## Abstract

Utility-scale wind turbines operate in dynamic flows that can vary significantly over time scales from less than a second to several years. To better understand the inflow to utility-scale turbines on time scales from seconds to minutes, the National Renewable Energy Laboratory installed and commissioned two inflow measurement towers at the National Wind Technology Center near Boulder, Colorado, in 2011. These towers are 135 m tall and instrumented with sonic anemometers, cup anemometers, wind vanes, and temperature measurements to characterize the inflow wind speed and direction, turbulence, stability and thermal stratification for two utility-scale turbines. In this paper, we present variations in mean and turbulent wind parameters with height, atmospheric stability, and as a function of wind direction that could be important for turbine operation, and for the persistence of turbine wakes. Wind speed, turbulence intensity, and dissipation are all factors that affect turbine performance. Our results show that these all vary with height across the rotor disk, demonstrating the importance of measuring atmospheric conditions that influence wind turbine performance at multiple heights in the rotor disk, rather than relying on extrapolation from conditions measured at lower levels.

## Introduction

Modern utility-scale wind turbines have hub heights of 80 m or more, and rotor diameters upwards of 100 m. Since the 1980s, there has been a trend of continuous growth in turbine size and power rating [1]. In 2011, several manufacturers announced turbines with hubs at more than 100 m above ground and rotor diameters of more than 120 m. Wind turbines operate in an atmospheric boundary layer characterized by turbulence. This layer experiences significant changes in heat fluxes at the lower boundary, switching from convective conditions during the day to stable conditions overnight. The change in stability is known to alter turbulence (which also varies by site [2]), impact turbine performance [3], and affect turbine loads [4]. Synoptic forcing, such as thermal winds (or baroclinicity), stability, wind direction veer, and jets all represent a departure from the predictable flow suggested by canonical power or logarithmic law flows [5]. This combination of continued growth in turbine size and dynamic boundary layer conditions requires careful, coupled monitoring of turbine behavior and wind inflow conditions to understand and improve performance and reliability [6].

The importance of atmospheric stability and coherent turbulent structures in wind for turbine behavior was shown by a series of measurements in a 41-row wind farm in the San Gorgonio Pass, California. Measurements showed that upwind turbines, particularly under stable nighttime conditions, enhanced turbulence within the turbine array [4]. Wavelet analysis methods revealed that organized or coherent turbulence was responsible for an increase in damage-equivalent loading. In typical turbulence, there is little correlation between the streamwise, vertical, and lateral components of turbulence. By comparison, in coherent turbulence, the components show higher correlation, over time scales up to a few seconds. These short, coherent periods have been found to cause increased loads in the wind turbine blades and drivetrain in simulations; therefore, the peak value of the CTKE during a 10-min interval was a good indicator of high loads during the same interval. Coherent turbulence is expected to increase for large arrays of turbines [4]. A later series of experiments at the National Renewable Energy Laboratory (NREL) National Wind Technology Center (NWTC), near Boulder, Colorado, used an array of sonic anemometers to measure inflow to the 42-m-diameter, 600-kilowatt (kW) Advanced Research Turbine (ART). These experiments were part of the Long-term Inflow and Structural Testing Program (LIST) [7]. Results from those tests suggested that turbine loads were sensitive to coherent structures found in stable nocturnal boundary layers [4]. The Lamar Low-Level Jet Program (LLLJP) measurement campaign quantified the frequency and magnitude of the low-level jet near Lamar in southeast Colorado in 2003 using a combination of an instrumented tower, SODAR, and NOAA's three-dimensional scanning wind LIDAR, the High Resolution Doppler LIDAR (HRDL). In these experiments, the jet (an acceleration of the flow between 50 and 200 m above ground, compared to a normal logarithmic wind profile) was found to occur in almost 30% of the nights. Results showed that the jet was responsible for the formation of Kelvin–Helmholtz instabilities (KHI) at elevations typical of modern turbine rotor disks [4]. The Kelvin–Helmholtz instabilities ultimately collapse to create coherent turbulent structures that then contribute to significantly enhanced turbine loads. A comparison of atmospheric data from the San Gorgonio and LIST measurement campaigns showed that loads peaked when the local turbine-layer Richardson number was in the range $0.01>RiTL>0.05$ [4]. This range corresponds with the formation of Kelvin–Helmholtz instabilities and peak values of the coherent turbulent kinetic energy. Low-level jets (and by implication KHI) occur throughout the U.S. Midwest [8–12] in states that represent a significant proportion of the installed and future potential wind energy capacity in the United States, and are also seen in Europe [13].

The stochastic wind field simulator TurbSim was created using lessons learned from San Gorgonio, LIST, and LLLJP to produce a desktop simulation of a realistic atmospheric boundary layer [4]. This tool generates a wind field with similar statistical properties to those seen during these studies and is designed to be interfaced to turbine aerostructural models to estimate structural loading. TurbSim can also be used to generate boundary conditions for computational fluid dynamics calculations.

