Campbell Scientific CR10X Measurement and Control System - Manual (Page 176)

SECTION 11. OUTPUT PROCESSING INSTRUCTIONS
11-2
scans when the sub-interval is 0. With a sub-
interval of 900 scans (15 minutes) the standard
deviation is the average of the four sub-interval
standard deviations. The last sub-interval is
weighted if it does not contain the specified
number of scans.
There are three Output Options that specify the
values calculated.
Option 0:
Mean horizontal wind speed, S.
Unit vector mean wind direction,
Θ1.
Standard deviation of wind direction,
σ(Θ1).
Standard deviation is calculated using the
Yamartino algorithm. This option complies
with EPA guidelines for use with straight-
line Gaussian dispersion models to model
plume transport.
Option 1:
Mean horizontal wind speed, S.
Unit vector mean wind direction,
Θ1.
Option 2:
Mean horizontal wind speed, S.
Resultant mean wind speed, U.
Resultant mean wind direction,
Θu.
Standard deviation of wind direction,
σ(Θu).
This standard deviation is calculated using
Campbell Scientific's wind speed weighted
algorithm.
Use of the Resultant mean horizontal wind
direction is not recommended for straight-
line Gaussian dispersion models, but may
be used to model transport direction in a
variable-trajectory model.
Measured raw data:
S
i
= horizontal wind speed
Θ
i
= horizontal wind direction
Ue
i
= east-west component of wind
Un
i
= north-south component of wind
N = number of samples
Calculations:
s
n
Θu
s
2
North
East
U
s
1
s
3
s
4
FIGURE 11-1. Input Sample Vectors
In Figure 11-1, the short, head-to-tail vectors
are the input sample vectors described by
s
i
and
Θ
i
, the sample speed and direction, or
by Ue
i
and Un
i
, the east and north components
of the sample vector. At the end of output
interval T, the sum of the sample vectors is
described by a vector of magnitude U and
direction
Θu. If the input sample interval is t,
the number of samples in output interval T is
N T t
= / . The mean vector magnitude is
U U N = / .
Scalar mean horizontal wind speed, S:
S=(
Σs
i
)/N
where in the case of orthogonal sensors:
S
i
=(Ue
i
2
+Uni
2
)
1/2
Unit vector mean wind direction, Θ1:
Θ1=Arctan (Ux/Uy)
where
Ux=( Σsin Θ
i
)/N
Uy=(
Σcos Θ
i
)/N
or, in the case of orthogonal sensors
Ux=(
Σ(Ue
i
/U
i
))/N
Uy=( Σ(Un
i
/U
i
))/N
where U
i
=(Ue
i
2
+Un
i
2
)
1/2
Standard deviation of wind direction, σσσσ(Θ Θ Θ Θ1),
using Yamartino algorithm:
σ(Θ1)=arc sin(ε)[1+0.1547 ε 3
]
where,
ε=[1-((Ux) 2
+(Uy)
2
)]
1/2