Wind speed measurements using distributed fiber optics: a wind tunnel study

Near-surface wind speed is typically only measured by point observations. The Actively Heated Fiber-Optic (AHFO) technique, however, has the potential to provide high-resolution distributed observations of wind speeds, allowing for better characterization of fine-scale processes. Before AHFO can be widely used, its performance needs to be tested in a range of settings. In this work, experimental results on this novel observational wind-probing technique are presented. We utilized a controlled wind-tunnel setup to assess both the accuracy and the precision of AHFO under a range of operational conditions. 5 The technique allows for wind speed characterization with a spatial resolution of 0.3 m on a 1 s time scale. The flow in the wind tunnel was varied in a controlled manner, such that the mean wind, ranged between 1 and 17 ms-1. The AHFO measurements are compared to sonic anemometer measurements and show a high overall correlation (0.85-0.98). Both the precision and accuracy of the AHFO measurements were also greater than 95%. We conclude that the AHFO has potential to be employed as an outdoor observational technique. It allows for characterization of spatially varying fields of mean wind in complex terrain, 10 such as in canopy flows or in sloping terrain. In the future, the technique could be combined with conventional Distributed Temperature Sensing (DTS) for turbulent heat flux estimation in micrometeorological/hydrological applications. Copyright statement.

Wind speed is most commonly observed using in-situ point measurement techniques. As a result, the spatial distribution of field observations is limited. While it is possible to obtain distributed wind speed observations with remote sensing (e.g., Goodberlet et al. (1989)), the spatial resolution is too low for many micrometeorological applications.
Many field experiments assume Taylor's frozen flow hypothesis (Taylor (1938)) in order to estimate fluxes with similarity theory (e.g., Higgins et al. (2009); Kelly et al. (2009);Bou-Zeid et al. (2010); Patton et al. (2011)). However, similarity theory 5 only holds for idealized homogeneous/stationary conditions, which are rarely met in practice, resulting in a model containing strong assumptions, which often leads to significant errors (Ha et al. (2007); Higgins et al. (2012); Thomas et al. (2012)). In real, non-idealized situations, even slight surface heterogeneities can lead to dramatic impacts on the spatial structure of the flow in the surface boundary layer. Further, even if perfect surface homogeneity was possible, other atmospheric (surface) conditions are often nonstationary as well (Holtslag et al. (2013)). 10 In the past decade, a new way to obtain spatial distributed measurements was introduced into environmental studies. Highresolution measurements could be used to check underlying assumptions and would reduce the need for such assumptions in real-world cases. Distributed Temperature Sensing (DTS) technology measures temperature at high temporal and spatial resolution over distances of up to several kilometers by using Fiber Optic (FO) cables as sensors (Selker et al. (2006a) ;Selker et al. (2006b); Tyler et al. (2009)). High-end DTS can measure the temperature at a 1 s and 0.3 m resolution (Sayde et al. 15 (2014)). The ability to report temperature at such high resolution has proven useful in many environmental studies (Selker et al. (2006a) Izett et al. (2018). It has also been shown that it is possible to observe air temperature and thermal structure of near-surface turbulence with DTS (Thomas et al. (2012); Euser et al. (2014); Zeeman et al. (2015), Jong et al. (2015)). 20 Recently, Sayde et al. (2015), introduced the AHFO technique as a means of performing independent explicit wind speed measurements using distributed temperature sensing (DTS) technology. The underlying concept of the proposed method is similar to that of a hotwire anemometer; however, instead of single point measurements, AFHO enables distributed measurements to be made at high spatial resolution. Instead of only passively measuring the temperature in the fiber (as is done with DTS), one segment of the cable is actively heated. The heated segment is positioned parallel to the unheated reference segment, 25 with a small separation, in our case 0.1 m. The temperature difference between the heated and reference segment is measured, i.e., the heated fiber and the air temperature. The temperature difference between the cables depends on the energy input as well as on the wind speed of the ambient air, which determines the magnitude of the lateral heat exchange, through advection of cooler ambient air. By setting up an energy balance for the heated cable, one can estimate the magnitude of this advective heat transport, which leads to an estimate of the wind speed. 30 Results from a field study by Sayde et al. (2015) demonstrated promising performance of the AHFO technique, but they recommended further tests be performed in controlled airflow conditions. First, the heat transfer model assumes the flow is normal to the axis of the fiber. Sayde et al. (2015) developed a first-order estimate of the influence of a non-normal angle of attack (the difference between the wind direction and the axis of the fiber), using a directional sensitivity equation from hotwire anemometry (Webster (1962); Hinze (1975); Perry (1982); Adrian et al. (1984)), but it needs to be tested in a controlled setting to determine its validity. Second, Sayde et al. (2015) highlight the importance of a sufficient signal-to-noise ratio when conducting measurements. They show that the temperature difference between the heated and reference segments gives a good estimate for this ratio. The influence of the directional sensitivity and the signal-to-noise ratio on the measurement accuracy and precision is investigated and the results are used to propose a method to estimate the precision for future experiments with AHFO, hence our work will improve the possibilities for successful application of AHFO in future field experiments.

