Numerico-empirical analyses of atmospheric diffusion theories

Numerico-empirical expressions for the particle displacement probability density function from which the mean concentration of material in turbulent fluid may be obtained are derived from the numerical planetary boundary layer model of Deardorff. These expressions are then used to compute profiles of the mean, cross-wind-integrated concentration of an inert pollutant issuing from a continuous point source below a stable layer. Profiles are derived for each of two conditions of atmospheric stability: zi/L=0 and –4.5, where zi is the inversion base height and L the Monin-Obukhov length. The resulting concentration profiles [referred to as the numerico-empirical (NE) profiles] are then used in two separate experiments designed to assess the adequacy of conventional atmospheric diffusion formulations. First, the validity of the atmospheric diffusion equation is assessed by determining for each of the two stabilities cited above the profile of vertical eddy diffusivity that produces the closest fit of the mean concentration predicted by the atmospheric diffusion equation with the NE profiles. Second, comparisons are made between the NE profiles and the corresponding concentration distributions predicted by the Gaussian plume formula with Pasquill-Gifford dispersion parameters, and the Gaussian puff equation with McElroy-Pooler travel-time-dependent dispersion parameters