1. science
2. physics
3. optics

SARS 2014
MONOSTATIC AND BISTATIC SODAR ERRORS DUE TO
SOUND BEING CARRIED DOWNSTREAM (WIND DRIFT)
Stuart Bradley and Alex Strehz
Physics Department, University of Auckland
SARS 2014
MOTIVATION
Over the years there have been a number of papers on acoustic refraction influences on sodar
winds. There have also been a few papers on wind drift, or the effect of the transmitted sound being
carried downwind. Refraction and wind drift both result in scattering from a place other than straightline propagation, so will affect the scattering angle and hence the Doppler shift.
Predicted errors due to these “beam wander” effects are large. But the errors are not seen in sodar
data.
However, we noticed large effects in two new sodar designs from our lab: a bi-static sodar and an
‘urban’ sodar which has a wide transmitter beam and narrow receiver beams.
None of the earlier works developed a theory or model which included the finite beam width which
sodars have. Also none of the earlier works produced measurements which unequivocally
demonstrated beam wander.
We felt it was time to really understand what is going on.
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2
SARS 2014
WIND DRIFT
REFRACTION
z
Height z
Height z
t
t
For example, a constant sound speed gradient gives propagation in a
circular arc of radius
R
c
e.g. for a temperature gradient dT/dz = 0.01 K m-1, and transmitter
zenith angle t = 18, then R = 2x105 m. Also
z
R
so the ray zenith angle at the receiver has changed by only 0.06 for
scattering from z = 100 m.
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For constant wind, the upward propagation direction does not change,
but the sound is blown downwind (blue arrows).
A greater backward zenith angle, r , is needed for the reflected ray to
reach the monostatic receiver, since the reflected ray is also blown
downwind.
dc
sin t
dz
sin  z  sin t 
r
Here
 1
1
tan r  tan t  M 

 cos t cos r



where M = u/c is the Mach number. For t = 18, and u = 10 m s-1, t
= 21, and change of 3.
CONCLUSION: Wind drift is much bigger effect than refraction.
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SARS 2014
2D WIND DRIFT
Height z
t
r
Assuming small angles, r  t+2M
Doppler shift f /fT = -(sinr + sint)M  -2Msin t-2M 2 giving a fractional error of M/sint
For example, if u = 10 m s-1 and t = 18, then u/u = 0.095. This is a 9.5% error in estimated wind
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4
SARS 2014
2D WIND DRIFT WITH FINITE BEAMS
Height z
Lower
Transmit
Doppler
Receive
beam
Higher
receive
Doppler
Shifted
Transmit
beam
The spectral peak is from a region of lower transmit Doppler
and higher receiver Doppler.
If the beam widths are the same, there is no resulting error
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Height z
Lower
Transmit
Doppler
Higher
receive
Doppler
Receive
beam
Transmit
beam
With asymmetry, the wider beam ‘wins’.
M  2r  2r 
Fractional wind speed error 
1
1
sin t  t2  t2 
1
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SARS 2014
MAGNITUDE OF ERROR (2D)
Fortunately, monostatic sodars use the
same transducers for transmit and
receive so r= t.
Fractional error in estimated wind
0.06
0.04
5 m/s
10 m/s
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1
0
Ray solution r= 0
0.5
1
r/t
1.5
2
M  2r  2r 
Fractional wind speed error 
1
1
sin t  t2  t2 
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1
6
SARS 2014
3D CASE
In practice, beams are 3D. Allowing for a bi-static receiver baseline b, and a
general Mach vector M,
z
2
f  r t 
R t
 1  2  R
 
     M      M  1  M    M    
fT  r t 
R t
 R 
R
 
Mt
t
For a phased-array bi-static sodar the drift error is zero if t = r . But this is not
generally the case.
R
1.0
r
x
0.8
y
b
Receiver
40m
upwind
Mr
-0.02
-0.01
Height z
Normalised
spectral
power
0.6
0.4
Cross-wind
0.2
0.0
0.00
df / fT
Receiver
40m
downwind
0.01
Transmit
beam
Receive
beam
0.02
Bi-static sodar with z = 80 m and t = r .
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7
BI-STATIC SODAR DATA
SARS 2014
Asymmetric transmitter and receiver.
Doppler shift measurements when r= t = 5,
compared with Doppler for r= 18 and t = 5
250
Apparent height of scattering volume
u
r
uh/c
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h/tanr
b
Height from timing [m]
h
200
h+(h2+b2)1/2=ct
h = h[1+M(1+sinr)/cosr]
150
100
Zero wind, zero gradients
50
Measurements
0
0
uh/(c sinr)
50
100
150
Height from steering [m]
h=btan r
200
250
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SARS 2014
MONOSTATIC 3D
Normalised
spectral
power
1.0
1.0
0.8
0.6
t = 5, r = 2
0.8
0.6
t = 5, r = 5
0.4
0.4
0.2
0.0
0.00
df/fT
-0.01
t = r
Wind at 0
t = 2,
r = 5
With vertical transmission, u = 10 m s-1
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Normalised
spectral
power
0.01
-0.03
-0.02
t = r
0.2
t = r
Wind at 180
Wind at 90
0.0
-0.01
0.00
df / fT
0.01
0.02
0.03
Transmission in x-z plane at 18 zenith, M = 10 m s-1/ 340 m s-1
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URBAN SODAR
SARS 2014
A monostatic sodar with
• Transmitter = single vertical beam
• Receiver = N beams tilted at r
• Wind speed error  1/(Nsinr) is similar to conventional monostatic
sodars, but r is smaller and N is larger.
Receiver zenith angle r
• Advantages:
1.
measurement volumes closer
2.
single transmit beam means faster sampling
18
Equivalent to 3 beam, 18 deg
15
Urban design
12
Equivalent to 3 beam, 30 deg
9
6
3
0
0
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8
16
24
Number N of receiver beams
32
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SARS 2014
URBAN SODAR PROBLEM #1: GAIN
Transmitted beam pattern
Receiver beams
No wind
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Beam drift
11
SARS 2014
URBAN SODAR PROBLEM #2: t r
1.0
0.8
0.6
0.4
0.2
-0.02
-0.01
0.0
0.00
df / fT
0.01
0.02
Downwind receivers have smaller magnitude Doppler than upwind receivers. The cross-wind receivers
show wind approaching them. However the shift is accurately described by
(see the purple arrow).
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
2
 2r
2 M  1 2
 t

2
 r
  1  2
t





1
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SARS 2014
SUMMARY
• We have developed an accurate, general, 3D theory for wind drift
• The theory includes finite beam width for receiver and transmitter
• A simple 2D thin-slice model (with wind in the plane of the transmitter and
receiver beams) gives a simple analytic expression for wind drift in terms of
beam widths
• It is found that, for this 2D case, monostatic sodars with matched transmitter
and receiver, there is no wind drift correction (but there is loss of gain!)
• The 3D model does predict small drift effects on monostatic tilted beams
• Measurements on a bi-static sodar are consistent with these models
• Measurements on the urban sodar (vertical beam transmitted, narrow tilted
receiver beams) show wind drift effects
• It appears that the 2D thin-slice model can be used to correct wind drift error
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