Comparison of Polarimetric Radar Drop Size Distribution Retrieval Algorithms

Edward A. Brandes National Center for Atmospheric Research, Boulder, Colorado

Search for other papers by Edward A. Brandes in
Current site
Google Scholar
PubMed
Close
,
Guifu Zhang National Center for Atmospheric Research, Boulder, Colorado

Search for other papers by Guifu Zhang in
Current site
Google Scholar
PubMed
Close
, and
J. Vivekanandan National Center for Atmospheric Research, Boulder, Colorado

Search for other papers by J. Vivekanandan in
Current site
Google Scholar
PubMed
Close
Restricted access

We are aware of a technical issue preventing figures and tables from showing in some newly published articles in the full-text HTML view.
While we are resolving the problem, please use the online PDF version of these articles to view figures and tables.

Abstract

Recently, two physically based algorithms, the “beta” (β) method and the “constrained-gamma” method, have been proposed for retrieving the governing parameters of the gamma drop size distribution (DSD) from polarimetric radar measurements. The β method treats the drop axis ratio as a variable and computes drop shape and DSD parameters from radar reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP). The constrained-gamma method assumes that the axis ratio relation is fixed and computes DSD parameters from reflectivity, differential reflectivity, and an empirical relation between the DSD slope and shape parameters. In this paper, the two approaches are evaluated by comparing retrieved rain DSD parameters with disdrometer observations and examining derived fields for consistency. Error effects on the β method retrievals are analyzed. The β approach is found to be sensitive to errors in KDP and to be inconsistent with observations. Large retrieved β values are found to associate with large retrieved DSD shape parameters and small median drop diameters. The constrained-gamma DSD method provides reasonable rain DSD retrievals that agree better with disdrometer observations.

Corresponding author address: Dr. Edward A. Brandes, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307. Email: brandes@ncar.ucar.edu

Abstract

Recently, two physically based algorithms, the “beta” (β) method and the “constrained-gamma” method, have been proposed for retrieving the governing parameters of the gamma drop size distribution (DSD) from polarimetric radar measurements. The β method treats the drop axis ratio as a variable and computes drop shape and DSD parameters from radar reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP). The constrained-gamma method assumes that the axis ratio relation is fixed and computes DSD parameters from reflectivity, differential reflectivity, and an empirical relation between the DSD slope and shape parameters. In this paper, the two approaches are evaluated by comparing retrieved rain DSD parameters with disdrometer observations and examining derived fields for consistency. Error effects on the β method retrievals are analyzed. The β approach is found to be sensitive to errors in KDP and to be inconsistent with observations. Large retrieved β values are found to associate with large retrieved DSD shape parameters and small median drop diameters. The constrained-gamma DSD method provides reasonable rain DSD retrievals that agree better with disdrometer observations.

Corresponding author address: Dr. Edward A. Brandes, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307. Email: brandes@ncar.ucar.edu

Save
  • Andsager, K., Beard K. V. , and Laird N. F. , 1999: Laboratory measurements of axis ratios for large drops. J. Atmos. Sci, 56 , 26732683.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Atlas, D., and Ulbrich C. W. , 1977: Path- and area-integrated rainfall measurement by microwave attenuation in the 1–3 cm band. J. Appl. Meteor, 16 , 13221331.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Aydin, K., Bringi V. N. , and Liu L. , 1995: Estimation of rain and hail rates in mixed-phase precipitation. J. Appl. Meteor, 34 , 404410.

    • Search Google Scholar
    • Export Citation
  • Beard, K. V., and Chuang C. , 1987: A new model for the equilibrium shape of raindrops. J. Atmos. Sci, 44 , 15091524.

