Skip to main content
SpringerLink
Log in

A stochastic model of particle dispersion in the atmosphere

  • Published:
Boundary-Layer Meteorology Aims and scope Submit manuscript

Abstract

Stochastic models of turbulent atmospheric dispersion treat either the particle displacement or particle velocity as a continuous time Markov process. An analysis of these processes using stochastic differential equation theory shows that previous particle displacement models have not correctly simulated cases in which the diffusivity is a function of vertical position. A properly formulated Markov displacement model which includes a time-dependent settling velocity, deposition and a method to simulate boundary conditions in which the flux is proportional to the concentration is presented. An estimator to calculate the mean concentration from the particle positions is also introduced. In addition, we demonstrate that for constant coefficients both the velocity and displacement models describe the same random process, but on two different time scales. The stochastic model was verified by comparison with analytical solutions of the atmospheric dispersion problem. The Monte Carlo results are in close agreement with these solutions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anbar, D.: 1978, ‘A Diffusion Model for Use With Directional Samplers’, Atmos. Envir. 12, 2131–2138.

    Google Scholar 

  • Arnold, L.: 1974, Stochastic Differential Equations: Theory and Applications, John Wiley and Sons, New York.

    Google Scholar 

  • Boughton, B. A.: 1983, ‘Turbulent Atmospheric Transport and Deposition of Particles with Settling and Evaporation’, Ph.D. Thesis, University of Illinois, Urbana, Illinois.

    Google Scholar 

  • Chandrasekar, S.: 1943, ‘Stochastic Problems in Physics and Astronomy’, Rev. Modern Phys. 15, 1–98.

    Google Scholar 

  • Cogan, J. L.: 1985, ‘Monte Carlo Simulation of Buoyant Dispersion’, Atmos. Envir. 19, 867–878.

    Google Scholar 

  • Corrsin, S.: 1974, ‘Limitations of Gradient Transport Models in Random Walks and in Turbulence’, Adv. Geophys. 18A, 25–60.

    Google Scholar 

  • Ermak, D. L.: 1977, ‘An Analytical Model for Air Pollutant Transport and Deposition From a Point Source’, Atmos. Envir. 11, 231–237.

    Google Scholar 

  • Fürth, R. (ed.): 1956, Investigations on the Theory of Brownian Movement, Dover Publications, Inc., New York.

    Google Scholar 

  • Haugen, D. A. (ed.): 1973, Workshop on Micrometeorology, American Meteorological Society, Boston, MA.

    Google Scholar 

  • Legg, R. P. and Raupach, M. R.: 1982, ‘Markov-Chain Simulation of Particle Dispersion in Inhomogeneous Flows: the Mean Drift Velocity Induced by a Gradient in Eulerian Velocity Variance’, Boundary-Layer Meteorol. 24, 3–13.

    Google Scholar 

  • McKean, H. P.: 1969, Stochastic Integrals, Academic Press, New York.

    Google Scholar 

  • Monin, A. S.: 1959, ‘On the Boundary Condition on the Earth Surface for Diffusing Pollution’, Adv. Geophys. 6, 435–436.

    Google Scholar 

  • Pasquill, F. and Smith, F. B.: 1983, Atmospheric Diffusion, third edition, Ellis Horwood Limited, England.

    Google Scholar 

  • Rounds, W.: 1955, ‘Solutions of the Two-Dimensional Diffusion Equation’, Trans. Amer. Geophys. Union 36, 395–405.

    Google Scholar 

  • Runchal, A. K., Bealer, A. W., and Segal, G. S.: 1978, A Completely Lagrangian Random-Walk Model for Atmospheric Dispersion, Proc. of the Thirteenth Symp. on Atmos. Poll., Paris, April 26–28.

  • Soo, S. L. and Chen, F. F.: 1982, ‘The Boundary Condition of the Diffusion Equation’, Powder Tech. 31, 117–119.

    Google Scholar 

  • Thomson, D. J.: 1984, ‘Random Walk Modeling of Diffusion in Inhomogeneous Turbulence’, Quart. J. Roy. Meteorol. Soc. 110, 1107–1120.

    Google Scholar 

  • Wilson, J. D., Legg, B. J., and Thomson, D. J.: 1983, ‘Calculation of Particle Trajectories in the Presence of a Gradient in Turbulent-Velocity Variance’, Boundary-Layer Meteorol. 27, 163–169.

    Google Scholar 

  • Wippermann, F. K.: 1966, ‘On Turbulent Diffusion in an Arbitrarily Stratified Atmosphere’, J. Appl. Meteorol. 5, 640–645.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sandia National Laboratories, P.O. Box 5800, 87185, Albuquerque, New Mexico, USA

    B. A. Boughton & J. M. Delaurentis

  2. Department of Mechanical Engineering, University of Illinois, 61801, Urbana, Illinois, USA

    W. E. Dunn

Authors
  1. B. A. Boughton
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. M. Delaurentis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W. E. Dunn
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work partially performed at Sandia National Laboratories supported by the U.S. Department of Energy under contract number DE-AC04-76DP00789.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boughton, B.A., Delaurentis, J.M. & Dunn, W.E. A stochastic model of particle dispersion in the atmosphere. Boundary-Layer Meteorol 40, 147–163 (1987). https://doi.org/10.1007/BF00140073

Download citation

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00140073

Keywords

Search

Navigation