17A.5 OPTIMIZING LIDAR SCANNING STRATEGIES FOR WIND ENERGYTURBULENCE MEASUREMENTS

Jennifer F. Newman1∗, Timothy A. Bonin1, Petra Klein1, Sonia Wharton2, and Philip B. Chilson1

1School of Meteorology, University of Oklahoma, Norman, OK2Atmospheric, Earth and Energy Division, Lawrence Livermore National Laboratory, Livermore, CA

1. INTRODUCTION

Initially, it was assumed that the power pro-duced by a wind turbine depends only on the av-erage wind speed at the turbine hub height. How-ever, recent studies have indicated that turbinepower production depends on a variety of otherfactors, including the thermodynamic stability ofthe atmosphere (e.g., Sumner and Masson 2006;Wharton and Lundquist 2012), turbulence (e.g.,Elliott and Cadogan 1990), and the entire windspeed profile intercepted by the turbine blades,i.e., across the rotor-disk swept area (e.g., Wag-ner et al. 2009). Wharton and Lundquist (2012)showed that the average power produced by awind turbine at a West Coast wind farm differed byas much as 20% according to the stability and tur-bulence present in the atmosphere (Fig. 1). Thisdifference in power production is extremely impor-tant for utility operators, who must decide whichcombination of energy sources will best meet con-sumer demand at a given time. In some areas,penalties are issued to wind farm owners if theamount of available wind energy is overestimatedand the wind power supply does not meet the en-ergy demand (Lundquist et al. 2010).

An accurate wind resource assessment re-quires an estimate of wind speeds across theheights spanned by a turbine rotor disk (typically40 to 120 m above ground level; AGL). Tradition-ally, these measurements have been made withcup anemometers on tall meteorological towers.However, as turbine hub heights extend furtherinto the atmosphere, it has become more diffi-cult and costly to build tall towers that reach theseheights. In response to this issue, remote sensingdevices have recently emerged as an alternativeto tall towers and are now commonly employed inwind energy studies.

∗Corresponding author address: Jennifer F. Newman,School of Meteorology, University of Oklahoma,120 David L. Boren Blvd., Norman, OK 73072.E-mail: jennifer.newman@ou.edu

Figure 1: Normalized power produced by a windturbine as a function of equivalent, or rotor disk-averaged, wind speed, and atmospheric stabil-ity regime. Stable regimes were associated withlow amounts of turbulence, while convective andstrongly convective regimes were associated withhigh amounts of turbulence. From Wharton andLundquist (2012).

One frequently used remote sensing instru-ment is a Doppler lidar (light detection and rang-ing), which utilizes the Doppler shift of backscat-tered laser energy to estimate the wind speedwithin a volume of air. Lidars can measure windspeeds up to several hundred meters above theground and are ideally suited for estimating windspeeds across a typical turbine rotor disk area.However, the measurement of turbulence with re-mote sensing devices such as lidars is not asstraightforward. Lidars estimate the mean windspeed of volumes of air that are typically 10–30meters in length, and thus cannot measure small-scale, high-frequency turbulent motions. In addi-tion, most lidar scanning strategies were designedto measure mean wind speeds, not turbulence. At-mospheric turbulence is extremely important in thewind energy field; turbulence has profound effectson turbine power production and can induce dam-aging loads on turbine blades (e.g., Kelley et al.2006). Thus, in order to be viewed as a viablealternative to meteorological towers, remote sens-

ing devices most be able to accurately measureturbulence.

This work explores the use of various lidarscanning strategies to measure turbulence in thelower boundary layer, i.e., the portion of the at-mosphere that is most important for wind energystudies. To this end, a feasibility study was carriedout during the summer of 2013 to evaluate differ-ent lidar scanning strategies. Two scanning lidarswere deployed at the Southern Great Plains Atmo-spheric Radiation Measurement (ARM) site, a fieldmeasurement site located in northern Oklahomaand instrumented with various in-situ and remotesensing devices. These lidars were used in con-junction with a vertically-scanning, commerciallyavailable WindCube lidar and an additional scan-ning lidar located permanently at the ARM site totest different scanning strategies.

While the scanning strategy of the Wind-Cube lidar could not be changed, the scanningstrategies of the three scanning lidars were en-tirely user-defined, allowing for the optimization ofscanning strategies for turbulence measurements.Three different scanning strategies were testedduring the experiment: a tri-Doppler technique, anovel six-beam technique, and a “virtual tower”technique, where all three scanning lidars wereused to measure wind speed and turbulence atseveral different heights above the WindCube li-dar. The turbulence and mean wind speeds mea-sured with these scanning strategies were com-pared to identical parameters measured by theWindCube lidar and sonic anemometers on a 60-m meteorological tower at the ARM site. In this pa-per, only results from the tri-Doppler and six-beamscanning strategies are discussed.

2. BACKGROUND

2.1. Experimental Overview

The field experiment took place from 12 Juneto 3 July 2013 at the Southern Great Plains ARMsite near Lamont, Oklahoma (Fig. 2). The siteis situated in flat, fairly uniform terrain in an areaof Oklahoma with high wind resource potential; infact, a large operational wind farm is located in thesame region. Strong wind speeds in the regionare often associated with the nocturnal low-leveljet (LLJ), a common phenomenon in the SouthernGreat Plains region that experiences a climatolog-ical maximum during the summer months in Okla-homa (Bonner 1968; Song et al. 2005).

Locations of the various instruments used in

the study are shown in Fig. 3. The OU Halo lidarand the ARM Halo lidar are the scanning lidarsowned by the University of Oklahoma (OU) andthe ARM site, respectively. The Galion lidar is alidar rented by OU that has identical hardware tothe two scanning Halo lidars.

