Interpretation of Polarimetric Radar Covariance Matrix for Meteorological Scatterers: Theoretical Analysis

Alexander V. Ryzhkov Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman, Oklahoma

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Abstract

A simple model of the radar scattering by atmospheric particles is used to interpret all elements of the covariance scattering matrix. The components of the covariance scattering matrix and corresponding polarimetric variables are expressed via a limited number of integral parameters that characterize distributions of sizes, shapes, and orientations of meteorological scatterers.

The co–cross-polar correlation coefficients ρxh and ρ measured in the horizontal–vertical linear polarization basis are the major focus of this study. It is shown that the magnitudes of both coefficients are almost entirely determined by orientation of particles and do not depend on particle sizes and shapes. The phases of these coefficients can be used to detect the presence of melting hail or wet snow in the radar resolution volume.

A model of the mean canting angle of raindrops varying along a propagation path is developed to examine effects of propagation on the depolarization variables such as ρxh, ρ, and linear depolarization ratio. Analysis shows that depolarization variables are very sensitive to the mean canting angle averaged over a long propagation path.

Corresponding author address: Dr. Alexander V. Ryzhkov, CIMMS/NSSL, 1313 Halley Circle, Norman, OK 73069.

Email: ryzhkov@nssl.noaa.gov

Abstract

A simple model of the radar scattering by atmospheric particles is used to interpret all elements of the covariance scattering matrix. The components of the covariance scattering matrix and corresponding polarimetric variables are expressed via a limited number of integral parameters that characterize distributions of sizes, shapes, and orientations of meteorological scatterers.

The co–cross-polar correlation coefficients ρxh and ρ measured in the horizontal–vertical linear polarization basis are the major focus of this study. It is shown that the magnitudes of both coefficients are almost entirely determined by orientation of particles and do not depend on particle sizes and shapes. The phases of these coefficients can be used to detect the presence of melting hail or wet snow in the radar resolution volume.

A model of the mean canting angle of raindrops varying along a propagation path is developed to examine effects of propagation on the depolarization variables such as ρxh, ρ, and linear depolarization ratio. Analysis shows that depolarization variables are very sensitive to the mean canting angle averaged over a long propagation path.

Corresponding author address: Dr. Alexander V. Ryzhkov, CIMMS/NSSL, 1313 Halley Circle, Norman, OK 73069.

Email: ryzhkov@nssl.noaa.gov

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  • Antar, Y. M. M., and A. Hendry, 1987: Correlation techniques in two-channel linearly polarized radar systems. Electromagnetics,7, 17–27.

    • Crossref
    • Export Citation
  • Aydin, K., and T. A. Seliga, 1984: Radar polarimetric backscattering properties of conical graupel. J. Atmos. Sci.,41, 1887–1892.

    • Crossref
    • Export Citation
  • Balakrishnan, N., and D. S. Zrnić, 1990: Use of polarization to characterize precipitation and discriminate large hail. J. Atmos. Sci.,47, 1525–1540.

    • Crossref
    • Export Citation
  • Beard, K. V., and A. R. Jameson, 1983: Raindrop canting. J. Atmos. Sci.,40, 448–454.

    • Crossref
    • Export Citation
  • Brandes, E. A., A. V. Ryzhkov, and D. S. Zrnić, 2001: An evaluation of radar rainfall estimates from specific differential phase. J. Atmos. Oceanic Technol.,18, 363–375.

    • Crossref
    • Export Citation
  • Bringi, V. N., and A. Hendry, 1990: Technology of polarization diversity radars for meteorology. Radar in Meteorology, D. Atlas, Ed., Amer. Meteor. Soc., 153–190.

    • Crossref
    • Export Citation
  • ——, V. Chandrasekar, N. Balakrishnan, and D. S. Zrnić, 1990: An examination of propagation effects on radar measurements at microwave frequencies. J. Atmos. Oceanic Technol.,7, 829–840.

