Surface-Layer Wind and Turbulence profiling from LIDAR: Theory ...

SurfaceLayer Wind and Turbulence Profiling from LIDAR: 

Theory and Measurements 

Régis DANIELIAN (Vestas Wind System) 

Hans Ejsing JØRGENSEN (Wind Energy Department, Risø. Contact: haej@risoe.dk) 

Torben MIKKELSEN (Wind Energy Department, Risø. Contact: tomi@risoe.dk) 

Jacob MANN (Wind Energy Department, Risø. Contact: jakob.mann@risoe.dk) 

Mike Harris (QinetiQ, contact: MHARRIS@qinetiq.com) 

Introduction 

As wind turbines become taller wind energy assessment and 

also turbine control require knowledge of the detailed mean 

and turbulence wind profiles at bigger heights (150 meters and 

more). A major challenge for wind power meteorology is 

therefore to circumvent the traditional role of the tall mettowers 

by replacing them with equally accurate, but groundbased 

remote sensing equipment. 

Compared to wind data from calibrated cup anemometers in 

tall mettowers, wind data from remotesensing 

instrumentation, such as SODARS and LIDARS, still lack 

precision and data availability compared to mat data acquired 

from a met tower, in particular for use in connection with 

power curve reference and wind turbine certification purposes. 

However, recent progress with worldwide optical telecom 

technology and stable fibre lasers has led to realisation of a 

new and small wind Lidar system named ‘ZephIR 1 ’able to 

profile the surface layer up to ~200 meters height [2] and [3]. 

In this paper we describe how improved signal processing has 

led to more accurate remote wind and turbulence profile 

measurements. 

The present study is based on a prototype of QinetiQ’s series 

produced ZephIR wind LIDAR system 

ZephIR consists of a CW (1.55m) wind LIDAR operating in 

the socalled LDA 2 mode: it performs conical scans of radial 

wind component at 30 degrees to zenith. By adjusting the 

Lidars focus, wind measurements can be obtained from 

heights ranging from 10 to 200 meters above ground. The 

ZephIR prototype Lidar was designed to measure 

instantaneous radial wind speeds based on observed Doppler 

shifts at a rate of 25 Hz. By realtime processing of the 

Doppler shifts from three full revolutions of conical scanning 

(75 measurements), the horizontal wind speed and direction is 

given by the instrument every 3. second. By subsequent 

averaging of these 3sec measurements over a 10min period, 

the LIDAR provides an estimate of the mean horizontal speed 

and direction from each preset focal range. 

Included in this study, we have furthermore, for the first time 

to our knowledge, investigated a method to extract turbulence 

quantities such as the surface friction velocity u * [m/s] directly 

from the LIDARs radial wind measurements. 

1 Produced by QinetiQ, Ltd; Malvern, U.K. 

2 Laser Doppler Anemometry 

Following a short description of the LIDAR and the applied 

data processing we compare the LIDARretrieved mean wind 

and friction velocities with corresponding measurements 

from tall meteorological towers equipped with calibrated cup 

anemometers and 3D sonic anemometers at heights ranging 

between 44 meters and 123 meters. 

LIDAR theory 

Doppler shifted backscatter from the range where the 

coherent transmitted radiation is focussed is mixed with unshifted 

radiation on the detector; ant the resulting detector 

power is FFTanalysed for Doppler shift. A~1 MHz Doppler 

shift corresponds to approximately ~1 m/s radial wind speed 

of the aerosols in the focal volume. With the purpose to 

extract the horizontal wind component from the radial 

measurements the laser beam is rotated about Zenith by 

means of an optical wedge, with a fixed angle =30.6, see 

Figure 1. 

Fig. 1: Rotating focussed Laser beam (red arrows). 

Corresponding horizontal wind components are shown in 

black.. 

The LIDARs measurement heights are determined 

by H = h 0 

+ p'cos( 30. 6° 

), where p’is the focal length 

and h 0 is the initial vertical displacement of the laser heads 

(~2m).

