Summing (Θ
i
')
2
over N samples and dividing by N yields the variance of Θu.
Note 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 Campbell Scientific;
the Air Resources Laboratory, NOAA, Idaho Falls, ID; and MERDI, Butte, MT.
In these tests, the maximum differences in
and
have never been greater than a few degrees.
The final form is arrived at by converting from radians to degrees (57.296
degrees/radian).
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