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JGCRI / fldgen

Given a global mean temperature pathway, generate random global climate fields consistent with it and with spatial and temporal correlation derived from an ESM
https://jgcri.github.io/fldgen/
GNU General Public License v2.0
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Prove property 2 #10

Closed rplzzz closed 6 years ago

rplzzz commented 6 years ago

Prove that within a single run the autocorrelation function for a grid cell is equal to that of the corresponding cell in the reference data.

This is guaranteed for the basis functions by the Wiener-Khinchin theorem. We need to show that applying the W-K theorem to each basis function independently produces the appropriate ACF for each grid cell individually.

abigailsnyder commented 6 years ago

I think I have this sketched out on paper. I need to go through the full details to be sure. This weekend, I'm going to take the time to typeset the appendix properly with lemmas and then the properties, so it's easier to see what parts we have and what part we need.