Can a Unique Model Describe the Raindrop Shape–Size Relation? A Clue from Polarimetric Radar Measurements

Eugenio Gorgucci Istituto di Scienze dell’Atmosfera e del Clima (CNR), Rome, Italy

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V. Chandrasekar Colorado State University, Fort Collins, Colorado

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Luca Baldini Istituto di Scienze dell’Atmosfera e del Clima (CNR), Rome, Italy

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Abstract

A method is proposed to retrieve raindrop shape–size relations from the radar measurements of reflectivity factor Zh, differential reflectivity Zdr, and specific differential phase Kdp at S band. This procedure is obtained using a domain defined by the two variables Kdp/Zh and Zdr where the drop size distribution (DSD) variability is collapsed onto a line and any variation is essentially due to the drop shape variability. To obtain information on the raindrop shape–size relation underlying a set of radar observations, this domain is studied in conjunction with another domain describing the relation between the drop axial ratio (or shape) and its equivolumetric diameter. Using an initial drop shape and choosing a set of DSDs described by a normalized gamma model, polarimetric radar measurements are produced by simulation. An averaged curve of Kdp/Zh versus Zdr is obtained and compared with the same curve obtained from the radar data. By changing the initial axial ratio relation, a procedure of minimization between the two curves is developed to derive the underlying drop shape–size relation governing the radar measurements under consideration. Three sets of radar data collected in different climatic regions are analyzed to evaluate whether there is a unique shape–size relation.

Corresponding author address: Eugenio Gorgucci, CNR-ISAC, Area della Ricerca Roma “Tor Vergata,” Via Fosso del Cavaliere, 100, 00133 Rome, Italy. Email: e.gorgucci@isac.cnr.it

Abstract

A method is proposed to retrieve raindrop shape–size relations from the radar measurements of reflectivity factor Zh, differential reflectivity Zdr, and specific differential phase Kdp at S band. This procedure is obtained using a domain defined by the two variables Kdp/Zh and Zdr where the drop size distribution (DSD) variability is collapsed onto a line and any variation is essentially due to the drop shape variability. To obtain information on the raindrop shape–size relation underlying a set of radar observations, this domain is studied in conjunction with another domain describing the relation between the drop axial ratio (or shape) and its equivolumetric diameter. Using an initial drop shape and choosing a set of DSDs described by a normalized gamma model, polarimetric radar measurements are produced by simulation. An averaged curve of Kdp/Zh versus Zdr is obtained and compared with the same curve obtained from the radar data. By changing the initial axial ratio relation, a procedure of minimization between the two curves is developed to derive the underlying drop shape–size relation governing the radar measurements under consideration. Three sets of radar data collected in different climatic regions are analyzed to evaluate whether there is a unique shape–size relation.

Corresponding author address: Eugenio Gorgucci, CNR-ISAC, Area della Ricerca Roma “Tor Vergata,” Via Fosso del Cavaliere, 100, 00133 Rome, Italy. Email: e.gorgucci@isac.cnr.it

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

    • Crossref
    • 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 raindrop 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
  • Bringi, V. N., and Chandrasekar V. , 2001: Polarimetric Doppler Weather Radar: Principles and Applications. Cambridge University Press, 648 pp.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., Chandrasekar V. , and Xiao R. , 1998: Raindrop axis ratio and size distribution 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., Chandrasekar V. , Hubbert J. , Gorgucci E. , Randeu W. L. , and Schoenhuber M. , 2003: Raindrop size distribution in different climatic regimes from disdrometer and dual-polarized radar analysis. J. Atmos. Sci., 60 , 354365.

    • 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 , 464477.

