## 1. Introduction

The wind component perpendicular to airport runways, the so-called crosswind (*U*_{⊥}), introduces a safety risk for airplanes landing and taking off. The crosswind *U*_{⊥} on the runway is in general measured by cup anemometers and wind vanes, which are point measurements. A scintillometer consists of a transmitter and a receiver spaced hundreds of meters to a few kilometers apart and obtains a path-averaged *U*_{⊥} (Lawrence et al. 1972; Wang et al. 1981; Poggio et al. 2000; among others). The *U*_{⊥} measured by a scintillometer can also be applied to increase safety for other transportation sectors, for example, trains (Baker et al. 2004) and bridges (Chen and Cai 2004). Furger et al. (2001) used a scintillometer to measure valley winds. Another application of *U*_{⊥} scintillometer measurements is along rivers in urban environments to measure the ventilation of cities (Wood et al. 2013).

Briggs et al. (1950) suggested that *U*_{⊥} can be determined from two spatially separated radio wave scintillometers. The time lag (*τ*) between the two scintillation signals is a measure of *U*_{⊥}. Two methods were suggested by Briggs et al. (1950) that use the time-lag correlation function [*r*_{12}(*τ*)] to find the following specific *τ* values. The first is defined as *τ* where the maximum in *r*_{12}(*τ*) is located. The second is defined as *τ* where the intersect between *r*_{12}(*τ*) and the time-lagged autocorrelation function [*r*_{11}(*τ*)] is located.

Lawrence et al. (1972) developed a theoretical scintillation model that describes *r*_{12}(*τ*) as a function of *U*_{⊥} and a given scintillometer setup defined by the pathlength, separation distance between the two scintillometers, and the aperture size of the scintillometer. This model can be used to find the constants that describe the relation between *U*_{⊥} and the specific *τ*, such as the two described by Briggs et al. (1950). Lawrence et al. (1972) used their model and the maximum *τ* suggested by Briggs et al. (1950) to obtain *U*_{⊥} from a dual-laser scintillometer. They also tested a method that uses the slope of *r*_{12}(*τ*) at zero time lag to obtain *U*_{⊥}. They claimed that their zero-slope method was also able to obtain *U*_{⊥} when *U*_{⊥} was variable along the scintillometer path.

Wang et al. (1981) obtained *U*_{⊥} from a dual large-aperture scintillometer (DLAS), using the methods suggested by Briggs et al. (1950) and Lawrence et al. (1972). They also introduced the frequency technique, which uses the width of *r*_{11}(*τ*) to obtain *U*_{⊥}. This frequency technique uses only one scintillometer signal, and can therefore also obtain *U*_{⊥} from single-aperture scintillometer measurements, while methods using *r*_{12}(*τ*) need dual-aperture scintillometer measurements. Wang et al. (1981) concluded that their frequency technique obtained better results than the methods that use *r*_{12}(*τ*).

More recently Poggio et al. (2000) investigated the three *r*_{12}(*τ*) methods and three methods based on the frequency technique by Wang et al. (1981). They found that all methods gave similar results. The methods based on the frequency technique, however, tended to give unrealistic high values during the transition periods from day to night and during nighttime periods. These results are contrary to the results of Wang et al. (1981), who found that their frequency technique gave better results than the methods based on *r*_{12}(*τ*).

Van Dinther et al. (2013) discussed three spectral methods that use scintillation power spectra to obtain *U*_{⊥}. The theoretical model of the scintillation power spectrum by Clifford (1971) is used by van Dinther et al. (2013) for calibration of the spectral methods. A new spectral method introduced in van Dinther et al. (2013), the so-called cumulative spectrum method, showed the best results. The spectral methods have the disadvantage of needing a significantly long time interval (~10 min) to obtain the scintillation power spectra and thereby *U*_{⊥}. The fact that these techniques do not obtain the sign of *U*_{⊥} is also a disadvantage. The main advantage of the spectral techniques is that they can be used for single-aperture scintillometers, which are the most common scintillometers on the market today.

In this study we will focus on the techniques that use *r*_{12}(*τ*) to obtain *U*_{⊥}. To measure *r*_{12}(*τ*) we use a DLAS manufactured by Scintec (Rottenburg, Germany) that consists of two transmitters spaced 0.17 m apart and one receiver. We will compare four methods: the peak method (Briggs et al. 1950), the Briggs method (Briggs et al. 1950), the zero-slope method (Lawrence et al. 1972), and the lookup table method. This last method is a new method introduced in this paper and obtains *U*_{⊥} from the *r*_{12}(*τ*) model of Lawrence et al. (1972). In addition we will investigate the influence of the wind component parallel to the scintillometer path (*U*_{‖}) on *r*_{12}(*τ*). The model of Lawrence et al. (1972) assumes that there is no influence of *U*_{‖} on *r*_{12}; however, in reality *U*_{‖} also advects eddies into the scintillometer path and thereby has an influence on *r*_{12}(*τ*). In this paper we will investigate the impact of *U*_{‖} on *U*_{⊥} obtained by a DLAS.

## 2. Theory

A scintillometer consists of a transmitter and receiver. The transmitter emits light with a certain wavelength that is scattered by the varying refractive indexes of turbulent eddies in the atmosphere caused by the transport of heat and water vapor. Eddy fields that are advected through the scintillometer path cause intensity fluctuations in the scintillometer signal. Assuming Taylor’s frozen turbulence hypothesis, the advection of eddies is the only phenomenon causing the light intensity fluctuations.

Another consequence of Taylor’s frozen turbulence hypothesis is that for two scintillometers installed next to each other, the intensity fluctuations will be the same except for a time shift between the two signals. The time shift is related to *U*_{⊥}: the higher *U*_{⊥}, the faster the eddy field is advected from one scintillometer to the other, so the smaller the time shift between the two signals will be. The time shift can be obtained from the time-lagged correlation function between the two signals [*r*_{12}(*τ*)].

*C*

_{12}(

*τ*)] of the log-intensity fluctuations for a dual-laser scintillometer. The model as given here is adapted for a large-aperture scintillometer (LAS) by including the aperture averaging terms of an LAS, which are given by Wang et al. (1981). The function

*C*

_{12}(

*τ*) then reads

*k*is the wavenumber of the emitted radiation,

*K*is the turbulent spatial wavenumber,

*L*is the scintillometer pathlength,

*x*is the relative location on the path,

*J*

_{0}is the zero-order Bessel function,

*d*(

*x*) is the separation distance between the two beams at location

*x*on the path,

*J*

_{1}is the first-order Bessel function,

*D*

_{r}is the aperture diameter of the receiver,

*D*

_{t}is the aperture diameter of the transmitter, and

*ϕ*

_{n}(

*K*) is the three-dimensional spectrum of the refractive index in the inertial range given by (Kolmogorov 1941)

For the DLAS used in this study, which has two transmitters and one receiver, *d*(*x*) in Eq. (1) is given by *d*(*x*) = (1 − *x*)*d*_{t}, where *d*_{t} is the separation distance between the transmitters. The theoretical model of the time-lagged autovariance function [*C*_{11}(*τ*)] is given by Eq. (1) taking *d*(*x*) = 0.

*r*

_{12}) is defined as the covariance (

*C*

_{12}) normalized by the variance of the two signals (

*C*

_{11}and

*C*

_{22})—that is,

*C*

_{11}(0). Assuming frozen turbulence, the variances of the two beams of a DLAS are identical—that is,

*C*

_{11}(0) =

*C*

_{22}(0). The

*r*

_{12}(

*τ*) is therefore given by

*r*

_{12}(

*τ*) is calculated from Eq. (3) by using

*C*

_{12}(

*τ*) and

*C*

_{11}(0) from Eq. (1).

*r*

_{12}(

*τ*) is obtained from the signal intensity measurements of a DLAS through

*I*

_{1}is the signal intensity of scintillometer beam 1,

*I*

_{2}is the signal intensity of scintillometer beam 2, and

*t*is time. The term

*r*

_{11}(

*τ*) follows from Eq. (4) by replacing

*I*

_{2}with

*I*

_{1}. Note that for the measured

*r*

_{12}(

*τ*),

*C*

_{11}is determined over the time-lagged

*I*

_{1}, while for the modeled

*r*

_{12}(

*τ*),

*C*

_{11}(0) is used. Therefore, we assume that

*U*

_{⊥}is constant over the time window used to calculate the measured

*r*

_{12}(

*τ*).

