Analysis along the isopycnal σ=24.5 kg/m^3 south of the Kuroshio Extension

NOTA

• In the following, relative vorticity was first calculated as the value along the isopycnal of relative vorticity computed from u and v in cartesian coordinates. The actual quantity I should have considered is the relative vorticity computed from u and v already along isopycnals. There is, however, little change between the two in practice and the calculation has seen been corrected; thus, if you redo the figures in the future, you might see slight differences with the ones presented here.
• Also, for some inexplicable reason, I calculated the in-situ density instead of the potential density referenced to the surface, so all above results need to be redone. I do not know why this mistake appears in iso_analysis.m; I was certain I referenced the calculation to z=0 and not local depth...

Description

Mean fields

Figs. 1 to 5 shows the 2004 mean fields along the isopycnal σ=24.5 kg/m^3 averaged zonally between 150°E and 170°E: depth, nitrate, potential vorticity (Q), thickness (h) and relative vorticity (ζ). In these figures, the thin lines show the mean plus or minus one standard deviation.

The meridional gradient of the depth of the isopycnal (Fig. 1) is consistent with the expected geostrophic currents: eastward North Equatorial Countercurrent south of 10°N, westward flow in the southern part of the subtropical gyre (10°N-15°N) and eastward flow in the northern part (15°N-25°N). North of 25°N is the region dominated by the eastward end of the Kuroshio Extenstion (KE), which is dominated by eastward and westward jets and strong baroclinic instabilities. The depth varies in time by about 25 m south of 15°N; the variability increases poleward reaching about 50 m north of 25 °N.

Figure 1: 2004 mean depth of the isopycnal σ=24.5 kg/m^3 averaged zonally between 150°E and 170°E. These quantities have been computed using /home/ipu1/userdirs/francois_moli5/RESEARCH/PROJECTS/MARINE_BIOLOGY/SUBMESOSCALE_PROCESSES/OFES/iso_analysis.m and have been saved in iso_analysis_sigma24_5.mat in the same directory.

Nitrate is high south of 10°N, within the 10N thermocline ridge, and varies in time by about 15% (Fig. 2a). Within the subtropical gyre (10°N-25°N), the mean nitrate is low and slowly decreasing norward, together with its temporal variability. North of 25°N, the mean nitrate becomes negative (an anomaly of the model that needs to be discussed) but its temporal variability increases; this high variability is due to the instabilities of the KE front.

Figure 2: 2004 mean nitrate along the isopycnal σ=24.5 kg/m^3 averaged zonally between 150°E and 170°E.

Mean Q is relatively low south of 20°N and increases, together with its temporal variability, poleward of 20°N (Fig. 3). The mean thickness of the layer increases 7°N to 20°N with little temporal variability (Fig. 4). North of 20°N, it slowly decreases poleward but its temporal variability is large. The temporal variability of the relative vorticity is relatively uniform in latitude south of 30°N and increases north of this latitude (Fig. 5).

Figure 3: 2004 mean Q along the isopycnal σ=24.5 kg/m^3 averaged zonally between 150°E and 170°E.

Figure 4: 2004 mean h of the isopycnal σ=24.5 kg/m^3 averaged zonally between 150°E and 170°E.

Figure 5: 2004 mean ζ along the isopycnal σ=24.5 kg/m^3 averaged zonally between 150°E and 170°E. There is a mistake in the label of the y axis; it should read 10^(-5) 1/s.

Large-scale temporal variability

The 2004 time series of the various fields averaged zonally over the domain (between 150°E and 170°E) are shown in Figs. 6 to 8. In these figures, the variability of the large-scale structure (larger than mesoscale) is shown. South of a line that varies periodically from 24°N at the beginning of the year to 22.5°N in Fall, the isopycnal layer stays relatively deep, shallowing slowly from its deeper position in Spring at 150 m to its shallower position in December at 125 m (Fig. 6). South of 10°N, the layer is shallower in Winter (80 m) and deeper in Summer (100 m). North of 25°N, the layer depth varies much more during the year, outcroping in the Winter-Spring and slowly deepening from Spring to Summer where it stays below the surface until December.

Figure 6: Depth of the isopycnal σ=24.5 kg/m^3 averaged zonally between 150°E and 170°E during 2004. White areas show where the surface is outcroping to the surface.