The National Wind Technology Center is situated about 20 miles to the northwest of Denver, Colorado, at the foot of the Front Range at an elevation of around 1850 m above sea level. Winds onsite are dominated by strong westerly winds, typically resulting from a drainage flow out of the nearby Eldorado Canyon [14], visible in the upper left quadrant of Fig. 1(a). The NWTC is flat and undeveloped (Fig. 1(b)), and forms a “wind reservation’’ with very uniform surface cover to help reduce the variation seen in the wind profiles that flow in to the east end of the site, by the time they reach the turbine test stands at the west end of the site. Although the mean wind speed on site is low, winds can be extremely gusty and turbulent. For this reason, and because of the NWTC's accreditation as a turbine test location with the American Association for Laboratory Accreditation (A2LA), the site is a preferred location for many manufacturers to test turbines and establish performance, reliability, and survivability. The U.S. Department of Energy (DOE) installed the DOE/GE 1.5-MW turbine with 80-m hub height and 78-m rotor diameter at the NWTC in 2009. Three other utility-scale turbines have been installed onsite since then, including a Siemens 2.3-MW turbine in 2009, and an Alstom 3-MW Eco100 and Gamesa 2-MW G97 turbine in 2011.

Fig. 1
Fig. 1
Close modal

Drawing on the lessons learned from the San Gorgonio, LIST, and LLLJP studies, 135-m inflow monitoring towers were installed upwind of two of the NWTC test turbines in late 2010. A key goal of the tower measurements is to quantify turbulence and thermal stratification for the validation of the TurbSim model. Coupled inflow and turbine condition data will be analyzed in detail when high-load events occur.

In this paper, we show how the 135-m meteorological towers and measurement systems have been specially designed to capture relevant flow parameters. Focusing on a month of data obtained in October and November 2011, we introduce some of the characteristics of the winds locally and discuss the implications of our measurements for turbine performance.

## Methods

NREL installed two new 135 m meteorological towers towards the eastern side of the NWTC site. The towers are approximately two rotor diameters upwind of two, utility-scale wind turbines and are designed to quantify the inflow into the turbines. The towers are designated M4, upwind of the Siemens 2.3-MW turbine and M5, upwind of the DOE/GE 1.5-MW turbine.

Turbine inflow is quantified in terms of wind speed, wind direction, three-dimensional turbulence, and temperature at several heights across the turbine rotor. A schematic of the instrumentation installed on the M4 tower is shown in Fig. 2 and listed in Table 1. The instrumentation includes six three-dimensional sonic anemometers on each tower; five pairs of colocated cup anemometers and vanes, logarithmically distributed up the tower; absolute, differential, and dew point temperature measurements; precipitation intensity; and barometric pressure. Instruments are at slightly different heights on the M4 and M5 towers to align precisely with the turbine hubs, blade tips and blade midspan. Instruments are calibrated annually by the manufacturers or the NREL calibration laboratory. Wind measurement devices are mounted on booms that extend horizontally from the tower structure into the prevailing winds at an angle of $285 deg$ (compare to Fig. 3). The length of the booms for the sonic anemometers are approximately 6 times the width of the tower face. Cup anemometers and wind vanes are on booms that are 2.5 times as long as the tower face width. The towers are guyed using wires from the ground to torque arms (horizontal braces) that prevent the tower from twisting.

Fig. 2
Fig. 2
Close modal
Fig. 3
Fig. 3
Close modal
Table 1

Devices used to measure atmospheric properties and boom motion on the M4 tower

ParameterHeight (m)Device
Wind speed3, 10, 26, 88, 134Met One SS-201 cup anemometer
Wind speed (class one)80Thies 4.3351.10.0000
Wind direction3, 10, 26, 88, 134Met One SD-201 vane
Air temperature3, 26, 88Met One T-200A platinum RTD
Dew point temperature3,26, 88, 134Therm-x 9400ASTD
Differential temperature3-26, 26-88, 88-134Met One T-200A
Wind speed components15, 30, 50, 76, 100, 131ATI K'-type sonic anemometer
Sonic temperature15, 30, 50, 76, 100, 131ATI K'-type sonic anemometer
Boom triaxial acceleration15, 30, 50, 76, 100, 131Summit 34201A
Barometric pressure3AIR AB-2AX
Precipitation3Vaisala DRD11A
ParameterHeight (m)Device
Wind speed3, 10, 26, 88, 134Met One SS-201 cup anemometer
Wind speed (class one)80Thies 4.3351.10.0000
Wind direction3, 10, 26, 88, 134Met One SD-201 vane
Air temperature3, 26, 88Met One T-200A platinum RTD
Dew point temperature3,26, 88, 134Therm-x 9400ASTD
Differential temperature3-26, 26-88, 88-134Met One T-200A
Wind speed components15, 30, 50, 76, 100, 131ATI K'-type sonic anemometer
Sonic temperature15, 30, 50, 76, 100, 131ATI K'-type sonic anemometer
Boom triaxial acceleration15, 30, 50, 76, 100, 131Summit 34201A
Barometric pressure3AIR AB-2AX
Precipitation3Vaisala DRD11A

Data are obtained at 20 Hz from the instruments on the M4 and the M5 towers, using a system built around National Instruments LabVIEW software and PCI hardware. Separate data acquisition systems are used on each tower and on the downwind turbines, and all measurements are synchronized using timestamps from Global Positioning System receivers. This high-accuracy synchronization allows us to link inflow winds with the turbine loads and power (not shown).

### Quantifying the Mean Flow.

We calculate the characteristics of the mean flow for a 10-minute averaging period, per IEC standard 61400-12-1 [15] for wind turbines.

