Remote-sensing devices such as lidars are currently being investigated as alternatives to cup anemometers on meteorological towers for the measurement of wind speed and direction. Although lidars can measure mean wind speeds at heights spanning an entire turbine rotor disk and can be easily moved from one location to another, they measure different values of turbulence than an instrument on a tower. Current methods for improving lidar turbulence estimates include the use of analytical turbulence models and expensive scanning lidars. While these methods provide accurate results in a research setting, they cannot be easily applied to smaller, vertically profiling lidars in locations where high-resolution sonic anemometer data are not available. Thus, there is clearly a need for a turbulence error reduction model that is simpler and more easily applicable to lidars that are used in the wind energy industry.
In this work, a new turbulence error reduction algorithm for lidars is described. The Lidar Turbulence Error Reduction Algorithm, L-TERRA, can be applied using only data from a stand-alone vertically profiling lidar and requires minimal training with meteorological tower data. The basis of L-TERRA is a series of physics-based corrections that are applied to the lidar data to mitigate errors from instrument noise, volume averaging, and variance contamination. These corrections are applied in conjunction with a trained machine-learning model to improve turbulence estimates from a vertically profiling WINDCUBE v2 lidar. The lessons learned from creating the L-TERRA model for a WINDCUBE v2 lidar can also be applied to other lidar devices.
L-TERRA was tested on data from two sites in the Southern Plains region of the United States. The physics-based corrections in L-TERRA brought regression line slopes much closer to 1 at both sites and significantly reduced the sensitivity of lidar turbulence errors to atmospheric stability. The accuracy of machine-learning methods in L-TERRA was highly dependent on the input variables and training dataset used, suggesting that machine learning may not be the best technique for reducing lidar turbulence intensity (TI) error. Future work will include the use of a lidar simulator to better understand how different factors affect lidar turbulence error and to determine how these errors can be reduced using information from a stand-alone lidar.
As turbine hub heights increase and wind energy expands to complex and
offshore sites, new measurements of the wind resource are needed to inform
decisions about site suitability and turbine selection. Currently, most of
these measurements are collected by cup anemometers on meteorological (met)
towers. Met towers are fixed in location and typically only collect
measurements up to and including the height corresponding to the turbine hub
height. However, the measurement of wind speeds across the entire turbine
rotor disk is extremely important for power estimation
While lidars are capable of measuring mean wind speeds at several different
measurement heights
In this work, a new turbulence error reduction model, the Lidar Turbulence
Error Reduction Algorithm (L-TERRA), was developed for the WINDCUBE v2
(WC) vertically profiling lidar. The model combines physics-based
corrections, such as a spectral correction, with machine-learning techniques
to improve estimates of lidar turbulence intensity (TI), defined as the
standard deviation of the stream-wise wind speed divided by the average wind
speed over a 10 min period and multiplied by 100 %. While the
physics-based corrections can be applied using data from the lidar itself,
the machine-learning portion of L-TERRA requires training with a
collocated lidar or met tower dataset. Unlike other methods for improving lidar
turbulence estimates, L-TERRA is a simple method that can be easily
applied to vertically profiling lidars. The goal of L-TERRA is to
bring lidar TI estimates closer to the values of TI that would be measured by
a cup anemometer on a tower. Although cup anemometers are affected by
overspeeding
The paper is organized as follows. Section
Although lidars are frequently used in wind energy studies
Lidars emit laser light into the atmosphere and measure the Doppler shift of
the backscattered energy to estimate the mean wind velocity of volumes of
air. Laser light from Doppler lidars is typically scattered by aerosol
particles in the atmosphere, which are normally prevalent in the boundary
layer
Vertically profiling lidars, which are commonly used in wind energy, involve
scanning a cone directly above the lidar to derive the
One lidar that is frequently used in the wind energy industry is the WC,
manufactured by Leosphere (Orsay, France). The WC employs a Doppler-beam
swinging (DBS)
In Doppler wind lidars, instrument noise results from factors such as the
