Finally, to complete the description of eq. (79), the surface portion of vertical dispersion (Fzgs)

in the SBL, is calculated from Venkatram (1992) as

 

For the direct and indirect sources in the CBL, the ambient portion of the vertical dispersion

(Fza of eq. (75)) is denoted as Fzaj (j = 1, 2) to distinguish between updrafts and downdrafts. Fzaj is

composed of an elevated (Fzej) and surface (Fzg) portion and is given by

where the elevated portion (Fzej) is obtained from Weil et al. (1997)as

 

where Fwj is a parameter in the bi-Gaussian pdf (eq.(53)).

The expression α ( ) is designed to be 1.0 above the surface layer b p i = Min 0.6 + 4 H z , 1.0

(Hp > 0.1 zi) and to otherwise match Venkatram’s (1992) result for vertical dispersion from a

surface source in a neutral boundary layer.

For the CBL, the vertical dispersion from a source within the surface layer (Hp{x} < 0.1 zi) is

parameterized by

where bc = 0.5, u* is the friction velocity, and L is the Monin-Obukhov length; above the surface

layer (Hp > 0.1zi), Fzg is assumed to equal zero. In the limit of a surface release (Hp = 0), the

parameterization of eq. (87) follows the form suggested by Venkatram (1992) for vertical

dispersion in the unstable surface layer; i.e., . The parameterization is designed ( ) σ

z u u x L *

~ 2 2

to: 1) agree with Venkatram’s result in the limit of a surface release, 2) provide good agreement

between the modeled and observed concentrations from the Prairie Grass experiment (Paine et al.,

2001), and 3) decrease with source height in the surface layer and ultimately vanish for above the

 

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