We calculate the mean wind speed and direction at each height by first converting the 20-Hz wind speed $U$ measured by the cup anemometers and direction $WD$ measured by the vanes into 20-Hz orthogonal wind components in the meteorological zonal (west-east, $um$) and meteorological meridional (south-north, $vm$) directions,
$um=-U·sin(π·WD180)$
(1)
$vm=-U·cos(π·WD180)$
(2)
where positive $um$ indicates a wind blowing to the east, and positive $vm$ is a wind blowing to the north. The mean wind speed is then calculated for each 10-minute interval as the vector mean of the orthogonal wind components,
$U¯=[um¯2+vm¯2]1/2$
(3)
The mean wind direction is the direction that the wind comes from, in degrees,
$WD¯=tan-1(-um¯-vm¯)×180π$
(4)

where the function $tan-1(x)$ is the arc tangent of $x$ in the range $±π$ radians.

### Quantifying Turbulence.

Because the spectrum of turbulent fluctuations includes both large and small scales, measurement devices must be capable of resolving a wide range of wind speeds, and capturing rapid changes. We use sonic anemometers to make wind turbulence measurements as they have no inertia, a small measurement volume, and can make high-frequency measurements. In comparison, the inertia of cup anemometers makes them unreliable for high-frequency turbulence measurements. Sonic anemometers measure winds in three orthogonal components, rather than a wind speed and direction as in the case of cups and vanes. To calculate the mean wind vector, 10-min blocks of sonic anemometer velocity measurements are rotated to form a three-dimensional wind vector with the largest stream-wise component $u$, but lowest absolute mean transverse component $v$ and vertical component $w$ for the 10-min interval [16]. The turbulent velocity components $u',v'$, and $w'$ are defined as the difference from the mean velocity component, so that $u'=u(t)-(U)¯$, $v'=v(t)-(v)¯$, and $w'=w(t)-(w)¯$, where after rotation into the prevailing wind, $(v)¯=(w)¯=0$. Turbulence intensity, $Ti$, is the ratio of the standard deviation of the turbulent components to the stream-wise mean speed, expressed as a percentage [17]. For flow in the streamwise direction ($u$), this percentage is
$Ti(u)=σ(u')U¯×100$
(5)
The local friction velocity $u*$ is calculated from the turbulent velocity fluctuations measured by each of the sonic anemometers. Following [18], it is defined as
$u*=([cov(u'w')]2+[cov(v'w')]2)1/4$
(6)

where “cov’’ indicates the covariance for a 10-min interval.

Turbulence kinetic energy (TKE) is a measure of the energy in the turbulent velocity fluctuations that includes all three velocity components, rather than the turbulence intensity, which only includes the streamwise component [19]. The mean TKE over a 10-min interval is defined as
$TKE=12[u'u'¯+v'v'¯+w'w'¯]$
(7)
As noted earlier, coherent turbulent kinetic energy (CTKE) is a significant contributor to turbine loads [4]. CTKE is defined at an instant as
$CTKE(t)=12([u'w']2+[u'v']2+[v'w']2)1/2$
(8)

TKE quantifies the energy in the flow that is created by the Reynolds stresses that arise from shearing of the mean flow by turbulence, and is widely used in atmospheric sciences and meteorology [17,19]. CTKE instead quantifies the energy contained in deviations from the mean in multiple directions at the same time; high instantaneous levels of CTKE can only be caused by large deviations of $u$ and $w$, $u$ and $v$, or $v$ and $w$ simultaneously, and it is this coherence that results in increased turbine loads [4].

Turbulence is generated at low frequencies by flow interacting with terrain (mechanical production), through buoyancy, and by the motion of the atmosphere. TKE is dissipated at high frequencies into heat through viscous dissipation. Understanding the power spectra of turbulence is important for turbine design, as this influences the energy that is transferred into the turbine structure. One useful measure of turbulence is the integral length scale, which describes the mean length scale of turbulent eddies in the flow. It is also the length scale at which the majority of turbulent kinetic energy can be found. For example, when comparing two flows of the same mean velocity, the flow with the larger integral length scale will have more energy at lower frequencies than the flow with the shorter integral length scale. The turbulence integral length scale ($Λ$) for a velocity component ($u'$, $v'$ or $w'$) is calculated from the time series of the turbulent velocity component. First, the characteristic time ($τe$) for the autocorrelation of the turbulent component to drop to $1/e$ is calculated. $τe$ is multiplied by the mean wind speed to give the turbulence integral length scale, $Λ(u')=U¯×τe(u')$ [20]. Because the integral length scale is of the order of the measurement height [19], the characteristic time of flows at a turbine hub (around 80 m) at rated speed (10–12 m s−1) is approximately 10 s, which can be resolved by our 20-Hz data acquisition system.

The dissipation rate $ɛ$ is the rate at which turbulent kinetic energy is dissipated into heat at the smallest eddy scale in turbulent flow. Correctly estimating the dissipation rate under varying atmospheric conditions may be important for correctly modeling the propagation of wakes downwind of wind turbines [21,22]. Because this occurs at higher frequencies than what can be resolved directly by the sonic anemometers, it has to be inferred from the turbulent power spectra [23,24]. Here we calculate $ɛ$ using the structure function method [17]. The structure function for a time $δt$ is the mean squared difference between $u'$ at times $t$ and $δt$,
$DAA(δt)=[u'(t+δt)-u'(t)]2¯$
(9)
Next, we calculate the ratio of the structure function to the cube root of the squared lag,
$Cv2(δt)=[DAA(δt)(U¯δt)2/3]$
(10)
The dissipation rate $ɛ$ is then given by
$ɛ=[Cv2˜2]3/2$
(11)

where the tilde operator indicates the median for all $δt$. The dissipation rate is limited to the inertial subrange by using $0.05≤δt≤2$, corresponding to frequencies between 0.5 and 20 Hz. From the power spectra of the turbulent velocity components (not shown), 0.5–20 Hz is in the inertial subrange where energy cascades from the larger scales to smaller scales at a constant rate.

