Is There a Method of Computing the Correlation Between Vector Fields?
The question comes up not only in meteorology and oceanography but also for the comparison of the student’s maps, for comparision of old maps, and in many other situations. There are in fact such correlation methods, and associated with these are regression-like predictors. Statistical significance tests are also available.
B. Hanson, et al, 1992, “Vector Correlation”, Annals, AAG, 82(1):103-116.