Nitrate stays consistently high in the 10°N thermocline ridge. There is a significant large-scale incursion of this nitrate-rich water north of 10°N in Fall. Otherwise, north of this latitude, the nitrate has moderate levels (>0.05 mmol N/m^3) and is highly variable, suggesting that sub/mesoscale eddy activity controls the variability in this region. North of 22.5°N and south of 35°N, that is on the equatorward edge of the KE, nitrate is low or negative most of the year. Because the nitrate-poor region corresponds to the region where the layer shallows poleward, it is not clear if the low level in nitrate seen in the large-scale is an artifact by the high consumption by phytoplankton or is true at all times and places. North of 35°N, high level of nitrate appears in Winter and Fall, likely due to the KE instabilities.

Figure 7: Nitrate along the isopycnal σ=24.5 kg/m^3 averaged zonally between 150°E and 170°E during 2004.

If we assume that Q is conserved as long as the layer stays below the Ekman layer (50-100 m deep), Q can help to trace where the water comes from. The region north of 10°N and south of 22.5°N has a relatively low Q all over the year (Fig. 8). To the south of this region, Q is moderately high most of the year, somewhat peaking in Summer near 10°N. At the end of 2004, water from south of 10°N seems to move poleward into the subtropical gyre, a motion also seen in the nortward intrusion of nitrate-rich water (Fig. 7).

To the north of the region, high Q values appears once the layer starts to deepen again in Spring. These high Q values propagate equatorward during Fall and is associated with a relatively small thickness (Fig. 9) and downward velocity (Fig. 10). The southernmost latitude reached by these high values of Q is about 22.5°N in Janurary, with weaker values propagating reaching 20°N in March. It is not clear if this southward water is high or low in nitrate; the beginning of 2004 suggests that the water may have moderate levels of nitrate, while the end suggests on the contrary near zero level (Fig. 7).

Starting in the northern edge of the domain in November, the layer suddenly shallows (Figs. 6 and 10), thickens (Fig. 9), thus reducing dramatically Q (Fig. 8), before outcroping to the surface. In February, the layer outcrops at its most southernmost latitude, after which the low level values of Q propagates southward, reaching 20°N in Summer. This water is associated with low but non-zero level of nitrate (Fig. 7) and may explain the somewhat poleward displacement of nitrate contours near 22.5°N during Spring.

Between the two equatorward propagating tongues of Q, it is not clear which ones should be attributed to the actual subduction of mode water. According to Ou abd Gordon (2002), we expect the subducted water to be low Q. However, in the simulation, the low-Q water appears before outcroping and not during the deepening of the layer during Summer.

Notice finally that the large-scale structure of Q cannot reveal the origin of the water that has an eddy-like variability in the signal of zonally-averaged nitrate (for instance in Summer around 15°N).

Figure 8: Q along the isopycnal σ=24.5 kg/m^3 averaged zonally between 150°E and 170°E during 2004.

Figure 9: Thickness h along the isopycnal σ=24.5 kg/m^3 averaged zonally between 150°E and 170°E during 2004.

Figure 10: Vertical velocity w along the isopycnal σ=24.5 kg/m^3 averaged zonally between 150°E and 170°E during 2004. The velocity is defined as the time rate of change of the isopycnal depth.

Animations

A set of animation is available:

• animation of layer depth
• animation of nitrate
• animation of nitrate with lower contours
• animation of Q

These animations show the full spatial and temporal variability of the various quantities and the importance of mesoscale eddies and submesoscale features in distruting the different fields within the subtropical gyre. The animation in N, in particular, seems to suggest that the eddy variability in N observed in the middle of the gyre originates from the 10°N thermocline ridge.

Snapshots of shallowing events

Here are snapshots of the various fields on Jan. 1, 2004.

Figure 11: Depth of the isopycnal σ=24.5 kg/m^3 on Jan. 1, 2004.

Figure 12: Nitrate along the isopycnal σ=24.5 kg/m^3 on Jan. 1, 2004.

Figure 13: Q along the isopycnal σ=24.5 kg/m^3 on Jan. 1, 2004.

Figure 14: Ratio R=ζ/f along the isopycnal σ=24.5 kg/m^3 on Jan. 1, 2004.

