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Some Simple Statistical Models For Relative And Absolute Dispersion

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Abstract

Observations of the dispersion of a contaminant plume in the atmospheric boundary layer, obtained using a Lidar, are analysed in the coordinate frame relative to the instantaneous centre of mass of the plume, as well as the absolute (or fixed) coordinate frame. The study extends the work presented in a previous article, which analysed the structure of the probability density function (pdf) of concentration within the relative coordinate frame. Firstly, the plume displacement component, or plume meander, is analysed and a simple parametric form for the pdf of the plume centreline position is suggested. This is then used to analyse the accuracy and applicability of absolute framework statistical quantities obtained by a convolution of the relative frame statistical quantity with the plume centreline pdf.

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References

  • Bachelor, G. K.: 1950, 'The Application of the Similarity Theory of Turbulence to Atmospheric Diffusion', Quart. J. Roy. Meteorol. Soc. 76, 133–146.

    Google Scholar 

  • Batchelor, G. K.: 1952, 'The Effect of Homogeneous Turbulence on Material Lines and Surfaces', Proc. Roy. Soc. A213, 349–366.

    Google Scholar 

  • Batchelor, G. K.: 1953, The Theory of Homogeneous Turbulence, Cambridge University Press, Cambridge, 197 pp.

    Google Scholar 

  • Bennett, M.: 1995, 'A Lidar Study of the Limits to Buoyant Plume Rise in a Well-Mixed Boundary Layer', Atmos. Environ. 29, 2423–2288.

    Google Scholar 

  • Bennett, M., Sutton, S., and Gardiner, D. R. C.: 1992, 'An Analysis of Lidar Measurements of Buoyant Plume Rise and Dispersion at Five Power Stations', Atmos. Environ. 26, 3249–3263.

    Google Scholar 

  • Chatwin, P. C.: 1990, 'Statistical Methods for Assessing Hazards Due to Dispersing Gases', Environmetrics 1, 143–162.

    Google Scholar 

  • Chatwin, P. C. and Sullivan, P. J.: 1979a, 'The Relative Diffusion of a Cloud of Passive Contaminant in Incompressible Turbulent Flow', J. Fluid Mech. 91, 337–355.

    Google Scholar 

  • Chatwin, P. C. and Sullivan, P. J.: 1979b, 'Measurements of Concentration Fluctuations in Relative Turbulent Diffusion', J. Fluid Mech. 94, 83–101.

    Google Scholar 

  • Chatwin, P. C., Lewis, D. M., and Sullivan, P. J.: 1995, 'Turbulent Dispersion and the Beta Distribution', Environmetrics 6, 395–402.

    Google Scholar 

  • Gifford, F.: 1959, 'Statistical Properties of a Fluctuating Plume Dispersion Model', Adv. Geophys. 6, 117–137.

    Google Scholar 

  • Lewis, D. M. and Chatwin, P. C.: 1995, 'The Treatment of Atmospheric Dispersion Data in the Presence of Noise and Baseline Drift', Boundary-Layer Meteorol. 72, 53–85.

    Google Scholar 

  • Lewis, D. M. and Chatwin, P. C.: 1997, 'A Three-Parameter pdf for the Concentration of an Atmospheric Pollutant', J. Appl. Meteor. 36, 1064–1075.

    Google Scholar 

  • Measures, R. M.: 1984, Laser Remote Sensing-Fundamentals and Applications, John Wiley and Sons Ltd., 510 pp.

  • Mikkelsen, T., Jørgensen, H. E., Thykier-Nielsen, S., Lund, S. W., and Santabarbara, J. M.: 1995, Final Data and Analysis Report on: High-Resolution in Plume Concentration Fluctuations Measurements Using Lidar Remote Sensing Technique, Technical Report No. Risø-R-852(EN), Risø National Laboratory, Roskilde, Denmark.

    Google Scholar 

  • Munro, R. J., Chatwin, P. C., and Mole, N.: 2003, 'A Concentration pdf for the Relative Dispersion of a Contaminant Plume in the Atmosphere', Boundary-Layer Meteorol. 106, 411–436.

    Google Scholar 

  • Mylne, K. R. and Mason, P. J.: 1991, 'Concentration Fluctuation Measurements in a Dispersing Plume at a Range of Up to 1000 m', Quart. J. Roy. Meteorol. Soc. 117, 177–206.

    Google Scholar 

  • Narayan, R. and Nityananda, R.: 1986, 'Maximum Entropy Image Restoration in Astronomy', Annu. Rev. Astron. Astrophys. 24, 127–170.

    Google Scholar 

  • Nielsen, M., Ott, S., Jørgensen, H. E., Bengtsson, R., Nyren, K., Winter, S., Ride, D., and Jones, C.: 1997, 'Field Experiments with Dispersion of Pressure Liquefied Ammonia', J. Hazard. Mater. 56, 59–105.

    Google Scholar 

  • Reynolds, A. M.: 2000, 'Representation of Internal Plume Structure in Gifford's Meandering Plume Model', Atmos. Environ. 34, 2539–2545.

    Google Scholar 

  • Roussas, G. G.: 1997, A Course in Mathematical Statistics, 2nd edn., Academic Press, 572 pp.

  • Sullivan, P. J.: 1990, 'Physical Modelling of Contaminant Diffusion in Environmental Flows', Environmetrics 1, 163–177.

    Google Scholar 

  • Yee, E. and Wilson, D. J.: 2000, 'A Comparison of the Detailed Structure in Dispersing Tracer Plumes Measured in Grid-Generated Turbulence with a Meandering Plume Model Incorporating Internal Fluctuations', Boundary-Layer Meteorol. 94, 253–296.

    Google Scholar 

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Munro, R.J., Chatwin, P.C. & Mole, N. Some Simple Statistical Models For Relative And Absolute Dispersion. Boundary-Layer Meteorology 107, 253–271 (2003). https://doi.org/10.1023/A:1022102526675

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  • DOI: https://doi.org/10.1023/A:1022102526675

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