The spatial correlation at every depth between the relative vorticity from the model and that from eSQG has been computed over a series of 5 deg. by 5 deg. domain that covers the entire North subtropical gyre and part of the subpolar one to the north. The correlation is computed for every day of 2004 and is then averaged. The same value of the effective buoyancy frequency and c, the two parameters of the eSQG method, is used. across all regions. The depth at which the correlation is 0.7 is plotted in Fig. 7. It shows that the eSQG accuracy shallows equatorward. Notice also that it is more accurate along the coast of the American continent.

The mean correlation itself is plotted in Fig. 2 for three different longitudes which repeats the conclusion drawn from Fig. 1. Notice the local maximum near 500 m.