Insights into wind turbine reflectivity and RCS and their variability using X-band weather radar observations

Abstract. The increasing need of renewable energy fosters the expansion of wind turbine sites for power production throughout Europe with manifold effects, both on the positive and negative side. The latter concerns, among others, radar observations in the proximity of wind turbine (WT) sites. With the aim of better understanding the effects of large, moving scatterers like wind turbines on radar returns, MeteoSwiss performed two dedicated measurement campaigns with a mobile X-band Doppler polarimetric weather radar (METEOR 50DX) in the north-eastern part of Switzerland in March 2019 and March 2020. Based on the usage of a X-band radar system, the performed campaigns are up to now unique. The main goal was to quantify the effects of wind turbines on the observed radar moments, to retrieve the radar cross section (RCS) of the turbine themselves, and to investigate the conditions leading to the occurrence of the largest RCS. Dedicated scan strategies, consisting of PPI (Plan Position Indicator), RHI (Range-height Indicator) and fixed-pointing modes, were defined and used for observing a wind park consisting of three large wind turbines. During both campaigns, measurements were taken in 24/7 operation. The highest measured maxima of horizontal reflectivity (ZH) and RCS reached 78.5 dBZ respectively 44.1 dBsm. A wind turbine orientation (yawing) stratified statistical analysis shows no clear correlation with the received maximum returns. However, the median values and 99th percentiles of ZH and RCS show different enhancements for specific relative orientations. Further, we show, based on investigating correlations and an OLS (ordinary least square) model analyses, that the fast changing rotor blade angle (pitch) is a key parameter, which strongly contributes to the variability of the observed returns.



Introduction
The rapid development and expansion of wind farms in the latest years are a significant source of concern for the weather (e.g., Norin, 2017) and aviation radar community (de la Vega et al., 2016;Cuadra et al., 2019). Wind turbines are very large, reflective and moving objects, which makes them a source of clutter that becomes difficult to filter or separate from return signals of interest. Over the last years, the demand for the quantification, modeling and mitigation of the effects of wind turbines on 20 radar systems is rising as the number of installed, planned or foreseen wind turbines is highly increasing. As analyzed by Komusanac et al. (2020) in 2019 about 15.4 GW of new wind power capacity was installed in the European Union (EU). This is 27 % higher than in 2018. The total capacity of wind energy in the EU in the end of 2019 is 205 GW, which is 15 % of the The main goal of the measurement campaigns in 2019 and 2020 was to study the interaction between electromagnetic waves at 9.84 GHz sent by the weather radar and the structure of wind turbines. For this type of investigation, a small wind park consisting of three large wind turbines, with the characteristics specified in Table 1, was selected near the city of Schaffhausen.
Many logistical requirements for the installation of the weather radar had to be met (e.g. sufficient power supply, radiation safety, permissions from the Swiss Federal Office of Communication), beside a good visibility towards the wind park. More 60 details on the observation site are provided in Section 2.1.
The field campaign in 2019 took place between 6 th and 28 th of March with totally 23 days of continuous observations, while the second one took place between 4 th and 25 th of March 2020 with a total of 22 days of measurements. During the latter campaign, the radar data were collected with a fixed-pointing antenna towards the nacelle of the closest wind turbine with respect to the radar site. The radar scanning protocol lasted 120 min, whereof 100 min were used for the fixed-pointing 65 measurements and about 12 min for a PPI volume acquisition as an overview scan for the whole wind park area.
The measurements presented in this paper have been collected with a dual-polarization, simultaneous transmission and reception (STAR), mobile Doppler weather radar, which operates at a frequency of 9.48 GHz. Due to the relatively small antenna size and overall weight, it is a transportable system integrated on a trailer and particularly suitable for field campaigns and agile relocations. Several configurations of the transmission protocols and data acquisition can be defined (e.g. PRF, pulse 70 widths, scan velocity, data acquisition rate). A detailed technical overview about the characteristics of the radar system can be found in Neely III et al. (2018). Some key specifications are listed in Table 2.
The radar system provides a set of single-polarization, dual polarization, and Doppler measurements: horizontal (vertical) reflectivity Z H (Z V ), differential reflectivity Z DR , co-polar correlation coefficient ρ HV , total differential phase shift Φ DP , specific differential phase shift K DP , Doppler velocity V and Doppler spectrum width W . If filters or thresholds are applied 75 to the data, not only the filtered data can be kept, but always also the raw data. Additionally it is possible to store full power spectrum (PSR) data. was performed, allowing now to acquire data when the radar antenna is not moving (something that was not possible to do in 2019). This new ability is hereafter referred to as fixed-pointing or stare-mode measurements of the weather radar.
The core data processing for both campaigns was done by the MeteoSwiss in-house-developed open-source real-time weather radar data processing framework Pyrad (Figueras i Ventura et al., 2020a), which is based on the Py-ART radar toolkit 85 (Helmus and Collis, 2016).

