Improved Parameterization of Ice Particle Size Distributions Using Uncorrelated Mass Spectrum Parameters: Results from GCPEx

Paloma Borque Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois

Search for other papers by Paloma Borque in
Current site
Google Scholar
PubMed
Close
,
Kirstin J. Harnos NOAA/Climate Prediction Center, College Park, Maryland

Search for other papers by Kirstin J. Harnos in
Current site
Google Scholar
PubMed
Close
,
Stephen W. Nesbitt Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Urbana, Illinois

Search for other papers by Stephen W. Nesbitt in
Current site
Google Scholar
PubMed
Close
, and
Greg M. McFarquhar Cooperative Institute of Mesoscale Meteorological Studies and School of Meteorology, University of Oklahoma, Norman, Oklahoma

Search for other papers by Greg M. McFarquhar in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Satellite retrieval algorithms and model microphysical parameterizations require guidance from observations to improve the representation of ice-phase microphysical quantities and processes. Here, a parameterization for ice-phase particle size distributions (PSDs) is developed using in situ measurements of cloud microphysical properties collected during the Global Precipitation Measurement (GPM) Cold-Season Precipitation Experiment (GCPEx). This parameterization takes advantage of the relation between the gamma-shape parameter μ and the mass-weighted mean diameter Dm of the ice-phase PSD sampled during GCPEx. The retrieval of effective reflectivity Ze and ice water content (IWC) from the reconstructed PSD using the μDm relationship was tested with independent measurements of Ze and IWC and overall leads to a mean error of 8% in both variables. This represents an improvement when compared with errors using the Field et al. parameterization of 10% in IWC and 37% in Ze. Current radar precipitation retrieval algorithms from GPM assume that the PSD follows a gamma distribution with μ = 3. This assumption leads to a mean overestimation of 5% in the retrieved Ze, whereas applying the μDm relationship found here reduces this bias to an overestimation of less than 1%. Proper selection of the a and b coefficients in the mass–dimension relationship is also of crucial importance for retrievals. An inappropriate selection of a and b, even from values observed in previous studies in similar environments and cloud types, can lead to more than 100% bias in IWC and Ze for the ice-phase particles analyzed here.

© 2019 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: Paloma Borque, paloma@illinois.edu

This article is included in the Global Precipitation Measurement (GPM) special collection.

Abstract

Satellite retrieval algorithms and model microphysical parameterizations require guidance from observations to improve the representation of ice-phase microphysical quantities and processes. Here, a parameterization for ice-phase particle size distributions (PSDs) is developed using in situ measurements of cloud microphysical properties collected during the Global Precipitation Measurement (GPM) Cold-Season Precipitation Experiment (GCPEx). This parameterization takes advantage of the relation between the gamma-shape parameter μ and the mass-weighted mean diameter Dm of the ice-phase PSD sampled during GCPEx. The retrieval of effective reflectivity Ze and ice water content (IWC) from the reconstructed PSD using the μDm relationship was tested with independent measurements of Ze and IWC and overall leads to a mean error of 8% in both variables. This represents an improvement when compared with errors using the Field et al. parameterization of 10% in IWC and 37% in Ze. Current radar precipitation retrieval algorithms from GPM assume that the PSD follows a gamma distribution with μ = 3. This assumption leads to a mean overestimation of 5% in the retrieved Ze, whereas applying the μDm relationship found here reduces this bias to an overestimation of less than 1%. Proper selection of the a and b coefficients in the mass–dimension relationship is also of crucial importance for retrievals. An inappropriate selection of a and b, even from values observed in previous studies in similar environments and cloud types, can lead to more than 100% bias in IWC and Ze for the ice-phase particles analyzed here.

© 2019 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: Paloma Borque, paloma@illinois.edu

This article is included in the Global Precipitation Measurement (GPM) special collection.

Save
  • Atlas, D., and C. Ulbrich, 2006: Drop size spectra and integral remote sensing parameters in the transition from convective to stratiform rain. Geophys. Res. Lett., 33, L16803, https://doi.org/10.1029/2006GL026824.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Barnes, S. L., 1964: A technique for maximizing details in numerical weather map analysis. J. Appl. Meteor., 3, 396409, https://doi.org/10.1175/1520-0450(1964)003<0396:ATFMDI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Baumgardner, D., and Coauthors, 2017: Cloud ice properties: In situ measurement challenges. Ice Formation and Evolution in Clouds and Precipitation: Measurement and Modeling Challenges, Meteor. Monogr., No. 58, Amer. Meteor. Soc., https://doi.org/10.1175/AMSMONOGRAPHS-D-16-0011.1.