Altitude [m] 

Length of the 

beam, p’[m] 

Diameter of 

scanning cone 

[m] 

40m 43.88m 44.77m 

60m 66.97m 68.18m 

80m 90.07m 91.70m 

100m 113.16m 115.21m 

200m 228.64m 232.77m 

against the direction of the wind, maximum Doppler shifts 

occur, see. Figure 3. 

Tabel 1: Geometrical characteristics of the conical scans 

The Doppler shift results from the difference of the wave 

vector k r e 

for the emission and k r r 

for the reflection. Let B r 

be the propagation vector of the transmitted Laser beam: 

Fig. 3:30minute of raw wind measurements obtained from 

Doppler shifts as function of conical scan angle [0; 2π]. 

In Fig. 3 the observed Doppler shifts have been transformed 

into velocities by the following equation: 

st ( , ) = ut ( )cos( − )sin( Φ ) + wt ( )cos( Φ) 

(3) 

θ θ θ 

d 

Fig. 2: Details of the interaction between the laser radiation 

and the horizontal component of the wind 

The mean wind direction is aligned along the xaxis: 

r µ ≡ u 

r , 

r r 

v = w= 0 

r 

. To calculate the resulting Doppler shift, we 

define two frequencies, one representing the emission of the 

signal, and one representing its reception: 

r r ⎛ u 

⎞ 

ω' e 

= ω 

0 

+ ke. µ ⇔ ν ' 

e 

= ν ⎜1− cos( θ)sin( Φ) 

⎟ 

⎝ c 

⎠ 

(1) 

r r ⎛ u 

⎞ 

ω' r 

= ω 

0 

+ kr. µ ⇔ ν ' 

r 

= ν ⎜1+ cos( θ)sin( Φ) 

⎟ 

⎝ c 

⎠ 

where ν is the frequency [Hz]. The modulus of wave vector is 

r 2πν 

defined as k = . The Doppler shift of an elastic 

c 

scattered photon results as the difference between the outgoing 

and the backscattered radiation: 

u 

∆ ν = ν ' 

r− ν ' 

e 

= 2 ν cos( θ)sin( Φ ) (2) 

c 

This represents the Doppler shift detected by the Lidar. The 

quantity is the angle between the aerosol transported by the 

wind and the beam. When /2 or 3/2, the Doppler shift is 

zero. The ideal cases are =0 or ; but due to the conical 

scanning at fixed angle to vertical there will always be nonzero 

Doppler shifts wherever the wind comes from. The 

Doppler shift frequency signal that appears on the Lidar’s 

detector will give the following typical picture if we sample 

complete rotations. When the Laser beam is pointing into or 

and then shown as function of scan angle . A curve has been 

fitted through the data points. The fitted curve allows 

calculation of u, w and if the Lidar has been properly 

oriented (to the North) a curve fit also yields the direction d 

of the mean wind speed. In normal operation mode the 

horizontal wind vector is determined from 3 full conical 

rotations of 1second duration each. During each revolution a 

total of 25 Doppler spectra are obtained with the present 

instrument. An average wind speed from the conical scans is 

then obtained by a curve fit to 3 full rotations of such Doppler 

measurements and encompasses therefore up to 75 raw 

spectra as obtained over three revolutions of 2. u(t), w(t) and 

d are consequently representing averages over 3 seconds in 

time. 

Geometry of the Gaussian beam: 

The radius and the focal width of the Laser beam changing as 

function of the measurement height and the effective 

measurement volume is consequently determined by the 

system optics. The laser beam is characterized by its Rayleigh 

length 

z 

R . 

