Campbell-scientific CR10X Measurement and Control System Instrukcja Użytkownika Pobierz pdf (Strona 177)

SECTION 11. OUTPUT PROCESSING INSTRUCTIONS

11-3

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=(ΣS

i

Sin Θ

i

)/N

Un=(ΣS

i

Cos Θ

i

)/N

or, in the case of orthogonal sensors:

Ue=(ΣUe

i

)/N

Un=(ΣUn

i

)/N

Resultant mean wind direction, Θ

ΘΘ

Θu:

Θu=Arctan (Ue/Un)

Standard deviation of wind direction, σ

σσ

σ(Θ

ΘΘ

Θu),

using Campbell Scientific algorithm:

σ(Θu)=81(1-

U

/S)

1/2

The algorithm for σ(θu) is developed by noting

(Figure 11-3) that

Cos U / s ; where

ii

(') '

ΘΘΘΘ

iii

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 ( ') ( ') /

ΘΘ

ii

≅−

12

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

iiiii

US sS sS

22

22 2

=− − +

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.

(( )) ( ')/ ( / ) (( ') ')/

σΘ Θ Θ

uNUSsNS

iii

i

N

i

N

22 2

11

21

==−−

∑∑

==

The term,

(( ') ')/

Θ

ii

sNS

2

∑

, 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 Θ

uNuUS

i

==−

∑

212 12

21 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).

σ

( )(( /)) ( /)

//

Θ

uUS US

=− =−

21 811

12 12

*** 70 SAMPLE ***

FUNCTION

This instruction stores the value from each

specified input location. The value(s) stored are

those in the input location(s) when Instruction

70 is executed with the Output Flag set high.

PARAM. DATA

NUMBER TYPE DESCRIPTION

01: 4 Repetitions

02: 4 Starting input location no.

Outputs Generated: 1 for each repetition

1 2 ... 172 173 174 175 176 177 178 179 180 181 182 ... 361 362

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