2.2. Instrumentation

The three scanning lidars (OU Halo, ARMHalo, and Galion) are pulsed heterodyne lidarsequipped with a scanner that can move in bothazimuth and elevation. The moveable scanner al-lows for the implementation of user-defined scan-ning strategies. In contrast, the WindCube lidaruses a rotating prism to steer the lidar beam inazimuth and is limited to scanning at a fixed ele-vation angle. Technical specifications of the lidarsare summarized in Table 1. Detailed informationfor the Halo system can be found in Pearson et al.(2009).

Data from a 60-m meteorological towerwere also available during the experiment. GillWindmaster Pro 3-D sonic anemometers andLicor infrared gas analyzers are mounted on thetower at 25 and 60 m. A 4-m flux tower is alsolocated near the base of the 60-m tower andcollects surface meteorological data in addition tosonic anemometer data. More information can befound in the instrument handbook: http://www.arm.gov/publications/tech_reports/handbooks/co2flx_handbook.pdf. Sonicanemometer data were collected at a frequencyof 10 Hz.

Unfortunately, sonic anemometer data wereonly available up to 60 m AGL at the ARM site,while the first useable range gate of the scanninglidars was centered at 105 m AGL. Although lidardata from some of the scanning strategies wereavailable at lower heights, the majority of windspeed data from the scanning lidars did not coin-cide with any sonic anemometer data. This madeit difficult to verify the accuracy of the wind speedsand variance values measured by the scanninglidars. Thus, the summer multi-lidar experimentwas treated as a feasibility study rather than adefinitive experiment on lidar turbulence scanningstrategies. Best practices learned from the sum-mer lidar experiment were later applied to the de-sign and execution of a similar experiment at theBoulder Atmospheric Observatory, a site in Col-orado with a heavily instrumented 300-m tower.

Figure 2: Google Earth image of the state of Oklahoma. Location of Southern Great Plains ARM site isdenoted by red marker.

300  m  

300  m  

130  m  

110  m  

90  m  

Figure 3: Google Earth image of the central facility of the Southern Great Plains ARM site. Instrumentlocations are denoted by red markers. Approximate distances between instruments are indicated by bluelines and labels.

2.3. Lidar Scanning Strategies

i. WindCube Scanning Strategy The Wind-Cube lidar used in the experiment measures wind

speed with a Doppler Beam-Swinging (DBS) tech-nique (e.g., Strauch et al. 1984). In each DBSscan, the lidar beam is pointed in the four cardi-nal directions (north, south, east, and west), then

Lidar SpecificationsLeosphere WindCube v2 Halophotonics Streamline Pro

Wavelength 1.5 µm 1.5 µmMin. Range 40 m 105 mMax. Range 200 m 9.6 km (4 km for Galion)

Range Resolution 20 m Variable - Typically 18–30 mSampling Rate 1 Hz 1 Hz

Scanning Azimuth Angles 0, 90, 180, 270◦ User-defined: 0–360◦

Scanning Elevation Angles 62, 90◦ User-defined: 0–90◦

Table 1: Technical specifications for lidars used in scanning strategy experiment. Unless otherwise noted,specifications for Galion lidar are identical to those listed for Halo lidar. Azimuth angles are measured fromtrue north and elevation angles are measured from ground level.

pointed vertically. Based on geometrical relations,the u, v, and w wind components can be derivedfrom the radial velocities measured at the differentbeam locations.

At each beam location, 20,000 pulses of laserenergy are emitted into the atmosphere. The sig-nal that is returned to the WindCube is separatedinto range gates and several Doppler spectra areproduced for each range gate. The Doppler spec-tra from each range gate are then averaged to pro-duce a smooth spectrum. The peak frequency inthe averaged spectrum is finally related to the ra-dial velocity at each beam location and range gate.This process takes just under one second perbeam location, such that a full DBS scan is com-pleted approximately every four seconds. How-ever, the WindCube velocity algorithm calculatesthe u, v, and w components every one second us-ing the current radial velocity and the radial veloc-ities obtained from the previous four beam loca-tions (Cariou and Boquet 2010).

Three major problems arise when using thistechnique to measure turbulence (e.g., Sathe et al.2011; Sathe and Mann 2012a). The first is the vol-ume averaging inherent in remote sensing tech-nology for any kind of scanning strategy; as previ-ously discussed, the velocity measured by a lidaris the weighted average of all aerosol velocitieswithin the probe volume. Thus, turbulence scalesthat are smaller than the probe volume cannot bemeasured accurately. Next, this type of scanningtechnique assumes that the velocity is uniformthroughout the scanning circle formed by the var-ious beam positions. For low heights and uniformterrain, this assumption is likely valid at times, butbecomes invalid for higher measurement heights

and complex terrain. (The WindCube v2 scanswith an elevation angle of 62◦, which translates toa scanning circle diameter of approximately 106m at a measurement height of 100 m.) Finally,the use of only four horizontal beams to calculatethree-dimensional turbulence introduces system-atic errors. Sathe and Mann (2012a) show thatthe calculated variance values of the wind compo-nents u, v, and w are contaminated by the cross-components of the Reynolds stress tensor; i.e.,the variance of the v component has contributionsfrom not just the v component of the wind, but theu and w components as well.

