• Andrić, J., , M. R. Kumjian, , D. S. Zrnić, , J. M. Straka, , and V. M. Melnikov, 2013: Polarimetric signatures above the melting layer in winter storms: An observational and modeling study. J. Appl. Meteor. Climatol., 52, 682700, doi:10.1175/JAMC-D-12-028.1.

    • Search Google Scholar
    • Export Citation
  • Balakrishnan, N., , and D. Zrnić, 1990: Use of polarization to characterize precipitation and discriminate large hail. J. Atmos. Sci., 47, 15251540, doi:10.1175/1520-0469(1990)047<1525:UOPTCP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Beard, K. V., , and R. J. Kubesh, 1991: Laboratory measurements of small raindrop distortion. Part 2: Oscillation frequencies and modes. J. Atmos. Sci., 48, 22452264, doi:10.1175/1520-0469(1991)048<2245:LMOSRD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Beard, K. V., , V. Bringi, , and M. Thurai, 2010: A new understanding of raindrop shape. Atmos. Res., 97, 396415, doi:10.1016/j.atmosres.2010.02.001.

    • Search Google Scholar
    • Export Citation
  • Brandes, E. A., , and K. Ikeda, 2004: Freezing-level estimation with polarimetric radar. J. Appl. Meteor., 43, 15411553, doi:10.1175/JAM2155.1.

    • Search Google Scholar
    • Export Citation
  • Brandes, E. A., , G. Zhang, , and J. Vivekanandan, 2002: Experiments in rainfall estimation with a polarimetric radar in a subtropical environment. J. Appl. Meteor., 41, 674685, doi:10.1175/1520-0450(2002)041<0674:EIREWA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., , and V. Chandrasekar, 2001: Polarimetric Doppler Weather Radar: Principles and Applications. Cambridge University Press, 636 pp.

  • Bringi, V. N., , T. A. Seliga, , and S. M. Cherry, 1983: Statistical properties of the dual-polarization differential reflectivity (ZDR) radar signal. IEEE Trans. Geosci. Remote Sens., GE-21, 215220, doi:10.1109/TGRS.1983.350491.

    • Search Google Scholar
    • Export Citation
  • Cao, Q., , and G. Zhang, 2009: Errors in estimating raindrop size distribution parameters employing disdrometer and simulated raindrop spectra. J. Appl. Meteor. Climatol., 48, 406425, doi:10.1175/2008JAMC2026.1.

    • Search Google Scholar
    • Export Citation
  • Cao, Q., , G. Zhang, , E. Brandes, , T. Schuur, , A. Ryzhkov, , and K. Ikeda, 2008: Analysis of video disdrometer and polarimetric radar data to characterize rain microphysics in Oklahoma. J. Appl. Meteor. Climatol., 47, 22382255, doi:10.1175/2008JAMC1732.1.

    • Search Google Scholar
    • Export Citation
  • Caylor, I. J., 1989: Radar observations of maritime clouds using dual linear polarisation. Ph.D. thesis, University of Manchester Institute of Science and Technology, Manchester, United Kingdom, 261 pp.

  • Caylor, I. J., , and A. J. Illingworth, 1989: Identification of the bright band and hydrometeors using co-polar dual polarization radar. Preprints, 24th Conf. on Radar Meteorology, Tallahassee, FL, Amer. Meteor. Soc., 352–357.

  • Doviak, R. J., , and D. Zrnić, 2006: Doppler Radar and Weather Observations. 2nd ed. Dover Publications, 562 pp.

  • Fisher, R. A., 1915: Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika, 10, 507521.

    • Search Google Scholar
    • Export Citation
  • Giangrande, S. E., , J. M. Krause, , and A. V. Ryzhkov, 2008: Automatic designation of the melting layer with a polarimetric prototype of the WSR-88D radar. J. Appl. Meteor. Climatol., 47, 13541364, doi:10.1175/2007JAMC1634.1.

