ISCST3 Tech Guide

Gaussian Plume Air Dispersion Model

6.1.1 The Gaussian Equation

The ISC short term model for stacks uses the steady-state Gaussian plume equation for a continuous elevated source. For each source and each hour, the origin of the source's coordinate system is placed at the ground surface at the base of the stack. 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. The calculation of the downwind and crosswind distances is described in Section 1.1.2. 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 steady-state Gaussian plume, the hourly concentration at downwind distance x (meters) and crosswind distance y (meters) is given by:

Gaussian Equation


Q = pollutant emission rate (mass per unit time)

K = a scaling coefficient to convert calculated concentrations to desired units (default value of 1 x 106 for Q in g/s and concentration in µg/m3)

V = vertical term

D = decay term

Fy,Fz = standard deviation of lateral and vertical concentration distribution (m)

us = mean wind speed (m/s) at release height

Equation (1-1) includes a Vertical Term (V), a Decay Term (D), and dispersion parameters (Fy and Fz) as discussed below. It should be noted that the Vertical Term includes the effects of source elevation, receptor elevation, plume rise, limited mixing in the vertical, and the gravitational settling and dry deposition of particulates (with diameters greater than about 0.1 microns).