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Why does the eSQG theory over and underestimate?ΒΆ

The domain over which I applied the eSQG theory in this note is shown in Fig. 1 by the dashed white lines. Fig. 1 also shows the standard deviation of the vertical velocity w at 60 m depth in the model. It indicates that the domain has two specific regimes of w: a regime of weak w variability north of 18.75N and a regime of strong w variability to the south of 18.75N as part of the variability that is generated at Big Island.

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Figure 1: Standard deviation of w at 60 m depth in the model. The dashed white lines indicate the domain over which the eSQG theory has been applied to, as well as the subdomain of different w regimes.

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Figure 2: Scattered plot of w at 60 m depth from the model versus w at 60 m depth from eSQG theory for all three months: for locations between 161.25W and 158.75W in both panels and between 18.75N and 20.25N in the upper panel and 17.75N and 18.75N in the lower panel.

Thus, when we plot now model w versus w estimated by eSQG separately within these two subdomains, one obtain in each case a more linear relationship between the two (Fig. 2). Fig. 3 shows the standard deviation for model and eSQG w. The pattern is similar with a region with relatively no w in the middle of the domain, surrounded to the north and south by bands of high w variability but the relative magnitude of each band varies between the two estimates.

The question is still why the eSQG theory underestimates w in the southern part and overestimate it in the northern part. One possible road of improvement is in the use of different values of N0 and c, the two parameters of the eSQG theory. I still do not really understand what they are, but it is possible that they may differ a lot between the two regimes which would explain the mismatch. Any other ideas?

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Figure 3: Standard deviation of w at 60 m depth from the model and from eSQG theory.