A probability density function (PDF) fumigation model is presented here to study the dispersion of air pollutants emitted from a tall stack on the shoreline. This work considers dispersion of the pollutants in the stable layer and within the thermal internal boundary layer (TIBL) proceeds independently. The growth of TIBL is considered parabolic with distance inland. Turbulence is taken as homogeneous and stationary. Dispersion of particles (contaminant) in lateral and vertical directions is assumed independent of each other. This assumption allows us to consider the position of particles in both directions as independent random variables. The lateral dispersion distribution within the TIBL is considered as Gaussian and independent of height. A skewed bi-Gaussian vertical velocity PDF is used to account for the physics of dispersion due to different characteristics of updrafts and downdrafts within the TIBL. We have used Weil (J.C. Weil, A diagnosis of the asymmetry in top-down and bottom-up diffusion using a Lagrangian stochastic model, J. Atmos. Sci., 47 (1990) 501-515) solutions to find out the parameters of this PDF. Incorporating finite Lagrangian integral time scale for the vertical velocity component, it is observed that it reduces the vertical dispersion in the beginning and moves the point of maximum concentration further downwind. Due to little dispersion in the beginning, there is more plume to be dispersed causing higher concentrations at large distances. The model has considered Weil and Brower's (J.C. Weil, P.R. Brower, Estimating convective boundary layer parameters for diffusion applications, Maryland Power Plant Siting Program Rep. PPSP-MP-48, Department of Natural Resources, Annapolis, MD, 1985, 37 pp.) convective limit to analyze dispersion characteristics within TIBL. The revised model discussed here is evaluated with the data available from the Nanticoke field experiment on fumigation conducted in summer of 1978 in Ontario, Canada. The results of revised model are in good agreement with the observed data.