    • Crossref
    • Export Citation
  • Bringi, V., and V. Chandrasekar, 2001: Polarimetric Doppler Weather Radar: Principles and Applications. Cambridge University Press, 636 pp.

    • Crossref
    • Export Citation
  • Brown, E. N., 1982: Ice detector evaluation for aircraft hazard warning and undercooled water content measurements. J. Aircr., 19, 980983, https://doi.org/10.2514/3.44800.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brown, P., and P. Francis, 1995: Improved measurements of the ice water content in cirrus using a total-water probe. J. Atmos. Oceanic Technol., 12, 410414, https://doi.org/10.1175/1520-0426(1995)012<0410:IMOTIW>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
  • Casella, D., G. Panegrossi, P. Sanò, A. C. Marra, S. Dietrich, B. T. Johnson, and M. S. Kulie, 2017: Evaluation of the GPM-DPR snowfall detection capability: Comparison with CloudSat-CPR. Atmos. Res., 197, 6475, https://doi.org/10.1016/j.atmosres.2017.06.018.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chandrasekar, V., and V. N. Bringi, 1987: Simulation of radar reflectivity and surface measurements of rainfall. J. Atmos. Oceanic Technol., 4, 464478, https://doi.org/10.1175/1520-0426(1987)004<0464:SORRAS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chandrasekar, V., W. Li, and B. Zafar, 2005: Estimation of raindrop size distribution from spaceborne radar observations. IEEE Trans. Geosci. Remote Sens., 43, 10781086, https://doi.org/10.1109/TGRS.2005.846130.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chase, R. J., and Coauthors, 2018: Evaluation of triple-frequency radar retrieval of snowfall properties using coincident airborne in situ observations during OLYMPEX. Geophys. Res. Lett., 45, 57525760, https://doi.org/10.1029/2018GL077997.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cober, S. G., G. A. Isaac, A. V. Korolev, and J. W. Strapp, 2001: Assessing cloud-phase conditions. J. Appl. Meteor., 40, 19671983, https://doi.org/10.1175/1520-0450(2001)040<1967:ACPC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cohard, J., and J. Pinty, 2000: A comprehensive two-moment warm microphysical bulk scheme. I: Description and tests. Quart. J. Roy. Meteor. Soc., 126, 18151842, https://doi.org/10.1256/smsqj.56613.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Delanoë, J. M. E., A. J. Heymsfield, A. Protat, A. Bansemer, and R. J. Hogan, 2014: Normalized particle size distribution for remote sensing application. J. Geophys. Res. Atmos., 119, 42044227, https://doi.org/10.1002/2013JD020700.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Delene, D. and M. R Poellot, 2012: GPM Ground Validation UND Citation Cloud Microphysics GCPEX Version 1. NASA Global Hydrology Resource Center DAAC, accessed 1 October 2016, https://doi.org/10.5067/GPMGV/GCPEX/MULTIPLE/DATA202.

    • Crossref
    • Export Citation
  • Ferrier, B. S., 1994: A double-moment multiple-phase four-class bulk ice scheme. Part I: Description. J. Atmos. Sci., 51, 249280, https://doi.org/10.1175/1520-0469(1994)051<0249:ADMMPF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Field, P. R., A. J. Heymsfield, and A. Bansemer, 2006: Shattering and particle interarrival times measured by optical array probes in ice clouds. J. Atmos. Oceanic Technol., 23, 13571371, https://doi.org/10.1175/JTECH1922.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Field, P. R., A. J. Heymsfield, and A. Bansemer, 2007: Snow size distribution parameterization for midlatitude and tropical ice clouds. J. Atmos. Sci., 64, 43464365, https://doi.org/10.1175/2007JAS2344.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Finlon, J. A., G. M. McFarquhar, S. W. Nesbitt, R. M. Rauber, H. Morrison, W. Wu, and P. Zhang, 2019: A novel approach to characterize the variability in mass–dimension relationships: Results from MC3E. Atmos. Chem. Phys., 19, 36213643, https://doi.org/10.5194/acp-19-3621-2019.

