Correlation between zeta from model and zeta from eSQG when zeta does not change sign with depth

In this note, we show that the percentage of area when the relative vorticity ζ changes sign increases from 30% at midlatitudes to 50% in the tropics and subtropics. I suggested that this could suggest that the model of Hoskins and Bretherton (1972; hereafter HB72) could be relevant in the tropics and subtropics. But Dongxiao pointed out another interpretation: in the tropics and subtropics, ζ is not specifically controlled by either eSQG or HB72 and there is at much chance to have ζ changing sign between the surface and depth than not.

It was suggested to calculate the spatial correlation between ζ from the model and from eSQG for the points where ζ changes or not sign between the surface and depth. The correlation has been calculated for a series of 5° by 5° domain located near 140°W. The 2004 mean correlation is plotted in Fig. 1. In (a), all the domain is considered, in (b) only the points where ζ has the same sign at the surface (0-55 m) than at depth (150-320 m) are taken and in (c) only the points where ζ changes sign between the surface and depth are taken.

In (b), the correlation is improved compared to (a) between 10° and 20° from the equator while, not surprisingly, the correlation is almost everywhere negative between 150 and 320 m in (c).

Does this help us or not to understand if indeed either model is more important or not for the tropics and subtropics?

Figure 1: 2004 mean spatial correlation between model and eSQG ζ. The correlation is calculated for every 3-day snapshot and over 5°by 5° domain located near 140°W. In (a), the whole domain is considered, in (b) only the points where ζ has the same sign at the surface (0-55 m) than at depth (150-320 m) are taken and in (c) only the points where ζ changes sign between the surface and depth are taken. Computed with /RESEARCH/PROJECTS/MARINE_BIOLOGY/SUBMESOSCALE_PROCESSES/eSQG/analysis/test_OFES/test_OFES.m.