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Fig. 4.118 Layer thickness adjustment in response to wind stress perturbations, described in Fig. 4.117. he is the original layer thickness along the eastern boundary. Curves labeled with he indicate changes in the layer thickness along the eastern boundary; hWW for changes of layer thickness at the western boundary and right at the equator; hsw for changes of maximum layer thickness along the western boundary of the subtropical gyre; and hw for changes of maximum layer thickness along the western boundary of the subpolar gyre.

a are depicted by the line labeled as hW in Figure 4.118b. In a separate calculation, the model is forced by a stronger Ekman pumping rate over the subtropical basin. In response to such an anomalous forcing, the thermocline in the subtropical gyre interior moves downward. On the other hand, the thermocline moves upward in both the equatorial gyre and the subpolar gyre to compensate for the downward motion in the subtropical gyre.

For the third case, the wind stress perturbation is imposed at the equator. For the parameters we have chosen, this leads to exactly zero wind stress at the equator (Fig. 4.117e). Again, such a perturbation leads to a decline in pumping rate in the equatorial gyre, and a downward motion in the subtropical and subpolar basin (Fig. 4.118c).

For he0 > 550 m, the lower layer is insulated from the air-sea interaction. Assuming that the balance of water mass sources and sinks for the lower layer does not change within a short period of 10-20 years, the total volume of the lower layer should remain unchanged. Since the total volume of the ocean remains the same, the total volume of the upper layer water should remain unchanged as well.

Under such an assumption, wind stress perturbation in either the subpolar gyre, the subtropical gyre, or the equatorial gyre can lead to vertical displacement of the thermocline in the whole basin. Depending on the original layer thickness along the eastern boundary, the vertical displacement is on the order of 5-20 m. If a very thin upper layer along the eastern boundary is chosen, say 100 m, the change due to this basin-wide adjustment can be more than 20 m.

This vertical movement of the thermocline is due to inter-gyre communication. In a departure from the traditional ways of studying the wind-driven circulation in each basin in isolation, a water mass conservation over the entire basin implies the dynamical consequence that changes in wind stress in an individual basin can lead to global changes in the thermocline. Such a global change will certainly give rise to new dynamics associated with the coupling of the thermocline with other components of the oceanic circulation.

As an example, wind stress changes at the mid latitudes can lead to substantial changes in the depth of the thermocline along the equator, which in turn will change the nature of the El Nino-Southern Oscillation (ENSO) cycle.

The discussion above is based on a simple reduced-gravity model, in which the density difference between the upper and lower layers is assumed to be uniform basin-wide. This assumption is a gross idealization. If an isopycnal surface is chosen as the interface, the density difference between water above and below this interface changes greatly from the subpolar basin to the equatorial basin. In order to include such a basin-wide density change, the reduced-gravity model can be converted into the so-called generalized reduced-gravity model (e.g., Huang, 1991b). The reduced gravity in the new model is now a function of horizontal coordinates, and the upper layer thickness can be calculated from a slightly modified equation:

where g'(X, 0) is the reduced gravity, which can be calculated from the model, or it can be specified from data. The total volume of water in the upper layer is ff dAÏ—ge— h2 + 2a f * ———dX

Parallel to the case with wind stress perturbation, a thermal perturbation gives rise to changes in the reduced gravity in a region of the basin. Within decadal time scales, the total amount of water in the lower layer remains unchanged. As a result, the volume of the upper-layer water remains unchanged. For simplicity, we will assume that reduced gravity in the unperturbed state depends on the latitude only, i.e., g' = g'(0). Using the volume conservation constraint and assuming a small perturbation, we obtain if dA rr f XXeP- Sg' (X, 0) d x he She -= a J X ,/ --—dA (4.553)

and Sg (X, 0 ) is a change in the reduced gravity whereh (X, 0) = specified.

The mechanism of this adjustment is very similar to that due to a wind stress anomaly. For example, if the subtropical ocean is cooled down, the upper layer density is increased, so g'(X, 0) < 0. According to Eqn. (4.553), She < 0, i.e., cooling will lead to an upward motion of the thermocline in the whole basin. We recall that cooling leads to a smaller density difference between the upper and lower layers. According to the reduced-gravity model, a smaller density difference across the interface gives rise to a deeper thermocline at the given latitude. Thus, cooling behaves like an increase in Ekman pumping. Since the effect of cooling/heating is rather similar to that due to a wind stress anomaly, we do not show the corresponding numerical examples here.

Thermocline reset by the first group of Rossby waves

Thermocline reset by the first group of Rossby waves

Equatorial thermocline Kelvin waves

Original position of the main thermocline

Fig. 4.ii9 Sketch of the adjustment in the subtropical-equatorial ocean induced by reduction of Ekman pumping rate in the subtropical basin interior.

Equatorial thermocline Kelvin waves

Original position of the main thermocline

Fig. 4.ii9 Sketch of the adjustment in the subtropical-equatorial ocean induced by reduction of Ekman pumping rate in the subtropical basin interior.

In summary, both wind stress anomalies and thermal anomalies in a localized region can lead to global adjustment of the thermocline. As an example, stronger Ekman pumping or cooling in the subtropical basin forces a downward motion of the thermocline in the subtropical basin. Since the total volume of water mass is conserved, this leads to a global upward displacement of the thermocline in the whole basin. This global adjustment of the thermocline will interact with other processes in the ocean and produce complicated climate changes.

The calculations above are based on the equilibrium states of the model. In a time-dependent model, perturbations will propagate in the form of waves going through the whole basin. In particular, both Rossby waves and Kelvin waves play important roles in setting up the final solution. As shown schematically in Figure 4.ii9, the reduction in Ekman pumping rate in the subtropical basin excites the westward baroclinic Rossby waves. At this time the layer thickness along the eastern boundary remains unchanged; however, the thermocline moves upward after the Rossby waves pass. As the Rossby waves reach the western boundary, Kelvin waves are excited, which carry the signals equatorward. Due to the constraint of mass conservation, the Kelvin waves must carry a downwelling signal as they reach the equator and move eastward along the equatorial wave guide. At the eastern boundary the equatorial Kelvin waves split and turn poleward along the eastern boundary. As the waves pass through, the thermocline depth along the eastern boundary increases. Along the eastern boundary the Kelvin waves gradually lose their energy by sending out the westward Rossby waves. The final stage of the solution will be established after this wave loop repeats a couple of times and other physical processes in the ocean, such as dissipation, should also play some role. The connection between the mid-latitude wind stress perturbations and the equatorial thermocline and surface temperature anomaly can be explored in detail using a numerical model (Klinger et al., 2002).

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