Turbulent velocity spectra derived from velocity–azimuth display (VAD)
scanning wind lidars deviate from spectra derived from one-point measurements
due to averaging effects and cross-contamination among the velocity
components. This work presents two novel methods for minimizing these effects
through advanced raw data processing. The squeezing method is based on the
assumption of frozen turbulence and introduces a time delay into the raw data
processing in order to reduce cross-contamination. The two-beam method uses
only certain laser beams in the reconstruction of wind vector components to
overcome averaging along the measurement circle. Models are developed for
conventional VAD scanning and for both new data processing methods to predict
the spectra and identify systematic differences between the methods.
Numerical modeling and comparison with measurement data were both used to
assess the performance of the methods. We found that the squeezing method
reduces cross-contamination by eliminating the resonance effect caused by the
longitudinal separation of measurement points and also considerably reduces
the averaging along the measurement circle. The two-beam method eliminates this
averaging effect completely. The combined use of the squeezing and two-beam
methods substantially improves the ability of VAD scanning wind lidars to
measure in-wind (

Wind speed measurements are an integral element of wind site assessment. Traditionally such measurements have been based on in situ sampling with anemometers attached to tall meteorological masts that reach up to hub height. Such masts are immobile and expensive to erect. It is therefore favorable to implement remote-sensing devices, such as conically scanning profiling lidars, that measure wind velocities at adjustable height levels above the ground remotely.

Pulsed and continuous-wave wind lidars are the two types of profiling lidars
that are currently commercially available. The velocity–azimuth display (VAD)
scanning strategy was introduced by

Validation studies that compare measurements from meteorological masts and
ground-based profiling lidars report good agreement for first-order
statistics, namely the 10

The six-beam method developed by

The research presented here demonstrates two methods aimed at overcoming the effects of cross-contamination and averaging along the measurement circle that are inherent in the standard VAD scanning strategy. Both methods are based on modified line-of-sight velocity data processing and can be applied to currently available lidars without changes in their hardware. The line-of-sight averaging effect remains unresolved.

The first method incorporates Taylor's frozen turbulence hypothesis and
introduces a time lag into the wind vector reconstruction process.

The second method is to use only the radial velocities from lines of sight
that point into the mean wind direction (downwind) and against it (upwind) to
determine the components of the wind that are oriented in line with the mean
wind direction (

The aim of the research presented here is to demonstrate whether one of the two modified data processing algorithms or their combination leads to improved turbulence measurements from standard VAD wind lidars. For each method, we present a numerical model and experimental results. We discuss the effects of the two methods individually and combined.

This research has several practical applications. The reliable elimination of cross-contamination and averaging along the measurement circle would lead to a reduction of the systematic error of wind lidar measurements that is dependent on the prevailing wind conditions and the measurement height. In particular, estimations of the timescale of turbulence could be made with higher certainty, which would support future boundary layer research by means of profiling wind lidars. In addition, estimating the energy content of the wind components at specific wave numbers with higher certainty could also help to better predict the operational wind loads of wind turbines and other structures.

Section

Lidar geometry definitions and coordinate system.

Figure

The frozen turbulence hypothesis published by

Continuous-wave wind lidars continuously
emit a focused infrared laser beam into the air and detect the small portion
of the radiation that is backscattered by particles along the beam path
towards the beam's origin. The velocity of the backscattering particles
relative to the beam direction is then determined by analyzing the Doppler
shift between the frequencies of outgoing and incoming radiation. It is
assumed that the backscatterers are lightweight enough to move with the
instantaneous wind speed

When VAD scanning is used, the beam is deflected by a wedge prism by a
constant half-cone opening angle

The wind velocity estimations that result from this processing underlie
several effects that distinguish them from one-point measurements. These
effects can be divided into

averaging

along the lines of sight

along the measurement circle and

cross-contamination

due to longitudinal separation

due to lateral separation.

In situ wind speed measurements taken with cup anemometers or ultrasonic
anemometers have a small measurement volume that can be considered a point.
Lidar measurements, in contrast, sense wind velocities along an extended
stretch of the line of sight of the laser beam. In the case of
continuous-wave lidars, the laser beam leaves the lidar optics with a
diameter that corresponds to its effective aperture size

A definite range gate, such as for pulsed lidars, is therefore not applicable
to continuous-wave lidars. Instead, the Rayleigh length

Key specifications of the lidar used in the measurements.

The intensity of backscattered radiation is a function of the distance

All Doppler spectra that are retrieved during the radial velocity acquisition
time are averaged, and the focus point sweeps over a considerable arc of the
measurement circle during this time. This arc length

The Doppler spectra of each line-of-sight measurement resemble the
probability density function of the radial wind velocities along the
line of sight

The additional temporal averaging along the lines of sight is very low, as
one measurement takes only

As described in Sect.

