We present two methods to characterize turbulence in the turbine inflow using radial velocity measurements from nacelle-mounted lidars. The first uses a model of the three-dimensional spectral velocity tensor combined with a model of the spatial radial velocity averaging of the lidars, and the second uses the ensemble-averaged Doppler radial velocity spectrum. With the former, filtered turbulence estimates can be predicted, whereas the latter model-free method allows us to estimate unfiltered turbulence measures. Two types of forward-looking nacelle lidars are investigated: a pulsed system that uses a five-beam configuration and a continuous-wave system that scans conically. For both types of lidars, we show how the radial velocity spectra of the lidar beams are influenced by turbulence characteristics, and how to extract the velocity-tensor parameters that are useful to predict the loads on a turbine. We also show how the velocity-component variances and co-variances can be estimated from the radial-velocity unfiltered variances of the lidar beams. We demonstrate the methods using measurements from an experiment conducted at the Nørrekær Enge wind farm in northern Denmark, where both types of lidars were installed on the nacelle of a wind turbine. Comparison of the lidar-based along-wind unfiltered variances with those from a cup anemometer installed on a meteorological mast close to the turbine shows a bias of just 2 %. The ratios of the unfiltered and filtered radial velocity variances of the lidar beams to the cup-anemometer variances are well predicted by the spectral model. However, other lidar-derived estimates of velocity-component variances and co-variances do not agree with those from a sonic anemometer on the mast, which we mostly attribute to the small cone angle of the lidar. The velocity-tensor parameters derived from sonic-anemometer velocity spectra and those derived from lidar radial velocity spectra agree well under both near-neutral atmospheric stability and high wind-speed conditions, with differences increasing with decreasing wind speed and increasing stability. We also partly attribute these differences to the lidar beam configuration.

Recently, lidars have been mounted on the nacelle of wind turbines to
investigate wake characteristics

Similar to ground-based lidars, there are two main types of FL nacelle
lidars, pulsed and continuous-wave (CW), which mainly differ, for the purpose
of turbulence estimation, on the measurement probe volume and the scanning
strategies (specific details are given later). As with any other Doppler
lidar, they only measure the radial velocity along the laser beam or
line-of-sight velocity. As their measurement probe volumes are generally
larger than those of cup and sonic anemometers, they might not be able to
measure small turbulent eddies, which leads to “filtered” turbulence
estimates; however, as they scan the atmosphere with laser beams in different
directions, there might be contributions (contamination) from different
velocity components that can lead, for some scanning configurations and under
certain turbulence conditions, to turbulence estimates that might be even
higher than those from cup or sonic anemometers. A detailed analysis on how
lidar-based turbulence estimates can be assessed, filtered, and contaminated
is presented in

Here we use time series of radial velocity measurements from different beams
emitted by a FL nacelle lidar to estimate the turbulence parameters of the
three-dimensional spectral velocity tensor model by

This paper is organized as follows. In Sect.

The wind field is described by a vector field

The spectral velocity tensor,

Two types of FL nacelle lidars are investigated: a CW and a pulsed lidar. The
lidars are assumed to be mounted close to the center of the rotor with

The

Geometry of the rotor and nacelle lidars. The

Examples of radial velocity spectra of the CW and pulsed lidars calculated
from Eq. (

Sonic and CW lidar velocity spectra from Eqs. (

Sonic and pulsed lidar velocity spectra from
Eqs. (

Figure

The unfiltered variance of
the lidar beams,

Assuming homogeneous turbulence, once

The strategy is to calculate theoretical spectra (in the form of a LUT) that
include both the effect of pointing the lidar in the direction

The computational burden of creating a lidar-based LUT using
Eq. (

(Left) Variance of the lidar beams' radial velocity (divided by the

Figure

Effect of lidar beam misalignment (with respect to the wind) on the
radial velocity spectra of a pulsed lidar for

The Nørrekær Enge wind farm is located in the Himmerland region in
northern Jutland, Denmark,

The measurements here analyzed correspond to the period 27 October 2015 to
7 January 2016. There are three types of measurements: supervisory control
and data acquisition (SCADA) on turbine 4, FL nacelle-lidar measurements from
systems mounted on the nacelle of turbine 4, and meteorological mast
observations. Both lidars were pre-tilted down

For this analysis we use the following SCADA 10 min means of turbine 4: yaw, power, and turbine and grid status. The yaw and power signals provide measurements of the position of the turbine and the converted power, and the grid and turbine status signals show whether the turbine was grid-connected (yes/no) and available (yes/no).

