The term “raw” IQ-data refers to IQ-data that has not been filtered using a clutter filter or a Doppler clutter filter. The IQ-data processing can be divided into two basic categories: time domain processing and frequency domain processing. In time domain, the complex IQ-signals samples are used to calculate autocorrelations and then the autocorrelations are used to compute the moments, whereas in frequency domain, the complex IQ-signals are first calculated to reveal Doppler power spectrum and then corresponding autocorrelations, which are then used to compute the moments. Time domain algorithms are very efficient, requiring minimal storage and computational power, but they are not as adaptive or flexible as frequency domain algorithms (SIGMET, 2006).

We should now consider the description of the original complex signal (Spq), which can be calculated by combining two simultaneous samples of I and Q from a given range-bin into a single complex value, and represented as: 1Spq=Ipq+jQpq where j2=-1, q represents transmit polarisation state, and p represents receive polarisation state. From this complex signal (Spq), the average back scattered power (Ppq) for time series at a given range-bin can be calculated as: 2Ppq=〈|Spq|2〉=1M∑n=1M(Spqn)∗Spqn where M is total number of pulses in the time average, Spq represents the original time series, and ∗ represents a complex conjugate. For meteorological radar, Ppq is proportional to the sum of the meteorological signal power (Ps), clutter power (C), and noise power (N).

The amount of transmitted power received back by the radar receiver is proportional to radar reflectivity (Z), and it is affected by the following physical parameters of the object: its size (target cross-section), shape (round, flat, oblate, etc.), material composition (liquid, solid, frozen, dry, wet, mixed, etc.), and particle concentration in a sample volume (Skow, 2013).

To calculate radar reflectivity from received power, we must first consider the monostatic radar equation for a single point target, which is as follows: 3PRX=PTXG2λ2σ4π3r4 where PRX [W] and PTX [W] are the received and transmitted powers, G [dBi] is the directional antenna gain, λ [m] is the wavelength, σ [m2] is the single point target radar scattering cross section, and r [m] is the target range. In the derivation of the radar equation for meteorological targets, one major assumption is that the pulse volume illuminated by the radar beam is uniformly filled with scattering targets (Melvin and Scheer, 2014), and the received power is simply the sum of the power scattered by all of the individual scattering centres in the pulse volume given as: 4PRX=PTXG2λ24π3r4∑iσi. The backscattering cross section per unit volume, η [m2 m-3], is defined as: in the pulse volume given as: 5η=1Vp∑iσi, where Vp [m3] is an illuminated pulse volume (see Fig. 1). By solving above Eq. (5) for ∑iσi, and substituting back into Eq. (4) gives 6PRX=PTXG2λ2ηVp4π3r4. The η can be further approximated for the raindrops using the Rayleigh approximation, and their individual scattering cross section per unit volume can be express as follows: 7η=∑iπ5K2Di6λ4, where K is the dielectric factor related to the complex index of refraction, and Di [mm] is the raindrop diameter. The Vp can be approximated as: 8Vp=πcτP2⋅rθH2⋅rθV2=πcτPr2θHθV8, where c [m s-1] is speed of light, τP [s] is pulse duration, θH [rad] and θV [rad] are horizontal and vertical beam widths.

