Variability of Drop Size Distributions: Time-Scale Dependence of the Variability and Its Effects on Rain Estimation

Gyu Won Lee J. S. Marshall Radar Observatory, Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada

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Isztar Zawadzki J. S. Marshall Radar Observatory, Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada

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Abstract

A systematic and intensive analysis is performed on 5 yr of reliable disdrometric data (over 20 000 one-minute drop size distributions, DSDs) to investigate the variability of DSDs in the Montreal, Quebec, Canada, area. The scale dependence (climatological scale, day to day, within a day, between physical processes, and within a physical process) of the DSD variability and its effect on rainfall intensity R estimation from radar reflectivity Z are explored in terms of bias and random errors. Detail error distributions are also provided. The use of a climatological R–Z relationship for rainfall—affected by all of the DSDs’ variability—leads on average to a random error of 41% in instantaneous rain-rate estimation. This error decreases with integration time, but the decrease becomes less pronounced for integration times longer than 2 h. Daily accumulations computed with the climatological R–Z relationship have a bias of 28% because of the day-to-day DSD variability. However, when daily R–Z relationships are used, a random error of 32% in instantaneous rain rate is still present because of the DSD variability within a day. This illustrates that most of the variability of DSDs has its origin within a storm or between storms within a day. Physical processes leading to the formation of DSDs are then classified according to the vertical structure of radar data as measured by a UHF profiler collocated with the disdrometer. The DSD variability among different physical processes is larger than the day-to-day variability. A bias of 41% in rain accumulations is due to the DSD variability between physical processes. Accurate rain-rate estimation (∼7%) can be achieved only after the proper underlying physical process is identified and the associated R–Z relationship is used.

Corresponding author address: Dr. GyuWon Lee, J. S. Marshall Radar Observatory, McGill University, Macdonald Campus, P.O. Box 198, Ste-Anne de Bellevue, QC H9X 3V9, Canada. gwlee@zephyr.meteo.mcgill.ca

Abstract

A systematic and intensive analysis is performed on 5 yr of reliable disdrometric data (over 20 000 one-minute drop size distributions, DSDs) to investigate the variability of DSDs in the Montreal, Quebec, Canada, area. The scale dependence (climatological scale, day to day, within a day, between physical processes, and within a physical process) of the DSD variability and its effect on rainfall intensity R estimation from radar reflectivity Z are explored in terms of bias and random errors. Detail error distributions are also provided. The use of a climatological R–Z relationship for rainfall—affected by all of the DSDs’ variability—leads on average to a random error of 41% in instantaneous rain-rate estimation. This error decreases with integration time, but the decrease becomes less pronounced for integration times longer than 2 h. Daily accumulations computed with the climatological R–Z relationship have a bias of 28% because of the day-to-day DSD variability. However, when daily R–Z relationships are used, a random error of 32% in instantaneous rain rate is still present because of the DSD variability within a day. This illustrates that most of the variability of DSDs has its origin within a storm or between storms within a day. Physical processes leading to the formation of DSDs are then classified according to the vertical structure of radar data as measured by a UHF profiler collocated with the disdrometer. The DSD variability among different physical processes is larger than the day-to-day variability. A bias of 41% in rain accumulations is due to the DSD variability between physical processes. Accurate rain-rate estimation (∼7%) can be achieved only after the proper underlying physical process is identified and the associated R–Z relationship is used.

Corresponding author address: Dr. GyuWon Lee, J. S. Marshall Radar Observatory, McGill University, Macdonald Campus, P.O. Box 198, Ste-Anne de Bellevue, QC H9X 3V9, Canada. gwlee@zephyr.meteo.mcgill.ca

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  • Amemiya, Y., 1997. Generalization of the TLS approach in the errors-in-variables problem. Recent Advances in Total Least Squares Techniques and Errors-in-Variables Modeling, S. Van Huffel, Ed., SIAM, 77–86.

  • Balakrishnan, N., D. S. Zrnić, J. Goldhirsh, and J. Rowland, 1989. Comparison of simulated rain rates from disdrometer data employing polarimetric radar algorithms. J. Atmos. Oceanic Technol. 6:476486.

    • Search Google Scholar
    • Export Citation
  • Bell, C., 2000. Detection of the riming process with a vertically pointing radar. M.S. thesis, Dept. of Atmospheric and Oceanic Sciences, McGill University, 74 pp.

