Several errors occur when a traditional Doppler beam swinging (DBS) or
velocity–azimuth display (VAD) strategy is used to measure turbulence with
a lidar. To mitigate some of these errors, a scanning strategy was recently
developed which employs six beam positions to independently estimate the

Results indicate that the six-beam strategy mitigates some of the errors
caused by VAD and DBS scans, but the strategy is strongly affected by errors
in the variance measured at the different beam positions. The ZephIR and
WindCube lidars overestimated horizontal variance values by over 60 %
under unstable conditions as a result of variance contamination, where
additional variance components contaminate the true value of the variance.
A correction method was developed for the WindCube lidar that uses variance
calculated from the vertical beam position to reduce variance contamination
in the

Atmospheric turbulence, a measure of small-scale fluctuations in wind speed,
impacts a number of fields, including air quality

In the wind power industry, turbulence is typically estimated from cup
anemometer measurements on meteorological towers. Measurements from cup
anemometers are limited by tower height and can be plagued by issues with
overspeeding and slow response times, which can lead to inaccurate mean wind
speed and turbulence measurements

While cup anemometers measure wind speed at a small point in space, remote
sensing devices report an average wind speed from a probe volume (typically
30–150

Most commercially available lidars employ a Doppler beam swinging

The six-beam technique, like the DBS and VAD techniques, is affected by
volume averaging within the lidar probe volume. All three of these techniques
also assume the three-dimensional flow is horizontally homogeneous across the
scanning circle used by the lidar, which is often not a valid assumption

The main goals of this study are to evaluate the accuracy of lidar turbulence measurements and to provide guidance about lidar scanning strategies for wind energy applications. To this end, three main research questions are addressed in this work: (1) how well do two commonly used scanning strategies (the DBS and VAD techniques) measure turbulence under different stability conditions? (2) How well does the new six-beam technique measure turbulence under different stability conditions? (3) Can new data processing techniques reduce the errors in velocity variance calculations from lidar DBS scans? To address these questions, turbulence measured with the various techniques is compared to turbulence measured by three-dimensional sonic anemometers on tall towers at sites in Oklahoma and Colorado. Sonic anemometer data from the Boulder Atmospheric Observatory (BAO) in Colorado are used to quantify the additional terms that occur as a result of variance contamination and to develop improved data processing techniques that reduce variance contamination errors. Data from the Southern Great Plains Atmospheric Radiation Measurement (ARM) site in Oklahoma provide a second location to test the new processing techniques with the DBS scan.

To the authors' knowledge, this work represents the first time the six-beam technique has been experimentally validated with high-frequency sonic anemometers and commercially available lidars. The use of commercially available lidars allows for an evaluation of turbulence measured with lidar technologies and scanning strategies that are commonly employed in the wind energy industry.

One frequently used lidar in the wind energy industry is the Leosphere
WindCube lidar, a pulsed Doppler lidar that emits short pulses of laser
energy to measure radial wind speed. The time series of the returned signal
is then split up into blocks that correspond to range gates and processed to
estimate the average radial wind speed at each range gate. The sign and
magnitude of the radial wind speed are determined from the Doppler shift of
the returned signal with respect to the original signal

Another type of Doppler lidar using pulsed 1.5

Unlike the WindCube and Halo lidars, the ZephIR is a continuous wave lidar
and focuses the laser beam at different heights to obtain wind speed
measurements. The ZephIR must collect velocity measurements individually at
each measurement height, so it takes approximately 15 s to complete a full
volumetric scan with 10 measurement heights. The probe length of the focused
ZephIR beam increases with height and, thus, the size of the range gates is
not constant. (The probe length is approximately 10

In this work, we follow standard meteorological conventions for

All three lidar systems evaluated in this study use some variant of
a plan-position indicator (PPI) scan to measure the three-dimensional wind
components, where the lidar takes measurements at several azimuth angles
around a scanning circle at a constant elevation angle. In a horizontally
homogeneous atmosphere, the radial velocity values measured by a lidar
completing a PPI scan should take the following form

The second method involves first computing the variance of the radial
velocities given by Eq. (

The different lidar scanning and data analysis approaches for computing mean
values and variances of

The WindCube v2 measures wind speed with a DBS technique, where an optical
switch is used to point the lidar beam in the four cardinal directions
(north, east, south, and west) at an elevation angle of 62

In lidar studies, Eqs. (

Equations (

The errors associated with the standard DBS variance method can be
illustrated by applying Reynolds decomposition to the instantaneous velocity
values at each beam position. For the first and third beam positions, the
following set of equations is obtained:

Taking the variance of Eq. (

Equation (

When we apply the standard DBS approach we inherently assume that
the velocity fluctuations at the different beam positions are the same, i.e.,
we assume that

Equation (

Similarly, an equation for the actual

Given the actual spatial separation and time shift between
different lidar beams, the autocorrelation function values are all less than
1 and the correction terms in
Eqs. (

In Sect.

