WORKBOOK
OF
ATMOSPHERIC DISPERSION
ESTIMATES
H
U.S. ENVIRONMENTAL PROTECTION AGENCY
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WORKBOOK OF
ATMOSPHERIC DISPERSION ESTIMATES
D. BRUCE TURNER
Air Resources Field Research Office,
Environmental Science Services Administration
ENVIRONMENTAL PROTECTION AGENCY
Office of Air Programs
Research Triangle Park, North Carolina
Revised 1970
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The AP series of reports is issued by the Environmental Protection
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and information of general interest in the field of air pollution.
Information presented in this series includes coverage of intramural
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Publications, Office of Air Programs, Environmental Protection
Agency, Research Triangle Park, North Carolina 27711, or from the
Superintendent of Documents.
6th printing January 1973
Office of Air Programs Publication No. AP-26
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ii
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Chapter 1 INTRODUCTION
NOTE: SEE PREFACE TO THE SIXTH PRINTING ON PAGE iii.
During recent years methods of estimating at-
mospheric dispersion have undergone considerable
revision, primarily due to results of experimental
measurements. In most dispersion problems the
relevant atmospheric layer is that nearest the
ground, varying in thickness from several hundred
to a few thousand meters. Variations in both
thermal and mechanical turbulence and in wind
velocity are greatest in the layer in contact with
the surface. Turbulence induced by buoyancy forces
in the atmosphere is closely related to the vertical
600r
500
400
300
o
200
100
temperature structure. When temperature decreases
with height at a rate higher than 5.4 °F per 1000 ft
(1CC per 100 meters), the atmosphere is in un-
stable equilibrium and vertical motions are en-
hanced. When temperature decreases at a lower
rate or increases with height (inversion), vertical
motions are damped or reduced. Examples of typ-
ical variations in temperature and wind speed with
height for daytime and nighttime conditions are
illustrated in Figure 1-1.
J L
_L
-1 0 1
234567
TEMPERATURE, "C
8 9 10 11 12
3456789
WIND SPEED, m/sec
10 11
Figure 1-1. Examples of variation of temperature and wind speed with height (after Smith, 1963).
The transfer of momentum upward or down-
ward in the atmosphere is also related to stability;
when the atmosphere is unstable, usually in the
daytime, upward motions transfer the momentum
"deficiency" due to eddy friction losses near the
earth's surface through a relatively deep layer,
causing the wind speed to increase more slowly
with height than at night (except in the lowest few
meters). In addition to thermal turbulence, rough-
ness elements on the ground engender mechanical
turbulence; which affects both the dispersion of
material in the atmosphere and the wind profile
(variation of wind with height). Examples of these
effects on the resulting wind profile are shown in
Figure 1-2.
As wind speed increases, the effluent from a
continuous source is introduced into a greater vol-
ume of air per unit time interval. In addition to
this dilution by wind speed, the spreading of the
material (normal to the mean direction of trans-
port) by turbulence is a major factor in the dis-
persion process.
The procedures presented here to estimate at-
mospheric dispersion are applicable when mean wind
speed and direction can be determined, but meas-
urements of turbulence, such as the standard de-
viation of wind direction fluctuations, are not avail-
able. If such measurements are at hand, techniques
such as those outlined by Pasquill (1961) are likely
to give more accurate results. The diffusion param-
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eters presented here are most applicable to ground-
level or low-level releases (from the surface to about
20 meters), although they are commonly applied at
higher elevations without full experimental ilida-
tion. It is assumed that stability is the same
throughout the diffusing layer, and no turbulent
transfer occurs through layers of dissimilar stability
characteristics. Because mean values for wind direc-
tions and speeds are required, neither the variation
of wind speed nor the variation of wind direction
with height in the mixing layer are taken into ac-
count. This usually is not a problem in neutral or
unstable (e.g., daytime) situations, but can cause
over-estimations of downwind concentrations in
stable conditions.
REFERENCES
Davenport, A. G., 1963: The relationship of wind
structure to wind loading. Presented at Int.
Conf. on The Wind Effects on Buildings and
Structures, 26-28 June 63, Natl. Physical Lab-
oratory, Teddington, Middlesex, Eng.
Pasquill, F., 1961: The estimation of the dispersion
of wind borne material. Meteorol. Mag. 90,
1063, 33-49.
Smith, M. E., 1963: The use and misuse of the at-
mosphere, 15 pp., Brookhaven Lecture Series,
No. 24, 13 Feb 63, BNL 784 (T-298) Brook-
haven National Laboratory.
600
500
.400
URBAN AREA
GRADIENT WIND
SUBURBS
LEVEL COUNTRY
Figure 1-2. Examples of variation of wind with height over different size roughness elements (Tigures are percentages
of gradient wind); (from Davenport 1963).
ATMOSPHERIC DISPERSION ESTIMATES
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Chapter 2BACKGROUND
For a number of years estimates of concentra-
tions were calculated either from the equations of
Sutton (1932) with the atmospheric dispersion
parameters C3-, C,, and n, or from the equations of
Bosanquet (1936) with the dispersion parameters
p and q.
