SQn78

where Cg,n is the Gaussian plume concentration for the nth set of hourly meteorological measurements and N is the total number of measurements. In prospective analyses performed to support permitting or licensing applications, background meteorological data are collected for at least a year (i.e., N = 8760, corresponding to 365 days of hourly measurements) and preferably longer. If Eq. 7.8 is applied to each node on a grid surrounding the release point, a map of concentration isopleths, such as illustrated in Figure 7.7, can be produced.

7.3.2.2 Sector-Averaged Approximation The sector-averaged approximation

(NRC 1977), which is not as computationally intensive as the summation of Gaussian plumes, is used by the Nuclear Regulatory Commission in the licensing of nuclear power plants. The region surrounding the release is divided into 16 sectors, each centered on one of the 16 compass points (N, NNE, NE, ENE, etc.). The sector is that region enclosed by two radii separated by the angle d from the point of release and the arc between the radii (Figure 7.8). Based on observations for each hourly period, a single sector is identiPed as the primary wind direction and the concentration (i.e., the sector-averaged concentration) is taken to be constant across the sector arc at a given downwind distance x.

The sector-averaged concentration is obtained by using the principle of conservation of mass and the predictions of the Gaussian plume model. The contaminant Bux leaving the sector at x is jSA = uHCSAxQ, where jSA is the sector-averaged Bux, H an arbitrary height, and CSA the (constant) sector-averaged concentration at x. The Bux for a Gaussian plume is

ISOPLETHS

Figure 7.7 Concentration isopleths in the vicinity of a release point.

ISOPLETHS

Figure 7.7 Concentration isopleths in the vicinity of a release point.

Figure 7.8 Sector-averaged approximation.

jGP = uH J"^ Cgp dy where CGP is concentration based on the Gaussian plume approximation, conservation of mass requires these Buxes to be equal, so

Substituting for CGP, Eq. 7.9 becomes

1 So

However, because the wind blows into the given sector only part of the time, a factor, f, is multiplied by the result to account for the fraction of time during the averaging period that winds blow into the sector. This yields

If the 16 compass points, (i.e., E, WSW, NE, etc.) are used to tabulate hourly meteorological observations, it is convenient to dePne a sector as a 360j/16 = 22.5j slice of the region surrounding the release point. Substituting Q = 22.5j/180j p into Eq. 7.11 and simplifying yields

Csa = J--exp I- 2—2" (7.12) \n n u—zx | 2—z )

However, V27p(8/p) = 2.032 , so this result may be approximated by

When used in conjunction with hourly meteorological data, the sector-averaged concentration is calculated by

X j=A i=1 U—z,j where I is the number of wind speed groups and fu is the fraction of time that winds blow into the given sector under stability j and with speed ui. Hourly meteorological observations for a year or several years are processed to yield tabulated values of ¡¡j, which comprise the joint frequency distribution of wind direction, wind speed, and stability class.

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