during this 11-year period, the entire northern region of the Labrador Sea is being cooled from top to bottom.
As the high-latitude region of the Labrador Sea is cooled, the meridional surface pressure gradient increases, since temperature gradients dominate over salinity gradients as in the weak phase. This increasing meridional pressure gradient implies an increasing zonal overturning, which, through divergence (and hence upwelling) at the western boundary and convergence (and hence downwelling) at the eastern boundary, leads to an enhanced zonal pressure gradient and hence an enhanced meridional overturning.
The time scale for the set-up of the zonal pressure gradient is linked to the zonal overturning time scale in the Labrador Sea, which, assuming a 10 cm s-1 surface current, 1 cm s-1 deep return flow, and vertical velocities of the order of 0.01 cm s-1 (from figures not shown), is about 4 years.
As the meridional overturning begins to increase slightly at high latitudes, the cold and now fresh-water starts to move slowly equatorward in a deep western boundary current. Once this cold water has traveled a few degrees southward it suddenly shuts off convection from below at the western boundary (e.g., Figure 11b), because the cold fresh deep water is denser than the overlying warm saline water. The zonal pressure gradient is then further enhanced; hence, the overturning strengthens even further. The time scale for this southward advection of this cold fresh-water is approximately 1 year, assuming an advective speed of 2 cm s-1 over a distance of 600 km.
Once convection is shut off in the west, the overturning starts to increase rapidly, and the cold fresh high-latitude water mass is advected equatorward (in a deep western boundary current) and replaced by a warm salty water mass that originated in the surface waters at lower latitudes (Figure 12b). This is now the strong phase of the oscillation when the system is most energetic (Figure 7a), the heat loss is greatest (Figure 7b), and the poleward heat transport is the strongest (Figure 8, lines 6 and 14). Deep water is now forming at the northern boundary of the Labrador Sea (Figures 10b and 14b), and the flow in the Labrador Sea is strongest and oriented meridionally.
The time scale associated with the removal of the cold fresh high-latitude water mass and its replacement by the warm saline mass is linked to the overturning time scale in the Labrador Sea region. Assuming a 10 cm s-1 surface flow (Figure 13b), a 3 cm s-1 deep flow (Figure 14b) over a distance of 25° (that is, from the latitude where the western boundary current separates from the coast, 50°N (Figure 13b), to the northern boundary, 75°N), and a vertical velocity of 0.01 cm s-1, this time scale is about 5 years.
Since the deep basin of the Labrador Sea is now filled with warm saline water, convection from the surface to the bottom of the basin is induced everywhere through cooling to the Levitus SST field. Hence, the zonal pressure gradient that drives the enhanced thermohaline circulation is reduced, and the whole process begins again.
The total time scale of the oscillation according to the discussion above is therefore:
11 years—Time scale for the cooling of Labrador Sea
4 years—Time scale for Labrador Sea zonal overturning and subsequent set-up of meridional pressure gradient
1 year—Time scale for the equatorward advection of cold fresh-water in the deep western boundary current
5 years— Labrador overturning time scale for the replacement of cold fresh-water mass by warm saline-water mass
21 years— Approximate total time scale
This agrees fairly well with the period of 22 years found in the model solutions.
It should be noted that the time period required for the cooling of the Labrador Sea does not scale linearly with tR. For example, in an additional run that was performed with tR= 100 days instead of 50 days, the time scale of variability remained nearly the same (now 21 years). This might be expected, since T1- TL in the region of the Labrador Sea (Equation 1 with Ta= TL) was, on average, about twice as large as in the integration with tR= 50 days. As a result, (T1- TL)/tR and hence the heat flux out of the Labrador Sea were similar in both integrations. The remainder of the mechanism was identical to that discussed above, although deep ocean temperatures were warmer in the second case.
In experiments 2 through 5 a flux boundary condition was applied to the top 210 m of the northern boundary in order to parameterize a transport of fresh-water from the Arctic. Table 1 summarizes the location and magnitude of the flux that was applied. In experiments 2 and 3, in which a fresh-water source was added at the northern boundary of the Labrador Sea, the internal variability discussed in the last subsection was suppressed. The external freshening was so strong as to cap convection in the Labrador Sea, so the aforementioned mechanism for the variability could not occur.
If the 0.1 Sv was not spread all along the northern boundary, but concentrated only in the Greenland-Iceland-Norwegian seas region (experiment 4) or only in the two grid boxes next to the Greenland coast in the eastern North Atlantic (experiment 5), the variability still occurred, although on a slightly shorter time scale (17 years). In the case when Arctic fresh-water was put directly into the East Greenland Current region, the SSS field (not shown) did a fairly reasonable job of reproducing the climatological Levi-