Ting-i Wang, G. R. Ochs, and R. S. Lawrence, "Wind measurements by the temporal cross-correlation of the optical scintillations," Appl. Opt. 20, 4073-4081 (1981)
Various methods of correlation analysis that have been used to deduce crosswind from a drifting scintillation pattern are briefly described and then compared with regard to their immunity to noise and their accuracy when faced with nonuniformities along the propagation path or changes in the characteristics of the turbulence. Of the techniques considered, none is ideal; but a new technique, using complete knowledge of the cross-covariance function, proves to be advantageous in a wide variety of situations.
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Result of Computer Simulation Giving Measured Crosswind Velocities for Five Techniques when Faced with a Crosswind that Varies Along Propagation Path a
Technique
σvx
σvy
Peak
Slope
Frequency
Briggs
Covariance
0.25
0.25
1.14
1.00
1.02
1.00
1.06
0.5
0.5
1.52
1.01
1.12
0.99
1.31
1.0
1.0
2.50
1.01
1.47
0.99
2.02
σvx and σvy are, respectively, the standard deviation normalized to mean crosswind of the horizontal and vertical crosswind components.
is assumed uniform along the path. Mean velocity
= 1.00.
Table II
Result of Computer Simulation Giving Measured Crosswind Velocities for Five Techniques when Faced with Nonuniform Distribution Along the Propagation Path of
a
Technique
u0
Peak
Slope
Frequency
Briggs
Covariance
0.075
1.04
1.03
0.97
1.01
1.01
0.175
1.25
1.16
0.97
1.14
1.07
0.275
1.38
1.33
0.97
1.27
1.17
0.375
1.21
1.42
0.98
1.20
1.17
0.475
1.04
1.11
1.03
1.05
1.06
0.575
0.89
0.77
1.03
0.93
0.93
0.675
0.81
0.64
0.98
0.85
0.84
0.775
0.79
0.67
0.98
0.84
0.82
0.875
0.92
0.82
0.98
0.94
0.91
0.975
0.99
0.98
0.98
0.98
0.99
Largest deviation
38%
42%
3%
27%
18%
Standard deviation
20%
27%
3%
15%
12%
Nonuniformity considered is a tenfold increase in
in the 1/10 of the path centered on u0. Wind velocity is assumed uniform along the path.
Table III
Result of Computer Simulation Giving Measured Crosswind Velocities for Five Techniques when Faced with Uncorrelated Nonuniform Distributions of Wind and
Along the Path a
Technique
σvx
σvy
Peak
Slope
Frequency
Briggs
Covariance
0
0
0.95
0.94
0.98
0.94
0.96
0
0.5
1.22
0.94
1.16
0.99
1.14
0.5
0
1.00
0.89
0.95
0.87
0.90
0.5
0.5
1.33
0.89
1.10
0.89
1.15
Largest deviation
33%
11%
16%
13%
15%
Standard deviation
23%
10%
11%
10%
12%
is assumed to be a log-normal random variable with a standard deviation of 1 decade.
Table IV
Our Qualitative Evaluation of Effectiveness of Five Wind-Measuring Techniques when Faced with Various Disturbing Factors
Peak
Slope
Frequency
Briggs
Covariance
Formula
Vs ~ S0
Wind fluctuation
P
E
A
E
P
fluctuation
P
P
E
P
A
incoherent
E
P
A
P
E
Noise
coherent
P
P
A
P
E
Saturation resistance
E
A
P
E
E
Spectrum influence
E
A
P
E
E
Ease of implementation
P
A
E
P
P
Direction
Yes
Yes
No
Yes
Yes
E, excellent; A, average; P poor.
Table V
Tabulation of Observed Standard Deviations of the Ratio of Various Optical Measurements to Propeller Anemometer Measurements a
Date
Path length (m)
Range of crosswind speeds (m/sec)
Covariance
Slope
Freq. zero cross
Autocorrelation
9/28/76
83
1.5–2.6
0.03
0.06
9/29/76
0.02
0.02
9/30/76
0.02
0.02
9/20/76
500
0.5–1.4
0.07
0.08
9/21/76
0.5–7.2
0.11
0.05
9/8/76
500
0.7–1.9
0.12
0.21
11/6/76
1–2.3
0.09
0.08
11/7/76
1–5
0.06
0.09
6/2/77
500
1.2–2.3
0.16
0.06
9/1/77
0.9–2.3
0.23
0.09
9/2/77
1.7–3.9
0.08
0.03
8/2/77
500
0.5–2.2
0.11
0.26
8/3/77
0.5–2.4
0.12
0.30
6/5/78
500
1.3–1.7
0.14
0.08
0.08
6/6/78
1.3–2.9
0.13
0.08
0.12
5/18/78
500
1–7
0.08
0.19
5/19/78
1–3.5
0.15
0.27
0.32
5/25/78
1–4
0.11
0.12
0.07
5/30/78
1–3.7
0.10
0.20
0.26
5/31/78
1–2
0.12
0.24
0.22
Each measurement was a 1-h average. The last five observations were made during rain in an effort to test the noise immunity of the various methods.