### Quantifying Thermodynamic Properties.

To calculate the thermal stability profile in the boundary layer, we must quantify the air temperature and humidity profile. This requires a series of calculations, set out below. Absolute and dew point temperature and barometric pressure are measured at 3 m above ground. These are denoted $T0$, $Td0$, and $P0$, respectively.

The absolute temperature profile $T(z)$ on the M4 tower is measured as the sum of $T0$ and temperature differences between 3 and 26 m, 26 and 88 m, and 88 and 134 m above ground. Using differential temperature measurements with an accuracy of $0.1 deg$ gives improved accuracy compared to using two local absolute temperature measurement with a typical accuracy of $0.5 deg$.

The local saturation vapor pressure $es$ is calculated at each height from the air temperature $T(z)$ in degrees Celsius,
$es(z)=6.11×10[(T(z)·A)/(T(z)+B))$
(12)

where $A$ = 7.5 and $B$ = 237.3 if $T(z)≥0°C$. Otherwise, $A$ = 9.5 and $B$ = 265.5. The actual local vapor pressure $e(z)$ is calculated from Eq. (12) by replacing $T(z)$ with the dew point temperature $Td(z)$ in degrees Celsius.

The specific humidity $q$ is the ratio of mass of water vapor to the total mass of the air [19]. It is a function of the ratio of the local vapor pressure $e$ to the ambient pressure $P$,
$q=0.622eP$
(13)

where 0.622 is the ratio of the gas constant for dry air (287 J kg−1 K−1) to the gas constant for water vapor (461.5 J kg−1 K−1).

The virtual temperature $Tv$ is [19]
$Tv=T(1+0.61q)$
(14)
The virtual temperature at the lowest height, $Tv0$, and barometric pressure are used to calculate the pressure gradient, $dP/dz$ from the hydrostatic pressure balance applied to a perfect gas [19],
$dPdz=-gP0RTv0$
(15)

where $g$ is the acceleration due to gravity (9.81 m s−2) and $R$ is the gas constant of dry air. The pressure profile is then calculated from the measured ground pressure, the pressure gradient, and the change of height $Δz$ as $P(z)=P0+Δz·dP/dz$.

The potential temperature $Θ$ is the temperature that air at the ground would have if moved adiabatically to a reference pressure level, $Pref=1000$ hPa [19]. Calculating the potential temperature requires the pressure profile to be known,
$Θ(z)=T(z)(PrefP(z))R/Cp$
(16)

where $Cp$ is the specific heat capacity at constant pressure (1005 J kg−1 K−1). The ratio $R/Cp=0.286$.

The virtual potential temperature $Θv$ is the potential temperature that dry air would require to have the same density as moist air [19]. The virtual potential temperature is
$Θv(z)=Θ(z)(1+0.61q(z))$
(17)

where $q$ is the specific humidity at each height (Eq. (13)). Profiles of $T$, $Θ$, and $Θv$ can then be used to visualize and quantify stability using a variety of metrics, described in Sec. 2.4.

### Quantifying Stability.

Several methods exist to quantify thermal stratification, that all are related to the ratio $|dΘv/dz|$. One method is to use the ratio of shear-driven turbulence to buoyancy-generated turbulence using the Monin–Obukhov length, $L$ [17],
$L=-u*3Θv¯κgw'Θ'v¯$
(18)

The buoyancy term $w'Θv'¯$ in Eq. (18) is actually calculated as $w'T'¯$ measured by the sonic anemometer, as the turbulent fluctuations of temperature measured by a sonic anemometer approximate the turbulent component of the virtual potential temperature, $Θv'$. The mean value of virtual potential temperature in Eq. (18), $Θv¯$, is calculated from the tower temperature and dew-point temperature profiles. The Monin–Obukhov length is usually normalized by the measurement height $z$ (in this case the sonic anemometer height) to give the ratio $ζ=z/L$. Locally convective conditions give $z/L<0$, and stable conditions give $z/L>0$, while in neutral conditions, $L→∞$ (Table 2).

Table 2

Stratification classes using $Ri$ or $z/L$

StratificationLabel$Ri$$z/L$
UnstableU<−0.01<−0.01
NeutralN$|Ri|≤$ 0.01$|z/L|≤$ 0.01
Slightly stableS1$0.011.25}S:z/L>0.01$
StableS2
Strongly stableS3
StratificationLabel$Ri$$z/L$
UnstableU<−0.01<−0.01
NeutralN$|Ri|≤$ 0.01$|z/L|≤$ 0.01
Slightly stableS1$0.011.25}S:z/L>0.01$
StableS2
Strongly stableS3
We also quantify stability with the gradient Richardson number, which is calculated from 10-min average temperatures and gradients of wind components and virtual potential temperature between two heights ($z1$ and $z2$) [19]. The Richardson number can then be considered representative of the entire layer between $z1$ and $z2$. The gradient Richardson number is [17]
$Ri=gΘv¯dΘv¯/dz(dum¯/dz)2+(dvm¯/dz)2$
(19)

where the mean virtual potential temperature between $z1$ and $z2$ is $Θv¯=12[ΘV(z1)+Θv(z2)]$.

