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The Vertical Term
The Vertical Term (V) accounts for the vertical distribution of the Gaussian plume. It includes the effects of source elevation, receptor elevation and plume rise. In addition to the plume height, receptor height and mixing height, the computation of the Vertical Term requires the vertical dispersion parameter (sigz). The Vertical Term without deposition effects is then given by:
V= exp{-0.5 [(zr-he)/ sigz]2}+exp{-0.5 [(zr+he)/ sigz]2}+
+{exp[-0.5 (H1/sigz)2]+exp[-0.5 (H2/sigz)2]}i=1,2,...+
+{exp[-0.5 (H3/sigz)2]+exp[-0.5 (H4/sigz)2]}i=1,2,...(34)
where:
he = hs + Dh
H1 = zr - (2izi - he)
H2 = zr + (2izi - he)
H3 = zr - (2izi + he)
H4 = zr + (2izi + he)
zr = receptor height above ground (flagpole) (m)
zi = mixing height (m)
The infinite series term in Equation {} accounts for the effects of the restriction on vertical plume growth at the top of the mixing layer. This equation assumes that the mixing height in rural and urban areas is known for all stability categories.
The model make the following assumption about plume behavior in elevated simple terrain (terrain that exceeds the stack base elevation but is below the release height):
• The plume axis remains at the plume stabilization height as it passes over elevated or depressed terrain.
• The mixing height is terrain following.
• The wind speed is a function of height above sea level.
Thus, a modified plume stabilization height he_ is substituted for the effective stack height he in the Vertical Term given by Equation (1-50). For example, the effective plume stabilization height at the point x, y is given by:
h’e=he+zs-z(x,y) (35)
where:
zs= height above mean sea level of the base of the stack (m)
z(x,y)= height above mean sea level of terrain at the receptor location (x,y) (m)
It should also be noted that, the ISC models truncate terrain at stack height as follows: if the terrain height z - zs exceeds the source release height, the elevation of the receptor is automatically chopped off at the physical release height. The user is cautioned that concentrations at these complex terrain receptors are subject to considerable uncertainty.
The Decay Term (D)
The Decay Term is a simple method of accounting for pollutant removal by physical or chemical processes. It is of the form:
D=exp(-psi x/us) for psi > 0 (36)
D=0 for psi = 0 (37)
where:
psi= the decay coefficient (s-1) (a value of zero means decay is not considered)
x= downwind distance (m)
For example, if T1/2 is the pollutant half life in seconds, the user can obtain y from the relationship:
psi=0.693/T1/2 (38)
The default value for psi is zero. That is, decay is not considered in the model calculations unless y is specified. However, a decay half life of 4 hours (y = 0.0000481 s-1) corresponds to SO2 when modeled.
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Canarina Algoritmos Numéricos, S.L.
Environmental software · environmental software solutions
Canary Islands, Spain
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European Union · network on Pollution
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Project funded by the European Commission
through the 6th Framework Programme for Research and Development
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