limited amount of aerosol scatterers in the probe volume
The scanning strategy used by a lidar can also induce errors in the
turbulence estimates. For example, the DBS technique used by the WC requires
the assumption that the instantaneous flow field is uniform across the
scanning circle. However, this assumption is generally not true in turbulent
flow, when the wind field changes significantly in both space and time
Several data processing techniques and state-of-the art measurement
configurations have already been developed for acquiring turbulence
measurements from lidars
One method for correcting lidar turbulence includes modeling the spatial
averaging effects of the lidar probe volume. This method involves convolving
the true radial velocity field with a spatial weighting function that is
controlled by the lidar beam pattern
The spectral velocity tensor can be modeled through the use of the
To reduce variance contamination caused by the DBS and velocity–azimuth
display
While single lidars require measurements around a scanning circle to estimate
the three-dimensional velocity field, multiple scanning lidars can be pointed
toward a particular volume of air to obtain turbulence estimates with much
higher spatial resolution
Structure functions describe the spatial correlation of a variable at
different separation distances
As discussed by
Several methods are currently available for obtaining more accurate
turbulence estimates from Doppler lidars. Only a few methods were discussed
here; a more extensive discussion of turbulence retrieval techniques can be
found in
The TI error model described in this work, L-TERRA, was initially developed for the WC pulsed Doppler lidar. Future work will involve expanding L-TERRA to different lidar configurations and scanning strategies, although the basic framework for the model will stay the same. The different modules of L-TERRA in its current form are described in this section.
A flowchart depicting different methods for correcting TI with L-TERRA
is shown in Fig.
Flowchart depicting different methods for correcting TI with L-TERRA. Starting and ending points are indicated by blue-outlined ovals and modules are indicated by red-outlined diamonds.
Some methods can only be applied to the
Several steps are taken before the lidar data enter the TI correction
process. First, values of
Next, the data are interpolated to a grid with constant temporal spacing (e.g., 1 Hz for the 1 s scans and 0.25 Hz for the 4 s scans), as statistical measures such as the calculation of variance and spectra require that the frequency resolution of the measurements is constant. The mean horizontal wind speed and shear parameter are calculated before L-TERRA is applied, as these parameters are required for implementation of L-TERRA and are relatively unaffected by the errors that plague turbulence measurements.
The 10 min mean horizontal wind speed,
The raw wind speeds are rotated into a new coordinate system by forcing
The next three modules comprise the physics-based corrections in L-TERRA. These corrections rely only on data from the lidar itself and use meteorological theories to apply corrections to the TI estimates.
After the lidar data are processed, different techniques are used to remove
noise and spurious data. A standard way to remove outliers from a time series
is to use a spike filter
The spike filter routine used in this work was based on one of the lidar
preprocessing steps presented by
A data point
The
Two methods were considered to mitigate the effects of volume averaging:
structure functions and spectral extrapolation. As discussed in Sect.
Another method of mitigating volume averaging is to model the lidar velocity
spectrum and use the model to extrapolate the spectrum to higher frequencies.
The high-frequency part of the modeled spectrum can then be integrated to
obtain an estimate of the variance that is not measured by the lidar as a
result of spatial and temporal resolution
Methods to reduce variance contamination include the six-beam technique
developed by
The last module in L-TERRA uses a trained machine-learning model to further reduce TI error. Inputs for the machine-learning module include lidar-measured parameters (e.g., mean wind speed and shear) and the corrected TI produced by the physics-based corrections. The model must first be trained on one or more datasets that contain data from a collocated met tower and lidar.
Inset: Google Earth image of the state of Oklahoma. Location of Southern Great Plains ARM site is denoted by white marker. Larger figure: Google Earth image of the central facility of the Southern Great Plains ARM site (outlined in red box) with overlaid elevation contours in feet. Elevation map is from the United States Geological Survey and uses contour intervals of approximately 10 feet (3.05 m). Locations of WC lidar and 60 m tower are indicated by white markers.