In the appendix three approaches are discussed by which *I*_{1} and *I*_{2} can be shifted with respect to each other to determine *r*_{12}(*τ*). The following time scales are relevant: the time window of *I*_{1} and *I*_{2} used *T*), and the time lag (*τ*) (in Fig. A1 the definitions of *T*, and *τ* are illustrated in more detail). The best results were achieved with approach 3, which has a constant *T*. In this study we will, therefore, use this approach to calculate *r*_{12}(*τ*).

Related to the performance of the three time-shift approaches is the length of *U*_{⊥}. For small *U*_{⊥} cannot be obtained reliably from *r*_{12}(*τ*). The length of *r*_{12}(*τ*). Although a long

The *U*_{⊥} is positive or negative depending on which side the wind blows into the scintillometer path. In this study we define signal 1 as the signal on the left-hand side, looking from transmitters to receiver. The sign of *U*_{⊥} is defined as positive when signal 1 is leading to signal 2 (i.e., *U*_{⊥} blows from the left-hand side into the scintillometer path when looking from the transmitters to receiver). The sign of *U*_{⊥} is defined as negative when signal 1 is trailing signal 2 (i.e., *U*_{⊥} blows from the right-hand side into the scintillometer path when looking from the transmitters to receiver). The sign of *U*_{⊥} can be obtained from *r*_{12}(*τ*), since it determines whether the peak in *r*_{12}(*τ*) is located at positive or negative *τ* (see Fig. 1). The sign of *U*_{⊥} does not influence *r*_{11}(*τ*); therefore, the sign cannot be obtained from *r*_{11}(*τ*) (see Fig. 1).

The value of *r*_{12}(*τ*) is determined by *U*_{⊥}(*x*), *d*(*x*), and the path-weighting function [*W*(*x*)]. In the following paragraphs we will discuss the effect on *r*_{12}(*τ*) of a varying *U*_{⊥}(*x*) and a varying *d*(*x*) along the scintillometer path. We will start by considering a scintillometer with a constant *d*(*x*) (0.17 m) and a *U*_{⊥}(*x*) that varies over two halves of the path with 3 and 5 m s^{−1} (see top and middle panels in Fig. 2, respectively). This is not a typical example, but it demonstrates the effect of *U*_{⊥}(*x*) on *r*_{12}(*τ*). The middle panels in Figures 2b and 2c indicate that the overall *r*_{12}(*τ*) in this case is clearly a combination of the *r*_{12}(*τ*) of the two halves of the path. The peak of *r*_{12}(*τ*) is, for the varying *U*_{⊥}, therefore clearly lower (0.62) than the peak of *r*_{12}(*τ*) for a constant *U*_{⊥} of 4 m s^{−1} along the scintillometer path (1.0, see middle panels in Fig. 2a). The location along the path of the varying *U*_{⊥} does not influence the shape of *r*_{12}(*τ*) when *d*(*x*) is constant along the path (see the middle panels in Figs. 2b and 2c).

Time-lagged-correlation function [*r*_{12}(*τ*)] for a scintillometer with (middle) two transmitters and two receivers and (bottom) two transmitters spaced 0.17 m apart and one receiver (top) with different crosswinds (*U*_{⊥}) along the scintillometer path. Solid black line represents *r*_{12}(*τ*) over the complete scintillometer path, while dashed lines represent *r*_{12}(*τ*) on one-half of the path [light gray near the transmitters and dark gray near the receiver(s)].

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Time-lagged-correlation function [*r*_{12}(*τ*)] for a scintillometer with (middle) two transmitters and two receivers and (bottom) two transmitters spaced 0.17 m apart and one receiver (top) with different crosswinds (*U*_{⊥}) along the scintillometer path. Solid black line represents *r*_{12}(*τ*) over the complete scintillometer path, while dashed lines represent *r*_{12}(*τ*) on one-half of the path [light gray near the transmitters and dark gray near the receiver(s)].

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Time-lagged-correlation function [*r*_{12}(*τ*)] for a scintillometer with (middle) two transmitters and two receivers and (bottom) two transmitters spaced 0.17 m apart and one receiver (top) with different crosswinds (*U*_{⊥}) along the scintillometer path. Solid black line represents *r*_{12}(*τ*) over the complete scintillometer path, while dashed lines represent *r*_{12}(*τ*) on one-half of the path [light gray near the transmitters and dark gray near the receiver(s)].

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Next we varied *d*(*x*), by having two transmitters spaced 0.17 m apart and one receiver (the scintillometer setup used in this study). We kept *U*_{⊥}(*x*) constant along the path with a value of 4 m s^{−1} (see Fig. 2a, bottom panel). Although *U*_{⊥}(*x*) is constant, *r*_{12}(*τ*) differs for the two halves of the path. When *d*(*x*) is higher (side of the two transmitters) it takes longer for the eddy field to be transported from one signal to the other; therefore, the peak in *r*_{12}(*τ*) is located at a higher *τ* (light gray line in Fig. 2a, bottom panel). The overall *r*_{12}(*τ*) is again a combination of *r*_{12}(*τ*) of the two halves of the path. Varying *d*(*x*) along the scintillometer path therefore results in a lower peak in *r*_{12}(*τ*) (0.80 instead of 1.0) and the peak is located at a lower *τ* (0.022 instead of 0.042 s). From this example, it can be concluded that the scintillometer setup should be taken into account when *U*_{⊥} is determined from *r*_{12}(*τ*).

The results of *r*_{12}(*τ*) for a varying *d*(*x*) and a varying *U*_{⊥}(*x*) are plotted in Figs. 2b and 2c (bottom panels). When *d*(*x*) varies along the scintillometer path, *r*_{12}(*τ*) is affected by where on the scintillometer path the higher *U*_{⊥} (5 m s^{−1}) and the lower *U*_{⊥} (3 m s^{−1}) are located. In Fig. 2b (bottom panel) *r*_{12}(*τ*) of the two halves of the path are similar: a higher *U*_{⊥} at the transmitters side causes a peak at a lower *τ*, while the higher *d*(*x*) at the transmitters side causes a peak at higher *τ*. This results in an overall *r*_{12}(*τ*) that is higher and narrower than *r*_{12}(*τ*) for *U*_{⊥}(*x*) = 4 m s^{−1}. In Fig. 2c (bottom panel) the opposite occurs: *r*_{12}(*τ*) is lower and wider than *r*_{12}(*τ*) for *U*_{⊥}(*x*) = 4 m s^{−1}. In reality *U*_{⊥} will not vary this extremely over the path; however, this example shows that a variable *U*_{⊥} lowers the peak in *r*_{12}(*τ*) and also influences the shape of *r*_{12}(*τ*).

The term *W*(*x*) is defined by integrating Eq. (1) only over *K*. Figure 3 visualizes *W*(*x*) for a scintillometer set up with two transmitters and one receiver, and *D*_{t} = *D*_{r}; *W*(*x*) is clearly largest in the middle of the scintillometer path, so this area contributes most to the scintillometer signal. Near the transmitters’ and receiver’s side, *W*(*x*) is very low (<0.1), which is beneficial since the flow can be distorted due to a mast or a building upon which the scintillometer is mounted. The influence of *d*(*x*) on the DLAS signal is also visible in Fig. 3a, where the higher *C*_{12} values are clearly seen at higher *τ* values at the transmitters’ side than at the receiver’s side. This is expected, since *d*(*x*) is larger at the transmitters’ side than at the receiver’s side. We can conclude that *d*(*x*), and thereby the scintillometer setup, influences the shape of *r*_{12}(*τ*). Therefore, when calculating *U*_{⊥} from *r*_{12}(*τ*), one has to take into account the specific scintillometer setup, concerning *d*(*x*) and *D*.

