In climate modelling, you're looking for a models that can adequately portray the Earth's climate. This includes showing patterns that are semi-cyclical: things like the El Nino Southern Oscillation. But model verification occurs generally over relatively short time periods, where there is decent observational data (last ~150 years). This means that your model could be displaying the right patterns, but be out of phase, such that linear comparisons, like correlation, will not pick up that the model is performing well..
Discrete Fourier transforms are commonly used to analyse climate data (here's an example), in order to pick up such cyclic patterns. Is there any standard measure of the similarity of two DFTs, that could be used as a verification tool (ie. a comparison between the DFT for the model, and the one for the observations)?
Would it make sense to take the integral of the minimum of the two area-normalised DFTs (using absolute real values)? I think this would result in a score $x\in[0,1]$, where $x=1\implies$ exactly the same patterns, and $x=0\implies$totally different patterns. What might the drawbacks of such a method be?