Two machine-learning methods were evaluated as part of L-TERRA: random
forests and multivariate adaptive regression splines (MARS). The use
of other machine-learning techniques such as neural networks could be an area
of future research, though we decided to focus mainly on the physical
corrections for this work. Random forest models are developed by averaging
multiple decision trees that were trained on different subsets of the data.
By averaging tens or hundreds of decision trees, the variance of the overall
model is reduced significantly
Potential predictor variables for the machine-learning models were divided
into two broad categories: atmospheric state and lidar operating
characteristics. Variables that were evaluated as predictor variables in
L-TERRA are given in Table
Potential predictor variables evaluated in the machine-learning module of L-TERRA.
In contrast to the methods discussed in Sect.
L-TERRA was tested on data from two different locations: the
Southern
Great Plains Atmospheric Radiation Measurement (ARM) site in Lamont, Oklahoma (Fig.
The ARM site, a field measurement site operated by the US Department of
Energy, contains several remote-sensing and in situ instruments
Stability classifications used in this work.
The WC was also deployed at an operational wind farm in the Southern Great
Plains. (Due to a nondisclosure agreement with the wind farm, we cannot
disclose the exact location of the wind farm.) Similarly to the ARM site, the
wind farm is located in fairly flat terrain with maximum elevation
differences of 5–10 m in the regions surrounding the WC deployments. The WC
was located on the wind farm from November 2013 to July 2014, with a break
from February to April 2014 while the WC was deployed for a different field
experiment. During the wind farm deployments, the WC was sited in the same
enclosure as a met tower with standard wind energy instrumentation, including
a cup anemometer at 80 m. For the winter deployment, the WC was located near
a met tower on the north end of the wind farm, and for the spring and summer
deployment, the WC was moved to a tower enclosure at the south end of the
wind farm, in accordance with the dominant wind direction during each season
at the wind farm. Directional sectors that may have been influenced by nearby
turbines were determined following the guidelines in Annex A of IEC
61400-12-1
Typical atmospheric stability parameters include the gradient Richardson
number (
One option for a lidar-based stability parameter is the shear exponent,
To test the ability of the lidar shear exponent to classify stability, values
of
A scatterplot of
Richardson number from tower data at the ARM site vs. shear exponent
calculated from WC data. Dashed lines denote stability thresholds as defined
in the text. Magenta, green, and blue circles correspond to times when the
classification based on both
Scatterplots of met tower vs. WC TI for data from 60 m measurement
height at the ARM site
At both sites, 10 min mean wind speeds measured by the WC and the met tower
instruments were well-correlated, with regression line slopes of
approximately 1 and
Mean absolute error (MAE) and slope and
At the ARM site,
As in Table
First, data from each site were examined individually to assess the performance of L-TERRA. Results from the physics-based corrections were analyzed separately from results from the full version of L-TERRA (physics-based corrections plus machine learning) to assess how well each set of corrections performed.
For both the ARM site and the wind farm, all possible combinations of the
physics-based corrections described in
Sect.
At the ARM site, the original TI MAE was 1.5 %, and MAE values that resulted from the application of L-TERRA ranged from 1.31 to 2.73 %. MAE values above the original value of 1.5 % indicate that for these model combinations, L-TERRA actually increased overall error in WC TI. For many of these model combinations with high MAE values, the MAE increased for stable conditions, while decreasing for unstable conditions and vice versa, indicating that some model combinations work better for particular stability conditions than others. Many of the high MAE values were also associated with model combinations that used the Lenschow noise removal techniques with the 4 s VAD scans. The Lenschow techniques are more aggressive with noise removal than a spike filter and also involve directly reducing the variance due to noise, rather than removing spikes in the raw velocity time series. It is possible that the noise apparent in the original WC data artificially brought the WC TI estimates closer to the sonic TI, and removing the noise variance decreased the WC TI values, bringing them further from the sonic values and increasing the MAE. In addition, spectra and auto-covariance functions derived from the 4 s data are expected to be less accurate than those derived from the higher-resolution 1 s data, which could affect the accuracy of the Lenschow techniques.