By combining Eqs. (6), (7), (8), and a correction factor of 1/ (2. ln 2) was introduced by Probert-Jones to account for the actual distribution of power within the beam generated by a parabolic antenna (Probert-Jones, 1962), we can rewrite receive power equation for weather radar as follows: 9PRX=PTXG2cτPθHθVπ3|K2|2ln2512r2λ2∑iDi6. In Eq. (9), ∑iDi6 can be described as equivalent radar reflectivity factor (Z) in [mm6 m-3] In this context, we can be rewrite Eq. (9) as follows: 10PRX=PTXG2cτPθHθVπ3|K2|2ln2512λ21r2Z. The Z is a physical quantity, which makes weather radar measurement independent to platform. In this context, Z can be given as: 11Z=PRXr2C, where C is a radar constant. Z should be normalized with Z0. Z0 is called the calibration reflectivity factor. It is the equivalent radar reflectivity factor at the reference range when the return signal power is equal to the noise power (i.e. SNR = 0 dB). It is sometimes called the minimum detectable dBZ or dBZ0 (decibels of Z) at references range (r0) 1 km, though it is more correct to call it the 0 dB SNR detection level. Z0 is given as mathematically as follows: 12Z0=Nr02C, where N is the average noise power. Reflectivity is measured in dBZ (decibels of Z), where Z represents the radar reflectivity-factor. Finally, the Z in dB at a given range-bin can be calculated as: 13ZdB=10log⁡10PRX-NN+dBZ0+20log⁡10r+αr, where PRX is received average back scattered power, 20log⁡10r is range normalization expressed in dB-form, α [dB km-1] is a two-way atmospheric path attenuation (the default value for a C-band system is 0.016 dB km-1), and r [km] is target distance from the radar.

Differential reflectivity (ZDR) is an important factor in determining the size of the target. It is a reflectivity weighted shape of the scatterers that tends to increase with more oblate targets (rain-drops) within the Rayleigh scattering regime. ZDR in dB is a measure of the difference between the horizontal and vertical reflectivities-factors, and can be calculated at a given range-bin as: 14ZDRdB=dBZHH-dBZVV. Typically, small ZDR values represent particles such as drizzle and small hailstones that are uniformly shaped. ZDR values greater than zero are characteristic of rain and melting hail. ZDR values less than zero are not always seen but can be seen sometimes in areas of vertically oriented ice crystals inside thunderstorms.

Differential propagation phase (PHIDP) is a measure of the phase difference between horizontally and vertically polarized pulses at a given range-bin, and can be calculated in “degrees” as: 15PHIDP∘=Arg1M∑n=1M(SVVn)∗SHHn. PHIDP increases rapidly for heavy rain because horizontally polarized pulses propagate slower than vertically polarized pulses, the horizontal phase appears to lag behind the vertical phase at least in C-band, resulting in positive PHIDP. Horizontally oriented particles contribute positive PHIDP values, whereas vertically oriented particles result in negative values. Non-meteorological targets tend to have complex and noisy PHIDP values.

Pulse pair processing (PPP) is common Doppler processing in meteorological radar. The mean Doppler velocity (V) is obtained directly from the autocorrelation argument at the first lag at a given range bin, and can be calculated in [m s-1] as: 16Vpqms-1=λ4πTS⋅Arg1M-1∑n=1M-1(Spqn)∗Spqn+1, where λ is the radar wavelength [m], TS is the sampling time [s] (1/pulse repeat frequency(PRF)). The argument of the autocorrelation at a first-lag is restricted to the interval [-π, π]. If the absolute value of the measured true velocity of the scatterers is greater than λ/4TS, then the measured true velocity is aliased into the interval [-λ/4TS, λ/4TS], which is known as the Nyquist interval.

Correlation coefficient (RHOHV) is a measure of the similarity between horizontally and vertically polarized backscattered pulses, and can be calculated as: 17RHOHV=1M∑n=1M(SHHn)∗SVVn1M∑n=1M(SHHn)∗SHHn1M∑n=1M(SVVn)∗SVVn. RHOHV is a dimensionless quantity that ranges between 0 to 1, and extremely beneficial for distinguishing or identifying meteorological and non-meteorological targets. High-RHOHV (more than 0.97) denotes areas of consistent rain or snow. A low-RHOHV (less than 0.8) is often caused by scattering from non-meteorological targets such as birds, insects, and man-made structures. A moderate-RHOHV (between 0.8 and 0.97) might reflect a variety of precipitation types, sizes, or states (Melvin and Scheer, 2014).

