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  • Wilczak, J. M., Oncley S. P. , and Stage S. A. , 2001: Sonic anemometer tilt correction algorithms. Bound.-Layer Meteor., 99, 127150.

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    Measured scintillation power spectrum with the zero-slope and power-law ranges indicated.

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    Theoretical scintillation spectra with crosswinds of 0.1 (solid black line) and 10 m s−1 (dashed gray line) in a log–log representation. The zero-slope and power-law lines are indicated for both crosswinds, as is the corner frequency (fCF).

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    Theoretical energy conserved representation of the scintillation spectra with crosswinds of 0.1 (solid black line) and 10 m s−1 (dashed gray line), with the maximum frequencies indicated by fMF.

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    Measured scintillation power spectrum calculated with FFT (solid black line) and wavelet (dashed gray line) approaches over 5 min of data.

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    Theoretical cumulative scintillation spectra with crosswinds of 0.1 (solid black line) and 10 m s−1 (dashed gray line). The frequencies where the cumulative spectra are 0.5, 0.6, 0.7, 0.8, and 0.9 are indicated by f0.5, f0.6, f0.7, f0.8, and f0.9, respectively.

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    Minimum record length necessary to solve at least 1% of the scintillation spectra for minimum crosswind for different scintillation setups: LAS [black in (a)], MWS [gray in (a)], and laser scintillometer [black in (b)].

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    Minimum measurement frequency necessary to solve at least 99% of the scintillation spectra for maximum crosswinds for different scintillation setups: LAS [black in (a)], MWS [gray in (a)], and laser scintillometer [black in (b)].

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    Aerial photo (courtesy of Google Maps) of the experimental setup, with the (a) sonic anemometer, (b) receiver of the BLS900, and (c) transmitters of the BLS900 indicated. The path of the scintillometer is indicated with the dotted white line.

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    Wind conditions on the Haarweg from DOY 133 till 140, with horizontal wind speed (U, gray solid line) and crosswind on the scintillometer path U, (gray dotted line) from the sonic anemometer on the left y axis, and wind direction of the sonic anemometer (black dots) on the right y axis; the orientation of the scintillometer path is given as a black line.

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    Measured scintillation spectrum plotted as a log–log representation used by the (a) CF algorithm, (b) the semilog representation used by the MF algorithm, and (c) the cumulative spectrum used by the CS algorithm for DOY 136 at 1200 UTC.

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    Scatterplots of 10-min crosswinds (U⊥SLAS against U⊥sonic) for the (a) CF, (b) MF, and (c) CS algorithms colored according to SNR.

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    Scatterplots of 10-min crosswinds averages obtained of 1-s wavelets for the (a) CF, (b) MF, and (c) CS algorithms, on DOY 136.

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    Scatterplots of 10-min standard deviations from 1-s crosswinds from wavelets with STDU⊥Sonic on the x axis and STDU⊥SLAS on the y axis for the (a) CF, (b) MF, and (c) CS algorithms, on DOY 136.

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    Scatterplots of 10-min-averaged crosswinds with U⊥Sonic on the x axis and U⊥DLAS on the y axis from Scintec’s algorithm with the corresponding regression equation (R2), percentage of data, and RMSE (a) without and (b) with an Ithreshold.

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    Error in grayscale of U obtained from the theoretical scintillation spectra with the (a) CF, (b) MF, and (c) CS algorithms over a slant scintillometer path in very unstable conditions.

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    Theoretical scintillation spectra with a variable (due to slant path) and weight-averaged U and along the scintillometer path used by the (a) CF, (b) MF, and (c) CS algorithms in very unstable conditions.

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    Error in U for a slant scintillometer path ranging from 2 to 100 m in different stability regimes.

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    (a) Variable U and (b) on a slant scintillometer path ranging from 2 to 100 m in different stability regimes.

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Crosswinds from a Single-Aperture Scintillometer Using Spectral Techniques

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  • 1 Meteorology and Air Quality Group, Wageningen, Netherlands
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Abstract

In this study, spectral techniques to obtain crosswinds from a single large-aperture scintillometer (SLAS) time series are investigated. The crosswind is defined as the wind component perpendicular to a path. A scintillometer obtains a path-averaged estimate of the crosswind. For certain applications this can be advantageous (e.g., monitoring crosswinds along airport runways). The essence of the spectral techniques lies in the fact that the scintillation power spectrum shifts linearly along the frequency domain as a function of the crosswind. Three different algorithms are used, which are called herein the corner frequency (CF), maximum frequency (MF), and cumulative spectrum (CS) techniques. The algorithms track the frequency shift of a characteristic point in different representations of the scintillation power spectrum. The spectrally derived crosswinds compare well with sonic anemometer estimates. The CS algorithm obtained the best results for the crosswind when compared with the sonic anemometer. However, the MF algorithm was most robust in obtaining the crosswind. Over short time intervals (<1 min) the crosswind can be obtained with the CS algorithm using wavelet instead of fast Fourier transformation to calculate the power scintillation spectra.

Corresponding author address: Daniëlle van Dinther, Meteorology and Air Quality Group, P.O. Box 47, Wageningen 6700 AA, Netherlands. E-mail: danielle.vandinther@wur.nl

Abstract

In this study, spectral techniques to obtain crosswinds from a single large-aperture scintillometer (SLAS) time series are investigated. The crosswind is defined as the wind component perpendicular to a path. A scintillometer obtains a path-averaged estimate of the crosswind. For certain applications this can be advantageous (e.g., monitoring crosswinds along airport runways). The essence of the spectral techniques lies in the fact that the scintillation power spectrum shifts linearly along the frequency domain as a function of the crosswind. Three different algorithms are used, which are called herein the corner frequency (CF), maximum frequency (MF), and cumulative spectrum (CS) techniques. The algorithms track the frequency shift of a characteristic point in different representations of the scintillation power spectrum. The spectrally derived crosswinds compare well with sonic anemometer estimates. The CS algorithm obtained the best results for the crosswind when compared with the sonic anemometer. However, the MF algorithm was most robust in obtaining the crosswind. Over short time intervals (<1 min) the crosswind can be obtained with the CS algorithm using wavelet instead of fast Fourier transformation to calculate the power scintillation spectra.

Corresponding author address: Daniëlle van Dinther, Meteorology and Air Quality Group, P.O. Box 47, Wageningen 6700 AA, Netherlands. E-mail: danielle.vandinther@wur.nl

1. Introduction

In this study we are interested in obtaining the wind component perpendicular to a path, the so-called crosswind (U), using scintillometer measurements. A scintillometer is a device that consists of a transmitter and receiver. The transmitter and receiver are placed over a path of 0.1–10 km. The transmitter emits a light beam that is refracted in the turbulent atmosphere, causing light intensity fluctuations that are measured by the receiver. The scintillometer is best known for measuring area-averaged surface fluxes (see, e.g., Meijninger et al. 2002a,b; Green et al. 2001; Beyrich et al. 2002), but it can also obtain the path-averaged crosswind (e.g., Lawrence et al. 1972; Heneghan and Ishimaru 1974; Wang et al. 1981; Poggio et al. 2000).

