Introduction
Atmospheric turbulence, a measure of small-scale fluctuations in wind speed,
impacts a number of fields, including air quality
e.g.,, aviation e.g.,, and
numerical weather prediction e.g.,. In particular,
lidar-measured turbulence is a significant parameter in the wind energy
industry, where high-resolution measurements are often needed in remote
locations. Wind power production can differ substantially as a result of
turbulence e.g.,, and
turbulence can induce damaging loads on the turbine blades, reducing the
turbine's reliability and expected lifetime e.g.,.
Thus, turbulence is an extremely important parameter to measure in the wind
farm site selection and design process.
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 . Sonic
anemometers can measure turbulence much more accurately than cup anemometers
but are also limited by tower height. In response to these issues, remote
sensing devices, such as sodars (sound detection and ranging) and lidars
(light detection and ranging), have recently emerged as a promising
alternative to anemometers on towers. Although the ability of wind lidars to
accurately measure mean horizontal wind speeds has been well-documented in
the literature
e.g.,,
the measurement of turbulence with lidars is still an active area of research
.
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 m in the vertical) and usually take measurements less
frequently than tower-mounted instruments. These differences in spatial and
temporal resolution lead to differences in the turbulence measured by cup
anemometers and remote sensing devices e.g.,. While turbulent scales of motion
can range from milliseconds to hours and from centimeters to kilometers
e.g.,, lidars are only capable of measuring turbulent
motions with timescales on the order of seconds and spatial scales on the
order of tens of meters. In addition to differences in spatial and temporal
sampling, the scanning strategy used by the remote sensing device can also
induce errors in the different turbulence components
.
Most commercially available lidars employ a Doppler beam swinging
DBS; technique or a velocity–azimuth display
VAD; technique to collect wind speed
measurements. Using lidar DBS and VAD scans, the variances of the u, v,
and w velocity components are not directly measured; rather, the DBS and
VAD techniques combine radial velocity measurements from different points
around the scanning circle to calculate instantaneous values of the velocity
components. The time series of u, v, and w are then used to calculate
the velocity variances, whereby it is implicitly assumed that the
instantaneous velocity values are constant across the scanning circle. In
turbulent flow, this assumption is not valid even if the mean flow is
homogenous across the scanning circle, and the standard DBS and VAD approach
for computing variances is thus flawed by variance contamination errors
. A different variance calculation approach was
proposed by using a novel six-beam scanning technique,
which utilizes the radial velocity variance values from six lidar beam
positions to independently calculate the six unique components of the
Reynolds stress tensor, i.e., the velocity variances and covariances.
evaluated the six-beam technique at the Danish National
Test Center for Large Wind Turbines in Høvsøre, Denmark, using the
WindScanner lidar developed at Denmark Technical University.
found that the six-beam technique measured higher values
of variance than the VAD technique for all stability classes, with values
that were greater in magnitude and closest to the cup anemometer values under
stable conditions. These findings are in contrast to observations presented
by for the same site, which indicates that lidars measure
much larger values of variance under unstable conditions due to the larger
turbulent motions present under these conditions.
attribute this difference to the wind directions selected for each of the
studies; while only westerly wind directions were analyzed in the six-beam
study, analyzed only data that were associated with
easterly wind directions. Since the WindScanner used by
was located 2 km east of the coast of the North Sea, data from the
westerly wind direction could be influenced by the land–sea transition. As
discussed by , this transition likely caused an internal
boundary layer to develop, which, in conjunction with the current atmospheric
stability regime, would affect the turbulent scales of motion intercepted by
the lidar and the cup anemometer.
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
e.g.,, especially in complex
terrain e.g.,. All lidar scanning strategies are
subject to sources of error, and the magnitude of these errors is largely
dependent on atmospheric stability, measurement height, and the particular
type of lidar used e.g.,. Wind energy developers and
researchers must know how accurately their lidar can measure turbulence under
different conditions if they want to use turbulence information for resource
assessment or site suitability studies.
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.
Lidar scanning strategies and estimation of turbulence parameters
Current lidar technology
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
. The Leosphere WindCube v2 model was used in
this work.
Another type of Doppler lidar using pulsed 1.5 µm lasers is the
Halo Streamline manufactured by Halo Photonics (Pearson et al., 2009). The
Halo Streamline (thereafter referred to as Halo lidar) is a scanning lidar,
which allows the user to configure and choose different types of scanning
routines. In our study, the Halo was used to evaluate both a six-beam and a VAD
scanning technique, which are further detailed in the next section.
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 m at a range of
100 m, but much smaller closer to the ground;
.) The ZephIR continuously receives
backscattered radiation, so it can collect data at ranges as low as
10 m. However, the ZephIR cannot determine the direction of the
Doppler shift in the received time series, and there is a 180∘
ambiguity in the wind direction. The ZephIR 300, which was used in this work,
has an attached met station with wind direction measurements, which can
provide an estimate for the remotely measured wind direction
. However, this estimated wind direction was not
always accurate during our field campaign in Colorado, and wind direction
information from the sonic anemometers had to be used to correct the ZephIR
wind direction measurements.
General conventions
In this work, we follow standard meteorological conventions for u, v, and
w, where u is the east–west component (u>0 for wind coming from the
west), v is the north–south component (v>0 for wind coming from the
south), and w is the vertical component (w>0 for upward motion). Lidar
data are presented using a spherical coordinate system, where θ is the
azimuthal angle of the lidar beam measured clockwise from true north and
ϕ is the elevation angle of the lidar beam measured from the ground. The
radial velocity, vr, measured by the lidar is defined as positive
for motion away from the lidar and negative for motion toward the lidar.
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 :
vr=usinθcosϕ+vcosθcosϕ+wsinϕ.
When calculating velocity variances from Eq. (), two
different approaches can be used. The standard method is to apply DBS or VAD
analysis techniques to the PPI data to compute instantaneous values of u,
v, and w for each time stamp. The variances are then computed using
ui′2‾=(ui(t)-ui‾)2‾,
where the index i= 1, 2, 3 refers to the three velocity components u,
v, and w and the overbar denotes temporal averaging.