Figures 3 and 4 show the resulting plots of raw IQ-signals and radar moments for both horizontal (h) and vertical (v) polarization channels, recorded during events with precipitation (rain) in the direction of the WP (between green bars), with an RHI scan at a fixed azimuth angle of 69.23∘ and lower elevation angles ranging from 0.23 to 0.76∘.

Figure 3 shows backscattering from the WTs (left) and WTI (right) using raw I and Q-signals plots. Backscattering from the WTs (between green bars) was significantly higher than backscattering from meteorological objects (here, rain-drops), as seen in Fig. 3 (left). Except for ground clutter at 12 km, the intensity levels of the I and Q signals between 11 and 13 km were observed to be low in comparison to the WTI regions beyond 13 km in Fig. 3 (right).

Figure 4 shows radar moments plot during events with precipitation (rain). WTs and WTI had a direct impact on all of the moments in region R2 (between green bars). The main finding was that WTI caused a slow upward trend in moments Zh, Zv, ZDR, Vh, and Vv in regions R1 and R2. At DWD, the reflectivity threshold values for thunderstorm and hail are 46 and 55 dBZ, respectively (Seltmann and Böhme, 2017). Zh and Zv values in region R2 were observed higher than 55 dBZ, resulting in a false hail detection on the weather radar display. WTs are massive tall structure with relatively higher vertically polarized reflectivity (Zv) than horizontally polarized reflectivity (Zh), resulting in negative ZDR values where the WTs were located in region R2. Due to the rotating blades of the WTs, the radial velocities Vh and Vv were measured higher for both channels in region R2 than the actual wind velocity of -8 to -6 m s-1. During precipitation events, WTI had almost no impact on PHIDP measurement except for region R2. A RHOHV was observed between 0.8 to 0.99 in region R2. WTI had almost no impact on the RHOHV in region R1, but in the shadowing region RHOHV was noticeable impacted up to 17 km and thereafter minor vibration observed throughout the 20 km range.

Figures 5 and 6 show the resulting plots of raw IQ-signals and radar moments for both horizontal (h) and vertical (v) polarization channels, recorded during events without precipitation (clear-air) in the direction of the WP (between green bars), with an RHI scan at a fixed azimuth angle of 69.23∘ and lower elevation angles ranging from 0.26 to 0.80∘. As no meteorological targets were present during the measurement, the recorded raw IQ-data only contains ground clutters and their interferences.

Figure 5 shows backscattering from the WTs (left) and WTI (right) using raw I and Q-signals plots. Backscattering from the WTs in Fig. 5 (left) was observed to be notably higher in comparison to the events with precipitation in Fig. 3 (left). Figure 5 (right) shows a similar WTI regions as stated in Sect. 3 with the exception of ground clutters around ranges of 11 and 12 km. The intensity levels of the I and Q signals were observed to be considerably reduced within the close shadowing range of 15.5 to 17 km.

Figure 6 shows radar moments plot during events without precipitation (clear-air). WTs and WTI had a direct impact on all of the moments in the region R2 (between green bars). Very similar reflectivities values greater than 55 dBZ were measured for both channels in comparison to those measured with precipitation events (Fig. 4), exceeding threshold values for thunderstorm and hail, despite the fact that there were no precipitation events during the measurement. Here, Positive reflectivity values were observed in regions R1 and R3 due to WTI, resulting in light rain on the radar display. Both ZDR and PHIDP between 13 and 17 km oscillated between a wide range of positive and negative values due to WTs and WTI, resulting in noisy measurements and no weather scenario prediction in weather radar operations. The real wind speed during the measurement was near 0 m s-1, and the observed same wind speed in region R2 was due to the fact that there were no rotating blades. In the regions R1 and R2, the observed velocities trend from negative to positive with a centered around 0 m s-1 for both channels, indicating a non-realistic detection of a tornado or mesocyclone on the radar display. A RHOHV was observed between 0.57 to 0.98 in region R2 and was noticeably impacted in region R1 and up to 17 km in shadowing region R3 due to WTI.