Rainfall correlations

A study of the relationship between rainfalls in various months of the year and in various seasons in southern Australia.

A page of The Ramblings of a Bush Philosopher
by David Clarke (email: daveclarkecb@yahoo.com)
Written 2003/04/28, modified 2016/03/10
Home
Index
Top
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.


Rainfall correlations at Crystal Brook

By seasons

(Crystal Brook is 200km north of Adelaide)
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 correlations by month from Crystal Brook

Using 119 years of data:
Home
Index
Top
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
Average 0.09
There seems to be a pattern here. In most cases there is a very weak positive correlation between the rainfall of consecutive months.

Seasonal rainfall correlations for several SA stations

By season

Home
Index
Top
Now let's put the correlation coefficients (CCs) for a number of places together...
Locality Summer-Autumn Autumn-Winter Winter-Spring Spring-Summer
SA general
Ceduna -0.04 0.16 0.03 0.10
Clare (Hill River) -0.11 0.25 0.07 0.05
Crystal Brook -0.06 0.14 0.17 0.12
Renmark -0.07 0.04 0.12 0.01
Strathalbyn -0.07 0.04 0.12 0.01
Willunga -0.01 0.10 0.24 0.14
Woodside 0.01 0.21 0.25 0.08
Lower Southeast
Millicent 0.03 0.02 0.15 -0.03
Mount Gambier 0.14 0.22 0.21 0.01
Penola 0.01 0.05 0.18 -0.07
Far south-central
Coulta -0.15 0.08 0.01 0.11
Kingscote -0.19 0.09 0.21 0.04
Port Lincoln -0.19 0.06 0.08 0.17
Yorketown -0.19 0.09 0.26 -0.03
Home
Index
Top
Several generalizations can be made about the data in this table.
So, in simple terms, what does this mean?

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.

Monthly correlations for several SA stations

Rainfall
periods
Ceduna Clare (H.R.) Kingscote Millicent Mount
Gambier
Penola Port
Lincoln
Renmark Strathalbyn Willunga Woodside Yorketown
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
Average 0.11 0.08 0.10 0.05 0.08 0.05 0.08 0.09 0.02 0.05 0.05 0.08
It's difficult to pick any significant pattern in these data, other than the consistent, although small, positive average correlations. Coefficients for the drier months are negligible while those of the wetter months are often around 0.1 or 0.2.


Rainfall correlations - NSW

By season, going from west to east

Having covered a number of stations in SA I thought that it could be interesting to take a line of stations across NSW, to see if any trend could be discerned.

Home
Index
Top
Locality Summer-Autumn Autumn-Winter Winter-Spring Spring-Summer
Broken Hill 0.17 0.06 0.17 0.15
Wilcannia 0.13 0.23 0.19 0.30
Cobar 0.00 0.23 0.16 0.07
Dubbo 0.04 0.12 0.32 0.32
Grafton (South) 0.05 -0.03 0.09 -0.02


Monthly correlations for several NSW stations, going from west to east

Rainfall
periods
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
Average 0.15 0.12 0.10 0.18 0.06

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.


Speculation

Climatologists tell us that El Nino/La Nina has little effect on South Australian weather, but that there is some correlation between sea surface temperatures in the south Indian Ocean and our rainfall. If there are such influences on our rainfalls and they last for periods of at least several months then one would expect to see positive correlations in rainfalls over similar periods, because of consecutive wet (or dry) months (or seasons).


Conclusion

This evidence indicates that the rainfall received in any one season or any one month in southern South Australia provides very little indication of what rainfall will be received in a following month or season. The rainfall received in each month or season is nearly random in relation to other months and seasons.

However, there is some connection between seasons and months, and the connection is slightly greater in some places and at some times of the year than others. Also, in some cases the connection is positive (eg. wet follows wet and/or dry follows dry) and in some cases it may be negative (eg. wet follows dry and/or dry follows wet).

I'd like to have comments from anyone interested enough to contact me (my email address is at the top of this page).

Home
Top

Acknowledgement

The data used for these calculations came from the Australian Bureau of Meteorology.

Index

Home
On this page...
Conclusion | Rainfall correlations - NSW | Rainfall correlations - SA | Rainfall correlations at Crystal Brook | Speculation | Top |