An application of line-averaged crosswinds obtained from scintillometers is in use at airports. Strong crosswinds along airport runways can introduce a serious safety risk to airplanes taking off or landing. Therefore, takeoffs and landings at airports are restricted by a crosswind limit of 20 kt (10 m s−1). When crosswind limitations are exceeded, the result is often a loss in the available operational capacity of the airport. Airports typically use cup anemometers and wind vanes to measure the crosswind. The disadvantage of these devices is that their measurements are representative of a small part of the runway, while the scintillometer averages the crosswind over a path. Other transportation sectors can also benefit from crosswind measurements. Strong crosswinds on trains can lead to instability and even derailments (Baker et al. 2004). Furthermore, strong crosswinds on bridges can also cause vehicle accidents (Chen and Cai 2004). We can also envision the use of crosswind measurements for military defense applications. The along-a-line averaging of a scintillometer also makes it suitable for measuring valley winds (Furger et al. 2001).

The application of a scintillometer to measure crosswinds is not new. Lawrence et al. (1972) constructed an optical wind sensor that consisted of a dual laser scintillometer, which used the motion of the scintillation pattern to obtain the crosswind. They used the time lag from the covariance function between the two signals to determine the crosswind by assuming Taylor’s frozen turbulence hypothesis.

Wang et al. (1981) constructed a dual large-aperture scintillometer (DLAS). For this DLAS they presented a technique where the frequency corresponding to the width of the autocovariance function is used to obtain the crosswind. This frequency technique, as they called it, can also be applied to a single-aperture scintillometer. They concluded that the frequency technique obtained the best results for the crosswind. However, the crosswind direction is not known with this technique.

Poggio et al. (2000) evaluated three techniques based on the covariance of a DLAS, and three techniques based on characteristic frequencies of intensity fluctuations of a single large-aperture scintillometer (SLAS). They compared the results of these six techniques with cup anemometer and wind vane measurements. They found, contrary to Wang et al. (1981), that the covariance techniques obtained better results than the frequency techniques.

The techniques suggested by Lawrence et al. (1972), Wang et al. (1981), and Poggio et al. (2000) all rely on experimental calibration. This calibration is necessary to find the constant describing the relation between the crosswind and the covariance or frequency point used by the technique.

Clifford (1971) developed a theoretical model for the scintillation power spectrum. In this model the crosswind over the scintillometer path determines its position along the frequency axis of the spectrum. Nieveen et al. (1998) used the theoretical scintillation spectra of Clifford (1971) to distinguish absorption from refraction fluctuations in the scintillometer signal. They noted that a characteristic frequency point in the spectrum, in their case the upper corner frequency, scales linearly with the crosswind. However, because the focus of Nieveen et al. (1998) was not on obtaining the crosswind, no validation was made of the crosswind obtained from the upper corner frequency against another measurement instrument.

Ward et al. (2011) investigated the consequences of variable, both in space and time, crosswinds along the scintillometer path on the spectrum of the scintillometer signal. They used the theoretical model of Clifford (1971) and found that a variable crosswind causes the spectrum of the scintillometer signal to be altered from the theoretical scintillation spectra of the weighted path-averaged crosswind.

The work presented here is divided into two parts. First, we explore three algorithms to obtain the crosswind from spectra of the signal of an SLAS (sections 2 and 3), though the techniques are applicable to any single-aperture scintillometer. Second, we evaluate the spectral techniques with experimental data retrieved with a BLS900 (a commercially available DLAS, manufactured by Scintec, Rottenburg, Germany) at a flat grassland site in the Netherlands (sections 4 and 5). Although the BLS900 is a DLAS, we will use it as a SLAS; that is, we will use only one of the two signals.

The three algorithms, used in this study, are named after the characteristic points in different representation in the spectra, notably, the corner frequency (CF), maximum frequency (MF), and cumulative spectrum (CS) algorithms. The characteristic points shift linearly along the frequency domain as a function of U. The CF algorithm is similar to the upper corner frequency described by Nieveen et al. (1998). The MF algorithm is similar to the fast Fourier transform (FFT) technique described in Poggio et al. (2000). The CS algorithm is a new technique devised to obtain the crosswind from scintillation spectra and uses Ogives described by Oncley et al. (1996). Another new aspect in our approach is that we will use the theoretical model for the scintillation spectra of Clifford (1971) to establish the relation between the location of the different characteristic points and the crosswind, unlike the frequency techniques described by Wang et al. (1981) and Poggio et al. (2000), which relied on experimental calibration.

The scintillation spectra can be obtained from the scintillometer signal intensity measurements using a FFT. However, with the FFT approach we need at least 5 min of data to represent the scintillation spectrum well enough to determine the crosswind from the spectrum [see section 3d(1)]. To obtain the crosswind from scintillation spectra for shorter time intervals (≤1 min), we will use spectra calculated with wavelets. The use of FFT and wavelets to obtain scintillation spectra is examined in section 3. The results are discussed in section 5, where we will also briefly review the result of Scintec’s BLS900 output of the crosswind, which uses a dual-aperture approach. In section 6, the conclusions from this study are drawn.

2. Theory

A scintillometer sends a monochromatic light beam from a transmitter to a receiver, with the devices typically a few hundred meters to a few kilometers spaced apart. This light is scattered by turbulent eddies, which are advected through the scintillometer path by the wind. Therefore, the amount of scattering varies in time, causing the measured light intensity to fluctuate. Assuming Taylor’s frozen turbulence hypothesis, the wind advecting the eddies through the path is the only phenomenon driving the light intensity fluctuations. If this assumption is not valid, the decay of eddies also contributes to the intensity fluctuations.

The amount and strength of the fluctuations of the scintillometer signal, caused by the difference in refractive indices of the eddies, are expressed as the variance of the log of the intensity of the light . Therefore, the structure parameter of the refractive index is linked to (Wang et al. 1978; Clifford and Churnside 1987; Churnside et al. 1988). Here, is a measure of the spatial variation of the refractive index.

A large-aperture scintillometer (LAS) is an optical scintillometer that is typically sensitive to eddies the size of its aperture diameter (D) (Wang et al. 1978). In this section we will focus on a LAS. Therefore, the equations given below are valid for a LAS. The relationship between and for a LAS is given by (Wang et al. 1978)
e1
where L is the pathlength of the scintillometer.

A scintillation spectrum shows how much each frequency contributes to . Figure 1 shows a typical measured spectrum of a LAS signal, which has been smoothed. We divided the spectrum into two ranges: the zero-slope range and the power-law range. These two ranges are perceptible by their slopes. The slope in the zero-slope range is, as the name already suggests, zero. For a LAS the slope in the power-law range is . At low frequencies the slope of the spectrum is fluctuating (Fig. 1), which is caused by the fact that these points are determined from only a few data points. Integrating the spectrum over all frequencies results in .

Fig. 1.
Fig. 1.

Measured scintillation power spectrum with the zero-slope and power-law ranges indicated.

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

Clifford (1971) describes a theoretical model, based on earlier work of Tatarskii (1961), that represents the spectrum of intensity fluctuations measured by a scintillometer for spherical waves. Wang et al. (1978) added terms to include the spatially incoherent transmitting and receiving optics in the theoretical model (i.e., the step from a point source to a finite aperture). The theoretical power spectrum S for a LAS is then defined by (Nieveen et al. 1998)
e2
where f is the frequency, k is the wavenumber of the emitted radiation, K is the turbulent spatial wavenumber, x is the relative location on the path, J1 is the first-order Bessel function, and φn(K) is the three-dimensional spectrum of the refractive index in the inertial range given by (Kolmogorov 1941)
e3
For a given scintillometer setup, all variables except U and are constant in Eq. (2). Therefore, these two variables influence the location of the spectrum, but when they are constant along the path, they do not alter the shape of the spectrum. Here, determines the height of the spectrum, since it is proportional to [see Eq. (1)]. In addition, U influences the location of the spectra on the frequency axis, without influencing . In a log–log representation of the spectrum (as in Fig. 1), the height of the spectrum is also influenced by U.