Tables (5)
Table I
Result of Computer Simulation Giving Measured Crosswind Velocities for Five Techniques when Faced with a Crosswind that Varies Along Propagation Path a
Technique
σvx
σvy
Peak
Slope
Frequency
Briggs
Covariance
0.25
0.25
1.14
1.00
1.02
1.00
1.06
0.5
0.5
1.52
1.01
1.12
0.99
1.31
1.0
1.0
2.50
1.01
1.47
0.99
2.02
σvx and σvy are, respectively, the standard deviation normalized to mean crosswind of the horizontal and vertical crosswind components.
is assumed uniform along the path. Mean velocity
= 1.00.
Table II
Result of Computer Simulation Giving Measured Crosswind Velocities for Five Techniques when Faced with Nonuniform Distribution Along the Propagation Path of
a
Technique
u0
Peak
Slope
Frequency
Briggs
Covariance
0.075
1.04
1.03
0.97
1.01
1.01
0.175
1.25
1.16
0.97
1.14
1.07
0.275
1.38
1.33
0.97
1.27
1.17
0.375
1.21
1.42
0.98
1.20
1.17
0.475
1.04
1.11
1.03
1.05
1.06
0.575
0.89
0.77
1.03
0.93
0.93
0.675
0.81
0.64
0.98
0.85
0.84
0.775
0.79
0.67
0.98
0.84
0.82
0.875
0.92
0.82
0.98
0.94
0.91
0.975
0.99
0.98
0.98
0.98
0.99
Largest deviation
38%
42%
3%
27%
18%
Standard deviation
20%
27%
3%
15%
12%
Nonuniformity considered is a tenfold increase in
in the 1/10 of the path centered on u0. Wind velocity is assumed uniform along the path.
Table III
Result of Computer Simulation Giving Measured Crosswind Velocities for Five Techniques when Faced with Uncorrelated Nonuniform Distributions of Wind and
Along the Path a
Technique
σvx
σvy
Peak
Slope
Frequency
Briggs
Covariance
0
0
0.95
0.94
0.98
0.94
0.96
0
0.5
1.22
0.94
1.16
0.99
1.14
0.5
0
1.00
0.89
0.95
0.87
0.90
0.5
0.5
1.33
0.89
1.10
0.89
1.15
Largest deviation
33%
11%
16%
13%
15%
Standard deviation
23%
10%
11%
10%
12%
is assumed to be a log-normal random variable with a standard deviation of 1 decade.
Table IV
Our Qualitative Evaluation of Effectiveness of Five Wind-Measuring Techniques when Faced with Various Disturbing Factors
Peak
Slope
Frequency
Briggs
Covariance
Formula
Vs ~ S0
Wind fluctuation
P
E
A
E
P
fluctuation
P
P
E
P
A
incoherent
E
P
A
P
E
Noise
coherent
P
P
A
P
E
Saturation resistance
E
A
P
E
E
Spectrum influence
E
A
P
E
E
Ease of implementation
P
A
E
P
P
Direction
Yes
Yes
No
Yes
Yes
E, excellent; A, average; P poor.
Table V
Tabulation of Observed Standard Deviations of the Ratio of Various Optical Measurements to Propeller Anemometer Measurements a
Date
Path length (m)
Range of crosswind speeds (m/sec)
Covariance
Slope
Freq. zero cross
Autocorrelation
9/28/76
83
1.5–2.6
0.03
0.06
9/29/76
0.02
0.02
9/30/76
0.02
0.02
9/20/76
500
0.5–1.4
0.07
0.08
9/21/76
0.5–7.2
0.11
0.05
9/8/76
500
0.7–1.9
0.12
0.21
11/6/76
1–2.3
0.09
0.08
11/7/76
1–5
0.06
0.09
6/2/77
500
1.2–2.3
0.16
0.06
9/1/77
0.9–2.3
0.23
0.09
9/2/77
1.7–3.9
0.08
0.03
8/2/77
500
0.5–2.2
0.11
0.26
8/3/77
0.5–2.4
0.12
0.30
6/5/78
500
1.3–1.7
0.14
0.08
0.08
6/6/78
1.3–2.9
0.13
0.08
0.12
5/18/78
500
1–7
0.08
0.19
5/19/78
1–3.5
0.15
0.27
0.32
5/25/78
1–4
0.11
0.12
0.07
5/30/78
1–3.7
0.10
0.20
0.26
5/31/78
1–2
0.12
0.24
0.22
Each measurement was a 1-h average. The last five observations were made during rain in an effort to test the noise immunity of the various methods.