    • Crossref
    • Export Citation
  • Brunkow, D. A., P. C. Kennedy, S. A. Rutledge, V. N. Bringi, and V. Chandrasekar, 1997: CSU-CHILL radar status and comparison of available operating modes. Preprints, 28th Conf. on Radar Meteorology, Austin, TX, Amer. Meteor. Soc., 43–44.

  • Caylor, I. J., and V. Chandrasekar, 1996: Time-varying ice crystal orientation in thunderstorms observed with multiparameter radar. IEEE Trans. Geosci. Remote Sens.,34, 847–858.

    • Crossref
    • Export Citation
  • Doviak, R. J., V. N. Bringi, A. V. Ryzhkov, A. Zahrai, and D. S. Zrnić, 2000: Considerations for polarimetric upgrades to operational WSR-88D radars. J. Atmos. Oceanic Technol.,17, 257–278.

    • Crossref
    • Export Citation
  • Hendry, A., Y. M. M. Antar, and G. C. McCormick, 1987: On the relationship between the degree of preferred orientation in precipitation and dual-polarization radar echo characteristics. Radio Sci.,22, 37–50.

    • Crossref
    • Export Citation
  • Holt, A. R., 1984: Some factors affecting the remote sensing of rain by polarization diversity radar in the 3-to 35-GHz frequency range. Radio Sci.,19, 1399–1412.

    • Crossref
    • Export Citation
  • ——, and J. W. Shepherd, 1979: Electromagnetic scattering by dielectric spheroids in the forward and backward directions. J. Phys. A Math. Gen.,12, 159–166.

    • Crossref
    • Export Citation
  • ——, V. N. Bringi, and D. Brunkow, 1999: A comparison between parameters obtained with the CSU-CHILL radar from simultaneous and switched transmission of vertical and horizontal polarization. Preprints, 29th Int. Conf. on Radar Meteorology, Montreal, PQ, Canada, Amer. Meteor. Soc., 214–217.

  • Hubbert, J. C., V. N. Bringi, and G. Huang, 1999: Construction and interpretation of S-band covariance matrices. Preprints, 29th Int. Conf. on Radar Meteorology, Montreal, PQ, Canada, Amer. Meteor. Soc., 205–207.

  • Jameson, A. R., 1985: Deducing the microphysical character of precipitation from multiple-parameter radar polarization measurements. J. Climate Appl. Meteor.,24, 1037–1047.

    • Crossref
    • Export Citation
  • ——, 1987: Relations among linear and circular polarization parameters measured in canted hydrometeors. J. Atmos. Oceanic Technol.,4, 634–645.

    • Crossref
    • Export Citation
  • Krehbiel, P., T. Chen, S. McCrary, W. Rison, G. Gray, and M. Brook, 1996: The use of dual-channel circular-polarization radar observations for remotely sensing storm electrification. Meteor. Atmos. Phys.,59, 65–82.

    • Crossref
    • Export Citation
  • Lutz, J., B. Rilling, J. Wilson, T. Weckwerth, and J. Vivekanandan, 1997: S-Pol after three operational deployments, technical performances, sitting experiences, and some data examples. Preprints, 28th Conf. on Radar Meteorology, Austin, TX, Amer. Meteor. Soc., 286–287.

  • Matrosov, S. Y., R. F. Reinking, R. A. Kropfli, and B. W. Bartram, 1996:Estimation of ice hydrometeor types and shapes from radar polarization measurements. J. Atmos. Oceanic Technol.,13, 85–96.

    • Crossref
    • Export Citation
  • McCormick, G. C., and A. Hendry, 1974: Polarization properties of transmission through precipitation over a communication link. J. Rech. Atmos.,8, 175–187.

  • ——, and ——, 1975: Principles for radar determination of the polarization properties of precipitation. Radio Sci.,10, 421–434.

  • Metcalf, J. I., 1988: A new slant on the distribution and measurement of hydrometeor canting angles. J. Atmos. Oceanic Technol.,5, 571–578.

