Plume Dispersion Coefficients, sigma_y s_y and sigma_z s_z

s_y = horizontal dispersion coefficient s_z = vertical dispersion coefficient

These s_y and s_z 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 s_y and s_z 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 = cx^d + f sy = ax^b

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 s_y 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 s_z 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