The diameter

In addition to the spatial separation of the measurement points along the
measurement circle, the acquisition time must be considered. The mean wind
motion carries the air while it is probed, which might further increase the
separation of measurement points in the mean wind direction. The ZephIR 300
measures one full rotation in 1 s, and the distance the air moves
within this time is usually small compared to

Another cause for differences in the shape of turbulence spectra from one-point measurements and their counterparts from VAD scanning lidars is
cross-contamination of different velocity components. VAD scanning lidars
combine measurements from spatially separated locations where differing
velocities may prevail as if they were collected at one point. This leads to
a redistribution of turbulent energy among the velocity components

Visualization of cross-contamination caused by longitudinal spacing
of measurement points 1 and 2. The wavelength of

The two beam directions in line with and against the mean wind direction can
be used to determine

The last column combines the two previous cases and shows the resulting
distribution of amplitudes that depends on the half-cone opening angle

In a more realistic situation, turbulence is non-isotropic and the amplitude
of

In Sect.

Modeled cross-contamination effect inherent in

When the lines of sight under consideration are not longitudinally but
laterally separated, they do not face resonance but instead a second form of
cross-contamination. The strength of the contamination depends then on the
coherence of the turbulence for the given lateral separation. When the
fluctuations at the two selected focus points are very coherent i.e., their
correlation is close to unity, we can expect that the lidar-derived wind
speed estimates are correct and no cross-contamination occurs. This can be
observed at very low wave numbers at which a high degree of coherence is
expected. The other extreme is found at the other end of the spectrum at
which
small fluctuations measured at both focus points are uncorrelated. The
lidar-derived spectrum is there a linear combination of the variances of the
involved components

VAD scanning along the whole measurement circle is more complex than using
only two beams. Examining the two beams aligned with or perpendicular to the
mean wind direction is not sufficient to fully understand the effect of
cross-contamination. For circle scans, all three wind speed components are
involved in contaminating all the beams that do not point in the four
cardinal directions. We refer to the model presented in
Sect.

The lidar can also be configured to perform a so-called 3 s scan, in which one measurement cycle is built from data from three full rotations. This limits the cross-contamination but comes at the cost of much stronger averaging along the measurement circle, especially in strong wind cases, and a sampling rate that is 3 times slower. The ability to measure turbulence with this approach is so weak that it is not further investigated in this paper. Instead, the next chapter suggests two methods that can be used to reduce both averaging and cross-contamination.

In conventional VAD data processing, each measurement cycle consists of the
radial velocities that are acquired during one full rotation of the prism.
The data used in the reconstruction of one wind vector thus originates from
an air volume with the shape of a cone with a diameter of

One way to eliminate the cross-contamination due to longitudinal separation
and mitigate the averaging along the measurement circle lies in making use of
Taylor's frozen turbulence hypothesis. As mentioned in
Sect.

The basic idea here is to introduce a time lag

Selection of
line-of-sight measurements for the reconstruction of one wind vector for when
(

A restriction that comes with the idea of squeezing is that the circle sample
rate

The conventional method of averaging data from all available lines of sight
to reconstruct three-dimensional wind vectors leads to strong averaging along the
measurement circle. The method is known to deliver reliable values for the
mean wind speed and direction. The directional information allows it to
determine the two beams that lie in the upstream and downstream directions.
Within the red and green segments of Fig.

When the two-beam method is combined with the idea of squeezing, then
measurements of the

That is unfortunately not true when estimating the

Like conventional VAD processing, the SMC method and two-beam method require a wind field that is statistically homogeneous in the horizontal directions to yield correct results.

The mathematics of deducing the lidar-measured spectrum
from the second-order statistics of turbulence is very convoluted. Therefore,
we make the assumption that the measurements are performed much faster than it
takes the air to move from one side of the scanning circle to the other;
i.e., we assume that

In order to model spectra obtained from conventionally
VAD-processed lidar data, we closely follow the method of

The

To apply the method of squeezing and model the spectra we obtain from SMC processing, we now substitute Eq. (

Only the up- and downwind beams to determine the

When the mean wind is blowing from the north, the unit vectors in the up- and
downwind directions are called

Parallel to Eq. (

When obtaining the spectrum of

To compare the different methods to calculate spectra from a lidar,
Eqs. (

The test data were collected at the Danish National Test Center for Large
Wind Turbines at Høvsøre. The test site is located in West Jutland,
Denmark, 1.7

Collocated with the meteorological mast, the lidar measurements were taken by
a Qinetiq lidar that was configured to continuously scan at 78

Measurement data of 32 subsequent 10

The time series of all 10

The effects of de-trending

Figure

Modeled
(solid lines) and measured (triangle markers)

To begin with, the model predictions of conventional VAD processing and the
new SMC method are compared against each other and with regard to the true

The SMC model spectrum predicts a similar shape but without the
cross-contamination effect from longitudinal separation. Thus, we find no
resonance in the computations. The total variance of the

First, when the model is compared with the measurement data, the chosen
spectral tensor does not fit the actual wind conditions in the wave number
range below

Apart from some exceptions (e.g., at

The spectrum derived from SMC-processed data shows a clear tendency towards
its modeled spectrum but does not completely reach it. It does not show the
resonance effect seen for VAD processing, but the overall energy level is
higher than predicted for

For

The plotted model spectrum for the conventional two-beam processing method shows a significantly lower averaging effect compared to whole circle processing methods at all wave numbers except in the very low wave number region, where the methods are expected to perform similarly well.

