• Baker, B., , and R. P. Lawson, 2006: Improvement in determination of ice water content from two-dimensional particle imagery. Part I: Image-to-mass relationships. J. Appl. Meteor. Climatol., 45, 12821290.

    • Search Google Scholar
    • Export Citation
  • Böhm, H., 1989: A general equation for the terminal fall speed of solid hydrometeors. J. Atmos. Sci., 46, 24192427.

  • Brandes, E. A., , K. Ikeda, , G. Zhang, , M. Schönhuber, , and R. Rasmussen, 2007: A statistical and physical description of hydrometeor distributions in Colorado snow storms using a video disdrometer. J. Appl. Meteor. Climatol, 46, 634650.

    • Search Google Scholar
    • Export Citation
  • Brown, P. R. A., , and P. N. Francis, 1995: Improved measurements of the ice water content in cirrus using a total-water probe. J. Atmos. Oceanic Technol., 12, 410414.

    • Search Google Scholar
    • Export Citation
  • Delanoë, J., , A. Protat, , J. Testud, , D. Bouniol, , A. J. Heymsfield, , A. Bansemer, , P. R. A. Brown, , and R. M. Forbes, 2005: Statistical properties of the normalized ice particle size distribution. J. Geophys. Res., 110, D10201, doi:10.1029/2004JD005405.

    • Search Google Scholar
    • Export Citation
  • Evans, K. F., , J. R. Wang, , P. E. Racette, , G. Heymsfield, , and L. Li, 2005: Ice cloud retrievals and analysis with the compact scanning submillimeter imaging radiometer and the Cloud Radar System during CRYSTAL FACE. J. Appl. Meteor., 44, 839859.

    • Search Google Scholar
    • Export Citation
  • Fabry, F., , and W. Szyrmer, 1999: Modeling of the melting layer. Part II: Electromagnetics. J. Atmos. Sci., 56, 35933600.

  • Field, P. R., , and A. J. Heymsfield, 2003: Aggregation and scaling of ice crystal size distributions. J. Atmos. Sci., 60, 544560.

  • Field, P. R., , R. J. Hogan, , P. R. A. Brown, , A. J. Illingworth, , T. W. Choularton, , and R. J. Cotton, 2005: Parameterization of ice particle size distributions for mid-latitude stratiform cloud. Quart. J. Roy. Meteor. Soc., 131, 19972017.

    • Search Google Scholar
    • Export Citation
  • Field, P. R., , A. J. Heymsfield, , and A. Bansemer, 2006: A test of ice self-collection kernels using aircraft data. J. Atmos. Sci., 63, 651666.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Field, P. R., , A. J. Heymsfield, , A. Bansemer, , and C. H. Twohy, 2008: Determination of the combined ventilation factor and capacitance for ice crystal aggregates from airborne observations in a tropical anvil cloud. J. Atmos. Sci., 65, 376391.

    • Search Google Scholar
    • Export Citation
  • Francis, P. N., , P. Hignett, , and A. Macke, 1998: The retrieval of cirrus cloud properties from aircraft multi-spectral reflectance measurements during EUCREX’93. Quart. J. Roy. Meteor. Soc., 124, 12731291.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., 1972: Ice crystal terminal velocities. J. Atmos. Sci., 29, 13481357.

  • Heymsfield, A. J., 2003a: Properties of tropical and midlatitude ice cloud particle ensembles. Part I: Median mass diameters and terminal velocities. J. Atmos. Sci., 60, 25732591.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., 2003b: Properties of tropical and midlatitude ice cloud particle ensembles. Part II: Applications for mesoscale and climate models. J. Atmos. Sci., 60, 25922611.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., , and C. D. Westbrook, 2010: Advancements in the estimation of ice particle fall speeds using laboratory and field measurements. J. Atmos. Sci., 67, 24692482.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., , S. Lewis, , A. Bansemer, , J. Iaquinta, , L. M. Miloshevich, , M. Kajikawa, , C. Twohy, , and M. R. Poellot, 2002: A general approach for deriving the properties of cirrus and stratiform ice cloud particles. J. Atmos. Sci., 59, 329.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., , A. Bansemer, , C. G. Schmitt, , C. Twohy, , and M. R. Poellet, 2004a: Effective ice particle densities derived from aircraft data. J. Atmos. Sci., 61, 9821003.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., , C. G. Schmitt, , A. Bansemer, , D. Baumgardner, , E. M. Weinstock, , J. T. Smith, , and D. Sayres, 2004b: Effective ice particle densities for cold anvil cirrus. Geophys. Res. Lett., 31, L02101, doi:10.1029/2003GL018311.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., , Z. Wang, , and S. Matrosov, 2005: Improved radar ice water content retrieval algorithms using coincident microphysical and radar measurements. J. Appl. Meteor., 44, 13911412.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., , A. Bansemer, , and C. Twohy, 2007: Refinements to ice particle mass dimensional and terminal velocity relationships for ice clouds. Part I: Temperature dependence. J. Atmos. Sci., 64, 10471067.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., , A. Bansemer, , S. Matrosov, , and L. Tian, 2008a: The 94-GHz radar dim band: Relevance to ice cloud properties and CloudSat. Geophys. Res. Lett., 35, L03802, doi:10.1029/2007GL031361.

