> Well it depends on what you are trying to do. If you are interested in
> the outgoing radiation, then using 4th powers may be meaningful
...
> So long as the deviations are small, the simple arithmetic average
> (basically the direct integral of the temperature, with no exponent or
> thresholding) will usually be close to what you might get from any more
> convoluted but perhaps application-relevant calculation.
Ok, I've thought a bit more about this. Mostly, world average
temperature is calculated in relation to the impact of well mixed
greenhouse gases, or anyway, when it's a world average, it's not about
agriculture etc..., and in the first instance, GHG impact via
radiation, they don't directly change convection ...
I am not sure why the impact of the averaging procedure would per se
be negligible. I've put +50C and -50C into a spreadsheet and come to
an average of 12.87C. Now, I suppose that the world consists of one
half at -50C and one half at +50C and use goal seek to work out how
much the "equator" half has to drop to compensate a 3C increase in the
"polar" half, and that comes to a 1C drop, ie -47C and +49C also
average to 12.87C, yet a simple arithmetic average would give a rise
of 1C.
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