Lévy and Klein (2004) shows that in their numerical simulation dominated by frontogenesis, the relative vorticity (ζ) is strongly anti-correlated with nutrient (N; -0.73 on average), less so, with phytoplankton (P; -0.47) and N and P are correlated (0.53 on average). I wanted to check if these statements hold true for the North Pacific subtropical gyre, specifically to the east of the Hawaiian Archipelago, in the 1/10-th deg. OFES simulation. Although N and P are positively correlated, at times strongly (0.9), near 60 m, the correlation between ζ and either N and P never reaches the values obtained in Lévy and Klein’s study. More than that: the best correlation is actually *positive* (about 0.3) and is the largest for ζ at 60 m depth and N and P vertically-averaged between 0 and 150 m depth.

The absence of correlations similar to those of Lévy and Klein might suggest that this part of the ocean may not be dominated by frontogenesis. A critic to this conclusion would be that the horizontal resolution of the model prevents frontogenesis to develop. However, the present results are nonetheless consistent with those of Rivière and Pondaven (2006), besides the claim of their own authors, in which in a model that allows frontogenesis and submesoscale to develop, ζ was found to be positively correlated with N (their Fig. 6b). Notice, however, that in their paper, the authors explain that their results are consistent with Lévy and Klein:

“[H]igh nutrient regions are located in positive vorticity structures whereas low nutrient regions are located in negative vorticity regions, and extrema of vorticity are associated with extrema of vertical velocities. These results are in agreement with the statistics calculated in Lévy and Klein (2004)”

Do I misunderstand?

The domain chosen is a zonal band between 22N and 27 extending 15 deg. to the east from the northern part of the Hawaiian Archipelago (Fig. 1). The period covers years 2000 to 2004. The domain and time-averaged nutrient (N) and phytoplankton (P) are shown in Fig. 2. Both the nutricline and the subsurface phytoplankton maximum are about 80 m deep.

Two types of correlation have been performed: one in horizontal space and one in time. We proceed first by calculating the correlation between each quantity at each depth (Figs. 3 and 4) and then by calculating the correlation between the relative vorticity (ζ) at several depths and N and P averaged between the surface and 150 m depth (Figs. 6 and 7).

At every depth, all domain-averaged correlation in time does not exceed 0.5 in absolute value. The correlation between ζ and N (Fig. 3a) increases from the surface reaching about 0.3 below 150 m. The positive correlation might simply suggest that both ζ and N are being advected and stirred in the horizontal direction. The correlation in space (Fig. 4a) has the same structure with positive correlation at depth and weak or negative correlation in the upper 80 m. The correlation in time between ζ and P (Fig. 3b) is weak at every depth: it decreases from +0.2 at the surface to -0.2 at 200 m. Similarly, the correlation in space (Fig. 4b) is also positive in the upper part and negative in the lower part with some suggestion of a downward propagation of the pattern with time at the interannual time scale. No idea if this means anything. Finally the correlation in time between N and P (Fig. 3c) is relatively weak in the upper 60 m then starts to decrease, not uniformely, to -0.4 near 200 m depth. The correlation in space (Fig. 4c) shows the strongest value with more than 0.9 near 60 m and -0.9 around 200 m. These large positive and negative correlations are obtained, however, at depth where one of the two quantities are either small or negligible; furthermore, for the depth range where both quantities are significative values (from 60 to 80 m depth), the correlation is near zero. So I am not sure what to conclude. The good correlation at 60 m depth might be the most meaningful: Fig. 5 shows a snapshot of P and N at 60 m 250 days after Jan. 1, 2000 where, according to the calculation, we expect strong correlation in space. Indeed, the spatial correlation is quite good.

Because Lévy and Klein (2004) was not clear on the exact correlation they performed, I also performed the correlation between ζ at several depths and the vertical average of N and P between the surface and 150 m. The correlation in time between ζ and N (Fig. 6a) is always positive over the upper 200 m, reaching a maximum of 0.35 near 90 m, the depth of the nutricline. The correlation in space (Fig. 7a) varies similarly in depth and has some significative interannual variability. The correlation in time between ζ and P (Fig. 6b) decreases from 0.23 at the surface to near zero at 200 m depth. The correlation in space (Fig. 7b) between ζ and P has the same variability than that between ζ and N. Fig. 8 shows ζ at 80 m compared to the vertically averaged field N and P, all 1000 days after Jan. 1, 2000, where we expect a weak positive correlation. Indeed, the structures are similar but differ in many details. This example illustrates the contradiction with Lévy and Klein; in the present simulation, *positive* ζ corresponds to positive anomaly of N and P. Finally, Fig. 7c shows the time series of the spatial correlation between the two vertically-averaged quantities, N and P: the correlation is most of the time larger than 0.5, at times reaching 0.8.

Computed with `RESEARCH/PROJECTS/MARINE_BIOLOGY/SUBMESOSCALE_PROCESSES/OFES/corr_in_OFES.m`.