8.3 Surface tracer flux

From the budget equation (8.7), it is possible to identify the total concentration flux (dimensions $tracer/volume \times velocity$) across the air-sea interface as

 

$$Q_{wT} = - F^{z}(T) + {\bf F}_{h}(T)\cdot \nabla_{h} \eta + T \, q_{w} \qquad z=\eta.$$ (8.8)

The area integral [Q_wT] represents the area integrated tracer concentration flux entering or leaving the ocean across the free surface interface. Equivalently, it is the total amount of tracer substance crossing the ocean surface per unit time (dimensions tracer/time). The subscript w signifies that the flux is measured at the ocean or ``water'' side of the interface. The sign convention is that Q_wT is counted as positive if it is directed into the ocean. It is useful to note that the total surface tracer flux (8.8) has a direct analogue in the equation (7.50) for the surface momentum stress, which is rewritten here for convenience

$$\frac{{\bf\tau}_{surf}}{\rho_{o}} \kappa_m {\bf u}_z - A \,(\nabla_{h}\eta) \cdot (\nabla_{h} {\bf u}) + q_{w}\, {\bf u}_{h} \qquad z=\eta.$$ = (8.9)

For momentum, the friction terms $\kappa_m {\bf u}_z - A \,(\nabla_{h}\eta) \cdot (\nabla_{h} {\bf u})$ are formally associated with parameterized turbulent momentum fluxes across the air-sea interface. Likewise, diffusive terms $- F^{z} + {\bf F}_{h} \cdot \nabla_{h} \eta$ are formally associated with parameterized turbulent tracer fluxes across the air-sea interface. These fluxes can be derived from a boundary layer model and are discussed in Section 8.4.