Queensland Rain: Quick ‘n’ Dirty Climatology

My last post, on the connection between the equatorial Pacific Ocean and the floods in Eastern Australia, closed with a graph of the Southern Oscillation Index (SOI) over the past 40 years, and with an assertion that major rains and flooding in Queensland were associated with this index. (As a reminder, it is derived from the difference in air pressure between Tahiti and Darwin, Australia, and is one indicator of El Niño and La Niña.) At least one Australian columnist says “we should have seen it coming”. Should they have? As Levar Burton would say, don’t take my word for it. Let’s check out that connection with some quick-and-dirty statistics.

First, we will need rainfall records to line up agains the SOI. These are available from the Australian Bureau of Meteorology here. Let’s look at the period from 1970 to the present:

Monthly Queensland rainfall (in millimeters), 1970-2010.

Very spiky. Looking closer, the spikes are all occurring mid-summer down under (that is, in December, January, and February). Rainfall in Queensland is extremely seasonal. A few of the spikes are higher than the rest, most notably in 1974, when there were also major floods in Queensland. On further reflection, it doesn’t make much sense to compare the SOI directly with rainfall, since the rain changes more from summer to winter than it does between years. We’ll want to remove the average seasonal cycle from the data to leave us with anomalies, or departures from that average.

The graph below shows each year of rainfall since 1900 plotted as a separate line over the twelve months of the year, giving us a sense of how the annual cycle of rainfall varies from year to year. From these we can calculate the average monthly rainfalls, shown by the black line.

Queensland rain climatology. Each line shows one year of rain totals over the 12 months.

This graph shows us several things. January is the rainiest month, and August the driest. Rainfall is also much more variable during the Austral summer (November-March) than it is during the rest of the year. We can also compare particular years to the mean. The last year of disastrous flooding, 1973-74, is shown in red (the line starts in the middle in July 1973, then runs off the right edge and wraps around to start 1974 on the left). November and December 1973 were among the rainiest on record. January 1974 set the all-time record, half again as rainy as the next highest. Rainfall in 2010 has been above average since July, and well above average since September. Last month was the rainiest December on record.

Now that we have the average rainfall for each month (a.k.a. the “climatology”), we can subtract it from the data to get anomalies, which then look like this (again, just plotted from 1970-present):

Monthly rainfall anomalies 1970-2010. Monthly totals minus the monthly averages.

Still spiky, but with no immediately obvious periodicity. Let’s go ahead and do a simple regression of Queensland rainfall on the SOI:

Rainfall anomaly vs. SOI, with best-fit regression line.

Aha! There is a positive correlation—higher values of the SOI are associated with above-average rainfall in Queensland. This result is highly significant (p << 0.001), meaning that it is very, very unlikely this result would occur by chance. Still, it isn't a particularly strong relationship. There is still a lot of scatter around the best-fit line, and our simple regression model only explains about 13% of the variability. There are evidently (and not surprisingly) other, more complicated dynamics going on.

Finally, let's dig a little deeper into this correlation. It would be reasonable to wonder if rain perhaps lags the SOI by some amount of time. Maybe it takes a month or two for the oceanic and atmospheric conditions expressed in the SOI to manifest themselves as increased rain in Queensland. To check this idea, we use a statistical tool called the cross-correlation function.

Cross-correlation of rainfall anomaly with SOI. When the lag is negative, SOI leads rainfall. When it is positive, rainfall leads SOI.

The graph above shows the strength of the correlation of rainfall with SOI as a function of the time lag between the two series. When the lag is negative, rainfall is regressed on previous values of SOI. When the lag is positive, SOI is in effect regressed on previous values of Queensland rainfall. When the bars stick out past the dotted blue lines, they are significant at the 5% level.

So what does this show? SOI and rainfall are positively correlated for about seven months in either direction. The correlations look a bit stronger on the left side—that is, the SOI is a better advance predictor of rain than vice-versa. But generally, SOI doesn’t look like a super-precise predictor of rainfall from month to month, even if it is a good indicator at a seasonal or yearly scale.

I’ll close out with a snippet from the Australian poet Dorothea McKellar. I’m told that little Aussies learn this in school the same way I learned Longfellow growing up in Boston…Listen, my children, and you shall hear, of the midnight ride of Paul Revere…er, ahem.

I love a sunburnt country,
A land of sweeping plains,
Of ragged mountain ranges,
Of droughts and flooding rains.

—————
NOTES

First, I should note that this really is quick-and-dirty climatology. I’m not an expert in this, nor am I familiar with this part of the world, and I didn’t go that far beneath the surface here, statistically speaking. I could dig deeper, but I have other things I should be doing, such as my thesis and laundry. Take it with a grain of salt.

All data analyzed here came from the Australian Bureau of Meteorology, as mentioned above. With the help of some Python magic, I compiled them into two data files, soi.csv and qlnd_rain.csv. Each has three columns for the year, month, and data value. All graphs and analysis in this post were done using R. The code, for those interested, is here.

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5 Responses to Queensland Rain: Quick ‘n’ Dirty Climatology

  1. Al Dove says:

    Great stuff, thank you. Hey, would it help to transform the data before you extract the anomalies? Every time I see a higher variance with values like you do in the Austral summer, it screams “transform” to me.

    • Sam says:

      The monthly variances can be normalized using this line of code:

      rain$rain.ds <- rain$rain.ds / rep(monthly.sd, 2011 - 1900)

      which, conveniently, puts them all on a standard normal scale (though they’re not normally distributed—they’re all skewed right). The data do look a little nicer afterwards. I redid the regression, and the R^2 went from 0.1292 to 0.1374…not a huge improvement. I also tried log-transforming the data, which improved the R^2 to 0.1584.

      So to answer your question, unfortunately no, not much…

  2. yank been 2 toowoomba says:

    Interesting, but perhaps more interesting would be the daily rainfall delivered to the catchments and the flood plain. Did the rain in Queensland didn’t make the flood? Or was it the rain in the catchments and the floodplain that made the flood?

  3. Keith says:

    I just wanted to Thank You. This is the most accessible analysis of the correlation between SOI and Queensland rainfall I’ve found on the net. The BOM hasn’t published anything comparable… a glaring omission, IMHO. This is great. I can follow your logic, even though your math skills evidently leave mine for dead. And for the record: The version I learned in school starts: I love a sunburnt country, but only when it bloody rains. I grew up post ’74… the bit between 1974 and 2011 is what we call “a bit of a drought”. I believe the Yanks are getting just a wee pre-taste of what 30 years of “bellow average rainfall” means, to real people, and my heart goes out to them.

  4. crikey : Member of.. http:// www.theaustralianweatherforum.com says:

    Excellent presentation of your research. I wish all research was presented like this.
    l got the jist quite easily
    Now here’s another one for you to calculate

    Is there a correlation between the length of time and /or magnitude in POS SOI and the rainfall anomaly.
    Thanks for your time on this l really enjoyed!!

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