The potential impact of wind turbines on weather radar performance has been extensively studied in the last few years, with several evidences of wind turbine clutter observations in meteorological radar applications (Isom et al., 2008; Gallardo-Hernando et al., 2011; Norin and Haase, 2012; Vogt et al., 2011; WMO, 2005, 2010). The main objective of these studies is to characterize and try to mitigate the so-called wind turbine clutter (WTC), mainly by means of digital signal processing such as clutter-filtering techniques.

Unfortunately, these solutions are not widely available yet. Meanwhile, the most practical approach to this issue is the prediction of the potential impact on a certain weather radar service before installing a wind farm. In most cases, the identification of a potential impact allows the planning of alternative solutions in order to guarantee the coexistence of wind energy and meteorological radar services.

Wind turbine clutter reflectivity depends on many factors including wind turbine dimensions, wind direction and velocity, angle of incidence and radar frequency (Gallardo-Hernando et al., 2011; Norin and Haase, 2012; Norin, 2015). In order to measure how efficiently radar pulses are backscattered by wind turbines, existing models of wind turbine clutter and weather radar recommendations rely on the turbines' radar cross section (RCS) (Tristant, 2006; ITU-R, 2009; Norin and Haase, 2012). The RCS is the projected area required to intercept and isotropically radiate the same power as the target scatters toward the receiver, and thus it is normally expressed in decibels with respect to a square meter (dBsm) (Skolnik, 2008; Rinehart, 1997).

In this context, the goal of this paper is to propose simplified formulae for the estimation of reflectivity values from wind turbines at frequencies used by weather radars. These formulae aim at being easily implementable in software tools for estimating the potential impact of wind farms on weather radars.

For this purpose, first RCS patterns for different working conditions of the wind turbines are obtained by means of physical optics (PO) simulations and subsequently analyzed. Additionally, separate RCS patterns of the parts of the turbine are also calculated in order to compare the relative contribution of each component. Based on these simulations, a simple algorithm to evaluate the potential impact of a wind farm on a nearby weather radar is proposed.

It should be mentioned that similar studies for characterizing RCS of wind turbines have been carried out for evaluating the impact on different services such as maritime radars (Grande et al., 2014) or television (Angulo et al., 2011). However, as scattering is very dependent on working frequency and illumination conditions, results cannot be extrapolated. Moreover, preliminary results of the analysis presented in this paper are included in a previous communication from the authors (Grande et al., 2015). Those results correspond to a single wind turbine model and a single working frequency. In the present paper, results are extended to three wind turbine models of different size and the three frequency bands assigned to weather radar services; besides, based on the obtained results, a novel formulation for estimating the WTC reflectivity values for weather radar applications is proposed. This work aims at making studies for the prediction of potential impacts between weather radar services and wind farm deployments easier to conduct.

In weather radars, wind turbines may lead to misidentification of precipitation features and to erroneous characterization of meteorological phenomena. These errors may be due to clutter caused by signal echoes from the wind turbines; signal blockage, as the physical size of the wind turbine creates a shadow zone behind them of diminished detection capacity; and interference to the Doppler mode of the radar, on account of frequency shifted echoes from the rotating blades (Angulo et al., 2014; Norin and Haase, 2012; Belmonte and Fabregas, 2010).

The clutter from wind turbines is due to radar echoes coming from a turbine and reaching the radar with a power level higher than the radar detection threshold, preventing the radar from correctly detecting the precipitation level in the affected area. Although most of current radars include signal processing techniques that remove static scattering from turbine masts, the scattered energy will increase the effective noise floor of the radar receiver, which degrades the detection capacity and therefore the data quality obtained by the radar. Detection of precipitation requires a signal that exceeds the noise floor by at least the signal-to-noise ratio. Energy scattered from wind turbines results in the occurrence of increased noise that might cause desired targets to be undetected. Although the signal processing techniques may mitigate the display of false targets generated by the stationary clutter from a wind farm, it will not eliminate effects that raise the noise floor of the radar (Tristant, 2006; Lemmon et al., 2008).