A simplified Richardson number has also been used in some applications [25–27]. This considers just the gradient of the mean wind speed $U¯$, rather than including directional shear as in Eq. (19). To distinguish this from the gradient Richardson number, this is described in this context as the “Speed Richardson Number,” $RiS$,
$RiS=gΘv¯dΘv¯/dz(dU¯/dz)2$
(20)

Calculations of $Ri$ and $RiS$ from the ground to the turbine hub or tip use the mean of all of the temperature, wind speed and wind component gradients [4].

For unstable conditions, $z/L≈RiS$, while $RiS$ tends towards a constant value as $z/L→∞$ [25]. If $ζ=z/L$, then
$RiS={0.74ζ(1+15ζ)1/2(1-9ζ)1/2 if RiS<0ζ(0.74+4.7ζ)(1+4.7ζ)2 if RiS>0$
(21)

We define several stratification classes from the Richardson number and normalized Monin–Obukhov length $ζ$ (Table 2). The Richardson number bands are based on previous work on the interaction of turbines and stability [4], and explicitly identify the slightly stable region that [4] is found to be linked to the production of CTKE. We also identify the strongly stable regime of $Ri>0.25$ in which turbulence is rapidly damped by negative buoyancy [19]. A range of $L$ has been used by different authors to define neutral conditions. When referenced back to the hub height, $zhub$, these correspond to $|zhub/L|~x<0.1$ [3,28]. Equation (21) shows that for near-neutral conditions, $Ri≈z/L$, but as stability increases, $z/L→∞$. Because a definition of neutral conditions as $|z/L|<0.1$ potentially includes the slightly stable regime, we use the narrower range of $|z/L|<0.01$ that allows us to better distinguish changes in the atmosphere in this region.

### Quality Control.

Calculating the Richardson number, Monin–Obukhov length, and turbulence requires low instrument noise, regular sampling intervals, and continuous sampling over long periods of time. We use high-quality, calibrated instruments and check the frequency of the data acquisition system as part of our postprocessing routines. We check data from each instrument against simple quality control measures. These quality control measures include testing for data acquisition rates of 20 Hz, and detecting flat-line data (which indicates a malfunctioning device) by checking for standard deviations that are less than 0.01%. A check is also made on the number of valid data points per 10-min interval, per channel. We flag data if the number is less than 95% of the 12,000 data points that could be collected during a 10-min interval. Flags propagate through calculations, so that if data from two channels $a$ and $b$ are used to calculate another value $y=f(a,b)$, output $y$ inherits the flags of variables $a$ and $b$.

### Tower Shadowing and Flow Impact.

A tower's own structure will impact flow measurements made around the tower. The tower is not completely porous, so flow is deflected around the tower structure, causing deceleration immediately upstream, and acceleration around the tower. A wake forms downwind of the structure, characterized by reduced wind speeds and high turbulence. These effects can lead to observable differences between free stream measurements and measurements on the tower. To understand the tower's impact on the wind speeds measured with the sonic and cup anemometers, we measured the free stream wind speed approximately 200 m to the west of the M4 tower using a commercial Doppler wind LIDAR system. Such LIDAR systems have been shown to give measurements within 2% of sonic anemometer measurements when averaged over a 10-min interval [29]. In contrast to the tower, LIDAR wind speed measurements are not impacted by any kind of support structure. The LIDAR measured the wind speed in a 20-m wide bin centered at 100 m above ground, and were compared to data from a sonic anemometer at 100 m on the M4 tower (Fig. 4(a)). A comparison was also made between the 131-m sonic anemometer and a cup anemometer at 134 m (Fig. 4(b)) using data from the October to November measurement period.

Fig. 4
Fig. 4
Close modal

When flows are aligned with the booms (flows from $285 deg$, Fig. 4(a)), wind speeds measured by the LIDAR are higher than those measured by the sonic anemometers, while sonic anemometer wind speeds are similar to the cup values. This suggests that the flow is slowing before it reaches the mast, and that this slowdown extends out to 5.8 times the face width. When flow is perpendicular to the booms (i.e., from approximately $195 deg$ or $15 deg$), the ratio between LIDAR wind speed and sonic anemometer wind speed is closer to 1.0 and the spread is reduced. When flow is perpendicular to the booms, wind speeds around the cups (mounted on the shorter booms) are lower than the wind speeds measured by the sonic. This suggests that the flow around the tower is distorted in a complex fashion, as suggested by studies of flow around tubular masts [30] and lattice towers [31]. When wind flows through the tower on to the sonics, there is a clear reduction in wind speed measured by the sonics compared to the free stream. This effect can be seen in Fig. 4(a) for winds between approximately $100 deg$ and $135 deg$. Assuming that the wake effect is largest when flow approaches the tower from $105 deg$ (the opposite direction to the booms) and so the instruments are in the middle of the wake, this implies a $60 deg$-wide wake region. To avoid the wake contaminating data, measurements made when the tower wake region crosses an instrument are omitted from the rest of this paper.