2 

πW0 

z R 

= 50.6µ 

m 

λ 

At the output of the fibre this quantity is 

= , where W 0 is the radius of the 

beam in the optical fiber. This Rayleigh length represents the 

halfwidth where most of the power of the laser beam is 

gathered, according to the Lorentzian distribution of energy 

among the beam. By adjusting the fiber end near the focal 

point of the lens, the beam can be focused to take wind 

measurements at preset heights. The characteristics of the 

laser beam at the fiber end is via the lens projected to the 

external focal volume of length z (Rayleigh length) and of 

focal width W. At a distance p’from the lens the beams crosssection 

is given by 1 : 

R

2 

⎛ 

2 2 

⎛ p' 

⎞ ⎞ 

W ( p') = W 

0 

1 

⎜ 

+⎜ ⎟ 

z ⎟ 

⎝ ⎝ R ⎠ ⎠ 

The outgoing beam diameter of the ZephIR lidar is ~ 4 cm so 

that the maximum power density at the instrument is of order 

of ~ 2 10 2 [ Wcm 2 ]. The Laser beam is focused at the preset 

distance corresponding to the decided measurement height. In 

the following the position of the output of the external fibre 

before the lens is donoted p; and the position of the waist 

after the lens by p’. When the Laser beam is focused, the 

characteristic (radius and focal width) will change, as shown 

in Fig.4. The radius and the focal width, W out (p’) and 2Z’ R , 

respectively evolve as function of measurement height. 

(4) 

radius increases linearly with distance while the focal width 

increases with distance squared. 

Wout [mm] 

6 

5 

4 

3 

2 

1 

0 

Wout(p') 

2 Z'r 

0 50 100 150 200 250 

H [m] 

140 

120 

100 

80 

60 

40 

20 

0 

2 Z'r [m] 

Fig. 6: Overview of the radius (W out , in blue) and the focal 

width (2Z’ R, in red) for different altitudes of scanning (H) 

Fig. 4: Beam propagation 

Fig.5 shows details at the waist position (focal point) for the 

focal width (2Z R ’), the radius W out (p’), and the angle of 

deflection of the Laser beam ’. 

Fig. 5: Details of the characteristics of the focalized Laser 

beam 

As p moves closer (within a fraction of a millimeter) to the 

focal point of the lens (F=20cm), the further away will the 

external Laser beam be focused (the waist location, p’) : 

The volume of the beam, from where plane coherent radiation 

backscatters, can to a first approximation be considered a 

doubletruncated cone (See figure 5). The radius of the beam 

is very small; the focus volume is always very small (0.153 

litre at 60m height, 1.174 litre at 100m height). As an 

approximation we will use only the quantity +/ Z’ R to 

express the length where the measure will be done. The 

radius of the beam (blue) increases linearly with the altitude, 

and is the order of the millimetres within our range of altitude 

of measurements (40m100m); but the focal width 2Z’ R (red 

curve) on the other hand grows quadratic about 1 orders of 

magnitude (from 4m at 40m until 32m at 100m). The focal 

width +/ “Z R ’represents the range where about 50% of the 

focussed radiation is gathered, and represents the range at 

which wind measurements will be taken. 

During an experiment at the test site Høvsøre in northwestern 

part of Denmark, the Lidar have been evaluate with 

respect to precision [2] and [3]. The Lidar data have been 

compared with calibrated Risø cup anemometers and Metek 

Sonics (Model USA1) all located on the met tower, the Lidar 

was installed 200m away from the tower, an example of the 

comparison are showen in figure 7 (Here measured at 80m 

height). This data set is obtained over a period of four days of 

measurements. The data have been filtered because of rainy 

days, or direction changes resulting in wake from the turbines 

at the test site and tower effects. 

H [m] p’[m] W out (p’) [mm] 2Z’ R [m] 

40m 43.88m 1mm 4.8m 

60m 66.97m 1.7mm 11m 

80m 90.07m 2mm 20.2m 

100m 113.42m 2.8mm 32.4m 

200m 228.64m 5.6mm 128.7m 

Tab. 2: Main data of the conical scan for different altitudes of 

scanning 

Figure 6 shows the characteristics of the external beam as 

function of measurement distance H. The focussed beams

Fig. 7: Regression of 10min averaged wind speeds from lidar 

and cup obtained on the31 st May 2004 at the Høvsøre test 

site, Denmark 

Fig. 8: Main view of interaction between the rotating Laser 

beam and the wind 

r r r 

If we let µ ( t) 