(a) Covariance (*C*_{12}) along the scintillometer path for different time lags (*τ*), given a scintillometer with two transmitters (2Tr), spaced 0.17 m apart, and one receiver (R). (b) Path weighting [*W*(*x*)] along the scintillometer path.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

(a) Covariance (*C*_{12}) along the scintillometer path for different time lags (*τ*), given a scintillometer with two transmitters (2Tr), spaced 0.17 m apart, and one receiver (R). (b) Path weighting [*W*(*x*)] along the scintillometer path.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

(a) Covariance (*C*_{12}) along the scintillometer path for different time lags (*τ*), given a scintillometer with two transmitters (2Tr), spaced 0.17 m apart, and one receiver (R). (b) Path weighting [*W*(*x*)] along the scintillometer path.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

## 3. Methods

We use four methods to obtain *U*_{⊥} from measured *r*_{12}(*τ*): the peak method, the Briggs method, the zero-slope method, and the lookup table method. All methods, except the lookup table method, obtain *U*_{⊥} by a typical point in *r*_{12}(*τ*) that is either multiplied or divided by a constant. In former studies (e.g., Poggio et al. 2000) this constant was determined through experimental calibration, by fitting the constant between measured *U*_{⊥} and the typical point in *r*_{12}(*τ*). The measured *U*_{⊥} is typically obtained by a series of cup anemometers and wind vanes along the scintillometer path, making the experimental calibration time consuming and expensive. In this study we obtain the constant for the different methods from the model of *r*_{12}(*τ*) [Eq. (1)], where we prescribe *U*_{⊥} and a scintillometer setup and calculate the constants from the resulting *r*_{12}(*τ*) values. More details on how these methods obtain *U*_{⊥} from *r*_{12}(*τ*) are discussed in this section.

### a. Peak method

*U*

_{⊥}can be determined from a radio wave scintillometer with two spatially separated receivers and one transmitter. The

*U*

_{⊥}is related to the time lag where the peak in

*r*

_{12}(

*τ*) (

*τ*

_{P}) is located (see Fig. 4). The relation between

*U*

_{⊥}and

*τ*

_{P}is given by

*U*

_{⊥}is obtained for this method by the location of the peak—that is, the sign of

*τ*

_{P}determines the sign of

*U*

_{⊥}(see Fig. 4).

Modeled *r*_{12}(*τ*) for *U*_{⊥} = 0.2 m s^{−1} (black line) and *U*_{⊥} = −0.2 m s^{−1} (gray line), with the time lag of the peak (*τ*_{P}) indicated.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Modeled *r*_{12}(*τ*) for *U*_{⊥} = 0.2 m s^{−1} (black line) and *U*_{⊥} = −0.2 m s^{−1} (gray line), with the time lag of the peak (*τ*_{P}) indicated.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Modeled *r*_{12}(*τ*) for *U*_{⊥} = 0.2 m s^{−1} (black line) and *U*_{⊥} = −0.2 m s^{−1} (gray line), with the time lag of the peak (*τ*_{P}) indicated.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Lawrence et al. (1972) tested if the peak method of Briggs et al. (1950) can be applied to dual-laser scintillometers. They found that this method is also applicable to laser beams but that an overestimation of *U*_{⊥} occurred mainly for low values. They attributed this overestimation to the decay of eddies—that is, the violation of Taylor’s frozen turbulence hypothesis. When eddies decay in the time interval it takes for an eddy to travel from one light beam to the other light beam, the two signals are no longer correlated. Therefore, violation of Taylor’s frozen turbulence hypothesis lowers *r*_{12}(*τ*). For lower *U*_{⊥} values, it takes more time to travel from one scintillometer path to the other scintillometer path; therefore, the violation of Taylor’s frozen turbulence hypothesis is more likely under these conditions.

### b. Briggs method

*r*

_{12}(

*τ*) intersects with

*r*

_{11}(

*τ*), which we will refer to as the Briggs method. This point of intersect is indicated in Fig. 1 by

*τ*

_{B}and is related to

*U*

_{⊥}following

*c*

_{B}is a constant depending on

*D*) of the scintillometer. In literature

*c*

_{B}is assumed constant for a given scintillometer setup (Briggs et al. 1950; Poggio et al. 2000). The modeled

*r*

_{12}(

*τ*) and

*r*

_{11}(

*τ*), however, indicate that

*c*

_{B}is not constant but varies for different

*U*

_{⊥}values. For our scintillometer setup [

*D*is 0.15 m],

*c*

_{B}is 0.043 for 0.2 m s

^{−1}≤ |

*U*

_{⊥}| ≤ 5 m s

^{−1}and

*c*

_{B}increases from 0.043 to 0.049 for 5 m s

^{−1}≤ |

*U*

_{⊥}| ≤ 10 m s

^{−1}(see Fig. 5). This increase makes the Briggs method less suitable to obtain

*U*

_{⊥}, especially for high

*U*

_{⊥}values (>5 m s

^{−1}). In this study we used a

*c*

_{B}of 0.043, since

*U*

_{⊥}is rarely above 5 m s

^{−1}in our dataset (for the sonic anemometer, only 1% of the time for the 10-s data). The value of

*c*

_{B}for a scintillometer setup is dependent on

*D*;

*c*

_{B}can range for typical scintillometer setups from 0.015 [

*D*= 5.0 cm] to 0.043 [

*D*= 15.0 cm].

Value of Briggs constant (*C*_{B}) (left *y* axis) given homogeneous *U*_{⊥} along the scintillometer path for a scintillometer setup with two transmitters, spaced 0.17 m apart, and one receiver. Error of assuming *C*_{B} = 0.043 is given in gray on the right *y* axis.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Value of Briggs constant (*C*_{B}) (left *y* axis) given homogeneous *U*_{⊥} along the scintillometer path for a scintillometer setup with two transmitters, spaced 0.17 m apart, and one receiver. Error of assuming *C*_{B} = 0.043 is given in gray on the right *y* axis.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Value of Briggs constant (*C*_{B}) (left *y* axis) given homogeneous *U*_{⊥} along the scintillometer path for a scintillometer setup with two transmitters, spaced 0.17 m apart, and one receiver. Error of assuming *C*_{B} = 0.043 is given in gray on the right *y* axis.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Another issue with the Briggs method is that when the measured *r*_{12}(*τ*) and *r*_{11}(*τ*) are disturbed in some way, multiple intersects between the two functions can be found. To find *τ*_{B}, we therefore only looked for intersects between *τ* = 0 and *τ* = *τ*_{P}. For some data there were, however, still multiple intersects or no intersects for 0 ≤ *τ*_{B} ≤ *τ*_{P}. To obtain *U*_{⊥} for as many situations as possible, we also looked at the results when *τ*_{B} was taken as the first or last intersect in case there were multiple intersects. The results of these approaches to obtain *τ*_{B} are discussed in section 5b.

### c. Zero-slope method

*τ*= 0 s of

*r*

_{12}(

*τ*), denoted by

*S*

_{0}, is related to

*U*

_{⊥}(see Fig. 6);

*S*

_{0}is related to

*U*

_{⊥}following

*c*

_{S}is a constant depending on

*D*.

Modeled *r*_{12}(*τ*) for *U*_{⊥} = 0.2 m s^{−1} (black line) and *U*_{⊥} = −0.2 = m s^{−1} (gray line), with *S*_{0} indicated.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Modeled *r*_{12}(*τ*) for *U*_{⊥} = 0.2 m s^{−1} (black line) and *U*_{⊥} = −0.2 = m s^{−1} (gray line), with *S*_{0} indicated.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Modeled *r*_{12}(*τ*) for *U*_{⊥} = 0.2 m s^{−1} (black line) and *U*_{⊥} = −0.2 = m s^{−1} (gray line), with *S*_{0} indicated.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

For our scintillometer setup [*D* is 0.15 m] *c*_{S} is −0.165. The value of *c*_{S} is highly dependent on *D*; it can for typical scintillometer setups range from −0.060 [*D* = 5.0 cm] to −8.0 [*D* = 30 cm]. The value of *c*_{S} also depends on over which *τ S*_{0} is determined. In this study *S*_{0} is determined between *τ* = −0.1 s and *τ* = 0.1 s. The sign of *U*_{⊥} is defined by the sign of *S*_{0}.