    • Search Google Scholar
    • Export Citation
  • Heymsfield, A. J., , P. Field, , and A. Bansemer, 2008b: Exponential size distributions for snow. J. Atmos. Sci., 65, 40174031.

  • 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.

    • Search Google Scholar
    • Export Citation
  • Hiley, M. J., , M. S. Kulie, , and R. Bennartz, 2011: Uncertainty analysis for CloudSat snowfall retrievals. J. Appl. Meteor. Climatol., 50, 399418.

    • Search Google Scholar
    • Export Citation
  • Hogan, R., , L. Tian, , P. Brown, , C. Westbrook, , A. Heymsfield, , and J. Eastment, 2012: Radar scattering from ice aggregates using the horizontally aligned oblate spheroid approximation. J. Appl. Meteor. Climatol, 51, 655671.

    • Search Google Scholar
    • Export Citation
  • Ishimoto, H., 2008: Radar backscattering computations for fractal-shaped snowflakes. J. Meteor. Soc. Japan, 86, 459469.

  • Kajikawa, M., 1982: Observations of the falling motion of early snowflakes. Part I: Relationship between the free-fall pattern and the number and shape of component snow crystals. J. Meteor. Soc. Japan, 60, 797803.

    • Search Google Scholar
    • Export Citation
  • Kessler, E., 1969: On the Distribution and Continuity of Water Substance in Atmospheric Circulations. Meteor. Monogr., No. 32, Amer. Meteor. Soc., 84 pp.

    • Search Google Scholar
    • Export Citation
  • Khvorostyanov, V. I., , and J. A. Curry, 2005: Fall velocities of hydrometeors in the atmosphere: Refinements to a continuous power law. J. Atmos. Sci., 62, 43434357.

    • Search Google Scholar
    • Export Citation
  • Kingsmill, D. E., and Coauthors, 2004: TRMM Common microphysics products: A tool for evaluating spaceborne precipitation retrieval algorithms. J. Appl. Meteor., 43, 15981618.

    • Search Google Scholar
    • Export Citation
  • Kneifel, S., , M. S. Kulie, , and R. Bennartz, 2011: A triple-frequency approach to retrieve microphysical snowfall parameters. J. Geophys. Res., 116, D11203, doi:10.1029/2010JD015430.

    • Search Google Scholar
    • Export Citation
  • Kulie, M. S., , and R. Bennartz, 2009: Utilizing spaceborne radars to retrieve dry snowfall. J. Appl. Meteor., 48, 25642580.

  • Langleben, M. P., 1954: The terminal velocity of snowflakes. Quart. J. Roy. Meteor. Soc., 80, 174181.

  • Lee, G. W., , I. Zawadzki, , W. Szyrmer, , 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
  • 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.

    • Search Google Scholar
    • Export Citation
  • Liu, G., 2004: Approximation of single scattering properties of ice and snow particles for high microwave frequencies. J. Atmos. Sci., 61, 24412456.

    • Search Google Scholar
    • Export Citation
  • Liu, G., 2008: A database of microwave single-scattering properties for nonspherical ice particles. Bull. Amer. Meteor. Soc., 89, 15631570.

    • Search Google Scholar
    • Export Citation
  • Locatelli, J. D., , and P. V. Hobbs, 1974: Fall speeds and mass of solid precipitation particles. J. Geophys. Res., 79, 21852197.

