Comments on: Hot and Dry Days Ahead for Australia

By: singingfish

singingfish — Sat, 14 Nov 2009 01:49:30 +0000

as well as the rainfall data it would also be nice to look at the correlation with temperature data.

By: JamesGlover

JamesGlover — Sat, 14 Nov 2009 01:49:06 +0000

Glad we sorted that out – guess it was clear from SOI graph that SD(SOI)>>1.

By: stubbornmule

stubbornmule — Sat, 14 Nov 2009 01:07:09 +0000

JamesGlover: your reasoning would be impeccable but for the fact that I neglected to mention that the SOI is also (arbitrarily) scaled by a factor of 10. Your reasoning can then be adapted to show that 0<= sd(dSOI)) <= 20 and the standard deviation of 9 does indeed lie in this range. I have updated the post with a reference to the scaling factor.

By: JamesGlover

JamesGlover — Sat, 14 Nov 2009 00:39:11 +0000

Adding the following
var(SOI(k+1)-SOI(k))=var(SOI)-2r(k+1,k)var(SOI)+var(SOI)
=2var(SOI)(1-r(k+1,k))
=2(1-r(k+1,1)) where r(k+1,k) is the first autocorrelation const for t.s. SOI

so 0<=var(SOI(k+1)-SOI(k))<=4
and 0<=SD(dSOI))<=2

It doesnt seem SD(dSOI)=9 which is intuitively true also if SD(SOI)=1.

It is difficult doing maths directly in an edit box so be gentle if I have made a mistake!

By: JamesGlover

JamesGlover — Sat, 14 Nov 2009 00:22:18 +0000

If SOI(k) = (P(k)-P_ave)/SD(P-P_ave) then SD(SOI)=1

By: stubbornmule

stubbornmule — Fri, 13 Nov 2009 11:46:16 +0000

JamesGlover: the SOI is scaled by the standard deviation of the air pressure deviation. The standard deviation I referred to is the standard deviation of the monthly changes in the SOI to give a measure of how significant the 14.7 drop is, historically speaking. As far as the relationship to rainfall is concerned, the change in the SOI is not supposed to be the significant factor, it's the outright value: negative values are often associated with El Niño events. Here is a chart of average annual SOI versus annual rainfall. It does show a rough correlation. I haven't dug up monthly data at this stage.

By: JamesGlover

JamesGlover — Fri, 13 Nov 2009 11:38:34 +0000

Isnt the SOI as described above already scaled by the monthly std dev of pressure changes? So 14 is 14 SDs of something???

I’d get some data on rainfall and plot R^2 of SOI chgs vs rainfall deviation from that months l.t.average. By plotting R^2 vs delays 0, 1, 2 etc mths if BOM is correct this should rise and then fall off.

By: stubbornmule

stubbornmule — Fri, 13 Nov 2009 10:54:55 +0000

singingfish: I have added a chart with the full history. As for a metric for the precipitousness of the most recent change, apart from the fact that the fall of 14.7 is in the lower 5% quantile, the standard deviation of monthly changes is 9, so the change represents a 1.6 standard deviation move. So, it’s a large move but certainly not unprecedented.

By: singingfish

singingfish — Fri, 13 Nov 2009 09:29:37 +0000

Nice work!

I’d like to see an SOI graph from where records began, and a metric to determine the occurence of precipitous changes of the magnitude of the current one.