### d. Lookup table method

The model of *r*_{12}(*τ*) [Eq. (1)] can, for a given scintillometer setup, be solved for a range of *U*_{⊥} and *τ*, thereby creating a lookup table that can be compared to measured *r*_{12}(*τ*) values. We created a lookup table for −10 m s^{−1} ≤ *U*_{⊥} ≤ 10 m s^{−1} with a resolution of 0.1 m s^{−1} and −1 s ≤ *τ* ≤ 1 s with a resolution of 0.002 s (related to the measurement frequency of 500 Hz) given the scintillometer setup [*D* and *d*(*x*)] used in this study (see section 4). The measured *r*_{12}(*τ*), calculated over *τ* varying from −1 to 1 s, is compared to all the modeled *r*_{12}(*τ*) with different *U*_{⊥} values. The modeled *r*_{12}(*τ*) that has the best fit with the measured *r*_{12}(*τ*) is the *U*_{⊥} representative for the time window over which the measurements were taken. An example is given in Fig. 7, where a measured *r*_{12}(*τ*) is plotted along with the theoretical *r*_{12}(*τ*), which has the best fit with the measured *r*_{12}(*τ*). As can be seen in Fig. 7, the measured *r*_{12}(*τ*) and the theoretical *r*_{12}(*τ*) are both calculated with a resolution for *τ* of 0.002 s. The best fit is determined over −1 s ≤ *τ* ≤ 1 s. This fit can be found using different criteria—for example, smallest difference, highest correlation, and smallest root-mean-square error (RMSE). We decided to use the highest correlation to determine the best fit.

Theoretical time-lagged correlation function (black dots) and measured time-lagged correlation function (gray dots) for a *U*_{⊥} of −2.0 m s^{−1}.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Theoretical time-lagged correlation function (black dots) and measured time-lagged correlation function (gray dots) for a *U*_{⊥} of −2.0 m s^{−1}.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Theoretical time-lagged correlation function (black dots) and measured time-lagged correlation function (gray dots) for a *U*_{⊥} of −2.0 m s^{−1}.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Potentially the lookup table method can also be used to investigate the variability of *U*_{⊥} along the path. This can be achieved by adding heterogeneous wind fields to the lookup table. It is also possible to incorporate specific path characteristics in the lookup table (e.g., height variation of the beam along the scintillometer path). However, in this study the scintillometer that was installed is measuring over a short path of 426 m over a homogeneous grass field. Therefore, strong heterogeneity of *U*_{⊥} is unlikely to occur and we created a lookup table for homogeneous wind fields only.

## 4. Experimental setup and data treatment

### a. Experimental setup

The data analyzed in this paper are the same as in van Dinther et al. (2013), which was collected at a flat grassland site at the Haarweg, Wageningen, The Netherlands. We will, therefore, only briefly outline the most important aspects of the experimental setup. For more details, see van Dinther et al. (2013). A Scintec BLS900 measured the scintillation signal with a frequency of 500 Hz over a 426-m path at a height of 3.53 m with an angle relative to north of 338° (see Fig. 8 in van Dinther et al. 2013). The BLS900 is a DLAS with two transmitters (spaced 0.17 m apart) and one receiver, all with an aperture diameter of 0.15 m. As already specified in section 2, *U*_{⊥} of the DLAS (*U*_{⊥DLAS}) is defined positive when, looking from the transmitters’ side to the receiver’s side, the wind blows from the left side into the scintillometer path. For the scintillometer setup in this study (roughly a north–south orientation), this implies that *U*_{⊥} is positive when the wind is blowing from the west, and *U*_{⊥} is negative when the wind is blowing from the east.

In this study, *U*_{⊥DLAS} is validated with sonic anemometer measurements (CSAT3, Campbell Scientific, Utah). This anemometer measured at a height of 3.44 m, with a frequency of 10 Hz, and was located roughly 300 m from the middle of the scintillometer path (see Fig. 8 in van Dinther et al. 2013). The wind direction and horizontal wind speed of the sonic anemometer were used to calculate *U*_{⊥} on the scintillometer path, which was used for the validation.

The DLAS and sonic anemometer measurements ran from 13 to 19 May 2010. The wind directions at the Haarweg during this measurement period according to the sonic anemometer were not very perpendicular to the scintillometer path, with wind directions mainly from the north/northwest (see Fig. 9 in van Dinther et al. 2013). Consequently, the longitudinal wind component is considerable during the measurement period (up to 4 m s^{−1}).

### b. Noise filtering

White noise by, for example, the sensor electronics introduces uncorrelated intensity fluctuations in the scintillometer signal. This noise, therefore, lowers *r*_{12}(*τ*) of the DLAS signal, which affects some of the *U*_{⊥} retrieval algorithms. The effect of noise is strongest when the scintillations are weak—that is, conditions where the structure parameter of the refractive index *τ*_{P} will not change due to noise; therefore, this method is not susceptible to noise. For the Briggs and zero-slope method, *τ*_{B} and *S*_{0} are, however, affected by noise (Wang et al. 1981): *S*_{0} will be lower when the peak in *r*_{12}(*τ*) is reduced due to noise, leading to an underestimation in *U*_{⊥}; *τ*_{B} will be higher when the peak in *r*_{12}(*τ*) is reduced due to noise, also leading to an underestimation in *U*_{⊥}. We expect that *U*_{⊥} of the lookup table method will not be affected by noise, since the shape of *r*_{12}(*τ*) does not change as a result of noise (see Fig. 9 in Wang et al. 1981).

The spectral techniques given by van Dinther et al. (2013) use the power spectrum of the scintillometer signal, which is affected by noise. Lowering of the measured intensity signal (e.g., due to fog) to a level lower than ⅔ of the undisturbed signal will cause an incorrect *U*_{⊥} to be obtained by the spectral techniques. Therefore, for the spectral techniques, van Dinther et al. (2013) had to apply a filter on signal intensity, causing a data loss of 17%. The *U*_{⊥} retrieval methods that rely on *r*_{12}(*τ*) should not be affected by a lowering of the signals, as long as this effect is the same for both signals. Fog (as occurred on some of the mornings during the experiment) should affect both signals in the same way; therefore, for this study no additional filter on signal intensity was necessary. We only filtered out data when the signal intensity was zero, which occurred when the data were transferred from the DLAS to the computer (which took 1 s every minute).

## 5. Results and discussion

In this section the results of the crosswind of the dual large-aperture scintillometer (*U*_{⊥DLAS}) are validated with *U*_{⊥} calculated from the sonic anemometer measurements (*U*_{⊥sonic}). We will first discuss the results of *U*_{⊥DLAS} obtained from *r*_{12}(*τ*) using the methods discussed in section 3. For every 10-s time window *U*_{⊥DLAS} is determined (see the appendix). However, *U*_{⊥DLAS} cannot be compared for every 10 s to *U*_{⊥sonic} because the measurement locations of the DLAS and sonic anemometer were not the same and their clocks were not synchronized to the second. Assuming a homogeneous wind field across the flat grass site, the 10-min averaged *U*_{⊥} values are used to validate the DLAS measurements with the sonic anemometer measurements. We will also discuss the results of *U*_{⊥DLAS} when using the Briggs method as a quality check. In addition we also compared the 10-min standard deviation of *U*_{⊥} (STD_{U⊥}) of the DLAS with that of the sonic anemometer, in order to validate the fluctuations of *U*_{⊥DLAS} given by the four methods.

The software of the DLAS used in this study (SRun, Scintec) also uses an algorithm based on *r*_{12}(*τ*) to calculate *U*_{⊥}. Van Dinther et al. (2013) reported that SRun, version 1.07, overestimates *U*_{⊥} by 20%. In this study we will shortly discuss the results of the latest software version of SRun (version 1.14).

### a. Mean crosswind

In Fig. 8 the modeled and the measured time-lagged correlation function [*r*_{12}(*τ*)] and the time-lagged autocorrelation function [*r*_{11}(*τ*)] are plotted for *U*_{⊥} = −2.0 m s^{−1}. The modeled and measured functions are similar in shape. The model of Eq. (1) can, therefore, be used to obtain the constants *c*_{B} and *c*_{S} and the lookup table, as was suggested in section 3.

