Problems associated with the prediction of dispersion of pollutants in the Planetary Boundary Layer (PBL) are investigated using numerical modelling and the available experimental data. Main aim of this 'study was to produce sigmas for elevated releases and to improve our understanding of atmospheric dispersion especially the effects of : (i) elevated releases, (ii) cross-wind shear and (iii) surface roughness. A general model to estimate atmospheric dispersion coefficients for elevated releases and for varying atmospheric stability conditions is presented. The velocity field (PBL model) for the model is either empirically specified or numerically computed from a simplified form of the equations of motion. A set of \"new\" K-profiles is proposed to model atmospheric turbulence, based on recent experimental evidence and theoretical developments. Finite-difference schemes are used for simulation of the flow on a digital computer.