An Integral Formulation for the Dispersion Parameters in a Shear–Buoyancy-Driven Planetary Boundary Layer for Use in a Gaussian Model for Tall Stacks

Abstract

An integral parameterization of the dispersion coefficients σy and σz in a shear?buoyancy-driven atmospheric boundary layer is developed by using a model for the frequency spectrum of eddy energy. The formulation relies on Taylor classical diffusion theory and further developments by Pasquill. The statistical independence of Fourier components for distant frequencies allows the specification of the turbulent kinetic energy spectrum as the sum of a buoyancy- and a shear-produced part. For both components the dispersion parameters are described in terms of the frequency of spectral peak and dissipation function. In this way they are directly related to energy-containing eddies that are most responsible for turbulent transport of any scalars in an atmospheric boundary layer generated by mechanical and thermal forcing mechanisms. As a consequence, the resulting dispersion parameters are more general than those found in the literature, because they do not utilize measurements of turbulent dispersion as most parameterizations do and provide a formulation valid for the whole unstable regime. The formulations are compared with field diffusion data, along with other schemes. The new parameters are well suited for application in air pollution modeling under unstable conditions.