Southern Australia is prone to drought. It is interesting to test the rainfall data to see if a season that starts off dry is likely to continue dry, and to test whether one dry month is more likely to be followed by another dry month than by a wet month. What is the likelihood that a wet Autumn will be followed by a dry Winter, or a dry Autumn by a dry Winter?
I am not a statistician. I wrote this because I am interested in the subject and enjoy 'number crunching' on a computer and writing for the Internet. I'd like to have comments from anyone interested enough to contact me.
The term correlation coefficient (CC) is much used in this page. It is a mathematical evaluation of the degree of relationship between one set of numbers and another. A correlation coefficient of 1 indicates a very strong relationship or similarity, a CC of 0 indicates no similarity. A CC of -1 indicates a very strong negative correlation. I can best explain it by giving some examples.
- If you were to measure the correlation between the age and height of a large group of children between 1 and 15 years you would find a strong positive correlation; ie. the older children would tend to be taller. At a guess the CC might be around 0.95
- If you were to test the correlation between the measurable predictions made about a person's future by an astrologer and what actually befell that person you would find a very low correlation. Ie. there would be very little in common between prediction and fact. The CC would be near 0.
- As an example of negative correlation consider the position of opposite ends of a sea-saw. When one end is up the other is down. Here the CC would be very close to -1.
|Rainfall periods||Correlation coefficient||Number of years of data||Comment|
|Summer and Autumn||-0.06||118||Extremely weak negative correlation|
|Autumn and Winter||0.14||119||This indicates that there is very little statistical connection between the total rainfall in Autumn and the total rainfall in the following Winter.|
|Winter and Spring||0.17||120||Again, little correlation. However, there is some correlation in this and the preceding test, so it appears that there is a very slight tendency in Crystal Brook for Winters to be similar to Autumns and Springs to be similar to Winters. For example, it seems likely that if an Autumn is wetter than average then there is a very slightly improved probability that the following Winter will also be slightly wetter than average.|
|Spring and Summer||0.12||119||Again, very weak positive correlation.|
|Rainfall periods||Correlation coefficient|
|Jan. to Feb.||0.13|
|Feb. to Mar.||0.02|
|Mar. to Apr.||-0.06|
|Apr. to May||0.12|
|May to Jun.||0.18|
|Jun. to Jul.||0.20|
|Jul. to Aug.||0.10|
|Aug. to Sep.||0.16|
|Sep. to Oct.||0.12|
|Oct. to Nov.||-0.05|
|Nov. to Dec.||0.12|
|Clare (Hill River)||-0.11||0.25||0.07||0.05|
If my calculations and my understanding of the results are right, it means that while there is very little detectable similarity between the rainfall in consecutive seasons, there is, overall, a very slight tendency for like to follow like; eg. in most places if the Winter is wetter (or drier) than average, then more often than not it will be followed by a wetter (or drier) Spring than average. It must be stressed that this effect is very slight.
On the other hand, in the rainfall recording stations listed in south-central SA, there is a very slight tendency for the Autumn to be unlike the Summer. Ie. if the Summer is drier than usual then the Autumn is likely to be wetter than usual. Again, the effect is extremely weak.
|Jan. to Feb.||0.11||0.03||0.21||-0.03||-0.04||-0.05||0.07||-0.04||-0.02||-0.03||-0.10||0.11|
|Feb. to Mar.||0.06||-0.02||-0.08||0.08||0.15||0.14||-0.02||0.17||0.04||0.03||0.03||-0.06|
|Mar. to Apr.||0.19||-0.11||0.13||-0.04||0.06||0.02||0.36||-0.11||-0.10||-0.04||-0.11||0.15|
|Apr. to May||0.14||0.11||-0.04||0.04||0.12||-0.16||0.01||0.20||0.04||-0.04||0.00||0.03|
|May to Jun.||0.03||0.12||0.17||0.06||0.05||0.04||0.10||0.16||0.08||0.07||0.13||0.16|
|Jun. to Jul.||0.22||0.18||0.16||-0.03||0.11||0.01||0.15||0.11||0.05||0.09||0.13||0.14|
|Jul. to Aug.||0.19||0.08||0.18||0.03||0.11||0.14||0.10||0.09||0.05||0.11||0.02||0.16|
|Aug. to Sep.||0.07||0.27||0.23||0.16||0.01||0.10||0.11||0.09||0.05||0.09||0.17||0.19|
|Sep. to Oct.||0.13||0.12||0.02||0.14||0.13||0.13||-0.04||0.22||-0.01||-0.02||0.00||0.03|
|Oct. to Nov.||-0.09||0.12||0.21||0.20||0.32||0.12||0.09||0.20||-0.02||0.20||0.20||0.04|
|Nov. to Dec.||0.04||-0.04||-0.03||-0.03||-0.02||0.01||-0.02||0.03||0.10||0.12||0.06||-0.03|
|Dec. to Jan.||0.19||-0.01||0.05||0.06||0.01||0.05||0.00||0.02||0.03||0.02||0.05||0.04|
|Broken Hill||Wilcannia||Cobar||Dubbo||Grafton (South)|
|Jan. to Feb.||0.14||0.14||0.01||0.14||-0.16|
|Feb. to Mar.||0.16||0.15||-0.03||0.10||-0.08|
|Mar. to Apr.||0.13||0.05||0.09||0.11||0.11|
|Apr. to May||0.33||0.18||0.08||0.11||0.10|
|May to Jun.||0.02||0.02||0.09||0.08||0.03|
|Jun. to Jul.||0.02||0.11||0.07||0.32||0.33|
|Jul. to Aug.||-0.06||0.04||0.10||0.24||0.03|
|Aug. to Sep.||0.12||0.03||0.06||0.11||-0.07|
|Sep. to Oct.||0.19||0.18||0.14||0.14||0.11|
|Oct. to Nov.||0.25||0.20||0.28||0.34||0.14|
|Nov. to Dec.||0.25||0.22||0.21||0.24||0.04|
|Dec. to Jan.||0.26||0.13||0.06||0.14||0.18|
What conclusions can one make about these data? Is there any significance in the relatively high correlation at Dubbo? If there was a similar, or higher, correlation at Grafton then one would probably think that we are seeing steadily increasing correlations toward the east because of increasing effects from El Nino/La Nina, but the Grafton figures seem to rule that out.
For Wilcannia, Cobar, and Dubbo there are much stronger correlations in the later part of the year than for other areas covered here.