## Abstract

An experimental study of the spatial wind structure in the vicinity of a wind turbine by a NOAA coherent Doppler lidar has been conducted. It was found that a working wind turbine generates a wake with the maximum velocity deficit varying from 27% to 74% and with the longitudinal dimension varying from 120 up to 1180 m, depending on the wind strength and atmospheric turbulence. It is shown that, at high wind speeds, the twofold increase of the turbulent energy dissipation rate (from 0.0066 to 0.013 m^{2} s^{−3}) leads, on average, to halving of the longitudinal dimension of the wind turbine wake (from 680 to 340 m).

## 1. Introduction

As a wind turbine operates, a fraction of the wind-flow energy is transferred to rotate the turbine blades; therefore, a wind-velocity deficit is generated downwind of the turbine. Studies on the influence of atmospheric conditions (in particular, wind velocity and wind turbulence intensity) on the length of a wind wake and the velocity deficit inside the wake are needed because of the increasing number of wind farms and the need to optimize the turbine arrangement in a wind farm.

Flow characteristics behind wind turbines have been studied extensively during the last three decades. The most comprehensive review of the theoretical and experimental studies is provided by Vermeer et al. (2003), wherein investigations of the wind turbine wake were conducted through the use of various techniques. Högström et al. (1987) employed four different techniques for probing the turbine wake: 1) tower-mounted instrumentation, 2) Tala Inc. kite anemometers, 3) tethered balloon soundings, and 4) Doppler sodar. Using these instruments, the velocity deficit and the turbulence characteristics in the wind turbine wake were investigated. Using data measured by wind and temperature sensors at two meteorological masts, Magnusson and Smedman (1996) derived analytical expressions for the velocity deficit and the added turbulence of the flow generated by the wind turbines. Measurement results of the velocity deficit with a ship-mounted sodar were compared with this empirical model in Barthelmie et al. (2003) and with other models in Barthelmie et al. (2006).

A coherent Doppler lidar system (CDL) is a powerful tool that can measure wind, turbulence, and aircraft wake vortices (Köpp et al. 1984; Hall et al. 1984; Hawley et al. 1993; Frehlich et al. 1994, 1998; Banakh et al. 1999; Köpp et al. 2005; Smalikho et al. 2005; Banta et al. 2006; Frehlich et al. 2006; Pichugina et al. 2008; Rahm and Smalikho 2008; Banakh et al. 2009; Pichugina and Banta 2010; O'Connor et al. 2010). Results of a study of the wake generated by a wind turbine with the aid of a continuous-wave CDL are presented in papers by Bingöl et al. (2010) and Trujillo et al. (2011). During the experiment, the lidar was located at the rear of the nacelle, and the laser beam scans were used to measure wind turbine wake dynamics and investigate the influence of different turbulence scales on the wake behavior. For a continuous-wave CDL, the longitudinal size of the sensing volume increases quickly with the increase of the focal length or range (Sonnenschein and Horrigan 1971). In the case of a pulsed CDL, the longitudinal size of the sensing volume does not depend on the range, and the radial velocities are measured at different ranges along the axis of the sensing beam as the pulse propagates outward and interacts with backscattering targets, generally atmospheric aerosol particles. Therefore, pulsed CDL opens up a wide range of possibilities to investigate the wind turbine wake, by using the geometry of scanning by the sensing beam during the measurement time, as was demonstrated by Käsler et al. (2010).

This paper describes the lidar data processing procedures that were performed to obtain information about the wind, turbulence, and wind turbine wake, and presents some results of a field experiment [described in detail in Lundquist et al. (2013), manuscript submitted to *Environ. Res. Lett.*] that was conducted with the use of a 2-μm pulsed CDL under various atmospheric conditions.

## 2. Estimation of the dissipation rate of turbulent energy from scanning CDL data

The use of conical scanning by a sensing beam of the coherent Doppler lidar around the vertical axis at a fixed elevation angle allows researchers to obtain information about wind direction and velocity. If measurements are conducted by a pulsed CDL, then the vertical profiles of these parameters can be retrieved from the data obtained for one full scan (azimuth angle varies from to ) using the velocity–azimuth display (VAD) technique (Browning and Wexler 1968; Banta et al. 2002). For the continuous-wave CDL, Banakh et al. (1999) showed that the wind speed and direction and the turbulence energy dissipation rate within the atmospheric boundary layer can be estimated from data measured by conical scanning. In addition, Frehlich et al. (2006) showed that information about wind turbulence can be retrieved from pulsed CDL data that are obtained by conical-sector scanning; that is, scanning in azimuth over a limited sector. We present a brief description of the approaches used to estimate the turbulence energy dissipation rate from the transverse and longitudinal structure functions of the radial velocity, as measured by a 2-μm pulsed CDL using conical scanning techniques (including one full scan and multiple sector scanning).

