Point Source Emissions
The Gaussian Sector Average Equation
The ISC long-term model makes the same basic assumption as the short-term model. In the long-term model, the area surrounding a continuous source of pollutants is divided into sectors of equal angular width corresponding to the sectors of the seasonal and annual frequency distributions of wind direction, wind speed, and stability. Seasonal or annual emissions from the source are partitioned among the sectors according to the frequencies of wind blowing toward the sectors. The concentration fields calculated for each source are translated to a common coordinate system (either polar or Cartesian as specified by the user) and summed to obtain the total due to all sources.
For a single stack, the mean seasonal concentration is given by:
Where:
K = units scaling coefficient (see Equation (1-1))
Q = pollutant emission rate (mass per unit time), for the ith wind-speed category, the kth stability category and the lth season
f = frequency of occurrence of the ith wind-speed category, the jth wind-direction category and the kth stability category for the lth season
)2´ = the sector width in radians
R = radial distance from lateral virtual point source (for building downwash) to the receptor = [(x+xy)2 + y2]1/2 (m)
x = downwind distance from source center to receptor, measured along the plume axis (m)
y = lateral distance from the plume axis to the receptor (m)
xy = lateral virtual distance (see Equation (1-35)), equals zero for point sources without building downwash, and for downwash sources that do not experience lateral dispersion enhancement (m)
S = a smoothing function similar to that of the AQDM (see Section 2.1.8)
us = mean wind speed (m/sec) at stack height for the ith wind-speed category and kth stability category
Fz= standard deviation of the vertical concentration distribution (m) for the kth stability category
V = the Vertical Term for the ith wind-speed category, kth stability category and lth season
D = the Decay Term for the ith wind speed category and kth stability category
The mean annual concentration at the point (r,2) is calculated from the seasonal concentrations using the expression:
The terms in Equation (2-1) correspond to the terms discussed in Section 1.1 for the short-term model except that the parameters are defined for discrete categories of wind-speed, wind-direction, stability and season. The various terms are briefly discussed in the following subsections. In addition to point source emissions, the ISC long-term concentration model considers emissions from volume and area sources. These model options are discussed in Section 2.2. The optional algorithms for calculating dry deposition are discussed in Section 2.3.
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