• Anagnostou, M. N., Anagnostou E. N. , and Vivekanandan J. , 2006: Correction for rain path specific and differential attenuation of X-band dual-polarization observations. IEEE Trans. Geosci. Remote Sens., 44, 24702480.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., Tang T. , and Chandrasekar V. , 2004: Evaluation of a new polarimetrically based Z–R relation. J. Atmos. Oceanic Technol., 21, 612623.

    • Search Google Scholar
    • Export Citation
  • Cao, Q., Zhang G. , Brandes E. A. , and Schuur T. J. , 2010: Polarimetric radar rain estimation through retrieval of drop size distribution using a Bayesian approach. J. Appl. Meteor. Climatol., 49, 973990.

    • Search Google Scholar
    • Export Citation
  • Chiu, J. C., and Petty G. W. , 2006: Bayesian retrieval of complete posterior PDFs of oceanic rain rate from microwave observations. J. Appl. Meteor. Climatol., 45, 10731095.

    • Search Google Scholar
    • Export Citation
  • Cifelli, R., Chandrasekar V. , Lim S. , Kennedy P. C. , Wang Y. , and Rutledge S. A. , 2011: A new dual-polarization radar rainfall algorithm: Application in Colorado precipitation events. J. Atmos. Oceanic Technol., 28, 352364.

    • Search Google Scholar
    • Export Citation
  • Di Michele, S., Tassa A. , Mugnai A. , Marzano F. S. , Bauer P. , and Baptista J. P. V. P. , 2005: Bayesian algorithm for microwave-based precipitation retrieval: Description and application to TMI measurements over ocean. IEEE Trans. Geosci. Remote Sens., 43, 778791.

    • Search Google Scholar
    • Export Citation
  • Doviak, R. J., Carter J. K. , Melnikov V. M. , and Zrnic D. S. , 2002: Modifications to the research WSR-88D to obtain polarimetric data. National Severe Storms Laboratory Rep., 49 pp.

  • Evans, K. F., Turk J. , Wong T. , and Stephens G. L. , 1995: A Bayesian approach to microwave precipitation profile retrieval. J. Appl. Meteor., 34, 260279.

    • Search Google Scholar
    • Export Citation
  • Fiebrich, C. A., Grimsley D. L. , McPherson R. A. , Kesler K. A. , and Essenberg G. R. , 2006: The value of routine site visits in managing and maintaining quality data from the Oklahoma Mesonet. J. Atmos. Oceanic Technol., 23, 406416.

    • Search Google Scholar
    • Export Citation
  • Fulton, R. A., Breidenbach J. P. , Seo D.-J. , Miller D. A. , and Bannon T. O. , 1998: The WSR-88D rainfall algorithm. Wea. Forecasting, 13, 377395.

    • Search Google Scholar
    • Export Citation
  • Giangrande, S. E., and Ryzhkov A. V. , 2008: Estimation of rainfall based on the results of polarimetric echo classification. J. Appl. Meteor. Climatol., 47, 24452462.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Hogan, R. J., 2007: A variational scheme for retrieving rainfall rate and hail reflectivity fraction from polarization radar. J. Appl. Meteor. Climatol., 46, 15441564.

    • Search Google Scholar
    • Export Citation
  • Lee, G. W., 2006: Sources of errors in rainfall measurements by polarimetric radar: Variability of drop size distributions, observational noise, and variation of relationships between R and polarimetric parameters. J. Atmos. Oceanic Technol., 23, 10051028.

    • Search Google Scholar
    • Export Citation
  • Lee, G. W., and Zawadzki I. , 2005: Variability of drop size distributions: Time-scale dependence of the variability and its effects on rain estimation. J. Appl. Meteor., 44, 241255.

    • Search Google Scholar
    • Export Citation
  • Lewis, J. M., Lakshmivarahan S. , and Dhall S. , 2006: Dynamic Data Assimilation: A Least Squares Approach. Vol. 104, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, 680 pp.

  • Li, Z., and Zhang Y. , 2011: Application of Gaussian mixture model (GMM) and estimator to radar-based weather parameter estimations. IEEE Geosci. Remote Sens. Lett., 8, 10411045.

    • Search Google Scholar
    • Export Citation
  • Li, Z., Zhang Y. , Zhang G. , and Brewster K. A. , 2011: A microphysics-based simulator for advanced airborne weather radar development. IEEE Trans. Geosci. Remote Sens., 49, 13561373.

    • Search Google Scholar
    • Export Citation
  • McPherson, R. A., and Coauthors, 2007: Statewide monitoring of the mesoscale environment: A technical update on the Oklahoma Mesonet. J. Atmos. Oceanic Technol., 24, 301321.

    • Search Google Scholar
    • Export Citation
  • Mishchenko, M. I., 2000: Calculation of the amplitude matrix for a nonspherical particle in a fixed orientation. Appl. Opt., 39, 10261031.

