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Test of Hoskins and Bretherton (1972)’s model in the North Pacific subtropical gyre using OFES

Conclusion

Over a 5 deg. by 5 deg. region near 137.5W and 15N, an event with high ration R=|ζ/f| has been identified. For this event, the dipole of relative vorticity reversed between the surface and the depth of local maximum of buoyancy frequency near 100-120 m, consistent with the model of Hoskins and Bretherton (1972; hereafter HB72).

It is not clear, however, what is the proportion of submesoscale features that have the same properties. Most (80%) of the relative vorticity at 120 m over the eastern North subtropical Pacific has the same sign than the relative vorticity at the surface. But about 20% have the reversed sign.

Results

The ratio R=|ζ/f|, where ζ is the relative vorticity and f the Coriolis parameter has been computed at the surface for the region extending from 140W to 135W, and 12N to 19N over 2004 in OFES. The percentage of the area for which R is larger than 0.4 and 0.5 is rather small (less than 1%) but this happens several times during the year especially during summer (Fig. 1). I choosed the event on May 20. Large R occurs over a small area near the center of the region (Fig. 2).

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Figure 1: Ratio R=|ζ/f| at the surface for the region extending from 140W to 135W, and 12N to 19N over 2004 in OFES. All calculations are in /home/francois/RESEARCH/PROJECTS/MARINE_BIOLOGY/SUBMESOSCALE_PROCESSES/eSQG/analysis/test_OFES/rel_vort_HB72.m.

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Figure 2: R on May 20, 2004.

At this location (and probably in a lot of places), the stratification has a shallow thermocline near 100-120 m (Fig. 3). There is a SW-NE gradient of potential temperature (Fig. 4) which corresponds to the intrusion of warm and nutrient-rich water from the south into the colder and nutrient-poor water of the north. The question is then if the model of Hoskins and Bretheron (1972; hereafter HB72) applies. According to this model, the relative vorticity at the surface and at 100-120 should be of opposite sign. The answer, for this event, seems to be yes (Fig. 5). This is best seen in the vertical-longitudinal section of relative vorticity at 15.1N (Fig. 6): The dipole of relative vorticity at the surface is reversed at 120 m although the deeper dipole is horizontally more confined. Isopycnals shallow eastward right across the region of high R (Fig. 7). All these observations seem to be in accord with the HB72’s model.

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Figure 3: Buoyancy frequency on May 20, 2005, averaged between 138W-137W and 14N-16N.

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Figure 4: Surface potential temperature on May 20, 2005.

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Figure 5: Relative vorticity on May 20, 2004 at (a) the surface and (b) 120 m.

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Figure 6: Relative vorticity on May 20, 2004 along 15.1N. The dark contours show where R equals 0.4 and 0.5.

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Figure 7: Potential temperature on May 20, 2004 along 15.1N. The dark contours show where R equals 0.4 and 0.5.

The question is then: Is this an isolated event? What is the proportion of submesoscale features in the subtropics that the HB72’s model can describe? Assuming that the local maximum of stratification is always near 120 m, I plotted the surface relative vorticity versus the relative vorticity at 120 m over the entire east subtropical North Pacific (150W-130W and 10N-25N) and over 2004 (Fig. 8). The dominant tendency (about 80%) seems to be the relative vorticity at depth has the same sign than that at the surface. But there is a significant portion (about 20%) the relative vorticity changes sign between the two depths. High R values is not enough to discriminate the two cases. What else could be used to isolate these regions where the relative vorticity reverses at depth?

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Figure 8: Relative vorticity at surface versus at 120 m over 150W-130W and 10N-25N during 2004 in the case where R is larger than 0.1. Blue squares are from the region between 138W-137W and 14N-16N on May 20.