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Section 6:

6. The ISC Short-term Dispersion Model Equations

6.1 Point Source Emissions

6.1.1 The Gaussian Equation

6.1.2 Downwind and Crosswind Distances

6.1.3 Wind Speed Profile

6.1.4 Plume Rise Formulas

6.1.5 The Dispersion Parameters

6.1.6 The Vertical Term

6.1.7 The Decay Term

6.2 Non-Point Source Emissions

6.2.1 General

6.2.2 The Short-Term Volume Source Model

6.2.3 The Short-Term Area Source Model

6.2.4 The Short-Term Open Pit Source Model

6.3 The ISC Short-Term Dry Deposition Model

6.3.1 General

6.3.2 Deposition Velocities

6.3.3 Point and Volume Source Emissions

6.3.4 Area and Open Pit Source Emissions

6.4 The ISC Short-Term Wet Deposition Model

6.5 ISC Complex Terrain Screening Algorithms

6.5.1 The Gaussian Sector Average Equation

6.5.2 Downwind, Crosswind and Radial Distances

6.5.3 Wind Speed Profile

6.5.4 Plume Rise Formulas

6.5.5 The Dispersion Parameters

6.5.6 The Vertical Term

6.5.7 The Decay Term

6.5.8 The Plume Attenuation Correction Factor

6.5.9 Wet Deposition in Complex Terrain

6.6 ISC Treatment of Intermediate Terrain

ISCST3 Tech Guide

Gaussian Plume Air Dispersion Model

6.5.6 The Vertical Term

The Vertical Term used in the complex terrain algorithm in ISC is the same as described in Section 1.1.6 for the simple terrain algorithm, except that the plume height and dispersion parameter input to the vertical term are based on the radial distance, as described above, and that the adjustment of plume height for terrain above stack base is different, as described in The Vertical Term in Complex Terrain.

The Vertical Term in Complex Terrain.

The ISC complex terrain algorithm makes the following assumption about plume behavior in complex terrain:

The plume axis remains at the plume stabilization height above mean sea level as it passes over complex terrain for stable conditions (categories E and F), and uses a "half-height" correction factor for unstable and neutral conditions (categories A - D)
The plume centerline height is never less than 10 m above the ground level in complex terrain.
The mixing height is terrain following, i.e, the mixing height above ground at the receptor location is assumed to be the same as the height above ground at the source location.
The wind speed is a function of height above the surface (see Equation (1-6)).

Thus, a modified plume stabilization height heĀ“ is substituted for the effective stack height he in the Vertical Term given by Equation (1-50). The effective plume stabilization height at the point x,y is given by:

Formula

Where:

he = plume height at point x,y without terrain adjustment, as described in Section 1.5.4 (m)
Ht = z*(x,y) - zs = terrain height of the receptor location above the base of the stack (m)
z|(x,y) = height above mean sea level of terrain at the receptor location (x,y) (m)
zs = height above mean sea level of the base of the stack (m)
FT = terrain adjustment factor, which is 0.5 for stability categories A - D and 0.0 for stability categories E and F.

The effect of the terrain adjustment factor is that the plume height relative to stack base is deflected upwards by an amount equal to half of the terrain height as it passes over complex terrain during unstable and neutral conditions. The plume height is not deflected by the terrain under stable conditions.

The Vertical Term for Particle Deposition

The Vertical Term for particle deposition used in the complex terrain algorithm in ISC is the same as described in Section 1.1.6 for the simple terrain algorithm, except that the plume height and dispersion parameter input to the vertical term are based on the radial distance, as described above, and that the adjustment of plume height for terrain above stack base is different, as described in this section.