Comparison and Terrain Influence on

Predictions with Linear and CFD

Models

CANWEA Annual Conference, Vancouver, BC

October 04, 2011

GILLES BOESCH, M.Eng, Wind Project Analyst

Hatch (Montreal), Canada

Overview

• Introduction

• Presentation of a test case

• Model comparison, terrain influence

• Conclusions and investigations

2

Introduction

• CFD is now well established in the wind

industry

• Need to quantify the uncertainty associated

to these models

• Compare the errors with linear models

• Influence of the errors with topography

complexity – And how to deal with it

3

Test case

• Comparison between linear (WAsP) and CFD

model (Meteodyn) on a potential project

• RANS equation with one-equation closure

scheme (k-L turbulence model)

• Project covers an area of 11km x 8km

• Equipped with 12 meteorological masts

(recording from 6 months to 6 years of data)

• Relatively complex (deep valleys, ridges,

rolling mountains)

• Mix of coastal and inland areas

4

Test case

• Forest diversity:

– Logged area

– 15m high trees

– Regrowth

• RIX (Ruggedness Index)

– % of slopes >30% in a 3500m radius

– RIX Variations:

• 2 to 25 over the entire project

• 2.7 to 22.4 at the meteorological masts

Variety of conditions to evaluate the

behavior of the models

5

Masts Altitude

(m)

RIX

(%)

M1 540 10.1

M2 560 11.0

M3 421 22.4

M4 420 17.9

M5 448 15.1

M6 521 16.6

M7 560 8.0

M8 433 22.1

M9 440 11.8

M10 665 14.3

M11 567 2.7

M12 540 12.1

Test Case

• Meteodyn settings :

– Structured Mesh (30m cell size within the

project area)

– Use of a forest model (windflow over canopy)

– Neutral stability class assumed (can induce

errors for sea shore sites) – Resulting shear

verified for some masts

• Data :

– Measured and Quality controlled

– At 50m or 60m high (to avoid extrapolation

errors)

– Adjusted to long term with standard MCP

method (to have the same reference)

6

Results – Methodology

• Cross-Prediction Matrix

– Predictors : Mast that predicts the others

– Predicted : Wind Speed at the « Predicted Mast »

7

Predicted

M1 M2 M3 … M12 P

red

icto

r

M1 M1 measured M1 predicts

M2

M2 M2 predicts

M1 M2 measured

M3 M3 measured

… …

M12 M12 measured

Results - Methodology

• Cross-Prediction Matrix

– 12 x 12 matrix 132 cross predictions

– For both WAsP and Meteodyn

– No correction is applied to both models output

– Correction often applied with WAsP because of

wind speed inconsistencies in complex terrain

• Converted into a Relative Error Matrix :

• Resulting in 132 relative error values for

each cross-prediction

measured

measuredpredicted

V

VVE%

8

Results - Comparison

• Mean absolute errors

Masts Altitude

(m) RIX (%)

M1 540 10.1

M2 560 11.0

M3 421 22.4

M4 420 17.9

M5 448 15.1

M6 521 16.6

M7 560 8.0

M8 433 22.1

M9 440 11.8

M10 665 14.3

M11 567 2.7

M12 540 12.1

9

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

Err

or

(%)

Prediction Errors

WAsP Error

Meteodyn Error

< 2km from

water

Results - Comparison

• Absolute errors (direct output from models)

• On average, reduction of the error by 40%.

