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In Equation (1-65), the integral in the longitudinal (i.e., upwind or x) direction is approximated using numerical methods based on Press, et al (1986).  Specifically, the ISCST model estimates the value of the integral, I, as a weighted average of previous estimates, using a scaled down extrapolation as follows:

where the integral term refers to the integral of the plume function in the upwind direction, and IN and I2N refer to successive estimates of the integral using a trapezoidal approximation with N intervals and 2N intervals.  The number of intervals is doubled on successive trapezoidal estimates of the integral.  The ISCST model also performs a Romberg integration by treating the sequence Ik as a polynomial in k.  The Romberg integration technique is described in detail in Section 4.3 of Press, et al (1986).  The ISCST model uses a set of three criteria to determine whether the process of integrating in the upwind direction has "converged."  The calculation process will be considered to have converged, and the most recent estimate of the integral used, if any of the following conditions is true:

1)   if the number of "halving intervals" (N) in the trapezoidal approximation of the integral 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 extrapolated estimate of the real integral (Romberg approximation) has converged to within a tolerance of 0.0001 (i.e., 0.01 percent), and at least 4 halving intervals have been completed; or

3)   if the extrapolated estimate of the real integral is less than 1.0E-10, and at least 4 halving intervals have been completed.

1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 - 16 - 17 - 18 - 19 - 20 - 21 - 22 - 23 - 24 - 25 - 26 - 27 - 28 - 29 - 30 - 31 - 32 - 33 - 34 - 35 - 36 - 37 - 38 - 39 - 40 - 41 - 42 - 43 - 44 - 45 - 46 - 47 - 48 - 49 - 50

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