A Comparison of the Monte Carlo and the Flux Gradient Method for Atmospheric Diffusion

In order to model the dispersal of atmospheric pollutants in the planetary boundary layer, various methods of parameterizing turbulent diffusion have been employed. These approaches differ greatly in sophistication and complexity (Monin and Yaglom, 1971). Historically, the Gaussian plume models were the first dispersion models. The Gaussian formula is based on statistical theory and empirical observation of the horizontal and vertical standard deviation of the wind speed σ y and σ y . In K-theory, the Eulerian diffusion-advection equation closure problem is circumvented by assuming a gradient transport paramaterization and the postulation of the turbulent diffusivity parameter K, which must be provided empirically. The stochastic Markov chain (Monte Carlo) method employs generally the Langevin equation to model dispersion with the use of very many particles. The approach needs the empirical prescription of the wind velocity variances σ u and the Lagrangian integral time scales T L. All three methods have two things in common: they rely on some mathematical scheme and they need empirically derived diffusion parameters. (Higher order closure models are not part of this discussion.)