Observation site and radar visibility
The observation site, where the radar system could be installed, was in the vicinity of the city of Schaffhausen. This site had several advantages: line of sight with the wind turbines, a minimum distance from the wind park to limit the risk of a receiver saturation, site accessibility, permission to transmit and power connection. The three wind turbines of the small wind park 90 located north of Schaffhausen are installed on a hill surrounded by forests. The corresponding terrain profile between the radar and the furthermost wind turbine (WT3) is shown in Fig. 1 Although trees were blocking part of the radiation towards the masts at a distance of 1 km, the rotor centers of all three 95 wind turbines were always visible at the center of the radar antenna beam. With radar ground echo clutter simulations based on GECSX (Ground Echo Clutter Simulator) and a digital elevation model (DEM) with 50 m resolution, the radar visibility towards the wind turbines could be determined. The used approach follows the technique and developed software described in Gabella and Perona (1998); Gabella et al. (2008). Figure 1(a) shows the minimal visible elevation map, which is the minimum radar antenna beam elevation angle to get maximum 50 % beam bloackage, starting from the weather radar observation site.

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The locations of the wind turbines are indicated as three red plus signs in the maps, while the radar location is shown as a black plus sign. Out of the first map ( Fig. 1a) we get the lowest elevation angles with visibility at the center of the radar beam: 2.25°( WT1), 2.10°(WT2) and 2.15°(WT3). With increasing elevation of the radar beam the visibility gets better (s. Fig. 1(b)). At an elevation of 3°all three turbine locations are visible with the whole HPBW (half power beam width) angle.
Given the distances to the wind turbines, ranging between 7.7 to 8.6 km with respect to the radar site, together with the 105 characteristics of the radar antenna (HPBW of 1.25°), a beam broadening between 175 and 195 m can be assumed at the ranges of the wind turbines. Compared to the spatial dimensions of the wind turbines, the beam shape is already larger when it is reaching the target. Due to the fact that the radar measurements are the result of a convolution between the beam shape and wind turbine structures, it is difficult to distinguish return signals from structures that are smaller than the beam shape during the radar scans.

Radar scanning strategy
The scanning strategy of the weather radar system in 2019 consisted in the continuous repetition of a protocol lasting 45 minutes, including three different scan types (PPI, RHI and solar scan). While the PPI and RHI scans were dedicated to the wind turbine measurements, the solar scan is used for the receiver quality control. One PPI sector scan sequence lasted 12 min, one RHI scan sequence took 18 min.

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The sequence of PPI scans is a narrow volume scan in the azimuth sector 331°to 349°consisting of 30 individual PPIs at increasing elevation angles. Regarding the RHI scans a sequence of 81 individual RHIs were set up. The RHI scans are  The detailed parameters of both scan types are listed in Table 3. The movement of the antenna is slow for all scans, ensuring data collection every 0.1°(one radial) in azimuth, while the PRF (Pulse Repetition Frequency) is high enough to ensure a large number of pulses for each radial and a reasonably good unambiguous (Nyquist) velocity range. No speckle or spatial filter were applied with the data acquisition. A Zero-Doppler filter has only been used to post-process some of the gathered power 125 spectra during PPI scanning modes.
With the upgraded system a new scanning method, the fixed-pointing, could be applied in 2020, which should complement the results obtained a year before, by help of a very high temporal resolution of the acquired data in stare-mode. During the fixed-pointing scans, the antenna of the radar was not moving and always pointing to the same wind turbine. For the whole campaign in 2020, we observed only that wind turbine (WT1), where the visibility was best. One goal we wanted to achieve 130 with the stare-mode was to have a complete overview of the variations in time and revolution cycles of the blades. This was not possible to achieve with the slow scanning strategy in PPI and RHI modes of 2019. However, every 2 hours a PPI volume scan similar to the ones during the first campaign was taken in order to get a broader overview across the wind farm area. The data acquisition time for the fixed-pointing measurements is as short as 64 ms. Other relevant characteristics of this new radar scan mode are summarized in Table 4.