The second method involves first computing the variance of the radial
velocities given by Eq. ():
vr′2‾=u′2‾cos2ϕsin2θ+v′2‾cos2ϕcos2θ+w′2‾sin2ϕ+2u′v′‾cos2ϕcosθsinθ+2u′w′‾cosϕsinϕsinθ+2v′w′‾cosϕsinϕcosθ.
The variances and covariances of the velocity components u, v, and w
create a set of six unknown variables. By using six different beam positions
(i.e., different combinations of θ and ϕ), a set of equations can
be solved for the six unknown variables .
The different lidar scanning and data analysis approaches for computing mean
values and variances of u, v, and w are discussed in more detail in the
following sections. For reference, a schematic of the DBS and VAD scanning
strategies can be found in Sect. 12.4.3 of .
WindCube v2: DBS technique
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∘ from the
ground. Equations for the instantaneous radial velocities measured at the
four beam positions can be derived by letting θ=0, 90,
180, and 270∘ in Eq. ():
vr1=v1cosϕ+w1sinϕ,vr2=u2cosϕ+w2sinϕ,vr3=-v3cosϕ+w3sinϕ,vr4=-u4cosϕ+w4sinϕ,
where uj, vj, and wj are the instantaneous values of the velocity
components at the four beam positions, and the index j=1,2,3, and 4
describes the values measured by the north-, east-, south-, and west-pointing
beams, respectively. Some WindCube lidars, including the model used here, add
a vertically pointing beam position, vr5, which provides a direct
measurement of the vertical velocity, w (vr5=w5). It takes the
WindCube lidar 1 s to collect data at each beam location, and steer the
beam to the next beam location such that a full DBS scan takes approximately
4–5 s. However, the WindCube velocity algorithm calculates the u, v,
and w components every second using the current radial velocity and the
radial velocities obtained from the previous three beam locations
.
In lidar studies, Eqs. ()–() are usually solved for u,
v, and w assuming that the flow is homogenous, i.e., the mean values of
the three-dimensional wind components do not change across the scanning
circle e.g.,. Letting u2‾=u4‾=u‾, v1‾=v3‾=v‾, and w1‾=w2‾=w3‾=w4‾=w‾, equations for the mean velocity values can be
found:
u‾=vr2‾-vr4‾2cosϕ,v‾=vr1‾-vr3‾2cosϕ,w‾=P(vr1‾+vr3‾)+Q(vr2‾+vr4‾)2sinϕ,
where P=cos2Θ, Q=sin2Θ, and Θ (degrees) is the
wind direction. The w‾ equation is a slightly modified version of
the true DBS solution and is used by Leosphere to calculate the w velocity
for the WindCube lidar e.g.,. If a fifth vertical
beam is used, the mean value of the vertical velocity component can also be
calculated as w‾=vr5‾.
Equations ()–() are derived assuming that the values
of u, v, and w remain constant across the scanning circle. While this
assumption is valid when computing mean values in homogenous flow,
instantaneous velocity values will be highly variable due to the nature of
turbulent flow, and the computation of instantaneous velocity values with
Eqs. ()–() is inaccurate. However, the standard DBS
velocity variance calculation method uses Eqs. ()–()
to compute instantaneous values of u, v, and w, which leads to the
variance contamination errors discussed in the literature
.
WindCube v2: novel method to reduce DBS variance contamination
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:
v1=v‾+v1′w1=w‾+w1′v3=v‾+v3′=v1-v1′+v3′w3=w‾+w3′=w1-w1′+w3′,
where the mean values v‾ and w‾ can be assumed to
be constant across the scanning circle but the turbulent velocity
fluctuations will differ (v1′≠v3′ and w1′≠w3′). Combining Eqs. ()–(), an equation
for the instantaneous velocity at beam position 1 can then be derived:
v1=vr1-vr3-dvcosϕ+dwsinϕ2cosϕ,
where dv=v3′-v1′ and dw=w3′-w1′. Comparing Eqs. () and ()
illustrates how turbulent fluctuations at the different beam positions,
reflected by nonzero values of dv and dw, affect the
computation of instantaneous velocity values.
Taking the variance of Eq. () gives the following equation:
v1′2‾=14cos2ϕ(vr1′2‾+vr3′2‾-2vr1′vr3′‾-2vr1′dv‾cosϕ+2vr1′dw‾sinϕ+2vr3′dv‾cosϕ-2vr3′dw‾sinϕ+dv2‾cos2ϕ-2dvdw‾sinϕcosϕ+dw2‾sin2ϕ).
The terms involving dv and dw appear because
data are being combined from two different beam positions to estimate the v
variance. These terms can be further modified by taking into account that
dv=v3′-v1′ and dw=w3′-w1′. For homogeneous flow,
we can assume that time-averaged correlations between different velocity
components (i.e., turbulent fluxes) become independent of the position along
the scanning circle as long as both components are measured at the same
location; thus, v1′w1′‾=v3′w3′‾=v′w′‾, v1′v1′‾=v3′v3′‾=v′2‾, etc. If the velocity components are measured at different
beam positions, the fluxes can be expressed using autocorrelation functions:
v3′w1′‾=v1′w3′‾=ρvwv′w′‾v3′v1′‾=v1′v3′‾=ρvv′2‾w3′w1′‾=w1′w3′‾=ρww′2‾,
whereby the autocorrelation functions of the different velocity
components describe the spatial and temporal correlation of the instantaneous
velocity components measured at beam positions 1 and 3. Equation then becomes the following:
v1′2‾=v′2‾=14cos2ϕvr1′2‾+vr3′2‾-2vr1′vr3′‾+2cos2ϕv′2‾(1-ρv)-2sin2ϕw′2‾(1-ρw).
Equation () can then be solved for v′2‾
to give a general expression for the actual v variance that is measured
when data are combined from different beam positions in the DBS technique:
v′2‾=2(1+ρv)14cos2ϕvr1′2‾+vr3′2‾-2vr1′vr3′‾-(1-ρw)sin2ϕ(1+ρv)cos2ϕw′2‾.
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 ρv= 1 and ρw= 1. Thus, the DBS equation for the
v variance becomes
v′DBS2‾=14cos2ϕvr1′2‾+vr3′2‾-2vr1′vr3′‾.