  • Magono, C., , and T. Nakamura, 1965: Aerodynamic studies of falling snowflakes. J. Meteor. Soc. Japan, 43, 139147.

  • Matrosov, S. Y., 2007: Modeling backscatter properties of snowfall at millimeter wavelength. J. Atmos. Sci., 64, 17271736.

  • Matrosov, S. Y., , and A. J. Heymsfield, 2008: Estimating ice content and extinction in precipitating cloud systems from CloudSat radar measurements. J. Geophys. Res., 113, D00A05, doi:10.1029/2007JD009633.

    • Search Google Scholar
    • Export Citation
  • Matrosov, S. Y., , A. J. Heymsfield, , and Z. Wang, 2005: Dual-frequency ratio of nonspherical atmospheric hydrometeors. Geophys. Res. Lett., 32, L13816, doi:10.1029/2005GL023210.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Mitchell, D. L., , and A. J. Heymsfield, 2005: Refinements in the treatment of ice particle terminal velocities, highlighting aggregates. J. Atmos. Sci., 62, 16371644.

    • 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.

    • Search Google Scholar
    • Export Citation
  • Mitchell, D. L., , R. P. d’Entremont, , and R. P. Lawson, 2010: Inferring cirrus size distributions through satellite remote sensing and microphysical databases. J. Atmos. Sci., 67, 11061125.

    • Search Google Scholar
    • Export Citation
  • Molthan, A. L., and , W. A. Petersen, 2011: Incorporating ice crystal scattering databases in the simulation of millimeter-wavelength radar reflectivity. J. Atmos. Oceanic Technol., 28, 337351.

    • Search Google Scholar
    • Export Citation
  • Pokharel, B., , and G. Vali, 2011: Evaluation of co-located measurements of radar reflectivity and particle sizes in ice clouds. J. Appl. Meteor., 50, 21042119.

    • Search Google Scholar
    • Export Citation
  • Schmitt, C. G., , and A. J. Heymsfield, 2009: The size distribution and mass weighted terminal velocity of low-latitude tropopause cirrus crystal populations. J. Atmos. Sci., 66, 20132028.

    • Search Google Scholar
    • Export Citation
  • Sekhon, R. S., , and R. C. Srivastava, 1970: Snow size spectra and radar reflectivity. J. Atmos. Sci., 27, 299307.

  • Sempere-Torres, D., , J. M. Porrà, , and J. D. Creutin, 1994: A general formulation for raindrop size distribution. J. Appl. Meteor., 33, 14941502.

    • Search Google Scholar
    • Export Citation
  • Szyrmer, W., , and I. Zawadzki, 2010: Snow Studies. Part II: Average relationship between mass of snowflakes and their terminal fall velocity. J. Atmos. Sci., 67, 33193335.

    • Search Google Scholar
    • Export Citation
  • Szyrmer, W., , and I. Zawadzki, 2014: Snow studies. Part IV: Ensemble retrieval of snow microphysics from dual wavelength vertically pointing radars. J. Atmos. Sci., 71, 11711186.

    • Search Google Scholar
    • Export Citation
  • Szyrmer, W., , S. Laroche, , and I. Zawadzki, 2005: A microphysical bulk formulation based on scaling normalization of the particle size distribution. Part I: Description. J. Atmos. Sci., 62, 42064221.

    • Search Google Scholar
    • Export Citation
  • Szyrmer, W., , E. Jung, , and I. Zawadzki, 2009: Snowflake distribution characteristics from HVSD measurements. Preprints, 34th Conf. on Radar Meteorology, Williamsburg, VA, Amer. Meteor. Soc., P2.9. [Available online at https://ams.confex.com/ams/34Radar/techprogram/paper_155471.htm.]

  • Szyrmer, W., , A. Tatarevic & , and P. Kollias, 2012: Ice clouds microphysical retrieval using 94-GHz Doppler radar observations: Basic relations within the retrieval framework, J. Geophys. Res., 117, D14203, doi:10.1029/2011JD016675.

    • Search Google Scholar
    • Export Citation
  • Testud, J., , S. Oury, , R. A. Black, , P. Amayec, , and X. K. Dou, 2001: The concept of “normalized” distribution to describe raindrop spectra: A tool for cloud physics and cloud remote sensing. J. Appl. Meteor., 40, 11181140.

