THE PARAMETERIZATION OF THE VERTICAL DISPERSION OF A SCALAR IN THE ATMOSPHERIC BOUNDARY-LAYER

This paper discusses the validity of two alternate ways of parameteriz ing the turbulent transport term of a scalar. One form assumes that w' C'BAR = -K partial derivative CBAR/partial derivative z (a) where K is the eddy diffusivity, CBAR is the concentration of the scalar express ed as mass per unit volume, and z is the vertical coordinate. The alte rnative formulation is w'C'BAR = -KrhoBAR partial derivative qBAR/part ial derivative z (b) where rhoBAR is the density of air, and qBAR is t he mixing ratio given by qBAR = CBAR/rhoBAR. (c) This paper shows that neither of these two parameterizations is strictly correct. However, the second equation is closer to the correct formulation, which is w'C 'BAR = -KrhoBAR partial derivative qBAR/partial derivative z + w'rhoqB AR, (d) We show that when equation (d) is substituted into the mass co nservation equation, only the first term is dominant. The resulting eq uation for qBAR is partial derivative qBAR/partial derivative t = 1/rh oBAR partial derivative/partial derivative z (KrhoBAR partial derivati ve qBAR/partial derivative z). (e)