Skip to main content
Log in

An Advanced Puff Model Based On A Mixed Eulerian/Lagrangian Approach For Turbulent Dispersion In The Convective Boundary Layer

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

Abstract

An advanced model aimed at describing the problem of dispersion in theconvective boundary layer is proposed. The pollutant particles are groupedin clusters and modelled as Gaussian puffs. The expansion of each puff ismodelled according to the concept of relative dispersion and expressed interms of the spectral properties of the energy containing eddies of the turbulent field. The centre of mass of each puff is moved along a stochastic trajectory, obtained using a Lagrangian stochastic model and filtering the velocity with a recursive Kalman filter. At any instant, a filtering procedure, depending both on travel time and on puff size, acts to select spectral components involved in the expansion and in the meandering of the puff. Such an approach requires only a moderate number of puff releases, so that the proposed model is faster to run than a standard Lagrangian model. On the other hand, unlike the traditional puff model, it allows us to simulate both expansion and meandering of the puff. Therefore, it is well suited to simulate dispersion when the turbulent structures are larger thanthe plume dimensions, as for example in convective conditions. Being based onspectral formulations in both Eulerian and Lagrangian parts, the model is consistent in all the turbulent parameterizations utilised. Comparisons with a standard Lagrangian particle model as well as with a classical convective experimental dataset show good performance of the proposed model.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Baerensten, J. H. and Berkowicz, R.: 1984, ‘Monte Carlo Simulation of Plume Dispersion in the Convective Boundary Layer’, Atmos. Environ. 18, 701–712.

    Google Scholar 

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

    Google Scholar 

  • Batchelor, G. K.: 1952, ‘Diffusion in a Field of Homogeneous Turbulence, II. The Relative Motion of Particles’, Proc. Camb. Phil. Soc. 48, 345–362.

    Google Scholar 

  • Borgas, M. S., Flesch, T. K., and Sawford, B. L.: 1997, ‘Turbulent Dispersion with Broken Reflectional Symmetry’, J. Fluid. Mech. 332, 141–156.

    Google Scholar 

  • Brier, G. W.: 1950, ‘The Statistical Theory of Turbulence and the Problem of Diffusion in the Atmosphere’, J. Meteorol. 7, 283–290.

    Google Scholar 

  • Briggs, G. A: 1993, ‘Final Results of the Condors Convective Diffusion Experiment’, Boundary-Layer Meteorol. 62, 315–328.

    Google Scholar 

  • Cassiani, M. and Giostra, U.: 1999, ‘Eulerian-Lagrangian Modelling of Dispersion in a Convective Boundary Layer’, Il Nuovo Cimento 22, 705–714.

    Google Scholar 

  • Caughey, S. J. and Palmer, S. G.: 1979, ‘Some Aspects of Turbulence Structure through the Depth of the Convective Boundary Layer’, Quart. J. Roy. Meteorol. Soc. 105, 811–827.

    Google Scholar 

  • Champagne, F. H., Friehe, C. A., Larve, J. C., and Wyngaard, J. C.: 1977, ‘Flux Measurements, Flux Estimation Techniques and Fine Scale Turbulence Measurements in the Unstable Surface Layer over Land’, J. Appl. Meteorol. 34, 515–520.

    Google Scholar 

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

    Google Scholar 

  • Degrazia, G. A. and Anfossi, D.: 1998, ‘Estimation of the Kolmogorov Constant C0 from Classical Statistical Diffusion Theory’, Atmos. Environ. 32, 3611–3614.

    Google Scholar 

  • Degrazia, G. A., Mangia, C., and Rizza, U.: 1998, ‘A Comparison between Different Methods to Estimate the Lateral Dispersion Parameter under Convective Conditions’, J. Appl. Meteorol. 37, 227–231.

    Google Scholar 

  • Degrazia, G. A., Rizza, U., Mangia, C. and Tirabassi, T.: 1997, ‘Validation of a New Turbulent Parametrization for Dispersion Models in Convective Conditions’, Boundary-Layer Meteorol. 85, 243–254.

    Google Scholar 

  • De Haan, P. and Rotach, M. W.: 1997, ‘The Treatment of Relative Dispersion within a Combined Puff-Particle Model (PPM)’, in Proceeding of the 22nd NATO/CCMS International Technical Meeting on Air Pollution Modeling and Its Application, Plenum Press, New York U.S.A.