  • Brandes, E. A., G. Zhang, and J. Vivekanand, 2003. An evaluation of a drop distribution–based polarimetric radar rainfall estimator. J. Appl. Meteor. 42:652660.

    • Search Google Scholar
    • Export Citation
  • Campos, E., and I. Zawadzki, 2000. Instrumental uncertainties in Z–R relations. J. Appl. Meteor. 39:10881102.

  • Chandrasekar, V., and V. N. Bringi, 1987. Simulation of radar reflectivity and surface measurements of rainfall. J. Atmos. Oceanic Technol. 4:464478.

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

    • Search Google Scholar
    • Export Citation
  • Direskeneli, H., K. Aydin, and T. A. Seliga, 1986. Radar estimation of rainfall rate using reflectivity and differential reflectivity measurements obtained during Maypole ’84: Comparison with ground-based raingauges. Preprints. 23d Conf. on Radar Meteorology, Snowmass, CO, Amer. Meteor. Soc., 116–120.

    • Search Google Scholar
    • Export Citation
  • Doelling, I. G., J. Joss, and J. Riedl, 1998. Systematic variation of Z-R relationships from drop size distributions measured in northern Germany during seven years. Atmos. Res. 47–48:635649.

    • Search Google Scholar
    • Export Citation
  • Fabry, F., and I. Zawadzki, 1995. Long-term radar observations of the melting layer of precipitation and their interpretation. J. Atmos. Sci. 52:838851.

    • Search Google Scholar
    • Export Citation
  • Fujiwara, M., 1965. Raindrop-size distribution from individual storms. J. Atmos. Sci. 22:585591.

  • Goddard, J. W. F., and S. M. Cherry, 1984. The ability of dual polarization radar (co-polar linear) to predict rainfall rate and microwave attenuation. Radio Sci. 19:201208.

    • Search Google Scholar
    • Export Citation
  • Gunn, R., and G. D. Kinzer, 1949. The terminal velocity of fall for water droplets in stagnant air. J. Meteor. 6:243248.

  • Hu, Z., and R. C. Srivastava, 1995. Evolution of raindrop size distribution by coalescence, breakup, and evaporation: Theory and observations. J. Atmos. Sci. 52:17611783.

    • Search Google Scholar
    • Export Citation
  • Joss, J., and A. Waldvogel, 1970. A method to improve the accuracy of radar measured amounts of precipitation. Proc. 14th Conf. on Radar Meteorology, Tucson, AZ, Amer. Meteor. Soc., 237–238.

  • Joss, J., and I. Zawadzki, 1997. Raindrop size distribution again? Preprints. 28th Conf. on Radar Meteorology, Austin, TX, Amer. Meteor. Soc., 326–327.

    • Search Google Scholar
    • Export Citation
  • Lee, G. W., 2003. Error in rain estimation by radar: Effect of the variability of drop size distributions. Ph.D. thesis, McGill University, 279 pp. [Available online at http://www.radar.mcgill.ca/gwlee/PAPERS/THESIS_2003/thesis_gwlee_single.pdf].

  • Lee, G. W., and I. Zawadzki, 2003. Sequential intensity filtering technique (SIFT): Filtering out noise to highlight the physical variability of drop size distributions. Preprints. 31st Conf. on Radar Meteorology, Seattle, WA, Amer. Meteor. Soc., 18–21.

    • Search Google Scholar
    • Export Citation
  • Lee, G. W., and I. Zawadzki, 2004. Radar calibration by gage, disdrometer, and polarimetry: Theoretical limit caused by the variability of drop size distribution and application to fast scanning operational radar data. J. Hydrol. in press.

    • Search Google Scholar
    • Export Citation
  • Lee, G. W., and I. Zawadzki, 2005. Variability of drop size distributions: Noise and noise filtering in disdrometric data. J. Appl. Meteor. in press.

    • Search Google Scholar
    • Export Citation
  • Lee, G. W., I. Zawadzki, W. Szymer, D. Sempere-Torres, and R. Uijlenhoet, 2004. A general approach to double-moment normalization of drop size distributions. J. Appl. Meteor. 43:264281.

    • Search Google Scholar
    • Export Citation
  • Marshall, J. S., and W. Mc K. Palmer, 1948. The distribution of raindrops with size. J. Meteor. 5:165166.