The Nørrekær Enge wind farm in northern Denmark on a digital surface elevation model (UTM32 WGS84). The wind turbines are shown in circles, that with the nacelle lidars in red and the mast in a triangle. The sector used for the analysis is also indicated. The waters of Limfjorden are shown in light blue.

A five-beam Avent pulsed lidar (hereafter known as Avent) was mounted on the
nacelle of turbine 4. Ten different ranges were measured simultaneously per
beam position (49, 72, 95, 109, 121, 142, 165, 188, 235, and 281 m). The
beam configuration is exactly as that in the right panel of Fig.

A ZephIR dual-mode CW lidar (hereafter known as ZephIR) was also mounted on
the nacelle of turbine 4. Five different ranges were considered (10, 30, 95,
120, and 235 m); for each range

We use measurements from cup anemometers (P2546A) at 80, 78, and 57 m
height, mounted on 3 m long booms 250

We analyze the time series of all data and their statistics in 10 min
periods. The total number of 10 min periods available for analysis is 9586.
The next steps are followed in the analysis:

We use the 10 min vane measurements to concentrate the analysis on a
wake-free sector covering the mast location (88.85–238.85

The availability of the Avent data is highest at the range 121 m
because this range is the closest to the focusing distance. Therefore, we
focus all our lidar-data analysis at this range, although the mast is at
232 m from turbine 4. Furthermore, when a carrier-to-noise (CNR) filter is
applied to the 5 s time series, the two lowest beams (3 and 4) return fewer
data than the others due to, among other things, obstruction from the blades (the
availability of beam 3 is lower than that of beam 4). A total of 3236 10 min periods
are available for analysis after filtering the 5 s Avent data so that for
each 10 min period there are a minimum of 110 samples for beams 0, 1, 2, and
4 with CNR

We then extract all radial velocities for all azimuthal positions of
the ZephIR for the range 120 m when no rain was detected by the instrument.
The azimuthal position of the

Finally, we extract the 1 Hz data of the sonic anemometer and cup anemometer at 80 m, in which there are a minimum of 600 samples per 10 min period. The final dataset thus contains 2273 10 min samples of concurrent turbine–lidars–mast data.

Furthermore, each 10 min time series has been post-processed. For the Avent
data, we linearly detrend each radial velocity time series for each beam
before applying a despiking filter, where values above and below 3 standard
deviations from the mean are filtered out. The missing values are then filled
in using linear interpolation. The top left panel of Fig.

An example of a 10 min time series of the radial velocity of
different beams for the Avent (top left) and the ZephIR (top right) lidar.
The radial velocities of the two lidars at all azimuthal positions are
illustrated in the bottom-left panel (see text for details). In the
bottom-right panel, we show a comparison of the 2273 10 min mean radial velocities of the Avent (beam 2) and ZephIR (bin 6) with the results of a
linear regression through the origin and coefficient of determination

For the ZephIR data, we construct time series of radial velocities at
azimuthal positions similar to those of the Avent. Since the azimuthal
positions of the ZephIR change from revolution to revolution, we extract
radial velocities within azimuthal position bins of 7.2

Comparison of sonic and 80 m cup anemometer statistics: mean wind speed (left frame) and horizontal-wind variance (right frame). Each 10 min
sample is shown in grey markers, a 1 : 1 line is shown for guidance in
black, and the results of a linear regression through the origin and

For each 10 min period, the 1 Hz sonic and cup anemometer data are
detrended and despiked as with the lidar data, and mean and turbulence
statistics are computed. The sonic-anemometer wind-speed components are
rotated so that

When compared to the measurements from the 80 m cup anemometer, the
sonic-anemometer mean horizontal wind speeds are 2.6 % lower (see
Fig.

