Theory and Observations of Controls on Lightning Flash Size Spectra

Eric C. Bruning Texas Tech University, Lubbock, Texas

Search for other papers by Eric C. Bruning in
Current site
Google Scholar
PubMed
Close
and
Donald R. MacGorman National Severe Storms Laboratory, Norman, Oklahoma

Search for other papers by Donald R. MacGorman in
Current site
Google Scholar
PubMed
Close
Restricted access

We are aware of a technical issue preventing figures and tables from showing in some newly published articles in the full-text HTML view.
While we are resolving the problem, please use the online PDF version of these articles to view figures and tables.

Abstract

Previous analyses of very high frequency (VHF) Lightning Mapping Array (LMA) observations relative to the location of deep convective updrafts have noted a systematic pattern in flash characteristics. In and near strong updrafts, flashes tend to be smaller and more frequent, while flashes far from strong vertical drafts exhibit the opposite tendency. This study quantitatively tests these past anecdotal observations using LMA data for two supercell storms that occurred in Oklahoma in 2004. The data support a prediction from electrostatics that frequent breakdown and large flash extents are opposed. An energetic scaling that combines flash rate and flash area exhibits a power-law scaling regime on scales of a few kilometers and a maximum in flash energy at about 10 km. The spectral shape is surprisingly consistent across a range of moderate to large flash rates. The shape of this lightning flash energy spectrum is similar to that expected of turbulent kinetic energy spectra in thunderstorms. In line with the hypothesized role of convective motions as the generator of thunderstorm electrical energy, the correspondence between kinematic and electrical energy spectra suggests that advection of charge-bearing precipitation by the storm’s flow, including in turbulent eddies, couples the electrical and kinematic properties of a thunderstorm.

Corresponding author address: Eric C. Bruning, Texas Tech University, Department of Geosciences, Atmospheric Science Group, Texas Tech University, Box 41053, Lubbock, TX 79409. E-mail: eric.bruning@ttu.edu

Abstract

Previous analyses of very high frequency (VHF) Lightning Mapping Array (LMA) observations relative to the location of deep convective updrafts have noted a systematic pattern in flash characteristics. In and near strong updrafts, flashes tend to be smaller and more frequent, while flashes far from strong vertical drafts exhibit the opposite tendency. This study quantitatively tests these past anecdotal observations using LMA data for two supercell storms that occurred in Oklahoma in 2004. The data support a prediction from electrostatics that frequent breakdown and large flash extents are opposed. An energetic scaling that combines flash rate and flash area exhibits a power-law scaling regime on scales of a few kilometers and a maximum in flash energy at about 10 km. The spectral shape is surprisingly consistent across a range of moderate to large flash rates. The shape of this lightning flash energy spectrum is similar to that expected of turbulent kinetic energy spectra in thunderstorms. In line with the hypothesized role of convective motions as the generator of thunderstorm electrical energy, the correspondence between kinematic and electrical energy spectra suggests that advection of charge-bearing precipitation by the storm’s flow, including in turbulent eddies, couples the electrical and kinematic properties of a thunderstorm.

Corresponding author address: Eric C. Bruning, Texas Tech University, Department of Geosciences, Atmospheric Science Group, Texas Tech University, Box 41053, Lubbock, TX 79409. E-mail: eric.bruning@ttu.edu
Save
  • Barthe, C., W. Deierling, and M. C. Barth, 2010: Estimation of total lightning from various storm parameters: A cloud-resolving model study. J. Geophys. Res., 115, D24202, doi:10.1029/2010JD014405.

    • Search Google Scholar
    • Export Citation
  • Boccippio, D. J., 2002: Lightning scaling relations revisited. J. Atmos. Sci., 59, 10861104.

  • Braham, R. R., Jr., 1952: The water and energy budgets of the thunderstorm and their relation to thunderstorm development. J. Meteor., 9, 227242.

    • Search Google Scholar
    • Export Citation
  • Braham, R. R., Jr., 1953: The energy of thunderstorm electrical activity. Pure Appl. Geophys., 25, 221222, doi:10.1007/BF02014068.

  • Bruning, E. C., W. D. Rust, T. J. Schuur, D. R. MacGorman, P. R. Krehbiel, and W. Rison, 2007: Electrical and polarimetric radar observations of a multicell storm in TELEX. Mon. Wea. Rev., 135, 25252544.

    • Search Google Scholar
    • Export Citation
  • Bruning, E. C., W. D. Rust, D. R. MacGorman, M. I. Biggerstaff, and T. J. Schuur, 2010: Formation of charge structures in a supercell. Mon. Wea. Rev., 138, 37403761.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., J. C. Wyngaard, and J. M. Fritsch, 2003: Resolution requirements for the simulation of deep moist convection. Mon. Wea. Rev., 131, 23942416.

    • Search Google Scholar
    • Export Citation
  • Calhoun, K. M., D. R. MacGorman, C. L. Ziegler, and M. I. Biggerstaff, 2013: Evolution of lightning activity and storm charge relative to dual-Doppler analysis of a high-precipitation supercell storm. Mon. Wea. Rev., 141, 2199–2223.