A different trend is shown in Fig. 4(b), in which measurements from the boom-mounted sonic are compared with cup data. There is a strong decrease in the ratio of the sonic wind speed to the cup wind speed when the flow is aligned with the booms, compared to the ratio during perpendicular flows. The cup anemometers are mounted on booms with lengths that are 3.5 times the tower face width, while the sonic anemometers are mounted on booms that are 5.8 times as long as the tower face width. Together, these data suggest that the tower modifies the free stream flow, causing flow to slow down some distance from the tower, before accelerating around the tower body. This effect appears to be independent of free stream wind speed. In the one-month data set shown in Fig. 4, the effect is well-defined using wind speed and flow direction and therefore could be corrected during postprocessing. However the spread in the ratio of winds speeds for a given wind direction would still be approximately 2%–3% around a ratio of 1.0. This spread can be considered the noise due to sensor uncertainty and atmospheric effects.

## Results

The long-term data record from the M2 tower show that the strongest winds onsite come from the west-northwest (WNW) at a direction of approximately $280 deg$$290 deg$ (Fig. 3). Winds from the $45 deg$ sector from west (W) to northwest (NW) represent 18% of all winds above 1 m s−1 at 80 m above ground. There are secondary peaks in wind frequency to the SSE, and slightly west of north. More detailed analysis of the 14 years of data available from the M2 tower (reported in [32]) reveals a strong annual wind cycle, with winds from the NW sector peaking during the winter months and weaker southerly or northerly winds occurring during the summer months.

This paper presents data collected on the 135 m tower during a four-week period from October 7, 2011 to November 7, 2011. Data are limited to observations passing the quality control tests described in Sec. 2.5 and includes flows from the WNW and south-southeast (SSE), with a mixture of stable, neutral, and unstable stratification. Over the one-month period described here, less than 3 h of neutral conditions coincided with wind speeds above 3 m s−1.

### Inflow Characteristics.

Because of the location of the NWTC at the western edge of the front range, winds from different sectors travel across markedly different terrain depending on flow direction. The following sections discusses the flow structure in WNW and SSE flows at hub height wind speeds ($U(76)$) between 11 and 13 m s−1, which are typical rated wind speeds for large turbines.

#### Prevailing Winds.

Flow from the WNW sector (a direction of $285 deg±15 deg$) at speeds between 11 and 13 m s−1 was detected by the sonic anemometer in seventy one 10-min intervals during the period from October 7, 2011 to November 7. Using the $Ri$ stability classes in Table 2, we found only one 10-min interval of neutral conditions, or less than 2% of the total. Conditions were unstable in 24% of the intervals, slightly stable (S1) in 4%, stable (S2) in 46%, and strongly stable (S3) in the remaining 24%.

A logarithmic increase of mean wind speed with height occurs in all WNW flows at hub-height wind speeds between 11 and 13 m s−1 (Fig. 5(a)) up to approximately 100 m above ground. This is expected for neutral flows [17], while stable and unstable flows show a clear departure from the logarithmic wind speed profile. Above 100 m, the rate of wind speed increase with height decreases in all stability cases, corresponding to reduced wind shear and a departure from the logarithmic wind profile [17]. Several measures of turbulence are presented in Fig. 5. These include the 10-min turbulence intensity ($Ti$) in Fig. 5(b), the 10-min average turbulent kinetic energy (TKE) in Fig. 5(c), and peak coherent turbulent kinetic energy (peak CTKE) in Fig. 5(d). Turbulence intensity decreases with height above ground and also in more stable conditions, compared to convective conditions. This trend has been seen in other studies of the atmospheric boundary layer [3,5]. Turbulence intensity is more than 20% at hub height wind speeds of 11 m s−1 in slightly stable (S1) and convective (U) conditions. During more stable (S2) conditions, $Ti$ drops to around 17%. TKE and peak CTKE are highest in slightly stable conditions (S1, see Figs. 5(c) and 5(d)) and decrease as stability increases or conditions become unstable.

Fig. 5
Fig. 5
Close modal

In the case of flow from the WNW, the integral length scale at each height is similar in all stability conditions, but continues to increase with height in convective conditions (Fig. 5(e)). This increase in the vertical length scale with height in unstable conditions, compared to stable conditions, reflects the vertical growth of the boundary-layer eddies in unstable (convective) conditions compared to stable conditions. The vertical length scale continues to grow in all conditions, and $Λw≈z$ (Fig. 5(f)), which would be expected as the vertical size of the eddies is constrained by the ground and the upper edge of the boundary layer. The vertical length scale does increase slightly in convective conditions, compared to stable conditions. Dissipation rate $ɛ$ gradually decreases with height, reaching a minimum at around 100 m in stable conditions, but continues to fall with increasing height in unstable conditions (Fig. 5(g)). The minimum $ɛ$ at about the hub height in stable conditions suggests that wakes will persist longest at the hub, but dissipate more closely to the ground and at the turbine top. In unstable conditions, wakes will dissipate more rapidly than in stable conditions.

Observations for this period show that for WNW flows above 3 m s−1, peak CTKE was highest in slightly stable or stable conditions (Fig. 6). The maximum values of TKE and CTKE occurred in the slightly stable (S1) range where $0 (lower panels of Fig. 6). This is the $Ris$ range in which Kelvin–Helmholtz instabilities are expected to form most rapidly, and thus have the most energy when they collapse, potentially leading to increased turbine damage-equivalent loads [4]. This $Ris$ range is consistent with data from locations in the Great Plains of the United States and in an operating wind farm in California [4]. Large variation in peak CTKE with stability depending on wind direction (compare Fig. 5(d) and Fig. 7(d)) suggests that at this location during this period, CTKE may be associated with both wind direction and stability, rather than just stability as in simpler sites. This dependence on wind direction suggests that CTKE can be increased by an interaction with terrain.