  • Beard, K. V., and Kubesh R. J. , 1991: Laboratory measurements of small drop distortion. Part II: Oscillation frequencies and modes. J. Atmos. Sci, 48 , 22452264.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brandes, E. A., Zhang G. , and Vivekanandan J. , 2002: Experiments in rainfall estimation with a polarimetric radar in a subtropical environment. J. Appl. Meteor, 41 , 674685.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brandes, E. A., Zhang G. , and Vivekanandan J. , 2003: An evaluation of a drop distribution- based rainfall estimator. J. Appl. Meteor, 42 , 652660.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brandes, E. A., Zhang G. , and Vivekanandan J. , 2004: Drop size distribution retrieval with polarimetric radar: Model and application. J. Appl. Meteor, 43 , 461475.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., Chandrasekar V. , and Xiao R. , 1998: Raindrop axis ratios and size distributions in Florida rainshafts: An assessment of multiparameter radar algorithms. IEEE Trans. Geosci. Remote Sens, 36 , 703715.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., Huang G-J. , Chandrasekar V. , and Gorgucci E. , 2002: A methodology for estimating the parameters of a gamma raindrop size distribution model from polarimetric radar data: Application to a squall-line event from the TRMM/Brazil campaign. J. Atmos. Oceanic Technol, 19 , 633645.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chandrasekar, V., and Bringi V. N. , 1987: Simulation of radar reflectivity and surface measurements of rainfall. J. Atmos. Oceanic Technol, 4 , 464478.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chandrasekar, V., Cooper W. A. , and Bringi V. N. , 1988: Axis ratios and oscillations of raindrops. J. Atmos. Sci, 45 , 13231333.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorgucci, E., Scarchilli G. , Chandrasekar V. , and Bringi V. N. , 2000: Measurement of mean raindrop shape from polarimetric radar observations. J. Atmos. Sci, 57 , 34063413.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorgucci, E., Scarchilli G. , Chandrasekar V. , and Bringi V. N. , 2001: Rainfall estimation from polarimetric radar measurements: Composite algorithms immune to variability in raindrop shape–size relation. J. Atmos. Oceanic Technol, 18 , 17731786.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorgucci, E., Chandrasekar V. , Bringi V. N. , and Scarchilli G. , 2002: Estimation of raindrop size distribution parameters from polarimetric radar measurements. J. Atmos. Sci, 59 , 23732384.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Green, A. W., 1975: An approximation for shapes of large drops. J. Appl. Meteor, 14 , 15781583.

  • Haddad, Z. S., Short D. A. , Durden S. L. , Im E. , Hensley S. , Grable M. B. , and Black R. A. , 1997: A new parameterizing of raindrop size distribution. IEEE Trans. Geosci. Remote Sens, 35 , 532539.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Illingworth, A. J., and Blackman T. M. , 2002: The need to represent raindrop size spectra as normalized gamma distributions for the interpretation of polarimetric radar observations. J. Appl. Meteor, 41 , 286297.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kozu, T., and Nakamura K. , 1991: Rain parameter estimation from dual-radar measurements combining reflectivity profile and path- integrated attenuation. J. Atmos. Oceanic Technol, 8 , 259270.

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

  • Pruppacher, H. R., and Beard K. V. , 1970: A wind tunnel investigation of the internal circulation and shape of water drops falling at terminal velocity in air. Quart. J. Roy. Meteor. Soc, 96 , 247256.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pruppacher, H. R., and Pitter R. L. , 1971: A semi-empirical determination of the shape of cloud and raindrops. J. Atmos. Sci, 28 , 8694.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., and Zrnić D. S. , 1995: Comparison of dual-polarization radar estimators of rain. J. Atmos. Oceanic Technol, 12 , 249256.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., and Zrnić D. S. , 1996: Assessment of rainfall measurement that uses specific differential phase. J. Appl. Meteor, 35 , 20802090.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Seliga, T. A., and Bringi V. N. , 1976: Potential use of radar differential reflectivity measurements at orthogonal polarizations for measuring precipitation. J. Appl. Meteor, 15 , 6976.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Testud, J., Oury S. , Black R. A. , Amayenc P. , and Dou X. , 2001: The concept of “normalized” distributions to describe raindrop spectra: A tool for cloud physics and cloud remote sensing. J. Appl. Meteor, 40 , 11181140.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ulbrich, C. W., 1983: Natural variations in the analytical form of the raindrop size distribution. J. Appl. Meteor, 22 , 17641775.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ulbrich, C. W., and Atlas D. , 1998: Rainfall microphysics and radar properties: Analysis methods for drop size spectra. J. Appl. Meteor, 37 , 912923.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vivekanandan, J., Zhang G. , Ellis S. M. , Rajopadhyaya D. , and Avery S. K. , 2003: Radar reflectivity calibration using differential propagation phase measurement. Radio Sci.,38, 8049, doi: 10.1029/2002RS002676.

    • Search Google Scholar
    • Export Citation
  • Vivekanandan, J., Zhang G. , and Brandes E. , 2004: Polarimetric radar estimators based on a constrained gamma model. J. Appl. Meteor, 43 , 217230.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Willis, P. T., 1984: Functional fits to some observed drop size distributions and parameterization of rain. J. Atmos. Sci, 41 , 16481661.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, G., Vivekanandan J. , and Brandes E. , 2001: A method for estimating rain rate and drop size distribution from polarimetric radar measurements. IEEE Trans. Geosci. Remote Sens, 39 , 830841.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, G., Vivekanandan J. , and Brandes E. , 2003: The shape–slope relation in observed Gamma raindrop size distribution: Statistical error or useful information? J. Atmos. Oceanic. Technol, 20 , 11061119.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 933 375 200
PDF Downloads 553 104 7