Weather radar and wind turbine data
Over the entire measurement campaign in 2019 we gathered in total 612 full PPI and 700 full RHI volume sector scans covering the wind park during the 23 measurement days with its various environmental conditions. The month of March 2019 had a reasonable variability in terms of weather. Wind conditions have been particularly interesting also due to many periods of strong winds. The wind rose plots in Fig. 2 show how the wind speeds and directions were stratified in March 2019 (a) and 140 2020 (b) as seen from a nearby wind profiler. Two main direction modes (from north-east and south-west) are dominating the statistics and this is also visible in the temporal evolution of the absolute, respectively relative, position of the turbine nacelles ( Fig. 3). In this Figure we representatively show the data for wind turbine WT1. As seen relative to the radar angle of attack, the main orientation is centered between 50°and 100°. The rotor speeds r s , which are presented in revolutions per minute, are plotted on top in red and reveal that a r s of about 11 rpm is the main power production operation mode of this kind of turbine.

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The data from the wind turbines has a temporal resolution of 10 minutes and was kindly provided by the wind park operator.
In order to illustrate the narrow sector PPI scans of the weather radar in 2019, the three top plots in Figure 4(a-c) are shown.
At an elevation of 3°PPIs of the horizontal reflectivity Z H , differential reflectivity Z DR and co-polar correlation coefficient are represented on 2019-03-24. The wind turbine clutter is clearly visible at the range from 7.7 to 8.6 km as high Z H , ρ HV and low Z DR and all three turbines can be distinguished from other ground clutter signals. While Z H shows values up to 40-50 dBZ for 150 the given elevation of 3°, Z DR attains low (close to zero) or slightly negative numbers and ρ HV is close to 1 (high correlation between vertical and horizontal returns). For the statistical analyses azimuth elevation plots at a fixed range or range span are used. Figure 4(d-e) show for a specific PPI (d) and RHI (e) scan sequence the maximum horizontal reflectivity within the range span of all the three wind turbines. Below 2°in elevation a software-based blanking was applied to the radiation transmitter for safety reasons. All three wind turbines can be distinguished in this kind of plot. WT1 (left signatures at 339°) with the best 155 visibility has in this example the highest returns of about 60 dBZ within the center region where the nacelle is located. The benefit of the RHI-based results is the larger overview for elevations up to 10°.
In March 2020 the radar was placed exactly at the same location as the year before. The whole campaign lasted 22 days and was dedicated solely to the observation of wind turbine WT1. The radar beam center was targeted at the elevation of the nacelle and thus towards the center of the rotors. The detailed characteristics are summarized in Table 4. In total we gathered 160 2.429 × 10 7 data samples, where one sample (or one radial) consists of 128 averaged radar pulses. The full Z H data set is illustrated also later in Section 3.1 with Fig. 8. Together with the available environmental wind turbine data, which is available at a 10 min resolution scale, we aim at finding relations for the occurrence of radar return maxima and minima as well as their variability.
3 Statistical analysis of the weather radar observations 165 In the following part of the paper, all the horizontal reflectivity Z H measurements and retrieved RCS data obtained from PPI and RHI scans in 2019 are statistically analyzed in order to characterize the returns from the three wind turbines by using the radar data processing framework Pyrad (Figueras i Ventura et al., 2020a). Global statistics considering the median and maximum Z H and RCS are presented. Given the stability of the location of the wind turbine signals, statistics can be computed at fixed ranges, on a two-dimensional plane that is given by azimuth (x-axis) and elevation (y-axis) (s. Sec. 3.1). While radar 170 reflectivity values may be informative, a core information allowing to generalize the measurements collected is the retrieved RCS, usually given in dBsm (dB square meters). Its added value with respect to reflectivity alone is that it is a pure property of the target. The RCS values that will be shown here are retrieved from the inversion of the formula for the radar reflectivity Z. According to Battan (1973) the received lossless power [P r ] = mW by a directional antenna from a single, isolated target can be expressed as: (1) The log-transformed power can be derived by P r = 10·log(P r /P 0 ), where P 0 = 1 mW. In Equation 1, the backscattering cross section or RCS is indicated as σ, the antenna gain as G 0 ≈ π 2 θ H θ V , the radar wavelength as λ, and the transmitted power as P t . θ H and θ V are the horizontal and vertical beam widths in radians. Usually σ is expressed as a scalar and the dependencies on angle and frequency are suppressed, e.g.