    Google Scholar 

  • De Haan, P. and Rotach, M. W.: 1998, ‘A Novel Approach to Atmospheric Dispersion Modelling: the Puff-Particle Model (PPM)’, Quart. J. Roy. Meteorol. Soc. 125, 2771–2792.

    Google Scholar 

  • Du, S.: 1997, ‘Universality of the Lagrangian Velocity Structure Function Constant (C0) across Different Kinds of Turbulence’, Boundary-Layer Meteorol. 83, 207–219.

    Google Scholar 

  • Du, S.: 1998, ‘Reply to ‘Comments on the Universality of the Lagrangian Velocity Structure Function Constant (C 0) across Different Kinds of Turbulence’, Boundary-Layer Meteorol. 89, 171–172.

    Google Scholar 

  • Gryning, S. E.: 1981, ‘Elevated Source SF6-Tracer Dispersion Experiments in the Copenhagen Area’, Risø National Laboratory, Røskilde, Denmark, Report R-446, 187 pp.

    Google Scholar 

  • Hanna, S. R.: 1989, ‘Confidence Limits for Air Quality Models, as Estimated by Bootstrap and Jacknife Resampling Methods’, Atmos. Environ. 23, 1385–1395.

    Google Scholar 

  • Hay, J. S. and Pasquill, F.: 1959, ‘Diffusion from a Continuous Source in Relation to the Spectrum and Scale of Turbulence’, in F. N. Frenkiel and P. A. Sheppard (eds.), Atmospheric Diffusion and Air Pollution, Adv. Geophys. 6, 345–365.

  • Højstrup, J.: 1982, ‘Velocity Spectra in the Unstable Boundary Layer’, J. Atmos. Sci. 39, 2239–2248.

    Google Scholar 

  • Hurley, P. J.: 1994, ‘Partpuff. A Lagrangian Particle-Puff Approach for Plume Dispersion Modelling Applications’, J. Appl. Meteorol. 33, 285–294.

    Google Scholar 

  • Jazwinski, A. H.: 1970, Stochastic Processes and Filtering Theory, Academic Press, New York, 376 pp.

    Google Scholar 

  • Kaimal, J. C., Eberhard, W. L., Moninger, W. R., Gaynor, J. E., Troxel, S. W., Uttal, T., Briggs, G. A., and Start, G. E.: 1986, ‘PROJECT CONDORS Convective Diffusion Observed by Remote Sensors’, NOAA/ERL Wave Propagation Laboratory, U.S. Department of Commerce.

  • Luhar, A. K. and Britter, R. E.: 1989, ‘A Random Walk Model for Dispersion in Inhomogeneous Turbulence in a Convective Boundary Layer’, Atmos. Environ. 23, 1911–1924.

    Google Scholar 

  • Mikkelsen, T., Larsen, S. E., and Pecsely, H. L.: 1987, ‘Diffusion of Gaussian Puffs’, Quart. J. Roy. Meteorol. Soc. 113, 81–105.

    Google Scholar 

  • Monin, A. S. and Yaglom, A. M.: 1975, Statistical Fluid Mechanics; Mechanics of Turbulence, Vol. II, MIT Press, Cambridge, MA, 874 pp.

    Google Scholar 

  • Olesen, H. R., Larsen, S. E., and Højstrup, J.: 1984, ‘Modelling Velocity Spectra in the Lower Part of the Planetary Boundary Layer’, Boundary-Layer Meteorol. 29, 285–312.

    Google Scholar 

  • Reynolds, A. M.: 1998a, ‘A Two-Dimensional Lagrangian Stochastic Dispersion Model for Convective Boundary Layers with Wind Shear’, Boundary-Layer Meteorol. 86, 345–352.

    Google Scholar 

  • Reynolds, A. M.: 1998b, ‘Comments on the University of the Lagrangian Velocity Structure Function Constant (C 0) across Different Kinds of Turbulence’, Boundary-Layer Meteorol. 89, 161–170.

    Google Scholar 

  • Richardson, L. F.: 1926, ‘Atmospheric Diffusion Shown on a Distance-Neighbour Graph’, Proc. Roy. Soc. A, 110, 709.

    Google Scholar 

  • Rizza, U., Mangia, C., Degrazia, G. A., and Tirabassi, T.: 1999, ‘A Model for Puff Dispersion into the Planetary Boundary Layer’, Int. J. Environ. Pollut., in press.

