The use of Lidars in complex terrain allows wind farm developers to assess the wind climate at multiple locations in an easier and cheaper way than by employing multiple masts with anemometers. Unfortunately Lidars give some discrepancies with the reference measurements (cup or sonic anemometers) especially in complex terrain where spatial variations of mean velocity exist along the Lidar measurement circumference. Therefore a tool is required to enable the correction of the Lidar in complex terrain to represent an anemometer at the Lidar location at the measured levels of the Lidar. Computations can be useful in order to correct the data as they are able to predict the flow on sharp and complex relief. As shown in a recent study presented in the 2009 NZWEA Conference, linear models are recommended for use only on simple terrain. Hence, the correction tools should be based on the full CFD software outputs, here with METEODYN WT outputs, namely the three components of the average velocity and wind direction. Comparisons are presented with two reference cases : simple and complex terrain.

1. 1
Correction tool for Lidar in complex terrains
based on Meteodyn WT outputs
Stéphane SANQUER - Meteodyn
New measurement tools are needed:
To reduce projects development risk and secure the investment .
To have reliable measurements in the upper atmosphere as the wind turbines are getting
higher.
Difficulties of traditional methods:
To have high measurements
To be easily mobile
To get information on the vertical profile
One Solution -> Use a Lidar
But remote sensing in complex terrain is a challenge:
Discrepancies between remote sensors and traditional anemometry
Data needs to be corrected
Meteodyn developed the “Lidar Correction Module”:

2. 2
Why need corrections in complex terrains
Velocity vectors aren’t be constant across the Lidar scan disk
We need the 3D vectors of the wind upstream and downstream the Lidar scan disk center
in order to project them on the beams
The method uses only the main direction informations i.e. along a line parallel to wind at
the center of the scan disk
ܸ‫ܮ‬ =
ܸ‫ݎ‬ሺ݀‫݊ݓ݋‬ሻ − ܸ‫ݎ‬ሺ‫݌ݑ‬ሻ
2 sinሺߠሻ
=
ܸ݀
ሬሬሬሬԦ. ݅Ԧ− ܸ‫ݑ‬
ሬሬሬԦ. ݆Ԧ
2 sinሺߠሻ
Analytic formulation of the velocity measured by LIDAR VL
General equation
Hypothesis : horizontal deviation is negligible across the Lidar disk (CFD gives <1°)
ܸ‫ܮ‬ =
1
2 sinሺߠሻ
ሺܸ݀ cosሺߚ݀ ሻ cosሺ߮݀ ሻ sinሺߠሻ + ܸ݀ cosሺߚ݀ ሻsinሺ߮݀ ሻ cosሺߠሻ
+ ܸ‫ݑ‬ cosሺߚ‫ݑ‬ሻcosሺ߮‫ݑ‬ ሻ sinሺߠሻ − ܸ‫ݑ‬ cosሺߚ‫ݑ‬ ሻ sinሺ߮‫ݑ‬ሻ cosሺߠሻሻ
ܸ‫ܮ‬ =
1
2 sinሺߠሻ
ሺܸ݀ sinሺߠ + ߮݀ ሻ + ܸ‫ݑ‬ sinሺߠ − ߮‫ݑ‬ ሻሻ
Where ߚ‫ݑ‬ and ߚ݀ are the deviation of the wind in the horizontal plane according to the direction
defined by the upstream and downstream point. And ߮‫ݑ‬ and ߮݀ are the incidence of the wind in the
vertical plane.
Lidar software assumes that upstream wind and downstream wind are horizontal
ܸ‫ܮ‬ =
1
2
ሺܸ݀ + ܸ‫ݑ‬ ሻ

3. 3
Correction of the velocity measured by LIDAR VL
The correction factor is defined in order to correct the lidar output
1.00
1.05
1.10
1.15
1.20
0 1 2 3 4 5
Correctionfactor
Wind incidence (°)
ܸ‫ܥ‬ = ܸ‫ܮ‬ × ߙ
If ߮‫ݑ‬ = −߮݀ and ܸ݀ = ܸ‫ݑ‬ = ܸܿ then ܸ‫ܮ‬ =
ܸܿ
sin ሺߠሻ
ሺsinሺߠሻ cosሺ߮‫ݑ‬ ሻ −cosሺߠሻsinሺ߮‫ݑ‬ ሻሻ
And ߙ =
sin ሺߠሻ
sin ሺߠሻcos ሺ߮‫ݑ‬ ሻ−cos ሺߠሻsin ሺ߮‫ݑ‬ ሻ
Discrepancies reach 10% when the upstream incidence is + 3° and the
downstream incidence is -3°
Corrections are necessary in complex terrains
Comparisons Lidar vs Mast in Two sites assessed by Meridian Energy
Validation of the method in a flat terrain (one mast 80 m) and in a complex terrain (two masts
20 m and 80 m)
Comparisons of corrected measurements from Meteodyn WT vs Met Mast measurements
Data from Lidar were filtered before in order to reduce the others sources of discrepancies
(rain, low velocity, mast wake on Lidar or on anemometers)
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
0 30 60 90 120 150 180 210 240 270 300 330 360
U(Lidar)/U(mast)
Wind direction(°)

4. 4
Comparisons Lidar vs Mast in Two Meridian sites
Flat terrains - Uncorrected data - MAE = 0.37 m/s - RMS = 0.50 m/s
y = 0.97x + 0.05
R² = 0.95
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
U(Lidar)/Uref
U (Mast) / Uref
Site n°1 - Mast n°1- H=80 m
Comparisons Lidar vs Mast in Two Meridian sites
Complex terrain (first point h=20 m) - Uncorrected data - MAE = 0.30 m/s – RMS = 0.42 m/s
y = 0.96x + 0.02
R²= 0.99
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
U(Lidar)/Uref
U (Mast) / Uref
Site n°2 - Mast n°1 - H=20 m

