For the mathematically minded:
There are a few different methods of how to calculate the SOI.
The method used by the Australian Bureau of Meteorology is the
Troup SOI which is the standardised anomaly of the Mean Sea Level
Pressure difference between Tahiti and Darwin.
It is calculated as follows:
[ Pdiff - Pdiffav ]
SOI = 10 -------------------
Pdiff = (average Tahiti MSLP for the month)
- (average Darwin MSLP for the month),
Pdiffav = long term average of Pdiff for the month in question, and
SD(Pdiff) = long term standard deviation of Pdiff for the month in question.
The multiplication by 10 is a convention.
Using this convention, the SOI ranges from about 35 to about +35,
and the value of the SOI can be quoted as a whole number. The dataset the Bureau uses has 1933 to 1992 as the climatology period.
The SOI is usually computed on a monthly basis,
with values over longer periods such a year being sometimes used.
Daily or weekly values of the SOI do not convey much in the way of useful
information about the current state of the climate,
and accordingly the Bureau of Meteorology does not issue them.
Daily values in particular can fluctuate markedly because of
daily weather patterns,
and should not be used for climate purposes.