Regarding the Doppler mode of the radar, as it is aimed at detecting moving targets, only the scattering from the blades should be considered in order to determine the influence of a wind turbine on this operation mode.

Therefore, both the clutter phenomenon and the interference to the Doppler mode depend on the scattering characteristics of wind turbines. By contrast, as the blocking of the radar beam is due to the physical obstruction of the radar beam by the wind turbine, the methodology to estimate a potential impact of a wind farm due to signal blockage is not related to the RCS of wind turbines but to the percentage of the beam section blocked by the wind turbine structure (Tristant, 2006; Belmonte and Fabregas, 2010). Consequently, this paper does not focus on addressing the signal blockage estimates.

As the RCS of a wind turbine depends both on fixed parameters, such as the dimensions and materials of each component of the wind turbine, and on variable parameters, such as position of the rotating blades and rotor orientation with respect to the radar, RCS values may vary drastically according to wind turbine working regimes and illumination conditions (Angulo et al., 2011; Grande et al., 2014).

The calculation of RCS values by conventional prediction methods, such as the method of moments (MoM) or the finite difference time domain (FDTD) method, provides accurate results but relies upon extremely detailed representations of the turbine, which requires significant modeling and complex calculations with great computational effort. Consequently, these RCS prediction methods cannot be easily implemented in computer simulation tools for analyzing the potential impact of a specific wind farm.

On the contrary, and due to the absence of simplified formulation, some published guidelines for analyzing the impact of wind turbines on radar services use typical fixed RCS values, disregarding the particular features of each installation (ITU-R, 2009; Tristant, 2006). This is a very simple way to deal with wind turbine scattering, but its main disadvantage is that the proposed RCS values do not take into account the characteristics of the real scenario under analysis: wind turbine dimensions, angle of incidence and working frequency, amongst others. As a result, these proposed typical constant RCS values may lead to important estimation errors.

In this paper, a simplified formulation for determining accurate WTC reflectivity values is proposed. The presented method requires neither complex calculations nor the use of a simulation tool, whereas it provides RCS values adapted to the particular features of the case under analysis: dimensions of the wind turbine models, illumination conditions and working frequency.

The main objective of this paper is to develop an estimation model of wind turbine reflectivity values for weather radars that consists in a simplified formulation, is easy to apply in the development of the impact studies, and does not require a complex software tool or a high amount of resources.

The estimation model should fulfill the following conditions.

Despite being a simplified formulation, the model should provide accurate radar cross-section values, which are directly translated into reflectivity values.

As mentioned in Sect. 3.2, simulations have been carried out for three frequencies representative of the different weather radar frequency bands (2.80, 5.65 and 9.40 GHz) and three wind turbine models based on actual commercial turbines.

As an example, Figs. 2 to 4 show the vertical variation of the RCS patterns of wind turbine models 1 to 3 for a specific rotor orientation for the three frequencies under analysis. It can be observed that the RCS patterns show great variability and a very directive main lobe is noticeable in all cases.

This maximum value of the RCS corresponds to an illumination direction of θ=89.56∘ with respect to the zenith in case of WT model 1, θ=89.48∘ in case of WT model 2, and θ=89.42∘ for WT model 3. Taking into account the slant surface of the masts, these directions correspond to the direction normal to the mast surface of each wind turbine model. As expected, the maximum RCS value is larger for the tallest wind turbine. Moreover, when comparing Fig. 2 to Fig. 4, it is clearly observed that the main lobe is both higher and narrower as the frequency increases. This maximum value of the RCS in the vertical pattern is maintained for all the azimuth values due to the symmetry of the mast in the horizontal plane.