While volume averaging decreases the valueof the lidar-estimated variance, the Reynoldsstress tensor contamination increases the vari-ance (Sathe et al. 2011). Thus, the variance con-tamination can often mask the effects of volumeaveraging, causing the lidar-estimated variance tobe higher than the variance that is actually beingmeasured by the lidar. In unstable environments,where turbulent motions tend to occur on largerspatial scales (e.g., Stull 2000), the effects of vari-ance contamination can overcome the effects ofvolume averaging and cause the lidar to overesti-mate the true value of the variance (Sathe et al.2011).

Examples of variance estimated from theWindCube lidar and the 60-m sonic anemometerare shown in Fig. 4. The variance componentsu′2, v′2, and w′2 were defined as follows:

u′2i = (ui − ui)2 (1)

where the different variance components aregiven for i = 1, 2, 3 and the overbar denotes a

temporal average. For the time series plots in Fig.4, a 30-min. temporal average was used. Theturbulence kinetic energy (TKE) is defined by thefollowing equation (Stull 2000):

TKE =1

2(u′2 + v′2 + w′2) (2)

The lidar-estimated u and v variance closelyfollow the variance estimated by the sonicanemometer for the first portion of the time series,until approximately 14 UTC (11 am local time). Af-ter this point, the lidar appears to overestimatethe u and v variance in comparison to the sonicanemometer. In contrast, the lidar underestimatesthe w variance throughout the entire time series. Itis likely that as the atmosphere became unstablein the late afternoon, the effects of volume aver-aging on the lidar-estimated variance were over-come by the effects of the variance contamination,causing the lidar to measure higher variance thanthe sonic anemometer. The w variance compo-nent does not seem to be as affected by variancecontamination, likely because turbulence scales inthe vertical direction are typically much smallerthan turbulence scales in the horizontal directionand volume averaging is more prominent (Satheet al. 2011). These variance trends are charac-teristic of most days from the experiment and arein agreement with the theoretical findings of Satheand Mann (2012b). It is interesting to note thatthe lidar-derived TKE values are quite close to thesonic TKE values throughout the time series, de-spite the differences in overestimates and under-estimates in the different variance components.Thus, it is important to employ caution when usingTKE as a proxy for turbulence, as the three vari-ance components are affected differently by differ-ent factors.

ii. Tri-Doppler Technique The three scanningstrategies tested in the experiment were designedto mitigate the turbulence errors induced by astandard DBS scan. In the first strategy, the tri-Doppler technique, the beams of the three scan-ning lidars were steered toward approximately thesame point in space to avoid the use of a scanningcircle. Although the effects of averaging within theprobe volume cannot be mitigated in this way, thetri-Doppler technique allows for the measurementof turbulence within a small area of space ratherthan a large scanning circle and does not requirethe assumption of horizontal homogeneity within ascanning circle.

Since three lidars are used in the tri-Dopplertechnique and there are three unknown wind com-ponents, u, v, and w, a set of three equationscan be used to solve for the wind components.For this experiment, the dual-Doppler lidar tech-nique described by Calhoun et al. (2006) was ex-tended to include an additional lidar. In this tech-nique, the radial velocity measured by each lidar iswritten as the dot product between the true three-dimensional velocity vector and the unit vector ofthe lidar system:

vr,lidar = rlidar ·U= ucos(φ)sin(θ) + vcos(φ)cos(θ)+ wsin(φ)

(3)

where u, v, and w are the zonal, meridional, andvertical components of the velocity, respectively, φis the elevation angle of the lidar beam, and θ isthe azimuthal angle of the lidar beam, measuredfrom true north. After the radial velocity equationsare written for each scanning lidar, a set of threeequations and three unknowns is obtained and theequations can be solved to estimate the three truewind components.

iii. Six-Beam Technique Sathe (2012) devel-oped a new lidar scanning strategy that minimizesthe variance contamination caused by the DBStechnique. A brief description of the developmentof the technique is presented here.

Following Eberhard et al. (1989), the varianceof the radial velocity measured by a Doppler lidarcan be written as follows:

v′2r = u′2sin2φcos2θ + v′2sin2φsin2θ + w′2cos2φ+ 2u′v′sin2φsinθcosθ + 2u′w′sinφcosφcosθ +2v′w′sinφcosφsinθ

(4)

where u′v′, u′w′, and v′w′ are the covariancesof the velocity components, and θ and φ refer tothe azimuth and elevation angle of the lidar beam,as before. For each beam position (i.e., for eachcombination of θ and φ), the variances and covari-ances create a set of six unknown quantities. Inorder to independently solve for the six unknownvariables, Sathe (2012) creates a set of six equa-tions with six different combinations of θ and φ.The optimum values for θ and φ are selected byusing a minimization algorithm to determine the

Figure 4: Time series plots of variance components and TKE measured by the WindCube lidar and 60-msonic anemometer at the ARM site.

combination of parameters that minimizes the ran-dom errors in the variance estimates. The optimalconfiguration is as follows: five beams at an el-evation 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. Thisscanning strategy is hereafter referred to as thesix-beam technique.

iv. Virtual Tower Technique The final scanningstrategy tested in the experiment involved the useof all three scanning lidars to build a “virtual tower”over the WindCube lidar. This strategy was identi-cal to the tri-Doppler technique, except the beamswere moved to different heights AGL every 10 min.Thus, a virtual tower was formed with mean windspeed and turbulence measurements at severaldifferent heights, similar to a meteorological tower.

3. Scanning Strategy Evaluation

3.1. Quality Control and Data Processing

i. Spike Filter Before being used for mean windspeed or variance calculations, the raw 10 Hzsonic anemometer data were passed through aspike filter to eliminate noisy data. Data pointsthat were more than six standard deviations awayfrom the 100-second running mean were set to thevalue of the running mean.

