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I had a long 2 day discussion with Daniel to investigate to see if the derivatives take by Mathematica on the volumetric data are numerically sound or the numbers are out of bound and unreasonable:
Sorry I have no energy for English, so please skim the pdf you see the results.
Basically a 3rd degree Spline along long lat and time on raw data produces reasonable temperature rate of change which are within the realm of temperature changes on the planet i.e. no large numbers.
Moreover after fierce hand to hand combat with NCDF format of NOAA figured out how to convert its integer into floats for programming use.
As such we can conclude that the Derivative Filters on volumetric data are numerically sound and suitable, which brings me to the original point that no need to take all those moving averages and dimensionality reductions and so on, just use the original data, spline it in multiple dimensions and then take derivatives.