With the two-beam method it is expected that fluctuations with the highest wave
numbers analyzed are to some extent included in the spectrum, while they were
close to zero when circle processing was applied. The normal two-beam
processing in the model is prone to cross-contamination at both resonance
points (vertical dashed lines). This situation is explained in detail in
Sect.

Overall, spectra calculated from the two-beam processed measurement data show
good agreement to the model. It is important to keep in mind that, due to the
poor fit of the measured spectra of the horizontal wind components and the
modeled spectra at low wave numbers, we can compare the relations between the
different methods but not absolute values. At low wave numbers, the measured
spectra are on average closer to the target spectrum than in the case of
circle processing. The slightly lower energy content of squeezed
measurements that we observed and explained for circle processing is found
here as well. Also, when it comes to deviations from the modeled behavior,
like for example the higher energy density at some wave numbers (e.g.,

The strong cross-contamination at the first resonance frequency is clearly
represented in the normal two-beam processing and can be completely avoided by
squeezing the two focus points to virtually one point. It is worth mentioning
that the squeezing procedure works more like expected when applied to the
two-beam method than when applied to the circle processing. This can be
explained by the error caused by not having continuous but only discrete
delaying times

At

Figure

Modeled (solid lines) and measured (triangle markers)

The modeled spectra of conventionally VAD-processed lidar measurements
predict energy densities that slightly exceed the target spectrum for very
long fluctuations with

By contrast, fluctuations shorter than approximately

When the model spectrum for SMC processing is analyzed, we find a higher
variance for all wave numbers above approximately

Now we compare the measurements with the model. Unfortunately, similar to the

The identity of VAD- and SMC-derived measurement spectra that we saw for

When the two-beam method is applied, i.e., using only the east and west beams to
derive the

The model cannot be compared with measurements because the line-of-sight
velocities of the east and west beams were erroneous. The absolute values we
measured are unrealistically biased towards nonzero values. This effect has
been previously reported

Figure

Modeled
(solid lines) and measured (triangle markers)

To begin with, we compare the model predictions of conventional VAD
processing and the new SMC method against one another and with regards to the

The fit between target spectrum and
measurement data in the low wave number
region is good for the

The modeled two-beam spectra in Fig.

At low wave numbers with

The results discussed here are extracted from a single data set that covers
one measurement height and a narrow band of mean wind speeds, turbulence
conditions and inflow directions at a single location. The reason for working
with such a limited data set lies in the fact that very few data are
available where a commercial VAD scanning wind lidar, collocated to a
meteorological mast, is scanning continuously at one height level, while
saving at least the line-of-sight velocities. Currently, the only option to
save line-of-sight velocities acquired by a ZephIR 300 is to stream the data
manually to a connected PC. The situation is further complicated by the
fact that in the normal “profiling mode” the lidar focuses to a reference
height of 38

In further studies different setups and turbulence conditions should be
investigated. Changing the measurement height has the strongest influence on
the lidar-derived spectra. For example, increasing the measurement height
would, first, make the averaging along the measurement circle more severe due
to the increased measurement circle diameter. Second, the resonance wave
numbers are then shifted towards lower values, which leads to different
cross-contamination due to lateral separation. Third, the cross-contamination
due to lateral separation becomes even more severe due to the longer
separation distances of opposite line-of-sight beams. Fourth, a further
increase in the focus distance leads to even stronger line-of-sight
averaging. Fifth, the time lag that is introduced for squeezing must be
longer, and the frozen turbulence hypothesis loses some more of its validity.
Changing the half-cone opening angle to a smaller value would on the one hand
reduce the first three of the aforementioned effects effectively, but on the
other hand it would lead to much stronger cross-contamination due to the
increased sensitivity to

This paper presents two advanced data
processing methods for improving turbulence spectrum estimations with VAD
scanning wind lidars, with an aim to reduce cross-contamination and averaging
effects. The models of these approaches, developed in Sect.

We found that the method of squeezing eliminates the resonance effect caused by the longitudinal separation of combined measurement points successfully. It also considerably reduces the averaging along the measurement circle.

The method of using only two beams for the estimation of the

Accurate measurements of the

In conventionally processed lidar data, cross-contamination compensates for averaging effects, meaning that in general total variance might be close to target values but for the wrong reasons. For systematically better turbulence measurements from VAD scanning lidars, the findings presented here should be included in raw data processing. Both approaches presented here can be applied to any existing VAD scanning continuous-wave profiling lidar unit.

Inquiries about and requests for access to data and source codes used for the analysis in this study should be directed to the authors.

FK contributed the initial idea for SMC, performed the data processing, analyzed the results and wrote the paper. JM suggested the two-beam method, developed the numerical model in Sect. 4 and supplied the measurement data.

The authors declare that they have no conflict of interest.

This research project was supported by Energy and Sensor Systems (ENERSENSE) at the Norwegian University of Science and Technology.

This paper was edited by Marcos Portabella and reviewed by two anonymous referees.