Vertical diffusivities of active and passive tracers

The climate models that include a carbon-cycle need the vertical diffusivity of a passive tracer. Since an expression for the latter is not available, it has been common practice to identify it with that of salt. The identification is questionable since T, S are active, not passive tracers. We present the first derivation of the diffusivity of a passive tracer in terms of Ri (Richardson number) and Rρ (density ratio, ratio of salinity over temperature z-gradients). The following results have emerged: ssive tracer diffusivity is an algebraic function of Ri, Rρ. bly stable regimes (DS, ∂T/∂z > 0, ∂S/∂z < 0), the passive scalar diffusivity is nearly the same as that of salt/heat for any values of Rρ < 0 and Ri > 0. regimes (diffusive convection, ∂T/∂z < 0, ∂S/∂z < 0, Rρ > 1), the passive scalar diffusivity is larger than that of salt. At Ri = O(1), it can be more than twice as large. regimes (salt fingers, ∂T/∂z > 0, ∂S/∂z > 0, Rρ < 1), the passive scalar diffusivity is smaller than that of salt. At Ri = O(1), it can be less than half of it. ssive tracer diffusivity predicted at the location of NATRE (North Atlantic Tracer Release Experiment) is discussed. s the most relevant conclusion is that the common identification of the tracer diffusivity with that of salt is valid only in DS regimes. In the Southern Ocean, where there is the largest CO2 absorption, the dominant regime is diffusive convection discussed in (c) above.