Note on the vertical velocity and diffusive salt flux induced by evaporation and precipitation

Abstract

Some (not all) of the oceanographic literature slightly miscalculates the vertical velocity (w) and diffusive salt flux induced by evaporation (E) and precipitation (P) at the sea surface. Short, simple, physical derivations are presented to show that, for a sea surface h = h(x, y, t) varying in space and time, 1) w = VH · h + ∂h/∂t + ρF(E − P)/ρ, where VH is the horizontal component of the aggregate parcel velocity, and ρF and ρ are the densities of freshwater and surface seawater, respectively; and 2) the vertical diffusive salt flux at the sea surface (whether molecular or turbulent) is −ρFS(E − P), where S is the surface salinity.