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Markov Chain Simulations of Vertical Dispersion in the Neutral Surface Layer for Surface and Elevated Releases

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Abstract

Vertical dispersion in the neutral surface layer is investigated using a Markov Chain simulation procedure. The conceptual basis of the procedure is discussed and computation procedures outlined. Wind and turbulence parameterizations appropriate to the neutral surface layer are considered with emphasis on the Lagrangian time scale. Computations for a surface release are compared with field data. Good agreement is found for the variation of surface concentration and cloud height to distances 500 m downwind of the source. The functional form of the vertical concentration profile is examined and an exponential with exponent ∼ 1.6 is found to give the best fit with simulations.

For elevated releases, it is demonstrated that an initial dip of the mass mean height from the simulation can be normalized for various release heights using a non-dimensionalized downwind coordinate incorporating advective wind speed and wind shear. The vertical distribution standard deviation (σz), as employed in Gaussian models, shows a fair degree of independence with source height but close examination reveals an optimum source height for maximum σz at a given downwind distance, x. This source height increases with downwind distance. Also the simulations indicate that vertical wind shear is more important than vertical variation of Lagrangian time scale close to the source, with a reverse effect farther downwind.

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References

  • Csanady, G. T.: 1973, Turbulent Diffusion in the Environment. D. Reidel Publishing Co., Dordrecht, 248 pp.

    Book  Google Scholar 

  • Gradshteyn, I. S. and Ryzhik, I. W.: 1965, Table of Integrals, Series and Products. Academic Press, New York, 1086 pp.

    Google Scholar 

  • Hall, C. D.: 1975, ‘The Simulation of Particle Motion in the Atmosphere by a Numerical Random-Walk Model’. Quart. J. R. Meteorol. Soc. 101, 235–244.

    Article  Google Scholar 

  • Joynt, R. C. and Blackman, D. F.: 1976, ‘A Numerical Model of Pollutant Transport’. Atmos. Env. 10, 433–442.

    Article  Google Scholar 

  • Kaimal, J. C., Wyngaard, J. C., Izumi, Y. and Coté, O. R.: 1972, ‘Spectral Characteristics of Surface-Layer Turbulence’. Quart. J. Roy. Meteorol. Soc. 98, 563–589.

    Article  Google Scholar 

  • Kampé de Fériet, M. J.: 1939, ‘Les Fonctions Aléatoires Stationnaires et la Théorie Statistique de la Turbulence Homogène’. Ann. Soc. Sci. Brux. 59, 145.

    Google Scholar 

  • Lange, R.: 1978, ‘ADPIC — A Three-Dimensional Particle-in-Cell Model for the Dispersal of Atmospheric Pollutants and its Comparison to Regional Tracer Studies’. J. Appl. Meteorol. 17, 320–329.

    Article  Google Scholar 

  • Lindberg, W. R. and Thompson, R.: 1974, ‘Simulation of Three-Dimensional Turbulence with Given Second-Order Statistical Structure’. Quart. J. R. Meteorol. Soc. 100, 608–623.

    Google Scholar 

  • Long, P. E. and Pepper, D. W.: 1976, ‘A Comparison of Six Numerical Schemes for Calculating the Advection of Atmospheric Pollution’. Proc. Third Symp. on Atmospheric Turbulence Diffusion and Air Quality, Amer. Meteorol. Soc., Boston, 181–187.

    Google Scholar 

  • Panofsky, H. A.: 1974, ‘The Atmospheric Boundary Layer Below 150 Meters’. Ann. Rev. Fluid Mech. 6, 147–177.

    Article  Google Scholar 

  • Pasquill, F.: 1961, ‘The Estimation of the Dispersion of Windborne Material’. Meteorol. Mag. 90, 33–49.

    Google Scholar 

  • Pasquill, F.: 1974, Atmospheric Diffusion. 2nd Edition, J. Wiley and Sons, New York, 429 pp.

    Google Scholar 

  • Philip, J. R.: 1967, ‘Relation between Eulerian and Lagrangian Statistics. Boundary Layers and Turbulence, Physics of Fluid Supplement, 69–71.

  • Poreh, M. and Cermak, J. E.: 1964, ’Study of Diffusion from a Line Source in a Turbulent Boundary Layer’. Intl. J. Heat Mass Transfer 7, 1083–1095.

    Article  Google Scholar 

  • Reid, J. D.: 1976, Dispersion in a Mountain Environment. ATS Paper 253, Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado, 150 pp.

    Google Scholar 

  • Smith, F. B.: 1957, ‘The Diffusion of Smoke from a Continuous Elevated Point-Source into a Turbulent Atmosphere’. J. Fluid Mech. 2.

  • Taylor, G. I.: 1921, ‘Diffusion by Continuous Movements’. Proc. Lond. Math. Soc., Ser. 2 XX, 196–212.

    Google Scholar 

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  1. Atmospheric Environment Service, 4905 Dufferin Street, Downsview, Ontario, MJH 5T4, Canada

    John D. Reid

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  1. John D. Reid
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Reid, J.D. Markov Chain Simulations of Vertical Dispersion in the Neutral Surface Layer for Surface and Elevated Releases. Boundary-Layer Meteorol 16, 3–22 (1979). https://doi.org/10.1007/BF03335351

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