Fig. 6
Fig. 6
Close modal
Fig. 7
Fig. 7
Close modal

#### Southerly Flows.

Southerly flows, from the sector $175 deg±15 deg$, were less frequent during this period than the WNW flows, with only seventeen 10-min periods where the 76-m wind speed was between 11 and 13 m s−1. Of these flows, 18% were stable (S2), while the rest were strongly stable (S3).

The speed profile of winds from the south shows a similar trend to that from the WNW. During stable conditions, winds have low shear above the 76-m anemometer. Below that height, wind speeds increase relative to winds during slightly stable conditions (Fig. 7(a)). The turbulence intensity of the SSE flow is lower than the WNW flows, but shows the same decrease with height as the WNW flows. This reduced turbulence compared to the WNW flow suggests that the increased turbulence seen in the WNW flows is generated by the interaction of the wind and terrain of the Front Range, rather than being generated by buoyancy. The TKE and peak CTKE are both reduced in the SSE flow compared to the WNW flow. As with flows from the NNW, TKE, and peak CTKE are both lowest in strongly stable (S2 or S3) conditions for flows from the SSE (Fig. 7).

The turbulence length scale $Λu$ profile of the SSE flow (Fig. 7(e)) behaves differently in changing stability conditions than the WNW flows (Fig. 5(e)). The length scale of the horizontal flows are markedly increased in strongly stable conditions compared to the slightly stable conditions, which is opposite to the trend seen in the WNW flows, although a maximum is seen in flows from both directions at around 76 m. Vertical length scales appear to peak at around 100 m, in comparison to the WNW flows where vertical length scales continued to increase with increasing height above ground. Dissipation rates for the SSE flows are about half that of the WNW flows, although strongly stable flows are the least dissipative in both cases. Both WNW and SSE flows appear to have a minimum in the dissipation rate profile near 100 m for strongly stable (S3) conditions.

### Choice of Stratification Measures.

As was noted in Sec. 2.4, stratification can be quantified using the Monin–Obukhov length $L$ and the Richardson number, $Ri$. Both calculations require data from several different instruments.

The Monin–Obukhov length compares the ratio of turbulent kinetic energy produced by shear to that produced by buoyancy. It is calculated from turbulent component and temperature data from sonic anemometers, and from virtual potential temperature from absolute and dew point temperature sensors on the tower (Eq. (18)). The Monin–Obukhov length $L$ is usually presented normalized by the measurement height $z$ as $ζ=zL-1$. Over large, flat areas, buoyancy in the boundary layer is driven by the surface heat flux and so the diurnal cycle of $ζ$ follows the general cycle of the heat flux, switching from stable conditions at night to unstable conditions during the day. Although heat fluxes are usually positive during the day and negative at night, this can change depending on surface cover. The daytime stable periods between 10/27 and 10/29 in Fig. 8 coincided with 24 h of snowfall followed by snow on the ground for several days, which potentially caused a heat flux into the ground during the day. Similarly, occasional positive heat fluxes during the evening cause infrequent nighttime unstable conditions at the hub-height (Fig. 8). At the NWTC these nighttime unstable conditions could be caused by warm air being convected from upwind of the monitoring towers.

Fig. 8
Fig. 8
Close modal

In comparison, the stability of a layer can be quantified by the Richardson number. This is based on measurements of wind speed and direction using cups and vanes at two or more heights, and absolute, differential and dew point temperature profiles (Eqs. (19) and (20)), and has been used in previous investigations of wind turbine performance [3,4]. At the NWTC from early October 2011 to early November 2011 the Richardson number indicated stable conditions overnight, switching to unstable conditions during the day (Fig. 8). The pattern of stable nights and unstable days agrees with the cycle from the normalized Monin–Obukhov length.

The occasional difference between layer stability quantified using $RiS$ and local stability quantified using $z/L$ reflects the complex stratification that may exist at this site. It is possible that a stable layer might overlay an unstable layer (or vice versa) for a short period of time, which can cause apparent differences in layer versus local stratification. This has been reported in other research, e.g., [33].

The two Richardson numbers defined in Sec. 2.4 agree in sign but not in magnitude (Fig. 9(a)). This difference is explained by a comparison of Eqs. (19) and (20), as it is likely that there will be a small amount of directional veer between the ground and 134 m, this and so $(dum/dz)2+(dvm/dz)2$ is always greater than $(dU/dz)2$. Comparing $Ri$ with $ζ$ (Fig. 9(b)) shows that the two measures do not always give the same stability, which is also shown in Fig. 8. There is also wide scatter around the Businger–Dyer relationships (Eq. (21)), which were generated from analysis of measurements over flat and uniform surfaces [34] and have been confirmed by other measurements [23]. Because the terrain upwind of the NWTC is not flat or uniform, more turbulence is generated mechanically than over flat, uniform terrain, particularly in the vertical and transverse directions. This modification of the turbulence leads to large scatter compared to flat-field reference cases. This difference may not be as large on sites with longer upwind fetch or more uniform terrain.

Fig. 9
Fig. 9
Close modal

### Implications for Other Sites.

Modern utility-scale turbines frequently have hubs at 80 m above ground or higher, and rotor disks of 80-m diameter or larger. Figures 5 and 7 suggest that in this particular location, for flows from the WNW and SSE and at this speed, turbines extend out of the surface layer where flows are strongly influenced by the surface, and into the outer planetary boundary layer, where regional circulation and the diurnal cycle play a greater role. Because of the change in gradients at around 80 m, extrapolation from measurements at lower elevations to the turbine hub height will be prone to error, particularly velocity profiles in stable conditions. Although the change in velocity profile and turbulence seen at the NWTC might not occur at all sites at this height, this behavior cannot be known a priori. This uncertainty argues for a careful survey of wind characteristics using direct measurement rather than extrapolation from lower elevation measurements, as part of the wind resource assessment process.

