Manual

Appendix B. Measurement Names and Meanings
Standard deviation of wind direction, σ(Θu), using Campbell Scientific
algorithm:
σ(Θu)=81(1-
U
/S)
1/2
The algorithm for σ(θu) is developed by noting (Figure B.3-3) that
Cos U / s ; where
ii
(') '
Θ
Θ
Θ
Θ
ii
u
i
=
=
−
FIGURE B.3-3. Standard Deviation of Direction
The Taylor Series for the Cosine function, truncated after 2 terms is:
Cos ( ') ( ') / ΘΘ
ii
≅− 1
2
2
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 +
Solving for
(') Θ
i
2
, one obtains;
(') / (')'/ '/ ΘΘ
iiii
U S sS sS
22
22 2 =− − +
i
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.
(( )) (')/ ( /) ((')')/ σ ΘΘ Θ uNUSs
ii
i
N
i
N
22 2
11
21 ==−−
==
∑∑
NS
i
B-6