Steady-state concentration at a point (x,y,z) located downwind
from a source:
Q
1 y2 
1 (z  H )2
1 (z  H )2 
C
exp( 
) exp( 
)  exp( 
)
2 
2
2
2u y z
2y 
2 z
2 z

C: Steady-state concentration at a point (x,y,z), g/m3
Q: emission rate, g/s
u: average wind speed at source level, m/s, if H< 10 m, use u(10m)
x: distance from source, meter
y: horizontal distance from plume center line, m
z: vertical distance from ground level, m
H: effective stack height, H=h+H, h=physical stack height,
=plume rise, m
y , z : horizontal and vertical spread parameters, m, function of
distance X and stability
Special cases:
1. Ground level concentration, z=0
1 y2
1 H2
C
exp( 
) exp( 
)
2
2
u y z
2y
2 z
Q
2. Ground-level centerline concentration, y=0, z=0
1 H2
C
exp( 
)
2
u y z
2 z
Q
3. Ground-level source, H=0
1 y2
1 z2
C
exp( 
) exp( 
)
2
2
u y z
2y
2 z
Q
4. Ground-level centerline concentration, (y=0, z=0), ground
level source, H=0
Q
C
u y z
Maximum downwind ground-level concentration:
(Cu/Q)max=exp(a+b ln H+c(ln H) 2+d(lnH) 3)
a,b,c,d in Table 19.4, H in meter, and Cu/Q in m-2
usually Q known, for a given u, can get C max
Example:
Class D stability, H=100 m, Q=110 g/s, u=5 m/s, estimate C max
Solution:
Use fig. 19.9, X max= 3km, Cu/Q is 8.1E-6/m2, (Cu/Q)max=8.1E-6
C max =8.1E-6*110E+6/5=178 g/m3
Or use the above equation,
C max = 110E+6/5 exp(..)=183 g/m3, need iteration to find X max
Necessary data to apply the Gaussian models
1. Emission and source data
a. Air pollutants (species)
b.Source location
c. Other stack parameters for plume rise calculation
d. Emission profile (e.g. duration, frequency, diurnal and
seasonal variation of emission rates)
2. Transport and dispersion data
a. Wind speed and direction (e.g. hourly data at source level)
b.Atmospheric stability
c. Mixing height (e.g. height of inversion height)
d.Air temperature (e.g. hourly data at source level)
e. Joint frequency distribution of at least a and b.
3. Receptor data: location of the area of interest.
Example: given emission rate of SO2 and stack parameters,
estimate annual average concentration at a residential area 1 km
from the source.
N
Solution:
1. Find joint distribution of winds speed, direction and stability,
fi.,  fi
2. Calculate plume rise and ground-level concentration for each
meteorological class, Ci.
3. Annual concentration =  fi Ci
Joint distribution of wind speed, direction, and stability, N flow
Wind speed class
Stability Class
a
b
c
d
e
f
1
.5%
.5%
.5%
.5% .5% .5%
2
1%
1%
1%
1% 1% 1%
3
1%
1%
1%
1% 1% 1%
4
.5%
.5%
.5%
.5% .5% .5%
Joint distribution of wind speed, direction, and stability, NNW
flow
Wind speed class
Stability Class
a
b
c
d
e
f
1
.5%
.5%
.5% .5% .5% .5%
2
1%
1%
1%
1% 1% 1%
3
1%
1%
1%
1% 1% 1%
4
.5%
.5%
.5% .5% .5% .5%
Joint distribution of wind speed, direction, and stability, NNE
flow
Wind speed class
Stability Class
a
b
c
d
e
f
1
.5%
.5%
.5% .5% .5% .5%
2
1%
1%
1%
1% 1% 1%
3
1%
1%
1%
1% 1% 1%
4
.5%
.5%
.5% .5% .5% .5%
Calculate ground-level concentration due to this point source for
each meteorological class. Winds from all other directions,
ambient concentration would be background value.
Annual average concentration due to this source=0.005*C(N, 1,
a)+0.01*C(N, 2,a)+..+0.005*C(NNW, 1, a)+0.01*C(NNW,
2,a)+..+..+0.46*0
Annual average ambient concentration at this point=conc. due to this
point source + background concentration
If multi-source, annual average concentration =  fij Cij
 fij =1, for all j
Line and area sources
Line source: e.g. roadway (CO, NOx, VOC, PM)
The finite length line source (FLLS) model, e.g. CALINE 3,
Can have more than one FLLS to handle sections with different
direction, emission rate, etc.
Line and area sources: roadway, VOC emission from forests.
A virtual point source (VPS) placed upwind of the line or area
source.
If more than one virtual point source, distance between them
must be small compare to X
Concentration at the receptor = C due to each FLLS or VPS