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Fig. 5.96 a-d Poleward heat flux in the world's oceans, diagnosed from a model based on observed SST and SSS (thin lines) and a model based on relaxation to observed SST and with constant salinity (heavy lines) (Huang, 2005b).

Upper boundary conditions for salinity balance The salinity boundary condition on the sea surface is directly linked to the air-sea freshwater flux, so that its formulation depends on how the free surface is handled. We begin with the formulation for models based on the rigid-lid application because the boundary conditions can be explained quite clearly in terms of the relevant physics. Then we will discuss the corresponding formulation for models with a free surface.

The rigid-lid approximation

Early in model development, the rigid-lid approximation was widely used. As explained in Section 4.1.1, the basic idea was to replace the free surface by the flat surface z = 0, so that the complexity of dealing with the moving free boundary z = Z is reduced to a fixed and flat boundary z = 0. The suitable boundary condition for the vertical velocity under the rigid lid is as follows.

The kinematic boundary condition on the free surface is

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