The behavior of the sonic-derived velocity spectra does not correspond well
with the notion of turbulence local isotropy within the inertial subrange,
where we expect the same spectral density for the

Power spectrum for different velocity components. The solid lines
show the ensemble-average spectra of all 10 min sonic-anemometer spectra;
the markers, the

Ensemble-average spectrum of all 10 min Avent radial velocity
spectra (per beam), sonic-anemometer

Due to the uncertainty on the sonic-derived statistics, we will use the
cup-anemometer variance as a proxy for

Although the variances of a velocity time series sampled over a 10 min
period at a frequency

The noise filter seems to recover the shape of the Avent radial velocity
spectra. However, when tested on the 18 s sonic ensemble-average

Figure

In the right panel of Fig.

For both lidars we need to reconstruct the horizontal wind speed at the
specific range of the lidars, which can later be used for spectral analysis
and for filtered along-wind variance estimates. We use a simplified version
of the linear-gradient model of

Comparison of reconstructed and 80 m cup anemometer horizontal wind
speeds. (Left) Cup anemometer against Avent. (Right) Avent against ZephIR.
Each 10 min sample is shown in grey markers. A 1 : 1 line is shown for
guidance in black, and the results of a linear regression through the origin
and

The Doppler-spectrum analysis is performed over all the 2273 10 min periods
using the ZephIR data (the Doppler spectrum information is not available for
the Avent). While each of the 10 min radial velocity time series per bin
position is thresholded and despiked (see Sect.

Examples of normalized Doppler radial velocity spectra measured over five 10 min periods with the ZephIR at the positions of bin 0 (left) and bin 31 (right). The markers show the observed distributions and the solid lines show a normal fit.

The results are divided into five parts. In Sect.

Figure

(Left) Turbulence intensity

Based on the observed turbulence characteristics and knowing that we need to
average a number of 10 min spectra to be able to robustly extract the Mann
parameters

Atmospheric-stability and wind-speed classes and ranges based on the
cup- and sonic-anemometers' observations (see text for details). The
ensemble-average values of the dimensionless stability, wind speed, and
friction velocity per range are also provided. For the speed ranges we use
the median of the dimensionless stability.

Based on the ZephIR configuration (

Comparison of the 80 m cup-anemometer and the unfiltered ZephIR
radial velocity variances for bins 0 (left) and 31 (right). We show a 1 : 1
line for guidance and the predictions of the Mann model using

As expected, based on the results in Fig.

Furthermore, we can also estimate

Comparison of the 80 m cup anemometer and the unfiltered (left) and
filtered (right)

In Fig.

We also compare the lidar-derived

We can also estimate

We also classify the 10 min 80 m cup anemometer variances and Avent radial
velocity spectra into the classes given in Table

Comparison of the 80 m cup anemometer with the Avent radial
velocity variances for different beams for the 10 turbulence classes (filled
circles) in Table

When the noise filter is applied, the ratio

The ensemble-average sonic and Avent radial velocity spectra are used
separately to extract two independent sets of Mann parameters for each of the
atmospheric stability classes in Table

Normalized power spectra of the different velocity components based on the sonic-anemometer observations (left) and of the Avent radial velocity for different beams (right). The top panels show the results for the first stability range (stability 1) and the bottom panels for the last stability range (stability 5).

For the stability 1 class, the Mann model agrees well with the sonic velocity
spectra and for stability 5 the differences between the model and the
sonic-anemometer observations are larger, as expected, since the Mann model
was developed for near-neutral atmospheric conditions. Both the sonic
observations and the Mann model show the spectral peaks to move to higher
wave numbers with increasing stability because the size of the turbulence
eddies decreases with stability in agreement with the study of

In Fig.

Mann parameters for a number of atmospheric-stability conditions
(see Table

We also have to notice that when using this type of lidar configuration, we
are extracting turbulence information from the radial velocity spectra of
beams, whose spectral densities are rather close (since all beams measure a
close to

We now perform a similar procedure as that in
Sect.

Similar to Fig.

The lidar radial velocity spectra also show similar features to the sonic-based spectra; lower normalized spectral densities for the high-wind compared to the low-wind class and spectral peaks that move to lower wave numbers with increasing wind speed. The agreement of the Mann-model-based spectra deteriorates with decreasing wind speed, but the lidar-based LUT also seems to follow the behavior of the radial velocity spectra for these two classes fairly well (similarly as it does when comparing spectra for the range of stability classes).