    • Search Google Scholar
    • Export Citation
  • Goddard, J., , J. D. Eastment, , and M. Thurai, 1994: The Chilbolton Advanced Meteorological Radar: A tool for multidisciplinary atmospheric research. Electron. Commun. Eng. J., 6 (2), 7786, doi:10.1049/ecej:19940205.

    • Search Google Scholar
    • Export Citation
  • Illingworth, A. J., , and I. J. Caylor, 1991: Co-polar correlation measurements of precipitation. Preprints, 25th Int. Conf. on Radar Meteorology, Paris, France, Amer. Meteor. Soc., 650–653.

  • Jameson, A., 1987: Relations among linear and circular polarization parameters measured in canted hydrometeors. J. Atmos. Oceanic Technol., 4, 634646, doi:10.1175/1520-0426(1987)004<0634:RALACP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Jameson, A., , and A. Kostinski, 1998: Fluctuation properties of precipitation. Part II: Reconsideration of the meaning and measurement of raindrop size distributions. J. Atmos. Sci., 55, 283294, doi:10.1175/1520-0469(1998)055<0283:FPOPPI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Johnson, R. W., , D. V. Kliche, , and P. L. Smith, 2014: Maximum likelihood estimation of gamma parameters for coarsely binned and truncated raindrop size data. Quart. J. Roy. Meteor. Soc., 140, 12451256, doi:10.1002/qj.2209.

    • Search Google Scholar
    • Export Citation
  • Liu, L., , V. N. Bringi, , V. Chandrasekar, , E. A. Mueller, , and A. Mudukutore, 1994: Analysis of the copolar correlation coefficient between horizontal and vertical polarizations. J. Atmos. Oceanic Technol., 11, 950963, doi:10.1175/1520-0426(1994)011<0950:AOTCCC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • McFarquhar, G. M., 2004: The effect of raindrop clustering on collision-induced break-up of raindrops. Quart. J. Roy. Meteor. Soc., 130, 21692190, doi:10.1256/qj.03.98.

    • Search Google Scholar
    • Export Citation
  • Papoulis, A., 1965: Probability, Random Variables, and Stochastic Processes. McGraw-Hill, 583 pp.

  • Park, H. S., , A. V. Ryzhkov, , D. Zrnić, , and K.-E. Kim, 2009: The hydrometeor classification algorithm for the polarimetric WSR-88D: Description and application to an MCS. Wea. Forecasting, 24, 730748, doi:10.1175/2008WAF2222205.1.

    • Search Google Scholar
    • Export Citation
  • Rogers, R., 1989: Raindrop collision rates. J. Atmos. Sci., 46, 24692472, doi:10.1175/1520-0469(1989)046<2469:RCR>2.0.CO;2.

  • Sachidananda, M., , and D. Zrnić, 1989: Efficient processing of alternately polarized radar signals. J. Atmos. Oceanic Technol., 6, 173181, doi:10.1175/1520-0426(1989)006<0173:EPOAPR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Schafer, R., , S. Avery, , P. May, , D. Rajopadhyaya, , and C. Williams, 2002: Estimation of rainfall drop size distributions from dual-frequency wind profiler spectra using deconvolution and a nonlinear least squares fitting technique. J. Atmos. Oceanic Technol., 19, 864874, doi:10.1175/1520-0426(2002)019<0864:EORDSD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Seliga, T., , and V. Bringi, 1976: Potential use of radar differential reflectivity measurements at orthogonal polarizations for measuring precipitation. J. Appl. Meteor., 15, 6976, doi:10.1175/1520-0450(1976)015<0069:PUORDR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Szakáll, M., , K. Diehl, , S. K. Mitra, , and S. Borrmann, 2008: A wind tunnel study on the oscillation of freely falling raindrops. Proc. Fifth European Conf. on Radar in Meteorology and Hydrology (ERAD 2008), Helsinki, Finland, Finnish Meteorological Institute, paper 7.6.