Equation () can thus be recast into
v′2‾=21+ρvvDBS′2‾-(1-ρw)sin2ϕ(1+ρv)cos2ϕw′2‾.
Similarly, an equation for the actual u variance given in terms of the DBS variance can be derived:
u′2‾=21+ρuuDBS′2‾-(1-ρw)sin2ϕ(1+ρu)cos2ϕw′2‾.
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. ()–()
may become significant. In particular, the second term in Eqs. ()–() contains the ratio sin2ϕ/cos2ϕ, which is approximately equal to 3.54 for the WindCube v2
elevation angle of 62∘. This illustrates that ignoring the
contribution of fluctuations in the instantaneous velocity for the WindCube
v2 can lead to a large overestimation of the horizontal velocity variances
during convective conditions when w′2‾ is large. The actual
values of the autocorrelation functions will depend on atmospheric stability
and wind speed, which complicates applying corrections to the DBS variance
calculations. However, Eqs. () and ()
provide the advantage that the variances of u and v computed from the DBS
equations can be corrected if the vertical velocity component is measured
with a direct vertical beam, as was the case in our study, and estimates of
the autocorrelation functions can be made.
In Sect. , sonic anemometer and lidar measurements are used to
evaluate the autocorrelation functions, and the feasibility of applying the
correction algorithm (Eqs. –) under a
range of different stability conditions is discussed.
ZephIR 300: VAD technique
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 (ϕ= 60∘ for the ZephIR compared to ϕ = 62∘
for the WindCube lidar). For the VAD technique, the radial velocities
measured by the instrument should create a rectified cosine curve as
a function of azimuth angle , as in
Eq. (). In a standard VAD analysis, the curve is assumed to
fit the following equation:
vr(θ)=a+bcos(θ-θmax),
where θ (degrees) is the azimuthal angle of the lidar beam, a (ms-1)
is the offset of the curve from the zero-velocity line, b
(ms-1) is the amplitude of the curve, and θmax
(degrees) is the phase shift of the curve. Assuming a homogeneous flow field
with no convergence or divergence, the horizontal wind speed, wind direction,
and vertical wind speed are then derived from the following relations:
vh=bcos(ϕ),WD=θmax,w=asin(ϕ),
where a, b, and θmax are typically determined from
a least-squares approach. The values of u and v can then be derived from
the horizontal wind speed, vh, and the wind direction.
Overview of instruments used to evaluate different scanning
strategies during LABLE 2 and LATTE.
Campaign instrumentation
Instrument
Campaign
Measurement range
Temporal resolution
Scanning strategy
Owner
WindCube v2
LABLE 2
40–200 m
1 Hz
DBS
LLNL
Pulsed Doppler lidar
LATTE
12 measurement heights
Full scan: 4 s
62∘ elevation angle
20 m range gates
ZephIR 300
LATTE
10–200 m
0.07 Hz
VAD
LLNL
Continuous wave Doppler lidar
10 measurement heights
Full scan: 15 s
60∘ elevation angle
Variable range gate size (0.1–44 m)
Halo Streamline Pro
LABLE 2
105 m–9.6 km
1 Hz
Six-beam
OU
Scanning Doppler lidar
LATTE
30 m range gates
Full scan: 30 s
45∘ elevation angle
Gill Windmaster Pro
LABLE 2
60 m
10 Hz
–
Lawrence Berkeley
Three-dimensional sonic anemometer
National Laboratory
RM Young
LATTE
50, 100, 150, 200, 250,
30 Hz
–
OU
Three-dimensional sonic anemometers
and 300 m, NW booms
Campbell Scientific CSAT3
LATTE
50, 100, 150, 200, 250,
60 Hz
–
NCAR
Three-dimensional sonic anemometers
and 300 m, SE booms
Equations ()–() are derived from the first-order
coefficients of a Fourier decomposition of the radial velocity field, while
higher-order terms in the Fourier decomposition are related to divergence and
deformation . Although these higher-order terms
are typically ignored in VAD analysis of lidar data, neglecting the terms can
lead to errors in the estimated wind speed and direction
e.g.,. Errors in the turbulent components can
arise as a result of variance contamination. Similar to the DBS technique,
the VAD technique involves combining data from different beam positions with
the assumption that the instantaneous velocity field is homogeneous across
the scanning circle.
Six-beam technique
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. ), which
involves solving a set of equations for different combinations of θ
and ϕ to obtain all six components of the covariance matrix.
In this work, the six-beam technique developed by was
evaluated using the user-configurable Halo lidar.
developed the technique by using a minimization algorithm to determine the
optimum combination of θ and ϕ values that minimizes the random
errors in the variance estimates. The optimal configuration found was as
follows: five beams at an elevation angle of 45∘ that are equally
spaced 72∘ apart (i.e., located at azimuths of 0, 72, 144, 216, and
288∘) and one vertically pointed beam. This scanning strategy is
hereafter referred to as the six-beam technique.
Solving Eq. () with the chosen values of θ and
ϕ, the equations for the variances u′2‾,
v′2‾, and w′2‾ based on the
six-beam technique are
u6b′2‾=-0.4vr1′2‾+1.05vr2′2‾+vr5′2‾+0.15vr3′2‾+vr4′2‾-vr6′2‾,v6b′2‾=1.2vr1′2‾-0.25vr2′2‾+vr5′2‾+0.65vr3′2‾+vr4′2‾-vr6′2‾,w6b′2‾=vr6′2‾,
where subscript 6b indicates that the horizontal velocity variances are
computed applying the six-beam technique, and subscripts 1–6 refer to the
beam positions, with beams 1–5 spaced 72∘ apart in the scanning
circle and beam 6 pointing vertically upward.
(a) Google Earth image of the state of Colorado. Location
of BAO site is denoted by red marker. (b) Google Earth image of the
BAO site. Instrument locations are denoted by red markers. Approximate
distance between instruments is indicated by blue line and label. Only the
initial location of the WindCube lidar is shown.
