Revisiting the Hail Radar Reflectivity–Kinetic Energy Flux Relation by Combining T-Matrix and Discrete Dipole Approximation Calculations to Size Distribution Observations

Micael A. Cecchini aUniversidade de São Paulo, São Paulo, Brazil
gDepartment of Atmospheric Science, Colorado State University, Fort Collins, Colorado

Search for other papers by Micael A. Cecchini in
Current site
Google Scholar
PubMed
Close
,
Andrew J. Heymsfield bNational Center for Atmospheric Research, Boulder, Colorado

Search for other papers by Andrew J. Heymsfield in
Current site
Google Scholar
PubMed
Close
,
Ryan Honeyager cUniversity Corporation for Atmospheric Research, College Park, Maryland

Search for other papers by Ryan Honeyager in
Current site
Google Scholar
PubMed
Close
,
Paul Field dMet Office, Exeter, United Kingdom
eInstitute for Climate and Atmospheric Science, University of Leeds, Leeds, United Kingdom

Search for other papers by Paul Field in
Current site
Google Scholar
PubMed
Close
,
Luiz A. T. Machado aUniversidade de São Paulo, São Paulo, Brazil
fMultiphase Chemistry Department, Max Planck Institute for Chemistry, Mainz, Germany

Search for other papers by Luiz A. T. Machado in
Current site
Google Scholar
PubMed
Close
, and
Maria A. F. da Silva Dias aUniversidade de São Paulo, São Paulo, Brazil

Search for other papers by Maria A. F. da Silva Dias in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The retrieval of hail kinetic energy with weather radars or its simulation in numerical models is challenging because of the shape complexity and variable density of hailstones. We combine 3D scans of individual hailstones with measurements of the particle size distributions (PSD) and T-matrix calculations to understand how hail reflectivity Z changes when approximating hailstones as spheroids, as compared to the realistic shapes obtained by 3D scanning technology. Additionally, recent terminal velocity relations are used to compare Z to the hail kinetic energy flux E˙. We parameterize the hail backscattering cross sections at L, S, C, and X bands as a function of size between 0.5 and 5.0 cm, matching the range of the observed PSDs. The scattering calculations use the T-matrix method for size parameters below 1.0 and the discrete dipole approximation (DDA) method otherwise. The DDA calculations are done for 48 digital models of realistic hailstones of sizes between 1 and 5 cm. The DDA cross sections are calculated for multiple orientations and averaged assuming a fully random orientation distribution to provide a single value per hailstone. The T-matrix reflectivity assuming solid ice spheres presents negligible differences to DDA results for size parameters below 1.0. Therefore, T matrix was used to fill in the gaps left by the DDA calculations. The results are mapped to the same size bins of the observed PSDs, allowing the calculation of the radar reflectivity. This is then correlated to E˙, allowing a potential improvement of past retrieval methods of E˙ from Z in multiple wavelengths.

© 2022 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: Micael A. Cecchini, micael.cecchini@gmail.com.br

Abstract

The retrieval of hail kinetic energy with weather radars or its simulation in numerical models is challenging because of the shape complexity and variable density of hailstones. We combine 3D scans of individual hailstones with measurements of the particle size distributions (PSD) and T-matrix calculations to understand how hail reflectivity Z changes when approximating hailstones as spheroids, as compared to the realistic shapes obtained by 3D scanning technology. Additionally, recent terminal velocity relations are used to compare Z to the hail kinetic energy flux E˙. We parameterize the hail backscattering cross sections at L, S, C, and X bands as a function of size between 0.5 and 5.0 cm, matching the range of the observed PSDs. The scattering calculations use the T-matrix method for size parameters below 1.0 and the discrete dipole approximation (DDA) method otherwise. The DDA calculations are done for 48 digital models of realistic hailstones of sizes between 1 and 5 cm. The DDA cross sections are calculated for multiple orientations and averaged assuming a fully random orientation distribution to provide a single value per hailstone. The T-matrix reflectivity assuming solid ice spheres presents negligible differences to DDA results for size parameters below 1.0. Therefore, T matrix was used to fill in the gaps left by the DDA calculations. The results are mapped to the same size bins of the observed PSDs, allowing the calculation of the radar reflectivity. This is then correlated to E˙, allowing a potential improvement of past retrieval methods of E˙ from Z in multiple wavelengths.

© 2022 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: Micael A. Cecchini, micael.cecchini@gmail.com.br

Supplementary Materials

    • Supplemental Materials (PDF 207 KB)
Save
  • American Meteorological Society, 2022: Hail. Glossary of Meteorology, http://glossary.ametsoc.org/wiki/Hail.

  • Barge, B. L., and G. A. Isaac, 1973: The shape of Alberta hailstones. J. Rech. Atmos., 1, 1120.

