Campbell-scientific CR9000X Measurement and Control System Manuel d'utilisateur Page 223

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Section 6. Data Table Declarations and Output Processing Instructions
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 may be expressed as the deviation about the mean speed,
ss'S
ii
=
+
Equating the two expressions for Cos (
θ) and using the previous equation for
;
s
i
12
2
−=+(')/ /(')Θ
iii
UsS
(')
Θ
i
2
(') / (')'/ '/ΘΘ
iiii
U S sS sS
22
22 2=− +
(')Θ
i
2
Solving for , one obtains;
i
Summing over N samples and dividing by N yields the variance of
Θu.
Note that the sum of the last term equals 0.
(( )) ( ')/ ( /) (( ') ')/
σ
ΘΘ ΘuNUSsNS
iii
i
N
i
N
22 2
11
21==
==
) /Θ sNS
(( ') '
ii
2
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 Resources Laboratory, NOAA, Idaho Falls,
ID; and MERDI, Butte, MT. In these tests, the maximum differences in
σσ
()((')/) ()(( /))
//
ΘΘ ΘuNuUS
i
==
212 12
21 and
have never been greater tan a few degrees.
The final form is arrived at by converting from radians to degrees (57.296
degrees/radian).
σ
()(( /)) ( /)
//
ΘuUS US=− =21 811
12 12
6-39
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