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11.2 General Gaussian Dispersion Model 327

In order to use Eq. (11.16), the wind speed at one elevation has to be known.
0 0
This pair of data, given notations of u ; zð Þ, allows us to determine the friction
speed using Eq. (11.18).
ku 0
u ¼ ð11:18Þ
0
ð
ln z =z 0 Þ
Example 11.2: Wind speed profile
In a rural area, the friction height is z 0 ¼ 0:25 m, and the wind speed measured at
10 m height is 4 m=s under neutral condition. Plot the vertical wind speed profile.
Solution
Equation (11.18) gives

u u 10 4
¼ ¼ ¼ 1:084:
k ln z 10 =z 0 Þ ln 10=0:25Þ
ð
ð
Then we have the velocity as a function of elevation:

z
u
u ¼ ln ¼ 1:084 ln 4zðÞ
k z 0
The plot is shown in Fig. 11.6. This profile is similar to what we saw in
boundary layer analysis in Chap. 2. With the decrease in speed change rate along
increasing elevations, the friction effect becomes negligible at high elevation.

11.2.6.2 Wind Speed Profile in Stable Atmosphere

For non-neutral conditions, the wind speed depends strongly on the stability of the
atmosphere, which in turn depends on the heat transfer q between the atmosphere
and the ground. We have to put forward a new but important parameter, Obukhov
Length, after the Russian scientist A.M. Obukhov. He set the foundation of modern
micrometeorology by introducing a universal length scale for exchange processes in
the surface layer in 1946 [9].
3
q c p T 0 u
0
L ¼ ð11:19Þ
g qk
Like surface roughness height, Obukhov length is not a physical length either. It
is related to the stability indicator at different elevations. Researchers in the area of
air dispersion modeling have developed a variety of equations for the calculation of
Obukhov Length, however, the simple yet practical equation given by Seinfeld and
Pandis [17] is widely used in air dispersion models.