  • Böhm, J. P., 1992: A general hydrodynamic theory for mixed-phase microphysics. Part I: Drag and fall speed of hydrometeors. Atmos. Res., 27, 253274, https://doi.org/10.1016/0169-8095(92)90035-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brown, T. M., W. H. Pogorzelski, and I. M. Giammanco, 2015: Evaluating hail damage using property insurance claims data. Wea. Climate Soc., 7, 197210, https://doi.org/10.1175/WCAS-D-15-0011.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Browning, K. A., and G. D. Beimers, 1967: The oblateness of large hailstones. J. Appl. Meteor., 6, 10751081, https://doi.org/10.1175/1520-0450(1967)006<1075:TOOLH>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cică, R., S. Burcea, and R. Bojariu, 2015: Assessment of severe hailstorms and hail risk using weather radar data. Meteor. Appl., 22, 746753, https://doi.org/10.1002/met.1512.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Detwiler, A., J. Scannell, D. Kliche, and S. Williams, 2012: Creating the long-term T-28 instrumented research aircraft data archive. Bull. Amer. Meteor. Soc., 93, 18171820, https://doi.org/10.1175/BAMS-D-11-00066.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Draine, B. T., 1988: The discrete-dipole approximation and its application to interstellar graphite grains. Astrophys. J., 333, 848872, https://doi.org/10.1086/166795.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Draine, B. T., and P. J. Flatau, 1994: Discrete-dipole approximation for scattering calculations. J. Opt. Soc. Amer., 11, 14911499, https://doi.org/10.1364/JOSAA.11.001491.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Field, P. R., A. J. Heymsfield, A. G. Detwiler, and J. M. Wilkinson, 2019: Normalized hail particle size distributions from the T-28 storm-penetrating aircraft. J. Appl. Meteor. Climatol., 58, 231245, https://doi.org/10.1175/JAMC-D-18-0118.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fraile, R., A. Castro, L. Lopez, J. L. Sanchez, and C. Palencia, 2003: The influence of melting on hailstone size distribution. Atmos. Res., 67–68, 203213, https://doi.org/10.1016/S0169-8095(03)00052-8.

    • Search Google Scholar
    • Export Citation
  • Garnett, J. C. M., and J. Larmor, 1904: Colours in metal glasses and in metallic films. Philos. Trans. Roy. Soc., 203, 385420, https://doi.org/10.1098/rsta.1904.0024.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Giammanco, I. M., T. M. Brown, M. R. Kumjian, and A. J. Heymsfield, 2014: Observations of hailstone sizes and shapes from the IBHS Hail Measurement Program: 2012–2014. 27th Conf. on Severe Local Storms, Madison, WI, Amer. Meteor. Soc., 16B.2, https://ams.confex.com/ams/27SLS/webprogram/Paper255294.html.

  • Giammanco, I. M., B. R. Maiden, H. E. Estes, and T. M. Brown-Giammanco, 2017: Using 3D laser scanning technology to create digital models of hailstones. Bull. Amer. Meteor. Soc., 98, 13411347, https://doi.org/10.1175/BAMS-D-15-00314.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gutierrez, R. E., and M. R. Kumjian, 2021: Environmental and radar characteristics of gargantuan hail–producing storms. Mon. Wea. Rev., 149, 25232538, https://doi.org/10.1175/MWR-D-20-0298.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heinselman, P. L., and A. V. Ryzhkov, 2006: Validation of polarimetric hail detection. Wea. Forecasting, 21, 839850, https://doi.org/10.1175/WAF956.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heymsfield, A., I. M. Giammanco, and R. Wright, 2014: Terminal velocities and kinetic energies of natural hailstones. Geophys. Res. Lett., 41, 86668672, https://doi.org/10.1002/2014GL062324.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heymsfield, A., M. Szakáll, A. Jost, I. Giammanco, and R. Wright, 2018: A comprehensive observational study of graupel and hail terminal velocity, mass flux, and kinetic energy. J. Atmos. Sci., 75, 38613885, https://doi.org/10.1175/JAS-D-18-0035.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heymsfield, A., M. Szakáll, A. Jost, I. Giammanco, R. Wright, and J. Brimelow, 2020: Corrigendum. J. Atmos. Sci., 77, 405412, https://doi.org/10.1175/JAS-D-19-0185.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hohl, R., H.-H. Schiesser, and I. Knepper, 2002: The use of weather radars to estimate hail damage to automobiles: An exploratory study in Switzerland. Atmos. Res., 61, 215238, https://doi.org/10.1016/S0169-8095(01)00134-X.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hong, G., 2007: Radar backscattering properties of nonspherical ice crystals at 94 GHz. J. Geophys. Res., 112, D22203, https://doi.org/10.1029/2007JD008839.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jiang, Z., M. R. Kumjian, R. S. Schrom, I. Giammanco, T. Brown-Giammanco, H. Estes, R. Maiden, and A. J. Heymsfield, 2019: Comparisons of electromagnetic scattering properties of real hailstones and spheroids. J. Appl. Meteor. Climatol., 58, 93112, https://doi.org/10.1175/JAMC-D-17-0344.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Johnson, G. N., and P. L. Smith Jr., 1980: Meteorological instrumentation system on the T-28 thunderstorm research aircraft. Bull. Amer. Meteor. Soc., 61, 972979, https://doi.org/10.1175/1520-0477(1980)061<0972:MISOTT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kaltenboeck, R., and A. Ryzhkov, 2013: Comparison of polarimetric signatures of hail at S and C bands for different hail sizes. Atmos. Res., 123, 323336, https://doi.org/10.1016/j.atmosres.2012.05.013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kim, M.-J., 2006: Single scattering parameters of randomly oriented snow particles at microwave frequencies. J. Geophys. Res., 111, D14201, https://doi.org/10.1029/2005JD006892.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Knight, N. C., 1986: Hailstone shape factor and its relation to radar interpretation of hail. J. Climate Appl. Meteor., 25, 19561958, https://doi.org/10.1175/1520-0450(1986)025<1956:HSFAIR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kry, P. R., and R. List, 1974: Angular motions of freely falling spheroidal hailstone models. Phys. Fluids, 17, 10931102, https://doi.org/10.1063/1.1694848.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kumjian, M., J. Picca, S. Ganson, A. Ryzhkov, A. Krause, D. Zrnić, and A. Khain, 2010: Polarimetric radar characteristics of large hail. 25th Conf. on Severe Local Storms, Denver, CO, Amer. Meteor. Soc., 11.2, https://ams.confex.com/ams/25SLS/techprogram/paper_176043.htm.

