a. Wave Direction Mean Angular Difference, <∆θ>.
∑ sin (Yi - X i )2
-1
∆θ = tan
(5)
2
∑ cos (Yi - X i )
b. Standard Deviation of Wave Direction Mean Angular Difference, σθ.
ε = 1 - ( sin ∆θ ) + ( cos ∆θ )
2
2
(6)
σθ = sin -1 ε 1 + 0.1547ε 3
(7)
c. Wave Direction Root-Mean-Square Error RMSEθ.
{
}
1
∑ cos Yi - cos X i - ( cos Y - cos X )
2
RMSEU =
(8)
N
{
}
1
∑ sin Yi - sin X i - ( sin Y - sin X )
2
RMSEV =
(9)
N
2
2
RMSEθ = RMSEU + RMSEV
(10)
where subscripts U and V indicate the u-vector and v-vector components.
d. Wave Direction Vector Scatter Index SIθ.
RMSEθ
SIθ =
*100
(11)
2
2
+ sin X
cos X
e. Wave Direction Vector Correlation Coefficient Rθ.
51
Chapter 5 Video-Based Wave Direction Measurement
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