The Doppler lidar used in this study was the National Oceanic and Atmospheric Administration's (NOAA's) high-resolution Doppler lidar (HRDL), as described by Grund et al. (2001). The main characteristics of this lidar are given in Table 1. In this table, we also included results of numerical simulation at weak ( = 0.2 m s^{−1}, = 100 m) and strong ( = 1.2 m s^{−1}, = 100 m) wind turbulence and at different signal-to-noise ratios (SNRs, the ratio of the mean signal power to the mean noise power in the spectral bandwidth of 50 MHz) for the error of lidar estimate of the radial velocity (Smalikho et al. 2013).

Consider the case of a 2-μm pulsed CDL, where the temporal power profile of the sensing radiation is well described by a Gaussian distribution with pulse duration , determined from the power drop to the level from the peak. The pulse repetition frequency is denoted . During measurements by this lidar, conical scanning with a constant angular rate is used. For different distances from the lidar and azimuth angles , raw data measured by the lidar are used to calculate the Doppler spectra with the use of the rectangular time window of width for each spectrum and the accumulation of individual estimates of spectra from lidar shots, where , , , , is the speed of light, , , , and . Then, the centroid of the spectral distribution is used to estimate the radial velocity (projection of the wind-velocity vector to the axis of the sensing beam) with an allowance made for the Doppler relation. If the estimate is unbiased (where the probability of a bad estimate caused by the system noise with an allowance for the Doppler relation is equal to zero), then can be represented in the following form by averaging over the azimuth angle (Banakh and Smalikho 1997; Frehlich and Cornman 2002):

where

is the radial velocity averaged over the sensing volume,

is the weight function of averaging along the axis of propagation of the sensing beam, is the standard error function, is the radial velocity at the point of the Cartesian coordinate system , , and is the random error of the estimation. This error has the following properties: , , and , where the angular brackets denote averaging over the ensemble of realizations, is the variance of the random error of estimation of the radial velocity, and is the Kronecker delta (, ). The integral correlation scale is determined by the longitudinal dimension of the sensing volume (Banakh and Smalikho 1997).

Assuming that the pulse repetition frequency is high and the conditions and are true, where is the integral scale of correlation of turbulent fluctuations of the wind velocity (Smalikho et al. 2005), we transformed the velocity from the polar coordinate system to the rectangular coordinate system on the plane ( is the longitudinal coordinate axis and is the transverse axis) and, replacing the summation with integration in Eq. (2), we obtained the equation

where and . This approximation is rigorous under the conditions and .

### a. Transverse structure function

For the case of statistically homogeneous and isotropic turbulent flow, we obtained from Eqs. (1)–(4) an equation for the transverse structure function of the radial wind velocity measured by Doppler lidar for azimuthal scanning, () in the form

where

is the transverse structure function of the radial velocity averaged over the sensing volume, is the two-dimensional spatial spectrum of turbulent fluctuations of the wind velocity,

is the function of the low-pass filter along the axis , and

is the function of the low-pass filter along the axis , . For the von Kármán model (Monin and Yaglom 1975; Vinnichenko et al. 1973)

where is the Kolmogorov constant. The variance of wind velocity is related to and by the equation:

Because the difference does not depend on the error [see Eq. (5)], from the measured transverse structure function of radial velocity , estimates of the turbulence energy dissipation rate and the integral scale can be obtained using the following algorithm (Smalikho and Banakh 2013):

and

where

, , and . The function was calculated using Eqs. (6)–(9). Then, using estimates and , the wind-velocity variance was calculated by Eq. (10).

In contrast to the approach of Frehlich et al. (2006), we used calculations of to take into account the averaging of the radial velocity across the probing beams (along the axis ). We used such an approach because, in our experiments at large ranges , the transverse distance between successive lidar beams, which is proportional to , can exceed the longitudinal size of the sensing volume.

