CR10X Reference Manual
11-4
Standard deviation of wind direction,
σσσσ
(
Θ
Θ
Θ
Θ
1)
, using Yamartino algorithm:
σσσσ
(
Θ
Θ
Θ
Θ
1)
=arc sin(
ε
)[1+0.1547
ε
3
]
where
ε
=[1-((Ux)
2
+(Uy)
2
)]
1/2
and Ux and Uy are as defined above.
Resultant mean horizontal wind speed, U:
U
=(Ue
2
+Un
2
)
1/2
U
Un
Ue
Figure 11-2 Mean Wind Vector
where for polar sensors:
Ue=(
Σ
S
i
sin
Θ
i
)/N
Un=(
Σ
S
i
cos
Θ
i
)/N
or, in the case of orthogonal sensors:
Ue=(
Σ
Ue
i
)/N
Un=(
Σ
Un
i
)/N
Resultant mean wind direction,
Θ
Θ
Θ
Θ
u:
Θ
Θ
Θ
Θ
u
=Arctan (Ue/Un)
Standard deviation of wind direction,
σσσσ
(
Θ
Θ
Θ
Θ
u)
, using Campbell Scientific algo-
rithm:
σσσσ
(
Θ
Θ
Θ
Θ
u)
=81(1-U/S)
1/2
The algorithm for
σ
(
θ
u) is developed by noting (Figure 11-3) that
Cos U / s ;
where
i
i
( ')
'
Θ
Θ
Θ Θ
i
i
i
u
=
=
−
s
i
Θ
'
i
Θ
u
U
i
U
Figure 11-3 Standard Deviation of Direction
The Taylor Series for the Cosine function, truncated after 2 terms is:
Cos ( ')
( ') /
Θ
Θ
i
i
≅ −
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%.