For the lidar data, the spike filter developed byHøjstrup (1993) and adapted by Vickers and Mahrt(1997) was used. A 10-min. moving window wasshifted through the raw lidar data one point at atime. For each window, the mean was calculatedand any point that was more than 3.5 standard de-viations from the mean was flagged as a possiblespike and removed from the dataset. This processwas repeated until no more spikes were detected.

For each iteration, the factor of 3.5 standard devi-ations was increased by 0.1 standard deviations.

ii. Signal-to-Noise Ratio and PrecipitationFilters By default, WindCube radial velocitiesthat were associated with Signal-to-Noise ratios(SNRs) lower than -23 dB were flagged as missingvalues. An SNR filter was not used with the scan-ning lidar systems, as most SNR values are above-20 dB in the lowest few hundred meters AGL forthe Halo lidar system (Pearson et al. 2009).

Doppler lidars use the backscattered radiationfrom atmospheric aerosols to determine the ra-dial wind speed and are adversely affected by thepresence of precipitation particles, which can re-sult in beam attenuation and increased vertical ve-locities (e.g., Huffaker and Hardesty 1996; Pear-son et al. 2009). Thus, lidar data were not usedwhen the rain gauge at the ARM site recorded pre-cipitation.

iii. Time and Location Synchronization Multi-lidar scanning strategies require that the scanninglidars are synchronized in time and that the exactlocations of the lidars are known (Calhoun et al.2006). The lidars must be scanning the same vol-ume of air at the same time in order to accuratelycombine the lidar data in velocity variance calcu-lations.

The instruments at the ARM site are locatedon the same network and are thus synchronizedin time with each other. Timestamps are derivedfrom the computer clocks associated with the var-ious instruments, and the computer clocks are up-dated regularly to avoid time drifting errors. Thetwo additional scanning lidars (the OU Halo lidarand the Galion lidar) are also synched with inter-nal computer clocks. At the beginning of the ex-periment, it was discovered that the Galion com-puter clock was consistently slower than the OUHalo computer clock by approximately 48 secondsand the ARM computer clock associated with theARM Halo lidar was 52 seconds faster than theOU clock. These timestamps were corrected inpost-processing. The WindCube lidar constantlyderives its timestamps from satellite information,so it was assumed that the WindCube timestampswere consistent and accurate.

Lidar alignment was verified following thetechnique of Calhoun et al. (2006). At the start ofthe experiment, the OU Halo lidar and the Galionlidar beams were pointed toward the 60-m tower

for several minutes. Short range-height indicator(RHI) scans were completed at low elevation an-gles, with samples taken every 0.5◦. These RHIscans were repeated until the tower appeared as ahard target on the lidar display. The azimuthal an-gle at which the tower appeared was recorded andcompared to the expected azimuthal angle calcu-lated from Google Earth. The difference betweenthese two angles was then used to adjust the bear-ing of the lidars such that true north correspondedto the 0◦ azimuthal angle.

iv. Coordinate Rotation Before derived prod-ucts, such as variance, were calculated, a coor-dinate rotation was applied to the lidar data. Fol-lowing the procedure outlined by Wilczak et al.(2001), the data were first rotated such that themean meridional wind speed, v, was set to zero.Next, the coordinate axes were rotated such thatu was aligned with the mean wind direction and wwas equal to zero.

3.2. Variance Estimation

Several errors can arise when atmosphericvariance is estimated from an in-situ or remotesensing instrument. Vickers and Mahrt (1997) dis-cuss three types of sampling errors that can oc-cur in the measurement of fluxes: systematic er-rors, random errors, and mesoscale flow variabil-ity. Vickers and Mahrt (1997) suggest several teststhat can be performed to determine the optimalaveraging times for turbulence calculations and toflag data that may affect the variance calculations.These tests were performed on data from the tri-Doppler portion of the experiment, as this was thefirst week of the experiment and all three scanninglidars were consistently measuring the wind speedat the same height AGL.

Systematic errors occur when the largest tur-bulent transport scales are not measured and thevariance is typically underestimated as a result.In order to avoid systematic errors, Vickers andMahrt (1997) recommend determining the opti-mal local averaging scale, L, which represents thelargest scale of turbulent motions that are includedin variance and flux calculations. For different val-ues of L (i.e., 5 min., 10 min., etc.), the instanta-neous flux w′φ′ is computed, where φ is some at-mospheric quantity, equal to φ + φ′ and the meanquantity φ is calculated over an averaging time L.For this work, the vector-averaged wind stress wasused to determine L, as in Mahrt et al. (1996). Thevector-averaged wind stress, 〈w′v′〉, is defined by

the following equation:

〈w′v′〉 =(〈w′u′〉2 + 〈w′v′〉2

)1/2

(5)

where the brackets indicate an average over thelength of the data record. In this work, one-hourlong data records were used, as in Vickers andMahrt (1997). Averaging times of 1, 5, 10, 15, 20,30, and 60 min. were used for L.

The instantaneous momentum fluxes werecalculated for the different values of L for eachone-hour data record, then averaged over theone-hour data record to form the vector-averagedwind flux. Finally, the one-hour averaged windstresses from each value of L were averaged overall stationary one-hour data records during the tri-Doppler portion of the experiment. Stationarity inthe along-wind direction was determined by us-ing the following metric from Vickers and Mahrt(1997):

RNu ≡ δu

〈u〉(6)

where u is aligned with the one-hour mean winddirection, δu is the difference in u between thestart and end of the one-hour record, and 〈u〉 isthe one-hour mean wind speed. The record isdeemed non-stationary if the absolute value ofRNu exceeds 0.50. Of the 81 records used tocalculate the vector-averaged wind stress, only sixrecords were flagged as non-stationary (approxi-mately 7%). Most of these records were associ-ated with frontal passages.