The ZephIR lidar employs a rotating mirror to conduct a 50-point VAD scan at
each measurement height, using a similar elevation angle to the WindCube
lidar (

Overview of instruments used to evaluate different scanning strategies during LABLE 2 and LATTE.

Equations (

As discussed in the previous two sections, the use of either the DBS or the
VAD technique introduces a number of known systematic errors into lidar
turbulence calculations. Some of these errors can be mitigated when applying
the second variance calculation method (Eq.

In this work, the six-beam technique developed by

Solving Eq. (

The DBS and six-beam strategies were evaluated at a field site in Oklahoma,
while all three scanning strategies were evaluated at a field site in
Colorado. As the Colorado site featured a large amount of three-dimensional sonic
anemometer verification data, this site will be described first and will be
primarily used to draw conclusions about the accuracy of lidar turbulence
measurements. These results will be corroborated by data collected during the
Oklahoma experiment. Instruments used to evaluate the various scanning
techniques are summarized in
Table

LATTE was conducted from 10 February to 28 March 2014, with a small-scale extension of
the project from 28 March to 28 April 2014. LATTE was conducted at the
BAO, a National Oceanic and Atmospheric
Administration (NOAA) facility located in Erie,
Colorado (Fig.

One of the primary goals of LATTE was to evaluate the accuracy of lidar
turbulence measurements. Thus, the 300

LABLE took place in two phases: LABLE 1 was conducted from 18 September to 13 November 2012 and
LABLE 2 was conducted from 12 June to 2 July 2013. LABLE 2 was a multi-lidar
experiment designed to test different scanning strategies and will be
discussed in this work. Detailed information on the research goals and
instrumentation of LABLE can be found in

Locations of the lidars deployed during LABLE 2 are shown in Fig.

A coordinate rotation was applied to the sonic
anemometer and lidar data to reduce the effects of alignment and tilt errors
on the variance estimates

Typically, the coordinate rotation is applied to the raw wind speed
components before the variance is calculated, such that the variance is also
defined in the new coordinate system. However, instead of first rotating the
raw wind speed components, the variance values themselves from the old
coordinate system can also be rotated such that

It was determined during our analysis that the covariance term

The actual sampling frequencies of the sonic anemometers and lidars drifted
slightly around their prescribed sampling frequencies throughout the
measurement campaigns, which is problematic for the calculation of variance.
Thus, the raw wind speed data from the different instruments were linearly
interpolated onto temporal grids with constant spacing that matched the
sampling frequency of each instrument (

The spike filter developed by

By default, WindCube radial velocities that were associated with
signal-to-noise ratios (SNRs) lower than

As Doppler lidars use the Doppler shift from aerosols to estimate radial
velocity, they are adversely affected by the presence of precipitation
particles, which can result in beam attenuation and increased vertical
velocities

In order to mitigate the effects of random errors on variance calculations,

Mesoscale motions can also induce errors in variance calculations, as the
mean of each variable can change significantly over the averaging period used
to calculate variance as a result of a frontal passage or wind direction
shift

At the BAO, temperature and wind speed data were available at multiple
heights on the tower, so the gradient Richardson number, Ri, was
used as a stability parameter. Ri is defined by the following
equation

Due to unexpected tower maintenance at the ARM site, it was not often
possible to measure the temperature and wind speed at two heights
simultaneously. Thus, the Monin–Obukhov length,

Figure

The following sections focus on measurements from 25 March 2014, which was
a calm, clear day with no precipitation when all three lidars had good data
availability. Variance estimates from each lidar and scanning strategy are
compared to similar measurements made by the sonic anemometers and the other
lidars. For most comparison plots, variance estimates from the measurement
height where the lidar data availability was greatest are shown. For the
WindCube and ZephIR lidars, which only collect measurements up to
200

During the overnight hours of 25 March, variance values computed from the
WindCube DBS data agreed well with sonic anemometer data, but between 15:00
and 21:00 UTC the WindCube substantially overestimated the

30 min

30 min

As discussed in Sect.

At the BAO tower, two sonic anemometers were located approximately 11.5 m
apart on opposite booms at each measurement height, which were used to
simulate the measurement technique used by the WindCube lidar. First, sonic
data were projected into the directions of the WindCube beam positions and
projected data from the south sonic were shifted forward in time by 2 s to simulate the time it takes the WindCube lidar beam to move from
one side of the scanning circle to the other. The time-shifted and projected
sonic data were then used to calculate values of

Sonic anemometer data from 22 to 26 March 2014 were used to estimate values
of the autocorrelation functions for times when neither sonic was waked by
the tower. Mean values of

30 min

The mean values of

Thirty-minute

30 min mean velocity values (left panels) and variance values
(right panels) for

Another method to calculate values of the autocorrelation functions is to use
a least-squares approach to find the values of

Contamination errors also affect the variance of the

During post-processing, a VAD technique

While the ZephIR-estimated

The ZephIR and Halo lidars measured similar

Variance measured using the six-beam technique with the Halo lidar is
compared to variance measured by the sonic anemometers in Fig.

