Continuous advancements in pulsed wind lidar technology have enabled compelling wind turbulence measurements within the atmospheric boundary layer with probe lengths shorter than 20 m and sampling frequency on the order of 10 Hz. However, estimates of the radial velocity from the back-scattered lidar signal are inevitably affected by an averaging process within each probe volume, generally modeled as a convolution between the true velocity projected along the lidar line-of-sight and an unknown weighting function representing the energy distribution of the laser pulse along the probe length. As a result, the spectral energy of the turbulent velocity fluctuations is damped within the inertial subrange, thus not allowing one to take advantage of the achieved spatio-temporal resolution of the lidar technology. We propose to correct the turbulent energy damping on the lidar measurements by reversing the effect of a low-pass filter, which can be estimated directly from the power spectral density of the along-beam velocity component. Lidar data acquired from three different field campaigns are analyzed to describe the proposed technique, investigate the variability of the filter parameters and, for one dataset, assess the corrected velocity variance against sonic anemometer data. It is found that the order of the low-pass filter used for modeling the energy damping on the lidar velocity measurements has negligible effects on the correction of the second-order statistics of the wind velocity. In contrast, the cutoff wavenumber plays a significant role in spectral correction encompassing the smoothing effects connected with the lidar probe length. Furthermore, the variability of the spatial averaging on wind lidar measurements is investigated for different wind speed, turbulence intensity, and sampling height. The results confirm that the effects of spatial averaging are enhanced with decreasing wind speed, smaller integral length scale and, thus, for smaller sampling height. The method proposed for the correction of the second-order turbulent statistics of wind-velocity lidar data is a compelling alternative to existing methods because it does not require any input related to the technical specifications of the used lidar system, such as the energy distribution over the laser pulse and lidar probe length. On the other hand, the proposed method assumes that surface-layer similarity holds.

Over the last decades, wind Doppler light detection and ranging (lidar) technology has provided compelling features to perform wind turbulence measurements within the atmospheric boundary layer (ABL) for different scientific and industrial pursuits, such as air quality, meteorology

Different scanning strategies can be designed to characterize different properties of the ABL velocity field through lidar measurements

Besides the easier deployment compared to the installation of classical meteorological towers, wind lidars tailored to investigations on atmospheric turbulence currently provide probe volumes smaller than 20 m along the direction of the laser beam and sampling frequency higher than 1 Hz, which are welcomed features for studies on ABL turbulence.

A Doppler wind lidar allows probing the atmospheric wind field utilizing a laser beam whose light is back-scattered in the atmosphere due to the presence of particulates suspended in the ABL. The velocity component along the laser-beam direction, denoted as radial or LOS velocity, is evaluated from the Doppler shift of the back-scattered signal. A pulsed Doppler wind lidar, like those used for the present work, emits laser pulses to perform quasi-simultaneous wind measurements at multiple distances from the lidar as the pulses travel in the atmosphere. The wind measurements performed over each probe volume can be considered as the convolution of the actual wind velocity field projected along the laser-beam direction with a weighting function representing the radial distribution of the energy associated with each laser pulse. Therefore, lidar measurements can be considered the result of low-pass filtering of the actual velocity field, where the characteristics of the low-pass filter are functions of the energy distribution of the laser pulse over the probe volume, probe length, and accumulation time

A reduced variance of the wind velocity is generally measured with a Doppler wind lidar compared with that measured through a sonic anemometer due to the laser-pulse averaging and different size of the measurement volume. For single-point measurements performed with a Windcube 200S lidar and azimuth angle of the laser beam set equal to the mean wind direction, a variance reduction of 8 % was predicted for a gate length of 25 m, while it was increased up to 20 % for a gate length of 100 m

Attenuation of the measured turbulent kinetic energy due to the averaging over each probe volume can be corrected through a spectral transfer function introduced in

Another method for spatial-averaging correction of wind lidar measurements was proposed in

In this work, a semiempirical procedure is proposed to correct the damping of turbulent kinetic energy associated with wavelengths comparable to the lidar probe length for turbulent velocity measurements collected within the atmospheric surface layer (ASL), which is defined as the lower portion of the ABL where momentum and thermal fluxes are assumed to be constant

The remainder of this paper is organized as follows: the theoretical aspects of the correction procedure are discussed in Sect.

Surface-layer scaling is typically used for spectral models of the wind speed assuming that the velocity integral length scale is proportional to the height from the ground,

The spectral model of Eq. (

Considering the Cartesian reference frame (

Flowchart for the iterative correction procedure of the lidar velocity measurements.

