1. Introduction and Motivation

The polarimetric parameter Slanted Linear Depolarization Ratio (SLDR) is normally delivered by a SLDR-mode cloud radar, implemented based on the conventional LDR mode by 45° rotation of the antenna system around the emission direction. SLDR is relevant to describe microphysics due to its strong sensitivity to shape and low sensitivity to the wobbling effect of particles at different antenna elevation angles (Matrosov et al., 2001, 2005, 2012, Reinking et al., 2002). A new method was developed, the VDPS method, aiming to determine the in-cloud particle shape using a SLDR mode 35-GHz scanning cloud radar (Teisseire et al., 2023, preprint). However, there is another way to calculate SLDR from hybrid-mode cloud radar allowing to use the VDPS method. The SLDR calculation mode is depicted in the second part and illustrated by a few case studies in a third part. Finally, in the last part of this report, we will elaborate on the advantages and weakness of the SLDR calculation.

2. SLDR Calculation

According to Myagkov et al., 2016a, it is possible to derive SLDR in the slanted basis, which cannot be directly measured in hybrid mode. The corrected coherency matrix can be represented in the linear basis rotated by 45°. However, it is difficult to rotate the coherency matrix by exactly 45° and this requires several calibrations of the initial coherency matrix. Basically h + v corresponds to a linear polarization when the phase shift at transmission is equal to 0. Furthermore, this linear polarization is at 45° angle when the h and v components have the same amplitude. Indeed, the phase and the magnitude of the h and v signals have to be correctly calibrated to obtain realistic values of SLDR after rotation of the coherency matrix by 45°. A way to calibrate the magnitude is proposed by Ferrone et al., 2021, aiming to calculate an interpolation of the median ZDR value of the chosen radar volumes performed in both rain and snow, during a Plan Position Indicator (PPI) scans at 90∘ elevation. Regrettably, this study does not account for phase shift transmission (treated as zero) due to the unavailability of a reliable method for its evaluation, introducing a potential source of error.

3. Results

During my stay in EPFL, I worked with the LTE team which is very experienced in radar calibration. The results presented in this section were taken from measurements recorded during the ICEGENESIS campaign deployed in 2021 in La Chaux-de-Fonds (Jura mountains), Switzerland.

1. Spectrograms at Zenith Pointing

   We needed some time to find the most suitable mathematical formula to calculate SLDR considering the antenna calibration. We started to test the formula on zenith pointing Doppler spectra in order to validate the applicability of the equation.

   1. Calculated SLDR in Rain
      

      Figure 1a: Spectrogram of SNR.

      

      Figure 1b: Spectrogram of SLDR.

      Figure 1: Spectrogram of (a) SNR and (b) SLDR at zenith pointing from radar measurements recorded on 28 January 2021 at 10:30 UTC during the ICEGENESIS campaign.

      We can start by examining a basic case study that revolves around a rain event. In Fig. 1, we can identify the melting layer around 300-400m height, characterized by an increase in fall velocity of particles and high values of SLDR (Fig. 1b). Below the melting layer, we can observe high values of SNR, associated with low values in SLDR around -25 dB, meaning that particles don’t depolarize. This configuration describes liquid droplets, spherical particles, consistent with the first assumption.

   2. Multi-Mode Detection

      In Fig. 2a, we can discern a secondary spectral mode in the SNR spectrogram, characterized by a near-zero fall velocity. This secondary mode is particularly noteworthy in Fig. 2b, representing a calculated SLDR spectrogram, by higher SLDR values describing columnar crystals. Apart from this specific region, the calculated SLDR values remain relatively low at zenith pointing, typically hovering around -25 dB. These values are within a reasonable range when observing directly at the zenith.

      

      Figure 2a: Spectrogram of SNR.

      

      Figure 2b: Spectrogram of SLDR.

      Figure 2: Spectrogram of (a) SNR and (b) SLDR at zenith pointing from radar measurements recorded on 27 January 2021 at 15:37 UTC during the ICEGENESIS campaign.
2. RHI Scans from 0° to 90° Elevation Angle
   
   Figure 3: RHI scan from 0° to 90° elevation angle of SLDR from radar measurements recorded on 28 January 2021 at 10:30 UTC during the ICEGENESIS campaign.

   Following the validation of the SLDR calculation method using Doppler spectra at zenith pointing, we proceeded to apply it in tests involving RHI scans conducted across elevation angles ranging from 0° (horizontal pointing) to 90° (zenith pointing). In Fig. 3, the melting is well recognizable around 500m height. Below the melting layer, we can observe consistently low SLDR values at all elevation angles, indicating the presence of spherical particles like liquid droplets.

   Figure 4 does not reveal the presence of a melting layer. However, in the lower portion of the cloud, there is a substantial rise in SLDR values as we move from a 90° to a 20° elevation angle, suggesting the presence of oblate particles, like snowflakes. Above this layer we have a less pronounced gradient of SLDR from 90° to 0° elevation angle indicating that we could have plates (Matrosov et al., 2012, Reinking et al., 2001). Towards the upper part of the cloud, we can observe high SLDR values at all elevation angles, indicating the presence of prolate particles, specifically columnar crystals.

   
   Figure 4: RHI scan from 0° to 90° elevation angle of SLDR from radar measurements recorded on 28 January 2021 at 10:30 UTC during the ICEGENESIS campaign.

4. Conclusion

My stay at EPFL provides me with the opportunity to deepen my understanding of antenna calibration and to develop a formula capable of calculating SLDR through the use of a STSR-mode scanning cloud radar. This SLDR calculation method can be applied to other radar systems and has been effectively tested on MBR7, a hybrid-mode radar from TROPOS, with successful results.

Nonetheless, the benefit of employing SLDR measurements lies in the 45° rotation of the antenna around the emission direction. This rotation reduces the sensitivity of polarimetric measurements to the wobbling effect, making them more sensitive to the particle shape determination. In my view, when we measure in hybrid mode and rotate only the matrix, we forfeit the advantages offered by using SLDR.