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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 1A #8

Closed rplzzz closed 6 years ago

rplzzz commented 6 years ago

Prove that the variance of a grid cell in generated data is equal to the variance of the same cell in the input data.

abigailsnyder commented 6 years ago

Done up to needing to be tweaked following the switch to 2d transformation. And assuming $covt(\phi{it}^\star, \phi_{jt}^\star) = 0$ for i != j . Note that, to use Parseval's Theorem, we do now have an extra condition on the means of phi and phi*.

abigailsnyder commented 6 years ago

Oh and also assuming I didn't make a mistake applying Parseval's theorem or elsewhere. The Parseval's theorem especially, I could see myself misunderstanding subscripts. It's also been a minimum of 4 years since I had to use that theorem. And even then, it was only the continuous version

rplzzz commented 6 years ago

We should talk more about this one, then.