Vertical diffusion from a ground level line source was estimated using the structure model of the atmospheric boundary layer proposed by Yokoyama et al. (1977a, b, c). The two-dimensional differential equation of diffusion was computed numerically for stationary and horizontally homogeneous conditions. Making the equation dimensionless, we showed that the characteristic spread (Zσ) divided by the height of the boundary layer (h), is a function of two dimensionless lengths, χ/Reh and z0/h, in the mixing and neutral layers (χ: downwind distance from the source, Re: the quantity formed from the characteristic scale of wind speed, eddy diffusivity and the height of the boundary layer, z0: the roughness length of the ground surface.) In the stable layer, another dimensionless length, h/L (L: Monin-Obukhov length), is needed in addition to the above two parameters.
From the relationship between Zσ/h and χ/Reh, it may be shown that in the mixing layer, Zσ is a function of traveling time of the smoke. In the neutral and stable layers, however, Zσ is independent of the mean wind speed and depends only on the downwind distance from the source.
As for the computed concentrations, vertical spread Zσ in the mixing layer increases rapidly in the early stage of the diffusion and tends to vary slowly when the upper part of the layer affects the diffusion. Profiles of vertical concentration in the mixing layer are nearly exponential when Zσ/h«1 and approach a Gaussian distribution gradually with an increase in the downwind distance. On the other hand, in the stable layer, these profiles are nearly Gaussian even at short downwind distances and become more rounded at long distances. The estimated vertical spread Zο and concentrations at the ground surface are discussed, comparing them with diffusion experiments and the Pasquill-Gifford chart.