In order to identify the contribution of the blades and nacelle, for the highest frequency and a specific rotor orientation, the RCS of WT model 3 is depicted in Fig. 5 for different positions of the blades (every 30∘ in the rotation movement). The RCS pattern of the isolated mast is also depicted in Fig. 5. As observed in the figure, whereas the contribution from the blades varies in amplitude and position with the rotation movement, the maximum RCS of the wind turbine is constant and it is clearly generated by the mast. Figure 5 also shows that the main contribution from the rotor is due to a blade being in vertical position (see curves related to P000 and P060 in Fig. 5).

As it can be expected, the contribution from the blades is strongly dependent on the rotor orientation with respect to the incident radar signal, whereas the contribution from the mast remains invariable in the horizontal plane due to its symmetry with respect to the vertical axis of the mast. This statement is confirmed by Fig. 6, in which the vertical RCS patterns of WT model 2 are compared for different illumination directions in the horizontal plane (different ϕ values).

A first important conclusion obtained from the extensive set of simulations carried out is that the main scatterer of the wind turbine for the different frequency bands used for weather radar is the supporting mast. Moreover, the main feature of the scattering pattern of the mast is a main lobe normal to the slant surface, extremely directive in the vertical plane and omnidirectional in the horizontal plane. The scattering from the mast can be approximated by the RCS of a right circular cylinder, which will be the basis of the proposed model for calculating the wind turbine RCS values, as later described in Sect. 5.1.

The blades, by contrast, provide variable levels of signal scattering depending on the rotor orientation and blade positions. Despite the variability of the scattering from the blades, their contribution to the total RCS of the wind turbine is always significantly lower than the amplitude of the main lobe due to the mast. Therefore, in order to provide a worst-case assumption with respect to the signal scattered by the blades, the proposed scattering model will provide an upper limit to the RCS values from the blades, as will be shown in Sect. 5.2.

In order to estimate the potential impact of a wind farm on a weather radar service, one of the main issues to be analyzed is wind turbine clutter reflectivity, which is directly related to the radar cross section of wind turbines.

A preliminary study about possible interference problems is the most appropriate way to proceed in order to make the coexistence of wind energy and meteorological services possible. To do so, an estimation of the RCS of the wind turbines to be installed is a must. Although it is possible to obtain RCS values by conventional methods such as MoM and FDTD, they require detailed representations of the wind turbines' design and complex calculations, which are too time consuming and difficult to obtain. On the contrary, typical values that do not take into account the particular features of the case under analysis may lead to significant errors in the impact analysis.

In this paper, the RCS patterns of wind turbines for the weather radar working frequencies have been analyzed. From the obtained results, it can be concluded that the mast is the main scatterer of the wind turbine, featuring a very directive lobe in the direction perpendicular to the slanted surface of the mast. The blades, by contrast, contribute to the total RCS of the wind turbine with secondary lobes that depend on the rotor orientation with respect to the illumination direction and the blades' position.

Based on the above-mentioned conclusions, a simple RCS model to characterize backscattering from wind turbines in the weather radar bands has been proposed. This model takes the RCS from the mast as a reference to estimate the maximum value of the RCS pattern of the whole wind turbine and then calculates the maximum RCS from the blades taking into account the actual dimensions of the wind turbine model. Finally, and assuming that the whole wind turbine is included within the beam cell resolution of the radar, the WTC reflectivity can be directly obtained.

The proposed RCS model can be used to estimate the maximum clutter due to the presence of a wind turbine, estimating the scattered power from the mast. However, even if the Doppler radar under study uses a clutter filter that suppresses stationary objects, the rotating blades of a wind turbine might still be detected. As proved in Norin (2015), weather information from radar cells affected by a wind turbine is not always lost. In fact, when precipitation gives rise to reflectivity values stronger than those due to wind turbines, radar data could still be used. Therefore, the reflectivity model proposed in this paper is of interest not only to assess a potential detrimental impact on the performance of a weather radar but also to evaluate to which extent this degradation might exist if reflectivity values from precipitation and wind turbine blades are compared.

This simple WTC reflectivity model aims at being implemented in software planning tools and is expected to make the preliminary impact studies of wind farms on weather radar services easier.