### b. Longitudinal structure function

As the measurement range increases, the transverse dimension of the sensing volume increases as well. However, the condition allows us to use the approximation in Eq. (4). That is, can be considered constant along the propagation path. Then, for the longitudinal structure function of the radial velocity measured by the lidar , we obtain from Eqs. (1)–(4)

where

From the measured transverse structure function of radial velocity , estimates of the turbulence parameters , , and can be obtained with the use of Eqs. (7)–(10) and (14) and the approaches described in the works of Frehlich and Cornman (2002) and Smalikho et al. (2005).

### c. Comparison of vertical profiles: Lidar technique versus sonic anemometer

To test the method of estimation of from lidar measurements of the transverse structure function , we used data from the experiment conducted in September 2003 in southeastern Colorado within the framework of the Lamar Lower-Level Jet Project (Banta et al. 2006; Kelley et al. 2007; Pichugina and Banta 2010). In this experiment, HRDL was operated along with four sonic anemometers installed on a 120-m meteorological tower (at heights of 54, 67, 85, and 116 m). The distance between the tower and the HRDL container was 167 m. For the comparative analysis of the results of joint measurements of the dissipation rate by HRDL and sonic anemometers, we selected the initial experimental data obtained on 15 September 2003, when the wind direction was such that wind-flow distortion effects introduced by the meteorological tower on the sonic anemometer measurements could be neglected.

During the HRDL measurements, different scanning geometries were used. In the work of Banakh et al. (2009), we applied the raw experimental wind data obtained on 15 September 2003 and conducted a comparative analysis of the estimation from the longitudinal structure function of the radial velocity measured by HRDL scanning in the vertical plane and from temporal spectra of the wind velocity measured by sonic anemometers. In that case, the resolution in the scanning angle was 0.25° and the transverse dimension of the sensing volume was much smaller than the longitudinal dimension 40 m out to the measurement range = 3 km. Because of this condition, the theoretical calculations of the longitudinal structure function by Banakh et al. (2009) were able to neglect the averaging of turbulent fluctuations of the velocity along the transverse coordinate, in contrast to Eq. (14). As a result of the analysis of estimated from lidar data, compared with that from sonic anemometer data measured for a ~16-min period (Smalikho 1997), Banakh et al. (2009) found that the relative error of the lidar estimation of did not exceed 25%.

During another time period on the same day, full 360° azimuth “VAD” scans were conducted at periodic intervals to determine wind speed and direction. The results of the wind estimation by the filtered sine-wave fitting method (Smalikho 2003) were reported in the paper of Banakh et al. (2010). We used these data here to retrieve vertical profiles of by applying the method of transverse structure function.

One full scan, covering in azimuth, was conducted at an elevation angle for one minute. The azimuth resolution was . In this case, at the distance = 1500 m, the transverse dimension of the sensing volume was nearly equal to the longitudinal dimension . Therefore, should be calculated by Eq. (6), to account for the transverse averaging of the radial velocity. The transverse structure function for the height (where = 3 m was the height above ground of HRDL's scanning telescope) was estimated by averaging over the entire circle of the scan cone and over five range gates along the axis of propagation of the sensing beam as

where , = 240 (), , and is the estimate of the mean wind-velocity vector obtained from the VAD sine-wave fitting procedure.

Figure 1 shows vertical profiles of retrieved from data measured by HRDL (curves) and by the four sonic anemometers (icons). According to estimates obtained from numerical simulation (Smalikho et al. 2013) for conditions of this experiment, the relative error of the lidar estimate of , determined as , is between 30% and 40%. Taking into account the high accuracy of the measurement by sonic anemometers (Banakh et al. 2009) and using the data shown in Fig. 1, we obtained an estimate of the relative error of the lidar estimate of , calculated by the equation

where , , and are estimates of the turbulent energy dissipation rates from data measured by HRDL (at heights corresponding to those of sonic anemometers) and sonic anemometers, respectively. The value obtained, , is larger than the theoretical error . It is quite possible that the uncertainty in the estimate was large because was small. An increase in the number of full scans would allow one to obtain data with a greater number of degrees of freedom and, correspondingly, to decrease the error significantly.

Section 5 will present estimates of both by the above transverse-structure-function method (each transverse structure function was calculated from data measured at one full scan) and by the longitudinal-structure-function approach using data obtained from conical-sector scans. These results were necessary to analyze the influence of turbulence on the wake generated by a wind turbine.

