5.2.1 DIRECT SOURCE CONTRIBUTION TO CONCENTRATION CALCULATIONS IN

THE CBL

Following Weil et al. (1997), the concentration due to the direct plume is given by:

u is the wind speed at stack top, Fy is the lateral distribution function with

meander (discussed in Section 5.4),w a w (aj is defined below in eq.(62) , )hd is the direct j j = *

source plume rise calculated from eq. (91), and z = zr and zp in the horizontal and terrainfollowing

states, respectively. Here, Qdj and Fzj are the effective source height and vertical

dispersion parameter corresponding to each of the two distributions in eq. (53). The subscript j is

equal to 1 for updrafts and 2 for downdrafts. The lateral and vertical dispersion parameters ( F

y and

Fzj), resulting from the combined effects of ambient, buoyancy-induced, and building-induced

turbulence are calculated as discussed in Sections 5.5.1.1 and 5.5.1.2 respectively. Here, Fzj (with

j = 1 or 2) is the vertical dispersion parameter corresponding to each of the Gaussian distributions

used in the bi-Gaussian pdf, (see Section 5.5.1.2) and 8

j, the weighting coefficient for each

distribution in eq.(53), is calculated from Weil et al. (1997) as

Recall that is the total effective vertical turbulence and is calculated from eq. (34). The ~σ

wT

parameters appearing in eq.(62) are given by

and R is assumed to be 2.0 (Weil et al., 1997). Likewise, the termw x u in eq. (60) follows j

from the Fz derivation and the w&j appearing in the bi-Gaussian form (see discussion of eq. (53)) .

The lateral dispersion parameter ( F

y,) is calculated from eq. (75) (Weil et al., 1997).

In eq. (59), an image plume is used to satisfy the no-flux condition at the ground, i.e., an

image plume from a source at z = -hs, which results in the exponential terms containing z +Qdj on

the right-hand side of eq. (59). This image source results in a positive flux of material at z = zi,

and additional image sources are introduced at z = 2 zi + hs, -2 zi - hs, 4zi + hs, -4zi - hs, etc. to

satisfy all the subsequent no-flux conditions occurring at z = 0 and zi.

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