5
An overview of the experimental setup is presented in section 2, with the accuracy and precision of the AHFO experiments presented in section 3. In section 4, a method for estimating the precision for future experiments is introduced, followed by a short note on future studies. 10 We conducted a series of experiments under tightly controlled airflow conditions to improve the applicability of AHFO in experimental (field) research and to study the directional sensitivity and influence of the signal-to-noise ratio. The experiments presented were performed in a wind tunnel at Oregon State University. This wind tunnel has a closed circuit, which means the air inside is recycled. The test section of the wind tunnel has a cross-section (height by width) of 1.23 by 1.52 m, and an undisturbed horizontal section of roughly 5 to 6 m which may be used for probing. During the experiment two segments of one 15 cable (which encloses the FOs) were placed 8 cm apart: one heated and one reference segment. For validation, an independent sonic anemometer was placed approximately 0.2 m downwind of the fibers, which measures the wind speed in 3 directions.

Wind tunnel experiments
All equipment was mounted using custom-designed support material.
The angle of the fiber related to the flow, wind speed and heating rate were systematically changed. An electrical current (I) is passed through the heated cable, to create the temperature difference (∆T , e.g., 2 • C) needed to determine wind speed. By 20 fixing the current through the stainless steel casing of the cable, the entire FO cable is heated because of the electrical resistance (R) of the stainless steel casing. The magnitude of the current needed to create a given temperature difference is dependent on the cable resistance and the wind speed, therefore the current is adjusted for each individual experiment. The amount of power applied per meter of cable, P s (Wm -1 ), necessary to heat the cable and to create a temperature difference, is referred to as the heating rate. 25 The cable was mounted at four different angles in the wind tunnel, resulting in different angles of attack, in order to gain more insights into directional sensitivity. In Figure 1b the 90°set-up is visible, however the cable was also mounted at a 45°, 30°and 15°angle, with respect to the floor of the wind tunnel (see: Figure 1a, inset). During all set-ups, the lower part of the FO cable was fixed to the opening in the bottom of the wind tunnel, while the upper end was attached to an extruded aluminum bar that was moved over the fixed horizontal bars, to achieve the desired cable angles. To test the performance for a range 30 of wind speeds, ten different wind speeds were tested at every angle: 1, 3,5,7,9,11,13,15,16 and 17 ms -1 (e.g., 4x10 = 40 setups). The AHFO wind speed measurements can be calibrated by comparing the AHFO wind speed to a reference sonic anemometer. The wind speed in the wind tunnel was fixed at a constant value to create a steady state flow. In field experiments the wind speed will vary, and the temperature difference will fluctuate accordingly if the current is fixed. For all angles and every wind speed, three temperature differences were applied in order to quantify the importance of the signal-to-noise ratio.
The current was fixed to create a temperature difference (∆T ) of 2, 4 and 6°C between the heated and reference cable. In total, 120 (4 x 10 x 3) trials were conducted with the different parameters, each with a minimum duration of 10 minutes.
The cable mounted in the wind tunnel consisted of a 1.34 mm outer diameter stainless steel casing that enclosed four multi-5 mode FOs with a diameter of 250 µm ( Figure 2). Only two FOs were used and these were spliced at the end of the cable to create a duplexed FO, which results in double measurements (Hausner et al., 2011). The FOs were connected to a Silixa Ultima DTS machine (Ultima S, 2 km range, Silixa, London, UK) outside the wind tunnel.
One cable segment was heated. The stainless steel casing was connected to a power controller (MicroFUSION uF1HXTA0-32-P1000-F040) by 12 AWG cables (3.31 mm 2 ), to heat the cable in a controlled way. Heating rates varying from 0.5-10 10 Wm -1 were used to create temperature differences to a fixed level, either 2, 4 and 6°C, depending on the setup. The electrical resistance per meter of stainless steel casing (R s ) is 1.67 (Ωm -1 ) and is constant along the length. For the length of a cable segment (B, (m)), R = R s B, where R (Ω) is the total resistance of a cable segment. The same holds for P = P s B, where P (W) is the total power input for a cable segment. The heating rate for a cable segment (Wm -1 ) was controlled by fixing the Hence, the known relation P = I 2 R (W), or in this specific case the heating rate is P s = I 2 R s (Wm -1 ) per meter of cable segment.
For calibration and validation of the DTS data, approximately 6 m of the FO cables was placed in a well-mixed ambient bath to calibrate the DTS temperature according to the method described by Hausner et al. (2011). The temperature was verified 5 with one probe (RBRsolo 2 T, RBR Ltd., Ottawa, Ontario, Canada). A circulating aquarium pump was placed inside the bath, to prevent stratification.
Temperatures along the FOs were sampled at 0.125 m resolution with a sampling rate of 1 Hz. The FOs were deployed in a double-ended configuration, however the data was acquired and treated as two separated single-ended channels of data. Splices between ends of fiber optic cables are known to create an additional loss in signal, i.e., local higher attenuation (Tyler et al. 10 (2009); van de Giesen et al. (2012)), this loss is normally independent of the direction. However, in processing of the raw DTS data it was found that the loss over the splice was not the same in both directions. Due to this asymmetrical structure of the splice loss, only the data of one channel was used to ensure the quality of the results, as this channel showed a regular splice loss.
To be able to test the accuracy of the DTS wind speed measurements independently, wind speed was sampled at 10 Hz 15 using a sonic anemometer (IRGASON+EC100 and CR3000, Campbell Scientific, Logan, UT,USA). The sonic anemometer was mounted approximately 0.2 m behind the fiber optic cables, in the middle of the wind tunnel. As the FOs are very thin, it is assumed that these do not significantly disturb the measurement of the sonic volume (particularly at larger averaging times).