In Fig. 2 the theoretical scintillation power spectra are plotted with crosswinds of 0.1 and 10 m s−1. From Fig. 2 it is apparent that a stronger crosswind causes the spectrum to shift to higher frequencies (to the right). This relation can be qualitatively explained as follows; the higher the crosswind, the faster the eddies are advected through the scintillometer path. The signal intensity fluctuations are not influenced by the crosswind, but the fluctuations will be squeezed in time when the crosswind is higher. Therefore, the higher frequencies contribute more to the variance of the signal when the crosswind is higher. An important feature is that the frequency shift scales linearly with the crosswind; that is, a characteristic point in the spectrum moves linearly across the frequency domain as a function of the crosswind. We will use the theoretical model of Clifford to establish the factor describing the relation between U and the characteristic frequency point. In this study we used three different characteristic points employing different representations of the scintillation spectrum, which will be discussed in section 3b.

Fig. 2.
Fig. 2.

Theoretical scintillation spectra with crosswinds of 0.1 (solid black line) and 10 m s−1 (dashed gray line) in a log–log representation. The zero-slope and power-law lines are indicated for both crosswinds, as is the corner frequency (fCF).

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

Although the crosswind and both influence the spectra, these two quantities do not influence each other, so the crosswind does not change and vice versa. This is also visible in Fig. 3 (semilog representation of the theoretical scintillation spectrum given two different crosswinds), where the area underneath the curve stays the same for the two different crosswinds.

Fig. 3.
Fig. 3.

Theoretical energy conserved representation of the scintillation spectra with crosswinds of 0.1 (solid black line) and 10 m s−1 (dashed gray line), with the maximum frequencies indicated by fMF.

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

3. Method

a. Determination of scintillation power spectra

1) FFT

To be able to obtain the characteristic frequency points from the FFT spectra, the data were detrended and spectra smoothed following Hartogensis (2006). Smoothing was applied by weighting each point in the scintillation spectrum by a fixed number of neighboring points using a bell-shaped function. The FFT spectra were determined over 10-min data blocks. Consequently, the results we discuss in this study for U based on FFT spectra represent an average value over 10 min. The shorter the time over which the spectra are determined, the higher the minimum crosswind that can be determined from the spectra [see section 3d(1)]. For application at airports, we would like to be able to obtain the crosswinds from scintillometers over reasonably short intervals (≤1 min). Therefore, we will investigate the use of wavelets over 5-min time blocks to obtain the spectra for 1-s intervals.

2) Wavelet

A wavelet spectrum, when properly scaled, yields a power spectrum for every data point (Torrence and Compo 1998). Therefore, with 500-Hz data a spectrum is obtained for every 0.002 s. In this study we obtained the spectra with wavelets over 5-min data blocks. However, for the first and last minute of these data blocks, the 0.002-s spectra at lower frequencies (<0.1 Hz) are lacking. Therefore, these spectra are not taken into account. To obtain the crosswind over every second, we averaged the 0.002-s spectra obtained by wavelets to 1 s. Due to the fact that 500 spectra were averaged to obtain the 1-s spectra, no additional smoothing was applied.

Different types of wavelets can be used to obtain the spectra. In this study we used the Paul 6 wavelet (Torrence and Compo 1998). Using another type did not alter the results significantly. This outcome has previously been suggested by Torrence and Compo (1998), who stated that the choice of the wavelet function is not critical for the power spectra.

In Fig. 4 the spectrum calculated with FFT and wavelet approaches is plotted for the same data series of 5 min. From this figure it is apparent that the FFT and wavelet methods yield similar results.

Fig. 4.
Fig. 4.

Measured scintillation power spectrum calculated with FFT (solid black line) and wavelet (dashed gray line) approaches over 5 min of data.

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

A disadvantage of wavelets is that considerably more computing power is needed than for an FFT. In this study we will therefore obtain U from the FFT for the 10-min time intervals for 7 days and obtain U⊥ from wavelets for 1-s time intervals for one specific day only.

b. Crosswind algorithms based on scintillation spectra

In this section we will describe the three algorithms we used to obtain the crosswind from measured scintillation spectra: CF, MF, and CS. The algorithms indicate characteristic points in different representations of the spectra that can easily be traced by a computer algorithm. The characteristic points in the spectrum shift linearly along the frequency domain as a function of the crosswind; so,
e4
where Calgorithm is a constant depending on the algorithm used and falgorithm is the frequency corresponding to the characteristic points of the different algorithms. The values of Calgorithm will be determined from the theoretical model for the scintillation spectrum of Clifford (1971). A LAS is sensitive to eddies the size of D. Other types of scintillometers are sensitive to other sizes of eddies [see Table 1, adopted from information specified in Nieveen et al. (1998)]. The spectral techniques can be used for these scintillometer, but D in Eq. (4) needs to be replaced by the first Fresnel zone (F) or in the case of a laser scintillometer Calgorithm needs to be determined as a function of f and the inner scale (l0). The spectral representations used in this study are log–log, semilog, and the cumulative spectrum for the CF, MF, and CS algorithms, respectively.
Table 1.

Types of scintillometers with their abbreviation, eddy size to which they are sensitive, and slope in the power-law range.

Table 1.

1) Corner frequency (CF)

The corner frequency is the inflection point in the log–log representation of the scintillation spectrum. In literature, different definitions of the corner frequency (fCF) are given. Medeiros Filho et al. (1983) states that fCF is the point of intersect between the zero-slope line and the power-law line. Nieveen et al. (1998) defines fCF as the frequency where the spectrum has dropped to half of the value of that at the zero-slope line. Ward et al. (2011) use yet another definition and state that fCF is at the same frequency location as the maximum frequency in the semilog representation of the spectrum. We will use the definition of Medeiros Filho et al. (1983), so fCF is the point of intersect between the zero-slope line and the power-law line (see Fig. 2). The slope of the power-law line is given in Table 1 for different types of scintillometers. From the theoretical spectra in Fig. 2 it is apparent that a higher crosswind also lowers the spectra. However, this lowering is only caused by the log–log representations of the spectra. The integral over scintillation spectra, , will not change as a result of a different crosswind.

The algorithm we developed to routinely find fCF from measured spectra consisted of finding the zero-slope line and the power-law line (see Fig. 2). To find these lines, a smoothing was applied on the spectra (see section 3a). After smoothing, the slopes were calculated over four spectral points. From these slopes the variance was calculated over five points. The following criteria were set to determine the zero-slope and the power-law lines:

  • The variance had to be below a threshold value, we used 0.15, for four consecutive points.

  • The slope of the zero-slope line had to be between −0.3 and 0.3.

  • The slope in the power-law line had to be between −3.2 and −4.8.

  • At least four consecutive points had to belong to the zero-slope line or power-law line.

Over the points that met the zero-slope line criteria mentioned above, a line was fitted. A line was also fitted through the points that met the power-law line criteria. The intersection between these two lines defines the corner frequency as used in this study. A high-pass filter (HPF) of 0.1 Hz [discussed in more detail in section 3d(2)] on the spectrum was used to make sure absorption did not influence the results. The routine above was also performed on the theoretical spectra to obtain the constant CCF in Eq. (4), which was 1.38. This is higher than the 1.25 found by Nieveen et al. (1998), but they used a different definition of fCF than we did.