## 3. Estimation of turbine wake parameters

A deficit of wind velocity takes place inside the wake generated behind a wind turbine on its leeward side. At some distance from the turbine, this deficit fully disappears. The most characteristic wake parameters are the maximum value of the wind-velocity deficit and the effective transverse and longitudinal dimensions of the wake. The transverse wake dimension is initially determined by the diameter of the circle described by the outer end of the turbine blade. The maximum velocity deficit and the longitudinal dimension of the wake depend on the turbine type and on atmospheric conditions. To investigate these parameters with the aid of a pulsed CDL, different geometries of scanning can be used. In this case, the lidar should be at a sufficient distance from the turbine, and the wind direction should be nearly aligned with the lidar–turbine line. As seen in Fig. 2, the angle of wind direction should, if possible, be close to the azimuth angle between the direction to the north and the line running from the lidar position to the turbine position (angle between the axis and the line in Fig. 2).

In this paper, we studied the wind field in the vicinity of the wind turbine using conical-sector scanning. The elevation angle should be set so that the sensing beam intersects with the largest area of the turbine wake, including the point of the maximum velocity deficit, if possible. Figure 2 shows the geometry of the lidar measurement for conical-sector scanning.

One of the aims of this study was to obtain information about the velocity deficit at a distance from a turbine along the wind direction from HRDL scan data. We defined the velocity deficit as

where is the mean ambient wind velocity outside of the wake, and is the mean wind velocity within the wake downstream of the turbine.

We assume that the velocity is horizontally homogeneous. Then, we can choose the point (see Fig. 2) on the scanning plane with the coordinates , which lies at the same radial distance from the lidar as the point with the turbine coordinates , where , , , , and is the distance between the lidar and the turbine. The angle , between the axis and the line , can be set as , where the arc length . In this case, the point can be located either to the right (+) or to the left (−) of the turbine.

As a result of the multiple repetitions of sector scans during the HRDL measurement and data processing, we obtained an array of estimated radial velocities , where is the scan number, for the shaded area in Fig. 2. Then we averaged these estimates as

and transformed from polar to the rectangular coordinates by interpolating the data to a computational grid with a fine mesh ().

According to the measurement geometry (see Fig. 2), the dependence of the mean wind velocity on the distance along the wind direction and on the arc length can be calculated as

where , is the angle between the lines and , , and . This derivation assumes that the vertical variation of the wind direction angle can be neglected over the interval , and that the mean radial velocity, measured at the azimuth angle and at very small elevation angle (), can be described by the equation . The measurement height does not depend on the arc length .

where and the axis is perpendicular to the wake axis .

The wind direction angle in Eqs. (19) and (20) can be computed from full 360° HRDL conical scans using the VAD procedure. On the other hand, using the sector data, we estimated the wind direction from the position of the wake generated by the turbine, because the wind velocity inside the wake was lower than that in the environment within the scanning sector. Supervisory Control and Data Acquisition (SCADA) data, which could also define the turbine yaw angle, were not available. Below we estimate the wind direction angle (in degrees) as

where , the azimuth angle varies within the scanning sector, and the coordinates are determined with respect to the point of minimum value of the mean radial velocity as a function of azimuth angle at the fixed distance , that is,

The interpolation used in obtaining the distribution of the mean radial velocity allows us to define and to be much smaller than and , respectively.

From the resulting dependence of the velocity deficit on distance , where , we estimated the maximum velocity deficit and the wake length . The was defined to be the location where the dropped down to 10%.

## 4. Experiment

We conducted a field program using HRDL to study the turbulent wind field in the vicinity of a wind turbine in April 2011 at the National Renewable Energy Laboratory (NREL) National Wind Technology Center (NWTC), located about 10 km south of Boulder, Colorado. Figure 3 shows the position of HRDL with respect to the research 2.3-MW wind turbine, which has a 101-m rotor diameter and a hub height of 80 m above ground level. The angle = 130.55°; the distance between the lidar and the wind turbine = 891 m. Because of a gentle slope, the wind turbine base was about 10 m lower than the base of the HRDL container. Ravines with a depth of no more than 20 m lay behind the wind turbine in the direction from the lidar along the black line in the figure.

During the HRDL measurements, a sequence of different geometries of scanning was employed. The geometries included both conical-sector scanning in azimuth at different elevation angles and scanning in elevation in the vertical plane at fixed azimuth angles close to . Full conical scanning was used roughly every half hour. This sequence of scanning allowed us to estimate the wind direction angle, which we used to set minimum and maximum azimuth scanning angles for the sector scans.