    • Crossref
    • Export Citation
  • Kumjian, M., Y. P. Richardson, T. Meyer, K. A. Kosiba, and J. Wurman, 2018: Resonance scattering effects in wet hail observed with a dual-X-band-frequency, dual-polarization Doppler on Wheels radar. J. Appl. Meteor. Climatol., 57, 27132731, https://doi.org/10.1175/JAMC-D-17-0362.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kumjian, M., and Coauthors, 2020: Gargantuan hail in Argentina. Bull. Amer. Meteor. Soc., 101, E1241E1258, https://doi.org/10.1175/BAMS-D-19-0012.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kunz, M., and P. I. S. Kugel, 2015: Detection of hail signatures from single-polarization C-band radar reflectivity. Atmos. Res., 153, 565577, https://doi.org/10.1016/j.atmosres.2014.09.010.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Leinonen, J., 2014: High-level interface to T-matrix scattering calculations: Architecture, capabilities and limitations. Opt. Express, 22, 16551660, https://doi.org/10.1364/OE.22.001655.

    • Crossref
    • 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, https://doi.org/10.1175/1520-0469(2004)061<2441:AOSSPO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Macklin, W. C., 1977: The characteristics of natural hailstones and their interpretation. Hail: A Review of Hail Science and Hail Suppression, S. W. Borland et al., Eds., Amer. Meteor. Soc., 6591.

    • Crossref
    • Export Citation
  • Matson, R. J., and A. W. Huggins, 1980: The direct measurement of the sizes, shapes and kinematics of falling hailstones. J. Atmos. Sci., 37, 11071125, https://doi.org/10.1175/1520-0469(1980)037<1107:TDMOTS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mätzler, C., 2006: Microwave dielectric properties of ice. Thermal Microwave Radiation—Applications for Remote Sensing, C. Mätzler et al., Eds., Electromagnetic Waves Series, Vol. 52, Institute of Engineering and Technology, 455462.

    • Crossref
    • Export Citation
  • Meyers, M. P., R. L. Walko, J. Y. Harrington, and W. R. Cotton, 1997: New RAMS cloud microphysics parameterization. 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, 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
  • Mishchenko, M. I., and L. D. Travis, 1994: T-matrix computations of light scattering by large spheroidal particles. Opt. Commun., 109, 1621, https://doi.org/10.1016/0030-4018(94)90731-5.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Morrison, H., and J. Milbrandt, 2011: Comparison of two-moment bulk microphysics schemes in idealized supercell thunderstorm simulations. Mon. Wea. Rev., 139, 11031130, https://doi.org/10.1175/2010MWR3433.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Oue, M., A. Tatarevic, P. Kollias, D. Wang, K. Yu, and A. M. Vogelmann, 2020: The Cloud-resolving model Radar Simulator (CR-SIM) version 3.3: Description and applications of a virtual observatory. Geosci. Model Dev., 13, 19751998, https://doi.org/10.5194/gmd-13-1975-2020.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rasmussen, R. M., and A. J. Heymsfield, 1987a: Melting and shedding of graupel and hail. Part I: Model physics. J. Atmos. Sci., 44, 27542763, https://doi.org/10.1175/1520-0469(1987)044<2754:MASOGA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rasmussen, R. M., and A. J. Heymsfield, 1987b: Melting and shedding of graupel and hail. Part II: Sensitivity study. J. Atmos. Sci., 44, 27642782, https://doi.org/10.1175/1520-0469(1987)044<2764:MASOGA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A., S. Ganson, A. Khain, M. Pinsky, and A. Pokrovsky, 2009: Polarimetric characteristics of melting hail at S and C bands. 34th Conf. on Radar Meteorology, Williamsburg, VA, Amer. Meteor. Soc., 4A.6, https://ams.confex.com/ams/34Radar/techprogram/paper_155571.htm.