    • 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
  • Chandrasekar, V., Bringi V. N. , Balakrishnan N. , and Zrnić D. S. , 1990: Error structure of multiparameter radar and surface measurements of rainfall. Part III: Specific differential phase. J. Atmos. Oceanic Technol., 7 , 621629.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chandrasekar, V., Lim S. , and Gorgucci E. , 2006: Simulation of X-band rainfall observations from S-band radar data. J. Atmos. Oceanic Technol., 23 , 11951205.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Goddard, J. W. F., Cherry S. M. , and Bringi V. N. , 1982: Comparison of dual-polarization radar measurements of rain with ground-based disdrometer measurements. J. Appl. Meteor., 21 , 252256.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Goddard, J. W. F., Tan J. , and Thurai M. , 1994: Technique for calibration of meteorological radars using differential phase. Electron. Lett., 30 , 166167.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorgucci, E., and Chandrasekar V. , 2005: Evaluation of attenuation correction methodology for dual-polarization radars: Application to X-band systems. J. Atmos. Oceanic Technol., 22 , 11951206.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorgucci, E., Scarchilli G. , and Chandrasekar V. , 1992: Calibration of radars using polarimetric techniques. IEEE Trans. Geosci. Remote Sens., 30 , 853858.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorgucci, E., Scarchilli G. , and Chandrasekar V. , 1999: A procedure to calibrate multiparameter weather radar using properties of the rain medium. IEEE Trans. Geosci. Remote Sens., 37 , 269276.

    • 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., 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
  • Gorgucci, E., Baldini L. , and Chandrasekar V. , 2006: What is the shape of raindrops? An answer from radar measurements. J. Atmos. Sci., 63 , 30333044.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gourley, J. J., and Illingworth A. J. , 2005: Calibration of absolute reflectivity at C-band using redundancy of the polarization parameters in rain. Preprints, 32nd Conf. on Radar Meteorology, Albuquerque, NM, Amer. Meteor. Soc., 9R.5. [Available online at http://ams.confex.com/ams/pdfpapers/96226.pdf].

    • Search Google Scholar
    • Export Citation
  • Keenan, T. D., Carey L. D. , Zrnić D. S. , and May P. T. , 2001: Sensitivity of 5-cm wavelength polarimetric radar variables to raindrop axial ratio and drop size distribution. J. Appl. Meteor., 40 , 526545.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Matrosov, S. Y., Clark K. A. , Martner B. E. , and Tokay A. , 2002: X-band polarimetric radar measurements of rainfall. J. Appl. Meteor., 41 , 941952.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 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
  • Ryzhkov, A. V., Giangrande S. E. , Melnikov V. M. , and Schuur T. J. , 2005: Calibration issues of dual-polarization radar measurements. J. Atmos. Oceanic Technol., 22 , 11381155.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sachidananda, M., and Zrnić D. S. , 1987: Rain rate estimates from differential polarization measurements. J. Atmos. Oceanic Technol., 4 , 588598.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scarchilli, G., Gorgucci E. , Chandrasekar V. , and Dobaie A. , 1996: Self-consistency of polarization diversity measurement of rainfall. IEEE Trans. Geosci. Remote Sens., 34 , 2226.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steiner, M., Houze R. A. , and Yuter S. E. , 1995: Climatological characterization of three-dimensional storm structure from operational radar and rain gauge data. J. Appl. Meteor., 34 , 19782007.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thurai, M., and Bringi V. N. , 2005: Drop axis ratios from 2D video disdrometer. J. Atmos. Oceanic Technol., 22 , 966978.

  • Thurai, M., Huang G. J. , Bringi V. N. , Randeu W. L. , and Schönhuber M. , 2007: Drop shapes, model comparisons, and calculations of polarimetric radar parameters in rain. J. Atmos. Oceanic Technol., 24 , 10191032.

    • 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
  • Yuter, S. E., and Houze R. A. Jr., 2003: Microphysical modes of precipitation growth determined by S-band vertically pointing radar in orographic precipitation during MAP. Quart. J. Roy. Meteor. Soc., 129 , 455476.

    • Crossref
    • Search Google Scholar
    • Export Citation
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