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Data processing
Coordinate rotation
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 . Following the procedure
outlined by , the coordinate axes were first
rotated such that the mean meridional wind speed, v‾, was set to
0 and u was aligned with the 10 min mean wind direction. In the next
step, the coordinate axes were rotated such that w‾ was equal to
0.
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 u is aligned with the mean
wind direction and v‾ is forced to 0, as in .
The rotated variance components are described as follows:
u′2‾rot=u′2‾sin2Θ+v′2‾cos2Θ+u′v′‾sin2Θ,v′2‾rot=u′2‾cos2Θ+v′2‾sin2Θ-u′v′‾sin2Θ,w′2‾rot=w′2‾,
where Θ is the mean wind direction and the subscript rot
refers to variance components in the rotated coordinate system. This rotation
has the same effect as applying the first coordinate rotation to the original
wind speed components before taking the variance. Thus, in comparisons with
the six-beam technique, only the first coordinate rotation was applied to the
lidar and sonic data to be consistent with the coordinate rotation used by
.
It was determined during our analysis that the covariance term
u′v′‾ in
Eqs. ()–()
is also affected by variance contamination when a DBS or VAD scan is used, in
addition to the u and v variance components. At the BAO, variance
contamination caused WindCube values of u′v′‾ to differ largely
from the sonic values under unstable conditions. However, the
u′v′‾ term measured by the sonics at both sites was near-zero
throughout the day and only had a negligible effect on the coordinate
rotations for the sonic variance. Thus, the u′v′‾ term was
neglected in Eqs. () and () for
rotation of the lidar data.
Quality control
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 (1Hz/0.25Hz for the
WindCube v2, 0.067 Hz for the ZephIR, 0.033 Hz for the Halo
lidar, and 30 Hz (60 Hz) for the north (south) sonic
anemometers at the BAO tower). The sonic anemometer data were additionally
averaged to form 10 Hz data streams. The 10 Hz data streams
were used in further calculations, as they served to reduce high-frequency
noise in the sonic anemometer data as well as reduce processing time. (Values
of the 30 min variance calculated from the 10 Hz data streams did
not differ significantly from values calculated from the raw sonic anemometer
data streams.) The 60 m sonic anemometer data at the ARM site were
also interpolated to a 10 Hz grid. No averaging was needed for the
ARM sonic data, as the output frequency of the ARM sonic anemometers is
already 10 Hz (Table ).
The spike filter developed by and adapted by
was used to flag outliers in the data. A 10 min
window was shifted through the raw lidar and sonic anemometer data, and any
point that was more than 3.5 standard deviations from the 10 min block
average was flagged as a possible spike and removed from the data set. This
process was repeated until no more spikes were detected. For each pass
through the spike filter, the factor of 3.5 standard deviations was increased
by 0.1 standard deviations.
By default, WindCube radial velocities that were associated with
signal-to-noise ratios (SNRs) lower than -23dB were flagged as
missing values. For the scanning lidars, SNR thresholds were set to -23 and
-17dB for the horizontal and vertical beams, respectively. The
ZephIR lidar obtains an estimate of the mean noise level by taking
measurements with the shutter closed before each full scan. Only signals with
power that exceeds a threshold of 5 standard deviations above this mean
noise level are used to estimate the velocity .
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 e.g.,. Thus,
lidar data that were collected when rain gauges at the different field sites
recorded precipitation were flagged as erroneous data.
Selection of averaging times
In order to mitigate the effects of random errors on variance calculations,
and recommend averaging
products of perturbations over a period of time that is longer than the local
averaging length, T, the averaging time that is used to calculate mean
values from which the perturbations are derived. In this work, the variance
of each velocity component was defined as the mean value of
ui′2 (calculated using T=10min) over a 30 min
period, with i=1,2,3 corresponding to the u, v, and w estimates,
respectively. The typical averaging period for wind energy studies is
10 min, but a 30 min averaging period was used in this work to
reduce the effects of noise on variance estimates, as in .
The variance calculated with this method is hereafter referred to as the
“30 min variance”, although it differs from the standard calculation of
30 min variance. These variance estimates represent turbulent motions with
timescales from 0.01 s to 10 min, with the smallest scales of turbulence
only measured by the sonic anemometers.
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 . Thus, raw wind speed data were detrended
using a linear detrend method for each hour-long record. The detrending
method served to reduce high variance values that were associated with large
shifts in wind speed or wind direction.
Stability classification
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 :
Ri=gTo∂θ∂z(∂U∂z)2,
where g (ms-2) is the gravitational acceleration, To (K) is
the surface temperature, and ∂U∂z (s-1)
and ∂θ∂z (Km-1) are the vertical
gradients of horizontal wind speed and potential temperature, respectively.
In this work, the potential temperature gradient was approximated by adding
the dry adiabatic lapse rate, Γd, to the temperature
gradient, and the derivatives of temperature and wind speed were approximated
by using a finite differencing approach, similar to the procedure used by
:
Ri=g[(Tz2-Tz1)/ΔzT+Γd]ΔzU2Tz1(Uz2-Uz1)2,
where z1 and z2 correspond to two different measurement heights, and
ΔzT and ΔzU refer to the differences in measurement levels
for T and U. As wind shear was often extremely low during the daytime
hours at the BAO, a bulk wind shear quantity was used in
Eq. (), i.e., z1=0m was assumed for wind
speed, with Uz1=0ms-1. This bulk approximation
eliminated the extremely large negative Ri values that were often
produced at the BAO under unstable conditions as a result of the small
difference between Uz2 and Uz1.
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, L (m), from the
60 m sonic was used to define stability instead. L is defined by
the following equation:
L=-u∗3θv‾κgw′θv′‾,
where u∗ (ms-1) is the friction velocity,
θv‾ (K) is the mean virtual potential temperature at the
measurement height, κ is the von Kármán constant (commonly set
to 0.4), and w′θv′‾ (ms-1K)
is the heat flux measured at the surface e.g.,. Negative
values of both L and Ri indicate unstable conditions while
positive values indicate stable conditions. As the data sets analyzed in this
work are relatively small, only a broad classification of conditions as
either stable or unstable was made.
