From equations (5.328), (5.39) and (5.330), we obtain the scale thickness for the main pycnocline:

There are two cases. First, for the case when diffusion dominates, the vertical scale of the pycnocline depth and the pycnocline thickness is the same; thus, Eqn. (5.331) gives rise to the same scale as Eqn. (5.318). Second, for the case with strong wind forcing and weak diapycnal mixing, the pycnocline depth obeys Eqn. (5.317), so the final expression of pycnocline thickness is f k

Note that the depth and thickness of the pycnocline depend on the relative strength of the Ekman pumping and the diffusion (Table 5.8). In the case with strong wind forcing, the thickness of the main pycnocline is linearly proportional to k 1/2, but inversely proportional to the 1 power of the Ekman pumping rate. This means that strong wind forcing produces a deep and thin main pycnocline.

Circulation forced by surface freshwater flux

A relaxation condition is not suitable for the haline circulation, and a more realistic way of simulating the haline circulation is to specify the freshwater flux at the surface. As discussed in Section 5.3, the salinity balance in the meridional cell is

where D is the depth of the halocline, S is basin mean salinity, AS is the meridional salinity difference, and E is the rate of evaporation minus precipitation. This leads to a simple relation between the scale of salinity difference and the evaporation rate:

Accordingly, the meridional density difference is

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