20
An energy balance is used to quantify the advective energy transport from the heated cable, and therefore estimate the wind speed with DTS. The advective cooling can be converted to wind speed, because it is a function of wind speed and the temperature difference between the heated and unheated segments. The full energy balance (in W) for a cable segment volume of length, B, is given by Sayde et al. (2015), and schematically shown in Figure 3: (1) Figure 3. Schematization of the energy balance, based on Sayde et al. (2015) Where, r is the radius of the cable (6.7 · 10 -4 m in our setup); V is the volume of the cable segment (πr 2 B, in m 3 ), c s is the specific heat capacity of the FO cable (502 Jkg -1 K -1 ) and ρ v is the FO cable density (800 kgm -3 ). P s is the heating rate per 5 meter of cable (in Wm -1 ); and B is the length of a cable segment (in m).S b ,S d and α sSt (in Wm -2 ) are the mean direct, diffuse and reflected short wave radiation fluxes, respectively, with α s being the surface albedo of the ground; and α f is the FO cable optic surface albedo.L ↓ +L ↑ (in Wm -2 ) are the average downward and upward longwave radiation fluxes, respectively; and is the FO cable surface emissivity. Based on the kind of stainless steel, emissivity values can range from 0.3 to 0.7 (Baldwin and Lovell-Smith (1992)); however, we assume a value of 0.5 (Madhusudana (2000)). σ is the Stefan-Boltzmann constant, 5.67 · 10 10 -8 (Wm -2 K -4 ); and σT 4 s is the outgoing longwave radiation of the fiber, i.e., L f iber ; T s and T f are the temperature (in K) of the heated cable segment and (unheated) reference segment (i.e., air temperature), respectively. Finally, h is the advective heat transfer coefficient (in Wm -2 K -1 ). By means of the dimensionless Nusselt (Nu), Prandtl (Pr), and Reynolds (Re) numbers, h can be expressed as function of the wind speed, h = f (u n ). Nu, is the ratio between the advective and conductive heat transfer, where the Nusselt number can be written as follows, (Žukauskas (1972)): (3) d s is the fibers characteristic length (2r); K a is the thermal conductivity of air and υ a the kinematic viscosity of air, respectively 0.0255 Wm -1 K -1 and 1.5 x 10 -5 m 2 s -1 (Tsilingiris (2008)). K a and υ a are assumed to be constant, due to the controlled 5 conditions in the wind tunnel, but in field experiments this should be included as a variable, as K a and υ a are temperature and relative humidity depend (Tsilingiris (2008)). C, m and n are empirical constants related to forced advection of heat by air movement. In Sayde et al. (2015), C, m and n values of 0.51, 0.5 and 0.37 are set, based on (Žukauskas (1972)). Pr is the Prandtl number and can be seen as the ratio between kinematic viscosity and thermal diffusivity, which, we assume Pr to be constant (0.72) for our range of temperatures (12-35°C), as in Tsilingiris (2008), with Pr s (the Prandtl number for the heated 10 fiber segment), assumed to be the same as Pr, due to the small temperature differences (max. 6°C). Lastly, Re is the Reynolds number which is used to determine the flow regime of the air along the fiber segments, i.e., Re expresses if the flow regime is laminar or turbulent. Combining Eq. 2-4 yields: The determination of the Nusselt number (Eq. 3) is only valid in the following ranges of Re (40-1000) and Pr (0.7-500). Re 15 can be a limitation for higher wind speeds, especially when the diameter of the fiber is large, in our case wind speeds higher than approximately 11 ms -1 would be out of range. In the derivation of the energy balance (1), there is assumed to be no free convection, induced by heating of the air close to the cable, and no conduction of heat in the axial direction of the FO cable.
It is also assumed there is no radiative exchange between objects close and parallel to the heated fiber, i.e., dispersion of heat from the heated cable to the reference cable is assumed to be negligible. Furthermore, a flow directed normal to the axis of 20 FO cable is assumed by the proposed energy balance, i.e., for flow directed in a different angle, compensation is necessary to accurately estimate the wind speed.
Finally, the energy balance is simplified, by dividing Eq. 1 by 2rπB, which is equal to the surface area of the FO cable. The energy balance now no longer depends on B, meaning the length of FO segment does not need to be defined. The proposed final energy balance by Sayde et al. (2015) is as follows and in Wm -2 : 25 c s ρr 2 where, ρ is the FO cable density per meter of cable segment: 4.5 x 10 -3 kgm -1 .