• Some exceptions : 33 cases out of 132

show better results with WAsP

WAsP Meteodyn

Min Error 0.0% 0.0%

Max Error 34.0% 14.1%

Average 7.7% 4.6%

10

Results - Comparison • Generally, errors from both models have

the same sign (positive/negative)

• The difference is in the magnitude

-20.0%

-10.0%

0.0%

10.0%

20.0%

30.0%

40.0%

Rela

tive E

rro

r (%

)

WAsP

Meteodyn

11

Results – RIX Analysis

• RIX dependency:

– WAsP : Error increase sharply when RIX > 15%

– Meteodyn : Error is more constant

12

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

0.0 5.0 10.0 15.0 20.0 25.0

Avera

ge E

rro

r (%

)

RIX (%)

RIX influence on cross-prediction errors

Wasp Meteodyn

Results – RIX Analysis

• RIX dependency:

– Possibility to correct WAsP with ΔRIX (between

2 masts)

– Correction based on a correlation between

logarithmic error and ΔRIX for each cross-

prediction : E(%) = A* ΔRIX + B

– Can we correct Meteodyn based on the RIX ?

13

y = 0.5552x

R² = 0.6345

-30.0%

-20.0%

-10.0%

0.0%

10.0%

20.0%

30.0%

40.0%

-30.0% -20.0% -10.0% 0.0% 10.0% 20.0% 30.0% Err

or

(%)

ΔRIX (%)

Error vs dRIX - Meteodyn

y = 1.0632x

R² = 0.7025

-30.0%

-20.0%

-10.0%

0.0%

10.0%

20.0%

30.0%

40.0%

-30.0% -20.0% -10.0% 0.0% 10.0% 20.0% 30.0%

Err

or

(%)

ΔRIX (%)

Error vs dRIX - Wasp

Results – RIX Analysis

• CFD RIX dependency:

– Error increases when ΔRIX increases

– Error and ΔRIX seem to be correlating (not as

good than Wasp however)

– The slope is lower for Meteodyn

Influence of site topography differences is lower

14

y = 0.5552x

R² = 0.6345

-30.0%

-20.0%

-10.0%

0.0%

10.0%

20.0%

30.0%

40.0%

-30.0% -20.0% -10.0% 0.0% 10.0% 20.0% 30.0% Err

or

(%)

ΔRIX (%)

Error vs dRIX - Meteodyn

y = 1.0632x

R² = 0.7025

-30.0%

-20.0%

-10.0%

0.0%

10.0%

20.0%

30.0%

40.0%

-30.0% -20.0% -10.0% 0.0% 10.0% 20.0% 30.0%

Err

or

(%)

ΔRIX (%)

Error vs dRIX - Wasp

Results – RIX Analysis

• Wasp RIX Correction:

– 12 towers available

– Equation based on 11 towers and evaluate how

it corrects the 12th tower

15

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

Err

or

(%)

Prediction Errors

WAsP Error

Meteodyn Error

WAsP RIX Corrected Error

Results – RIX Analysis

• Meteodyn RIX Correction:

– Same methodology with updated correction

equation

16

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

Err

or

(%)

Prediction Errors

WAsP Error

WAsP RIX Corrected Error

Meteodyn Error

Meteodyn RIX Corrected Error

Results – RIX Analysis

• Summary of average error:

– RIX correction with Meteodyn produces

promising results

– Reduction by 44% of the error after correcting

Wasp with the RIX.

– Reduction by 33% of the error after correcting

Meteodyn with the RIX.

– RIX correction with Wasp compared to

Meteodyn direct output shows similar errors.

17

Wasp 7.7 %

Wasp RIX Corrected 4.3 %

Meteodyn 4.6 %

Meteodyn RIX Corrected 3.1 %

Conclusions

• In general, a project in complex terrain

requires lots of masts

• An alternative is the use of a CFD model

but linear corrected models can give good

results too

• Only few litterature over relation between

RIX and CFD models

• But quantification of CFD errors is more

complex (topography / volume

discretisation, forest model etc.)

In some cases error is bigger

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Conclusions

• To go further :

– Try with concurrent data (when possible) to

avoid MCP related errors

– How does RIX correction with CFD performs for

other sites ?

– Introduction of new complexity index (takes

into account RIX, distance, vegetation,

stability…)

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Thank you for your attention

Gilles Boesch, M.Eng

Wind Project Analyst

Hatch Ltd

GBoesch@hatch.ca

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