Plume Dispersion Coefficients, sigmay  sy  and  sigmaz  sz

sy = horizontal dispersion coefficient    sz = vertical dispersion coefficient

These sy and sz dispersion coefficients (sometimes called standard deviations) have units of meters and correspond to an air pollutant sampling time of 10 minutes.  The dispersion coefficients are function of the atmospheric stability class and the downwind distance x from the air pollutant emission source.  The magnitude of the sy and sz dispersion coefficients can be estimated using the equations reported by D. O. Martin (1976) “The Change of Concentration Standard Deviations with Distance”, J. Air Pollution Control Assoc. Vol 24 p 832.

sz = cxd + f         sy = axb

Values for 4 of the stability dependent constants (a, c, d, and f) are given in the table.  Note that there are different values for the downwind distance x less than 1 km and x greater than 1 km.  b is always = 0.894.    The units of x are in kilometers.

 Stab   Class x < 1 km x > 1 km a c d f c d f A      1 213 440.8 1.041 9.27 459.7 2.094 -9.6 B      2 156 106.6 1.149 3.3 108.2 1.098 2.0 C      3 104 61.0 0.911 0.0 61.0 0.911 0.0 D      4 68 33.2 0.725 -1.7 44.5 0.516 -13.0 E      5 50.5 22.8 0.675 -1.3 55.4 0.305 -34.0 F      6 34 14.35 0.740 -0.35 62.6 0.180 -48.6

Approximate values of sy as a function of downwind distance x in km are shown in the table below.

 Downwind sy Values (meters) Distance    x  (km) A B C D E F 0.1 27 19 13 8 6 4 0.2 50 36 23 15 11 8 0.4 94 67 44 29 21 14 0.7 155 112 74 48 36 24 1.0 215 155 105 68 51 34 2.0 390 295 200 130 96 64 4.0 550 370 245 180 120 7.0 890 610 400 300 200 10.0 1190 840 550 420 275 20.0 2150 1540 1000 760 500

Approximate values of sz as a function of downwind distance x in km are shown in the table below:

 Downwind sz Values (meters) Distance   x  (km) A B C D E F 0.1 14 11 7 5 4 2 0.2 29 20 14 8 6 4 0.4 72 40 26 15 11 7 0.7 215 73 43 24 17 11 1.0 455 110 61 32 21 14 2.0 1950 230 115 50 34 22 4.0 500 220 77 49 31 7.0 780 360 109 66 39 10.0 1350 510 135 79 46 20.0 2900 950 205 110 60