Proposed simplified determination of Wind Speed
Due to the setup inside the wind tunnel, as opposed to outdoor conditions, some simplifications can be made. The short wave radiation can be neglected because it is an indoor experiment (no sunlight). Furthermore, we assume that there is a uniform temperature inside the wind tunnel, due to the enclosed conditions. This means the incoming radiation is dependent on the air temperature, T f . Assuming incoming (L ↓ +L ↑ ) to be black body radiation (i.e., L in = σT 4 s ), the net longwave radiation loss 5 for the fiber can be simplified accordingly by merging the incoming longwave and outgoing longwave radiation as: One more additional change is made, based on our results obtained during testing of the performance of the AHFO technique.
In processing of the obtained wind tunnel data it was found that by using the calculation of the Nusselt number from Žukauskas (1972), Eq. 2, a ∼ 20% additional bias in calculating the wind speed was created. By using a more recent version for calculating 10 the empirical Nusselt number (Cengel and Ghajar (2014)), the bias in our study is reduced to ∼ 5% Therefore, Eq. 8 is proposed to calculate the Nusselt number, where the constants C, m and n are still used; however, with the values from Table   7-1 (C = 0.683, m = 0.466 and n = 1/3) in Cengel and Ghajar (2014), rather than those in Žukauskas (1972). Next to the improved fit, the range of Re over which the equation is valid is much wider (40-4000 compared with 40-1000), and therefore more applicable in future AHFO experiments.

15
Nu = CRe m Pr n = 0.683Re 0.466 Pr 1/3 Consequently, the expression of h changes as well.
With the long-and short-wave radiation simplifications, the simplified energy balance becomes: 20 By substituting the expression for h (Eq. 9), we can rearrange Eq. 10 to obtain an expression for wind speed. Eq. 11 will be used to estimate the wind speed in our wind tunnel study.

Directional Sensitivity analysis
Equation 11 is derived for flows normal to axis of the cable (as in Figure 1b). However, in reality the wind will not always have a 90°angle compared to the axis of the cable, especially in outside atmospheric experiments. For angles smaller than 90°t he wind speed will be underestimated, as the advective heat transfer is less efficient. To be able to still determine the wind speed for all angles of attack, Sayde et al. (2015) adjusted the wind speed obtained in Eq. 11 using a geometric correction from 5 hotwire anemometry (e.g., Adrian et al. (1984)) to get the true wind speed (u DTS ): k is the directional sensitivity and ϕ is the angle of attack of the wind with respect to the axis of the cable, ranging from 0°to 90°.

