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# ISCST3 Tech Guide

Gaussian Plume Air Dispersion Model

## 7.1.1 The Gaussian Sector Average Equation

The Gaussian Sector Average Equation

The ISC long-term model uses input meteorological data that have been summarized into joint frequencies of occurrence for particular wind speed classes, wind direction sectors, and stability categories. These summaries, called STAR summaries for STability ARray, may include frequency distributions over a monthly, seasonal or annual basis. The long term model has the option of calculating concentration or dry deposition values for each separate STAR summary input and/or for the combined period covered by all available STAR summaries. Since the wind direction input is the frequency of occurrence over a sector, with no information on the distribution of winds within the sector, the ISC long-term model uses a Gaussian sector-average plume equation as the basis for modeling pollutant emissions on a long-term basis.

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

)2ยด = 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.