A High-Precision and Fast Solution Method of Gamma Raindrop Size Distribution Based on 0-Moment and 3-Moment in South China

Xiantong Liu aInstitute of Tropical and Marine Meteorology, China Meteorological Administration, Guangzhou, China

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Huiqi Li aInstitute of Tropical and Marine Meteorology, China Meteorological Administration, Guangzhou, China

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Sheng Hu aInstitute of Tropical and Marine Meteorology, China Meteorological Administration, Guangzhou, China

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Qilin Wan aInstitute of Tropical and Marine Meteorology, China Meteorological Administration, Guangzhou, China

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Hui Xiao aInstitute of Tropical and Marine Meteorology, China Meteorological Administration, Guangzhou, China

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Tengfei Zheng aInstitute of Tropical and Marine Meteorology, China Meteorological Administration, Guangzhou, China

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Minghua Li bHuizhou Meteorological Bureau, Huizhou, China

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Langming Ye cJiangmen Meteorological Bureau, Jiangmen, China

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Zheyong Guo dYangjiang Meteorological Bureau, Yangjiang, China

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Yao Wang bHuizhou Meteorological Bureau, Huizhou, China

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Zhaochao Yan bHuizhou Meteorological Bureau, Huizhou, China

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Abstract

According to the high-accuracy linear shape–slope (μ–Λ) relationship observed by several two-dimensional video disdrometers (2DVD) in South China, a high-precision and fast solution method of the gamma (Γ) raindrop size distribution (RSD) function based on the zeroth-order moment (M0) and the third-order moment (M3) of RSD has been proposed. The 0-moment M0 and 3-moment M3 of RSD can be easily calculated from rain mass mixing ratio Qr and total number concentration Ntr simulated by the two-moment (2M) microphysical scheme, respectively. Three typical heavy-rainfall processes and all RSD samples observed during 2019 in South China were selected to verify the accuracy of the method. Relative to the current widely used exponential RSD with a fixed shape parameter of zero in the 2M microphysical scheme, the Γ RSD function using the linear constrained gamma (C-G) method agreed better with the Γ-fit RSD from 2DVD observations. The characteristic precipitation parameters (e.g., rain rate, M2, M6, and M9) obtained by the proposed method are generally consistent with the parameters calculated by Γ-fit RSD from 2DVD observations. The proposed method has effectively solved the problem that the shape parameter in the 2M microphysical scheme is set to a constant, and therefore the Γ RSD functions are closer to the observations and have obviously smaller errors. This method has a good potential to be applied to 2M microphysical schemes to improve the simulation of heavy precipitation in South China, but it also paves the way for in-depth applications of radar data in numerical weather prediction models.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Qilin Wan, qlwan@gd121.cn

Abstract

According to the high-accuracy linear shape–slope (μ–Λ) relationship observed by several two-dimensional video disdrometers (2DVD) in South China, a high-precision and fast solution method of the gamma (Γ) raindrop size distribution (RSD) function based on the zeroth-order moment (M0) and the third-order moment (M3) of RSD has been proposed. The 0-moment M0 and 3-moment M3 of RSD can be easily calculated from rain mass mixing ratio Qr and total number concentration Ntr simulated by the two-moment (2M) microphysical scheme, respectively. Three typical heavy-rainfall processes and all RSD samples observed during 2019 in South China were selected to verify the accuracy of the method. Relative to the current widely used exponential RSD with a fixed shape parameter of zero in the 2M microphysical scheme, the Γ RSD function using the linear constrained gamma (C-G) method agreed better with the Γ-fit RSD from 2DVD observations. The characteristic precipitation parameters (e.g., rain rate, M2, M6, and M9) obtained by the proposed method are generally consistent with the parameters calculated by Γ-fit RSD from 2DVD observations. The proposed method has effectively solved the problem that the shape parameter in the 2M microphysical scheme is set to a constant, and therefore the Γ RSD functions are closer to the observations and have obviously smaller errors. This method has a good potential to be applied to 2M microphysical schemes to improve the simulation of heavy precipitation in South China, but it also paves the way for in-depth applications of radar data in numerical weather prediction models.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Qilin Wan, qlwan@gd121.cn
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  • Brandes, E. A., G. Zhang, and J. Vivekanandan, 2004a: Drop size distribution retrieval with polarimetric radar: Model and application. J. Appl. Meteor., 43, 461475, https://doi.org/10.1175/1520-0450(2004)043<0461:DSDRWP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brandes, E. A., G. Zhang, and J. Vivekanandan, 2004b: Comparison of polarimetric radar drop size distribution retrieval algorithms. J. Atmos. Oceanic Technol., 21, 584598, https://doi.org/10.1175/1520-0426(2004)021<0584:COPRDS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., G.-J. Huang, V. Chandrasekar, and E. Gorgucci, 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, https://doi.org/10.1175/1520-0426(2002)019<0633:AMFETP>2.0.CO;2.