Comparison of turbulence parameters: LATTE
Figure demonstrates the typical diurnal cycle of
turbulence (σu2, σv2, and σw2) at the BAO, with
low values of turbulence occurring during the evening and overnight hours
(approximately 00:00–12:00 UTC) and high values of turbulence occurring
during daytime, convective conditions (approximately 12:00–00:00 UTC).
(Note that for all LATTE plots, data from the NCAR sonics are shown, unless
the mean wind direction corresponded to the NCAR sonic wake sector, in which
case the OU sonics were used. Local time is UTC-7.) During this period, the
wind direction generally shifted between easterly/southeasterly and northerly
(Fig. e). However, from approximately 18:00 UTC 23 March
to 06:00 UTC 24 March, winds were primarily from the west/northwest, which
is the direction of the Rocky Mountains. Flow from the mountains was
associated with higher mean wind speeds and variances of the u and v
velocity components in comparison to the rest of the period (Fig. ).
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 ma.g.l., data from 100 ma.g.l. are shown. For the
Halo lidar, which has a minimum range gate of 105 m, data from
200 ma.g.l. are shown.
DBS technique: WindCube
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 u and v
variance (Fig. a and b). attribute this
overestimation to variance contamination, which artificially increases the
lidar-measured variance and is most prominent under unstable conditions, when
the effects of volume averaging are minimized due to the relatively large
turbulent eddy sizes. In Sect. , we presented a framework
that further details the causes of variance contamination errors and provides
equations for correcting variances computed from lidar DBS scans. These
equations are now evaluated using sonic and lidar data.
30 min (a) u variance, (b) v variance,
(c) w variance, (d) mean wind speed,
and (e) mean wind direction at 100 m from sonic
anemometers at BAO and (f) Richardson number calculated from tower
data. Data are shown from 22 to 26 March 2014, and tick marks for each date
correspond to 00:00 UTC on that day.
![]()
30 min (a) u variance, (b) v variance, and
(c) w variance at 100 m from sonic anemometers and
WindCube DBS technique at BAO and (d) Richardson number calculated
from tower data. Data are shown from 25 March 2014. In (a) and
(b), solid blue line indicates DBS-calculated variance and dashed
black line indicates corrected variance. In (c), solid blue line
indicates DBS-calculated w variance and dashed blue line indicates w
variance calculated from vertically pointing beam. The corrected u and v
variance data show substantial improvement over the uncorrected data set
during unstable conditions.
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Variance correction
As discussed in Sect. , instantaneous velocity values
calculated from lidar DBS data contain extra terms, for example, the
dv and dw terms in Eq. (), which become large
under convective conditions. The addition of these extra terms can cause the
WindCube to overestimate the magnitude of the instantaneous u and v
velocity and contaminate the true value of the variance, as shown in Eqs. () and () and seen in Fig. a, b. Since these extra terms cannot be easily quantified
from lidar data, sonic anemometer data were used to examine the impacts of
temporal and spatial changes in the instantaneous velocity components on the
resultant variance estimates.
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 ρu, ρv, and
ρw.
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 ρu, ρv, and ρw under unstable
conditions were 0.96, 0.81, and 0.66, respectively. Under stable conditions,
the average values were 0.95, 0.71, and 0.69. These values indicate that the
u, v, and particularly w wind components do change significantly in
both space and time and that values of w become decorrelated more quickly
than values of u and v as a result of the presence of smaller turbulent
scales of motion in the vertical direction.
30 min (a) u variance, (b) v variance,
and (c) w variance at 100 m from sonic
anemometers and lidar VAD techniques at BAO and (d)
Richardson number calculated from tower data. Data are shown from 25
March 2014. Comparison of the Halo and ZephIR VAD-processed data
suggests that a lower elevation angle may be advantageous (e.g.,
lower v variance values measured by the Halo lidar, which uses a lower elevation angle, shown in b).
Note the smaller u and v variance values shown here for the Halo and ZephIR (VAD)
as compared to the Wind Cube (DBS) in Fig. .
![]()
The mean values of ρu, ρv, and ρw calculated from the sonic
data were then used with
Eqs. () and ()
to correct the WindCube DBS variance values, where the value of
w′2‾ in the correction equations was taken to be the velocity
variance measured by the WindCube vertical beam. Corrected u and v
variance values on 25 March 2014 are indicated by the black dashed lines in
Fig. . The variance correction does not significantly change
variance values under stable conditions, when the value of w′2‾
is small, but it serves to reduce estimates of u′2‾ and
v′2‾ by over 20 % under unstable conditions, bringing them
closer to the values measured by the sonics. In reality, the values of the
autocorrelation functions needed for the correction should be smaller than
the values that were calculated for the sonics, as the sonics were only
located 11.5 m apart while the WindCube scanning cone has a diameter of 106 m
at a measurement height of 100 m. Thus, there is still some variance
contamination present in the corrected u and v variance values shown in
Fig. , as the values of the autocorrelation functions used
in the correction do not fully represent the degree of decorrelation that
occurs between the WindCube beams.
Thirty-minute (a) u variance, (b) v variance, and
(c) w variance at 200 m from sonic anemometers and Halo
lidar six-beam technique at BAO and (d) Richardson number calculated
from tower data. Data are shown from 25 March 2014. Note the high agreement
between the six-beam Halo method and sonic in (c) as compared to the
VAD Halo method in Fig. c for w variance. (The difference
in vertical variance accuracy is also likely related to the different
turbulent scales present at 100 and 200 m.)
![]()
30 min mean velocity values (left panels) and variance values
(right panels) for (a) vr1, (b) vr2,
(c) vr3, (d) vr4, (e) vr5, and
(f) vr6 measured by Halo lidar and calculated from projected
sonic data. Values of (g) u variance and (h) v variance
are also shown for reference, where sonic values are from standard variance
calculation and Halo values are from six-beam calculation. Mean wind speed
from sonic is shown in (i) and Richardson number from tower is shown
in (j). Data are shown from 25 March 2014 at 200 ma.g.l.
at the BAO tower.