Measured (black solid line) and theoretical (gray dashed line) (a) time-lagged correlation function and (b) time-lagged autocorrelation function for *U*_{⊥} = −2.0 m s^{−1}.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Measured (black solid line) and theoretical (gray dashed line) (a) time-lagged correlation function and (b) time-lagged autocorrelation function for *U*_{⊥} = −2.0 m s^{−1}.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Measured (black solid line) and theoretical (gray dashed line) (a) time-lagged correlation function and (b) time-lagged autocorrelation function for *U*_{⊥} = −2.0 m s^{−1}.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

The results of *U*_{⊥DLAS} of the four methods are shown in Fig. 9. The results are color coded with the longitudinal wind (*U*_{‖}). Note that all the methods obtain a similar *U*_{⊥} as the sonic anemometer, but they all tend to overestimate *U*_{⊥} when *U*_{‖} is high (>2.5 m s^{−1}, orange and red colors in Fig. 9) and *U*_{⊥} is low <2 m s^{−1}. The model of Eq. (1) assumes that there is no influence of *U*_{‖} on *r*_{12}(*τ*). However, in reality *U*_{‖} influences the DLAS signal by advecting eddies into the scintillometer path. The influence of *U*_{‖} is, however, much smaller than that of *U*_{⊥}, since the scintillometer path (~10^{2} m) is several orders of magnitude higher than the spacing between the DLAS beams (~10^{−1} m). Eddies that are advected into the scintillometer path by *U*_{‖} are uncorrelated for the two signals. Potvin et al. (2005) found that *r*_{11}(*τ*) decorrelates faster in time as a result of *U*_{‖}. Therefore, *r*_{12}(*τ*) also decorrelates faster in time, leading to an overestimation of *U*_{⊥DLAS}. However, if *U*_{⊥} is high (>2 m s^{−1}), then there is no clear overestimation of *U*_{⊥DLAS} for the four methods for when *U*_{‖} is also high (>2.5 m s^{−1}), which indicates that *U*_{⊥} indeed has a bigger influence on *r*_{12}(*τ*) than *U*_{‖} for this dataset. The DLAS data used in this study are obtained over a relatively short scintillometer path of only 426 m. For a longer scintillometer path (e.g., microwave scintillometer), the influence of *U*_{‖} should be even lower. For a shorter scintillometer path (e.g., laser scintillometer), the influence of *U*_{‖} should be higher.

Results showing *U*_{⊥DLAS} for (a) the peak method, (b) the Briggs method, (c) the zero-slope method, and (d) the lookup table method plotted against *U*_{⊥sonic} over 10 min, colored with *U*_{‖}.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Results showing *U*_{⊥DLAS} for (a) the peak method, (b) the Briggs method, (c) the zero-slope method, and (d) the lookup table method plotted against *U*_{⊥sonic} over 10 min, colored with *U*_{‖}.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Results showing *U*_{⊥DLAS} for (a) the peak method, (b) the Briggs method, (c) the zero-slope method, and (d) the lookup table method plotted against *U*_{⊥sonic} over 10 min, colored with *U*_{‖}.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

The corresponding regression statistics of Fig. 9 are given in Table 1, where the RMSE is defined by the error of DLAS compared to the sonic anemometer. This table also shows the regression statistics for when we use a Briggs quality check (QC), which will be discussed later. For now we focus on the results without the Briggs quality check (i.e., Briggs quality check is “none”). The peak method has the most scatter, with an *R*^{2} of 0.80 leading to a high RMSE of 0.82 m s^{−1}. The peak method uses only one point, the time lag of the peak (*τ*_{P}), in the measured *r*_{12}(*τ*). As our measurement frequency was 500 Hz, *τ*_{P} is determinable with a resolution of 0.002 s, which means that *U*_{⊥} can only be solved for specific values. For higher *U*_{⊥} values (>4 m s^{−1}) corresponding to a low *τ*_{P} (<0.022 s), these specific *U*_{⊥} values have a limited resolution (see Fig. 10). For example, *τ*_{P} = 0.014 s corresponds to *U*_{⊥} = 7.2 m s^{−1}, while *τ*_{P} = 0.012 s corresponds to *U*_{⊥DLAS} = 6.1 m s^{−1}; thus, for one 0.002-s step, the difference in *U*_{⊥} is 1.1 m s^{−1}. The limited resolution for high *U*_{⊥} makes the peak method less practical than the other methods. The solution is to increase the measurement frequency. To solve *U*_{⊥} values up to 15 m s^{−1} with a resolution of 0.2 m s^{−1}, a measurement frequency of 1.3 kHz is necessary for the scintillometer setup of this study

Regression equations, *R*^{2}, RMSE, and data availability (*N*) validating *U*_{⊥DLAS} with *U*_{⊥sonic} with or without applying the QC.

Results showing *U*_{⊥DLAS} of the peak method for 10 s on DOY 136.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Results showing *U*_{⊥DLAS} of the peak method for 10 s on DOY 136.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Results showing *U*_{⊥DLAS} of the peak method for 10 s on DOY 136.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

The zero-slope method and the lookup table method show similar results, with a low amount of scatter (*R*^{2} = 0.86 for both) and both with a low RMSE (of 0.59 and 0.61 m s^{−1}, respectively). The fit of *U*_{⊥DLAS} and *U*_{⊥sonic} is better for the lookup table method than for the zero-slope method (regression slope of 0.88 compared to 0.76); this is especially the case for higher *U*_{⊥} values (>3 m s^{−1}, see Figs. 9c and 9d).

The Briggs method implicitly uses a quality check. In the next section we will discuss this quality check in more detail. For now we focus on the results of the Briggs method with the strict quality check as is (see Fig. 9b; Table 1). The results of the Briggs method compare best with those of the sonic anemometer, with a regression slope of 0.89 and an RMSE of only 0.52 m s^{−1}. However, the Briggs method is also the method with the lowest data availability of only 56%. From Fig. 9 it is apparent that most data where the Briggs method is not able to find a solution occur when *U*_{‖} is high (>2.5 m s^{−1}, orange colors in Fig. 9). These are also the data points where the other three methods show the most scatter with *U*_{⊥sonic}. In the next section, we will discuss in more detail when the Briggs method does not find a solution. Further, we will investigate the usability of the Briggs method as a quality check for the other methods. Van Dinther et al. (2013) used the same dataset as the one used in this study. Therefore, the results of the spectral techniques in van Dinther et al. (2013) are directly comparable to the results obtained in this study. The results of this study [based on the dual-beam approach; i.e., using *r*_{12}(*τ*)] are similar to the results in van Dinther et al. (2013) (based on the single-beam approach; i.e., using the scintillation power spectra), with similar scatter (*R*^{2} for both approaches is 0.88 and 0.89) and RMSE (between 0.47 and 0.67 m s^{−1} for the dual-beam approaches and between 0.46 and 0.70 m s^{−1} for the single-beam approaches). An advantage of the dual-beam approaches is that unlike the single-beam approaches, they do not need a filter on the signal intensity, resulting in a data availability of 100% for every dual-beam method except the Briggs method. In summary the dual-beam approaches have the following advantages over the single-beam approaches: *U*_{⊥} is determinable over shorter time intervals (~10 s), the sign of *U*_{⊥} is determinable, and the data availability is higher (100% compared to ≤83%). Therefore, the dual-beam approaches are preferable to the single-beam approaches.

### b. Briggs quality check

The Briggs method obtains *U*_{⊥} from the time lag where *r*_{12}(*τ*) and *r*_{11}(*τ*) intersect (*τ*_{B}). The Briggs quality check refers to data where the Briggs method does not find a solution, which occurs where there are no or multiple intersects between *r*_{12}(*τ*) and *r*_{11}(*τ*), indicating that these functions are distorted. We will differentiate between a “loose” and “strict” Briggs quality check. “Loose” refers to the quality check for data points where there are no intersects between *r*_{12}(*τ*) and *r*_{11}(*τ*) for 0 ≤ |*τ*_{B}| ≤ |*τ*_{P}|. “Strict” refers to the quality check for data points where there are no or multiple intersects between *r*_{12}(*τ*) and *r*_{11}(*τ*) for 0 ≤ |*τ*_{B}| ≤ |*τ*_{P}|. With the loose quality check, 67% of the data are left, while with the strict quality check, only 56% of the data are left.

