where:

 θj´ =  the angle measured in radians from north to the centerline of the jth wind‑direction sector θ´ =  the angle measured in radians from north to the receptor point (R, θ) where R, defined above for equation 2‑1, is measured from the lateral virtual source.

Fi

=    the frequency of occurrence for the ith sector

 Fi+1 =    the frequency of occurrence for the i+1th sector

 Θi =    the central wind direction for the ith sector

 Θi+1 =    the central wind direction for the i+1th sector

 θij =    the specific wind direction between Θi and Θi+1

 fij =    the interpolated (smoothed) frequency of occurrence for the specific wind direction θij

The ISCLT model uses a set of three criteria to determine whether the process of calculating the sector average concentration has "converged."  The calculation process will be considered to have converged, and the most recent estimate of the trapezoidal integral used, if any of the following conditions is true:

1)   if the number of "halving intervals" (N) in the trapezoidal approximation of the sector average has reached 10, where the number of individual elements in the approximation is given by 1 + 2N-1 = 513 for N of 10;

2)   if the estimate of the sector average has converged to within a tolerance of 0.02 (i.e., 2 percent), for two successive iterations, and at least 2 halving intervals have been completed (a minimum of 5 wind direction simulations); or

3)   if the estimate of the sector average concentration is less than 1.0E-10, and at least 2 halving intervals have been completed.

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