For the tri-Doppler data, the mean value of thevector-averaged wind stress calculated at 105 mAGL using a local averaging time of 10 min. isapproximately 90% of the value of the wind stresscalculated with an averaging time of one hour (thelength of the data record). Thus, an averaging timeof 10 min. should be sufficient to capture the vari-ance associated with the majority of the turbulenttransport eddies present in a one-hour time frame.

Random sampling errors occur as a result ofthe random variability of the location and strengthof turbulent eddies. Following Vickers and Mahrt(1997), flux variability due to random errors andmesoscale motions can be estimated by dividingthe 10-min. flux into a linear trend over the one-hour data record and the deviation from the lineartrend:

Fi = 〈Fi〉+ Ftr + F ∗i (7)

where Fi is the 10-min. vector-averaged windstress, 〈Fi〉 is the average 10-min. stress over the1-hour data record, Ftr is the linear trend of the10-min. stress over the 1-hour data record (minusthe 1-hour mean), and F ∗i is the deviation of the10-min. stress from the linear trend. The relativeflux error, RFE, and the error due to mesoscalemotions, RN , are defined as follows:

RFE ≡ σF ∗|〈Fi〉|N1/2

(8)

and

RN ≡ σFtr

|〈Fi〉|N1/2(9)

where σF ∗ is the standard deviation of the fluxdeviation over the 1-hour data record, σFtr

is thestandard deviation of the linear trend line, and Nis the number of 10-min. stress values in the datarecord (N = 6 in this case). Data records whereeither RFE or RN exceeded 0.3 were flagged.

In order to mitigate the effects of random er-rors on variance calculations, Vickers and Mahrt(1997) recommend averaging turbulent fluxes overa period of time that is longer than the local aver-aging length, L. Thus, for records without a flag,the variance was defined as the mean value of u′2i(calculated using L = 10 min.) over a 30-minuteperiod. For data records with a flag, the averagingperiod was increased from 30 to 60 min. to re-duce the effects of random errors and mesoscalevariability on the wind speed variance.

3.3. Tri-Doppler Technique

The tri-Doppler technique was evaluated from12 to 19 June 2013. Between approximately 0000and 1500 UTC (7 pm and 10 am local time) ev-ery day, the OU Halo and Galion lidars were setto perform a constant horizontal stare scan at apoint approximately 105 m above the ARM Halolidar. (This height corresponds to the first use-able range gate from the Halo system.) Duringthis time, the ARM Halo lidar performed a con-stant vertical stare scan directly above the lidar.(For the remainder of the day, the OU Halo andGalion lidars were set to a vertical stare mode fora different experiment.) The range gate length forthe OU Halo and Galion lidars was set to 30 mto match the range gates of the ARM Halo lidar.Unfortunately, the lidar alignment was not verifieduntil the second week of the experiment, so there

was some uncertainty regarding the true bearingof the scanning lidars to the ARM Halo lidar.

After the data were collected, timestampsfrom the Galion and ARM Halo lidars were ad-justed to match those from the OU Halo lidar. Ra-dial velocity data from the different lidars were theninterpolated to a one-second grid using a linear in-terpolation. Finally, the tri-Doppler technique, dis-cussed in the previous section, was used to calcu-late u, v, and w every one second. Correspond-ing WindCube data were interpolated to the sameone-second grid.

Sample time series plots of rotated raw windspeed data are shown in Fig. 5. (Note thatthe v and w components oscillate around 0 ms−1 because the coordinate rotation forces themean v and w values to 0.) In general, the rawWindCube and tri-Doppler data correspond wellto one another, both displaying large wind speedshifts at approximately 0600 and 0900 UTC in as-sociation with a cold frontal passage. The tri-Doppler data do appear to capture slightly higher-frequency fluctuations than the WindCube data,as discussed later in this section.

A time series of velocity variance and TKEfrom 13 June 2013 is shown in Fig. 6. While thevariance measured by the two techniques is gen-erally in agreement, some deviations do occur –at certain times, the tri-Doppler variance is largerwhile at other times, the WindCube variance islarger. In order to provide insight into this discrep-ancy, scatter plots were developed for all variancevalues measured during the tri-Doppler portion ofthe campaign. In addition, the variance was strati-fied by stability class according to Monin-Obukhovlength, L, where L = − u3

∗θv

κgw′θ′v. u∗ is the friction ve-

locity, θv is the mean virtual potential temperatureat the measurement height, κ is the von Karmanconstant (commonly set to 0.4), g is the accelera-tion due to gravity, and w′θ′v is the heat flux mea-sured at the surface (e.g., Arya 2001). Stabilitythresholds were defined as follows:

Unstable: −600 < L < 0Neutral: |L| ≥ 600Stable: 0 ≤ L < 600

Unfortunately, maintenance work was being per-formed on the 60-m tower during the first week ofthe experiment, so the only sonic data that wereconsistently available throughout the evaluation ofthe tri-Doppler technique were from the 4-m eddycovariance tower. Thus, Obukhov length from the4-m sonic anemometer was used to classify stabil-

ity at the 105-m tri-Doppler measurement height.For all other scanning techniques, the Obukhovlength at 60 m was used to classify stability.