[σ] = m 2 , respectively σ dBsm = 10 · log(σ/σ 0 ), where σ 0 = 1 m 2 . Precipitation 180 particles act as distributed scatterers in the volume of air illuminated by the weather radar. The resolution volume V r filled by a transmitted pulse can be approximated by a cylindrical shape, given the radar pulse width τ and the range r: Accounting for the actual distribution of power within the beam generated by a circular parabolic antenna, a correction factor of 1/(2 · ln 2) was introduced by Probert-Jones (1962): The backscattered signal from a volume of randomly distributed scatterers is the sum over all scattered signals. The summation of the backscattered cross sections from precipitation scatterers in a unit volume is called the reflectivity and is defined as The general assumption behind the formulation presented in Equation 4 is that of a pulse volume homogeneously filled by a huge number of randomly distributed backscatterers. For a weather radar the average returned power has to be related to the physical characteristics of the particles within the resolution volume. The Rayleigh approximation of the backscattering cross 195 section of a single water drop σ d can be expressed as 8 https://doi.org/10.5194/amt-2020-384 Preprint. Discussion started: 9 October 2020 c Author(s) 2020. CC BY 4.0 License.
where |K| is related to the complex index of refraction. By changing from σ i to σ d in Equation 4 the radar equation for spherical drops is composed by The final conversion from [Z] = dBZ to the wind turbine RCS σ t used in our study is finally shown by Equation 7.
The conversion factor, which has to be subtracted from the retrieved [Z] = dBZ, for example for WT1 at range r = 7740 m is With the much better temporal resolved measurements acquired in 2020 with the fixed-pointing scan mode of the weather 205 radar, the impact of the turbine orientation, blade pitch angle θ, rotor speed r s and wind speedŪ , as a measure of blade bending, on the retrieved horizontal reflectivities is investigated later in Sec. 3.2. In a first step the relative turbine (nacelle) orientation is solely used to stratify the returns with an azimuth bin of 10°width. Following, in order to measure the strength and direction of possible relationships between the different WT data sets, we perform a correlation analysis based on the Pearson correlation coefficient. In order to simplify the use of a linear regression, we converted the relative nacelle positions 210 α to normalized positions Ψ, such that values between 0 and 1 map symmetrically independent between backward or forward and sideward facing of the WT nacelle. We calculate Ψ simply as Ψ = | sin α|. For clarification, a Ψ value of 0 means that the turbine's angle of attack is either facing towards the radar or away from the radar while a value of 1 shows the sideward case when the angle of attack is perpendicular to the radar beam. With the Ψ parameter a more reasonable calculation of the linear Pearson correlation coefficient is achievable because the polar 360°projection of the turbine position alone has a symmetry. refers to all PPI scans, while for Fig. 6 all RHI scans were processed. As it can be seen in those images, the visibility over the 220 wind turbines was very good for the selected site. At elevation angles lower than 2°sector blanking has been applied, where the radar transmission was turned off for safety reasons. While the elevation span of the PPI scans is enough to fully observe the wind turbines, the increased vertical span of the RHI scans allowed the observation of the returns that are not associated to the main lobes of the radar antenna. signal could not be assigned to a source. Multi-path effects could be a possibility. By looking at the range gates in Fig. 4(f) it is evident that this peculiar signal has its maximum at the same range as the wind turbine WT1, and is thus likely related to the interference with this turbine.
While the location of the intense signals is stable in time, the intensity of the returns varies significantly. This is evident when we look at the differences between the maximum and median Z H values, which are on the order of 20 dB. with the fixed-pointing acquisition mode was as high as one radial collected every 64 ms. This increases the confidence that actual maxima of the radar returns are captured within our long dedicated observation period towards WT1. In order to give an idea about the amount of data that was captured the scatter plot in Fig. 8 is visualized, showing the whole time series of Z H (in black) and the corresponding 10 min moving median values (in red).
The variability of the returns remains extremely high, with typical short-term spans on the order of 20 dB. A first conclusion 260 is that the variability which has been observed during the 2019 field campaign was not caused by the scanning strategy itself.
With the radar stare-mode, frequently higher maxima than during the PPI and RHI scans of 2019 were observed in the reflec-tivity data. Thus the usage of fixed-pointing data acquisition indeed improved the sampling of the right tail of the distribution of Z H values. This is especially important, when worst case scenarios are of interest, e.g. for aviation safety issues. RCS maxima of 44 dBsm, about 4 dBsm higher than what has been observed in 2019, could be derived. From the time series shown in Fig. 8 265 some interesting periods can be identified, when the spread between the maxima and minima of Z H is suddenly increasing.
Between 2020-03-14 and 2020-03-21 such sudden increases were more frequently observed. In Sec. 3.2 we investigate these findings in depth by performing correlation analyses with i. a. the pitch angle θ of the rotor blades.The 10 min moving median mostly stays between 50 and 60 dBZ over the 2020 campaign period, occasionally going up to 65-70 dBZ.
3.2 Impact of WT orientation, blade pitch angle, rotor speed and wind speed on Z H