    • Search Google Scholar
    • Export Citation
  • Tian, L., , G. M. Heymsfield, , A. J. Heymsfield, , A. Bansemer, , L. Li, , C. H. Twohy, , and R. C. Srivastava, 2010: A study of cirrus ice particle size distributions using TC4 observations. J. Atmos. Sci., 67, 195216.

    • Search Google Scholar
    • Export Citation
  • Wang, Z., , G. M. Heymsfield, , L. Li, , and A. J. Heymsfield, 2005: Retrieving optically thick ice cloud microphysical properties by using airborne dual-wavelength radar measurements. J. Geophys. Res., 110, D19201, doi:10.1029/2005JD005969.

    • Search Google Scholar
    • Export Citation
  • Westbrook, C. D., , R. C. Ball, , P. R. Field, , and A. J. Heymsfield, 2004: Universality in snowflake aggregation. Geophys. Res. Lett., 31, L15104, doi:10.1029/2004GL020363.

    • Search Google Scholar
    • Export Citation
  • Zawadzki, I., , W. Szyrmer, , and S. Laroche, 2000: Diagnostic of supercooled clouds from single Doppler observations in regions of radar detectable snow. J. Appl. Meteor., 39, 10411058.

    • Search Google Scholar
    • Export Citation
  • Zawadzki, I., , E. Jung, , and G. W. Lee, 2010: Snow studies. Part I: A study of natural variability of snow terminal velocity. J. Atmos. Sci., 67, 15911604.

    • Search Google Scholar
    • Export Citation
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Snow Studies. Part III: Theoretical Derivations for the Ensemble Retrieval of Snow Microphysics from Dual-Wavelength Vertically Pointing Radars

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  • 1 Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada
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Abstract

As a first step toward retrieval of snow microphysics from two vertically pointing radars operating at X band and W band, a theoretical model of snow microphysics is formulated in which the number of unknown parameters is reduced to snow particle density and to two bulk quantities controlling the particle size distribution. This reduction of parameters is achieved by normalizing not only the size distribution but also the snow particle mass in the mass–size relationship as well as by using a relationship between snow density and snow terminal fall velocity. However, no single snow microphysical model could describe the observed variability in the radar measurements. The uncertainty in the developed deterministic relations that map the microphysical parameters to the observables is shown to be mainly associated with the assumed dependence of particle velocity on its mass and on the particle size distribution (PSD) representation. Hence, various mass–velocity relationships together with different generic functional forms of the PSD reported in literature are described in this paper and then used in the retrieval. The derived relations provide a reasonable range of uncertainty associated with the microphysics when used for the actual retrieval of snow properties from observations in Part IV. The uncertainty in the backscattering computations of an individual particle, performed using Mie theory assuming spherical form with nonuniform density, is not taken into account in this study.

Corresponding author address: Isztar Zawadzki, Dept. of Atmospheric and Oceanic Sciences, McGill University, 05 Sherbrooke St. West, Montreal, QC H3A 0B9, Canada. E-mail: isztar.zawadzki@mcgill.ca

Abstract

As a first step toward retrieval of snow microphysics from two vertically pointing radars operating at X band and W band, a theoretical model of snow microphysics is formulated in which the number of unknown parameters is reduced to snow particle density and to two bulk quantities controlling the particle size distribution. This reduction of parameters is achieved by normalizing not only the size distribution but also the snow particle mass in the mass–size relationship as well as by using a relationship between snow density and snow terminal fall velocity. However, no single snow microphysical model could describe the observed variability in the radar measurements. The uncertainty in the developed deterministic relations that map the microphysical parameters to the observables is shown to be mainly associated with the assumed dependence of particle velocity on its mass and on the particle size distribution (PSD) representation. Hence, various mass–velocity relationships together with different generic functional forms of the PSD reported in literature are described in this paper and then used in the retrieval. The derived relations provide a reasonable range of uncertainty associated with the microphysics when used for the actual retrieval of snow properties from observations in Part IV. The uncertainty in the backscattering computations of an individual particle, performed using Mie theory assuming spherical form with nonuniform density, is not taken into account in this study.

Corresponding author address: Isztar Zawadzki, Dept. of Atmospheric and Oceanic Sciences, McGill University, 05 Sherbrooke St. West, Montreal, QC H3A 0B9, Canada. E-mail: isztar.zawadzki@mcgill.ca
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