2) Maximum frequency (MF)

The maximum frequency (fMF) is the frequency where the maximum of the energy conserved representation of the scintillation spectrum is located (Fig. 3). The routine used to obtain fMF is straightforward and consists of simply determining the maximum of the spectrum (see Fig. 3). The constant CMF in Eq. (4), obtained from the theoretical model, is 1.59. This value is similar to the 1.63 value found by Ward et al. (2011).

The MF algorithm is sensitive to errors when there are unwanted contributions to the scintillation spectra. Therefore, it is advisable to use a HPF and a low-pass filter (LPF) [see section 3d(2)]. A HPF of 0.1 Hz and a LPF of 90 Hz were used in this study, with corresponding U values of 0.024 and 21 m s−1, respectively. The LPF is set to a lower value than is discussed in section 3d(2), since the MF algorithm is susceptible to noise in the high-frequency domain (>90 Hz), which could give unrealistic high values of the crosswinds. Unlike the other two algorithms, the MF algorithm takes into account one point in the spectrum that is typically not at a high frequency. Therefore, removing the high frequencies with the LPF only influences the results when noise is present in these frequencies.

3) Cumulative spectrum (CS)

The cumulative spectrum, also known as Ogives (Oncley et al. 1996), is obtained by integrating a spectrum from high to low frequencies. However, we integrate the spectrum from low to high frequency (left to right) and normalize the spectra with the variance . The CS is a new algorithm we propose to obtain U from a scintillation spectrum. Unlike the previously discussed algorithms, the CS algorithm takes into account the complete shape of the spectrum.

We used five frequency points, which corresponded to the following points in the cumulative spectrum: 0.5, 0.6, 0.7, 0.8, and 0.9 (see Fig. 5). The constants CCS obtained from the theoretical spectra corresponding to these frequency points are 2.31, 1.88, 1.55, 1.27, and 1.00, respectively. The crosswinds obtained, by applying Eq. (4), for these five points are averaged to obtain one crosswind per scintillation spectrum.

Fig. 5.
Fig. 5.

Theoretical cumulative scintillation spectra with crosswinds of 0.1 (solid black line) and 10 m s−1 (dashed gray line). The frequencies where the cumulative spectra are 0.5, 0.6, 0.7, 0.8, and 0.9 are indicated by f0.5, f0.6, f0.7, f0.8, and f0.9, respectively.

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

The CS algorithm is also sensitive to errors due to unwanted contributions to the scintillation spectrum. Therefore, data where the maximum frequency [as stated in section 3d(2) without the HPF and LPF] was below 0.1 Hz or above 90 Hz were filtered out.

c. Crosswind algorithm used by SRun

The exact algorithm that SRun, the processing software provided by Scintec, uses to retrieve the crosswind from the BLS900 data is unknown. However, in the manual it is stated that the time-lagged cross-covariance function is used [B12(t)]. This function is in theory defined by Clifford (1971), here added with aperture averaging terms given by Wang et al. (1978)
e5
where J0 is the Bessel function of the first kind and zeroth order, t is the time lag between the two signals, d(x) is the spacing in between the two apertures as a function of x, Dr is the aperture diameter of the receiver, and Dt is the aperture diameter of the transmitter. The crosswind is derived from Eq. (5) by applying a stepwise deconvolution technique.

d. Validity of the spectral techniques

For which crosswinds the spectral techniques are valid is determined by the measurement frequency and the record length. The minimum and maximum crosswinds resolvable with different scintillometer setups are discussed in section 3d(1).

Errors can occur in the crosswind if the scintillation spectra are not obtained correctly. The spectra can be influenced by unwanted contributions to the spectra, a low signal or signal-to-noise ratio, and variability of U along the path. In sections 3d(2)3d(4) the influence these phenomena have on the spectra and how their influence can be minimized are discussed.

1) Minimum and maximum crosswind resolvable with spectral techniques

The minimum crosswind resolvable by the spectral techniques is determined by the sample length taken, while the sample frequency determines the maximum crosswind that can be resolved. The scintillometer type and setup also determine the maximum and minimum crosswinds that are resolvable. In this section five typical scintillometer setups were investigated (see Table 2). The theoretical spectrum for laser scintillometers (not given in this paper) also includes the inner scale. Typical values of l0 range from 2 to 20 mm (Hartogensis 2006), we used values of 2, 7, and 15 mm. The theoretical spectra were calculated for the different setups and crosswind values.

Table 2.

Scintillometer setups used to calculate the minimum and maximum resolvable crosswinds.

Table 2.

We define the minimum sample length by the frequency where the cumulative spectrum was 0.01 (i.e., at least 1% of the scintillations contributions to the spectra are accounted for). The results for the minimum sample lengths are plotted in Fig. 6. Note that the spectra should be determined over blocks of at least 10 times the minimum sample length, since the value of the power spectrum is then represented by at least 10 data points. The lines in Fig. 6 are not linear, because the frequencies are converted to minutes. For the BLS900 used in this study (D = 0.15 m), the minimum sample length required to measure crosswinds as low as 0.5 m s−1 is 30 s. Therefore, we should determine the scintillation power spectra over data blocks of at least 5 min. For a laser scintillometer the minimum record length necessary to resolve the same minimum crosswind is one order of magnitude lower than that of an LAS and a microwave scintillometer (MWS).

Fig. 6.
Fig. 6.

Minimum record length necessary to solve at least 1% of the scintillation spectra for minimum crosswind for different scintillation setups: LAS [black in (a)], MWS [gray in (a)], and laser scintillometer [black in (b)].

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

The maximum crosswind resolvable is determined by the crosswind where the sample frequency is located at the 0.99 point of the cumulative spectrum. The results for the maximum crosswind resolvable for a given sample frequency are plotted in Fig. 7. The frequency up to which the spectra can be calculated is half of the measurement frequency. For the BLS900 the measurement frequency is 500 Hz and D is 0.15 m. Therefore, the maximum crosswind that can be resolved is 20 m s−1. From Fig. 7 it is apparent that the measurement frequency necessary to be able to resolve the same maximum crosswind is lower for an MWS than for an LAS. However, in Fig. 7 the slope of an MWS is less steep than that of an LAS, indicating that the scintillation spectra of an MWS shifts less in the frequency domain due the crosswind than for an LAS. Therefore, it is more difficult to distinguish one crosswind from the other with an MWS than an LAS. An MWS is therefore less suitable than an LAS for determining the crosswind using spectral techniques. For the laser scintillometer (Fig. 7b) the minimum measurement frequency has to be very high (>2500 Hz) to be able to obtain the crosswind till 30 m s−1. The results of the minimum and maximum resolvable crosswinds vary for different values of l0. To use the spectral techniques, which are sensitive to the eddy sizes of the inner scale, for a scintillometer, Calgorithm needs to be determined as a function of f and l0.

Fig. 7.
Fig. 7.

Minimum measurement frequency necessary to solve at least 99% of the scintillation spectra for maximum crosswinds for different scintillation setups: LAS [black in (a)], MWS [gray in (a)], and laser scintillometer [black in (b)].

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

2) Unwanted contributions to the scintillation spectra

Fluctuations caused by sources other than scintillations (e.g., absorption, electronic noise, and tower vibrations) can also contribute to and, thereby, alter the scintillation spectra. Alterations to the spectra can potentially influence the crosswind obtained from them.

Errors due to absorption fluctuations can be circumvented relatively easily, as absorption of an LAS signal occurs at frequencies lower than those associated with refraction (Nieveen et al. 1998). A correctly chosen HPF will suffice. One has to make sure not to set the HPF on a too high frequency since, especially for the CS algorithm, the complete scintillation spectrum contributing to is necessary. The lower the crosswind, the greater the contribution of the lower frequencies to , and the more critical the HPF choice becomes. We would like to resolve crosswinds from 0.5 to 20 m s−1 using an LAS with a D of 0.15 m. A HPF of 0.1 Hz will suffice in this case.