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Given the availability of the WT and wind sensor data it is possible to perform turbine orientation stratified statistics with Z H , respectively RCS. The first experiment, which has been conducted in 2019, provided non-conclusive results with respect to the orientation of the wind turbines and this was another reason that motivated a second experiment in 2020. Now, with the high temporal resolution data, we are more confident about the obtained results that we intend to show here. Both, March 2019 and March 2020 had similar statistical meteorological wind patterns (s. Fig. 2), which led to comparable distributions of the relative 275 nacelle orientations (s. Fig. 3). To clarify a bit the relative positions, a value of 0°means that the long axis of the rotor blades is perpendicular aligned to the direction of the radar beam center and the WT is pointing towards the radar (left WT schematic in Fig. 3). On the contrary, a value of 180°represents a WT pointing away from the radar and with 90/270°the long axis of the blades is parallel aligned to the center of the radar beam (right WT schematic in Fig. 3).
From the polar plots in Fig. 9(a, c) we see that the relative orientation of the turbine/nacelle is insensitive to the maximum (red scatter points). It is interesting to observe how, in median terms the relative orientations near 180°are associated to higher returns, while for 95 % (not shown) or 99 % quantiles, similar signals are observed also at orientations near 90°and 270°. In conclusion, higher Z H returns and RCS seem to be observed when the nacelle is fully exposed to the incoming radiation in orthogonal directions. It can be argued, that those enhancements of RCS within the 99 th percentiles to values slightly above 35 dBsm are directly linked to the surface area of the WT1 nacelle, where also the center of the radar beam was pointing to.

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The elongated shape of the nacelle indeed leads to larger surface areas in the orthogonal nacelle positions of 90 and 270°, that might explain those peaks in the orientation stratified RCS distribution. The fact that a small offset of about 10°is noticeable in the azimuth cannot be explained by the nacelle orientation alone. Taking into account the circumstance of the very broad radar beam, it is clear that also the rotor blades are biasing the results in the polar plots. Future work should take also into account numerical simulations to assess the complex interactions in more detail.