Hay and Pasquill (1957) have presented experi-
mental evidence that the vertical distribution of
spreading particles from an elevated point is re-
lated to the standard deviation of the wind eleva-
tion angle, OK, at the point of release. Cramer (1957)
derived a diffusion equation incorporating standard
deviations of Gaussian distributions: ;> calculated from
wind measurements made with a bi-directional
wind vane (bivane). Values for diffusion param-
eters based on field diffusion tests were suggested
by Cramer, et al. (1958) (and also in Cramer 1959a
and 1959b). Hay and Pasquill (1959) also pre-
sented a method for deriving the spread of pollut-
ants from records of wind fluctuation. Pasquill
(1961) has further proposed a method for esti-
mating diffusion when such detailed wind data are
not available. This method expresses the height
and angular spread of a diffusing plume in terms of
more commonly observed weather parameters. Sug-
gested curves of height and angular spread as a
function of distance downwind were given for sev-
eral "stability" classes. Gifford (1961) converted
Pasquill's values of angular spread and height into
standard deviations of plume concentration distri-
bution,
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Chapter 3 ESTIMATES OF ATMOSPHERIC DISPERSION
This chapter outlines the basic procedures to
be used in making dispersion estimates as sug-
gested by Pasquill (1961) and modified by Gifford
(1961).
COORDINATE SYSTEM
In the system considered here the origin is at
ground level at or beneath the point of emission,
with the x-axis extending horizontally in the direc-
tion of the mean wind. The y-axis is in the hori-
zontal plane perpendicular to the x-axis, and the
z-axis extends vertically. The plume travels along
or parallel to the x-axis. Figure 3-1 illustrates the
coordinate system.
DIFFUSION EQUATIONS
The concentration, x, of gas or aerosols (parti-
cles less than about 20 microns diameter) at x,y,z
from a continuous source with an effective emission
height, H, is given by equation 3.1. The notation
used to depict this concentration is \ (x,y,z;H).
H is the height of the plume centerline when it
becomes essentially level, and is the sum of the
physical stack height, h, and the plume rise, AH.
The following assumptions are made: the plume
spread has a Gaussian distribution (see Appendix
2) in both the horizontal and vertical planes, with
standard deviations of plume concentration distri-
bution in the horizontal and vertical of ery and a,,
respectively; the mean wind speed affecting the
plume is u; the uniform emission rate of pollutants
is Q; and total reflection of the plume takes place
at the earth's surface, i.e., there is no deposition
or reaction at the surface (see problem 9).
(x,y,z;H) =
(3.1)
*Note: exp a/b = e~»/b where e is the base of natural logarithms
and is approximately equal to 2.7183.
(x,-y,Z)
(x,-y,0)
Figure 3-1. Coordinate system showing Gaussian distributions in the horizontal and vertical.
Estimates
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Any consistent set of units may be used. The most
common is:.
X (g m~3) or, for radioactivity (curies m~s)
Q (g sec"1) or (curies sec"1)
u (m sec"1)
6
1
Day
Night
J,) Incoming Solar Radiation Thinly Overcast
' , .. -' -=0/0
Strong
A
A-B
B
C
C
Moderate
A-B
B
B-C
C-D
D
Slight -4/8 Low Cloud
B
C E
C D
D D
D D
Cloud
F
E
D
D
The neutral class, D, should be assumed for overcast conditions during
day or night.
"Strong" incoming solar radiation corresponds
to a solar altitude greater than 60° with clear skies;
"slight" insolation corresponds to a solar altitude
from 15° to 35° with clear skies. Table 170, Solar
Altitude and Azimuth, in the Smithsonian Mete-
orological Tables (List, 1951) can be used in deter-
mining the solar altitude. Cloudiness will decrease
incoming solar radiation and should be considered
along with solar altitude in determining solar radia-
tion. Incoming radiation that would be strong
with clear skies can be expected to be reduced to
moderate with broken (% to % cloud cover) mid-
dle clouds and to slight with broken low clouds.
An objective system of classifying stability from
hourly meteorological observations based on the
above method has been suggested (Turner, 1961).
These methods will give representative indica-
tions of stability over open country or rural areas,
but are less reliable for urban areas. This differ-
ence is due primarily to the influence of the city's
larger surface roughness and heat island effects
upon the stability regime over urban areas. The
greatest difference occurs on calm clear nights; on
such nights conditions over rural areas are very
stable, but over urban areas they are slightly un-
stable or near neutral to a height several times the
average building height, with a stable layer above
(Duckworth and Sandberg, 1954; DeMarrais, 1961).
ATMOSPHERIC DISPERSION ESTIMATES
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Some preliminary results of a dispersion experi-
ment in St. Louis (Pooler, 1965) showed that the
dispersion over the city during the daytime behaved
somewhat like types B and C; for one night experi-
ment CT}. varied with distance between types D and E.
ESTIMATION OF VERTICAL AND
HORIZONTAL DISPERSION
Having determined the stability class from
Table 3-1, one can evaluate the estimates of o-y and
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