Electronic noise can also cause unwanted fluctuations in the scintillometer signal. This noise is in general in the high-frequency domain. Therefore, an LPF on frequency can help to eliminate fluctuations caused by noise. For our purposes an LPF of 280 Hz would allow crosswinds up to 20 m s−1 to be measured. However, the measurement frequency of the BLS900 is 500 Hz, so the spectral density can be determined till 250 Hz. Therefore, a LPF cannot be applied on our scintillometer data.

Unwanted contributions to the fluctuations of the scintillometer signal can be removed relatively easily for a DLAS. Absorption fluctuations are nearly identical for the two beams, since the homogeneities have a spatial scale on the order of the pathlength. For electronic noise and tower vibrations we also expect the fluctuations to be nearly identical for the two signals, though this is not necessarily the case and also depends upon the scintillometer setup. Therefore, we propose a new method for eliminating the unwanted contributions to the spectra by subtracting the cospectra of two signals from one of the spectra. However, due to this subtraction the theoretical scintillation spectrum is slightly altered, which alters the constants of the algorithm describing the relation between the crosswind and the characteristic frequency point. This alteration implies that it is not only the unwanted contributions to the scintillation spectra that are eliminated, but also part of the scintillation contribution is removed as well. In Table 3 the values of the constants are given for a DLAS with correction where the two apertures are spaced 17 cm apart (as is the case for a BLS900 of Scintec).

Table 3.

Constants describing the relation between U and the characteristic frequency point for the three algorithms when the DLAS correction is applied.

Table 3.

3) Scintillometer signal threshold and signal-to-noise ratio

The scintillometer intensity signal (I) drops drastically when it is foggy. The light emitted by the transmitter is spread under large angles due to the fog particles; therefore, only a small portion or even none of the light arrives at the receiver (Earnshaw et al. 1978) resulting in loss of U data. In general, the wind speed is low during foggy conditions; therefore, this drop in signal will not influence the application at airports. This drop in signal intensity can even be considered to be an advantage, since the light intensity measured by the receiver can be a measure of the visibility along the scintillometer path (Beyrich et al. 2002). Moreover, the visibility along the runway also induces a safety risk for airport operations. In this study, we used an Ithreshold of 20 000 (⅔ of the clear-sky signal), so data where I was below 20 000 were filtered out. The value of Ithreshold is dependent on the scintillometer type and setup used.

A low signal-to-noise ratio (SNR) can result in errors in the crosswind obtained with the spectral techniques. Here, signal does not refer to the mean signal, but the scintillation signal, . A low SNR, therefore, means that the due to scintillations is relatively small in relation to because of noise from any source. Low SNR mainly occurs in near-neutral conditions. In these conditions the sensible heat flux is small, which is associated with small fluctuations in the refractive index (De Bruin et al. 2002). Therefore, the spectrum of the scintillometer signal is less reliable in near-neutral conditions.

4) Variability of U along the scintillometer path

In practice the height of a scintillometer is often not constant along its path (Hartogensis et al. 2003). In the appendix we specify how the effective height of the crosswind measurement can be obtained. A varying beam height influences the scintillation spectra, since the crosswind and will vary along a slant scintillometer path due to their vertical profile.

In the appendix we investigate the influence of a slant path on U obtained with the CF, MF, and CS algorithms. From the results we conclude that measuring along slant paths only results in a small error in the crosswind obtained by the CF and CS algorithms. Even when the scintillometer path is very slanted (from 2 to 100 m) the error for these two methods is less than 4%. For the MF algorithm the error in the crosswind is somewhat bigger (up to 8%). This larger error is caused by the fact that this algorithm focuses on one specific frequency (the maximum frequency), while the other two algorithms take the overall shape of the spectrum into account.

Although a slant path does not influence the results of U substantially, a strong variability of U along the path might. Ward et al. (2011) investigated the influence of a nonuniform crosswind on the scintillation spectra. They found that under extreme conditions where the crosswind on one-half of the path was substantially different (≥2 m s−1) from that on the other half of the path, the scintillation spectrum was a combination of two spectra of the two crosswinds. For the MF algorithm this combined spectrum will exhibit two peaks. Therefore, the crosswind obtained with the MF algorithm will be representative of only half of the path, that with the lowest crosswind. The CF and CS algorithms take into account the general shape of the spectrum, which probably will result in a better average of the crosswind along the path. That the CF and CS algorithms obtain a better average of the crosswind under variable wind conditions is visible in the appendix, where the error for these two algorithms for a variable crosswind due to a slant path is lower than that of the MF algorithm. Therefore, a wind gust for example at an airport runway will leave a trace in the scintillation spectrum, while a point measurement can miss this fine structure. However, the amplitude of the gust remains unknown to the scintillometer, since it depends on where in the scintillometer path the gust is located, due to the path weighting.

Variability of the wind along the scintillometer path can be an issue affecting the accuracy of the crosswind determined with the spectral techniques, but variability in time can also be an issue. The scintillation spectrum is determined over a certain time interval. If the crosswind changes during that time interval, the scintillation spectrum will be influenced by the different crosswinds. Therefore, it is advisable not to make the time intervals too long (>10 min), to ensure as much as possible a stable wind regime.

4. Experimental setup

The data studied in this paper were collected at the meteorological site at the Haarweg, Wageningen, the Netherlands, from 13 to 19 May 2010 (DOY 133 until 139). This site is a flat, homogeneous grassland. An aerial photo of the experimental setup is presented in Fig. 8.

Fig. 8.
Fig. 8.

Aerial photo (courtesy of Google Maps) of the experimental setup, with the (a) sonic anemometer, (b) receiver of the BLS900, and (c) transmitters of the BLS900 indicated. The path of the scintillometer is indicated with the dotted white line.

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

We deployed a boundary layer scintillometer (BLS900, Scintec, Rottenburg, Germany). The BLS900 was installed at a height of 3.53 m with a pathlength of 426 m. The geographical orientation of the BLS900 was 338°N. We stored the raw 500-Hz intensity signal from the fitted processing unit (running SRun software version 1.07 from Scintec). The BLS900 is a DLAS; it has two transmitters and one receiver with aperture diameters of 15 cm. Even though the BLS900 is a DLAS, we will use it as an SLAS; that is, we will use only one of the two signals in our study. However, we will shortly discuss the results of the crosswind given by SRun.

The output of the BLS900 was validated against a CSAT3 sonic anemometer manufactured by Campbell Scientific (Logan, Utah), which was also located at the meteorological site at the Haarweg. The sonic anemometer was not located in the center of the scintillometer path, but at a distance of roughly 300 m. Assuming a homogeneous wind field, this should not result in a substantial difference in wind speeds measured by the BLS900 and the sonic anemometer, given the short distance between the scintillometer and the sonic anemometer and the relatively short scintillometer path. The sonic anemometer was installed at a height of 3.44 m and sampled at 10 Hz. The wind components measured by the sonic anemometer were aligned with the flow using a planar fit correction (Wilczak et al. 2001) and the horizontal wind components were then used to calculate the wind perpendicular on the scintillometer path. The spectral techniques obtained the absolute crosswind; that is, the sign of the crosswind is unknown. Therefore, the crosswind from the SLAS was compared to the absolute value of the crosswind from the sonic.

