which allows to rewrite Eq.7.11 as: where the nonadvective PV flux is given by:
Its first component is linked to the buoyancy forcing^{7.1}:
and the second one to the nonconservative body forces per unit mass:
7.7.5.2 Determining the PV flux at the ocean's surfaceIn the context of mode water study, we're particularly interested in how the PV may be reduced by surface PV fluxes because a mode water is characterised by a low PV level. Considering the volume limited by two , PV flux is limited to surface processes and then vertical component of . It is supposed that and will only be nonzero in the mixed layer (of depth and variable density ) exposed to mechanical forcing by the wind and buoyancy fluxes through the ocean's surface.
Given the assumption of a mechanical forcing confined to a thin surface Ekman layer (of
depth
, eventually computed by the package) and of hydrostatic and geostrophic
balances, we can write:
where: is the full velocity field composed by the geostrophic current and the Ekman drift: (where is the wind stress) and last by other ageostrophic components of which are neglected.
Partitioning the buoyancy forcing as:
and using Eq.7.21 and Eq.7.22, the Eq.7.20 becomes:
revealing the "winddriven buoyancy forcing":
Note that since:
must be uniform throughout the depth of the mixed layer and then being related to the surface buoyancy flux by integrating Eq.7.23 through the mixed layer: where is the vertically integrated surface buoyancy (in)flux:
with the thermal expansion coefficient (computed by the package otherwise), the specific heat of seawater, the net heat surface flux (positive downward, warming the ocean), the saline contraction coefficient, and the net freshwater surface flux with the surface salinity and the fresh water flux.
Introducing the body force in the Ekman layer:
the vertical component of Eq.7.14 is:
and given the assumption that , the second term vanishes and we obtain:
Note that the windstress forcing does not appear explicitly here but is implicit in through Eq.7.27: the buoyancy forcing is determined by the difference between the integrated surface buoyancy flux and the integrated "winddriven buoyancy forcing":
Finally, from Eq.7.14, the vertical surface flux of PV may be written as:
Next: 8. Ocean State Estimation Up: 7.7 Potential vorticity Matlab Previous: 7.7.4 Technical details Contents mitgcmsupport@mitgcm.org 