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The complexity of an operating wind turbine is not only related to the nacelle, respectively rotor orientation (yaw angle) but also to the varying blade pitch angles θ, which are used to control the rotor speed (power production) when the wind speed is changing. The profile of the blade rotates outgoing from the hub towards the blade tip in order to maintain the angle of attack (Gipe, 2004). θ is a parameter that may vary at the time scale of the seconds. Unfortunately, the granularity of the available wind turbine data (10 min resolution) does not allow us to match the observed maxima with the actual wind turbine parameters 300 at the exact same time, but while looking at how the maxima and minima appear in the data (s. Fig. 10) it is reasonable to assume that the blade angle is a key parameter. deflection of a blade is generally known as aero-elastic tailoring (Weisshaar, 1981).
From the viewpoint of a MW-class turbine operator the stability of power production is important when delivering electricity into the grid. When the wind conditions are not good enough (e.g. too low wind speeds) and stable power production can not be assured anymore, the wind turbine is put into a so called sailing position. In such a position the pitch angle of the blades θ is highly increased (θ ∼ 70°) compared to normal operation, allowing the rotor to slowly turn (usually below 1 rpm) while 320 keeping the bearings of the system greased. Further the axial turbine load is constantly varying, which is also important to reduce the mechanical stress. During certain, mostly rare time periods, θ is put over 90°to aerodynamically break the rotors.
Possible reasons are temporal fast changing gusts of wind, for instance during thunderstorm activity, or an external slow-down triggering to reduce i.e. bird and bat fatalities.
Next, a Pearson-based correlation analysis between the WT1 operation data and the radar returns is presented for the fixed-325 pointing measurements of 2020. One idea was to oppose the correlation results with data during a normal (power production) and abnormal (breaking or sailing) wind turbine operation. Therefore a threshold of 1 rpm for the rotor speed has been chosen to sub-divide the re-sampled (10 min) data sets of horizontal reflectivity (Z H,max , Z H,min , Z H,r , Z H,med ) and WT parameters (θ, Ψ, r s ,Ū ). First we present with Fig. 11(a) the correlation heatmap matrix between all the parameters presented before for the whole measurement campaign period in March 2020. For the moving maximum Z H,max (green line in Fig. 10) and the pitch angle a weak positive Pearson coefficient r of 0.32 resulted. More interesting is the result between the moving minimum Z H,min (blue line in Fig. 10) and θ. A strong downhill linear relationship with r = −0.67 is present for them.
However the abnormal turbine modes with less variable blade angles bias this result, and by only taking into account the data where r s ≥ 1 rpm the correlation coefficient is reduced to −0.56. For Z H,max in contrast the change is small with r reaching 0.34.

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Furthermore, when drawing in Fig. 11(a) strong uphill (positive) linear relations can be found between the rotor speed and the moving minimum Z H,min (r = 0.63) and between the blade pitch angle θ and the min/max difference Z H,r (r = 0.64).
From this point of view we deduce that θ is a good measure for the observed variability in the horizontal reflectivity of a wind turbine. Naturally, the rotor speed r s and θ have a very high anti-correlation (r = −0.87) and further it is interesting to see that without sub-dividing the data sets no significant relevant linear relation is evident between the Z H data sets (including the 340 99.9 and 0.1 % quantiles) and Ψ (simplified relative nacelle orientation) or average wind speedŪ (measure of blade bending).
By looking at the r s threshold split correlation heatmaps in Fig. 11(b) and (c), this picture changes. For the r s < 1 rpm case Ψ now has a low positive correlation towards the maximum returns (r = 0.33) and the coefficients forŪ even reach 0.5 (moderate uphill linear relation) when the turbine is in sailing or aero-breaking mode. On the other hand the Z H,r loses the high correlation towards the pitch angle when the rotor is only slowly idling with the wind. This can be explained by the fact 345 that θ is not much adjusting during these abnormal operation modes as it is evident in the top scatter plot of Fig. 12 (vertical aligned scatter points for r s < 1 rpm). In more detail the plots in Fig. 12 show 4 different color coded scatter plots between the blade pitch angle θ (top) or normalized relative yaw angle Ψ (bottom) and Z H,max , respectively Z H,min , below and above the rotor speed threshold of 1 rpm. In addition, the linear regression lines with 95 % confidence intervals are drawn. The maximum returns increase as the blade pitch θ increases, and this is especially true when the turbine rotors rotate slowly (sailing mode).