In Fig. 9 the wind measurements (speed and direction) of the sonic anemometer during the measurement period are plotted. In stable conditions during nighttime the 2-m wind speed was suppressed and therefore relatively low (in general <2 m s−1). In unstable conditions during daytime the wind speed is in general higher with a maximum of 7 m s−1 on DOY 136. The wind direction during the measurement period was variable, but mainly from the north-northwest, which was unfortunately not very perpendicular to the scintillometer path, resulting in an average U of 1 m s−1.

Fig. 9.
Fig. 9.

Wind conditions on the Haarweg from DOY 133 till 140, with horizontal wind speed (U, gray solid line) and crosswind on the scintillometer path U, (gray dotted line) from the sonic anemometer on the left y axis, and wind direction of the sonic anemometer (black dots) on the right y axis; the orientation of the scintillometer path is given as a black line.

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

5. Results and discussion

In this section, results of the spectral techniques are compared to sonic anemometer–estimated crosswinds. In section 5a the results obtained from FFT spectra are discussed, and the absorption correction (using two apertures) is briefly covered. In section 5b results obtained from wavelet spectra are presented. In section 5c the results of Scintec’s BLS900 algorithm, using a dual-aperture approach, are discussed.

a. Crosswinds from FFT spectra

In Fig. 10 typical measured FFT spectra calculated over a 10-min time interval are shown for the spectral techniques used in this study. The measured scintillation spectra in Fig. 10 have the same shape as the theoretical scintillometer spectra (see Figs. 2, 3, and 5).

Fig. 10.
Fig. 10.

Measured scintillation spectrum plotted as a log–log representation used by the (a) CF algorithm, (b) the semilog representation used by the MF algorithm, and (c) the cumulative spectrum used by the CS algorithm for DOY 136 at 1200 UTC.

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

In Fig. 11, scatterplots are given of the crosswind measured by the sonic anemometer (U⊥Sonic) against crosswinds determined with the BLS900 (used as an SLAS–U⊥SLAS) for the three algorithms obtained from FFT spectra over 10-min time intervals. The points are color coded with SNR. The noise level was determined in the field as the standard deviation of the light intensity measured by the receiver when the transmitter was switched off, which for our setup was 15 arbitrary units.

Fig. 11.
Fig. 11.

Scatterplots of 10-min crosswinds (U⊥SLAS against U⊥sonic) for the (a) CF, (b) MF, and (c) CS algorithms colored according to SNR.

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

Figure 11 indicates that all spectral techniques obtained similar results as U⊥Sonic. This similarity between the spectral techniques and the sonic anemometer is also visible in the regression statistics outlined in Table 4. In Table 4 the filters applied, the linear regression parameter and corresponding square of the correlation coefficient (R2), the root-mean-square error (RMSE), and the percentage of data points left after filtering (N) are shown. In total, 1007 data points were considered. However, 17% of the data were already lost due to Ithreshold. This high percentage is mainly caused by fog in the morning during this particular measurement period. The fit of U⊥CS with U⊥Sonic is best, with a regression slope of 0.95 and an RMSE of 0.41 m s−1. However, the number of data points is smallest for this algorithm, with an N of only 75%. For the CF algorithm the fit with the sonic anemometer is also very good (with a regression slope of 0.95). However, the scatter is somewhat higher than that of the CS algorithm (R2 of 0.81 in comparison to 0.87, and an RMSE of 0.50 in comparison to 0.41). We assumed that the CS algorithm would not be valid for crosswinds below 0.5 m s−1. However, restricting U⊥CS to values higher than 0.5 m s−1 did not improve the results, but did result in an extra loss of data (11%). The fit of the MF algorithm with the sonic anemometer is the worst of the three spectral techniques (regression slope of 0.83 and RMSE of 0.56 m s−1). On the other hand, all the data points, where the I is above Ithreshold, result in a value for the crosswind. Therefore, the MF algorithm is most robust in determining the crosswind. From Fig. 11b it is apparent that some outliers in UMF occur when the SNR is low (<10).

Table 4.

Regression equations, R2, and RMSE for U⊥SLAS with U⊥Sonic for the CF, MF, and CS algorithms with different filters.

Table 4.

The CF algorithm has a built-in data quality check, since the zero-slope and power-law ranges need to be well defined in the scintillation spectrum. Without taking into account Ithreshold, this built-in quality check resulted in a data loss of 22% from the total number of points. Most of this data loss (80%) occurred when I was below Ithreshold, indicating that a drop in the intensity signal of a scintillometer results in a scintillation spectrum that differs from its theoretical shape. The other 20% of the rejected data can partly be explained by low SNR values. Half (49%) of this data loss occurs when the SNR is low (<10). Therefore, 90% of the data lost due to the built-in quality check of the CF algorithm occurs when the signal intensity is low (<Ithreshold) or the SNR is low (<10), thereby making this built-in quality check useful for quality controlling the scintillometer data.

Poggio et al. (2000) compared results of the crosswind of DLAS and SLAS approaches with wind data from nine cup anemometers placed along the scintillometer path. They found for 10-min-averaging intervals correlation coefficients varying from 0.94 to 0.99, which is higher than our correlation coefficients of 0.90, 0.84, and 0.94 for the CF, MF, and CS algorithms, respectively. However, this higher correlation coefficient is expect, since they use a spatially averaged crosswind along the scintillometer path. Furthermore, they only investigated a 12-h time period when the crosswind was reasonably low, varying from 0 to 3 m s−1. In these low-wind conditions the correctness of the cup anemometer measurements may be questionable due to their threshold velocities. However, the horizontal wind speed may be significantly higher than the crosswind, but the values of the horizontal wind speeds are not mentioned by Poggio et al. (2000).

We also tested the results when the DLAS absorption correction was applied. In theory this correction should eliminate fluctuations of absorption from the scintillation spectra. Therefore, only Ithreshold was applied to the data. The results were not as expected. There were some outliers of U calculated with the MF and CS algorithms, which resulted in an overestimation of the crosswind. Apparently, the fluctuations in the intensity signal due to electronic noise were not filtered out by subtracting the cospectrum of the two signals from the spectrum of one signal. The crosswind of the CF algorithm was more similar to U⊥Sonic, although there was an overestimation of 10%, which was not the case without the absorption correction.

b. Crosswinds from wavelet spectra

As previously mentioned, the crosswind can be calculated using wavelets for every second. For this analysis we used data from only one day: 16 May 2010 (DOY 136). To compare the crosswinds for every second does not make sense, since the clocks on the BLS900 and sonic anemometer were not synchronized to the second and the location of the two instruments was not the same. Therefore, in order to validate the BLS900 with the sonic anemometer, crosswinds obtained from 1-s wavelet spectra were averaged over 10 min. At least 70% of the 1-s data had to be present to average over 10 min.

Results for the wavelets for DOY 136 are plotted in Fig. 12, and regression statistics are shown in Table 5. From these observations we conclude that the three algorithms all yield results similar to those of the 10-min FFT spectra for U⊥SLAS compared to U⊥sonic when wavelets are used, although the RMSEs are higher for the CF and CS algorithms.

Fig. 12.
Fig. 12.

Scatterplots of 10-min crosswinds averages obtained of 1-s wavelets for the (a) CF, (b) MF, and (c) CS algorithms, on DOY 136.

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

Table 5.

Regression equations, R2, and RMSE for U⊥SLAS with U⊥Sonic for the CF, MF, and CS algorithms with wavelets for DOY 136.

Table 5.