  • Szakáll, M., , S. K. Mitra, , K. Diehl, , and S. Borrmann, 2010: Shapes and oscillations of falling raindrops—A review. Atmos. Res., 97, 416425, doi:10.1016/j.atmosres.2010.03.024.

    • Search Google Scholar
    • Export Citation
  • Szakáll, M., , S. Kessler, , K. Diehl, , S. K. Mitra, , and S. Borrmann, 2014: A wind tunnel study of the effects of collision processes on the shape and oscillation for moderate-size raindrops. Atmos. Res., 142, 6778, doi:10.1016/j.atmosres.2013.09.005.

    • Search Google Scholar
    • Export Citation
  • Tabary, P., , A. Le Henaff, , G. Vulpiani, , J. Parent-du Châtelet, , and J. Gourley, 2006: Melting layer characterization and identification with a C-band dual-polarization radar: A long-term analysis. Proc. Fourth European Radar Conf. on Radar in Meteorology and Hydrology, Barcelona, Spain, Centre de Recerca Aplicada en Hidrometeorologia, 17–20.

  • Tang, L., , J. Zhang, , C. Langston, , J. Krause, , K. Howard, , and V. Lakshmanan, 2014: A physically based precipitation–nonprecipitation radar echo classifier using polarimetric and environmental data in a real-time national system. Wea. Forecasting, 29, 11061119, doi:10.1175/WAF-D-13-00072.1.

    • Search Google Scholar
    • Export Citation
  • Thurai, M., , and V. Bringi, 2005: Drop axis ratios from a 2D video disdrometer. J. Atmos. Oceanic Technol., 22, 966978, doi:10.1175/JTECH1767.1.

    • Search Google Scholar
    • Export Citation
  • Thurai, M., , D. Hudak, , and V. Bringi, 2008: On the possible use of copolar correlation coefficient for improving the drop size distribution estimates at C band. J. Atmos. Oceanic Technol., 25, 18731880, doi:10.1175/2008JTECHA1077.1.

    • Search Google Scholar
    • Export Citation
  • Thurai, M., , M. Szakáll, , V. N. Bringi, , and S. K. Mitra, 2013: Collision-induced drop oscillations from wind-tunnel experiments. Proc. 36th Conf. on Radar Meteorology, Breckenridge, CO, Amer. Meteor. Soc., 9B.2. [Available online at https://ams.confex.com/ams/36Radar/webprogram/Paper228158.html.]

  • Tokay, A., , A. Kruger, , and W. F. Krajewski, 2001: Comparison of drop size distribution measurements by impact and optical disdrometers. J. Appl. Meteor., 40, 20832097, doi:10.1175/1520-0450(2001)040<2083:CODSDM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Torlaschi, E., , and Y. Gingras, 2003: Standard deviation of the copolar correlation coefficient for simultaneous transmission and reception of vertical and horizontal polarized weather radar signals. J. Atmos. Oceanic Technol., 20, 760766, doi:10.1175/1520-0426(2003)20<760:SDOTCC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ulbrich, C. W., 1983: Natural variations in the analytical form of the raindrop size distribution. J. Climate Appl. Meteor., 22, 17641775, doi:10.1175/1520-0450(1983)022<1764:NVITAF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Unal, C., 2015: High resolution raindrop size distribution retrieval based on the Doppler spectrum in the case of slant profiling radar. J. Atmos. Oceanic Technol., 32, 11911208, doi:10.1175/JTECH-D-13-00225.1.

    • Search Google Scholar
    • Export Citation
  • Williams, C. R., 2002: Simultaneous ambient air motion and raindrop size distributions retrieved from UHF vertical incident profiler observations. Radio Sci., 37, doi:10.1029/2000RS002603.

    • Search Google Scholar
    • Export Citation
  • Williams, C. R., and et al. , 2014: Describing the shape of raindrop size distributions using uncorrelated raindrop mass spectrum parameters. J. Appl. Meteor. Climatol., 53, 12821296, doi:10.1175/JAMC-D-13-076.1.