    • Search Google Scholar
    • Export Citation
  • Carey, L. D., M. J. Murphy, T. L. McCormick, and N. W. Demetriades, 2005: Lightning location relative to storm structure in a leading-line trailing stratiform mesoscale convective system. J. Geophys. Res., 110, D03105, doi:10.1029/2003JD004371.

    • Search Google Scholar
    • Export Citation
  • Coleman, L. M., T. C. Marshall, M. Stolzenburg, T. Hamlin, P. R. Krehbiel, W. Rison, and R. J. Thomas, 2003: Effects of charge and electrostatic potential on lightning propagation. J. Geophys. Res., 108, 4298, doi:10.1029/2002JD002718.

    • Search Google Scholar
    • Export Citation
  • Cummer, S. A., and W. A. Lyons, 2004: Lightning charge moment changes in U.S. High Plains thunderstorms. Geophys. Res. Lett.,31, L05114, doi:10.1029/2003GL019043.

  • Cuntz, H., F. Forstner, J. Haag, and A. Borst, 2008: The morphological identity of insect dendrites. PLoS Comput. Biol.,4, e1000251, doi:10.1371/journal.pcbi.1000251.

  • Deierling, W., and W. A. Petersen, 2008: Total lightning activity as an indicator of updraft characteristics. J. Geophys. Res., 113, D16210, doi:10.1029/2007JD009598.

    • Search Google Scholar
    • Export Citation
  • Deierling, W., W. A. Petersen, J. Latham, S. Ellis, and H. J. Christian, 2008: The relationship between lightning activity and ice fluxes in thunderstorms. J. Geophys. Res.,113, D15210, doi:10.1029/2007JD009700.

  • Devadoss, S. L., and J. O’Rourke, 2011: Discrete and Computational Geometry. Princeton University Press, 280 pp.

  • Dolan, B., and S. A. Rutledge, 2010: Using CASA IP1 to diagnose kinematic and microphysical interactions in a convective storm. Mon. Wea. Rev., 138, 16131634.

    • Search Google Scholar
    • Export Citation
  • Ely, B. L., R. E. Orville, L. D. Carey, and C. L. Hodapp, 2008: Evolution of the total lightning structure in a leading-line, trailing-stratiform mesoscale convective system over Houston, Texas. J. Geophys. Res., 113, D08114, doi:10.1029/2007JD008445.

    • Search Google Scholar
    • Export Citation
  • Emersic, C., P. L. Heinselman, D. R. MacGorman, and E. C. Bruning, 2011: Lightning activity in a hail-producing storm observed with phased-array radar. Mon. Wea. Rev., 139, 18091825.

    • Search Google Scholar
    • Export Citation
  • Garik, P., K. Mullen, and R. Richter, 1987: Models of controlled aggregation. Phys. Rev., 35A, 30463055, doi:10.1103/PhysRevA.35.3046.

    • Search Google Scholar
    • Export Citation
  • Garik, P., D. Barkey, E. Ben-Jacob, E. Bochner, N. Broxholm, B. Miller, B. Orr, and R. Zamir, 1989: Laplace- and diffusion-field-controlled growth in electrochemical deposition. Phys. Rev. Lett., 62, 27032706, doi:10.1103/PhysRevLett.62.2703.

    • Search Google Scholar
    • Export Citation
  • Kasemir, H. W., 1960: A contribution to the electrostatic theory of a lightning discharge. J. Geophys. Res., 65, 18731878.

  • Kolmogorov, A. N., 1941: The local structure of turbulence in in- compressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR, 30, 301305.

    • Search Google Scholar
    • Export Citation
  • Krehbiel, P. R., R. J. Thomas, W. Rison, T. Hamlin, J. Harlin, and M. Davis, 2000: GPS-based mapping system reveals lightning inside storms. Eos, Trans. Amer. Geophys. Union, 81, 2125.

    • Search Google Scholar
    • Export Citation
  • Kuhlman, K. M., C. L. Ziegler, E. R. Mansell, D. R. MacGorman, and J. M. Straka, 2006: Numerically simulated electrification and lightning of the 29 June 2000 STEPS supercell storm. Mon. Wea. Rev., 134, 27342757.

    • Search Google Scholar
    • Export Citation
  • Kuhlman, K. M., D. R. MacGorman, M. I. Biggerstaff, and P. R. Krehbiel, 2009: Lightning initiation in the anvils of two supercell storms. Geophys. Res. Lett., 36, L07802, doi:10.1029/2008GL036650.

    • Search Google Scholar
    • Export Citation
  • Lang, T. J., and Coauthors, 2004: The Severe Thunderstorm Electrification and Precipitation Study. Bull. Amer. Meteor. Soc., 85, 11071125.

    • Search Google Scholar
    • Export Citation
  • Leyvraz, F., 1985: The ‘active perimeter’ in cluster growth models: A rigorous bound. J. Phys., 18A, L941, doi:10.1088/0305-4470/18/15/007.

