Geoscience Reference
In-Depth Information
For the parameter of mechanical scattering
˃
zm
the ratio to the rate of mechanical
turbulence
˃
wm
is not so simple as in the case of convective turbulence. This is
connected with the fact that the size of the scale characterizing the mechanical scat-
tering, in contrast to the case of convective changes with altitude, is less than the
convection scale. Therefore, for the unstable state the following dependences are used:
(
2
2u
2
t
2
r
zmu
¼
1
:
exp
0
ð
:
6tu
=
Þ
tu
=
;
h
s
for
h
s
\
1
2
r
zm
¼
2
zmu
¼ 1
2u
2
t
2
r
:
exp
ð
0
:
6
Þ
for
tu
=
h
s
1
For stable conditions the following approximation is valid:
zmu
1
þ
1
:
11tu
=
2
2
r
zm
¼
r
ð
L
Þ
where L is the Monin-Obukhov length.
Thus, both terms on the right in formula (
5.14
) are estimated. Now determine the
˃
ʻ
parameter in Eq. (
5.11
). The characteristic of horizontal scattering of the pol-
lutant is well approximated with the formula:
1
=
2
25w
2
0
:
u
u
w
=
uz
i
þ
u
2
r
k
¼
ð
5
:
19
Þ
1
þ
0
:
9
first and second terms in brackets represent the contri-
bution of convective and mechanical turbulence, respectively. For nocturnal con-
ditions, the
In this expression the
r
st term is equal to zero. For the stable atmosphere and at weak winds,
the ratio u
=
u decreases rapidly with the growing stability. Nevertheless, numerous
observations have shown that the horizontal scattering with an hourly averaging can
exceed the values for the unstable atmosphere. The horizontal rate
fluctuates with
the constant amplitude about 0.5 m s
−
1
. As the horizontal scattering remains pro-
portional to fluctuations of horizontal wind, the u
*
parameter in Eq. (
5.19
) for the
case of stable strati
fl
cation can be changed for 0.5 m s
−
1
. It means that
˃
ʻ
will never
be less than 0
u=
u.
Estimate the parameter of horizontal scattering:
:
5
d
.
p
r
k
f
¼
D
p
u;
2
where
d is the change of wind direction in radians.
According to the Eq. (
5.11
), the accuracy of calculation of the aerosol con-
centration at a point with coordinates (
D
) depends substantially on wind speed.
An estimate of the aerosol density in a given space volume depends on the accuracy
of its estimation at a given height. For instance, in the case of unstable strati
ˆ
,
ʻ
cation
the wind speed is approximated with its value at a height of the source, and under
stable conditions the wind speed is calculated by the vertical averaging of its values.
According to Monin and Obukhov (1954), we have
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