A note on boundary conditions for salt and freshwater balances

The derivation of surface boundary conditions for salt and freshwater budgets, in the presence of an imbalance of evaporation and precipitation, is revisited in order to: (i) clarify the physical concepts involved and (ii) derive consistent approximations. Proper surface boundary conditions can be obtained by assuming that the air-sea interface is a material surface for the salt continuum. This requires all the mass exchange at the air-sea interface to be fulfilled by the freshwater continuum. The need of diffusive fluxes is crucial for this assumption to hold. If the air-sea interface varies in time (either by seawater advection, an imbalance of evaporation minus precipitation, or a combination of both) there must be a corresponding salt flux, in order for the transport across such moving surface to be nil. Here it is essential to distinguish the flux vector of a property from its transport across a (possibly moving) surface. Only in a motionless ocean surface approximation, which includes the classical rigid lid approximation, the advective and diffusive salt fluxes perpendicular to the surface cancel out exactly.