where C x y z is the concentration in the absence of the hill for stable conditions. In s r r r { , , }

convective conditions, H and c p = 0 ϕ = 0.

As described by Venkatram et al. (2001), the plume state weighting factor f is given by

f ( ). When the plume is entirely below Hc the concentration p = 0.5 1+ ϕ (ϕ ) p = 1.0 and f = 1.0

is determined only by the horizontal plume. When the plume is entirely above the critical

dividing streamline height or when the atmosphere is either neutral or convective,

ϕ Therefore, during convective conditions the concentration at an elevated p = 0 and f = 0.5.

receptor is simply the average of the contributions from the two states. As plumes above Hc

encounter terrain and are deflected vertically, there is also a tendency for plume material to

approach the terrain surface and to spread out around the sides of the terrain. To simulate this

the estimated concentration is constrained to always contain a component from the horizontal

state. Therefore, under no conditions is the plume allowed to completely approach the terrain

following state. For flat terrain, the contributions from the two states are equal, and are equally

weighted.

Figure 12 illustrates how the weighting factor is constructed and its relationship to the

estimate of concentration as a weighted sum of two limiting plume states.

Figure 12: Treatment of Terrain in AERMOD. Construction of the weighting factor used in

calculating total concentration.

The general form of the expressions for concentration in each term of eq. (48) for both the

CBL and the SBL can be written as follows:

where Q is the source emission rate, u~ is the effective wind speed, and py and pz are probability

density functions (pdf) which describe the lateral and vertical concentration distributions,

respectively. AERMOD assumes a traditional Gaussian pdf for both the lateral and vertical

distributions in the SBL and for the lateral distribution in the CBL. The CBL’s vertical

distribution of plume material reflects the distinctly non-Gaussian nature of the vertical velocity

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