In Fig.

Mann parameters for a number of wind-speed ranges (see
Table

(Left panel) Pulsed lidar radial velocity spectra for different
beams. (Right panel) Contributions of the spectral velocity tensor components
to the lidar radial velocity spectrum for beams 2 (solid lines) and 3 (dashed
lines). Values of

It is important to notice that some of the differences between turbulence
statistics estimated from the sonic-, cup-anemometer, and lidars'
measurements are not only due to the way they probe the atmosphere but also
because the lidar measurements are affected by optical and instrumental noise
(and by the blades, hard targets, and fog, among other factors), the cup- and
sonic-anemometers are inherently affected by flow distortion from the mast
structure and by the instrument itself, which we do not take into account, and
that there are differences in the heights of the measurements. For example,
the axes of the lidars pointed close to hub height when the wind turbine was
operating, and the 80 m cup and sonic anemometer are 1.8 and 5.8 m below
hub height, respectively. Also, the mast is 111 m from the range that we use
to extract the lidar measurements when the wind is directly from the mast to
the turbine. Wind speeds, variances, and velocity spectra from the mast and
the lidars' selected range are expected to be comparable due to the
topographic conditions of the site for the selected wind directions, but not
equal. Further details regarding how cup anemometers, sonic anemometers and
lidars measure turbulence are provided in

We assume turbulence to be homogeneous within the lidar scanning area, both
when extracting the Mann parameters and when studying the unfiltered
turbulence. This is a rather simplistic assumption as shown in the study by

In Sects.

We find very good agreement between the along-wind variance estimate of the
ZephIR (when using the ensemble-average Doppler radial velocity spectrum) and
the cup-anemometer measurement, but for the other velocity-component variances
and co-variances, when compared to those from the sonic anemometer, the
biases are too large. But, can we improve such estimates, e.g., increasing the
cone angle

On the other hand, using a lidar with

It is also important to highlight to the reader that wind turbine loads and power
performance are directly impacted by turbulence, in particular

We characterize turbulence using measurements from two types of
forward-looking nacelle lidars that were mounted on the nacelle of a wind
turbine. We compare such characteristics with those from sonic- and
cup-anemometer measurements on a mast, which is 111 m from the lidar
measurement range when the turbine and mast are aligned with the wind (thus
this distance increases for other wind directions). By using information of
the 10 min ensemble average Doppler radial velocity spectrum, we are able to
estimate 10 min unfiltered radial-velocity variances of the beams of a CW
lidar. These unfiltered beam variances are well predicted by the Mann model.
Assuming homogeneous turbulence within the lidar scanned area,

We divide the 10 min time series and the sonic-anemometer and lidar beam radial velocity spectra into atmospheric-stability and wind-speed classes based on the mast measurements. Most of the conditions are stable and relatively windy. We observe that the pulsed lidar beam variances are affected by noise as clearly seen in the lidar radial velocity spectra. Therefore, we noise filter the lidar beam spectra, and the resulting variances show very good agreement with the prediction using the Mann and spatial averaging models.

We also extract the Mann parameters from sonic-anemometer and lidar beam radial velocity spectra and intercompare them for each of the classes. Under high wind and near-neutral atmospheric conditions the agreement is good, and the differences increase with higher stability and lower wind speed, where the Mann model also has limitations fitting the sonic-anemometer velocity spectra. This is partly because increasing stability and decreasing wind speed results in turbulence length scales comparable to or lower than the length of the lidar probe volume. We suggest to improve lidar-based Mann-parameter estimations by increasing the lidars' cone angle, always keeping a central beam, which will also aid in the estimations of the non-wind-aligned velocity variances and covariances, although the flow homogeneity assumption becomes less valid.

Turbine data are not publicly available because there is a non-disclosure agreement between the partners in the UniTTe project. Lidar and mast data can be requested from Rozenn Wagner at DTU Wind Energy (rozn@dtu.dk).

The authors declare that they have no conflict of interest.

Funding from Innovation Fund Denmark, grant number 1205-00024B, to the UniTTe
project (