I'll start by saying that my statistics knowledge is quite limited. I want to find in which locations two 2D climate fields are correlated, and what the sign of this correlation is. The issue is that both datasets are highly autocorrelated, which makes significance testing tricky. So far I've simply split the domain into small boxes, and computed a simple correlation between the two datasets at each box, but this doesn't take the autocorrelation into account.
I'm also interested in how the relationship between the two variables varies as a function of lengthscale. For example, given my simple method above, I could take larger and larger boxes (or coarse-grain the data), but I wonder if there is a better way. For example I have computed the coherency between two 1D datasets before (in my head I interpreted this as a correlation between fourier transforms, giving correlations as function of scale), but I have no idea how this could be done in 2D.
Finally, I work mainly in python and IDL, so any ideas on how to implement any suggested methods in these languages would also be greatly appreciated.