Derivation of an eddy diffusivity coefficient depending on source distance for a shear dominated planetary boundary layer

In this study an integral and an algebraic formulation for the eddy diffusivities in a shear driven planetary boundary layer are derived for pollutant dispersion applications. The expressions depend on the turbulence properties and on the distance from the source. They are based on the turbulent kinetic energy spectra, Taylor’s statistical diffusion theory and measured turbulent characteristics during intense wind events. The good agreement between the algebraic and the integral formulation for the eddy diffusivities corroborate the hypothesis that using an algebraic formulation as a surrogate for the eddy diffusivities in the neutral planetary boundary layer is valid. As a consequence, the vertical eddy diffusivity provided by the algebraic formulation and its asymptotic limit for large time (diffusion time much larger than the Lagrangian integral time scale), were introduced into an analytical air pollution model and validated against data from the classic Prairie Grass project. A statistical analysis, employing specific indices shows that the results are in good agreement with the observations. Furthermore, this study suggests that the inclusion of the memory effect, which is important in regions near to a continuous point source, improves the description of the turbulent transport process of atmospheric contaminants. Therefore, the major finding of this paper is the necessity of including the downwind distance-dependent eddy diffusivity for low continuous point sources in air quality modeling studies.