Polarimetry

Spectral polarimetric variables can be calculated for two configurations: STSR and LDR.

Scheme of the polarimetric configurations

Scheme of the polarimetric configurations.

LDR mode

With this configuration, the LDR can be calculated directly

\[\mathrm{LDR} = \frac{<E_\mathrm{x}^2>}{<E_\mathrm{c}^2>}\]

LDR and LDRmax

The polarimetric properties are calculated as a peak average (with filtering of cross-channel noise and decoupling) as well as at the maximum of the co-channel reflectivity (ignoring cross-channel noise level and decoupling).

Illustration of LDR and LDRmax

Illustration of LDR and LDRmax.

STSR mode

A radar in STSR mode configuration transmits and receives the signal Simultaneous in the V and H channel. The co- and cross channel signal have to be calculated [Myagkov_et_al_2016]. In the files provided for the RPG FMCW the total spectra are saved in the VSpec variable, \((H + V + 2 \,\operatorname{\mathbb{R}e} \{\mathrm{Cov}\})/4\), while the H spectrum is given as it is.

  • (re-)calculate the V spec
  • calculate spectral rhv
  • calculate the LDR

With the STSR configuration, the LDR cannot be observed directly, but has to be calculated from the correlation coefficient. Following the assumption of isotropic scatterers [Galletti_Zrnic_2012] and reflection symmetry [Galletti_et_al_2011], as done in rpgpy calc_spectral_LDR():

\[\mathrm{SLDR} = 10 \log_{10} \left( \frac{1-\varrho_\mathrm{hv}}{1+\varrho_\mathrm{hv}} \right)\]

With \(\varrho_\mathrm{hv} = \varrho_s\) for vertical looking observations (Eq. 12 [Galletti_Zrnic_2012]).

Alternatively, there is also an alternative approach by Myagkov [Myagkov_pers_comm]:

\[\begin{split}\mathrm{SLDR} &= 10 \log_{10} \left( \frac{Z_\mathrm{cx}}{Z_\mathrm{co}} \right) \\ Z_\mathrm{cx} &= \left( Z_\mathrm{h} + Z_\mathrm{v} \right) \left(1 - \varrho_s \right) \\ Z_\mathrm{co} &= \left( Z_\mathrm{h} + Z_\mathrm{v} \right) \left(1 + \varrho_s \right)\end{split}\]

where low signals in the cross-channel can be more easily filtered.

[Galletti_et_al_2011]Galletti, M., Zrnic, D.S., Melnikov, V.M., Doviak, R.J., 2011. Degree of polarization: theory and applications for weather radar at LDR mode, in: 2011 IEEE RadarCon (RADAR). Presented at the 2011 IEEE Radar Conference (RadarCon), IEEE, Kansas City, MO, USA, pp. 039–044. https://doi.org/10.1109/RADAR.2011.5960495
[Galletti_Zrnic_2012](1, 2) Galletti, M., Zrnic, D.S., 2012. Degree of Polarization at Simultaneous Transmit: Theoretical Aspects. IEEE Geosci. Remote Sensing Lett. 9, 383–387. https://doi.org/10.1109/LGRS.2011.2170150
[Myagkov_et_al_2016]Myagkov, A., Seifert, P., Bauer-Pfundstein, M., and Wandinger, U., 2016. Cloud radar with hybrid mode towards estimation of shape and orientation of ice crystals, Atmos. Meas. Tech., 9, 469–489, https://doi.org/10.5194/amt-9-469-2016
[Myagkov_pers_comm]personal communication