10
However, during analysis of the wind tunnel data it was found that Eq. 12 was not giving satisfying results (e.g., a 22% bias between the 90°and 15°angle). In Adrian et al. (1984) it is shown that in hotwire anemometry a variety of theoretical and empirical formulas have been proposed in the past, in order to account for directional sensitivity. Alternatively, using the formula suggested by Bruun (1971) gives more satisfying results, diminishing the bias between the 90°and 15°angle to only 5%. This is shown in Figure 4. Therefore, Eq. 13 is used to account for directional sensitivity in our study, with the scaling exponent, m 1 , able to be optimized during calibration of the AHFO measurements. The value for m 1 obtained during calibration of our set up was 1.05.

DTS and Signal-to-Noise ratio analysis
Based on the backscattered signal of a laser pulse inside fiber optic cables, a Distributed Temperature Sensing (DTS) machine measures temperature along a complete fiber optic cable (Selker et al. (2006b)). These fiber optic cables can have lengths up to several kilometers with a spatial resolution down to 0.3 m, i.e., one DTS machine makes to thousands of near-simultaneous individual measurements. Laser pulses are sent with a fixed wavelength and most backscattered light keeps this wavelength, 5 however some backscattered laser shifts to a shorter or longer wavelength, these frequency-shifted reflections are referred to as Raman-backscatter (Selker et al. (2006a)). By counting the backscattered photons with a longer (Stokes) and shorter (Anti-Stokes) frequency, a ratio between these two can be calculated. The strength of the Anti-Stokes signal depends on temperature, hence the ratio between the power of the Stokes and Anti-Stokes changes with temperature. This principle is used to measure the temperature along the cable. Consequently, a main source of noise in DTS data is white noise induced by the statistical 10 variability in photon count from backscatter (optical shot noise). Furtherr sources of noise include Johnson-Nyquist noise.
A sufficiently high signal-to-noise ratio is essential for measurement precision with DTS. In Sayde et al. (2015) it is shown that the signal-to-noise ratio can be described as: (T s − T f )/σ T . Hence the signal-to-noise ratio is related to the ∆T ( T s − T f ) and the measurement error of the DTS, σ T (in this study at a 1 s sample resolution), which can be assumed constant in a lab experiment. A large ∆T is obviously desirable, however, ∆T cannot be increased infinitely. The power controller can only 15 deliver a limited amount of power to heat the fiber, which is especially relevant for the heating of long lengths of FO cable (i.e. several hundreds of meters of FO cable). Also the creation of larger temperature differences means the importance of other modes of energy transfer changes. To find realistic solutions, the effect of ∆T is investigated by using three temperature differences during the experiment. The effect of the signal-to-noise ratio is quantified, and an equation to estimate the precision is presented. The precision is an indication of the variability of wind speed (e.g., RMSD), as opposed to accuracy which 20 describes a systematic measurement error that can be removed through calibration (e.g., a bias).