Scatter plots of tri-Doppler variance versusWindCube variance are shown in Fig. 7. For theu variance component, the variance associatedwith stable conditions was quite similar for boththe tri-Doppler technique and the WindCube lidar,with most points lying close to the one-to-one line.However, there was a slight tendency for the tri-Doppler technique to measure higher cross-windvariances (Fig. 7b) and lower vertical variances(Fig. 7c) in comparison to the WindCube understable conditions. It is possible that the tri-Dopplertechnique was able to measure smaller scales ofturbulence because it was not using a large scan-ning cone like the WindCube lidar. The lack ofaveraging over a scanning circle would generallylead to the measurement of higher v and w vari-ance values, as the cross-wind and vertical turbu-lent eddies tend to occur on much smaller scalesthan the alongwind turbulent eddies, particularlyunder stable conditions (e.g., Panofsky 1962). It isunclear why the WindCube lidar measured slightlyhigher values of the w variance under stable con-ditions. The WindCube did have a smaller rangegate length (20 m) in comparison to the scanninglidars (30 m), so the difference in w variance mayhave been largely affected by volume averaging.

The variance associated with unstable condi-tions did not appear to follow any kind of consis-tent trend, possibly because there were fewer datapoints under unstable conditions. (The majority ofthe variances were associated with stable condi-tions due to the lack of access to the scanning li-dars during the daytime, convective period.) How-ever, the WindCube tended to measure higher vvariances under convective conditions. It is possi-ble that this variance overestimation is due to vari-ance contamination, which is most prevalent dur-ing unstable periods (Sathe et al. 2011).

Although the WindCube lidar and the ARMHalo lidar (where the tri-Doppler scans were di-rected) were separated by approximately 150m (Fig. 3), winds were primarily southeasterlythroughout the duration of the tri-Doppler experi-ment, which is along the orientation of the lidars.Thus, if Taylor’s frozen turbulence hypothesis (Tay-lor 1938) is valid, the lidars should sample thesame turbulent eddies as they move along withthe mean wind (Panofsky and Dutton 1984). In-deed, the along-wind variance was quite similar forboth techniques, even though the measurements

Figure 5: Time series of raw rotated wind speed from WindCube lidar and tri-Doppler technique at 105 mAGL on 13 June 2013.

were taken at different locations (Fig. 7a). Moresubstantial differences occurred for the cross-windand vertical variance components (Figs. 7b–7c).

Average velocity spectra were also calculatedfor the two different scanning techniques. First,the raw velocity data were separated into 30-min.blocks. Missing values were filled in using linearregression. The 30-min. mean was removed anda Fourier transform was performed on the velocitydeviations. Finally, all 30-min. spectra for eachstability class were averaged to produce averagespectra. Averaged spectra for unstable and stableconditions are shown in Figs. 8 and 9.

The large dip in the u and v WindCube spectrathat occurs at approximately 0.25 Hz correspondsto the time it takes the WindCube lidar to com-

plete a full scan (approximately 4 seconds). Everyfour seconds, the WindCube observations of u andv become completely independent again, so thevariance for the four-second time period is greatlyreduced. Because the w calculation changes withthe addition of each new beam, the dip is not asevident in the w spectra.

The unstable spectra agree well at the lowerfrequencies, but the WindCube u and v spectrahave slightly higher energy for the high frequen-cies (Fig. 8). Canadillas et al. (2011) foundsimilar results when comparing averaged Wind-Cube spectra to sonic anemometer spectra andattribute the increase in spectral energy to vari-ance contamination. Indeed, Canadillas et al.(2011) showed that this energy increase was not

Figure 6: Rotated velocity variance and TKE from WindCube lidar and tri-Doppler technique at 105 m AGLon 13 June 2013.

present when the spectra were calculated with theradial velocity rather than the u and v velocitiesfrom the DBS technique. However, despite thevariance contamination, the spectra agree quitewell up until 0.25 Hz, when the WindCube spec-tra drop off rapidly due to the 4-s scan time. At thehighest frequencies, the spectra for both lidars in-crease slightly, likely due to high-frequency noisein the velocity time series (e.g., Mann et al. 2008;Sjoholm et al. 2009). Spectra from both lidar tech-niques approximately follow the theoretical inertialsubrange slope of -2/3 for intermediate frequen-cies but drop off due to volume averaging at thehighest frequencies.

In comparison to the unstable spectra, thestable spectra peak at higher frequencies and

have lower spectral energy (Fig. 9), as expected(Kaimal et al. 1972). There is no energy increaseassociated with velocity contamination, likely be-cause the velocity contamination is not as preva-lent under stable conditions (Sathe et al. 2011).Unlike the unstable spectra, the stable WindCubespectra appear to begin deviating from the tri-Doppler spectra slightly before the 0.25 Hz scan-ning frequency. Starting just after 0.1 Hz, theWindCube spectra begin dropping off and the tri-Doppler spectra start to have higher spectral en-ergy than the WindCube spectra for all three veloc-ity components. This suggests that the tri-Dopplertechnique can measure higher-frequency turbu-lence than the WindCube lidar under stable condi-tions, possibly due to the scanning circle used bythe WindCube lidar. This difference is not evident

(a) (b)

(c)

Figure 7: Scatter plots of tri-Doppler variance versus WindCube variance at 105 m AGL stratified by stability(circles) and regression lines for different stability classes (dashed lines). In all figures, one-to-one line isshown in black for reference. Scatter plots for a) u variance, b) v variance and c) w variance are shown.Data from neutral stability cases are not shown due to the small amount of data points in this stabilityclassification.

under unstable conditions, as turbulence tends tooccur on larger spatial and temporal scales (e.g.,Stull 2000) and averaging within the WindCubescanning circle does not have a large effect on themeasured velocity variance.