Possible causes for a distorted *r*_{12}(*τ*) and *r*_{11}(*τ*) are variable *U*_{⊥} values along the scintillometer path and a strong *U*_{‖} (>2.5 m s^{−1}). We cannot investigate the variable *U*_{⊥} along the scintillometer path directly, since only one sonic anemometer was measuring the wind field. However, by assuming frozen turbulence, the variability along the scintillometer path is high when the standard deviation over 10 min of *U*_{⊥sonic} (STD_{U⊥sonic}) is high. The data filtered out with the strict quality check often coincides with STD_{U⊥sonic} > 0.5 m s^{−1} (57% of the filtered data) and *U*_{‖} > 2.5 m s^{−1} (58% of the filtered data). Therefore, we can conclude that a high STD_{U⊥} and/or high *U*_{‖} indeed causes a distorted *r*_{12}(*τ*) and *r*_{11}(*τ*).

We tested which intersect (the first or the last) is best to use with the Briggs method in case of multiple intersects between *r*_{12}(*τ*) and *r*_{11}(*τ*) for 0 ≤ |*τ*_{B}| ≤ |*τ*_{P}|. Using the last intersect as *τ*_{B} showed better results than using the first intersect as *τ*_{B}: less scatter (*R*^{2} of 0.89 vs 0.59) and a lower RMSE (0.51 vs 1.0 m s^{−1}). Therefore, the regression statistics shown in Table 1 for the Briggs method with the loose quality check is obtained by using the last intersect (i.e., the intersect closest to *τ*_{P}) as *τ*_{B} in the case of multiple intersects. Although the results of *U*_{⊥DLAS} by using the last intersect are similar to *U*_{⊥sonic}, still only 67% of *U*_{⊥DLAS} are resolved by the Briggs method.

Results of the four methods filtered with the Briggs quality control are also shown in Table 1, and those filtered with the loose quality check are plotted in Fig. 11. Comparing the results of the data with and without the Briggs quality check, it is clear that this quality check is valuable. We first compare the results of *U*_{⊥} with and without the loose Briggs quality check. For the peak method, the zero-slope method, and the lookup table method, all aspects of the linear regression improve when applying the loose Briggs quality check. The RMSE decreases, ranging from 0.59 to 0.82 without the Briggs quality check to 0.47–0.67 with the loose Briggs quality check. The fit of *U*_{⊥DLAS} with *U*_{⊥sonic} improves, with regression slopes closer to one when the loose Briggs quality check is used. Only for the peak method is this not the case, as the regression slope for this method increases from 1.01 to 1.07, but the offset does decrease from 0.48 to 0.34. The *R*^{2} increases by using the loose Briggs quality check: for the peak method it rises from 0.80 to 0.88, while for the zero-slope and lookup table methods it rises from 0.86 to 0.89.

Plots of *U*_{⊥DLAS} for (a) the peak method, (b) the Briggs method, (c) the zero-slope method, and (d) the lookup table method against *U*_{⊥sonic} over 10 min using the loose quality check, colored with *U*_{‖}.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Plots of *U*_{⊥DLAS} for (a) the peak method, (b) the Briggs method, (c) the zero-slope method, and (d) the lookup table method against *U*_{⊥sonic} over 10 min using the loose quality check, colored with *U*_{‖}.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Plots of *U*_{⊥DLAS} for (a) the peak method, (b) the Briggs method, (c) the zero-slope method, and (d) the lookup table method against *U*_{⊥sonic} over 10 min using the loose quality check, colored with *U*_{‖}.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Applying the strict Briggs quality check instead of the loose Briggs quality check does not improve the results; the regression statistics stay similar. The RMSE even increases slightly for the four methods (by 0.01–0.03 m s^{−1}). However, the strict Briggs quality check does decrease the data availability to 56%.

Besides the Briggs quality check, two other quality checks were also investigated: the value of the maximum *r*_{12}(*τ*) and the correlation between the measured and modeled *r*_{12}(*τ*). To improve the results of *U*_{⊥DLAS}, strict thresholds had to be chosen for these quality checks. The maximum in *r*_{12}(*τ*) had to be at least 0.3. The correlation between the measured and modeled *r*_{12}(*τ*) had to be at least 0.9. The results of these quality checks did not improve *U*_{⊥DLAS} as much as with the Briggs quality check. Moreover, the data availability after using the maximum *r*_{12}(*τ*) or the correlation between the measured and modeled *r*_{12}(*τ*) as a quality check was lower (≤65%) than that after using the loose Briggs quality check. Therefore, we advise to use the loose Briggs quality check.

### c. Standard deviation of the crosswind

The standard deviation of *U*_{⊥} (STD_{U⊥}) gives an indication of how well the methods are performing over 10 s. There are some clear outliers in STD_{U⊥DLAS} (STD_{U⊥DLAS} > 2 m s^{−1}) for the peak method (16% of the data up to 7.6 m s^{−1}), the Briggs method (3% of the data up to 7.2 m s^{−1}), and the lookup table method (3% of the data up to 4.5 m s^{−1}) when the Briggs quality check is not used (except for the Briggs method where the loose Briggs quality check is used). These outliers mainly occur on 2 days of the experiment [day of year (DOY) 138 and 139]. The cause of these outliers remains unclear. We investigated rain, wind direction, scintillometer signal level, and sign changes in *U*_{⊥}, but we could not find an explanation for the outliers. The zero-slope method does not have outliers and compares well with STD_{U⊥sonic} for all days of the experiment. The outliers (STD_{U⊥DLAS} > 2 m s^{−1}) were filtered out to be able to compare STD_{U⊥DLAS} with STD_{U⊥sonic}; for the results, see Fig. 12 and Table 2. Another approach to remove the outliers is by applying an outlier filter model—for example, the one given by Thompson (1985).

Results of STD_{U⊥DLAS} for (a) the peak method, (b) the Briggs method, (c) the zero-slope method, and (d) the lookup table method against STD_{U⊥sonic} over 10 min colored with DOY (DOY indicated by color scale at right).

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Results of STD_{U⊥DLAS} for (a) the peak method, (b) the Briggs method, (c) the zero-slope method, and (d) the lookup table method against STD_{U⊥sonic} over 10 min colored with DOY (DOY indicated by color scale at right).

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Results of STD_{U⊥DLAS} for (a) the peak method, (b) the Briggs method, (c) the zero-slope method, and (d) the lookup table method against STD_{U⊥sonic} over 10 min colored with DOY (DOY indicated by color scale at right).

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Regression equations, *R*^{2}, RMSE, and *N* validating STD_{U⊥DLAS} with STD_{U⊥sonic} with or without applying the QC and filtering on STD_{U⊥DLAS} > 2 m s^{−1}.

The STD_{U⊥DLAS} of the peak method, despite filtering on STD_{U⊥DLAS} > 2 m s^{−1} and thereby excluding 16% of the data, still showed a poor fit with STD_{U⊥sonic}: low *R*^{2} (0.38) and high RMSE (0.43 m s^{−1}). The fit of the Briggs method and the lookup table method with the sonic anemometer measurements was also poor, although better than that of the peak method (*R*^{2} ≤ 0.44 and RMSE ≥ 0.26). The best results for STD_{U⊥DLAS} were obtained by the zero-slope method, with the highest *R*^{2} (0.63), lowest RMSE (0.19), and highest data availability (100%).

Applying the Briggs quality check (higher *R*^{2} and lower RMSE) improved the results of all the methods, except for the zero-slope method. Although applying the Briggs quality check did result in a lower regression slope for the peak method, the zero-slope method, and the lookup table method. However, for the peak method and lookup table method, this is compensated by the offset of the regression equation, which decreases (from 0.16 to 0.078 for the peak method and from 0.094 to 0.053 for the lookup table method). After taking into account the results after applying the Briggs quality check, the best results were still obtained by the zero-slope method without the Briggs quality check. This indicates that the zero-slope method is able to obtain the fluctuations in *U*_{⊥DLAS} over 10 min correctly.

### d. SRun version 1.14

The manufacturer of the BLS900 (Scintec) has a software package SRun that uses an algorithm based on *r*_{12}(*τ*) to calculate *U*_{⊥}. Until now, the algorithm used by SRun was undocumented both in scientific literature and the SRun manual. Van Dinther et al. (2013) reported that SRun, version 1.07, overestimates *U*_{⊥} by almost 20%, resulting in an RMSE of 0.62 m s^{−1}. This prompted Scintec to revise its *U*_{⊥} retrieval algorithm in SRun, version 1.14. The results of this new version will be presented here, together with a global outline of the algorithm used by SRun to obtain *U*_{⊥} provided by Scintec (A. C. van den Kroonenberg, Scintec AG, 2013, personal communication).