  • Rotach, M. W., Gryning, S. E., and Tassone, C.: 1996, ‘A Two-Dimensional Lagrangian Stochastic Dispersion Model for Daytime Conditions’, Quart. J. Roy. Meteorol. Soc. 122, 367–389.

    Google Scholar 

  • Sawford, B. L.: 1982, ‘Comparison of Some Different Approximation in the Statistical Theory of Relative Dispersion’, Quart. J. Roy. Meteorol. Soc. 108, 191–206.

    Google Scholar 

  • Sawford, B. L.: 1991, ‘Reynolds Numbers Effects in Lagrangian Stochastic Models of Turbulent Dispersion’, Phys. Fluids A3, 1577–1586.

    Google Scholar 

  • Sawford, B. L.: 1993, ‘Recent Development in the Lagrangian Stochastic Theory of Turbulent Dispersion’, Boundary-Layer Meteorol. 62, 197–215.

    Google Scholar 

  • Sawford, B. L. and Guest, M: 1987, ‘Lagrangian Stochastic Analysis of Flux Gradient Relationships in the Convective Boundary Layer’, J. Atmos. Sci. 44, 1152–1165.

    Google Scholar 

  • Sawford, B. L. and Guest, M: 1988, ‘Uniqueness and Universality of Lagrangian Stochastic Models of Turbulent Dispersion’, in 8th Symposium on Turbulence and Diffusion, San Diego, CA, Amer. Meteorol. Soc. Boston, MA, pp. 96–99.

    Google Scholar 

  • Smith, F. B. and Hay, J. S.: 1961, ‘The Expansion of Cluster of Particles in the Atmosphere’, Quart. J. Roy. Meteorol. Soc. 87, 82–101.

    Google Scholar 

  • Taylor, G. I.: 1921, ‘Diffusion by Continuous Movements’, Proc. London Math. Soc. Ser. 2, 20, 196–212.

    Google Scholar 

  • Tennekes, H.: 1982, ‘Similarity Relations, Scaling Laws and Spectral Dynamics’, in F. T. M. Nieuwstadt and H. van Dop (eds.), Atmospheric Turbulence and Air Pollution Modelling, D. Reidel, Dordrecht, pp. 37–68.

    Google Scholar 

  • Thomson, D. J.: 1987, ‘Criteria for the Selection of Stochastic Models of Particle Trajectories in Turbulent Flows’, J. Fluid Mech. 180, 529–556.

    Google Scholar 

  • Yamada, T. and Bunker, S.: 1988, ‘Development of a Nested Grid, Second Moment Turbulence Closure Model and Application to the 1982 Brush Creek Data Simulation’, J. Appl. Meteorol. 27, 562–578.

    Google Scholar 

  • Wandel, C. F. and Kafoed-Hansen, O.: 1962, ‘On the Eulerian-Lagrangian Transform in the Statistical Theory of Turbulence’, J. Geophys. Res. 67, 3089–3093.

    Google Scholar 

  • Willis, G. E. and Deardorff, J. W.: 1976, ‘A Laboratory Model of Diffusion into the Convective Planetary Boundary Layer’, Quart. J. Roy. Meteorol. Soc. 102, 427–445.

    Google Scholar 

  • Willis, G. E. and Deardorff, J. W.: 1978, ‘A Laboratory Model of Dispersion from an Elevated Source within a Modelled Convective Planetary Boundary Layer’, Atmos. Environ. 12, 1305–1311.

    Google Scholar 

  • Willis, G. E. and Deardorff, J. W.: 1981, ‘A Laboratory Study of Dispersion from a Source in the Middle of the Convective Boundary Layer’, Atmos. Environ. 12, 109–117.

    Google Scholar 

  • Wilson, J. D. and Sawford, B. L.: 1996, ‘Review of Lagrangian Stochastic Models for Trajectories in the Turbulent Atmosphere’, Boundary-Layer Meteorol. 78, 191–210.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rizza, U., Cassiani, M., Giostra, U. et al. An Advanced Puff Model Based On A Mixed Eulerian/Lagrangian Approach For Turbulent Dispersion In The Convective Boundary Layer. Boundary-Layer Meteorology 95, 319–339 (2000). https://doi.org/10.1023/A:1002653406071

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1002653406071

Navigation