Pref dX f dy f

(see Appendix A.2.2, III). The Ekman pumping velocity defined in Eq. 10-8 depends on the curl of (Twind/f). Note, however, that typically Twind varies much more than f, and so the pattern of wEk is largely set by variations in Twind. We can estimate the magnitude of wEk as follows. Figure 10.2 shows that Twind changes from +0.1Nm-2 to -0.1Nm-2 over 20° of latitude, or 2000 km. Thus Eq. 10-8 suggests

Ekrnan Pumping (m/y)

Ekrnan Pumping (m/y)

i in i inn im * v'vk v.-1 mivj h 'w ni li ii mi -hi h< ihi'i i <11

I iingMurl-?

FIGURE 10.11. The global pattern of Ekman vertical velocity (m y-1) computed using Eq. 10-8 from the annual mean wind stress pattern shown in Fig. 10.2. Motion is upward in the green areas, downward in the brown areas. WEk is not computed over the white strip along the equator because f —> 0 there. The thick line is the zero contour. Computed from Trenberth et al (1989) data. The broad regions of upwelling and downwelling delineated here are used to separate the ocean into different dynamical regimes, as indicated by the colors in Fig. 9.13.

i in i inn im * v'vk v.-1 mivj h 'w ni li ii mi -hi h< ihi'i i <11

I iingMurl-?

FIGURE 10.11. The global pattern of Ekman vertical velocity (m y-1) computed using Eq. 10-8 from the annual mean wind stress pattern shown in Fig. 10.2. Motion is upward in the green areas, downward in the brown areas. WEk is not computed over the white strip along the equator because f —> 0 there. The thick line is the zero contour. Computed from Trenberth et al (1989) data. The broad regions of upwelling and downwelling delineated here are used to separate the ocean into different dynamical regimes, as indicated by the colors in Fig. 9.13.

WEk ~ 103kgm-3 X 10-4s-1x2x106m _ 32my . Tt is interesting to compare this with the annual-mean precipitation rate over the globe of about 1 m y-1 (this quantity is plotted in Fig. 11.6). We see that the wind, through the action of Ekman layers, achieves a vertical volume flux that is some 30-50 times larger than a typical annual-mean precipitation rate!

Figure 10.11 shows the global pattern of WEk computed from the surface stress distribution shown in Fig. 10.2, using Eq. 10-7. First of all, note the white band along the equator, where the calculation was not attempted because f —> 0 there. In fact, however, the equatorial strip is a region of upwelling, because the trade winds on either side of the equator drive fluid away from the equator in the surface Ekman layer, and so demand a supply of fluid from below (as will be seen in Section 12.2).

Away from the equator we observe down-welling in the subtropics and upwelling in subpolar regions with typical magnitudes of 50my-1, pushing down and pulling up the isopycnals in Fig. 9.7. It takes about 8 y to pump water down from the surface to 400 m, a typical thermocline depth (cf. Fig. 9.8) indicative of the timescale operating in the thermocline. Note that the zero Ekman pumping contours in Fig. 10.11 separate the ocean into geographical domains that will be central to our understanding of the pattern of ocean gyres seen in Figs. 9.14 to 9.16 and large-scale property distributions.3 It is these broad domains, demarcated by zero wind stress curl lines, that are color-coded in Fig. 9.13: subpolar regions (blue) are generally subjected to upwelling, subtropical regions (yellow) to downwelling, and tropical regions (red) to upwelling.

3The pattern of Ekman pumping imposed on the ocean by the wind, Fig. 10.11, has a profound influence on the distribution of dynamically important tracers (such as T, S) the focus of attention here, but also on biologically important properties, such as nutrients. Subpolar gyres, for example, are replete in nutrients because of upwelling of nutrient-rich waters from below and so are regions of high biological productivity. Conversely, subtropical gyres are relative deserts, biologically speaking, because downwelling driven by the wind pushes the nutrients away from the sunlit upper layer where photosynthesis can take place. Thus Ekman pumping has both physical and biogeochemical consequences for the ocean.

What, then, is the response of the interior ocean to this pattern of upwelling and downwelling imposed from above?

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