Solutions of the integral equation of diffusion and the random walk model for continuous plumes and instantaneous puffs in the atmospheric boundary layer

The integral equation method is related to the random walk modelling that has proved so effective and popular in recent years. The I.E. method, by using simple probability techniques, avoids the inefficient determination of thousands of trajectories in order to build up concentration profiles. In fact it is so simple and efficient it can be run on a conventional programmable calculator. The method is applied to passive material being released from an elevated source within a neutrally stable surface layer over a uniform surface, and also to an instantaneous release when the effect of wind shear is examined. The latter scenario is also studied using random walk techniques and a comparison of the solutions obtained. Agreement is very good, although downwind spread is shown to be quite sensitive to gridlength size in the I.E. method.