![]()
Another method to calculate values of the autocorrelation functions is to use
a least-squares approach to find the values of ρu, ρv, and
ρw that provide the best estimate for the sonic variance. This method
yielded similar values of ρu and ρv to the values calculated from
the sonic data and much lower values of ρw in comparison to the sonic
values (approximately 0.29 under unstable conditions and 0.13 under stable
conditions). True estimates of the autocorrelation functions for the
distances spanned by the WindCube beams would require either sonic
anemometers at different towers or a numerical model that provides wind speed
data with high spatial and temporal resolution.
Methods for estimating <inline-formula><mml:math display="inline"><mml:mi>w</mml:mi></mml:math></inline-formula> variance
Contamination errors also affect the variance of the w component if it is
computed applying the DBS method, although it generally does not lead to
variance overestimates, as volume averaging for the w component is more
significant than it is for the u and v components .
However, the WindCube v2 lidar utilizes a vertical beam position once per
scan to obtain a direct measurement of the vertical velocity directly above
the lidar, which is only minimally affected by variance contamination. Both
the vertical beam method and the DBS method (Eq. ) were
investigated in this work to determine the advantage of having a vertically
pointed beam position to measure w variance. At the BAO, the w variance
measured by the WindCube lidar's vertical beam was much higher and more
accurate than the w variance calculated from the DBS equations,
particularly under convective conditions (Fig. c). This is
not surprising, as the vertical beam variance is a measure of the variance
directly above the lidar (barring the effects of volume averaging), while the
DBS-estimated variance is an average across the scanning circle. Thus, in all
further plots, w variance from the WindCube lidar is calculated from the
vertical beam.
VAD technique: ZephIR, Halo
During post-processing, a VAD technique was used
to calculate variance from the six-beam Halo data. The five off-vertical
beams were fit to a sine curve to estimate the horizontal wind speed, wind
direction, and vertical wind speed from each scan. This information was then
used to create a time series for the u, v, and w components from which
the variance could be calculated. Variance from the Halo VAD technique was
compared to the variance estimated by the ZephIR lidar, which employs
a 50-point VAD at each height as part of its scanning strategy, as well as
variance measured by the sonic anemometers.
While the ZephIR-estimated u variance values were quite close to those
measured by the sonic anemometers and the Halo lidar (Fig. a), the ZephIR overestimated the v variance under
unstable conditions during some half-hourly periods (Fig. b), which could indicate that the ZephIR lidar VAD
technique is also affected by variance contamination, similar to the WindCube
lidar. Although the WindCube and ZephIR lidars use similar elevation angles
(Table ), the overestimation of v variance by the
ZephIR lidar was not nearly as large as it was for the WindCube lidar. The
ZephIR has variable range gate sizes and takes nearly 4 times as long to
complete a full scan from 10 to 200 m as the WindCube lidar, so the
lower temporal resolution of the ZephIR scans may have caused it to measure
lower variance values than the WindCube lidar. The Halo lidar produced the
most accurate VAD-estimated u and v variance values throughout the day
(Fig. a and b), suggesting that a VAD technique with
a lower elevation angle can measure horizontal variance values more
accurately. The Halo lidar used an elevation angle of 45∘ while the
WindCube and ZephIR lidars used elevation angles of 62∘ and
60∘, respectively. Although the values of dv and
dw were likely larger for the Halo lidar, since it used a wider
scanning cone, the contribution of the dw2‾ term to the
v variance in Eq. () is smaller for lower values of ϕ.
Additionally, the temporal resolution of the Halo lidar likely led to the
measurement of lower variance values than the WindCube and ZephIR lidars,
which may have masked the effects of variance contamination.
The ZephIR and Halo lidars measured similar w variance values with
the VAD technique, which were underestimates in comparison to the
sonic anemometer values for nearly all stability conditions throughout
the day (Fig. c). As previously discussed, the most
accurate lidar method for measuring the w variance appears to be the
use of a vertical beam position to obtain a direct measurement of the
vertical wind speed (Figs. c and c).
Halo: six-beam technique
Variance measured using the six-beam technique with the Halo lidar is
compared to variance measured by the sonic anemometers in Fig. . Similar to the WindCube lidar, the six-beam
technique includes a vertically pointed beam to obtain a direct measurement
of the vertical velocity. Vertical variance estimated by the Halo six-beam
technique was much higher and more accurate than the vertical variance
measured by the Halo VAD technique (Figs. c and c). However, larger discrepancies occurred in the u
and v variance values. During strongly unstable conditions from 17:00 to
21:00 UTC, the Halo six-beam technique often underestimated the u and v
variance in comparison to the sonic anemometers
(Fig. a and b). In some extreme cases, the u and v
variance values became negative, which should be mathematically impossible
given the definition of variance (σui2=(ui-ui‾)2‾).
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. –).
Equations () and () for the u and
v variance, respectively, both include the term -vr6′2‾,
meaning that the variance calculated from the vertical beam radial velocity
is subtracted from the combination of the other terms. Thus, when
vr6′2‾ is large, as is often the case under
convective conditions (Fig. c), or overestimated due
to instrument noise, a large value is subtracted in
Eqs. () and (), and the u and v
variance can become negative if the other radial variances are not measured
accurately. The other negative terms in Eqs. () and () could also decrease the horizontal variance components
and cause them to become negative. Similarly, if the positive terms in
Eqs. () and () are underestimated,
the variance values would also likely be underestimated. Although negative
values of σu2 and σv2 only comprised approximately 5 %
of the horizontal variance values at 200 m during the 5-day analysis
period, the underestimation of horizontal variance components by the six-beam
technique is a significant issue that warrants further investigation.
