Vertical Diffusion Parameter in the Atmospheric Boundary Layer

Abstract

This paper presents relations between the mean vertical displacement ($\bar z$) of pollutants and their mean horizontal displacement (x$\bar x$ ) in the atmospheric boundary layer. A modification of the lagrangian similarity theory applied to atmospheric diffusion extended to the atmospheric boundary layer is developed. According to Pasquill and Smith (1983) the similarity theory of Monin-Obukhov applied to atmospheric diffusion states

$$\frac{{d\bar x}}{{d\bar z}} - \frac{{\bar u\left( {c\bar z} \right)\bar z}}{{k\left( {\bar z} \right)}}$$

(1)

where ū is the mean wind speed, c depends on stability and K is the vertical material diffusivity. Considering the eddy diffusivity for momentum and the form of the friction velocity introduced by Yokoyama et al.(1979) a form of ū(c$\bar z$)for the atmospheric boundary layer is developed. Substituting ū(c$\bar z$) in Eq.(1), equating K to the heat diffusivity given by Yokoyama et al.(1979) and integrating, the following expressions can be obtained (where z₁ is the boundary layer depth, L is the Monin-Obukhov length, θ=$\bar x$/z₁; α=$\bar z$/z₁; αo = zo/z₁; k=0.41, β=6.9 and γ=0.92): - neutral and stable conditions: (η=z₁/L ≥ 0)