The application of Equation (2-6a) to calculate the sector average concentration from area sources is an iterative process.  Calculations using the ISC Short Term algorithm (Equation (1-58)) are initially made for three wind directions, corresponding to the two boundaries of the sector and the centerline direction.  The algorithm then calculates the concentration for wind directions midway between the three directions, for a total of five directions, and calculates the error term.  If the error is less than 2 percent, then the concentration based on five directions is used to represent the sector average, otherwise, additional wind directions are selected midway between each of the five directions and the process continued.  This process continues until the convergence criteria, described below, are satisfied.

In order to avoid abrupt changes in the concentrations at the sector boundaries with the numerical integration algorithm, a linear interpolation is used to determine the frequency of occurrence of each wind direction used for the individual simulations within a sector, based on the frequencies of occurrence in the adjacent sectors.  This "smoothing" of the frequency distribution has a similar effect as the smoothing function used for the ISC Long Term point source algorithm, described in Section 2.1.8.  The frequency of occurrence of the jth wind direction between sectors i and i+1 can be calculated as:

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