    • Search Google Scholar
    • Export Citation
  • Grecu, M., L. Tian, W. Olson, and S. Tanelli, 2011: A robust dual-frequency radar profiling algorithm. J. Appl. Meteor. Climatol., 50, 15431557, https://doi.org/10.1175/2011JAMC2655.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Haddad, Z. S., S. L. Durden, and E. Im, 1996: Parameterizing the raindrop size distribution. J. Appl. Meteor., 35, 313, https://doi.org/10.1175/1520-0450(1996)035<0003:PTRSD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., 2003: Properties of tropical and midlatitude ice cloud particle ensembles. Part I: Median mass diameters and terminal velocities. J. Atmos. Sci., 60, 25732591, https://doi.org/10.1175/1520-0469(2003)060<2573:POTAMI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., and J. L. Parrish, 1978: A computational technique for increasing the effective sampling volume of the PMS two-dimensional particle size spectrometer. J. Appl. Meteor., 17, 15661572, https://doi.org/10.1175/1520-0450(1978)017<1566:ACTFIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., P. Field, and A. Bansemer, 2008: Exponential size distributions for snow. J. Atmos. Sci., 65, 40174031, https://doi.org/10.1175/2008JAS2583.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., C. Schmitt, A. Bansemer, and C. H. Twohy, 2010: Improved representation of ice particle masses based on observations in natural clouds. J. Atmos. Sci., 67, 33033318, https://doi.org/10.1175/2010JAS3507.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hogan, R. J., and C. D. Westbrook, 2014: Equation for the microwave backscatter cross section of aggregate snowflakes using the self-similar Rayleigh–Gans approximation. J. Atmos. Sci., 71, 32923301, https://doi.org/10.1175/JAS-D-13-0347.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hogan, R. J., M. P. Mittermaier, and A. J. Illingworth, 2006: The retrieval of ice water content from radar reflectivity factor and temperature and its use in evaluating a mesoscale model. J. Appl. Meteor. Climatol., 45, 301317, https://doi.org/10.1175/JAM2340.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hogan, R. J., L. Tian, P. R. A. Brown, C. D. Westbrook, A. J. Heymsfield, and J. D. Eastment, 2012: Radar scattering from ice aggregates using the horizontally aligned oblate spheroid approximation. J. Appl. Meteor. Climatol., 51, 655671, https://doi.org/10.1175/JAMC-D-11-074.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hong, S., J. Dudhia, and S. Chen, 2004: A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation. Mon. Wea. Rev., 132, 103120, https://doi.org/10.1175/1520-0493(2004)132<0103:ARATIM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hou, A., and Coauthors, 2014: The Global Precipitation Measurement Mission. Bull. Amer. Meteor. Soc., 95, 701722, https://doi.org/10.1175/BAMS-D-13-00164.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hudak, D., 2013: GPM ground validation dual polarized C-band Doppler radar King City GCPEx. NASA EOSDIS Global Hydrology Resource Center DAAC, accessed 1 November 2016, https://doi.org/10.5067/GPMGV/GCPEX/MUTIPLE/DATA201.

    • Crossref
    • Export Citation
  • Jackson, R. C., and Coauthors, 2012: The dependence of ice microphysics on aerosol concentration in arctic mixed-phase stratus clouds during ISDAC and M-PACE. J. Geophys. Res., 117, D15207, https://doi.org/10.1029/2012JD017668.

    • Search Google Scholar
    • Export Citation
  • Korolev, A. V., and P. R. Field, 2015: Assessment of the performance of the inter-arrival time algorithm to identify ice shattering artifacts in cloud particle probe measurements. Atmos. Meas. Tech., 8, 761777, https://doi.org/10.5194/amt-8-761-2015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Korolev, A. V., J. W. Strapp, G. A. Isaac, and A. N. Nevzorov, 1998: The Nevzorov airborne hot-wire LWC–TWC probe: Principle of operation and performance characteristics. J. Atmos. Oceanic Technol., 15, 14951510, https://doi.org/10.1175/1520-0426(1998)015<1495:TNAHWL>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Korolev, A. V., E. F. Emery, J. W. Strapp, S. G. Cober, and G. A. Isaac, 2013: Quantification of the effects of shattering on airborne ice particle measurements. J. Atmos. Oceanic Technol., 30, 25272553, https://doi.org/10.1175/JTECH-D-13-00115.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kumar, L. S., Y. H. Lee, and J. T. Ong, 2011: Two-parameter gamma drop size distribution models for Singapore. IEEE Trans. Geosci. Remote Sens., 49, 33713380, https://doi.org/10.1109/TGRS.2011.2124464.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kummerow, C., W. Barnes, T. Kozu, J. Shiue, and J. Simpson, 1998: The Tropical Rainfall Measuring Mission (TRMM). J. Atmos. Oceanic Technol., 15, 809817, https://doi.org/10.1175/1520-0426(1998)015<0809:TTRMMT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lang, S. E., W. Tao, J. Chern, D. Wu, and X. Li, 2014: Benefits of a fourth ice class in the simulated radar reflectivities of convective systems using a bulk microphysics scheme. J. Atmos. Sci., 71, 35833612, https://doi.org/10.1175/JAS-D-13-0330.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • L’Ecuyer, T., W. Petersen, and D. Moiseev, 2010: Light Precipitation Validation Experiment (LPVEx). National Aeronautics and Space Administration Doc., 28 pp., https://pmm.nasa.gov/sites/default/files/document_files/lpvex_science_plan_Jan29_2010.pdf.