To estimate the Doppler spectrum, we used = 100 lidar shots. Because the pulse repetition frequency was = 200 Hz, the duration of measurement of one spectrum (or the radial velocity) equaled 0.5 s. Lidar estimates of the radial velocity were obtained with a step of = 30 m along the axis . The azimuth resolution was 0.9° in the case of sector scanning. For full VAD scanning, was 2° or 3°.

Examples of some realizations (without averaging and interpolation) of two-dimensional distributions of HRDL estimates of the radial velocity in the scanning plane, including the distribution in the vertical plane observed in these experiments, are reported in Pichugina et al. (2011). The figures in Pichugina et al. (2011) and Newsom and Banta (2004) for these distributions show that, as the measurement range increases, the number of bad estimates of the radial velocity also increases because of the decrease in SNR. In addition, estimates of the radial velocity are roughly zero at points lying near the wind turbine as a result of the reflection of the lidar pulse by the turbine blades (Käsler et al. 2010). Therefore, to obtain the results presented below, we used a specialized procedure, which allowed us to replace the velocity values at “zeroing” points with the result of interpolation by neighboring points, at which the radial velocity was estimated from aerosol backscatter unaffected by signal reflections off the turbine blades. To minimize the influence of bad estimates on the radial velocity at a long distance , we used the procedure of filtering of good estimates through maximization of the functional

[in place of Eq. (18)] when determining the 2D distribution of the mean radial velocity. The parameter was taken as equal to 3 m s^{−1} in this case, that is, the mean radial velocity was estimated as

Figure 4 illustrates the distribution of the radial velocity in the scanning plane obtained from HRDL measurements at elevation angles (Fig. 4a) and (Fig. 4b). For each of these two cases, we estimated the wind direction angle using the technique described in section 3. The white lines in Figs. 4a and 4c are directed along the estimated wind direction angle . Quantifications of the wind speeds along those lines appear in Figs. 4b and 4d, and start from the turbine location (line 1) or the point *A* (line 2) at = 120 m (see section 3). The difference between the wind velocities shown in the figure as curves 1 and 2 persists for a longer downwind distance from the wind turbine at than at . At the same time, the maximum deviation of velocities (consequently, the maximum velocity deficit) took place at . This deviation was related to the different position of scanning planes as they intersected the turbine wake.

## 5. Results

For this case, sector scanning at elevation angles of 3°–3.5° was optimal for obtaining the information about the wake structure. At a range of 890 m (the location of the turbine), heights of the laser beam relative to the wind turbine base equaled 60 m (20 m below the turbine hub) at = 3° and 67 m (13 m below the turbine hub) at = 3.5°. At a range of 1890 m, the heights of the laser beam were 110 m ( = 3°) and 128 m ( = 3.5°) above the turbine base elevation. Only these elevation angles (3° and 3.5° alternately after each scan) were used for HRDL measurements from 1920 LT 14 April 2011 to 1730 LT 15 April 2011. The duration of individual scan sequences was, as a rule, 7 min (57% of all cases) and 12 min (41%). For each case, all data measured alternately at elevation angles of 3° and 3.5° were used for averaging [see Eqs. (23) and (24)]. We present the data processing results of such measurements below.

Examples of the 2D distribution of the radial velocity (Figs. 5a, 6a, and 7a), wind velocity (curve 1) and (curve 2) (Figs. 5b, 6b, and 7b), distribution of the wind-velocity deficit along the wake axis (Figs. 5c, 6c, and 7c), and distributions of the wind-velocity deficit perpendicular to the wake at different distances from the wind turbine (Figs. 5d, 6d, and 7d) are shown. One can see a significant difference in the wake length and velocity deficit for the three time periods under consideration. We estimated the transverse size of the wake , by fitting the Gaussian model to the measured value of by the least squares method. Estimates of , which were obtained from the data of Figs. 5d, 6d, and 7d, vary from 43 to 83 m. Individual estimates at different distances are provided in the captions of Figs. 5–7. In general increases with increasing .

In Fig. 8, curves 1–4 show the dependency of velocity deficit on the normalized distance on the leeward side of the turbine, as obtained from HRDL measurements. For comparison, curve 5 shows the velocity deficit estimated from the data measured by a CDL near Bremerhaven, Germany, during nighttime at stable thermal stratification and very weak turbulence (Käsler et al. 2010). It can be seen that curves 1 and 2, obtained from nighttime HRDL data, are closest to curve 5. The values of the normalized turbine wake length are shown in the axis as closed circles. It can be seen that can change nearly tenfold for different realizations. For the data shown in Fig. 8, the maximum velocity deficit varied from 32% to 74%.

