Campbell Scientific CR200/CR200X-series Dataloggers - Manual (Page 136)

Section 11. Programming Resource Library
where
Figure 47: 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;
Summing (Θ
i
') 2 over N samples and dividing by N yields the variance of Θu.
Note that the sum of the last term equals 0.
The term,
is 0 if the deviations in speed are not correlated with the deviation in direction.
This assumption has been verified in tests on wind data by CSI; the Air
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