  • Liao, L., and R. Meneghini, 2005: A study of air/space-borne dual-wavelength radar for estimation of rain profiles. Adv. Atmos. Sci., 22, 841851, https://doi.org/10.1007/BF02918684.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liao, L., R. Meneghini, and A. Tokay, 2014: Uncertainties of GPM DPR rain estimates caused by DSD parameterizations. J. Appl. Meteor., 53, 25242537, https://doi.org/10.1175/JAMC-D-14-0003.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lin, Y., 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
  • Mardiana, R., T. Iguchi, and N. Takahashi, 2004: A dual-frequency rain profiling method without the use of a surface reference technique. IEEE Trans. Geosci. Remote Sens., 42, 22142225, https://doi.org/10.1109/TGRS.2004.834647.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marks, D. A., D. B. Wolff, L. D. Carey, and A. Tokay, 2011: Quality control and calibration of the dual-polarization radar at Kwajalein, RMI. J. Atmos. Oceanic Technol., 28, 181196, https://doi.org/10.1175/2010JTECHA1462.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McFarquhar, G. M., M. S. Timlin, R. M. Rauber, B. F. Jewett, J. A. Grim, and D. P. Jorgensen, 2007: Vertical variability of cloud hydrometeors in the stratiform region of mesoscale convective systems and bow echoes. Mon. Wea. Rev., 135, 34053428, https://doi.org/10.1175/MWR3444.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McFarquhar, G. M., J. Um, and R. Jackson, 2013: Small cloud particle shapes in mixed-phase clouds. J. Appl. Meteor. Climatol., 52, 12771293, https://doi.org/10.1175/JAMC-D-12-0114.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McFarquhar, G. M., T. Hsieh, M. Freer, J. Mascio, and B. F. Jewett, 2015: The characterization of ice hydrometeor gamma size distributions as volumes in N0λ-μ phase space: Implications for microphysical process modeling. J. Atmos. Sci., 72, 892909, https://doi.org/10.1175/JAS-D-14-0011.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McFarquhar, G. M., and Coauthors, 2017: Processing of ice cloud in situ data collected by bulk water, scattering, and imaging probes: Fundamentals, uncertainties, and efforts toward consistency. Ice Formation and Evolution in Clouds and Precipitation: Measurement and Modeling Challenges, Meteor. Monogr., No. 58, Amer. Meteor. Soc., https://doi.org/10.1175/AMSMONOGRAPHS-D-16-0007.1.