We used the data measured by full conical scanning and an elevation angle of 10° (where there was no reflection of the signal by the wind turbine blades to contaminate the measurement results) every half hour for 24 h, starting from 1800 LT 14 April, to retrieve the vertical profiles of the ambient wind velocity and direction . The same lidar data were also used to retrieve vertical profiles of the turbulent parameters (such as dissipation rate , integral scale , and wind-velocity variance ) obtained using the transverse-structure-function method described in section 2a. The resulting temporal profiles of , , and [indicated as the turbulence energy dissipation rate (TEDR)] at = 80 m (height of the wind turbine hub) are shown in Figs. 9a–c as open squares connected with solid lines. Estimates of the standard deviation [indicated as the standard deviation of wind velocity (SDWV)] are shown in Fig. 9c as closed squares connected by dashed lines. It can be seen that during the period considered (from 1800 LT 14 April to 1800 LT 15 April), the wind velocity varied from 2 to 18 m s^{−1}. Most of the time, the wind velocity exceeded 10 m s^{−1}. In Fig. 9b, the obtained values of the wind direction angle are shown by circles. These circles are mostly concentrated near the dash-dotted line that corresponds with the azimuth angle , between the line passing through the lidar point in the direction to the north and the line running through the lidar point and the point of location of the turbine (see Fig. 3). Typically, the deviations of the angle from did not exceed 30° in absolute value, which allowed the turbine wake information to be obtained from the lidar data and main wake parameters to be monitored for almost the entire period (when the turbine operated).

The processing procedures described earlier were used to determine the ambient wind velocity ( = 80 m) and direction , the maximum velocity deficit , and the wake length , which are shown as circles in Figs. 9a, 9b, 9d, and 9e, from the lidar data measured by conical-sector scanning across the wind turbine location. The same data were also used to obtain the temporal profile of at a height of 80 m, by using the longitudinal-structure-function method (see section 2b), which is shown as circles in Fig. 9c. The results that are shown as circles and open squares connected by solid lines in Figs. 9a–c are in a good agreement most of the measurement time.

As seen in Fig. 9c, the experiment was mostly carried out under conditions of strong () and moderate () turbulence. This was possibly related to the fact that wind speeds exceeded 10 m s^{−1} and the upwind fetch included very complex terrain. Both transverse- and longitudinal-structure-function methods yielded the values in the periods from 2220 to 2330 LT (14 April) and from 0500 to 0820 LT (15 April). Unfortunately, it was impossible to obtain the information about the turbine wake from the data measured during these periods. The point is that, in the first case, the wind velocity was very low, and from 0310 to 0930 LT (15 April) the research 2.3-MW wind turbine was shut down, the turbine blades did not rotate, and no wake with a velocity deficit was generated behind the turbine. In addition, during the period from 1020 to 1100 LT (15 April), the deviations of the angle from were too large to estimate the turbine wake parameters from the HRDL data.

The results depicted in Figs. 9d and 9e reveal that the maximum velocity deficit varied from 27% to 74%, and the turbine wake length varied from 120 to 1180 m. The largest values of and were obtained during the period from 0000 to 0100 LT. We failed to explain the sharp decrease of these parameters for the period from 0100 to 0300 LT. This decrease was possibly caused by the sharp intensification of the wind starting from 0100 LT.

To analyze the effect of wind and turbulence on the turbine wake length , we selected data that were measured during the night (from 2350 LT 14 April to 0300 LT 15 April) and during the day (from 1220 to 1525 LT 15 April). Using the data shown in Figs. 9a, 9c, and 9e as circles, we present estimates of versus and in Fig. 10, obtained from nighttime lidar measurements (indicated as closed circles and triangles) and daytime lidar measurements (indicated as open squares and triangles). The circles and squares are single estimates of , , and , and the triangles are averaged estimates. For Fig. 10a, single estimates of were averaged over wind-velocity intervals of 9–12 and 13–16 m s^{−1} and for Fig. 10b, single estimates of and (at any observed wind velocities) were averaged separately for the nighttime and daytime cases. According to the results shown in Fig. 10a, an increase of the wind velocity from 10.5 to 14.5 m s^{−1} led to a decrease of the turbine wake length both during the night and the day by a factor of 2.5 as indicated by the large triangles. At wind speeds of both 10.5 and 14.5 m s^{−1}, the turbine wake length was approximately 2 times larger at night than in the daytime. In Fig. 10b, one can see the averaged estimates as = 0.0066 m^{2} s^{−3}, = 680 m for nighttime (closed triangle), and = 0.013 m^{2} s^{−3}, = 340 m for daytime (indicated as an open triangle). In other words, increases in turbulence strength (as quantified by ) by half reduced the wake lengths by the same factor.

