5.2.2 INDIRECT SOURCE CONTRIBUTION TO CONCENTRATION CALCULATIONS

IN THE CBL

The concentration due to the indirect source is calculated from:

where Qrj = Qdj - )hi, and z is either zr.(for the horizontal plume state) or zp (for the terrainfollowing

state). As shown in Figure 14, the indirect plume is modeled as a reflected version of

the direct plume with an adjustment ()hi - calculated from eq. (92)) to the reflected plume height

to account for the delay in vertical mixing due to plume lofting at the top of the boundary layer.

5.2.3 PENETRATED SOURCE CONTRIBUTION TO CONCENTRATION

CALCULATIONS IN THE CBL

For the penetrated source the concentration expression has a Gaussian form in both the

vertical and lateral directions. The concentration due to this source is given by:

where zieff is the height of the upper reflecting surface in a stable layer (see Section 5.3) and z is

either zr for the horizontal plume state or zp for the terrain-following state. The vertical dispersion

parameters (Fzp) are calculated as described in Section 5.5.1.2.

The penetrated plume height, hep, is taken as the height of the plume centroid above the

mixed layer and is calculated from eq. (94).

5.3 Concentrations in the SBL

For stable conditions, the AERMOD concentration expression (Cs in eq. (48)) has the

Gaussian form, and is similar to that used in many other steady-state plume models (e.g., HPDM

(Hanna and Paine 1989)). The Cs is given by

where zieff is the effective mechanical mixed layer height, Fzs is the total vertical dispersion in the

SBL (see discussion in Section 5.5), and hes is the plume height (i.e., stack height plus the plume

rise - see Section 5.6.2).

Above the mechanical mixed layer height, zim (eq. (26)), the turbulence level is generally

expected to be small and thus supports little vertical mixing of the plume. AERMOD is designed

(in the SBL) with an effective mixing lid, zieff, that retards but does not prevent plume material

from spreading into the region above the estimated mechanical mixed layer. When the final

plume height is well below zim, the plume does not interact with zim. When the plume is below zim

yet the “upper edge” (plume height plus 2.15 Fzs) of the stabilized plume reaches zim, the effective

mixing lid is allowed to increase and remain at a level near the upper edge of the plume. In this

way, AERMOD allows the plume to disperse downwards, but where the turbulence aloft is low,

vertical plume growth is limited by an effective reflecting surface that is folding back only the

extreme tail of the vertical plume distribution. There is no strong concentration doubling effect as

occurs with reflections from an assumed hard lid. Downward dispersion is primarily a factor of

Fw averaged from the receptor to the plume height. If the plume height is above the mixed layer

height, the calculation of the effective Fw will include regions in which Fw is likely to be small.

This, in effect, retards plume growth by an amount dependent upon how much of the plume is

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