    • Crossref
    • Export Citation
  • Meneghini, R., T. Kozu, H. Kumagai, and W. C. Boncyk, 1992: A study of rain estimation methods from space using dual-wavelength radar measurements at near-nadir incidence over ocean. J. Atmos. Oceanic Technol., 9, 364382, https://doi.org/10.1175/1520-0426(1992)009<0364:ASOREM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Meyers, M. P., R. L. Walko, J. Y. Harrington, and W. R. Cotton, 1997: New RAMS cloud microphysics. Part II: The two-moment scheme. Atmos. Res., 45, 339, https://doi.org/10.1016/S0169-8095(97)00018-5.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Milbrandt, J. A., and M. K. Yau, 2005: 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
  • Mitchell, D. L., 1996: Use of mass- and area-dimensional power laws for determining precipitation particle terminal velocities. J. Atmos. Sci., 53, 17101723, https://doi.org/10.1175/1520-0469(1996)053<1710:UOMAAD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mitchell, D. L., R. Zhang, and R. L. Pitter, 1990: Mass-dimensional relationships for ice particles and the influence of riming on snowfall rates. J. Appl. Meteor., 29, 153163, https://doi.org/10.1175/1520-0450(1990)029<0153:MDRFIP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moisseev, D. N., and V. Chandrasekar, 2007: Examination of the μλ relation suggested for drop size distribution parameter. J. Atmos. Oceanic Technol., 24, 847855, https://doi.org/10.1175/JTECH2010.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Morrison, H., and J. A. Milbrandt, 2015: Parameterization of cloud microphysics based on the prediction of bulk ice particle properties. Part I: Scheme description and idealized tests. J. Atmos. Sci., 72, 287311, https://doi.org/10.1175/JAS-D-14-0065.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Morrison, H., G. Thompson, and V. Tatarskii, 2009: Impact of cloud microphysics on the development of trailing stratiform precipitation in a simulated squall line: Comparison of one- and two-moment schemes. Mon. Wea. Rev., 137, 9911007, https://doi.org/10.1175/2008MWR2556.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Munchak, S. J., and A. Tokay, 2008: Retrieval of raindrop size distribution from simulated dual-frequency radar measurements. J. Appl. Meteor. Climatol., 47, 223239, https://doi.org/10.1175/2007JAMC1524.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Naeger, A. R., B. A. Colle, and A. Molthan, 2017: Evaluation of cloud microphysical schemes for a warm frontal snowband during the GPM Cold Season Precipitation Experiment (GCPEx). Mon. Wea. Rev., 145, 46274650, https://doi.org/10.1175/MWR-D-17-0081.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Petersen, W., and M. Schwaller, 2008: Global precipitation mission (GPM) ground validation science implementation plan. National Aeronautics and Space Administration Doc., 41 pp., https://pmm.nasa.gov/sites/default/files/document_files/GPM_GVS_imp_plan_Jul08.pdf.

  • Seto, S., T. Iguchi, and T. Oki, 2013: The basic performance of a precipitation retrieval algorithm for the global precipitation measurement mission’s single/dual-frequency radar measurements. IEEE Trans. Geosci. Remote Sens., 51, 52395251, https://doi.org/10.1109/TGRS.2012.2231686.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Skofronick-Jackson, G., and Coauthors, 2015: Global Precipitation Measurement Cold Season Precipitation Experiment (GCPEX): For measurement’s sake, let it snow. Bull. Amer. Meteor. Soc., 96, 17191741, https://doi.org/10.1175/BAMS-D-13-00262.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Skofronick-Jackson, G., and Coauthors, 2017: The Global Precipitation Measurement (GPM) Mission for science and society. Bull. Amer. Meteor. Soc., 98, 16791695, https://doi.org/10.1175/BAMS-D-15-00306.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tang, G., Y. Wen, J. Gao, D. Long, Y. Ma, W. Wan, and Y. Hong, 2017: Similarities and differences between three coexisting spaceborne radars in global rainfall and snowfall estimation. Water Resour. Res., 53, 38353853, https://doi.org/10.1002/2016WR019961.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Testud, J., S. Oury, R. A. Black, P. Amayenc, and X. Dou, 2001: The concept of “normalized” distribution to describe the raindrop spectra: A tool for cloud physics and remote sensing. J. Appl. Meteor., 40, 11181140, https://doi.org/10.1175/1520-0450(2001)040<1118:TCONDT>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 snow parameterization. Mon. Wea. Rev., 136, 50955115, https://doi.org/10.1175/2008MWR2387.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Toyoshima, K., H. Masunaga, and F. A. Furuzawa, 2015: Early evaluation of Ku- and Ka-band sensitivities for the Global Precipitation Measurement (GPM) Dual-Frequency Precipitation Radar (DPR). SOLA, 11, 1417, https://doi.org/10.2151/sola.2015-004.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ulbrich, C., 1983: Natural variations in the analytical form of the raindrop size distribution. J. Climate Appl. Meteor., 22, 17641775, https://doi.org/10.1175/1520-0450(1983)022<1764:NVITAF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Williams, C. R., and Coauthors, 2014: Describing the shape of raindrop size distributions using uncorrelated raindrop mass spectrum parameters. J. Appl. Meteor. Climatol., 53, 12821296, https://doi.org/10.1175/JAMC-D-13-076.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wu, W., and G. M. McFarquhar, 2018: Statistical theory on the functional form of cloud particle size distributions. J. Atmos. Sci., 75, 28012814, https://doi.org/10.1175/JAS-D-17-0164.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhang, G., J. Vivekanandan, and E. A. 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. A. Brandes, R. Meneghini, and R. 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. 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
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 773 344 18
PDF Downloads 465 112 13