3.4. Six-Beam Technique

The six-beam technique proposed by Sathe(2012) was evaluated from 20 to 26 June 2013.The scanning strategy of the WindCube lidar can-not be modified to implement the six-beam tech-

nique, but the scanning lidars in the experimentwere able to implement the technique. During thisportion of the experiment, the Galion scanning li-dar mimicked the scanning technique of the Wind-Cube lidar, pointing the lidar beam toward the fourcardinal directions then vertically upward in eachDBS scan. In order to maximize the overlappingheights between the vertical range gates and thehorizontal range gates, an elevation angle of 45◦

was used for the Galion scans. Unfortunately, thiscaused the Galion to have a larger scanning conethan the WindCube lidar, which uses an elevation

Figure 8: Average velocity spectra from tri-Doppler technique and WindCube lidar at 105 m AGL from 12to 19 June 2013 under unstable conditions. Black solid line indicates -2/3 slope (inertial subrange). Blackdotted line indicates 0.25 Hz WindCube frequency cut-off.

angle of 62◦.

The OU Halo lidar employed the scanningstrategy described by Sathe (2012), using an ele-vation angle of 45◦ and beams at 0, 72, 144, 216,and 288◦, in addition to a vertical beam. The av-erage variance of the radial velocity from each ofthe beams was used in Eq. 4 to produce six equa-tions with six unknowns. The equations were thensolved simultaneously to obtain values for the ve-locity variances and covariances from the OU Halolidar.

Because the WindCube uses a simple rotatingprism to steer the beam in different directions, itonly takes one second for the WindCube to movefrom one beam position to another and accumu-late measurements at the new beam position. Incontrast, the scanning lidars need to mechanicallymove the scanner in elevation and azimuth andlock the scanner in place before taking measure-ments at each beam location. As a result, it takesapproximately four seconds for the scanning lidars

to move the beam to a different location and takemeasurements. For the six-beam technique, ittook approximately 30 seconds for the OU Halolidar to complete a single six-beam scan, so theradial velocity data from each beam were interpo-lated to a 30-s grid. In order to match the tempo-ral resolution of the OU Halo lidar, the u, v, andw components of the WindCube and Galion lidarswere also interpolated to a 30-s grid.

To calculate the variance from the DBS andsix-beam scans, a similar technique to that em-ployed with the tri-Doppler lidar data was used.The raw velocity data were first passed througha spike filter to remove outliers. The RFE (Eq.8) and RN (Eq. 9) were calculated and used toflag data where the variance could be impactedby random errors or mesoscale variations. As be-fore, the 30-min. averaged fluxes were used forthe variance when no flag was present; otherwise,the fluxes were averaged over 60 min. While rawvelocity data from the WindCube and Galion lidarswere rotated into the 1-hour mean wind direction

Figure 9: As in Fig. 8, but for stable conditions.

before the variance was calculated, the variancevalues from the six-beam technique needed to berotated into the mean wind direction at the finalstep. The Velocity-Azimuth Display (VAD) tech-nique (Browning and Wexler 1968) was used tocalculate the mean wind direction from the OUHalo lidar to use for the coordinate rotation.

Sample velocity variance and TKE time seriesfrom the DBS and six-beam techniques are shownin Fig. 10. (Data from 74 m AGL are shown,which corresponds to the first useable range gateof the scanning lidars.) Although the WindCubeand the Galion lidar were using very similar scan-ning strategies, the WindCube nearly always mea-sured higher velocity variances. This likely oc-curred because the WindCube had both a smallerscanning circle and a smaller probe length in com-parison to the Galion lidar. However, the variancemeasured by both lidars appears to follow similartemporal trends.

For the u and v variance, the Galion and OUHalo measured similar values, although the OUHalo measured slightly lower values toward the

end of the time series, when convective conditionswere beginning to dominate. This is expected,as the six-beam strategy used by the OU Halolidar is designed to mitigate variance contamina-tion, which is most prominent during unstable con-ditions. The vertical velocity variance measuredby the OU Halo lidar was consistently higher thanthe variance measured by both the WindCube andthe Galion lidars from the DBS technique. How-ever, the vertical variance measured by all threelidars was similar when the data from the verti-cal beam only were used to calculate the verti-cal variance from the WindCube and Galion lidardata (Fig. 10). In short, higher vertical velocityvariances were measured by the WindCube andGalion lidars when the radial velocity were col-lected in a probe volume directly above the lidarrather than from several points around a scanningcircle. This allows the lidars to measure smallerscales of variance, which are averaged out in thescanning circle.

Scatter plots of the variance values measuredat 74 m AGL throughout the six-beam portionof the experiment are shown in Fig. 11. For

Figure 10: Rotated velocity variance and TKE from WindCube lidar, five-beam DBS technique used bythe Galion lidar, and six-beam technique used by the OU Halo lidar at 74 m AGL on 21 June 2013. In wvariance image, solid red and blue lines indicate vertical variance calculated from the DBS technique forthe WindCube and Galion lidars, while dashed lines indicate variance calculated from the vertical beam ofthe lidars.

the u variance, the WindCube measured highervariance values than the Galion for both stableand unstable cases, nearly always measuring vari-ances that were 75% larger than the Galion (Fig.11a). This can likely be attributed to the smallerscanning circle and smaller range gate lengthused by the WindCube lidar. In contrast, the OUHalo lidar measured slightly smaller u variancesthan the Galion lidar for stable conditions, butmeasured significantly smaller variances for un-stable conditions.