5. 5
Comparisons Lidar vs Mast in Two Meridian sites
Complex terrain (second point h=80 m) - Uncorrected data - MAE = 0.57 m/s – RMS = 0.75 m/s
y = 0.95x + 0.01
R²= 0.96
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
U(Lidar)/Uref
U (Mast) / Uref
Site n°2 - Mast n°2- H=80 m
Correction factor from Meteodyn WT outputs
First step : calculation for each wind directions with a 10° step
Flat terrain (one mast 20 m) Complex terrain (2 masts : 20 m and 80 m)

6. 6
Correction factor from Meteodyn WT outputs
Computation parameters
Computation domains
Flat terrain : square domain 3000 m
Complex terrain : square domain 5000 m
Minimum horizontal and vertical resolution (ground – 50 Lidar points)
Normal 5 m x 5 m or refined 2 m x 2 m
Expansion coefficients (horizontal – vertical)
1.1 – 1.2
Smoothing
No
Stability
Neutral
Correction factor from Meteodyn WT outputs
First step : calculation of flows for each wind directions with a 10° step
Speed up factor for flat terrain Complex terrain (wind direction 210°)

7. 7
Correction factor from Meteodyn WT outputs
Second step : calculation of speed up factor and wind incidence over the
Lidar disk for each wind directions with a 10° step
Speed up factor
H=20 m ∆∆∆∆SF=0.03
H=80 m ∆∆∆∆SF=0.05
1.50
1.55
1.60
1.65
1.70
1.75
1.80
0
7 14
22
29
36
43
50
58
65
72
79
86
94
101
108
115
122
130
137
144
151
158
166173
180
187194
202
209
216
223
230
238
245
252
259
266
274
281
288
295
302
310
317
324
331
338
346 353 speed up factor at the Lidar scan points
Site n°2 - H=80m
Site n°2 - H=20 m
Main wind direction = 180°
Lidar wind direction at 80 m = 175°
Lidar Wind direction at 20 m = 166°
Correction factor from Meteodyn WT outputs
Second step : calculation of speed up factor and wind incidence over the
Lidar disk for each wind directions with a 10° step
Wind incidence
H=20 m - ∆ϕ∆ϕ∆ϕ∆ϕ=0.8°
H=80 m - ∆ϕ∆ϕ∆ϕ∆ϕ=1.4°
-2
-1.5
-1
-0.5
0
0.5
1
0
7 14
22
29
36
43
50
58
65
72
79
86
94
101
108
115
122
130
137
144
151
158
166173
180
187194
202
209
216
223
230
238
245
252
259
266
274
281
288
295
302
310
317
324
331
338
346 353 Wind incidence (°) at the Lidar scan points
Site n°2 - H=80m
Site n°2 - H=20 m
Main wind direction = 180°
Lidar wind direction at 80 m = 175°
Lidar Wind direction at 20 m = 166°

8. 8
Correction factor from Meteodyn WT outputs
Third step : calculation of correction factor for each wind directions with a
10° step according to the following equation
Site 1 - H=80 m : αααα in [1.;1.01]
Site 2 - H=20 m : αααα in [1;1.05]
Site 2 - H=80 m : αααα in [1;1.06]
ܸ‫ܮ‬ =
1
2 sinሺߠሻ
ሺܸ݀ sinሺߠ + ߮݀ ሻ + ܸ‫ݑ‬ sinሺߠ − ߮‫ݑ‬ ሻሻ and ߙ =
ܸ‫ܥ‬
ܸ‫ܮ‬
ൗ
1
1.01
1.02
1.03
1.04
1.05
1.06
0 30 60 90 120 150 180 210 240 270 300 330 360
Correctionfactor
Wind direction(°)
Mesh 5 x 5
Mesh 2 x 2
Validation of the Lidar Correction Module with the Meridian sites
Third step : correction of the Lidar data at every time step
Complex terrain (first point h=20 m) - corrected data - MAE = 0.40 m/s –RMS = 0.52 m/s
y = 0.95x+ 0.01
R²= 0.96
y = 1.00x + 0.01
R²= 0.96
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
U(Lidar)/Uref
U (Mast) / Uref
Site n°2 - Mast n°1 - H=20 m

9. 9
Validation of the Lidar Correction Module with the Meridian sites
Complex terrain (second point h=80 m) - corrected data - MAE = 0.40 m/s – RMS = 0.65 m/s
y = 0.95x + 0.01
R² = 0.96
y = 1.00x+ 0.01
R² = 0.96
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
U(Lidar)/Uref
U (Mast) / Uref
Site n°2 - Mast n°2- H=80 m
Analysis:
Such remote sensing systems need to be corrected in complex
terrains because of the variability of wind magnitude and incidence
throw the scanning circle.
Without correction : gap Mast vs Lidar about 3 to 5 %
With correction : gap vanishes less than 1%
CFD could be used to calculate the correction coefficients
Needs to check the correction with others stabilities. Temperature
and velocity profiles give the Richardson number

10. 10
The Lidar Correction Module:
An integrated module within the CFD software Meteodyn WT
Developed in close cooperation with Lidar developers
Correction of all measurements heights at the same time with mesh
refinement at the Lidar points. Use several Lidars for the same project
Consideration of the thermal stability.
Automatic delivering of a corrected outputs to be used in the
Meteodyn WT synthesis
Thanks to Meridian for delivering all the data and site informations
necessary to compute the flow.
Thanks to Natural Power for the help to define the correction method for
LIDAR Zephyr
stephane.sanquer@meteodyn.com
info@meteodyn.com
www.meteodyn.com