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Both FQ(x) and P(x,z) depend on the size and density of the particles being modeled, because this effects the total deposition velocity (See Section 1.3.2).  Therefore, for a given source of particulates, ISC allows multiple particle-size categories to be defined, with the maximum number of particle size categories controlled by a parameter statement in the model code (see Volume I).  The user must provide the mass-mean particle diameter (microns), the particle density (g/cm3), and the mass fraction (φ) for each category being modeled.  If we denote the value of FQ(x) and P(x,z) for the nth particle-size category by FQn(x) and Pn(x,z) and substitute these in Equation (1-54), we see that a different value for the vertical term is obtained for each particle-size category, denoted as Vdn.  Therefore, the total vertical term is given by the sum of the terms for each particle-size category, weighted by the respective mass-fractions:

FQ(x) is a function of the total deposition velocity (vd), V(x,zd,hed), and P(x,zd):

where zd is a height near the surface at which the deposition flux is calculated.  The deposition reference height is calculated as the maximum of 1.0 meters and 20z0.  This equation reflects the fact that the material removed from the plume by deposition is just the integral of the deposition flux over the distance that the plume has traveled.  In ISC, this integral is evaluated numerically.  For sources modeled in elevated or complex terrain, the user can input a terrain grid to the model, which is used to determine the terrain elevation at various distances along the plume path during the evaluation of the integral.  If a terrain grid is not input by the user, then the model will linearly interpolate between the source elevation and the receptor elevation.

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