Vertical profiles of the wind speed, turbulence, and dissipation rate also show that there are significant differences between conditions that a turbine experiences, as stability changes while wind speed and direction stay constant. Figures 5 and 7 show that TKE can vary by a factor 2 between strongly stable and unstable conditions, while TKE and peak CTKE are both highest in low $RiS$ conditions that are also linked to high turbine loads. Stability, TKE, peak CTKE, and dissipation all influence wake propagation [28], so including their real values or probability distributions in a site optimization process may lead to improved turbine siting.

The relative insensitivity of the Richardson number to local effects, compared to normalized Monin–Obukhov length (Figs. 8 and 9(b)), provides a good argument for the use of the Richardson number to quantify flows when considering the interaction of a turbine with the wind. Another reason to use the Richardson number is that the Richardson number integrates conditions over the entire height of the turbine, and the turbine uses all of the flow through the turbine rotor to produce power. In comparison, the Monin–Obukhov length $L$ uses data measured at a few discrete heights, and is therefore local rather than spanning the entire rotor diameter.

Our study demonstrates that the atmosphere is dynamic in ways that can impact turbine performance. Changes in the atmosphere can be characterized in terms of stability, mean flow, and turbulence (and potentially changes in other properties, such as power spectra, that are not investigated here). The Richardson number can be calculated over a 10-min interval from data taken at 1 Hz by cup anemometers, wind vanes, differential temperature sensors, and humidity sensors, and so meaningful stability data can be obtained as part of a typical wind resource assessment campaign. High-quality turbulence data can be obtained using three-dimensional sonic anemometers, which would allow a site developer to detect the occurrence of potentially damaging KH instabilities, or large directional variation in TKE or turbulence length scales that could change turbine loads and performance depending on wind direction. However, recording representative values of turbulence will require relatively high bandwidth sonic anemometry, as described in this paper. Thus, the need is apparent for improved instrumentation to be used on resource assessment towers. This improved instrumentation could include using dual sonic anemometers at multiple levels to measure orthogonal velocity components, mounted on two arms to avoid tower shading.

## Conclusion

Designing and instrumenting a measurement mast for inflow characterization requires careful consideration of the measurement goals and flow characteristics. At the National Wind Technology Center, two new 135-m meteorological towers have been instrumented with sonic anemometers, temperature sensors, cup anemometers, and wind vanes. The NWTC measurement suite allows inflow mean conditions, turbulence, local and layer stability to be quantified. We will use this high-resolution data set to investigate atmospheric conditions when high turbine loads occur, to investigate links between turbulence and stability, to further validate the stochastic flow model TurbSim [4] and aeroelastic design model FAST [35], for comparison with remote sensing instrumentation [36], and as test data for nacelle-mounted LIDAR turbine control techniques [37].

First data from the new 135-m tower in October and November 2011 show that wind conditions vary considerably depending on wind direction and atmospheric stability. For the same wind speeds, as conditions become strongly stable, wind shear increases, but turbulence intensity and dissipation rate decreases compared to unstable conditions. The change in dissipation rate will be important for the duration of wakes downstream of operational turbines, resulting in more persistent wakes in stable, nighttime conditions. Wind speed, turbulence, dissipation, and length scales all show different vertical profiles depending on wind direction. TKE, peak CTKE, and the dissipation rate $ɛ$ in flows from the same direction all peak under slightly stable conditions, supporting previous studies. Results also show changes in wind speed gradients at or near turbine hub heights (80–100 m above ground). Therefore, incorrect estimates of turbine hub or rotor disk conditions would be made if data are extrapolated from lower-level data, such as 60- or 80-m-tall towers.

The data resulting from the long-term operation of these towers and turbines will be crucial for validating existing aerostructural design models for multimegawatt turbines, and for developing improved models for designing larger, more efficient next-generation turbines.

## Acknowledgment

This work was supported by the U.S. Department of Energy under Contract No. DE-AC36-08GO28308 with the National Renewable Energy Laboratory.

### Nomenclature

Nomenclature

• Cp =

specific heat capacity at constant pressure, 1005 J kg−1 K−1

•
• e =

vapor pressure

•
• f =

cyclical frequency

•
• g =

acceleration due to gravity, 9.81 m s−2

•
• L =

Monin–Obukhov length

•
• P =

barometric pressure

•
• q =

specific humidity

•
• Q0 =

surface heat flux

•
• R =

gas constant of dry air, 287 J kg−1 K−1

•
• Ri =

•
• RiS =

speed Richardson number

•
• T =

absolute temperature

•
• Td =

dew point temperature

•
• Tv =

virtual temperature

•
• Ti =

turbulence intensity

•
• U =

streamwise velocity

•
• u* =

friction velocity

•
• um =

zonal (west-east) wind component

•
• vm =

meridional (south-north) wind component

•
• w =

vertical wind component

•
• z =

height above ground

•
• ε =

dissipation rate

•
• κ =

Von Kármán constant, 0.41

•
• θ =

potential temperature

•
• θv =

virtual potential temperature

•
• ζ =

ratio z/L

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