The algorithm is similar to the lookup table method described in section 3d, where a measured *r*_{12}(*τ*) is compared to the theoretical *r*_{12}(*τ*). The measured *r*_{12}(*τ*) is calculated between *τ* is −6 and 6 s with 109 steps on a logarithmic scale to decrease computation time. The theoretical *r*_{12}(*τ*) are determined by Gaussian functions [*F*(*τ*)] using several combinations of *U*_{⊥} (varying between 0.05 and 30 m s^{−1}) and standard deviations of *U*_{⊥} (varying between 0.15 and 3.0 m s^{−1}). The measured *r*_{12}(*τ*) is broader than the theoretical *F*(*τ*) due to the spatial expansion of the turbulence elements. Therefore, *F*(*τ*) has to convolve with a second Gaussian function [*G*(*τ*)]. This *G*(*τ*) describes the distribution of the eddy sizes and depends on the wavelength that contributes most to the scintillometer signal. The Gaussian fit function is calculated as the discrete convolution of *F*(*τ*) and *G*(*τ*). This fit function is scaled with a factor to obtain the same amplitude as the measured correlation. The fit function that matches the measured *r*_{12}(*τ*) closest (which is determined by a chi-squared test) provides *U*_{⊥} and the standard deviation of *U*_{⊥}. In SRun, version 1.07, the functions describing the turbulence expansion in space [i.e., *G*(*τ*)] were too broad, resulting in overestimations of the standard deviation of *U*_{⊥} and overestimation of the higher *U*_{⊥} values. In SRun, version 1.14, the function *G*(*τ*) was improved (A. C. van den Kroonenberg, Scintec AG, 2013, personal communication).

Results of SRun, version 1.14, are shown in Fig. 13, including a data filtering used by SRun leading to a data availability of 99%. The same dataset is used in this study as in van Dinther et al. (2013); therefore, the results of SRun, version 1.14, are directly comparable to that of SRun, version 1.07 (see Fig. 14 in van Dinther et al. (2013). The results of *U*_{⊥DLAS} improved, especially for the high *U*_{⊥} values (>2 m s^{−1}), where the fit of *U*_{⊥DLAS} with *U*_{⊥sonic} is better than before. However, there are also some outliers that underestimate *U*_{⊥}, leading to a regression slope of only 0.80. These outliers cause an RMSE of 0.60 m s^{−1}, which is only a bit lower than that of software version 1.07, where it was 0.62 m s^{−1}. Although the error in software version 1.14 seems comparable to software version 1.07, given the better fit for higher *U*_{⊥} values (>2 m s^{−1}), we would recommend using version 1.14 over version 1.07 to obtain *U*_{⊥}, especially for the application at airports, where the higher *U*_{⊥} values are more important.

Plot of *U*_{⊥DLAS} for SRun, version 1.14, against *U*_{⊥sonic} over 10 min, colored with *U*_{‖}.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Plot of *U*_{⊥DLAS} for SRun, version 1.14, against *U*_{⊥sonic} over 10 min, colored with *U*_{‖}.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Plot of *U*_{⊥DLAS} for SRun, version 1.14, against *U*_{⊥sonic} over 10 min, colored with *U*_{‖}.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

## 6. Conclusions

In this study the crosswind (*U*_{⊥}) is determined from dual large-aperture scintillometer (DLAS) measurements. The *U*_{⊥DLAS} is obtained from the time-lagged correlation function [*r*_{12}(*τ*)] and the time-lagged autocorrelation function [*r*_{11}(*τ*)], which are determined over a 10-s time window. We used four methods to obtain *U*_{⊥}: the peak method, the Briggs method, the zero-slope method, and the lookup table method. This last method is a new method introduced in this paper. The *U*_{⊥} obtained from the DLAS measurements is validated against sonic anemometer measurements. The sonic was not located in the center of the DLAS path. Therefore, for the validation *U*_{⊥} is averaged to 10 min.

The 10-min averages of *U*_{⊥DLAS} for all the four methods compare reasonably well to *U*_{⊥sonic}, with root-mean-square errors (RMSE) varying from 0.52 to 0.82 m s^{−1}. However, all methods showed an overestimation of *U*_{⊥DLAS} when *U*_{⊥} is low (<2 m s^{−1}). Lawrence et al. (1972) attributed this overestimation of low *U*_{⊥} values to eddy decay, which causes the assumption of frozen turbulence to be violated. Our results, however, show that the overestimation of *U*_{⊥DLAS} compared to *U*_{⊥sonic} occurs when the longitudinal wind (*U*_{‖}) is high (>2.5 m s^{−1}). Potvin et al. (2005) showed that *r*_{11}(*τ*) decorrelates faster when *U*_{‖} is high, which is caused by the fact that *U*_{‖} also brings in and blows out eddies in the scintillometer path. A faster decorrelation in time of *r*_{12}(*τ*) will be misinterpreted as a higher *U*_{⊥} value. Thereby, a high *U*_{‖} will result in an overestimation of *U*_{⊥DLAS}. The fact that the overestimation of *U*_{⊥DLAS} only occurs for low values of *U*_{⊥} (<2 m s^{−1}) indicates that for higher *U*_{⊥} values, the influence of *U*_{⊥} is dominant over *U*_{‖}. We expect the influence of *U*_{‖} to be less for a longer scintillometer path.

The term *U*_{⊥DLAS} of the peak method has the worst fit with *U*_{⊥sonic}, which is caused by the low resolvable resolution of *U*_{⊥} for high values (>4 m s^{−1}). This low resolution is caused by the fact that the measurement frequency of the DLAS determines the accuracy with which the time lag of the peak in *r*_{12}(*τ*) can be found (e.g., if the measurement frequency is 500 Hz, then accuracy of the peak is determinable to 0.002 s).

The Briggs method seems to obtain the best result for *U*_{⊥DLAS}. However, this method has an implicit internal filter, which is caused by the fact that the Briggs method does not find a solution when there are no or multiple intersects between *r*_{12}(*τ*) and *r*_{11}(*τ*). We showed that there is a relation between data points when the Briggs method does not find a solution and when *U*_{‖} is high (>2.5 m s^{−1}) or STD_{U⊥} is high (>0.5 m s^{−1}). The loss of data due to this internal filter can be used as a quality check for the other data. We defined a loose quality check where only the data when there was no intersect between *r*_{12}(*τ*) and *r*_{11}(*τ*) were removed, leading to a data availability of 67%. We defined a strict quality check where data when there was no intersect or multiple intersects between *r*_{12}(*τ*) and *r*_{11}(*τ*) were removed, leading to a data availability of 56%. Besides the loss of data, another problem of the Briggs method is that the constant used by this method (*c*_{B}) is, in fact, not constant: *c*_{B} decreases with high *U*_{⊥} values (>5 m s^{−1}). The error made by assuming that *c*_{B} is constant amounts to −1.3 m s^{−1} for *U*_{⊥} = 10 m s^{−1}.

The term *U*_{⊥DLAS} of both the zero-slope method and the lookup table method compared well to *U*_{⊥sonic}, with low RMSE (≤0.61 m s^{−1}) and high *R*^{2} values (≥0.86). However, for high *U*_{⊥} values (>2 m s^{−1}), the lookup table method gave better results, since the zero-slope method showed a small underestimation of *U*_{⊥DLAS} for these values. When applying the loose quality check, the results improved for the zero-slope method and the lookup table method. Therefore, one can choose to optimize the results for data availability (by not applying the Briggs quality check) or to optimize the results for accuracy (by applying the Briggs quality check).

The software (SRun) of the manufacturer of the DLAS used in this study (BLS900, Scintec, Rottenburg, Germany) also obtains *U*_{⊥} from *r*_{12}(*τ*). The results of *U*_{⊥} of SRun, version 1.14, are better than that of version 1.07 (given by van Dinther et al. 2013), mainly because there is no longer an underestimation of *U*_{⊥DLAS} for high values (>2 m s^{−1}). The results for *U*_{⊥DLAS} of SRun, version 1.14, are similar to that of the zero-slope method and the lookup table method in this study.