  • Mitchell, D. L., 1988. Evolution of snow-size spectra in cyclonic storms. Part I: Snow growth by vapor deposition and aggregation. J. Atmos. Sci. 45:34313451.

    • Search Google Scholar
    • Export Citation
  • Passarelli Jr., R. E., 1978. Theoretical and observational study of snow-size spectra and snowflake aggregation efficiencies. J. Atmos. Sci. 35:882889.

    • Search Google Scholar
    • Export Citation
  • Passarelli Jr., R. E., and R. C. Srivastava, 1979. A new aspect of snowflake aggregation theory. J. Atmos. Sci. 36:484493.

  • Richards, W. G., and C. L. Crozier, 1983. Precipitation measurement with a C-band weather radar in southern Ontario. Atmos.–Ocean 21:125137.

    • Search Google Scholar
    • Export Citation
  • Rogers, R. R., I. I. Zawadzki, and E. E. Gossard, 1991. Variation with altitude of the drop-size distribution in steady light rain. Quart. J. Roy. Meteor. Soc. 117:13411369.

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

    • Search Google Scholar
    • Export Citation
  • Sempere-Torres, D., R. Sánchez-Diezma, I. Zawadzki, and J-D. Creutin, 1999. DSD identification following a pre-classification of rainfall type from radar analysis. Preprints. 29th Conf. on Radar Meteorology, Montreal, QC, Canada, Amer. Meteor. Soc., 632–635.

    • Search Google Scholar
    • Export Citation
  • Sheppard, B. E., 1990. Measurement of raindrop size distribution using a small Doppler radar. J. Atmos. Oceanic Technol. 7:255268.

  • Sheppard, B. E., and P. I. Joe, 1994. Comparison of raindrop size distribution measurements by a Joss–Waldvogel disdrometer, a PMS 2DG spectrometer, and a POSS Doppler radar. J. Atmos. Oceanic Technol. 11:874887.

    • Search Google Scholar
    • Export Citation
  • Smith, P. L., and J. Joss, 1997. Use of a fixed exponent in “adjustable”. ZR relationships. Preprints, 28th Conf. on Radar Meteorology, Austin, TX, Amer. Meteor. Soc., 254–255.

    • Search Google Scholar
    • Export Citation
  • Smith, P. L., L. Zhong, and J. Joss, 1993. A study of sampling-variability effects in raindrop size observations. J. Appl. Meteor. 32:12591269.

    • Search Google Scholar
    • Export Citation
  • Srivastava, R. C., 1967. On the role of coalescence between raindrops in shaping their size distribution. J. Atmos. Sci. 24:287292.

  • Tokay, A., and D. A. Short, 1996. Evidence from tropical raindrop spectra of the origin of rain from stratiform versus convective clouds. J. Appl. Meteor. 35:355371.

    • Search Google Scholar
    • Export Citation
  • Uijlenhoet, R., J. A. Smith, and M. Steiner, 2003a. The microphysical structure of extreme precipitation as inferred from ground-based raindrop spectra. J. Atmos. Sci. 60:12201238.

    • Search Google Scholar
    • Export Citation
  • Uijlenhoet, R., M. Steiner, and J. A. Smith, 2003b. Variability of raindrop size distributions in a squall line and implications for radar rainfall estimation. J. Hydrometeor. 4:4361.

    • Search Google Scholar
    • Export Citation
  • Valdez, M. P., and K. C. Young, 1985. Number fluxes in equilibrium raindrop populations: A Markov chain analysis. J. Atmos. Sci. 42:10241036.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Young, K. C., 1975. The evolution of drop spectra due to condensation, coalescence and breakup. J. Atmos. Sci. 32:965973.

  • Zawadzki, I., and G. W. Lee, 2004. The physical causes of the variability of drop size distributions. Preprints, 14th Int. Conf. on Clouds and Precipitation, Bologna, Italy, ICCP. 698701.

  • Zawadzki, I., E. Monteiro, and F. Fabry, 1994. The development of drop size distributions in light rain. J. Atmos. Sci. 51:11001114.

  • Zawadzki, I., F. Fabry, and W. Szyrmer, 2001. Observations of supercooled water and secondary ice generation by a vertically pointing X-band Doppler radar. Atmos. Res. 59–60:343359.

    • Search Google Scholar
    • Export Citation
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