We see that over the top kilometer or so of the column, height variations due to salt are more than offset by the 2 m of expansion due to the warmth of the surface lens. These estimates of gradients in surface elevation are broadly consistent with Fig. 9.19 (top).

The thermal wind relation, Eq. 7-17, is the key theoretical relationship of observational oceanography, providing a method by which observations of T and S as a function of depth can be used to infer ocean currents.12 Let us vertically integrate, for example, Eq. 7-16 a from level z to z1 (see Fig. 9.18) to obtain:

Pref

is known as the dynamic height.

Given observations of T and S with depth (for convenience, pressure is typically used as the vertical coordinate) from a hydrographic section, such as Fig. 9.21, we compute a from our equation of state of seawater, Eq. 9-1, and then vertically integrate to obtain D from Eq. 9-16. The geostrophic flow ug at any height relative to the geostrophic current at level ug (zi ) is then obtained from Eq. 9-15 by taking horizontal derivatives. This is called the dynamic method. Note, however, that it only enables one to determine geostrophic velocities relative to some reference level. If we assume, or choose, z1 to be sufficiently deep that, given the general decrease of flow with depth, ug (z1 ) is far smaller than ug (z), then we can proceed. Indeed, upper ocean velocities are insensitive to the assumption of a deep ''level of no motion.'' However, deep water transport calculations, \ugdz, are extremely sensitive to this assumption that is rarely true . Alternatively we can use altimetric measurements or surface drifters, such as those shown in Figs. 9.13 and 9.19, choose the sea surface as our level of known geostrophic flow and integrate downwards.

As an example of the dynamic method, we show D in Fig. 9.21 (bottom) cutting across the Gulf Stream computed relative to a depth of 2 km. It increases from zero at 2 km to an order of 1 m at the surface. Taking

Georg Wust (1890—1975), a Berliner who dedicated his life to marine research, was the first to systematically map the vertical property distribution and circulation of the ocean. In 1924, using the Florida Current as an example, Wust apparently confirmed that the geostrophic shear measured by current meters were broadly consistent with those calculated from the pressure field using geostrophic balance and the dynamic method.

FIGURE 9.21. Top: Temperature section (in °C) over the top 2km of the water column crossing the Gulf Stream along 38° N, between 69° W and 73° W (as marked on the inset). Middle: Salinity (in psu) across the same section. Bottom: Dynamic height, D (in m computed from Eq. 9-16) relative to 2 km. Produced using Ocean Data View.

FIGURE 9.21. Top: Temperature section (in °C) over the top 2km of the water column crossing the Gulf Stream along 38° N, between 69° W and 73° W (as marked on the inset). Middle: Salinity (in psu) across the same section. Bottom: Dynamic height, D (in m computed from Eq. 9-16) relative to 2 km. Produced using Ocean Data View.

horizontal derivatives and using Eq. 9-15, we deduce that ug (z) relative to 2 km is = 0.85 ms-1. This is a

2Hsin 52° s-1 x 100x103 m swift current but typical of Gulf Stream speeds which, instantaneously, can reach up to 1-2ms-1.

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