Air Pollution Modeling and Its Application XII pp 429-440 | Cite as

# A New Formulation of the Probability Density Function in Random Walk Models for Atmospheric Dispersion

## Abstract

Simulation of at mospheric diffusion in vertically inhomogeneous skewed turbulence, which is typical for the daytime boundary layer, is investigated. Particle trajectories are simulated by using the Langevm equation. The main objective is to introduce a formulation of the probability density function (PDF) of the vertical velocity fluctuation based on a fourth order expansion after Hermite polynomials (Gram-Charlier expansion). The statistics of the turbulence are introduced by forcing the moments of the Gram-Charlier expansion to equal the parametrized moments of atmospheric turbulence.

## Keywords

Probability Density Function Probability Density Function Hermite Polynomial Atmospheric Dispersion Stochastic Lagrangian Model## Preview

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## References

- Deardorff, J.W. and Willis, G.E., 1985,
*Further results from a laboratory model of the connective planetary boundary layer.*Boundary-Layer Meteorology,**32**pp. 205–236CrossRefGoogle Scholar - Rotach, M.W., Gryning, S.-E. and Tassone, C., 1996,
*A two-dimensional Lagrangian stochastic dispersion model for daytime conditions.*Q.J.R.Met.Soc.,**122**, pp. 367–389CrossRefGoogle Scholar - Tassone, C., Gryning, S.-E., Rotach, M.W., 1994,
*A random walk model for atmospheric dispersion in the daytime boundary layer.*In Air Pollution Modelling and its Application X, Edited by Gryning, S.-E. and Millan, M.M., Plenum. New York and London, pp.204–250Google Scholar - Tassone, C., 1995,
*A Lagrangian model for dispersion in the daytime boundary layer*, Ph.D.-thesis, Risø National LaboratoryGoogle Scholar - Willis, G.E. and Deardorff, J.W., 1976,
*A laboratory model of diffusion into the connective planetary boundary layer*, Q.J.R.Met.Soc.,**102**, pp. 427–445CrossRefGoogle Scholar - Willis, G.E. and Deardorff, J.W., 1978,
*A laboratory study of dispersion from an eeavated source within a modeled connective planetary boundary layer*, Atmospheric Environment,**12**, pp. 1305–1311CrossRefGoogle Scholar - Willis, G.E. and Deardorff, J.W., 1981,
*A laboratory study of dispersion from a source in the middle of the convectively mixed layer*, Atmospheric Environment,**15**, pp. 109–117CrossRefGoogle Scholar