Geoscience Reference
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(10
−
12
W) but well above the noise produced by the Browian movement of the atmo-
spheric molecules (6
10
−
19
W). The used sound frequencies of 1500-4500 Hz are
well within the sensitivity range of the human ear.
The ratio between emitted and received power is described by the SODAR
equation,
×
r
−
2
(
c
s
τ
2)
P
0
β
s
e
−
2
σ
r
P
R
=
A
ε/
+
P
bg
,
(3.11)
with the received power
P
R
, the emitted power
P
0
, the antenna efficiency
,the
effective antenna area
A
, the sound absorption in air
, the distance between the
scattering volume and the instrument
r
, the pulse duration
σ
τ
(typically between 20
β
s
(typically in the order of 10
−
11
m
−
1
sr
−
1
), the sound speed
c
s
, and the background noise
P
bg
. The background
noise also comprises contributions from ambient noise having the same sound fre-
quency, e.g. traffic noise. The ratio of the two terms on the right-hand side of the
SODAR equation is called signal-to-noise ratio (usually abbreviated as SNR). The
backscattering cross-section
and 100 ms), the backscattering cross-section
β
s
is a function of the temperature structure function
C
T
2
(Tatarskii
1971
). For a monostatic SODAR, we find (Reitebuch
1999
) when
using the wave number
k
=
2
π
/λ
,
β
s
(180
◦
)
0.00408 k
1
/
3
C
T
/
T
2
.
=
(3.12)
This equation forms an average over all scattering elements within the atmo-
spheric volume that is hit by the cone-shaped beam. The pulse duration
τ
determines
the height resolution of the instrument via the relation
z
=
0.5 c
τ
.
(3.13)
The SODAR equation above showed that the backscattered power was propor-
tional to the pulse duration, too. Therefore, the choice of the pulse duration is a
trade-off between height resolution (preferably short pulse durations) and maximum
range (preferably long durations).
The backscattered signal of a SODAR is representative for an atmospheric vol-
ume. For pulse durations of 100 ms we simultaneously receive backscatter from a
volume of 33 m depth. In a height of 500 m above ground this volume has a radius of
44 m (assuming an opening angle of the emitted sound beam of 5
◦
). Additionally,
the three-dimensional wind information has to be integrated from a full measure-
ment cycle over one vertical and two to four tilted beams. This increases the radius
of the detected atmospheric volume in 500 m height to about 150-200 m. Further,
in order to enhance the signal-to-noise ratio, averages over all measurement cycles
with 10-30 min are formed. This makes the SODAR a volume and time averaging
measurement device.
In addition to mono-frequency SODARs, multi-frequency SODARs are also
available, which emit several subsequent pulses with different frequencies within
one shot. Field tests have proved significant advantages of the multi-frequency
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