or, in the case of orthogonal sensors:
Resultant mean wind direction, Θu:
Standard deviation of wind direction, σ (Θu), using Campbell Scientific
algorithm:
The algorithm for σ (Θu) is developed by noting, as shown in the figure Standard
Deviation of Direction
(p. 300), that
where
Standard Deviation of Direction
Figure 78. Standard Deviation of Direction
The Taylor Series for the Cosine function, truncated after 2 terms is:
For deviations less than 40 degrees, the error in this approximation is less than
1%. At deviations of 60 degrees, the error is 10%.
The speed sample can be expressed as the deviation about the mean speed,
Equating the two expressions for Cos (θ') and using the previous equation for s
i
;
Solving for (Θ
i
')
2
, one obtains;
300
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