The development and validation of a new stochastic model for predicting the dispersion of a passive tracer in the convective boundary layer are presented. The methods and procedures employed and the results obtained from the Atterbury-87 field study of the dispersion of fog-oil smoke and hexachloroethane (HC) smoke are also described. The stochastic model represents a substantial improvement over previous modelling approaches in that it provides a more realistic treatment of the atmospheric turbulence, especially for the large-scale convective motions occurring in the daytime planetary boundary layer which are largely responsible for driving the dispersion process. Using the Langevin equation to model the Lagrangian velocities, the dispersion of a large number of passive tracer particles is computationally simulated. The shape of the resulting probability density function closely matches observations. The behavior of the autocorrelation of the modelled Lagrangian velocities also matches the non-exponential form computed from balloon-borne measurements by using the local integral time scale of the turbulence. The model was verified against data gathered from laboratory simulations of the boundary layer carried out in water tanks and wind tunnels as well as from actual field measurements. The predictions of the stochastic model were in agreement with the trends and magnitudes observed in the data, including the lift-off of the plume centerline from the ground due to the influence of the rising thermal updrafts. Comparisons of crosswind-integrated concentration and plume spread computed from the test data with the results of previous field studies of atmospheric dispersion indicated strong agreement. These comparisons revealed that the centerline of the smoke plume rose as the plume moved downwind due to the effects of thermal convection. Comparison of concentration data with the predictions of the stochastic model also showed good agreement and confirmed that the centerline of the smoke plume lifted off the ground. This was in sharp contrast to the calculations of a generic Gaussian plume model which did not predict the rising centerline and substantially overpredicted the ground level concentrations. (Abstract shortened with permission of author.)