This technical note introduces some corrections to the Lagrangian particle dispersion model of Rotach et al. (Q J R Meteorol Soc 122:367–389, 1986). Careful mathematical derivation following the detailed explanations in that paper uncovered some unit inconsistencies that were the result of mistaken function definitions. Errors are noted in the drift correction, or “probability current” of the particle dispersion model as well as in parameterization of turbulence terms, which are necessary inputs to the model. The probability current comprises Gaussian, convective, and solenoidal components, with derivation errors discovered in the latter two components. All errors are presented along with new formulations that are mathematically consistent, correct the original problems, and adhere to the underlying Gaussian nature of the particle dispersion phenomenon. The corrections shown here should provide more accurate results for particle dispersion models based upon the work of Rotach et al., as well as resolve points of confusion for future researchers referring to that work.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
Kljun N, Rotach MW, Schmid HP (2002) A three-dimensional backward Lagrangian footprint model for a wide range of boundary-layer stratifications. Boundary-Layer Meteorol 103: 205–226
Langevin P (1908) On the theory of Brownian motion. CR Acad Sci (Paris) 146: 530–533
Luhar AK, Britter RE (1989) A random walk model for dispersion in inhomogeneous turbulence in a convective boundary layer. Atmos Environ 23: 1911–1924
Rodean HC (1996) Stochastic Lagrangian models of turbulent diffusion. American Meteorological Society, Boston
Rotach MW, Gryning S-E, Tassone C (1996) A two-dimensional Lagrangian stochastic dispersion model for daytime conditions. Q J R Meteorol Soc 122: 367–389
Thomson DJ (1987) Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J Fluid Mech 180: 529–556
About this article
Cite this article
Gibson, M., Sailor, D.J. Corrections to the Mathematical Formulation of a Backwards Lagrangian Particle Dispersion Model. Boundary-Layer Meteorol 145, 399–406 (2012). https://doi.org/10.1007/s10546-012-9739-0