TI MAE values also varied a large amount at the wind farm, with an original MAE of 1.46 % and L-TERRA MAE values ranging from 1.38 to 2.9 %. Similarly to the ARM site, many of the higher MAE values were associated with model combinations that decreased the MAE for certain stability conditions while increasing the MAE for other stability conditions.
Overall, the model combination that minimized the TI MAE was nearly the same
for both sites and is shown in the first row of Table
L-TERRA model combinations that minimized TI MAE for different stability conditions at the ARM site and Southern Plains wind farm.
By examining the change in lidar TI after each step in L-TERRA, it was
determined that some corrections decreased error under stable conditions but
increased error under unstable conditions and vice versa. This is not
surprising, as the magnitude and sign of TI errors was strongly dependent on
atmospheric stability at both sites (Tables
For stable and unstable conditions, a spike filter was the optimal noise
removal technique. Only the model chain for stable conditions included a
volume averaging correction, likely because volume averaging effects on TI
are largest under stable conditions. For unstable conditions, using the
velocity time series from the VAD technique produced the largest reduction in
MAE. While the raw output time series from the WC is available at 1 Hz
(Sect.
The impact of each of the different physics-based correction modules on the
TI error is shown in Fig.
Progression of MAE (top), regression line slope (middle), and
Scatterplots of ARM site TI data after L-TERRA-S was applied are
shown in Fig.
Results for the wind farm were similar, with overall MAE decreasing from 1.46
to 1.19 % and regression line slopes becoming 1.00, 1.04, and 1.05 for
stable, neutral, and unstable conditions, respectively
(Table
One possible explanation for the increase in scatter at both sites could be
the misclassification of atmospheric stability by the shear exponent,
Of the 56 TI outliers identified that were associated with valid values of
Percent difference between WC and sonic TI for the ARM site as a
function of
The physics-based corrections described in the previous section require only
data from the lidar itself and do not require any training data. In contrast,
machine-learning models must be trained on a dataset before being applied to
new data. Typically, a single dataset is split into training and testing
datasets in a method known as cross validation
Scatterplots of met tower vs. WC TI for data from 60 m measurement
height at the ARM site
To determine appropriate predictor variables for the machine-learning module,
a sensitivity analysis was conducted for the WC TI error at both sites.
The sensitivity of the lidar TI error to the various predictor variables in
Table
Sample plots showing the response of TI percent error to different variables
at the ARM site are shown in Fig.
Overall, the six variables for the ARM site with the highest sensitivity values after the application of L-TERRA-S were as follows: integral timescale (vertical), SNR, corrected TI, integral timescale (horizontal), mean wind speed, and shear parameter. (For highly correlated variables, the variable with a higher sensitivity was retained in the list.) These six variables were then used to train a random forest with the wind farm data.
Results from the application of the trained random forest on the ARM site
L-TERRA-S TI values are shown in Fig.
To determine the cause of this positive bias, the sensitivity values from
both sites were compared for the six input variables. While the regression
line slope and sensitivity values for the vertical integral timescale, SNR,
mean wind speed, and shear were very similar at both sites, sensitivity
values for the horizontal integral timescale and corrected TI differed
substantially. In particular, the sensitivity of TI error to the corrected TI
was 6.86 % at the ARM site and over 5 times larger at 39.6 % at
the wind farm. After the removal of the horizontal integral timescale and the
corrected TI from the input parameter list, the bias at low TI values largely
disappeared (Fig.