Results
The accuracy and precision of the DTS wind speed calculations is given in Figures 5 and 6, where the velocity calculated using AHFO (calculated by Eq. 11 and 13) is compared with the velocity measured from the sonic anemometer. The temperatures measured with AHFO are spatially averaged over 10 measurements (2 fibers, each with 5 measurements), i.e., this is equivalent 25 to a height of ∼ 0.9 m in the wind tunnel. Only the temperatures from the middle of the wind tunnel are used, to prevent using data with side/boundary effects. Figure 5 shows the 1 s sample rate DTS data against the 1 s average sonic anemometer data, for the four different angles of attack. Figure 6 shows the same dataset, but temporally averaged over 30 s, and for all angles.
A clear improvement of the precision is visible when temporal averaging is performed. Even though the directional sensitivity formula is not yet fully calibrated, the bias is negligible, with coefficients of determination ranging from 0.85-0.98. Finally, as 30 expected, the wind speed measurement are less accurate when the wind speed angle is smaller.
To get more insight in the quality of the results, a dimensionless analysis is performed. In Figure 7, the non-dimensional wind speed accuracy for the whole wind tunnel experiment is shown. For all combinations (120 individual cases of varying  ind speed, angle and ∆T ), the accuracy is calculated according to Eq. 14. The accuracy is then averaged over wind speed for each ∆T and angle combination in Figure 7, indicating the size of the bias by σ a .  For the whole uncalibrated data set, the maximum σ a is 5%, which is promising for future applications. The 90°angle should be the best performing angle, however it is maximal overestimating with 5%, which is probably due to neglecting small energy losses, like free convection due to heating of air close to the heated cable (Sayde et al. (2015)). With such an energy loss included, the bias of each angle will change. As a flow directed normal to the axis of FO cable is assumed by the proposed energy balance, it is better to compare the other angles to the 90°angle instead of 0 bias. Doing this, it can been seen that the 5 directional sensitivity formula is not yet optimally calibrated (e.g., the 5% difference between the 90°and 15°angle biases).
This kind of error is not uncommon and in accordance with previous hotwire anemometry work, especially with small angles of attack (Adrian et al. (1984)). Nevertheless, the bias is fairly constant with increasing averaging time, which means extensive calibration can probably increase the accuracy.
While the accuracy (bias) remains constant over the averaging period, the relative precision, σ p increases significantly (Fig.   10 8). The precision is calculated for all 120 ∆T , angle and wind speed combination, using Eq. 15. To be able to present the precision clearly, the precision is averaged over wind speed for all ∆T and angle combinations in Figure 8: While calculating the precision of u DT S , the natural variability of the wind is excluded, by assuming the sonic anemometer is able to capture this. As a result, the variability of the DTS machine u DT S estimates are obtained. For each of the 120 combi-  nations, u sonic and u DT S are the average wind speeds for a given combination. u sonic (i) and u DT S (i) are single measurements during this combination.
The precision increases to a σ p less than 5% by averaging over time. Improvement by averaging is expected due to the reduction of noise (van de Giesen et al. (2012)). As mentioned, the main source of noise in DTS data is white noise, this explains the visible improvement of the precision by 1 √ n , as signal averaging is applied, where n is the amount of measurements 5 (Selker et al. (2006b); Kaiser and Knight (1979)).

Normalized precision
In order to remove the influence of different settings (such as the choice of ∆T ) and determine a general prediction of precision in future experiments, we normalize the precision. First, the precision is normalized to ∆T (Figure 9a), by multiplying by 10 ∆T Terror . As a results, 1 √ n dependence becomes even more clear, as shown by the black solid line showing γ √ n , where γ is σ p at a 1 s temporal, and 10 measurement spatial, resolution. Second, the precision is also normalized to the 1 √ n behavior, by multiplying by tavg t sample . Where, T error and t sample are given constants which depend on the performance of the DTS, in this case T error = 0.25 K and t sample = 1 s, according to the factory specifications. It appears that the precision can be condensed in a number, 1.6, which we denote by the symbol C int (Figure 9b). Intermediate constant C int can be defined as, Eq. 16:  the scientific research question to be answered with AHFO. By using the shown 1 √ n dependency, we can easily convert C int into C DT S , by multiplying C int by 10 1 , as n is 10 times less.

Precision prediction
At the start of a new AHFO experiment it is unknown how to make sure the signal-to-noise ratio is sufficient, such that σ p is 5 small. However, given the result that the increase in precision behaves independent of ∆T and the averaging time, it is possible to make a prediction for the precision of future work.
In outdoor experiments, the only setting which can be changed is the heating rate, P s , which is assumed to be fixed at a single value. The idea behind the precision prediction is to guide the choice of a heating rate, such that a preferred precision is achieved for a known dominant wind speed range. As the wind speed outside will vary naturally, ∆T will change accordingly.
10 Therefore, to obtain an expression where P s is the only unknown, ∆T first needs to be expressed as a function of the wind speed u n and the heating rate (P s ). This can be done by using Eq. 11. To obtain a first estimate, some assumptions can be made. The numerator of Eq. 11 consists of three terms, of which the first one with heating rate (P s ) is dominant compared to the other ones, namely 10-100 times bigger. When these minor terms are neglected Eq. 11 can be simplified to: Knowing this expression of ∆T , Eq. 19 can again be rewritten into Eq. 20, which expresses the precision estimate, with P s as only parameter which can be changed during an experiment.
Where n is the number of measurements over which the observed wind speed is averaged, in either space or time domain.
By assuming that all constants are known from literature and the set-up, a first estimate of the error can be made for every velocity or heating rate given. If a dominant wind speed range for a new project is known, an associated heating rate can be found, such that the error is sufficiently small.
As an example, Figure 10 shows the estimated precision for our experiment at 1 s and 0.675 m resolution over a range of wind speeds and heating rates. If the diameter of the fiber is different, this is taken into account via term A from Eq. 20, which includes the radius (d = 2r). Also, when a DTS machine with a different performance is used, this can be implemented by changing T error accordingly. Of course different applications will demand different space-time averaging windows, depending on the scientific research question to be answered with AHFO, which option is included by 1 n .
5 Figure 10. Expected precision (contour lines) for a given heating rate and wind speed as calculated from Eq. 20, with a 1 s temporal resolution, averaged over 10 measurements.
In outdoor experiments, the influence of the short and long wave radiation will be present. However, as long as the radiation is the same for the heated and non-heated segment, this does not influence the error estimation, as for the signal-to-noise ratio, ∆T is the most important factor. When the heated and reference fiber are close to each other, which is also needed for properly estimating the wind speed, both fibers will experience a similar contribution of external radiation, such that the overall ∆T will be relatively unaffected by this factor.