    • Crossref
    • 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, https://doi.org/10.1175/2008JAMC2026.1.

    • Crossref
    • 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, https://doi.org/10.1175/2008JAMC1732.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chen, B., J. Yang, and J. Pu, 2013: Statistical characteristics of raindrop size distribution in the Meiyu season observed in eastern China. J. Meteor. Soc. Japan, 91, 215227, https://doi.org/10.2151/jmsj.2013-208.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fan, S. J., 1989: A new extracting formula and a new distinguishing means on the one variable cubic equation (in Chinese). Nat. Sci. J. Hainan Teach. Coll., 2, 9198.

    • Search Google Scholar
    • Export Citation
  • Feng, L., H. Sheng, X. Liu, H. Xiao, X. Pan, F. Xia, G. Ou, and C. Zhang, 2020: Precipitation microphysical characteristics of Typhoon Mangkhut in southern China using 2D video disdrometers. Atmosphere, 11, 975, https://doi.org/10.3390/atmos11090975.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gao, W., C.-H. Sui, T.-C. Chen Wang, and W.-Y. Chang, 2011: An evaluation and improvement of microphysical parameterization from a two-moment cloud microphysics scheme and the Southwest Monsoon Experiment (SoWMEX)/Terrain influenced Monsoon Rainfall Experiment (TiMREX) observations. J. Geophys. Res., 116, D19101, https://doi.org/10.1029/2011JD015718.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorgucci, E., V. Chandrasekar, V. N. Bringi, and G. Scarchilli, 2002: Estimation of raindrop size distribution parameters from polarimetric radar measurements. J. Atmos. Sci., 59, 23732384, https://doi.org/10.1175/1520-0469(2002)059<2373:EORSDP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., and K.-S. S. Lim, 2006: The WRF single-moment 6-class microphysics scheme (WSM6). J. Korean Meteor. Soc., 42, 129151.

  • Igel, A. L., M. R. Igel, and S. C. van den Heever, 2015: Make it a double? Sobering results from simulations using single-moment microphysics schemes. J. Atmos. Sci., 72, 910925, https://doi.org/10.1175/JAS-D-14-0107.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jin, Q., Y. Yuan, H. J. Liu, C. E. Shi, and J. B. Li, 2015: Analysis of microphysical characteristics of the raindrop spectrum over the area between the Yangtze and the Huaihe River during summer (in Chinese). Acta Meteor. Sin., 73, 778788.