    • Search Google Scholar
    • Export Citation
  • Russell, S., and Norvig P. , 2009: Artificial Intelligence: A Modern Approach. 3rd ed. Prentice Hall, 1152 pp.

  • Ryzhkov, A. V., Giangrande S. E. , and Schuur T. J. , 2005a: Rainfall estimation with a polarimetric prototype of WSR-88D. J. Appl. Meteor., 44, 502515.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., Schuur T. J. , Burgess D. W. , Heinselman P. L. , Giangrande S. E. , and Zrnic D. S. , 2005b: The joint polarization experiment: Polarimetric rainfall measurements and hydrometeor classification. Bull. Amer. Meteor. Soc., 86, 809824.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Shafer, M. A., Fiebrich C. A. , Arndt D. S. , Fredrickson S. E. , and Hughes T. W. , 2000: Quality assurance procedures in the Oklahoma mesonetwork. J. Atmos. Oceanic Technol., 17, 474494.

    • Search Google Scholar
    • Export Citation
  • Vulpiani, G., Marzano F. S. , Chandrasekar V. , Berne A. , and Uijlenhoet R. , 2006: Polarimetric weather radar retrieval of raindrop size distribution by means of a regularized artificial neural network. IEEE Trans. Geosci. Remote Sens., 44, 32623275.

    • Search Google Scholar
    • Export Citation
  • Vulpiani, G., Giangrande S. , and Marzano F. S. , 2009: Rainfall estimation from polarimetric S-band radar measurements: Validation of a neural network approach. J. Appl. Meteor. Climatol., 48, 20222036.

    • Search Google Scholar
    • Export Citation
  • Waldvogel, A., 1974: The N0 jump of raindrop spectra. J. Atmos. Sci., 31, 10671078.

  • Wang, Y., and Chandrasekar V. , 2010: Quantitative precipitation estimation in the CASA X-band dual-polarization radar network. J. Atmos. Oceanic Technol., 27, 16651676.

    • Search Google Scholar
    • Export Citation
  • Zhang, G., Xue M. , Cao Q. , and Dawson D. , 2008: Diagnosing the intercept parameter for exponential raindrop size distribution based on video disdrometer observations: Model development. J. Appl. Meteor. Climatol., 47, 29832992.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 121 55 0
PDF Downloads 82 41 0

Rainfall-Rate Estimation Using Gaussian Mixture Parameter Estimator: Training and Validation

View More View Less
  • 1 School of Electrical and Computer Engineering, and the Atmospheric Radar Research Center, University of Oklahoma, Norman, Oklahoma
  • | 2 Brookhaven National Laboratory, Upton, New York
Restricted access

Abstract

This study develops a Gaussian mixture rainfall-rate estimator (GMRE) for polarimetric radar-based rainfall-rate estimation, following a general framework based on the Gaussian mixture model and Bayes least squares estimation for weather radar–based parameter estimations. The advantages of GMRE are 1) it is a minimum variance unbiased estimator; 2) it is a general estimator applicable to different rain regimes in different regions; and 3) it is flexible and may incorporate/exclude different polarimetric radar variables as inputs. This paper also discusses training the GMRE and the sensitivity of performance to mixture number. A large radar and surface gauge observation dataset collected in central Oklahoma during the multiyear Joint Polarization Experiment (JPOLE) field campaign is used to evaluate the GMRE approach. Results indicate that the GMRE approach can outperform existing polarimetric rainfall techniques optimized for this JPOLE dataset in terms of bias and root-mean-square error.

Corresponding author address: Yan Zhang, 110 W. Boyd Street, Devon Energy Hall 150, University of Oklahoma, Norman, OK 73019. E-mail: rockee@ou.edu

Abstract

This study develops a Gaussian mixture rainfall-rate estimator (GMRE) for polarimetric radar-based rainfall-rate estimation, following a general framework based on the Gaussian mixture model and Bayes least squares estimation for weather radar–based parameter estimations. The advantages of GMRE are 1) it is a minimum variance unbiased estimator; 2) it is a general estimator applicable to different rain regimes in different regions; and 3) it is flexible and may incorporate/exclude different polarimetric radar variables as inputs. This paper also discusses training the GMRE and the sensitivity of performance to mixture number. A large radar and surface gauge observation dataset collected in central Oklahoma during the multiyear Joint Polarization Experiment (JPOLE) field campaign is used to evaluate the GMRE approach. Results indicate that the GMRE approach can outperform existing polarimetric rainfall techniques optimized for this JPOLE dataset in terms of bias and root-mean-square error.

Corresponding author address: Yan Zhang, 110 W. Boyd Street, Devon Energy Hall 150, University of Oklahoma, Norman, OK 73019. E-mail: rockee@ou.edu
Save