= u( 

t) 

+ w( 

t) 

, and denote the tilt angle of 

the wind, then can be positive or negative, and then also 

w(t) will be respectively positive and negative. At these two 

points, the interaction between the transmitted Laser beam, 

and the backscattered light and the aerosols can be described 

in the following way: 

The LidarCup comparison shows nearly the same quality as a 

Cup vs. Cup intercomparison from the same height. The 

separation between the Lidar and tower is in the order of 200 

meters. The good correlation is also described in [3]. 

Remote measurement of the friction velocity 

Secondly, we have investigated a method of estimating the 

the surface friction velocity e.g. entering into the horizontal 

mean wind profile equation: 

u ⎛ 

* 

z ⎞ 

uz ( ) = ln ⎜ ⎟ 

Eq.:7 

κ ⎝ z0 

⎠ 

Here, is the von Karman constant equal to ~0.4; and z 0 is the 

roughness length of the surface. 

In the following we write the instantaneous velocities as 

u(t) and w(t) and split them into a perturbation and an a mean 

part i.e u(t)=+u’and w(t)=+w’, the friction velocity, 

u * , over a specified averaging time is the defined as: 

u* = − uw ' ' 

Eq.:8 

The points named P 1 and P 5 ,(see figure 8) which are within the 

direction of the main stream of the wind, which means that the 

term d of the fitted curve s() is equal to 0 or . 

Fig. 9a: In P 1 Fig. 9b: In P 5 

In P 1 (Fig. 9a) we will get the following Doppler shift: 

ν 

∆ν 

1( 

t) 

= 2 ( u( 

t)sin( 

Φ) 

− w( 

t)cos( 

Φ) 

) 

c 

Eq.:9 

In P 5 (Fig. 9b) we will get the following Doppler shift: 

ν 

∆ν 

5( 

t) 

= −2 

( u( 

t)sin( 

Φ) 

+ w( 

t)cos( 

Φ) 

) 

c 

Eq.:9.1 

Detecting only the absolute value of these backscattered 

Doppler shifts we observe: 

ν 

∆ν 

1( 

t) 

= 2 

c 

ν 

∆ν 

5 

( t) 

= 2 

c 

( u( 

t)sin( 

Φ) 

− w( 

t)cos( 

Φ) 

) 

( u( 

t)sin( 

Φ) 

+ w( 

t)cos( 

Φ) 

) 

Eq.:10 

u(t) is always positive and w(t) can be either positive or 

negative depending on the tilt angle (respectively >0 or 

using the Reynolds decomposition of u(t)=+u’ 

and w(t)=+w’. By subtracting the fitted curves at these

specific points, then squaring and averaging both of them, 

results in : 

= 

2 

1 

∆P 

⎛ c 

⎞ 

⎜ ∆ν 

1( 

t). 

− sin( Φ) 

+ < w > cos( Φ) 

⎟ 

⎝ 2ν 

⎠ 

=< u' 

2 

> sin( Φ) 

+ < w' 

− 2 < u' 

w' 

> cos( Φ)sin( 

Φ) 

= σ u 

sin( Φ) 

+ σ w 

cos( Φ) 

− 2 < u' 

w' 


Φ) 

∆P 

2 

5 

2 

> cos( Φ) 

2 

Eq.:11 

= 

⎛ c 

⎞ 

⎜ ∆ν 

5 

( t). 

− sin( Φ) 

− < w > cos( Φ) 

⎟ 

⎝ 2ν 

⎠ 

=< u' 

2 

> sin( Φ) 

+ < w' 

+ 2 < u' 

w' 


Φ) 

= σ u 

sin( Φ) 

+ σ w 

cos( Φ) 

+ 2 < u' 

w' 


Φ) 

2 

> cos( Φ) 

2 

Eq.:11.1 

The sheer stress in the surface layer is known to be a 

negative term, then is bigger than . This 

explain why the points gathered in green (P 1 ) are more 

scattered than the corresponding part in blue (P 5 ). Due to this 

we are able to obtain information about the direction which 

solve the ambiguity regarding the 180 degree. 