    • Crossref
    • Export Citation
  • Ryzhkov, A., M. Pinsky, A. Pokrovsky, and A. Khain, 2011: Polarimetric radar observation operator for a cloud model with spectral microphysics. J. Appl. Meteor. Climatol., 50, 873894, https://doi.org/10.1175/2010JAMC2363.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A., M. R. Kumjian, S. M. Ganson, and A. P. Khain, 2013: Polarimetric radar characteristics of melting hail. Part I: Theoretical simulations using spectral microphysical modeling. J. Appl. Meteor. Climatol., 52, 28492870, https://doi.org/10.1175/JAMC-D-13-073.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schuster, S. S., R. J. Blong, and K. J. McAneney, 2006: Relationship between radar-derived hail kinetic energy and damage to insured buildings for severe hailstorms in eastern Australia. Atmos. Res., 81, 215235, https://doi.org/10.1016/j.atmosres.2005.12.003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Seifert, A., and K. D. Beheng, 2006: A two-moment cloud microphysics parameterization for mixed-phase clouds. Part 1: Model description. Meteor. Atmos. Phys., 92, 4566, https://doi.org/10.1007/s00703-005-0112-4.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Shedd, L., M. R. Kumjian, I. Giammanco, T. Brown-Giammanco, and B. R. Maiden, 2021: Hailstone shapes. J. Atmos. Sci., 78, 639652, https://doi.org/10.1175/JAS-D-20-0250.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Skripniková, K., and D. Řezáčová, 2014: Radar-based hail detection. Atmos. Res., 144, 175185, https://doi.org/10.1016/j.atmosres.2013.06.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Snyder, J. C., H. B. Bluestein, G. Zhang, and S. J. Frasier, 2010: Attenuation correction and hydrometeor classification of high-resolution, X-band, dual-polarized mobile radar measurements in severe convective storms. J. Atmos. Oceanic Technol., 27, 19792001, https://doi.org/10.1175/2010JTECHA1356.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stržinar, G., and G. Skok, 2018: Comparison and optimization of radar-based hail detection algorithms in Slovenia. Atmos. Res., 203, 275285, https://doi.org/10.1016/j.atmosres.2018.01.005.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Waldvogel, A., W. Schmid, and B. Federer, 1978: The kinetic energy of hailfalls. Part I: Hailstone spectra. J. Appl. Meteor. Climatol., 17, 515520, https://doi.org/10.1175/1520-0450(1978)017<0515:TKEOHP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Walko, R. L., W. R. Cotton, M. P. Meyers, and J. Y. Harrington, 1995: New RAMS cloud microphysics parameterization part I: The single-moment scheme. Atmos. Res., 38, 2962, https://doi.org/10.1016/0169-8095(94)00087-T.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Warren, R. A., H. A. Ramsay, S. T. Siems, M. J. Manton, J. R. Peter, A. Protat, and A. Pillalamarri, 2020: Radar‐based climatology of damaging hailstorms in Brisbane and Sydney, Australia. Quart. J. Roy. Meteor. Soc., 146, 505530, https://doi.org/10.1002/qj.3693.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Witt, A., M. D. Eilts, G. J. Stumpf, J. T. Johnson, E. D. W. Mitchell, and K. W. Thomas, 1998: An enhanced hail detection algorithm for the WSR-88D. Wea. Forecasting, 13, 286303, https://doi.org/10.1175/1520-0434(1998)013<0286:AEHDAF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Witt, A., D. W. Burgess, A. Seimon, J. T. Allen, J. C. Snyder, and H. B. Bluestein, 2018: Rapid-scan radar observations of an Oklahoma tornadic hailstorm producing giant hail. Wea. Forecasting, 33, 12631282, https://doi.org/10.1175/WAF-D-18-0003.1.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 557 150 0
Full Text Views 329 219 32
PDF Downloads 329 191 31