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1.1.5.2 Lateral and Vertical Virtual Distances.

The equations in Tables 1‑1 through 1‑4 define the dispersion parameters for an ideal point source.  However, volume sources have initial lateral and vertical dimensions.  Also, as discussed below, building wake effects can enhance the initial growth of stack plumes.  In these cases, lateral (xy) and vertical (xz) virtual distances are added by the ISC models to the actual downwind distance x for the σy and σz calculations.  The lateral virtual distance in kilometers for the rural mode is given by:

where the stability‑dependent coefficients p and q are given in Table 1‑5 and σyo is the standard deviation in meters of the lateral concentration distribution at the source.  Similarly, the vertical virtual distance in kilometers for the rural mode is given by:

where the coefficients a and b are obtained form Table 1‑2 and σzo is the standard deviation in meters of the vertical concentration distribution at the source.  It is important to note that the ISC model programs check to ensure that the xz used to calculate σz at (x + xz) in the rural mode is the xz calculated using the coefficients a and b that correspond to the distance category specified by the quantity (x + xz).

To determine virtual distances for the urban mode, the functions displayed in Tables 1‑3 and 1‑4 are solved for x.  The solutions are quadratic formulas for the lateral virtual distances; and for vertical virtual distances the solutions are cubic equations for stability classes A and B, a linear equation for stability class C, and quadratic equations for stability classes D, E, and F.  The cubic equations are solved by iteration using Newton's method.

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