Even though it does not make sense to compare U⊥SLAS with U⊥sonic for every second, the 1-s crosswinds enables us to calculate the standard deviation (STD) for every 10-min interval, which can then be compared with each other. It is important to note here that the SLAS measures a path-averaged crosswind, while the wind of the sonic anemometer is a point measurement. We therefore expect the standard deviation of U⊥SLAS to be lower than that of USonic, since crosswind extremes are already averaged out by an SLAS because of its path weighting.

We present the results for the 10-min standard deviations in Fig. 13 and the regression statistics are shown in Table 5. Unexpectedly, the standard deviations for the CF and MF algorithms are even somewhat overestimated compared to the standard deviations of U⊥Sonic. For the MF algorithm, this is probably caused by the fact that this method takes into account only one point in the spectrum. Only considering one point can introduce extra noise when the location of this point is not well defined, resulting in a larger . The CF algorithm takes into account multiple points along the spectrum, since the corner frequency is determined from the zero-slope and power-law lines. The zero-slope line is located at low frequencies, and the power-law line is located at high frequencies. Therefore, the power-law line can fluctuate for the different 1-s spectra, while the zero-slope line is more fixed, which can cause the overestimation of . The CS algorithm takes into account the whole shape of the spectrum. The standard deviations of the crosswind of this algorithm are, as expected, lower than those of the sonic. This lower standard deviation enhances our trust in this algorithm to obtain the crosswind over short averaging times using wavelets.

Fig. 13.
Fig. 13.

Scatterplots of 10-min standard deviations from 1-s crosswinds from wavelets with STDU⊥Sonic on the x axis and STDU⊥SLAS on the y axis for the (a) CF, (b) MF, and (c) CS algorithms, on DOY 136.

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

c. Crosswind with Scintec’s BLS900 algorithm

Scintec also implemented an algorithm to obtain the crosswind. They use a DLAS approach, which has the advantage that the sign of the crosswind is known. The 10-min results of this DLAS approach are plotted against U⊥Sonic in Fig. 14, without (panel a) and with (panel b) an Ithreshold. We find that U⊥DLAS overestimates U⊥Sonic considerably (regression slope of 1.19). Apparently, there is a difference in time lag between Eq. (5) and the measured time-lagged cross covariance. A possible explanation for this difference is longitudinal wind on the scintillometer path. Potvin et al. (2005) investigated the effect of longitudinal wind on the scintillation decorrelation times. They found that the longitudinal wind alters the scintillation decorrelation time, since the longitudinal component of the wind constantly introduces new turbulent air at one end of the path and expels turbulent air at the other end of the path. Thereby, the longitudinal component of the wind causes the scintillation signal to be decorrelated faster (Potvin et al. 2005). The longitudinal wind is not taken into account in Eq. (5), but if it causes the signal to decorrelate faster, this will also be the case for the cross signal of the two apertures. Therefore, the time lag measured will be smaller than the theoretical time lag, which will cause an overestimation of U. During the experiment the wind direction was unfortunately not very perpendicular on the path (Fig. 9). Therefore, there is a longitudinal component on the scintillometer path present in the data. Although there is a reasonable overestimation of U⊥DLAS, the scatter of U⊥DLAS with U⊥Sonic is reasonably low (R2 of 0.77). However, the scatter of U⊥DLAS with U⊥Sonic is slightly higher than that of U⊥SLAS using our three algorithms (R2 values of 0.88 and 0.89). This reasonably low scatter indicates that there is information about the crosswind in the time-lagged covariance function, but SRun’s algorithm is not able to obtain an accurate value of the crosswind compared to our sonic anemometer.

Fig. 14.
Fig. 14.

Scatterplots of 10-min-averaged crosswinds with U⊥Sonic on the x axis and U⊥DLAS on the y axis from Scintec’s algorithm with the corresponding regression equation (R2), percentage of data, and RMSE (a) without and (b) with an Ithreshold.

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

Although the fit of Scintec’s algorithm with the sonic anemometer is not very good, the number of data points is higher for their algorithm than from the spectral techniques. Apparently, Scintec’s algorithm is also able to obtain the crosswind when the scintillometer signal is low, albeit not the correct value of U. Using Ithreshold did not improve the results of Scintec’s algorithm.

6. Conclusions

We obtained the crosswind from a single large-aperture scintillometer (SLAS) signal using three different algorithms, which are based on scintillation spectra without calibration in the field. These algorithm are the corner frequency (CF), maximum frequency (MF), and cumulative spectrum (CS). All three algorithms obtained similar results for the crosswind compared with a sonic anemometer, thereby, demonstrating that the three algorithms are able to obtain the crosswind from a scintillometer signal. However, some filters needed to be applied to obtain these results. A threshold on the scintillometer intensity signal (Ithreshold) was applied to all algorithms.

The CF algorithm has the disadvantage that it does not yield a result when the zero-slope and power-law lines are not clearly present in the scintillometer spectrum. On the other hand, this does serve as a quality check for how well the spectrum of the scintillometer signal is defined. This built-in quality check is why this method achieves good results, also without additional filtering. Applying a high-pass filter did improve the results of the CF algorithm.

The MF algorithm was most robust in obtaining crosswind results, only an additional high-pass filter and low-pass filter were applied. These filters did not result in a loss of data. For the MF algorithm it was also possible to use a less strict Ithreshold (5000 instead of 20 000) and still achieve results similar to those for the regression statistics when using the strict Ithreshold (not shown). In this study we also investigated a signal-to-noise filter, but in the end we did not apply this filter to our data.

The CS algorithm, a new algorithm that we have introduced in this paper, achieved the best results. The fit of this algorithm with the sonic anemometer was best, and the root-mean-square error was smallest. On the other hand, the amount of data points in the CS algorithm was smallest, since all the data points where the maximum frequency was below 0.1 Hz or above 90 Hz were filtered out.

For short time intervals (≤1 min) we recommend using wavelets in combination with the CS algorithm. The 10-min average of crosswinds obtained from wavelet spectra averaged over 1 s showed results similar to those of the sonic anemometer. We expected the 10-min standard deviations of the crosswind of the SLAS to be lower than those of the sonic anemometer, since the scintillometer levels out the extremes due to its path averaging. For the CS algorithm this expectation held. However, the standard deviations of the CF and MF algorithms were similar to those of the sonic anemometer. A probable cause for the MF algorithm is that it only uses one point, which can introduce extra noise when the maximum frequency point is not well defined and, thereby, lead to a higher standard deviation. For the CF algorithm the high standard deviation of the crosswind is probably caused by strong variations in the location of the power-law line. Fluctuations in the crosswind and structure parameter of the refractive index will influence the location of the power-law line. Fluctuations in the structure parameter can therefore by misinterpreted as fluctuations in the crosswind, causing an overestimation of the standard deviation of the crosswind of the CF algorithm.

From the results we obtained, we conclude that the CS algorithm is best qualified to obtain crosswinds. First, because it is the algorithm with the best fit and lowest scatter with the sonic anemometer. Second, the results of the wavelet spectra have also indicated that this method is best suited to obtaining the crosswind over 1 s.

In this study we used the BLS900, a commercially available dual large-aperture scintillometer (DLAS) manufactured by Scintec (Rottenburg, Germany), which for our analysis we treated as an SLAS. Scintec’s SRun software (version 1.07) provides a crosswind estimate. The crosswind obtained from the SRun algorithm showed a clear overestimation of almost 20%, which is possibly caused by the appreciable longitudinal wind component in our study resulting in a faster decorrelation of the two signals (Potvin et al. 2005). In addition, the scatter of U⊥DLAS with U⊥sonic was higher than that of U⊥SLAS with U⊥sonic. These results imply that our spectral techniques achieve better crosswind results than those of Scintec’s SRun algorithm. A disadvantage of the spectral techniques is that the sign of the crosswind is not known. We suggest that the value of the crosswind from a spectral technique in combination with the sign information from a DLAS algorithm be used.