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We also see a high variability of Z H,min when θ is roughly at 70°or 90°(r s < 1rpm). A positive correlation of Z H,max and negative correlation of Z H,min when the wind turbine is in normal operation mode.
One question that arises is, what is causing the high variability of the minimum and maximum radar returns when θ is The second and more fuzzy and thus difficult WT parameter to assess is the blade bending. One way to increase the transformation of wind energy into power is to produce and use longer blades without a large increase in weight. Such blades, which are in use nowadays, tend to be less stiff and will be easier bended towards the tower with wind load on it. Thus as a first guess, we assume that the blade bending is strongly related to the wind speed. In consequence we try to find now relations between Z H,max andŪ by still keeping the blade pitch in mind. The information of all three variables is combined in the scatter plot of Fig. 13. The WT sailing mode with blade pitch angles close to 70°happens mostly when the average wind speed is basically below the cut-in wind speed of 3 m s −1 , when the power production is not economic or even possible. Clusters of scatter points at high Z H,max are more likely accompanied by θ values of 90°, when the average wind velocity is high. The fact that the turbine is still not going into normal operation during the high wind speed cases might be related to too strong and changing 370 wind gusts making a stable electricity production difficult. For those cases we find also a highly reduced variability of Z H,max .
When the WT is in normal mode (grey scatter points) no obvious linear relation between Z H,max and the wind speed is visible. In order to not overload the information given in the plot, the color coded blade pitch dimension is only shown for the abnormal WT modes (r s < 1 rpm). The tendency for higher Z H,max with increasingŪ is perceivable and adds up to the positive correlation with the change in WT orientation Ψ.

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In conclusion, complex interactions between θ, Ψ andŪ should explain to a large extent the occurrence of the maximum returns as well as the overall captured variability. With this knowledge a statistical methods like OLS (ordinary least square) fits can be deployed to the data as introduced in the next Sect. 3.3.

Ordinary least square fitting to explain Z H,max variability
Here we briefly present the outcome of a ordinary least square model fit for the dependent variable Z H,max (2406 data samples) 380 by using the independent wind turbine parameters θ and Ψ (Pearson r = −0.0051) during normal WT operation (r s ≥ 1 rpm; Fig. 11c). The method should not be applied during the abnormal operation as θ and Ψ have a linear correlation (s. Fig. 11b) and cannot be handled as independent variables anymore. For the computation we make use of the Python package scipy.stats and for more details, also on OLS, we refer to Seabold and Perktold (2010).
The key summary of the OLS model fit results is shown in Table 5. The coefficient of determination, denoted as R-squared, 385 is the proportion of the variance in the dependent variable that is predictable from the explanatory variables. The general use of an adjusted R-squared value is the attempt to account for the phenomenon that R-squared can automatically and spuriously increase when extra explanatory variables are added to the model. In our case there is no difference for both R-squared values, which reach in case of Z H,max 0.914, meaning that over 90 % of the observed variance can be explained by the parameters θ and Ψ. Also with the fact that the p-value of the F-statistic is less than the significance level, our sample data provides sufficient 390 evidence to conclude that the used regression model fits the data better than a model with no independent parameters.
The OLS model can now be used to rebuild the reflectivity time series Z H,max,ols from the independent variables θ and Ψ.
A simple comparison between the original and rebuilded time series for r s ≥ 1 is provided in Figure 14. Time periods of good agreements between the violet and black scatter points can be identified besides those with large differences. With the help of machine learning algorithms in the future, better results are likely to be achieved.

