A First Order Lagrangian Stochastic Model for Long Range Transport

The dispersion model is based on a 3-D first order Langevin equation for the turbulent component of the wind. Turbulence is assumed to be quasi-stationary. Horizontal gradients in turbulence statistics, as well as the covariances among of the three turbulent wind components, are neglected. Turbulent velocity variances are obtained by partitioning the turbulent kinetic energy (TKE) given by CMC’s operational Global Environmental Multiscale (GEM) model (Cote et all, 1998), depending on local thermal stability. The Lagrangian velocity time scale appearing in the Langevin equation is expressed in terms of the turbulent velocity variances and of the TKE dissipation rate, which is estimated from the TKE and a lengthscale calculated according to Mailhot and Benoit (1982), from the boundary layer height and stability, both provided by GEM. The synoptic components are obtained directly from GEM. The vertical profiles of wind and temperature within the lowest GEM model layer, defined as the surface layer, are diagnosed using Delage (1988) formulation. Particles trajectories are obtained by the time integration the 3-D wind.