ATMOSPHERIC POLLUTION 
numerical parameter with an average value of 0.05 
and a range from a minimum of 0.02 for low turbulence 
to a maximum of 0.15 for very turbulent air flow. 
Bosanquet and Pearson also give a formula for the 
eround-level concentration x during a brief interval 
of time due to a continuous point source, in the form 
x 6 So ex Ce Se Gor La (2) 
‘ VJ Qrpqua : DL 2g? x* 
where y is the distance crosswind from the axis of the 
smoke cloud, g is a second numerical parameter with 
an average value of 0.08, and the other symbols are as 
defined for equation (1). 
In 1947, Sutton [84] extended his treatment to cover 
elevated point sources and assigned values to the various 
parameters involved. The general expression derived is 
_ Qexp (-7'/C,2"”) 
is 1C, CO, ua (3) 
-[exp {—@ — Dy Coe) + exp {—(e+ De NCe come 
where z is distance upward; C, and C. are virtual 
diffusion coefficients for the crosswind and vertical 
directions, respectively; n is a numerical parameter 
whose value, lying between 0 and 1, is related to the 
diffusing power of the turbulence; and the other sym- 
bols are as given above. With z = 0, (8) gives the 
concentration at the surface as 
i 20 Lisl ys =) 
oa elbte tie 
and its maximum as 
_ 20 (22) 
Xm ~ exh? \Cy)? 
which occurs at a distance x» from the source, given by 
as SCHOO. (6) 
The parameter n, obtained by fitting the theoretical 
profile uw = mz”/°-™ to the observed change of wind 
speed with height, has the value 14 under average 
conditions of lapse rate, with a range from 14 for a 
large inversion to 14 for a large lapse. For average con- 
ditions, Sutton gives values of C, varying from 0.21 for 
a source at the surface to 0.07 for one at 100 m and 
values of C, from 0.12 to 0.07 for the same range of 
heights of sources; for sources at 25 m and higher the 
values of C, and C. are the same. For inversions the 
coefficients are smaller; for large lapse rates they are 
greater. The values of the numerical parameters n, C,, 
and C, given above have been obtained by Sutton from 
basic meteorological data, but their validity has been 
checked through measurement of concentrations from 
surface sources only. Their use does not give instan- 
taneous values of concentrations, but rather the average 
at a fixed point for a period of not less than three 
minutes; Sutton states that in the absence of systematic 
changes in wind direction near the surface the time- 
mean values for longer intervals are not significantly 
different. The validity of the numerical values of the 
(5) 
1141 
parameters for elevated sources has not been estab- 
lished. Figure 1 gives maximum concentrations at the 
ground and the distance from the stack at which such 
maxima occur as functions of stack height and of 
groups of vertical temperature gradients; the curves 
are derived from equations (5) and (6) above. 
MAXIMUM CONCENTRATION (MG M ©) 
0. 
0.003 | 0.01 0.04 0.1 0.4 1.0 
100 T Y, 
. LARGE INVERSION 
MODERATE INVERSION 
S ON AVERAGE 
3 oe BS LARGE LAPSE 
3 \ 
\ S 
= N 
w 
= SO 
iS 
ae 
©) 
Ww 
= 25 
10 eye ees 4 
30 4 100 400 1000 4000 10,000 
DISTANCE (M) 
Fic. 1.—Maximum ground concentrations (dashed curves) 
and distances from stack base (solid curves) at which they 
occur with various vertical temperature distributions for 
stacks of different heights, according to Sutton. Rate of emis- 
sion: 1 g sec™!. 
Lowry [52] has given an equation for maximum sur- 
face concentrations which embodies features of both 
(1) and (5). It has the form 
a 2Q [Gn 
Km = oe =) (7) 
where Xm is the time-mean concentration at a fixed 
point for a period of one hour; a, 1s the frequency 
during the hour of the most frequent wind direction at 
the top of the stack; and the other symbols are as 
defined previously. The location of the maximum 
ground concentration is also specified: its direction 
from the stack is given by the most frequent wind 
direction at the top of the stack during the hour; its 
distance is given by the empirical expression 
Im = hese c, (8) 
where o is the standard deviation of the wind direction 
in degrees during a period of 10 or 15 minutes. Equa- 
tion (8) applies only for sources at a height of the 
order of 100 m and when the range of direction is 
greater than 10 or 15 deg. The general validity of 
equations (7) and (8) has been verified by measure- 
ments of surface concentrations of oil-fog emitted from 
the 108-m experimental stack at Brookhaven National 
Laboratory. For further details and a suggested use of 
these two equations in climatological planning, see 
page 1152. 
An equation for concentrations under very stable 
conditions has been given by Barad [5]. His approach 
derives generically from Roberts’ work [70], but in- 
corporates certain modifications. Barad assumes that 
in the horizontal layer of air near an elevated source, 
the variation with height of the eddy coefficient for 
vertical transfer is sufficiently small in very stable 