    • Crossref
    • Export Citation
  • Oguchi, T., 1983: Electromagnetic wave propagation and scattering in rain and other hydrometeors. Proc. IEEE,71, 1029–1078.

    • Crossref
    • Export Citation
  • Olsen, R. L., 1981: Cross-polarization during precipitation on terrestrial links: A review. Radio Sci.,16, 761–779.

    • Crossref
    • Export Citation
  • Pruppacher, H. R., and R. L. Pitter, 1971: A semi-empirical determination of the shape of cloud and rain drops. J. Atmos. Sci.,28, 86–94.

    • Crossref
    • Export Citation
  • Ryzhkov, A. V., 1991: Polarimetric information measurements in radar meteorology. Theoretical model (in Russian). Radioelectron. Commun. Syst.,2, 17–23.

  • ——, and D. S. Zrnić, 1996: Assessment of rainfall measurement that uses specific differential phase. J. Appl. Meteor.,35, 2080–2090.

    • Crossref
    • Export Citation
  • ——, ——, V. N. Bringi, G. Huang, E. A. Brandes, and J. Vivekanandan, 1999: Characteristics of hydrometeor orientation obtained from radar polarimetric measurements in a linear polarization basis. Proc. IGARSS ’99, Hamburg, Germany, IEEE, 702–704.

  • ——, ——, J. C. Hubbert, V. N. Bringi, J. Vivekanandan, and E. A. Brandes, 2000: Interpretation of polarimetric radar covariance matrix for meteorological scatterers. Proc. IGARSS 2000, Honolulu, HI, IEEE, 1584–1586.

  • Sachidananda, M., and D. S. Zrnić, 1986: Differential propagation phase shift and rainfall rate estimation. Radio Sci.,21, 235–247.

    • Crossref
    • Export Citation
  • Saunders, M. J., 1971: Cross-polarization at 18 and 30 Ghz due to rain. IEEE Trans. Antennas Propag.,AP19, 273–277.

    • Crossref
    • Export Citation
  • Seliga, T. A., and V. N. Bringi, 1976: Potential use of radar differential reflectivity measurements at orthogonal polarizations for measuring precipitation. J. Appl. Meteor.,15, 69–76.

    • Crossref
    • Export Citation
  • Straka, M. J., and D. S. Zrnić, 1993: An algorithm to deduce hydrometeor types and contents from multiparameter radar data. Preprints, 26th Int. Conf. on Radar Meteorology, Norman, OK, Amer. Meteor. Soc., 513–515.

  • Torlaschi, E., and A. R. Holt, 1993: Separation of propagation and backscattering effects in rain for circular polarization diversity S-band radars. J. Atmos. Oceanic Technol.,10, 465–477.

  • ——, and ——, 1998: A comparison of different polarization schemes for the radar sensing of precipitation. Radio Sci.,33, 1335–1352.

    • Crossref
    • Export Citation
  • Ulbrich, C. W., 1983: Natural variations in the analytical form of the raindrop size distributions. J. Appl. Meteor.,22, 1764–1775.

    • Crossref
    • Export Citation
  • Vivekanandan, J., W. M. Adams, and V. N. Bringi, 1991: Rigorous approach to polarimetric radar modeling of hydrometeor orientation distributions. J. Appl. Meteor.,30, 1053–1063.

    • Crossref
    • Export Citation
  • ——, D. S. Zrnić, S. M. Ellis, R. Oye, A. V. Ryzhkov, and J. Straka, 1999: Cloud microphysics retrieval using S-band dual-polarization radar measurements. Bull. Amer. Meteor. Soc.,80, 381–388.

    • Crossref
    • Export Citation
  • Zrnić, D. S., 1991: Complete polarimetric and Doppler measurements with a single receiver radar. J. Atmos. Oceanic Technol.,8, 159–165.

  • ——, and A. V. Ryzhkov, 1999: Polarimetry for weather surveillance radars. Bull. Amer. Meteor. Soc.,80, 389–406.

    • Crossref
    • Export Citation
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