In the two following graphics the curves of the backscattered 

signal is shown over a 10 minute period, here show as the 

complete rotations of the Laser beam (Fig.10a), P 1 (in green) 

and P 5 (in blue) is shown in (Fig.10b). These data have been 

taken the 31 st May 2004 at height of 80m in Høvsøre test site: 

Fig. 11: Regression line of u(t), over 10mn average, the31 st 

May 2004 in Høvsøre 

Although some values are biased (about 10 out of 144), the 

correlation is good, with a R 2 >0.8. 

The corresponding shear stress u * 

subtracting to : 

∆P 

2 2 

1 5 

( u) 

* 

− ∆P 

= Φ +< w > Φ 

2 2 

' sin( ) ' cos( ) 

− 2 < uw ' ' > cos( Φ)sin( Φ) 

− Φ −< w > Φ 

2 2 

' sin( ) ' cos( ) 

− 2 < uw ' ' > cos( Φ)sin( Φ) 

=−< uw ' ' > 4cos( Φ)sin( Φ) 

2 

= 4cos( Φ)sin( Φ) 

can ve calculated by 

Eq.:12 

The first test of comparison of u * (144 points of over 24 hours 

and 10mn average) gave the following results: 

Fig. 10a: Left: Raw LIDAR wind measurements s(t,) as 

function of azimuth angle (2) obtained over 10 minutes of 

sampling. 

Fig. 10b: Right: selection of P 1 (in green) and P 5 (in blue) 

The quality of the correlation between the data from the 

LIDAR and MET mast, the fitted regression line for 10min 

average comparison of u(t) between the Lidar and the cup 

anemometer on the 31 st May 2004 is shown in figure 11 

calculated : 

Fig. 12: u * , at 80m, 10mn average, the 31 st May 2004 at 

Høvsøre (Blue: sonic anemometer. Red: Lidar).

We notice on Fig.12 that for low values of u * the correlation is 

very good (u * 0.4) the measurements 

from the Lidar is biased, but the Lidar follows the dynamic 

evolution of u * . measured by the sonic anemomter The 

corresponding regression line over the 144 points is: 

Danielian, (2005) Wind lidar evaluation at the Danish wind 

test site in Høvsøre : To appear in Journal of windEngi. 

u * (Sonic) 

u * (Lidar) 

Fig. 13: Regression line of u * Lidar vs.sonic at 80m, 10min 

average, data measured on 31st May 2004 at Høvsøre 

In this paper we have shown that is possible to measure the 

friction velocity u * by a remote sensing equipment. This opens 

new perspectives for further research and investigation with 

regard to characterise entrainment turbulence and wind in 

wind farms by mounting the Lidar on the hub and measureing 

above the wind farm, Similar investigation of the flow over 

forests and cities with high roughness can be done where 

towers are difficult to erect. 

Acknowledges support from the EC "Wind Energy 

Assessment Studies and Wind Engineering" (WINDENG) 

Training Network (contract nr. . HPRNCT200200215) and 

the Danish ENS project nr 1363/03. 

References 

[1]: ”Introduction to modern optics”, Grant R Fowles, Second 

Edition, p.:280 

[2]: Jørgensen et al. (2004) Site wind field determination 

using a CW Doppler lidar comparison with cup anemometers 

at Risø. In: Proceedings. Special topic conference: The 

science of making torque from wind, Delft (NL), 1921 Apr 

2004. (Delft University of Technology, Delft, 2004) p. 261 

266 

[3]: David A. Smith, Michael Harris, Adrian S. Coffey, 

Torben Mikkelsen, Hans E. Jørgensen, Jakob Mann, Régis

Surface-Layer Wind and Turbulence profiling from LIDAR: Theory ...

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