Summary and conclusions
The interaction between wind turbines and radar systems is complex in nature due to a large set of parameters affecting the scattering behavior of the turbine object. In this context, MeteoSwiss was in charge of organizing two measurement campaigns, lasting 23 (2019) and 22 (2020) days each, with a mobile X-band weather radar (METEOR 50DX) in the proximity of the city of Schaffhausen (Switzerland). The area of a small wind park consisting of three large wind turbines was the target area for 400 the radar measurements. The radar was located at a distance between 7.7 and 8.6 km away from the individual wind turbines.
There was a fairly good visibility towards the three wind turbines. The measurements taken during March 2019 were close to a receiver saturation, while during March 2020 and the fixed-pointing radar observations with highest returns reaching 78.5 dBZ a saturation was more likely to happen. Indeed, the observed discrepancy between the correlations of Z H,min /Z H,max and the blade pitch angle θ, for which Z H,min is much higher downhill correlated then Z H,max is uphill correlated, could be attributed 405 to a receiver saturation issue. So to say, the receiver was not anymore able to capture the highest intrinsic returns from the wind turbine.
At the distance of the wind turbines, the beam size was large enough (∼ 200 m) to entirely include the complex obstacle within the beam shape. Measurement data have been collected with a scanning sequence composed of slowly moving PPI and RHI scans, with a repetition time of 45 minutes in March 2019 and with a fixed-pointing antenna observation in March 2020.

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Although the radar data included polarimetric moments and power spectra, the focus of this paper, was the statistical analyses of horizontal reflectivity Z H and radar cross section RCS of large wind turbines for a weather radar operated within the X-band.
The maximum returns are describing a general worst case scenario, which is of interest, for example, to the aviation safety sector.
RCS values on the order of 40 dBsm, with extremely narrow peaks up to 45 to 55 dBsm, for angles of incidence of about 2.5°. For other angles of incidence large decreases between 15 to 30 dBsm resulted. Those simulated values do not excessively deviate from our retrieved results. According to those simulations, peak RCSs occur at extremely precise angles of incidence and the worst case situations actually can be observed at slightly negative incidence angles (Angulo et al., 2015), a setup that could not be realized with the presented measurement campaigns. In those conditions, for wind turbines of similar size with 420 respect to the ones shown in this report, RCS values can rapidly increase to more than 60 dBsm. For future campaigns it may thus be interesting to perform measurements in a site that allows observing wind turbines at negative incidence angles. With the high temporal continuous staring observations up to 44.1 dBsm were reached in case of the closest wind turbine (WT1) with the best visibility from the radar location.
The pattern of the secondary returns depends on the full characteristics of the antenna pattern in all the possible planes, but 425 it is relevant to mention that secondary (or tertiary peaks) have been measured with intensities 20-30 dB lower than the median returns during the measurement campaign in 2019.
Although the derivation of wind turbine RCS is possible by using CEM (commercial computational electromagnetic) tools as proven by Danoon and Brown (2013), the computational requirements are huge and accounting for the incidence angle, radar range, the rotation of the blades and the yaw angle is difficult and requires very large lookup tables. Thus dedicated 430 measurement campaigns with e.g. mobile radars offer another approach to assess wind turbine reflectivity and RCS in a broad range of real environmental scenarios.
An enhancement of median Z H could be related to the nacelle orientation, with the highest values being observed when the wind turbine is facing away with respect to the radar location. Interestingly, the 99 th percentile of RCS showed also enhancements towards 80-90°and 260-270°(sideward facing towards radar). The reason could not be quantitatively deduced.

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A combination of an increase of the effective nacelle area (elongated shape) and change in the blade RCS due to yawing are potential sources.
A short summary of the key results from the correlation and OLS analyses between the WT and Z H data sets at the 10 min time resolution are given below: -The maximum returns increase as the blade pitch angle θ increases, and this is especially true when the wind turbine 440 rotors rotate slowly (sailing or aero-breaking).
-High variability of Z H,min observed, a bit less for Z H,max , when the blade pitch is at 70°or 90°(r s < 1 rpm).
-Positive correlation of Z H,max and negative correlation of Z H,min resulted, when the turbine was in normal (power production) operation mode (r s ≥ 1 rpm).
-For high wind speeds, accompanied by aero-breaking pitch angles, we find a highly reduced Z H,max variability com-445 pared to sailing WT modes in low wind speeds. Additional, a moderate positive correlation (Z H,max vs.Ū ) is present for r s below 1 rpm, which could be related to the aero-elastic bending of the blades.