Sunday, 11 January 2015

Rainfall in the Big Sandy Bit

The day after Australian news was dominated by a large bushfire on the outskirts of Adelaide the media began reporting on heavy rain falling in the North of South Australia (SA) and the South of the Northern Territory (NT).  The area concerned is that inside the red line in this snip of the Australian weather radar image. (The blue swirl in the SE of the country is where the rain was falling on 11 January - we are right under that and have got a welcome 30mm thus far on that date!)
In the past I have been known to refer to that area as the Great Big Sandy Bit, which I think is a pretty reasonable statement.

Apart from people being swept away by raging torrents in normally dry river beds ..,
... the coverage was notable for comments such as  "The manager of Up Sand Downs Station, North of Oodnawoopwoop reported 140mm of rain, 14 times their monthly average."   Obviously I have obfuscated the property name a bit - mainly because I couldn't remember it  for reasons hinted at in the next section.  There were a few aspects of this statement that intrigued me.

Modern measurements

The first thought that went through my "brain" was that this area gets (140/14 =)10 per year, not 10 per month.  That came about through knowledge of Goyder's Line which roughly follows the 10 inch isohyet.  then my cerebrum focused on inches rather than mm and things made a bit more sense.

The annoying thing was that this was the second time I had perpetrated this anachronism in about a week.  The first one involved a very fit and slim young person who said they had a 36cm waist.  I thought this was the same as mine, and then I recalled my 36 inch waist (possibly in itself an understatement).

How the citizens of the USA will go when they eventually move onto the rational metric system is a matter for great amusement.

Fact Checker

Is it in fact likely that the station concerned would average 10mm of rain in the month of January?  I couldn't remember the actual name, nor precisely where it was, so looked up the BoM Climate Data on line for Alice Springs (NT) and Coober Pedy (SA).  I was surprised to find the mean January rainfall for Alice Springs was 38.5mm (but the median was 17mm - see below for more on this).  For Coober Pedy  the mean was 17mm and the median an arid 4.6mm.  For Coober Pedy the value of the 10th percentile fall for all months was 0!

So depending on exactly where the station was located an average (=mean) fall of 10mm is quite reasonable.  Give them a tick.

What is the average fall?

The default definition of 'average' is the mean fall - add up all the observations and divide by the number of observations.   The next chart shows the mean rainfall for Coober Pedy and Alice Springs by month.
This shows Alice Springs (I hate references to 'the Alice' with a passion) to be a bit damper, probably reflecting wet weather from the North getting that far South a bit more frequently than making it to Coober Pedy.  Also, the comment which started this was about South Australia, so I'll focus on Coober Pedy from here on.

A second definition of average is the median defined as the value for which half observation are greater and half are smaller.  BoM are kind enough to also offer a median value.  The next chart shows the mean and median values for each month for Coober Pedy.
In every month the mean is much higher than the median,  This is to be expected since the minimum value (0) is not far below the mean but the the maximum value (268mm in one March, and over 100mm in several months) is well above the mean.

The third definition of 'average' is the mode, referring to the most frequently occurring value.  Its a bit difficult to state this when, apart from zero each value occurs once in the set of observation.  To get around this I created a series of classes and counted the number of occurrences falling in each class.  I didn't put the ranges exactly equal sizes which I don't think is a great issue.

The most frequently recorded value is clearly 'less than 0.5', mainly due to the large number of observations of 0.  I suggest that a qualitative statement such as "The modal value is for Very Little Rain" summarises the situation fairly well.  To put this into context, in the 8 years we have been at Carwoola we have recorded less than 10mm for 4 months only and our lowest registration was 3.4mm.

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