The 10-min standard deviation (STD) of *U*_{⊥} gives an indication of how well the 10-s fluctuations in *U*_{⊥DLAS} are resolved. STD_{U⊥DLAS} of both the peak method and the Briggs method was not similar to STD_{U⊥sonic}, even after filtering on STD_{U⊥DLAS} > 2 m s^{−1}, mainly due to some outliers. The lookup table method was able to obtain STD_{U⊥DLAS}; however, the strict Briggs quality check had to be applied. The zero-slope method clearly showed the best results for STD_{U⊥DLAS}; even without one of the Briggs quality checks, the correspondence with the sonic anemometer was good. The fact that the zero-slope method is also able to obtain the correct STD_{U⊥DLAS} enhances our trust in this method.

To conclude, the zero-slope method and the lookup table method showed the best results; *U*_{⊥DLAS} and STD_{U⊥DLAS} were both similar to that of the sonic anemometer. The zero-slope method obtained better results for low *U*_{⊥} values (<2 m s^{−1}), while the lookup table method obtained better results for high *U*_{⊥} values (>2 m s^{−1}). The peak method and the Briggs method had some issues either concerning resolution, data availability, or obtaining the correct STD_{U⊥DLAS}. The Briggs method did prove to be valuable as a quality check for the other methods.

## Acknowledgments

The authors thank Frits Antonysen and Willy Hillen for their assistance with the BLS900 installation. We also thank Aline van den Kroonenberg (Scintec AG, Germany) for giving us more insight into the algorithm used by SRun. This study was funded by the Knowledge for Climate program as project “WindVisions” (HSMS01).

## APPENDIX

### Determination of the Time-Lag Correlation Function

When calculating *r*_{12}(*τ*) from DLAS measurements using Eq. (4), the following time scales are relevant: the time lag (*τ*), the time period (*T*) over which *r*_{12} is determined, and the window size *r*_{12}(*τ*). First, we will discuss the three approaches by which the two signals (*I*_{1} and *I*_{2}) can be shifted with respect to each other. Second, we will discuss which *r*_{12}(*τ*).

#### a. Shifting the two signals with respect to each other to obtain r_{12}(τ)

We investigated three approaches to calculate *r*_{12}(*τ*), which have the following characteristics (see also Fig. A1):

is constant, *I*_{1}is fixed while*I*_{2}shifts, and; is variable, both *I*_{1}and*I*_{2}shift with respect to each other, and; and is constant, both *I*_{1}and*I*_{2}shift with respect to each other, and.

*U*

_{⊥DLAS}), which was validated against sonic anemometer measurements (

*U*

_{⊥sonic}).

Approaches (a) 1, (b) 2, and (c) 3 of shifting the two signals in time with respect to each other, concerning time period (the total bar, *T*), time window (the filled bar, *τ*). Black blocks represent one signal and gray blocks the other; the time-lagged correlation functions are determined over the filled color.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Approaches (a) 1, (b) 2, and (c) 3 of shifting the two signals in time with respect to each other, concerning time period (the total bar, *T*), time window (the filled bar, *τ*). Black blocks represent one signal and gray blocks the other; the time-lagged correlation functions are determined over the filled color.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Approaches (a) 1, (b) 2, and (c) 3 of shifting the two signals in time with respect to each other, concerning time period (the total bar, *T*), time window (the filled bar, *τ*). Black blocks represent one signal and gray blocks the other; the time-lagged correlation functions are determined over the filled color.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

The results of the three approaches and four methods are shown in Table A1. In general, the results are similar for the three approaches, with comparable regression equations and RMSE. The similarity for the three approaches indicates that the approach by which *r*_{12}(*τ*) is calculated from DLAS measurements does not influence *U*_{⊥DLAS} severely. However, there are small differences in *U*_{⊥DLAS} for the three approaches: for the Briggs method and the zero-slope method, approach 3 gave the best results (lowest RMSE and best fit with *U*_{⊥sonic}). Given the fact that approach 3 gave the best results for two of the methods and that this approach has a low *T* and a constant *U*_{⊥DLAS}.

Regression equations, *R*^{2}, RMSE, and *N* validating *U*_{⊥DLAS} with *U*_{⊥sonic} using approaches 1–3 to shift the signals with respect to each other. Note that *N* of the Briggs method is not 100% because this method does not yield a solution when there is no intersect between *r*_{11}(*τ*) and *r*_{12}(*τ*).

#### b. Time window over which r_{12}(τ) should be determined

The *r*_{12}(*τ*) should be determined over a sufficient *U*_{⊥} is located at *τ* = 0.072 s. However, for *r*_{12}(*τ*) at other *τ* values that are not associated with *U*_{⊥}. Figure A2 indicates that the longer the *U*_{⊥}. In particular, the peaks unassociated with *U*_{⊥} decrease when

Measured time-lagged-correlation function [*r*_{12}(*τ*)] for time windows of 3, 10, 30, and 60 s.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Measured time-lagged-correlation function [*r*_{12}(*τ*)] for time windows of 3, 10, 30, and 60 s.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

Measured time-lagged-correlation function [*r*_{12}(*τ*)] for time windows of 3, 10, 30, and 60 s.

Citation: Journal of Atmospheric and Oceanic Technology 31, 1; 10.1175/JTECH-D-13-00118.1

For the application at airports, *U*_{⊥DLAS} should be available over the shortest *U*_{⊥DLAS} values.

## REFERENCES

Baker, C. J., Jones J. , Lopez-Calleja F. , and Munday J. , 2004: Measurements of the cross wind forces on trains.

,*J. Wind Eng. Ind. Aerodyn.***92**, 547–563.Briggs, B. H., Phillips G. J. , and Shinn D. H. , 1950: The analysis of observations on spaced receivers of the fading of radio signals.

,*Proc. Phys. Soc.***63B**, 106–121.Chen, S. R., and Cai C. S. , 2004: Accident assessment of vehicles on long-span bridges in windy environments.

,*J. Wind Eng. Ind. Aerodyn.***92**, 991–1024.Clifford, S. F., 1971: Temporal-frequency spectra for a spherical wave propagating through atmospheric turbulence.

,*J. Opt. Soc. Amer.***61**, 1285–1292.Furger, M., Drobinski P. , Prévôt A. S. H. , Weber R. O. , Graber W. K. , and Neininger B. , 2001: Comparison of horizontal and vertical scintillometer crosswinds during strong foehn with lidar and aircraft measurements.

,*J. Atmos. Oceanic Technol.***18**, 1975–1988.Kolmogorov, A., 1941: The local structure of turbulence in an incompressible viscous fluid for very large Reynolds numbers.

,*Dokl. Akad. Nauk SSSR***30**, 299–303.Lawrence, R. S., Ochs G. R. , and Clifford S. F. , 1972: Use of scintillations to measure average wind across a light beam.

,*Appl. Opt.***11**, 239–243.Poggio, L. P., Furger M. , Prévôt A. H. , Graber W. K. , and Andreas E. L. , 2000: Scintillometer wind measurements over complex terrain.

,*J. Atmos. Oceanic Technol.***17**, 17–26.Potvin, G., Dion D. , and Forand J. L. , 2005: Wind effects on scintillation decorrelation times.

,*Opt. Eng.***44**, 016001, doi:10.1117/1.1830044.Thompson, R., 1985: A note on restricted maximum likelihood estimation with an alternative outlier model.

,*J. Roy. Stat. Soc.***47B**, 53–55.van Dinther, D., Hartogensis O. K. , and Moene A. F. , 2013: Crosswinds from a single-aperture scintillometer using spectral techniques.

,*J. Atmos. Oceanic Technol.***30**, 3–21.Wang, T. I., Ochs G. R. , and Lawrence R. S. , 1981: Wind measurements by the temporal cross-correlation of the optical scintillations.

,*Appl. Opt.***20**, 4073–4081.Wood, C. R., Pauscher L. , Ward H. C. , Kotthaus S. , Barlow J. F. , Gouvea M. , Lane S. E. , and Grimmond C. S. B. , 2013: Wind observations above an urban river using a new lidar technique, scintillometry and anemometry.

,*Sci. Total Environ.***442**, 527–533.