Monday, 2 October 2017

Is the weather in Carwoola 'normal'?

Reader advisory: there is going to be lotsa graphs in this, and it is pretty much my thinking evolving as I write so may all be bulldust.  You have been warned.

I recently exchanged emails about the rainfall in the last month and my correspondent's final words were " 'Normal' has ceased to mean much."  This led me to think about what "Normal" meant in the past, and whether it has ceased to be relevant.

Cutting to the chase, my initial thoughts are that temperatures are pretty much normal but rainfall is all over the place!  As always there is cope for further investigation and that may change.

The basic meaning of normal would seem to be something along the lines of "fits within the range of past experience". For example it is normal for January to be hotter than July.  

Something that is not normal could be exemplified by setting a new record for the variable: for example the maximum temperature in September 2017 was 29.2oC.  However looking at one variable and one event is a bit of a stretch to say the weather wasn't normal.  I think where this takes me is to say that normal means "the overall pattern fits within the range of past experience".

Determining whether something fits within a range can be viewed as a matter of probabilities and the statistical concept of the normal curve comes in to play.  Here is a picture of a normal curve with a bell shape.  (For some reason the x-axis isn't labelled, but it is Standard Deviations (SD).) 




The point of particular interest in this chart is the percentages below the x axis.  They show that, if values are distributed normally, 68.3% of observations will be within + 1 SD of the average.  So one way of looking at whether a series is showing "an overall pattern within the range of past experience" is to calculate how many values are within 1SD of the average.  If matters are coming "less normal" one would expect to see a higher proportion of values outside the 1SD range.  (It is common in analysis to use a 5% significance test where the significant values are those >1.96SD for the average.  I rate that as a convention and have used the narrower band on typical values, which possibly overstates the degree of unusualness.)

My method was in several steps for the three variables Maximum Temperature, Minimum Temperature and Rainfall.  For each of the variables:

  • Calculate the monthly average and SD;
  • Calculate whether each monthly observation is greater or less than 1 SD from the average and if so whether above the range (High) or below (Low);
  • Count the number of High or Low readings in each year.

For the temperatures I used the entire Carwoola series back to 1993 (since I only have 4 years of Whiskers Creek observations.  For rainfall I used the Whiskers Creek readings back to 2007.

Temperatures

The number of "out of range" observations x year is summarised in this chart.  The data is shown for two series where the cold refers to temperatures below average (both maximum and minimum) and hot for the equivalent above averages.
In summary the picture that is shown is of a pretty stable series after a period of unusual coldness early in the series.  Eyeballing BoM data for the Canberra Airport comparison site from 1993 to 2010 shows a cool, but not dramatically cold period.  This suggests that something odd was going on early in the Carwoola series especially for the low temperatures:  I have no idea what.  

Removing the period 1993-1998 from the chart amplifies the stability since 1999. (Note that I didn't recalculate the average and SD, just truncated the graph.
Referring back to the normal curve, one could expect 15% of observations to be below the average+1SD  band and 15% below it.  Thus with 2 observations for 25 months random chance should give 7-8 outside readings per month for each series.  In summary I don't think there is much evidence of abnormality here.  Certainly the trend lines don't suggest any decrease in normality in recent years.

Rainfall 

For rainfall I decided to use my own series, thus ensuring there was consistent of siting.  I followed much the same process as before although the series was shorter - 10 years instead of 25.
In this case the rules indicate that there should be about 2 outliers for each series each year.  We have achieved a bit worse than that and 2015-16 is particularly unusual with a majority of months being either low or high.  2017 is not looking good with 4 of the 9 elapsed months unusually low (and the next three not looking too promising!

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