More data are needed to test the spectral techniques more extensively, especially, the 1-min crosswind obtained from wavelets. This can be achieved by measuring the wind along the scintillometer path with a large number of cup anemometers and wind vanes. The crosswind on the scintillometer path of these cups and wind vanes can be path weighted according to the scintillometer path weighting, which enables a direct validation of the 1-min crosswind of the scintillometer.

Acknowledgments

The authors thank Frits Antonysen and Willy Hillen for their assistance with the BLS900 setup and the reviewers for their valuable comments. This study was funded by Knowledge for Climate Project HSMS01.

APPENDIX

Varying Scintillometer Beam Height and Crosswind

In practice, the height of a scintillometer beam is often not constant along its path (Hartogensis et al. 2003), in which case it is not straightforward to identify for which height the measured crosswind is representative. In this appendix we will first describe how the effective crosswind height of a scintillometer (zeff_U) can be calculated. Second, we will investigate to what extend the spectral techniques are still applicable for a scintillometer with variable beam height. To facilitate this validity study, we will consider a slant scintillometer path.

a. The effective crosswind height of a scintillometer

To calculate zeff_U, one has to account for its path-weighting function and the logarithmic wind profile. We follow the same method as suggested by Hartogensis et al. (2003), who obtained the effective height of the structure parameter of temperature of a scintillometer. However, where they use the vertical profile of the structure parameter of temperature, we will use the vertical profile of wind.

The path-weighting function W(x) of an LAS is given by
ea1
where x is the relative location on the scintillometer path and J1(y1) and J1(y2) are Bessel functions of the first kind with y1 = KDx/2 and y2 = KD(1 − x)/2.
The crosswind measured by the scintillometer is equal to the integral of the crosswind along the path times its relative weighting function G(x). Therefore, we can write
ea2
where z(x) is the height at location x and G(x) is given by .
For simplicity we assume that the wind direction is constant over the height range along the scintillometer beam, which allows us to describe the crosswind profile by the wind profile relation of Businger et al. (1971):
ea3
where U(z) is the wind speed at height z, u* is the friction velocity, κ is the von Kármán constant (0.4), z0 is the roughness length, LO is the Obukhov length, and Ψm is the integrated stability function of momentum, given by the Businger–Dyer expression (Businger 1988).
To obtain zeff_U, the expressions of U(zeff_U) and U[z(x)] given by Eq. (A3) are inserted into Eq. (A2). For neutral conditions, Ψm is zero, which leads to
ea4
For stable conditions, we inserted Ψm given by Dyer (1974) into Eqs. (A2) and (A3), which led to the following equation, which can be solved by iteration:
ea5
For unstable conditions, we inserted the Ψm given by Paulson (1970), leading to
ea6
where y is given by .

b. Validity of the spectral techniques used to obtain U with a scintillometer over a slant path

In this section we will investigate the influence of a slant path on the crosswind obtained with the spectral techniques. Scintillation spectra are influenced by a variable U and when the scintillometer measures over a slant path, because these quantities are not constant with height. The stability of the atmosphere influences the vertical profiles of U and . Therefore, we tested the influence of a slant path on the crosswind obtained by the spectral techniques for seven stability regimes. These regimes are outlined in Table A1. For neutral conditions, LO is specified as ∞, but in these conditions the equations are independent of LO. The value of U at a position along the scintillometer beam in relation to the value of U at a reference height [U(zref)] is given by
ea7
We used a reference height of 1 m and a value of U of 3 m s−1. For stable conditions we used the function of Ψm described by Dyer (1974). For unstable conditions we used the function of Ψm described by Paulson (1970).
Table A1.

Stability regimes with corresponding abbreviations and LO values.

Table A1.
The value of at a position along the scintillometer beam in relation to the value of at a reference height is given by
ea8
where fT is the Monin–Obukhov stability function for . For fT, we used the relations given by Andreas (1989). We used a reference value of of 1 × 10−14 m−2/3 at 1-m height. We used measurement heights for the transmitter zt and receiver zr of 2, 10, 25, 50, and 100 m. The height along the scintillometer path is for zt > zr given by for zt < zr it is given by ; the value of L does not influence the results.

Both U and were calculated using Eqs. (A7) and (A8) finely discretized (100 points) for the different slant paths. These finely discretized values were averaged to 10 points along the path, since a considerable amount of computational power is needed to calculate the theoretical scintillation spectra. Instead of integrating the theoretical spectra of Eq. (2) over the complete scintillometer path, the integrations were carried out over 10 parts of the path with the different values of U and . These spectra were combined to form one theoretical scintillation spectrum over a slant path, from which U was obtained using the CF, MF, and CS algorithms. We define the error as the percentage difference between U obtained from the spectra and the weight-averaged U.

In Fig. A1 error plots are shown for the CF, MF, and CS algorithms over a slant path in very unstable conditions, which had the largest errors from the cases we tested. The error in U is larger when the scintillometer path is steeper. It is apparent that the MF algorithm shows the most sensitivity to a slant path with an error in U up to 8%. This algorithm takes into account a single point in a spectrum, which is apparently located at frequencies that are affected by the slant path of a scintillometer.

Fig. A1.
Fig. A1.

Error in grayscale of U obtained from the theoretical scintillation spectra with the (a) CF, (b) MF, and (c) CS algorithms over a slant scintillometer path in very unstable conditions.

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

In Fig. A2 we plot the theoretical spectra of a very slant path (from 2 to 100 m) together with the theoretical spectra of its weight-averaged U and in very unstable conditions. The slant path does not influence the scintillation spectra severely. However, the maximum frequency is slightly shifted when the scintillometer measures over a slant path. The CF and CS algorithms are able to obtain U with a maximum error of only <4% along a very steep scintillometer path, since the shape of the scintillation spectra did not change severely.

Fig. A2.
Fig. A2.

Theoretical scintillation spectra with a variable (due to slant path) and weight-averaged U and along the scintillometer path used by the (a) CF, (b) MF, and (c) CS algorithms in very unstable conditions.

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

In Fig. A3 the error is plotted of a scintillometer with a slant path from 2 to 100 m in the seven stability regimes specified in Table A1. It is apparent that for all the stability regimes the error is largest for the MF algorithm. The errors are smallest in neutral-stable conditions ranging from 2% to 4%. These small errors are caused by the fact that U changes most in stable conditions, while changes most in unstable conditions (see Fig. A4). Therefore, the overall change in spectra due to U and is smallest in neutral-stable conditions.

Fig. A3.
Fig. A3.

Error in U for a slant scintillometer path ranging from 2 to 100 m in different stability regimes.

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

Fig. A4.
Fig. A4.

(a) Variable U and (b) on a slant scintillometer path ranging from 2 to 100 m in different stability regimes.

Citation: Journal of Atmospheric and Oceanic Technology 30, 1; 10.1175/JTECH-D-12-00069.1

From these results we conclude that the spectral techniques can be used to obtain U along a slant scintillometer path. In particular, the CF and CS algorithms are suitable for obtaining the U along a slant path. However, the steeper the scintillometer path and the more unstable or stable the atmosphere, the larger the error in U⊥SLAS will be.

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