Sensitivity Analysis of Lagrangian Stochastic Models for CBL with Different PDF’s and Turbulence Parameterizations

  • E. Ferrero
  • D. Anfossi
Part of the NATO • Challenges of Modern Society book series (NATS, volume 22)


It is known (Thomson, 1987) that Ito’s type stochastic models (LS) satisfy the well-mixed condition and hence are physically consistent. An Eulerian probability density function (PDF) of the turbulent velocities, as close as possible to the actual atmospheric PDF, must be prescribed in order to specify the model. Unfortunately these models have a unique solution in one-dimension only (Sawford and Guest, 1988). For this reason the present study will focus on one-dimensional diffusion simulation.


Probability Density Function Convective Boundary Layer Normalise Mean Square Error Turbulence Parameterization Lagrangian Stochastic Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anfossi D., Ferrero E., Tinarelli G. and Alessandrini S., 1997, A simplified version of the correct boundary conditions for skewed turbulence in Lagrangian particle models, Atmos. Environ., 31, 301–308CrossRefGoogle Scholar
  2. Anfossi D., Ferrero E., Sacchetti D. and Trini Castelli S., 1996, Comparison among empirical probability density functions of the vertical velocity in the surface layer based on higher order correlations, Boundary Layer Meteorology, 82, 193–218CrossRefGoogle Scholar
  3. Antonia R.A. and Atkinson J.D., 1973, High-order moments of Reynolds shear stress fluctuations in a turbulent boundary layer, J. Fluid Mech., 58, part 3, 581–593CrossRefGoogle Scholar
  4. De Baas H.F., Van Dop H., and Nieuwstadt F.T.M., 1986, An application of the Langevin equation for inhomogeneous conditions to dispersion in a convective boundary layer, Quart. J. Roy. Meteor. Soc., 112, 165–180CrossRefGoogle Scholar
  5. Du S., Wilson J.D. and Yee E., 1994, Probability density functions for velocity in the convective boundary layer and implied trajectory models, Atmos. Environ., 28, 1211–1217CrossRefGoogle Scholar
  6. Durst F., Jovanovic J. and Johansson T.G., 1992, On the statistical properties of truncated Gram-Charlier series expansions in turbulent wall-bounded flows, Phys. Fluids, A 4, 118–126Google Scholar
  7. Ferrero E., Anfossi D., Tinarelli G. and Trini Castelli S., An intercomparison of two turbulence closure schemes and four parametrizations for stochastic dispersion models, Nuovo Cimento 20C, 315-329Google Scholar
  8. Flesch T.K. and Wilson D.J., 1992, A two-dimensional trajectory simulation model for non-Gaussian inhomogeneous turbulence within plant canopies, Boundary Layer Meteorology, 61, 349–374CrossRefGoogle Scholar
  9. Frenkiel F.N. and Klebanoff P.S., 1967, Higher order correlations in a turbulent field, Phys. Fluids, 10, 507–520CrossRefGoogle Scholar
  10. Kendall M. and Stuart A., 1977, The advanced theory of statistics, MacMillan, New YorkGoogle Scholar
  11. Lenschow D.H., Mann J., Kristensen L., 1994, How long is long enough when measuring fluxes and other turbulence statistics, J. Atm., Ocean. Techn., 661-673Google Scholar
  12. 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, 1191–1924Google Scholar
  13. Morselli M.G. and Brusasca G., 1991, MODIA: Pollution dispersion model in the atmosphere, Environmental Software Guide, 211-216.Google Scholar
  14. Nagakawa H. and Nezu I, 1977, Prediction of the contributions to the Reynolds stress from bursting events in open-channel flows, J. Fluid Mech., 80 part 1, 99–128CrossRefGoogle Scholar
  15. Rodean H.C., 1994, Notes on the Langevin model for turbulent diffusion of “marked” particles, UCRL-ID-115869 Report of Lawrence Livermore National LaboratoryGoogle Scholar
  16. Sawford B.L. and Guest F.M., 1988, Uniqueness and universality of Lagrangian stochastic models of turbulent dispersion, 8th Symposium on Turbulence and Diffusion, San Diego, CA, A.M.S., 96-99 Tampieri F. (personal communication)Google Scholar
  17. Thomson D.J., 1987, Criteria for the selection of stochastic models of particle trajectories in turbulent flows, J. Fluid Mech., 180, 529–556CrossRefGoogle Scholar
  18. Weil J.C., 1990, A diagnosis of the asymmetry in top-down and bottom-up diffusion using a Lagrangian stochastic model, JW. Atmos. Sci., 47, 501–515CrossRefGoogle Scholar
  19. Willis G.E. and J. Deardorf, 1976: A laboratory model of diffusion into the convective planetary boundary layer. Q.J.R. Meteor. Soc., 102, 427–445CrossRefGoogle Scholar
  20. Willis G.E. and J. Deardorf, 1978, A laboratory study of dispersion from an elevated source within a modelled convective boundary layer, Atmos. Environ., 12, 1305–1311CrossRefGoogle Scholar
  21. Willis G.E. and J. Deardorf, 1981, A laboratory study of dispersion from a source in the middle of the convective mixed boundary layer’, Atmos. Environ., 15, 109–117CrossRefGoogle Scholar
  22. Wilson J.D. and Flesch T.K. (1993) Flow boundaries in random-flight dispersion models: enforcing the well-mixed condition. J. Appl. Meteor., 32, 1695–1707CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • E. Ferrero
    • 1
  • D. Anfossi
    • 2
  1. 1.Dip. Scienze Tecn. Avanz.Universita’ di TorinoAlessandriaItaly
  2. 2.Istituto di CosmogeofisicaC.N.R.TorinoItaly

Personalised recommendations