Using AHFO outdoors
The experiments described here were performed in a controlled wind tunnel environment. When performing outdoor AHFO experiments, several factors need to be considered. First of all, during field experiments the relative humidity and tempera- ture might have such a big range that assuming certain parameters (e.g., K a and υ a ) as constant is not applicable anymore (Tsilingiris (2008)). Furthermore, for small wind speeds (e.g., < 1 ms −1 ), the neglection of energy losses like free convection seems not entirely applicable, as is visible in the strong convergence of the contour lines in Figure 10. This is confirmed in our study, where it was visible that the response is different between a well ventilated and non-ventilated cable, hence the accuracy is dependent on the wind speed. Although not shown in this paper, it seemed there was no time response difference 5 between a vertical or horizontal mounted heated cable, however by mounting the cable in a horizontal or vertical direction, free convection might influence the temperature measurements as the heated air is moving upward. It is shown that AHFO can give reliable wind speed measurements, however the precision and accuracy is not as good as with a sonic anemometer. The major addition of AHFO is the possibility to sample the wind speed with a high spatial distribution. Finally, when measuring in the field, the use of high quality reference point measurements (e.g., sonic anemometer) is recommended, for example to be able 10 to compensate for possible biases. A sonic anemometer can also be useful to determine the angle of attack, as this is not (yet) possible with one single fiber. A more complex 3D set-up is necessary to be able to do this with DTS/AHFO (Zeeman et al. (2015)).
Despite these remarks, it will be interesting to perform outdoor tests in complex terrain, for both micrometeorological and hydrological applications, as AHFO gives a lot of insights in spatial varying wind fields. AHFO can be especially interesting 15 in non-homogenous field sites, like forests, which are already studied with other DTS applications ).
Moreover, the ability to measure spatial varying wind fields can be useful for estimating sensible heat fluxes in a variety of atmosphere-vegetation-soil continuums.

Conclusions
Through a series of controlled wind tunnel experiments, new insights into the accuracy and precision of the newly introduced 20 AHFO wind speed measuring technique were obtained. With high spatial (0.3 m) and temporal (1 s) resolution, the AHFO wind speed measurements agreed very well with the sonic anemometer measurements, with a coefficients of determination ranging from 0.85-0.98. It is also shown that the AHFO technique has the possibility to measure with a precision and accuracy of 95%. Some additional work is needed, as there still is a small overestimation, which may be caused by neglecting some energy fluxes, such as free convection due to heating of the air close the heated cable. Furthermore, it is possible to optimize 25 the directional sensitivity compensation by extended calibration.
The error prediction equation (Eq. 20) is an important result of this work that will aid in the design of future experiments.
This design tool helps with choosing a heating rate for the actively heated fiber in order to be able to create a sufficiently high precision. Based on the prevalent wind speeds of a potential field experiment site, a first estimate of an associated sufficient heating rate can be calculated. Due to the way this design tool is constructed, it can be generalized for all kinds of fibers, DTS 30 precisions, and user preferred spatial and temporal resolutions.
The AHFO technique can reliably measure wind speeds under a range of conditions. The combination of high spatial and temporal resolution with high precision of the technique opens possibilities for outdoor application, as the key feature of the