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Analysis of trajectories along the isopycnal σ= 24.5 kg/m^3 in the center of the North Pacific subtropical gyre

Summary

Trajectories of parcels along a single isopycnal are calculated. They show two potential pathways for nutrients into the center of the subtropical gyre. The first pathway would be from parcels advected westward that have crossed the latitudes of nutrient-rich 10°N thermocline ridge. The second pathway is from parcels advected southeastward from Spring to Summer that carry moderate level of nutrients and low potential vorticity.

The Lagrang-mean flow is estimated from the net displacement of parcels and is compared to the total time-mean transport (time-mean of velocity times the thickness, the whole weighted by the time-mean thickness). The estimates for the zonal transport agree very well except for the parcels that comes from the northwest. In this case, the time-mean transport is still weakly westward inconsistent with parcel trajectories. The estimates for the meridional transport agree but only in the center of the gyre where it is weakly southward. In the southern part of the gyre, the transport estimated from the trajectories is large and northward while the time-mean transport is still weak and southward.

The difference between the two estimates may be due to the fact that the “bolus” velocity is not expected to be equal to the Stokes drift. A term involving the correlation between velocity and parcel displacement is missing (see Lee (JPO, 2002) and Bühler “Waves and mean flows” section 10.1.2). Thus more work is needed.

Results

We computed the trajectories of water parcels that arrive in the center of the North Pacific subtropical gyre in the middle of winter (Fig. 1) and summer (Fig. 2). For both periods, zonal migration is larger than meridional one. Parcels arrive from the northwest and everywhere from the east. No parcel arrives from the southwest or west.

This is consistent with the idea that westward advection is important in the subtropical gyre. Although during April to December, only two parcels have come from the northern edge of the 10°N thermocline ridge, from January to July, a significant larger number comes from or has passed through these nutrient-rich latitudes, suggesting one pathway to bring nutrients into the center of the gyre.

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Figure 1: Trajectories of water parcels that arrive in the middle of the North Pacific subtropical gyre (red dots) on Dec. 31, 2004. Their positions on April 5, 2004 are shown by green dots. The trajectories were computed using the the horizontal velocity field along the isopycnal σ= 24.5 kg/m^3; that means we assume that the diffusion is negligible and the parcels have kept their densities during that period (NOTA: Bower et al. (2009; see Supplementary Information) show no dramatic differences between trajectories computed from a velocity field at constant field and that from a velocity field at constant potential density, besides the active region of study (Deep Western Bounday Current in the North Atlantic), suggesting that the present trajectories might still be closed to the actual trajectories in the model). The background is the 2004 mean nutrient concentration along the same isopycnal. These trajectories are from traj_iso_24_5_start_Dec31_2004_17_5N_150E_170E.mat in RESEARCH/PROJECTS/MARINE_BIOLOGY/SUBMESOSCALE_PROCESSES/OFES.

From the north, parcels are coming from a narrow band in latitudes centered around 25°N and stronger/more structured from January to July. This is consistent with the southward displacement of parcels of relatively moderate nutrient level and low potential vorticity (Figs. 7 and 8 from the isopycnal analysis at 24.5 kg/m^3). The westward displacement of these parcels is unexpected; I would have guessed, on the contrary, that this southward displacement is part of the subduction of mode waters and as such these waters should have migrated to the southwest. No parcels are coming from north of 30°N where strong injections of nutrients occur due to the instabilities of the Kuroshio Extension (KE).

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Figure 2: As in Fig. 1 except that the parcels started on Jan. 3, 2004 and arrive in the middle of the gyre on July 1, 2004. These trajectories are from traj_iso_24_5_start_July1_2004_20N_150E_170E.mat.

The zonally-averaged Lagrangian-mean zonal and meridional flow for the two periods is estimated and plotted in Fig. 3. They are compared to the total time-mean mass transport. Possible causes for the differences between the two estimates are 1) the fact that trajectories are estimate of the Lagrangian-mean flow for a certain position and period, not necessarily for the entire year 2004, 2) numerical error in computing the trajectories 3) the assumption of weak diffusion is wrong, etc. Besides these, the different estimates in the zonal direction are remarkably similar south of 22°N (Fig. 3a), for which the transport is westward. The estimates differ north of 22°N, for which the transport estimated from parcel displacement is opposite in sign and strongly eastward.

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Figure 3: Zonally-averaged Lagrangian-mean zonal (upper) and meridional (lower) velocities deduced from the calculation of trajectories. The estimate of the period from April to December is show in open black squares, that of the period from April to December is shown in closed back squares. Each velocity is representative of the Lagrangian flow at the barycenter of the trajectory (Andrews and McIntyre 1978);the velocities are then averaged over a regular set of bins in latitudes. The plain blue lines are the total mass transport (time-mean velocity times layer thickness weighted by the time-mean thickness) and the dashed blie lines are the transport due to the time-mean flow. The difference between the two shows the time-mean eddy transport, also called the “bolus” velocity. The zonally-averaged Lagrangian-mean velocities are computed using Get_UL_VL_barycenter.m in RESEARCH/PROJECTS/MARINE_BIOLOGY/SUBMESOSCALE_PROCESSES/OFES.

The estimates in the meridional transport agree in the middle of the gyre with mostly weak southward transport. However, near the southern edge of the gyre, estimates from the trajectories are strongly northward while the time-mean transport is still weakly southward.

It would be nice to understand the cause of the difference (NOTA: It is not because the zonal extent over which the zonal average of the time-mean transport is computed is different from the zonal extent of the barycenter of the trajectories; NOTA #2: I just found out that the “bolus” velocity is not the Stokes drift which might explain the above difference. What is missing is the term of correlation between velocity and displacement –see Lee (JPO, 2002) and Bühler “Waves and mean flows” section 10.1.2; NOTA #3: Despites these remarks, I think the cause of the difference is because the calcul from trajectories is biased because all the trajectories necessary have to bring parcels toward the center of the gyre and the resulting Lagrangian-mean flow is convergent. To correct for this bias, I would need to use other trajectories).

The transport due to the time-mean flow is shown in dashed blue lines in Fig. 3. The difference with the total time-mean transport is the time-mean eddy transport or “bolus” velocity. This shows that most of the transport is due to the time-mean flow and the eddy transport is more important to the north at the latitudes of the KE.