouth

Registered: 27/08/2003
Posts: 7213
Loc: Adelaide Hills.
Originally Posted By: Surly Bond
This episode is a reminder that there is nothing permanent about the internet. This may be the technology with the shortest life-span of any in history.
Make paper copies of everything that you value.

I think the operative word is copy. Don't move material from file (be it USB, laptop, stand-alone PC, or similar) to the net without a backup, and even print it off if unsure smile .


Edited by Seira (20/07/2017 22:18)
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