8.4.1 Fresh water flux into the free surface model

The calculation of the fresh water flux requires a boundary layer model to be coupled with MOM. Here, a very simple version is described which permits a first order guess for the fresh water flux. Fresh water flux may have two different components, rain Q_w^R and vapour from condensation or evaporation at the sea surface, Q_w^V,

Q_w = Q_w^R + Q_w^V, (8.15)

The fresh water velocity, q_w, which is needed in the boundary condition is

$$\frac{Q_{w}}{\rho}$$ q_w = (8.16)

The amount of rain can be provided by an atmosphere model or field data might be used.

If the boundary layer is in a turbulent steady state the water vapour flux through the boundary layer can be parameterized as

$$\rho_a C_w u^{wind}\left(h_a - h_s\right).$$ Q_w^V = (8.17)

Here the thermodynamic forcing is the difference of the specific humidity h_ain some reference height (usually 10 m) and at the sea surface, h_s. The specific humidity is defined as the mass ratio

$$\frac{m_w}{m} = \frac{\rho_w}{\rho_a}$$ h = (8.18)

where m is the total mass of the air in a volume element and m_w the mass of water vapour in the same volume. Alternatively the difference of the water vapour pressure or the partial density of water vapour can be used. The kinetic coefficient C_w u^wind describes the vertical turbulent diffusion in the boundary layer and is a function of the wind speed u^windin the reference height and of the stability of the atmospheric boundary layer. There is a considerable literature on empirical parameterizations of C_w from experimental data sets. Details can be found for example in Large and Pond (1982), Smith and Dobson (1984), Rosati and Miyakoda (1988) and in the literature cited there.

As a result for the calculation of the fresh water flux the specific humidity h_a and the wind velocity u^wind must be known in some reference height. This information may come from an atmosphere model. For the calculation of the drag coefficient C_w additional information on the stability of the boundary layer, i.e, on the atmosphere temperature is necessary. The specific humidity at the sea surface, h_s, can be calculated from the assumption of saturated water vapour immediately over the sea surface.