First, the premultiplied spectrum of the radial velocity projected in the horizontal mean wind direction is fitted with the spectral model of Eq. (

The present study is based on wind lidar measurements collected from three different experimental campaigns. The first dataset was acquired during the period from 9–24 June 2018 at the Surface Layer Turbulence and Environmental Science Test (SLTEST), which is part of the U.S. Dugway Proving Ground facility in Utah (GPS location: 40

Aerial views of the test sites:

The second field campaign was carried out at a test site in Celina, TX (GPS location: 33

Technical specifications of the pulsed scanning Doppler wind lidars used for this work, namely a Streamline XR by Halo Photonics and a Windcube 200S by Leosphere.

The third campaign considered in this study is the XPIA, performed during the period from 2 March–31 May 2015 at the Boulder Atmospheric Observatory (BAO) research facility in Erie, Colorado. For the XPIA campaign, 12 Campbell CSAT3 3D sonic anemometers were mounted on the BAO meteorological tower at heights of 50, 100, 150, 200, 250, and 300 m above the ground. Each height was monitored with two sonic anemometers pointing towards the northwest and southeast, respectively. Three velocity components and the temperature were recorded with a sampling rate of 20 Hz. For a complete description of the scanning strategies and the instruments utilized during the XPIA experiment see

In the present study, from the XPIA experiment we focus on tests performed during the period from 21–24 March 2015 with a Windcube 200S scanning Doppler pulsed wind lidar manufactured by Leosphere. Technical specifications of the Windcube 200S wind lidar are reported in Table

For the Celina and SLTEST field campaigns, the regime of the atmospheric stability was monitored through sonic anemometers mounted at a height of 3 m in the proximity of the lidar location. The sampling frequency of the sonic anemometer data was 20 Hz, while atmospheric stability was characterized through the Obukhov length calculated as follows

The lidar velocity signals undergo a quality control process to ensure statistical significance and accuracy of the measurements. Only datasets with a variability of the 10 min averaged wind direction within the range

The quality of the lidar signals is then checked based on the intensity of the back-scattered signal. For the Windcube 200S lidar, the samples with a carrier-to-noise ratio (CNR) higher than

The statistical steadiness of the lidar signals is estimated for both first- and second-order statistics. For the mean velocity, the absolute percentage error is calculated as follows:

Subsequently, a gradient-based procedure is used to remove outliers from the lidar radial velocity signals. Specifically, the partial derivative in time of the radial velocity is calculated through a second-order central finite-difference scheme, and velocity samples with absolute partial derivative larger than 15 times the respective median value calculated over the entire signal are marked as outliers and replaced through the inpaint-nans function available in Matlab

Description of the selected datasets:

The radial velocity,

In this section, the procedure proposed in Sect.

Based on the instantaneous wind direction measured by the sonic anemometer and neglecting the vertical velocity due to the very low elevation angle of the lidar laser beam, the horizontal equivalent velocity,

Subset of the horizontal velocity measured with a lidar and sonic anemometer from the XPIA dataset. The gray dots represent the original 20 Hz sampled sonic-anemometer data, the red line is the sonic anemometer signal downsampled at 2 Hz, the yellow line is the sonic anemometer signal after the convolution of Eq. (

Correction of the lidar velocity spectrum from the XPIA dataset:

In case significant noise in the velocity spectra is observed in the proximity of the Nyquist wavenumber (see, e.g.,

For modeling purposes, the velocity spectra are then smoothed in the wavenumber domain following the Savitzky–Golay filter

A deviation of the lidar velocity spectrum from the

To assess the accuracy of the estimated low-pass filter in representing the lidar averaging process over a probe volume, first we apply the estimated low-pass filter to the simultaneous and colocated sonic anemometer velocity signal. The horizontal velocity retrieved from the sonic anemometer is first down-sampled with the sampling frequency of the lidar measurements, namely 2 Hz, using the Matlab function “decimate” with a finite-impulse response (FIR) low-pass filter with order equal to 10

Comparison of lidar velocity data against sonic anemometry data for the XPIA dataset:

The comparison between lidar and sonic anemometer data is now presented through a linear regression analysis, which is reported in Fig.

Linear regression between lidar horizontal equivalent velocity,

We now aim to correct the lidar velocity signal from the energy damping due to the laser pulse distribution over the probe volume. First, the lidar velocity spectrum is corrected by using the existing models of Eqs. (

According to the correction technique proposed in this paper, the lidar velocity spectrum can now be corrected for the averaging process by reversing the effect of the estimated low-pass filter through Eq. (

For the SLTEST and Celina field campaigns, lidar velocity measurements were collected for periods between 2 and 3 h (see Table

The mean values and variance of the lidar equivalent velocity are plotted in Fig.

First- and second-order statistics of the equivalent velocity,

The vertical profiles of streamwise velocity variance are reported in Fig.

For the SLTEST dataset, the PSD of the lidar velocity signals acquired at the different gates from 10 up to 60 m with a vertical spacing of 1 m are plotted in Fig.

