where F (T T )w r is the stack momentum flux, is the stack buoyant m s s s = 2 2 F gw r ( T T ) b s s s = 2 Δ

flux, rs is the stack radius corrected for stack tip downwash, and $

1 (= 0.6) is an entrainment

parameter. It should be noted that up is the wind speed used for calculating plume rise. In the

CBL up is set equal to u{hs}.

As shown in Figure 14, the indirect plume, which is included to treat the no flux condition at

z = zi, is modeled as a reflected version of the direct plume with an adjustment ()hi) to the

reflected plume height to account for the delay in vertical mixing due to plume lofting at the top

of the boundary layer. That height adjustment is given by

where ry and rz are the lofting plume half-widths in the lateral and vertical directions, up is the

wind speed used for plume rise, and "

r = 1.4. The produce of cross-wind dimensions of the

assumed elliptical plume is calculated from Weil et al. (1997) as


where , $

2 = 0.4, 8

y r (z h ) = 2.3, and ae = 0.1 (dimensionless entrainment parameter). h i s = − β


For a derivation and discussion of )hi see Weil et al. (1997).

The height that the penetrated source achieves above zi is calculated as the equilibrium plume

rise in a stratified environment and is determined by the source buoyancy flux, the stable

stratification above zi, and the mean wind speed. In line with Weil et al. (1997), the penetrated

source plume height, hep, is taken as the centroid of plume material above the inversion. For

complete penetration (fp = 0) hep = hs+)heq. However, for partial penetration ( fp > 0), hep is

chosen as the average of the heights of the upper plume edge hs + 1.5 )heq and zi, or

where )heq is defined in eq. (56).


Plume rise in the SBL is taken from Weil (1988b), which is modified by using an iterative

approach which is similar to that found in Perry et al. (1989). When a plume rises in an

atmosphere with a positive potential temperature gradient, plume buoyancy decreases because the

ambient potential temperature increases as the plume rises; thus, plume buoyancy with respect to

the surroundings decreases. To account for this, the plume rise equations have to be modified.

With this modification, AERMOD computes stable plume rise, )hs, from Weil et al. (1988b) as



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