I often hear the explanation that weather equals "noise" and climate
equals "long term trends". Putting that into a simple mathematical
example, we might have "noise" being a six sided dice multiplied by
0.01C and the trend being 0.01C per year. Then we can have a 1 year
drop of 0.04C and five years of no trend in spite of there really
being a trend.
So far so simple, except how do we know that "noise" is mostly about
short time scales and mostly random?
What's the physical explanation behind that?
How do we know that "noise" is unlikely to have a time scale also of
decades, centuries or millennia with a significant amplitude?
One way to assess this is to look at past data. If temperature
randomly fluctuated in the past with an amplitude of 1 C and a time
scale of around 100 years, or with an amplitude of 0.3 C over 30
years, we should see that, if we have 1000 years of data, and if 900
of those are flat to +/- 0.1 C that's pretty good counter evidence,
even in the absence of physical understanding.
I don't think we have such good temperature data, nor do I think we've
got good enough data for aerosol and other forcings over the 20th
century and temperature data for that period that we could merely
compare model outputs and actual temperature history.
What I would really like is a good underlying physical reason/
explanation why noise with an amplitude of 0.3 C and a frequency of 30
years between peaks and troughs is unlikely.
Coming back to my above example of noise and trend, after 10 years the
trend must be roughly visible (even with an initial value of 0.06 =
0.06 random + 0 trend, and an end value of 0.11 = 0.01 random + 0.1
trend) and after 30 years clearly visible.
Not so when the "noise" rises regularly by 0.01 C per year for 30
years and then regularly falls by 0.01C per year for 30 years, we can
then have a measured trend of 0.02C per year for 30 years and a 0C per
year trend for 30 years when the real underlying long term trend is
0.01 C per year.
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