Velocity spectra for the SLTEST dataset at different heights:

Lidar velocity signals from the SLTEST dataset acquired at

Since the correction procedure is based on two consecutive best-fit operations, the robustness of the model is assessed for each lidar gate through the

The proposed spectral correction of the lidar measurements is now applied to all the datasets collected at the Celina and SLTEST sites (see Table

Correction of the lidar spectra. Left column: the black lines are

The second step of the correction procedure consists of approximating the lidar-to-Kaimal spectral ratio with the low-pass filter of Eq. (

As the last step, to retrieve the corrected lidar velocity spectra, the original spectrum is divided by the modeled correction function,

The corrected variance of the lidar velocity signals is compared with the respective quantity calculated for the raw lidar data in Fig.

Correction of the second-order statistics:

For the SLTEST dataset (see Table

Correction of the streamwise velocity variance with different methods for the SLTEST dataset:

We now focus on the variability of the parameters of the low-pass filter of Eq. (

Median and interquartile (IQ) values of the estimated order,

To investigate the effects of the spatial averaging on wind lidar measurements for different mean wind speed, turbulence intensity, and sampling height of the velocity signals, synthetic turbulent velocity spectra are generated using the spectral model of Eq. (

Within the inertial sublayer, namely for heights smaller than about 30 % of the surface layer height

According to the spectral model of Eq. (

The first analysis is performed by varying the friction velocity,

The parameter

Variation of the percentage variance damping,

The second test case, whose results are reported in Fig.

The last case study is performed for a given wind condition, namely with

Pulsed Doppler wind lidar technology is gradually achieving compelling technical specifications, such as probe lengths smaller than 20 m and sampling frequencies higher than 1 Hz, which are instrumental to investigating atmospheric turbulence with length scales typical of the inertial subrange. However, the emission of a laser pulse over the probe volume to measure the radial velocity entails a spatial smoothing process leading to damping on the measured variance of the velocity fluctuations. Existing methods propose correcting the effects of spatial averaging on lidar measurements using as input technical specifications of the lidar systems used, such as probe length and pulse energy distribution, which might not be available and, thus, often approximated with analytical functions. According to previous works, and also confirmed through this study, existing methods have limited accuracy in correcting the lidar velocity fluctuations.

In this work, we have proposed to correct the measured lidar velocity signals by inverting the effects of a low-pass filter representing the energy damping on the velocity fluctuations due to the lidar measuring process. The filter characteristics, namely order and cutoff wavenumber, are directly estimated from the spectrum of the LOS velocity under investigation. Specifically, the spectrum of the lidar velocity signal is fitted through the Kaimal spectral model for streamwise turbulence only for wavenumbers lower than a cutoff value for which the slope of the lidar velocity spectrum is observed to deviate from the expected

For this study, the proposed method for correction of the lidar data has been applied to datasets collected during three different field campaigns and for one dataset the procedure has been assessed against simultaneous and colocated sonic anemometer data. For this case, it has been shown that the proposed procedure allows us to correct the second-order statistics of the lidar data to estimate a velocity variance comparable to that measured by a sonic anemometer. The compelling results obtained for the correction of the second-order statistics of lidar data corroborate the advantage of applying the proposed method, which does not require as input any information of the lidar system used, such as probe length and energy distribution over the laser pulse. In contrast to existing methods for the correction of lidar spatial averaging, all the method parameters are directly estimated from the collected lidar data. However, the proposed method can only be applied for lidar data collected within the ASL.

To better understand the role of the cutoff wavenumber and order of the low-pass filter representing the lidar energy damping, further analysis has been conducted on synthetic turbulent velocity spectra. This analysis has been performed by varying mean wind speed, turbulence intensity, and sampling height. This analysis has shown that the main parameter for efficiently correcting the lidar energy damping is the cutoff wavenumber of the low-pass filter, which is mainly affected by the probe length, while the velocity statistics are weakly affected by the filter order. Furthermore, the results have confirmed that for a given probe length, effects of spatial averaging are enhanced with decreasing wind speed, smaller integral length scale and, thus, for a lower sampling height.

The Matlab code for the spectral correction of lidar velocity signals is available for free download at

The data are available upon request by email to G. Valerio Iungo at valerio.iungo@utdallas.edu.

MP contributed to the field campaigns at SLTEST and Celina. GVI is the principal investigator of the lidar field campaigns, provided guidance for the research strategy, and mentored his PhD student. MP and GVI performed the data analysis, examined the results, and prepared the paper.

The authors declare that they have no conflict of interest.

This work was supported by the National Science Foundation (NSF) CBET grant # 1705837, program manager Ronald Joslin. The authors are thankful to Eric Pardyjak, Marc Calaf, and Sebastian Hoch for their support during the SLTEST experiment, and to Julie K. Lundquist for leading the XPIA field campaign.

This research was supported by the National Science Foundation, Directorate for Engineering (grant no. 1705837).

This paper was edited by Laura Bianco and reviewed by three anonymous referees.