SILSOE RESEARCH INSTITUTE Spatial variation of wind speeds between sites Andrew Quinn.

SILSOE RESEARCH INSTITUTE

Spatial variation of wind speeds between sites

Andrew Quinn

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Why consider wind?

Many problems require a knowledge of the natural environmentDesign and construction, Transport risk analysisPollution control, Pollen and aphid movementWind Power, Forestry management, etc etc

Some require single design valuesOthers require distributions

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0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Wind Speed

Pro

portio

n of

tim

e

Wind speed distribution

How does this change with site?

Data from Shap Meteorological site, hourly maximum gust 4/1994 – 3/2003

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General form of the CDF

Weibull distribution

Where c and k are site specific constantsFits both mean hourly data and “gust” data

))(exp(1)(][ UfUEUuP

))(exp(1)( kcUUE

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Extreme value analysis

Majority of previous studiesTypical approach is to take linear

approximation to the tail of the distribution

Where LHS is known as reduced variate

)~

()))(ln(ln( UUUE

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Gumbel plot

0

5

10

15

20

25

30

35

-2 0 2 4 6 8 10 12-ln(-ln(CDF))

Win

d sp

eed

(m/s

)

Data from Shap meteorological site - hourly mean and gust up to 1 year return period

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Extreme value analysis

0

5

10

15

20

25

30

35

-2 0 2 4 6 8 10 12-ln(-ln(CDF))

Win

d sp

eed

(m/s

)

Shap data hourly mean and gust up to 1 year return period

Gumbel plot of Shap gust extrapolated to 50-year return period

50 year return period design value

47 m/ s

0

5

10

15

20

25

30

35

40

45

50

-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4

reduced variate (-ln(-ln(P)))

Win

d sp

eed

Peak v

alues

Such approaches require long data sets

Therefore not local to sites of interest

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Wind Speed map methodsBS6399:Part2, Eurocode 1, ESDU

“Wind Atlas” method

Miller et al (1998) Fig. 5. Estimated 50-year return hourly-mean wind speed for the United

Kingdom. Values given in m/s.

After Abild et al (1992)

Design wind speed methodsfor dealing with spatial effects

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Objective

Obtain a wind speed distribution for a site:Objective (no subjective estimates of parameters)Realistic (rather than a conservative design value)Based on short-term data recordsConsistent with other methods (EVA)

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Approach

Consider the wind distribution at two sites

Where cA and kA known (from long records)

Define UB+ such that

))(exp(1)(

))(exp(1)(B

A

kBBBB

kAAAA

UcUE

UcUE

AB kAA

kBBAABB UcUcUEUE )()()()(

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Approach

For consistency with standard EVA where

assume kA = kB (i.e. distributions same shape)

General form E(UB+) ≈ E(γUA)

)~

()~

()( UUUccU kk

)~

(

)~

()(

)~

()(

AA

kAA

kAA

kBB

kBB

UU

UcUc

UcUcAA

BB

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Evaluating γ from short term records using ranked simultaneous data

9 years data 3 months (winter) data

0

5

10

15

20

25

30

35

40

0 10 20 30 40

Eskdalemuir wind speed (m/ s)

Shap

win

d sp

eed

(m/s

)

0

5

10

15

20

25

30

35

40

0 10 20 30 40

Eskdalemuir wind speed (m/ s)

Shap

win

d sp

eed

(m/s

)

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Reliability of short term data

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Individual 3 month estimates and estimate from long term data

Spat

ial c

orre

lation

coe

ffic

ient

MeanGust

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Solution

Thus we knowLong term wind speed probability distribution

from a reference siteCan calculate expected wind speed & return period

Relationship between two sites

Objective Realistic Small data set

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Example anomalous results

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10

15

20

25

30

35

0 5 10 15 20 25 30 35

Shap wind speed

Brisc

o w

ind

spee

d

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including wind direction

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30

35

0 5 10 15 20 25 30 35

Shap (gust) wind speed

Brisc

o (g

ust) w

ind

spee

d

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Conclusions

Method for objective, realistic estimates based on short term site data

Data from 8 sites used and estimates for hourly mean and gust wind speedsAccuracy level similar to direct MO

records

Wind direction can be a significant factor


Spatial variation of wind speeds between sites

Acknowledgements

Roger Hoxey, Chris Hampson, Nick Teer and the other members of the project team at SRI

Russell Pottrill, William Bradbury and David Deaves (Atkins)

SILSOE RESEARCH INSTITUTE Spatial variation of wind speeds between sites Andrew Quinn.

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