These results highlight two major limitations of using machine-learning
techniques to improve lidar TI accuracy in L-TERRA: (1) the most
significant input parameters can change from one site to another and will not
be known a priori for a new site, and (2) the sensitivity of TI error to different
input variables depends on the training site and the particular lidar and
reference measurements used. To investigate the effect of the training
dataset used, a random forest was also trained on 75 % of the ARM site
data and then applied to the remaining 25 %. Training and testing a
random forest on data from the same site did decrease MAE values in
comparison to results from L-TERRA-S, but
Although machine learning can be a useful tool for turbine power prediction
Results from the sensitivity analysis conducted in this section will greatly
assist in determining areas of focus for the lidar uncertainty framework. For
example, TI error at both sites was extremely sensitive to the integral timescale of the
Lidars are currently being considered as a replacement for meteorological towers in the wind energy industry. Unlike met towers, lidars can be easily deployed at different locations and are capable of collecting wind speed measurements at heights spanning the entire turbine rotor disk. However, lidars measure different values of TI than a cup or sonic anemometer, and this uncertainty in lidar TI estimates is a major barrier to the adoption of lidars for wind resource assessment and power performance testing. In this work, a lidar turbulence error reduction model, L-TERRA, was developed and tested on WC lidar data from two different sites. The model incorporates both physics-based corrections and machine-learning techniques to improve lidar TI estimates.
The main findings from this work can be summarized as follows:
The difference between TI measured by a cup or sonic anemometer and that measured by a vertically profiling lidar can be reduced using appropriate physical models of the lidar measurements. Performance of L-TERRA improves substantially when different model configurations are used for different stability conditions (i.e., in L-TERRA-S). In addition to reducing MAE, L-TERRA-S also reduces the sensitivity of lidar TI error to atmospheric stability. The accuracy of a machine-learning method in L-TERRA-S is highly dependent on the sensitivity of the lidar TI error to the input parameters at both the training and testing sites.
Further improvements to L-TERRA-S can be made through a better
understanding of how atmospheric conditions and lidar operating
characteristics impact TI error. This understanding can be achieved through
the development of a lidar uncertainty framework and testing of the framework
with modeled atmospheric data. Future work on L-TERRA-S will also
include testing with additional datasets, including datasets from complex
terrain and different areas of the world. Practical applications of
L-TERRA for site assessment and power prediction will also be explored
in future work.
The development of L-TERRA and other TI correction techniques has significant implications for the wind energy industry, which has traditionally relied on data from fixed met towers. L-TERRA can be applied to vertically profiling lidars that are commonly used in the wind industry, thus expanding the use of lidars for wind energy applications. Lidars with improved TI estimates can be used for wake characterization, site classification, power curve testing, site monitoring, and resource assessment. Improved lidar TI estimates could also help wind energy developers make more informed decisions about turbine selection and wind farm layout. The use of lidars in place of met towers for wind energy applications should allow for a more rapid development of wind in regions where it is difficult or costly to install met towers, and the improvement of lidar turbulence estimates will greatly assist in the adoption of lidars in the wind industry.
Mean sonic anemometer wind speed data from the 60 m tower at the ARM site
are publicly available at
The authors declare that they have no conflict of interest.
The authors would like to thank the staff of the Southern Great Plains ARM site and the Southern Plains wind farm for assisting with the lidar field deployments. Sebastien Biraud and Marc Fischer of Lawrence Berkeley National Laboratory supplied sonic anemometer data for the ARM site. Sonia Wharton of Lawrence Livermore National Laboratory provided the WINDCUBE lidar used in this work and assisted with field deployments. Leosphere and NRG Systems provided technical support for the WINDCUBE lidar during the experiments. Conversations with Caleb Phillips at NREL greatly enhanced our understanding of different machine-learning models. We also thank Rozenn Wagner and an anonymous reviewer whose comments helped improve the paper. The ARM Climate Research Facility is a US Department of Energy Office of Science user facility sponsored by the Office of Biological and Environmental Research. This work was supported by the US Department of Energy under contract no. DE-AC36-08GO28308 with the National Renewable Energy Laboratory. Funding for the work was provided by the DOE Office of Energy Efficiency and Renewable Energy, Wind and Water Power Technologies Office.
The US Government retains and the publisher, by accepting the article for publication, acknowledges that the US Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for US Government purposes. Edited by: J. Mann Reviewed by: R. Wagner and one anonymous referee