    • Search Google Scholar
    • Export Citation
  • Wilson, D. R., , A. J. Illingworth, , and T. M. Blackman, 1997: Differential Doppler velocity: A radar parameter for characterizing hydrometeor size distributions. J. Appl. Meteor., 36, 649663, doi:10.1175/1520-0450-36.6.649.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 47 47 11
PDF Downloads 34 34 10

High-Precision Measurements of the Copolar Correlation Coefficient: Non-Gaussian Errors and Retrieval of the Dispersion Parameter μ in Rainfall

View More View Less
  • 1 Department of Meteorology, University of Reading, Reading, United Kingdom
© Get Permissions
Restricted access

Abstract

The copolar correlation coefficient ρhv has many applications, including hydrometeor classification, ground clutter and melting-layer identification, interpretation of ice microphysics, and the retrieval of raindrop size distributions (DSDs). However, the quantitative error estimates that are necessary if these applications are to be fully exploited are currently lacking. Previous error estimates of ρhv rely on knowledge of the unknown “true” ρhv and implicitly assume a Gaussian probability distribution function of ρhv samples. Frequency distributions of ρhv estimates are in fact shown to be highly negatively skewed. A new variable, = log10(1 − ρhv), is defined that does have Gaussian error statistics and a standard deviation depending only on the number of independent radar pulses. This is verified using observations of spherical drizzle drops, allowing, for the first time, the construction of rigorous confidence intervals in estimates of ρhv. In addition, the manner in which the imperfect collocation of the horizontal and vertical polarization sample volumes may be accounted for is demonstrated. The possibility of using L to estimate the dispersion parameter μ in the gamma drop size distribution is investigated. Including drop oscillations is found to be essential for this application; otherwise, there could be biases in retrieved μ of up to approximately 8. Preliminary results in rainfall are presented. In a convective rain case study, the estimates presented herein show μ to be substantially larger than 0 (an exponential DSD). In this particular rain event, rain rate would be overestimated by up to 50% if a simple exponential DSD is assumed.

Corresponding author address: W. J. Keat, Dept. of Meteorology, University of Reading, Earley Gate, P.O. Box 243, Reading RG6 6BB, United Kingdom. E-mail: w.j.keat@pgr.reading.ac.uk

Abstract

The copolar correlation coefficient ρhv has many applications, including hydrometeor classification, ground clutter and melting-layer identification, interpretation of ice microphysics, and the retrieval of raindrop size distributions (DSDs). However, the quantitative error estimates that are necessary if these applications are to be fully exploited are currently lacking. Previous error estimates of ρhv rely on knowledge of the unknown “true” ρhv and implicitly assume a Gaussian probability distribution function of ρhv samples. Frequency distributions of ρhv estimates are in fact shown to be highly negatively skewed. A new variable, = log10(1 − ρhv), is defined that does have Gaussian error statistics and a standard deviation depending only on the number of independent radar pulses. This is verified using observations of spherical drizzle drops, allowing, for the first time, the construction of rigorous confidence intervals in estimates of ρhv. In addition, the manner in which the imperfect collocation of the horizontal and vertical polarization sample volumes may be accounted for is demonstrated. The possibility of using L to estimate the dispersion parameter μ in the gamma drop size distribution is investigated. Including drop oscillations is found to be essential for this application; otherwise, there could be biases in retrieved μ of up to approximately 8. Preliminary results in rainfall are presented. In a convective rain case study, the estimates presented herein show μ to be substantially larger than 0 (an exponential DSD). In this particular rain event, rain rate would be overestimated by up to 50% if a simple exponential DSD is assumed.

Corresponding author address: W. J. Keat, Dept. of Meteorology, University of Reading, Earley Gate, P.O. Box 243, Reading RG6 6BB, United Kingdom. E-mail: w.j.keat@pgr.reading.ac.uk
Save