# ISCST3 Tech Guide

## 6.5.1 The Gaussian Sector Average Equation

The Short Term complex terrain screening algorithm for stacks uses the steady-state, sector-averaged Gaussian plume equation for a continuous elevated zsource. As with the simple terrain algorithm described in Section 1.1, the origin of the source's coordinate system is placed at the ground surface at the base of the stack for each source and each hour. The x axis is positive in the downwind direction, the y axis is crosswind (normal) to the x axis and the z axis extends vertically. The fixed receptor locations are converted to each source's coordinate system for each hourly concentration calculation. Since the concentrations are uniform across a 22.5 degree sector, the complex terrain algorithms use the radial distance between source and receptor instead of downwind distance. The calculation of the downwind, crosswind and radial distances is described in Section 1.5.2. The hourly concentrations calculated for each source at each receptor are summed to obtain the total concentration produced at each receptor by the combined source emissions.

For a Gaussian, sector-averaged plume, the hourly concentration at downwind distance x (meters) and crosswind distance y (meters) is given by:

Where:

Q = pollutant emission rate
(mass per unit time),

K = units scaling coefficient (see Equation (1-1))

)2ยด = the sector width in radians(=0.3927)

R = radial distance from the point source to the receptor = [(x+x_{y})^{2}
+ y^{2}]^{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)

x_{y }= lateral virtual
distance for volume sources (see Equation (1-35)), equals zero for point
sources (m)

u_{s }= mean wind speed (m/sec)
at stack height

F_{z }= standard deviation of
the vertical concentration distribution (m)

V = the Vertical Term (see Section 1.1.6)

D = the Decay Term (see Section 1.1.7)

CORR = the attenuation correction factor for receptors above the plume
centerline height (see Section 1.5.8)

Equation (1-93) includes a
Vertical Term, a Decay Term, and a vertical dispersion term (F_{z}).
The Vertical Term includes the effects of source elevation, receptor
elevation, plume rise, limited vertical mixing, gravitational settling and
dry deposition.