Figure 15: w along the isopycnal σ=24.5 kg/m^3 on Jan. 1, 2004.

Analysis

Questions to answer

In the animations, we see that the layer shallows, Q is being advected zonally and meridionally, and high level of nitrate is found in the middle of subtropical gyre at the meso and submesoscale. The questions that I would to answer are:

1. Between upwelling and horizontal advection, which mechanim is responsible for the shallowing of the layer?
2. What is the nitrate and Q content of this shallowing water? Can these information tells us if the water comes from locally (upwelling) or remotely (advection)?
3. When advection applies, can we trace back the origin of the advected water?
4. What maintains the background level of nitrate in the middle of the gyre?

Q as a tracer

If we assume that the ocean is adiabatic below the Ekman layer (50-100 m max in Winter in the subtropical gyre), Q is a tracer for water masses. The zonally-averaged Q (Fig. 8) already suggests some large-scale transport of water otward the center of the subtropical gyre: semi-annually from the latitudes of the KE and intermittently (once a year) from the 10°N thermocline ridge. The zonally-averaged picture, however, does not explain the eddy-like structure in N seen in the animations in the center of subtropical gyre. The animation suggests that this eddy variability is mixing the meridional gradient of N with a net flux poleward into the subtropical gyre.

Meridional transport of nitrate

The 2004 mean meridional transport of nitrate (N.h.v, where v is the meridional velocity) has been computed and its zonal average across the domain plotted in Fig. 16. There is a convergent transport of nitrate within the layer centered near 10°N. There is a southward transport of nitrate in the subtropical gyre, south of 22.5°N at which location the transport is divergent. Within the gyre, the transport is relatively uniform in latitude south of 17.5°N; thus, there is no accumulation of nitrate there. Between 22.5°N and 17.5°N, there is, however, a net transfer of nitrate from north to south with maximum transport at 20°N; there is thus accumulation of nitrate at 17.5°N and depletion at 22.5°N due to meridional advection. Interestingly, most of this advection is due to the mean advection of the mean field (Fig. 17), especially the local maximum in southward flux at 20°N. Thus, the southward flux within the gyre can be attributed to the mean southward flow we expect from the equatorward subduction of water that forms the tropical thermocline. Eddies play a role in increasing the southward flux in the southern part of the gyre and the northward flux south of 10°N, as well as in the KE region.

Figure 16: 2004 mean meridional transport of nitrate along the isopycnal σ=24.5 kg/m^3 averaged zonally between 150°E and 170°E. The transport is computed with the negative values of N (blue) and without (red).

Figure 17: 2004 mean meridional transport of nitrate (plain) and component from the mean advection of the mean field (dashes) along the isopycnal σ=24.5 kg/m^3 averaged zonally between 150°E and 170°E

The meridional transport within the gyre is consistent with the 2004 mean nitrate times thickness (Fig. 17), that tends to have larger value in the southern half of the gyre than in the northern half.

Figure 18: 2004 mean nitrate times thickness along the isopycnal σ=24.5 kg/m^3 averaged zonally between 150°E and 170°E.

Problems to explain: The eddies are mixing N up-gradient (southward) in the southern half of the gyre and (N.h) up-gradient (southward) in the northern half of the gyre.

Discussion

• see Nishikawa et al. (2010) for the analysis of the subducted mode water in the North Pacific in a high-resolution OGCM. For comparison with the OFES model: - I need to calculated Q along 25.05 kg/m^3 and averaged it over several years to compare with their Fig. 4a: Do we have a low Q region between 30°N and 35°N. - I could also compute the “thickness flux” to compare with their Fig. 9 and the stramfunction to compare with their Fig. 10. - I could also compute the entrainment velocity as in their Fig. 11 showing upward diapycnal flux in the subtropical gyre below the isopycnal I studied here. This could explains how to maintain the meridional gradient of nitrate. How good need to be the 3-day output of vertical velocity and Dz/Dt to deduce e? - Because of the diapycnal flux, Q is not hence not conserved, is not it? This is limiting as I cannot use Q as a tracer and trajectories along isopycnal are not representative of real trajectories.

To do

• Dz/Dt should tell if the layer is upwelled or not. Correlate this with values of Q, N, ζ/f, etc.
• Compute streamfunction for nutrient