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* 3.1 Sv is the sum of the localized subduction south of Iceland (1.9 Sv) and in the Labrador Sea (1.2 Sv).

The most interesting features of these maps are the ambiductive regions in the oceans, where the local water mass conversion rate can reach 80 m/yr. These local conversion rate maxima are very closely related to the heat flux maxima from the ocean to the atmosphere, as indicated by the dashed lines in Figure 5.40.

The water mass formation (erosion) rate, computed as the sum of the subduction (obduction) rate integrated over the corresponding outcropping density range, is plotted in Figure 5.41. The peaks of the subduction rate correspond to the subtropical mode water in the North Atlantic Ocean and North Pacific Ocean. A second peak in the North Atlantic Ocean indicates the subpolar mode water, which has no corresponding part in the North Pacific Ocean because shallow marginal seas, such as the Sea of Okhotsk, were not included in the calculation.

One of the most interesting features from Table 5.4 is that the basin-integrated obduction rate in the North Atlantic Ocean is 1o times larger than the total Ekman sucking rate. This indicates the critical dynamical role of the sloping mixed layer depth. Thus, it is clear that using the term "Ekman upwelling" to describe water mass erosion in the ocean can be very inaccurate and misleading.

Final remarks

In this section we discussed the formation of mode water through subduction and water mass erosion through obduction. In contrast to the wide interest in understanding water mass formation, there have been only a very few studies related to water mass erosion. It

Local conversion rate (m/year)

Local conversion rate (m/year)

Fig. 5.40 Local mass conversion rate in the North Atlantic Ocean, defined within the ambiductive region, with a contour interval of 40 m/yr. The shaded areas are insulated regions where neither subduction nor obduction takes place. The dashed lines indicate the annual heat loss from the ocean to the atmosphere, in W/m2, adapted from Hsiung (1985) (Qiu and Huang, 1995).

Fig. 5.40 Local mass conversion rate in the North Atlantic Ocean, defined within the ambiductive region, with a contour interval of 40 m/yr. The shaded areas are insulated regions where neither subduction nor obduction takes place. The dashed lines indicate the annual heat loss from the ocean to the atmosphere, in W/m2, adapted from Hsiung (1985) (Qiu and Huang, 1995).

is obvious that a complete theory of water mass balance in the world's oceans requires the more comprehensive study of both processes.

In particular, water mass erosion is often related to the upwelling branch of the circulation in the oceans. Upwelling in the ocean is highly non-uniform in space. For example, the strong austral westerlies drive the upwelling in the core of the ACC, which is the strongest large-scale upwelling system in the world's oceans. In addition, there are other narrow upwelling systems, such as the equatorial upwelling, and the strong coastal upwelling along the edges of the basins. These upwelling systems are the major contributors to water mass erosion in the world's oceans.

5.2 Deep circulation 5.2.1 Observations

Deep currents in the oceans

Circulation in the deep ocean is directly related to deepwater formation. The mean flow in the deep ocean interior is very slow, with the horizontal velocity on the order of 0.01 m/s or less and vertical velocity on the order of 10-7 m/s; thus, direct observation of deep

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