Variance trends were similar for the v compo-nent (Fig. 11b). Once again, the WindCube mea-

sured higher variance values than the Galion lidarfor both stability classes. Trends for the OU Haloand Galion lidars were less pronounced. Similarto the u variance, the Galion tended to overesti-mate v variance values under unstable conditions.Under stable conditions, the Galion and OU Halolidars measured similar values of the v variance attimes, but the Galion tended to overestimate the vvariance for other cases. It is possible that sincethe cross-wind variance is typically smaller thanthe along-wind variance (Panofsky 1962), the tem-poral resolution of the OU Halo lidar caused it tomiss some of the smaller cross-wind turbulent ed-dies. While the Galion lidar updated the values of

(a)

(b)

(c)

Figure 11: Scatter plot of a) u, b) v and c) w velocity variance from five-beam DBS technique used by theGalion lidar versus variance estimated by the WindCube lidar (left panels) and six-beam technique used bythe OU Halo lidar (right panels) at 74 m AGL from 20 to 26 June 2013. Individual velocity variance valuesare denoted by circles and best-fit regression lines are shown with dashed lines. For all three lidars, only thevelocity measurements from the vertically pointing beam were used to calculate the w variance. Data fromneutral stability cases are not shown due to the small amount of data points in this stability classification.

u, v, and w every time the beam moved to a differ-ent position (i.e., every 4 s), the OU Halo lidar es-timated the variance from velocity measurementsthat were taken 30 s apart in time. Although thevelocity data from both lidars were interpolated toa 30-s grid, the Galion lidar may have still cap-tured higher-frequency turbulence in the raw ve-locity data.

The Galion lidar measured slightly higher wvariance than the WindCube lidar when just thevertical beam was used to calculate the variance,which eliminates averaging within the scanningcircle (Fig. 11c). This is somewhat surprising, asthe WindCube used a smaller range gate then theGalion lidar and was thus expected to measurehigher w variance values. However, anecdotally,raw data from the scanning lidars tend to be morenoisy than data from the WindCube lidar, so it ispossible that some of the w variance measured bythe Galion lidar was actually associated with ran-dom noise. The Galion and OU Halo lidars mea-sured very similar vertical variance, which is ex-pected since the lidar hardware is the same andthe range gates used for both lidars were 30 m inlength.

4. Summary and Conclusions

In this work, two different lidar scanning strate-gies, the tri-Doppler technique and the six-beamtechnique, were evaluated for their ability to mea-sure low-level turbulence. A third scanning strat-egy, the virtual tower technique, will be evaluatedin future work. These scanning strategies attemptto mitigate the systematic errors induced by typi-cal DBS scans, including averaging over a scan-ning circle and contamination caused by cross-components of the Reynolds stress tensor.

The tri-Doppler technique involved pointingthree scanning lidars at the same point in spaceand solving a set of equations to calculate u, v,and w every one second. Because the velocitydata were not averaged over a scanning circle, thistechnique enabled the lidars to measure higher-frequency turbulence in comparison to a lidar us-ing a DBS technique. This turbulence informationwas only available at the one height where thelidars were pointed. However, velocity data col-lected at other points along the two horizontal li-dar beams can still be used to calculate the aver-age wind speed profile (Klein et al. 2013). On anoperational wind farm, this strategy could be de-signed to collect high-frequency turbulence mea-surements at the turbine hub height and collect av-erage wind speed measurements at other heights

across the rotor-disk area. Clearly, using threescanning lidars for a scanning strategy is mainlyonly feasible in a research setting. But a singlescanning lidar could be pointed into the mean winddirection to measure line-of-sight turbulence andwind speed.

The six-beam technique only requires one li-dar and could potentially be implemented into asmall vertically pointing lidar with a rotating prism.By including six beams instead of the four or fivethat are typically used with a DBS scan, the six-beam technique can be used to decrease thevariance contamination that is caused by cross-components of the Reynolds stress tensor. Al-though this was a limited data set, the six-beamtechnique did show a decrease in variance con-tamination under unstable conditions when com-pared to a similar lidar using a DBS scan. How-ever, no sonic anemometer data were availableat the heights scanned by the Halo lidars, so it isdifficult to determine how accurately either of thescanning lidars were measuring variance. A re-cent field campaign that was conducted at a heav-ily instrumented site in Boulder, Colorado will pro-vide a larger data set with sonic anemometer ver-ification data. The same Halo lidar that was de-ployed at the ARM site was deployed at the Boul-der site, so the Boulder campaign will provide in-sight into how accurately the Halo lidars can mea-sure turbulence under a variety of stability condi-tions.

Although the ARM site experiment took placeover a short period of time and did not feature alarge amount of corresponding sonic anemometerand lidar data, it served as a feasibility experimentfor the use of unique lidar scanning strategies.Several best practices, including techniques for li-dar alignment and data processing, were learnedduring the experiment and later applied to theBoulder experiment. The tri-Doppler techniquecould be used with either three scanning lidars or asingle scanning lidar (as a horizontal stare scan).This technique can provide high-frequency turbu-lence measurements at a single height and meanhorizontal wind speeds at several heights. The six-beam technique showed promise for decreasingthe effects of variance contamination under unsta-ble conditions. This technique only requires onelidar and could potentially be implemented into alidar with a rotating prism, such as a WindCubelidar.

5. ACKNOWLEDGMENTS

The authors would like to thank the staff of theSouthern Great Plains ARM site, the members ofthe Boundary Layer Remote Sensing and Simula-tion group at OU, and the technical support staffat Sgurr Energy for their assistance during the ex-periment. In addition, we are grateful to Rob New-som for sharing his lidar expertise and operatingthe ARM Halo lidar.

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