∑ (cos X - cos X )(cos Y - cos Y )
i
i
=
RU
(12)
∑ ( X - cos X ) ∑ (Y - cos Y )
2
2
i
i
∑ (sin X - sin X )(sin Y - sin Y )
i
i
RV =
(13)
∑ ( X - sin X ) ∑ (Y - sin Y )
2
2
i
i
1
Rθ =
(RU 2 + RV 2 )
(14)
2
Figure 37 contains scatterplots of wave directions near the spectral peak for
collocated CIIS and ADV observations. Only CIIS observations meeting the
coherence cutoff criterion were selected for comparison. Table 6 summarizes the
scatterplots. The statistics show good correlation between the two measurement
techniques, with low scatter indices. Where the CIIS coherence cutoff criterion
is met, wave directions are typically within the reported margin of error for the
ADV probe measurements.
Table 6
Structure 1: ADV versus CIIS Validation Statistics for Mean Wave
Directions Measured Near the Spectral Peak
σθ
<∆θ>
RMSEθ
Experimental
deg
deg
deg
SIθ
Rθ
Arrangement
a
Structure 1
2.64
4.57
4.58
8
0.89
Structure 2
1.98
7.02
6.99
12
0.79
b
Structure 3
-5.16
13.08
13.14
24
0.77
c
Structure 4
-1.27
7.78
7.66
14
0.93
a
Structure 1: Only experiments X4, X5, X6 analyzed.
b
Structure 3: X1c and X2c did not meet coherence cutoff criterion.
c
Structure 4: X2 did not meet coherence cutoff criterion.
Results
Analysis of pixel array timestacks resulted in estimates of mean spectral
density S( f ) and vector-mean wave direction θm( f ). To demonstrate the video
system application, peak vector-mean wave direction for Structure 1, Experiment
2 (random wave, fpeak = 1.25 Hz) is indicated by arrows (scaled by wave celerity)
superimposed on a rectified snapshot of the wave field in Figure 38. Arrows
with a circled tail represent directions obtained from analyses meeting the strict
coherence cutoff criterion. Some arrows without circled tails are spurious in
direction and magnitude in the diffraction area behind the breakwater.
52
Chapter 5 Video-Based Wave Direction Measurement
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