On the comparison between two sets of 500 mb geopotential height eigenfunctions

When the largest eigenvalues of an Empirical Orthogonal Function (EOF) analysis are of similar magnitude, the corresponding EOFs do not hold great interest when they are considered one at a time; only the vector subspace generated by the first EOFs is significant. In this case, the comparison between two EOF analyses may be summarized by a distance index between the two subspaces. Such a method is applied to EOF analyses over the northern hemisphere of the 500 mb geopotential height from 10 winters of simulation (using a version of the ECMWF spectral model) and 13 observed winters. For more than the first three low-order EOFs, the agreement between simulation and observation is statistically significant.