We also estimated the turbulence intensity , using data shown in Fig. 9a, indicated as open squares, and in Fig. 9c, indicated as closed squares. After averaging single estimates of for periods 0000–0300 LT (when averaged wake length 680 m) and 1200–1500 LT (when averaged wake length 340 m), we obtained = 0.09 and = 0.15, respectively. Therefore, when the turbulence intensity increased by a factor of , the wake length reduced by half.

## 6. Conclusions

We investigated the turbulent wind field in the vicinity of an operating wind turbine at the NWTC. In the field experiment, our research team tested the method of estimation of the turbulent energy dissipation rate from the transverse structure function of the radial velocity measured by a pulsed CDL using full 360° conical scanning. It was shown that this method was applicable even in the case of one full conical scan. Methods were also proposed for processing Doppler lidar–measured, conical-sector scan data in the vicinity of a wind turbine to estimate the wind speed and direction, the turbulent energy dissipation rate, and parameters of the wake generated by the wind turbine (maximum wind-velocity deficit, and the longitudinal wake dimension).

Using these approaches, we have determined the parameters of the turbulent wind field in the vicinity of the wind turbine from measurements by the 2-μm pulsed CDL on 14 and 15 April 2011, near Boulder, Colorado, at the NWTC test field. In particular, it was found that the wake behind the 2.3-MW research wind turbine, with a rotor diameter of 101 m and a hub height of 80 m, had the maximum velocity deficits of 27%–74% and lengths from 120 to 1180 m, depending on atmospheric conditions. It has been shown that a doubling of the turbulent energy dissipation rate (from .0066 to 0.013 m^{2} s^{−3}) corresponded, on the average, to a halving of the wake length (from 680 to 340 m). Similarly, this halving of the wake length is accompanied by an increase in turbulence intensity by a factor of 1.7.

The study results indicate the high effectiveness of using a pulsed 2-μm CDL to investigate turbulent wind fields near wind power stations and wind farms, and extend the range of problems addressed by atmospheric laser sensing (Zakharov et al. 2010; Tsvyk et al. 2011; Matvienko and Pogodaev 2012; Razenkov et al. 2012; Banta et al. 2013). Future experiments similar to those described in section 4 can yield the results necessary to construct an empirical model of a turbine wake for various atmospheric conditions.

## Acknowledgments

We thank our colleagues from the National Oceanic and Atmospheric Administration (NOAA), including R. M. Hardesty, R.-J. Alvarez, S. P. Sandberg, and A.M. Weickmann, and J. Mirocha from the Lawrence Livermore National Laboratory for preparing and conducting the experiment; John Brown from NOAA for his help with weather forecasting; Andrew Clifton from the National Renewable Energy Laboratory (NREL) for providing updates on tall-tower measurements; Padriac Fowler and Paul Quelet for updates on turbine operations; and Michael Stewart from NREL for his help with security and safety issues. Funding for this experiment was from the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Wind and Hydropower Technologies program. This work was also supported by the Russian Foundation for Basic Research (Project 10-05-9205) and the Civilian Research and Development Foundation (Project RUG1-2981-TO-10).

## REFERENCES

*Bull. Amer. Meteor. Soc.,*

**94,**883–902.

*J. Appl. Meteor.,*

**7,**105–113.

*Windpower Conf. and Exhibition,*Los Angeles, CA, American Wind Energy Association, NREL/CP-500-417.

*Mechanics of Turbulence.*Vol. 2,

*Statistical Fluid Mechanics,*The MIT Press, 874 pp.

*Proc. 16th Coherent Laser Radar Conf.,*Long Beach, CA, Universities Space Research Association, 4 pp. [Available online at http://sti.usra.edu/clrc2011/presentations/Session%209/Summary%20Y%20Pichugina.pdf.]

*Turbulence in the Free Atmosphere.*Consultant's Bureau, 263 pp.