are the velocity shear from the thermal wind relation. If the determinant of Eqns. (2.244, 2.245) is non-zero, the coefficient at these two levels, and A^m), can be determined,

Longitude

Fig. 2.31 A map of horizontal velocity diagnosed from the P-vector method for the North Atlantic (Chu, 1995).

Longitude

Fig. 2.31 A map of horizontal velocity diagnosed from the P-vector method for the North Atlantic (Chu, 1995).

so the horizontal velocity can be determined at these two levels. This method is called the P-vector method (Chu, 1995), and the application of this method to the North Atlantic produced maps of the horizontal velocity at different levels (Fig. 2.31).

The P-vector method is quite similar to the fi-spiral method in that they are both based on many important assumptions, including geostrophy and conservation of potential vorticity. To determine the coefficient A, we have to calculate the determinant of Eqns. (2.232,2.233); thus, the second-order derivatives of the density field are included in the calculation.

A major substantial difficulty in applying the fi-spiral method or the P-vector method is that such calculations involve the second derivatives of the isopycnal slope. Owing to internal waves and meso-scale eddies in the ocean, hydrographic datasets contain a rather high level of noise. Therefore, using the fi-spiral method or other similar extensions to infer the absolute velocity from hydrographic data has not been very successful. With the rapid development in modern instrumentation, there are more accurate ways of determining the absolute velocity directly from observations.

Net short-wave radiation (W/m2)

Net short-wave radiation (W/m2)

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