A random walk model for dispersion in the planetary boundary layer has been developed. The model is based on a stochastic differential equation, the Langevin equation and is one-dimensional in the sense that turbulent velocity fluctuations are only modelled in the vertical.
Horizontal transport is assumed to be performed by the meanwind.
A formulation of the PDF as a fourth-order expansion in Hermite polynomials is tried out and the resulting model is validated against convective watertank experiments. The dispersion model is used for footprint analysis under convective conditions where the PDF is skewed. Footprints are calculated from both forward and backward trajectories. It is found that the former method agrees well with forward footprints whereas the latter gives unsatisfactory results. A mass-flux balance that relates the area under the footprint curve to the normalized flux profile is set up.