Numerical and Observational Evidence
163
Fig. 3.11.2c
Observational Evidence
In the midocean, on the large scale, the relative vorticity makes a negligible
contribution to the potential vorticity. In general, for an isopycnal layer of
thickness Az, the potential vorticity on the planetary scale is simply:
(3.11.1)
which is a finite difference approximation (using density as a vertical
coordinate) for the continuous representation of potential vorticity on the
planetary scale (Pedlosky 1987):
q=f{)p
{)z
(3.11.2)
for which (3.10.6) (without the relative vorticity) is the geostrophic
approximation.
It follows that in the midocean it is possible to calculate q directly from
hydrographic data, that is, entirely from the density field without any reference
to the velocity field, which is generally not known. It is therefore possible to
prepare maps of the large-scale planetary potential vorticity and to determine
163
Fig. 3.11.2c
Observational Evidence
In the midocean, on the large scale, the relative vorticity makes a negligible
contribution to the potential vorticity. In general, for an isopycnal layer of
thickness Az, the potential vorticity on the planetary scale is simply:
(3.11.1)
which is a finite difference approximation (using density as a vertical
coordinate) for the continuous representation of potential vorticity on the
planetary scale (Pedlosky 1987):
q=f{)p
{)z
(3.11.2)
for which (3.10.6) (without the relative vorticity) is the geostrophic
approximation.
It follows that in the midocean it is possible to calculate q directly from
hydrographic data, that is, entirely from the density field without any reference
to the velocity field, which is generally not known. It is therefore possible to
prepare maps of the large-scale planetary potential vorticity and to determine