    • Search Google Scholar
    • Export Citation
  • Johnson, M., Y. Jung, D. Dawson, T. Supinie, M. Xue, J. Park, and Y.-H. Lee, 2018: Evaluation of unified model microphysics in high-resolution NWP simulations using polarimetric radar observations. Adv. Atmos. Sci., 35, 771784, https://doi.org/10.1007/s00376-017-7177-0.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kumjian, M. R., and Coauthors, 2019: A moment-based polarimetric radar forward operator for rain microphysics. J. Appl. Meteor. Climatol., 58, 113130, https://doi.org/10.1175/JAMC-D-18-0121.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lim, K.-S. S., and S.-Y. Hong, 2010: Development of an effective double-moment cloud microphysics scheme with prognostic cloud condensation nuclei (CCN) for weather and climate models. Mon. Wea. Rev., 138, 15871612, https://doi.org/10.1175/2009MWR2968.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lin, Y., and B. A. Colle, 2011: A new bulk microphysical scheme that includes riming intensity and temperature-dependent ice characteristics. Mon. Wea. Rev., 139, 10131035, https://doi.org/10.1175/2010MWR3293.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lin, Y.-L., R. D. Farley, and H. D. Orville, 1983: Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteor., 22, 10651092, https://doi.org/10.1175/1520-0450(1983)022<1065:BPOTSF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, X., Q. Wan, H. Wang, H. Xiao, Y. Zhang, T. Zheng, and L. Feng, 2018: Raindrop size distribution parameters retrieved from Guangzhou S-band polarimetric radar observations. J. Meteor. Res., 32, 571583, https://doi.org/10.1007/s13351-018-7152-4.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Luo, Y., and Coauthors, 2017: The Southern China Monsoon Rainfall Experiment (SCMREX). Bull. Amer. Meteor. Soc., 98, 9991013, https://doi.org/10.1175/BAMS-D-15-00235.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mansell, E. R., C. L. Ziegler, and E. C. Bruning, 2010: Simulated electrification of a small thunderstorm with two-moment bulk microphysics. J. Atmos. Sci., 67, 171194, https://doi.org/10.1175/2009JAS2965.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Milbrandt, J. A., and M. K. Yau, 2005a: A multimoment bulk microphysics parameterization. Part I: Analysis of the role of the spectral shape parameter. J. Atmos. Sci., 62, 30513064, https://doi.org/10.1175/JAS3534.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Milbrandt, J. A., and M. K. Yau, 2005b: A multimoment bulk microphysics parameterization. Part II: A proposed three-moment closure and scheme description. J. Atmos. Sci., 62, 30653081, https://doi.org/10.1175/JAS3535.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Morrison, H., J. A. Curry, and V. I. Khvorostyanov, 2005: A new double-moment microphysics parameterization for application in cloud and climate models. Part I: Description. J. Atmos. Sci., 62, 16651677, https://doi.org/10.1175/JAS3446.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Morrison, H., M. R. Kumjian, C. P. Martinkus, O. P. Prat, and M. van Lier-Walqui, 2019: A general N-moment normalization method for deriving raindrop size distribution scaling relationships. J. Appl. Meteor. Climatol., 58, 247267, https://doi.org/10.1175/JAMC-D-18-0060.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Qian, Q., Y. Lin, Y. Luo, X. Zhao, Z. Zhao, Y. Luo, and X. Liu, 2018: Sensitivity of a simulated squall line during Southern China Monsoon Rainfall Experiment to parameterization of microphysics. J. Geophys. Res. Atmos., 123, 41974220, https://doi.org/10.1002/2017JD027734.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shi, X., B. Wang, X. Liu, and M. Wang, 2013: Tow-moment bulk stratiform cloud microphysics in the grid-point atmospheric model of IAP LASG (GAMIL). Adv. Atmos. Sci., 30, 868883, https://doi.org/10.1007/s00376-012-2072-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tang, Q., H. Xiao, C. Guo, and L. Feng, 2014: Characteristics of the raindrop size distributions and their retrieved polarimetric radar parameters in northern and southern China. Atmos. Res., 135–136, 5975, https://doi.org/10.1016/j.atmosres.2013.08.003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tao, W.-K., J. Simpson, and M. McCumber, 1989: An ice-water saturation adjustment. Mon. Wea. Rev., 117, 231235, https://doi.org/10.1175/1520-0493(1989)117<0231:AIWSA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thompson, G., P. R. Field, R. M. Rasmussen, and W. D. Hall, 2008: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part II: Implementation of a new now parameterization. Mon. Wea. Rev., 136, 50955115, https://doi.org/10.1175/2008MWR2387.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tokay, A., W. A. Petersen, P. Gatlin, and M. Wingo, 2013: Comparison of raindrop size distribution measurements by collocated disdrometers. J. Atmos. Oceanic Technol., 30, 16721690, https://doi.org/10.1175/JTECH-D-12-00163.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, D. H., J. F. Yin, and G. Q. Zhai, 2014: In-situ measurements of cloud-precipitation microphysics in the East Asian monsoon region since 1960 (in Chinese). Acta Meteor. Sin., 72, 639657, https://doi.org/10.1007/s13351-015-3235-7.

