Spatial correlation in large data sets

Dear Fellow Members,

I have a data set consisting of 1000+ variables, each having
spatio-temporal data. I want to access and filter the variables that show
evidence of spatial patterns so that I can model spatial behavior
accordingly.

For a univariate spatial data, one could plot empirical variograms and
visually assess the presence of spatial pattern in the data. I don't have
that luxury with 1000+ variables. What is your suggestion to do this in an
automated fashion? I'm thinking calculating a spatial correlation measure
like Moran's I for each variable and at each time point and assess by
summarizing appropriately. What are my alternatives?

Appreciate your time.
- Surya