Velocity data from the 200 m sonic anemometers were projected into
the directions of the different Halo beam locations in order to assess the
accuracy of the measurements from each beam position. Time series plots of
the 30 min mean radial wind speeds and radial variance values measured by
the sonics and Halo lidar on 25 March 2014 are shown in
Fig. . During the afternoon of 25 March, mean
wind speeds were very low (Fig. i), which is
reflected by the low radial wind speeds measured by the Halo lidar and
calculated from the projected sonic data
(Fig. a–f). Some minor differences in the
radial wind speeds measured by the Halo and sonic anemometer were evident in
the late afternoon, as well as strongly underestimated and negative Halo u
and v variance values (Fig. g and h). The
largest discrepancies between the radial variance values also occurred in the
late afternoon, when the Halo strongly underestimated the variance of the
radial velocity at the third, fourth, and fifth beam positions
(Fig. c–e). In the initial six-beam
equations, terms vr3′2‾,
vr4′2‾, and vr5′2‾ have
positive coefficients in the u variance equation
(Eq. ), and terms vr3′2‾ and
vr4′2‾ have positive coefficients in the v
variance equation while the vr5′2‾ term has
a negative coefficient (Eq. ). The actual coefficients of
the radial beam variances will change once the coordinate rotation is applied
(Eqs. –), but for the most
part weighted values of vr3′2‾,
vr4′2‾, and vr5′2‾ are
added to the weighted values of the other radial beam variances to obtain
values for the u and v variance. Thus, if the variance measured at beam
positions 3, 4, and 5 is underestimated, the u and v variance will also
be underestimated. Similar trends were also observed on 24 March 2014 (not
shown).
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 ma.g.l.
Horizontal heterogeneity and high values of variance could cause large
amounts of scatter about the VAD sine curve . The
differences between the instantaneous radial velocities and the fit VAD sine
curve (Eq. ) were examined for 25 March, but no noticeable
differences were evident for the different beam positions, although residuals
were much larger under unstable conditions. A modeled flow field and lidar
simulator would likely be needed to definitively quantify the effect of
horizontal heterogeneity on the variances measured by the different lidar
beam positions.
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 . In a coherent heterodyne lidar, RIN
appears as pink noise; i.e., it is mainly present in the low-frequency part
of the Doppler spectrum . Since low wind speeds would
also be detected in the low frequency part of the spectrum, RIN can impact
the accuracy of Doppler velocity measurements under low wind speeds.
found that a ZephIR lidar most strongly underestimated the
turbulence intensity measured by cup anemometers when weak wind speeds were
measured.
As in Fig. but for 6 March 2014.
Richardson number is not shown, because the 10 m temperature sensor
had data quality issues on this day (possibly related to tower icing).
![]()
Thirty-minute (a) vr1, (b) vr2, (c)
vr3, (d) vr4, and (e) vr5 variance values
measured by WindCube lidar and calculated from projected sonic data, where
positions 1–4 are located at azimuths of 0, 90, 180, and 270∘,
respectively, at an elevation angle of 62∘ and position 5 is pointed
vertically. Values of (f) u variance and (g) v variance
are also shown for reference, where sonic values are from standard variance
calculation and WindCube values are shown from DBS calculation (solid blue
line), five-beam calculation (green line), and corrected DBS calculation
(dashed black line). Mean wind speed from sonic anemometer is shown in
(h). Data are shown from the BAO on 25 March 2014 at
100 ma.g.l. (left panels) and from the ARM site on 23 June 2013 at
60 ma.g.l. (right panels). The WindCube five-beam method results in
large underestimates of u and v variance, especially under convective
conditions at the BAO, while much better agreement is seen with the new
variance correction method.
![]()
Thirty-minute (a) u variance, (b) v variance,
(c) w variance, (d) mean wind
speed,(e) mean wind direction, and
(f) Monin–Obukhov length at 60 m from sonic anemometer at
the ARM site. Data are shown from 19 to 23 June 2013, and tick marks for each
date correspond to 00:00 UTC on that day.
![]()
Averaged (a) u spectra, (b) v spectra, and
(c) w spectra for unstable conditions measured by the south BAO
sonic at 50 and 100 m and the ARM sonic at 60 m. Black line
denotes theoretical -2/3 slope for inertial subrange. Note the larger
amount of energy contained at the lowest frequency scales at the BAO for the
w component at both measurement heights.
![]()
As several of the Halo radial beams measured radial wind speeds that were
close to 0 ms-1 during the afternoon of 25 March
(Fig. a–f), it is possible that RIN caused
the Halo lidar to underestimate the variance at certain beam positions. To
further investigate this possibility, mean radial velocity and variance
values were calculated for 6 March 2014, a date from the campaign when
atmospheric conditions were less strongly convective and wind speeds were
higher during the late afternoon (Fig. ).
Although there were some small biases in the radial wind speed measurements
from the Halo lidar (Fig. a–f), there were
no large discrepancies in the radial variance measurements on 6 March and no
strongly underestimated or negative u and v variance values
(Fig. g–h). This suggests that the six-beam
technique is more accurate when wind speeds are higher, as radial variance
estimates are more accurate under higher wind speed conditions and more
accurate horizontal variance estimates are produced as a result. However, it
is difficult to make this assessment with the limited data set available. For
the 5-day period selected for this study, there was no clear trend between
the mean radial wind speed measured at each beam location and the error in
Halo-measured variance at each beam location. It should be noted that the
mean wind speeds measured during the afternoon of 25 March rarely exceeded
3 ms-1, which is below the typical cut-in speed for a modern
wind turbine e.g.,. Thus, variance measurements under
low wind speeds would likely not be used for wind energy applications.
Application of six-beam technique to WindCube lidar
A technique similar to the six-beam strategy can be applied to the WindCube
data by substituting the DBS values of θ and ϕ into
Eq. (). The u′v′‾ term
drops out because either cosθ or sinθ is equal to 0 for
every beam position, resulting in five equations and five unknowns. Similar
to the Halo six-beam technique, these equations can be solved simultaneously
to obtain values of the u, v, and w variance, which can then be rotated
into the coordinate system aligned with the mean wind.
Variance measured by the individual WindCube beams is compared to variance
calculated from projected sonic data in Fig. .
Similar to the Halo lidar (Figs. and
), the variance of the radial velocities was
sometimes overestimated by the WindCube lidar and sometimes underestimated.
Although there were no large discrepancies between the WindCube and sonic
radial variance under unstable conditions (14:00–23:00 UTC), the five-beam
technique produced large u and v variance underestimates and several
negative variance values (Fig. f and g). Thus,
even when a lidar with better temporal resolution and a smaller scanning
circle than the Halo lidar is used, the simultaneous use of all the radial
beam velocity variances to calculate the u and v variance can result in
large uncertainties, especially during unstable conditions.
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.