In order to determine the cause of this horizontal variance underestimation
and the negative variance values, it is instructive to examine the equations
used to calculate the variance components with the six-beam technique
(Eqs.

Velocity data from the 200

Several factors may have caused the Halo lidar to underestimate the variance
at certain beam positions more strongly than at other beam positions. One
possible explanation for the variance discrepancies could be the presence of
horizontal heterogeneity across the lidar scanning circle. The six-beam
technique requires the assumption that flow is homogeneous in the scanning
circle encompassed by the five off-vertical beams, and this assumption may
not have been valid at the BAO, which is located in the vicinity of complex
terrain, especially at a measurement height of 200

Relative intensity noise (RIN) also may have affected the variance values
measured by the Halo lidar on 25 March. RIN results from spontaneous
radiation emissions from the laser, which cause intensity fluctuations in the
laser oscillator

As in Fig.

Thirty-minute

Thirty-minute

Averaged

As several of the Halo radial beams measured radial wind speeds that were
close to 0

A technique similar to the six-beam strategy can be applied to the WindCube
data by substituting the DBS values of

Variance measured by the individual WindCube beams is compared to variance
calculated from projected sonic data in Fig.

In summary, at this site, the WindCube and Halo lidars were not able to measure the radial beam variances accurately enough to estimate the horizontal variance values with a five- or six-beam technique, possibly because wind speeds at the site were often too low to accurately measure variance with lidars. In the next section, the five-beam technique is evaluated at the ARM site, where mean wind speeds were much higher in comparison to the BAO.

The temporal resolution between the sonic anemometers and the lidars at the
BAO is drastically different; while the NCAR and OU sonics collect data at
frequencies of 60 and 30 Hz, respectively, the lidars collect data at a
frequency of 1 Hz, with most scanning strategies taking much longer than 1 s. In order to examine the effect of temporal resolution on variance
estimates, the sonic data streams were artificially degraded in temporal
resolution and then used to calculate the three-dimensional variance
components. Temporal resolutions of 1, 4, 15, and 30 s were selected to
represent the time it takes the WindCube to update the wind vector, the time
for a full WindCube scan, the time for a full ZephIR scan, and the time for a
full Halo six-beam scan, respectively. On 25 March 2014, the use of either
1 or 4 s temporal resolution resulted in percent errors around 5 % for

Plots of the 30 min variance, mean wind speed and direction, and
Monin–Obukhov length from the 60

Time series of 30 min radial variance values estimated at
60

The five-beam method and the variance correction method described in Sect.

Velocity spectra from the two sites were calculated in order to examine the
scales of turbulence measured at the different locations. Averaged spectra
for unstable conditions are shown in Fig.

The VAD and DBS scanning strategies, a novel correction method for the DBS
strategy, and the six-beam lidar scanning strategy

One of the primary disadvantages of using a VAD or DBS technique with a high
scanning elevation angle is the variance contamination that can occur as a
result of differences in the instantaneous velocity at different parts of the
scanning circle. In our work, the VAD and DBS techniques often measured
variance values that were 60–80 % larger than those measured by a sonic
anemometer as a result of variance contamination. Although using a smaller
scanning cone mitigates the effects of horizontal heterogeneity on wind speed
estimates, it also increases the contribution of variance contamination (Eqs.

Another way to reduce variance contamination is to combine the radial
velocity variance values and solve a set of equations to calculate the
variance. This method was suggested by

The authors would like to thank the staff of the Southern Great Plains ARM site, Tim Lim from NCAR, Lucas Root from NorthWest Research Associates, Shiril Tichkule from the University of Colorado at Boulder, Bruce Bartram and Daniel Wolfe from NOAA/ESRL's Physical Sciences Division, Marc Fischer and Sebastien Biraud from Lawrence Berkeley National Laboratory, the Boundary Layer Integrated Sensing and Simulation group at OU, and the technical support staff at Campbell Scientific, Leosphere, and Halo Photonics for their assistance during the experiments. We would also like to acknowledge the efforts of two reviewers, whose comments and suggestions helped improve the manuscript. LABLE 2 data were obtained from the Atmospheric Radiation Measurement (ARM) Climate Research Facility, a US Department of Energy Office of Science user facility sponsored by the Office of Biological and Environmental Research. J. F. Newman and S. Wharton received funding from the Laboratory Directed Research and Development (LDRD) award number 12-ERD-069 from the Lawrence Livermore National Laboratory. Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the US Department of Energy, National Nuclear Security Administration, under contract DE-AC52-07NA27344. Edited by: M. Rapp