    • Search Google Scholar
    • Export Citation
  • Wang, H., J. F. Yin, and D. H. Wang, 2014: Comparative analysis of single-moment and double-moment microphysics schemes on a local heavy rainfall in South China (in Chinese). Plateau Meteor., 33, 13411351.

    • Search Google Scholar
    • Export Citation
  • Wen, G., H. Xiao, H. Yang, Y. Bi, and W. Xu, 2017: Characteristics of summer and winter precipitation over northern China. Atmos. Res., 197, 390406, https://doi.org/10.1016/j.atmosres.2017.07.023.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wen, L., K. Zhao, G. F. Zhang, M. Xue, B. W. Zhou, S. Liu, and X. C. Chen, 2016: Statistical characteristics of raindrop size distributions observed in East China during the Asian summer monsoon season using 2-D video disdrometer and Micro Rain Radar data. J. Geophys. Res. Atmos., 121, 22652282, https://doi.org/10.1002/2015JD024160.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wen, L., K. Zhao, M. Y. Wang, and G. F. Zhang, 2019: Seasonal variations of observed raindrop size distribution in East China. Adv. Atmos. Sci., 36, 346362, https://doi.org/10.1007/s00376-018-8107-5.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xu, H., and Y. Duan, 1999: Some questions in studying the evolution of size distribution spectrum of hydrometeor particles (in Chinese). Acta Meteor. Sinica, 57, 450460.

    • Search Google Scholar
    • Export Citation
  • Yin, J., D. Wang, G. Zhai, and H. Xu, 2014: An investigation into the relationship between liquid water content and cloud number concentration in the stratiform clouds over north China. Atmos. Res., 139, 137143, https://doi.org/10.1016/j.atmosres.2013.12.004.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, G., J. Vivekanandan, and E. Brandes, 2001: A method for estimating rain rate and drop size distribution from polarimetric radar measurements. IEEE Trans. Geosci. Remote Sens., 39, 830841, https://doi.org/10.1109/36.917906.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, G., J. Vivekanandan, E. Brandes, R. Meneghini, and T. Kozu, 2003: The shape–slope relation in observed gamma raindrop size distributions: Statistical error or useful information? J. Atmos. Oceanic Technol., 20, 11061119, https://doi.org/10.1175/1520-0426(2003)020<1106:TSRIOG>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, G., J. Z. Sun, and E. A. Brandes, 2006: Improving parameterization of rain microphysics with disdrometer and radar observations. J. Atmos. Sci., 63, 12731290, https://doi.org/10.1175/JAS3680.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, Y. D., D. H. Wang, J. F. Yin, and H. B. Xu, 2016: Impacts of terminal velocity and drop size distribution shape on the numerical simulation of precipitation (in Chinese). Chinese J. Atmos. Sci., 40, 841852.

    • Search Google Scholar
    • Export Citation
  • Zheng, K. L., and B. J. Chen, 2014: Sensitivities of tornadogenesis to drop size distribution in a simulated subtropical supercell over eastern China. Adv. Atmos. Sci., 31, 657668, https://doi.org/10.1007/s00376-013-3143-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
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