Note on the effects of temporal resolution
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 u
and v and 10 % for w while the use of either 15 or 30 s resolution
resulted in larger errors of 20 to 50 % in the variance estimates (not
shown). Thus, the temporal resolution of the lidar scans likely influenced
the variance estimates in addition to the scanning strategy used,
particularly for the ZephIR and Halo lidars.
Comparison of turbulence parameters: LABLE 2
Plots of the 30 min variance, mean wind speed and direction, and
Monin–Obukhov length from the 60 m sonic over 5 days at the ARM
site are shown in Fig. . Diurnal trends in the LABLE 2
turbulence parameters are similar to those seen in the LATTE data: turbulence
is fairly low during overnight, stable conditions before increasing during
daytime, convective conditions. However, mean wind speeds at the ARM site
were generally much higher than at the BAO, and winds were nearly constantly
from the south/southeast. In addition, variance values were generally much
higher at the ARM site. In comparison to the BAO, the ARM site is located in
much simpler terrain and SNR values tended to be much higher, so lidar
variance measurements are expected to be more accurate.
Time series of 30 min radial variance values estimated at
60 m from projected sonic data and WindCube lidar data during
LABLE 2 on 23 June 2013 are shown in the right panels of
Fig. . In contrast to the case shown
from the BAO (left panels in Fig. ),
variance values are higher throughout the day and the WindCube lidar
nearly always underestimated the radial variance values calculated
from the projected sonic data
(Fig. a–e). However, when applying the
DBS method, the WindCube again overestimated the u and v variance
under unstable conditions as a result of variance contamination
(Fig. f and g).
The five-beam method and the variance correction method described in Sect. were also applied to the 60m WindCube data at the ARM
site. Values of ρu, ρv, and ρw obtained from the sonics at
the BAO were used in the variance correction equations (Eqs. –) to determine how well this
correction worked at a different site. At the ARM site, both the five-beam
method and variance correction method produced nearly identical variance
values under stable conditions, while the five-beam method produced much
lower variance values under unstable conditions (Fig. f, g). However, none of the five-beam u and
v variance values were negative, in contrast to the BAO data. This likely
occurred because the WindCube underestimated the variance from the radial
velocities by approximately the same amount throughout the day. In
particular, the WindCube measured lower w variance values than the sonic
anemometer during nearly all time periods on 23 June 2013 at the ARM site
(Fig. e, right panel) while the WindCube
measured w variance values that were approximately the same as or slightly
higher than those measured by the sonic anemometers at the BAO (Fig. e, left panel). Similar to the six-beam
equations, the value of the vertical variance is subtracted from the sum of
the other terms in the five-beam equations. As discussed in Sect. , when the value of the vertical variance is large or the
vertical variance is overestimated, this can cause the calculated u and v
variance to become negative. This did not occur at the ARM site, as values of
the vertical variance were much smaller than variance values from the other
beam positions under unstable conditions, in contrast to the BAO, where the
vertical variance values were similar to the variance estimated from the
horizontal radial beams. Thus, the vertical variance term had a much larger
influence on the u and v variance values for the example shown at the BAO
than it did at the ARM site.
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. for the 60 m
ARM sonic data and the 50 and 100 m BAO sonic data. The spectral power
calculated from the ARM site data is much higher than for the BAO data, which
is reflected by the higher values of variance measured at the ARM site in
comparison to the BAO (Figs. and ). The
largest difference between the spectral shapes occurs for the w spectra,
where the peak in the ARM site spectrum is shifted to higher frequencies in
comparison to the BAO spectra at both 50 and 100 m. Thus, the vertical
turbulent scales present during the campaign at the ARM site appear to be
generally smaller than those measured at the BAO site under unstable
conditions. This caused the WindCube lidar to often underestimate the w
variance at the ARM site, as the effects of temporal resolution and volume
averaging are more significant for smaller turbulent scales. SNR values were
also generally higher at the ARM site than at the BAO, so lower amounts of
noise in the raw velocity data also likely led to the measurement of smaller
vertical variance values. In addition, differences in season and measurement
site characteristics may have affected the turbulent scales observed at the
two sites. Higher mean wind speeds at the ARM site (Fig. h) also likely led to more accurate variance
values in comparison to the BAO.
Summary and conclusions
The VAD and DBS scanning strategies, a novel correction method for the DBS
strategy, and the six-beam lidar scanning strategy were
evaluated at two measurement sites: the Southern Great Plains ARM site and
the Boulder Atmospheric Observatory. As a 300 m tower with 12
sonic anemometers was located at the BAO, the evaluation primarily focused on
data collected there.
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. –). In this work, a method was
developed to correct DBS-estimated variance values for contamination. The
additional variance terms were quantified using estimates of the
autocorrelation functions ρu, ρv, and ρw from sonic
anemometer data at the BAO and vertical variance measured by the WindCube's
vertical beam. This correction method was not expected to completely
eliminate variance contamination, as estimations of the autocorrelation
functions from the sonic anemometers were not fully representative of the
decorrelation that actually occurs across the DBS scanning circle. In
addition, it was assumed that turbulent fluxes remain constant across the
scanning circle, which is not always true. However, the correction method
still reduced WindCube variance overestimates by over 20 % under unstable
conditions at both the BAO and the ARM site. The correction method can be
applied to other lidars that have a vertical beam position and does not
require the use of a scanning lidar or complex calculations. Thus, it is a
method that can be easily used by wind farm managers or researchers with
commercially available lidars.
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 as a scanning
strategy with six beam positions, and it can also be applied to the five beam
positions used by the WindCube lidar. At the BAO, the calculation of
horizontal variance with the five- and six-beam equations often led to
variance underestimates and even negative u and v variance values
(Figs. and ). The
technique appears to be strongly affected by inaccurate variance measurements
from one or more beam positions, which could be due to the low wind speeds
and low SNR values measured at the BAO. At the ARM site, wind speeds were
much higher and the WindCube lidar nearly always underestimated the radial
velocity variances, likely as a result of the smaller turbulent scales
present at the ARM site. The uniform underestimation of the radial velocity
variances around the scanning circle led to more accurate five-beam variance
estimates at the ARM site.