A Closed-Form Formulation for Pollutant Dispersion in the Atmosphere

Transport and diffusion models of air pollution are based either on simple techniques, such as the Gaussian approach, or on more complex algorithms, such as the K-theory differential equation. The Gaussian equation is an easy and fast method, which, however, cannot properly simulate complex nonhomogeneous conditions. The K-theory can accept virtually any complex meteorological input, but generally requires numerical integration, which is computationally expensive and is often affected by large numerical advection errors. Conversely, Gaussian models are fast, simple, do not require complex meteorological input, and describe the diffusive transport in an Eulerian framework, making easy use of the Eulerian nature of measurements. For these reasons they are still widely used by environmental agencies all over the world for regulatory applications. However, because of its wellknown intrinsic limits, the reliability of a Gaussian model strongly depends on the way the dispersion parameters are determined on the basis of the turbulence structure of the planetary boundary layer (PBL) and the model’s ability to reproduce experimental diffusion data. The Gaussian model has to be completed by empirically determined standard deviations (the “sigmas”), while some commonly measurable turbulent exchange coefficient has to be introduced in the advection–diffusion equation.