    • Search Google Scholar
    • Export Citation
  • Lhermitte, R., and P. R. Krehbiel, 1979: Doppler radar and radio observations of thunderstorms. IEEE Trans. Geosci. Electron., 17, 162171.

    • Search Google Scholar
    • Export Citation
  • Lilly, D. K., 1983: Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci., 40, 749761.

  • Lu, G., W. P. Winn, and R. G. Sonnenfeld, 2011: Charge transfer during intracloud lightning from a time-dependent multidipole model. J. Geophys. Res.,116, D03209, doi:10.1029/2010JD014495.

  • Lu, G., S. A. Cummer, R. J. Blakeslee, S. A. Weiss, and W. H. Beasley, 2012: Lightning morphology and impulse charge moment change of high peak current negative strokes. J. Geophys. Res.,117, D04213, doi:10.1029/2011JD016890.

  • Lund, N. R., D. R. MacGorman, T. J. Schuur, M. I. Biggerstaff, and W. D. Rust, 2009: Relationships between lightning location and polarimetric radar signatures in a small mesoscale convective system. Mon. Wea. Rev., 137, 41514170.

    • Search Google Scholar
    • Export Citation
  • MacGorman, D. R., and Coauthors, 2008: TELEX: The Thunderstorm Electrification and Lightning Experiment. Bull. Amer. Meteor. Soc., 89, 9971013.

    • Search Google Scholar
    • Export Citation
  • MacGorman, D. R., A. A. Few, and T. L. Teer, 1981: Layered lightning activity. J. Geophys. Res., 86 (C10), 99009910.

  • MacGorman, D. R., J. M. Straka, and C. L. Ziegler, 2001: A lightning parameterization for numerical cloud models. J. Appl. Meteor., 40, 459478.

    • Search Google Scholar
    • Export Citation
  • MacGorman, D. R., W. D. Rust, P. R. Krehbiel, W. Rison, E. C. Bruning, and K. Wiens, 2005: The electrical structure of two supercell storms during STEPS. Mon. Wea. Rev., 133, 25832607.

    • Search Google Scholar
    • Export Citation
  • Maggio, C. R., and Coauthors, 2005: Lightning-initiation locations as a remote sensing tool of large thunderstorm electric field vectors. J. Atmos. Oceanic Technol., 22, 10591068.

    • Search Google Scholar
    • Export Citation
  • Mansell, E. R., D. R. MacGorman, C. L. Ziegler, and J. M. Straka, 2002: Simulated three-dimensional branched lightning in a numerical thunderstorm model. J. Geophys. Res., 107 (D9), doi:10.1029/2000JD000244.

    • Search Google Scholar
    • Export Citation
  • Marshall, T. C., M. Stolzenburg, C. R. Maggio, L. M. Coleman, P. R. Krehbiel, T. Hamlin, R. J. Thomas, and W. Rison, 2005: Electric field magnitudes and lightning initiation in thunderstorms. J. Geophys. Res.,100 (D4), 7097–7103.

    • Search Google Scholar
    • Export Citation
  • Mazur, V., 2002: Physical processes during development of lightning flashes. C. R. Phys., 3, 13931409.

  • Mazur, V., and L. H. Ruhnke, 1993: Common physical processes in natural and artificially triggered lightning. J. Geophys. Res., 94 (D7), 12 91312 930.

    • Search Google Scholar
    • Export Citation
  • McCaul, E. W., S. J. Goodman, K. M. LaCasse, and D. J. Cecil, 2009: Forecasting lightning threat using cloud-resolving model simulations. Wea. Forecasting, 24, 709729.

    • Search Google Scholar
    • Export Citation
  • Mo, Q., J. H. Helsdon, and W. P. Winn, 2002: Aircraft observations of the creation of lower positive charges in thunderstorms. J. Geophys. Res., 107 (D22), 46164630.

    • Search Google Scholar
    • Export Citation
  • Murphy, M., 2006: When flash algorithms go bad. Preprints, First Int. Lightning Meteorology Conf., Tucson, AZ, Vaisala. [Available online at http://www.vaisala.com/en/events/ildcilmc/Documents/When%20Flash%20Algorithms%20Go%20Bad.pdf.]

  • Rasmussen, E. N., and J. M. Straka, 1998: Variations in supercell morphology. Part I: Observations of the role of upper-level storm-relative flow. Mon. Wea. Rev., 126, 24062421.

    • Search Google Scholar
    • Export Citation
  • Ray, P. S., D. R. MacGorman, W. D. Rust, W. L. Taylor, and L. Walters-Rasmussen, 1987: Lightning location relative to storm structure in a supercell storm and a multicell storm. J. Geophys. Res., 92 (D5), 57135724.

    • Search Google Scholar
    • Export Citation
  • Rust, W. D., W. L. Taylor, and D. MacGorman, 1982: Preliminary study of lightning location relative to storm structure. AIAA J., 20, 404409, doi:10.2514/3.51084.

    • Search Google Scholar
    • Export Citation
  • Rust, W. D., and Coauthors, 2005: Inverted-polarity electrical structures in thunderstorms in the Severe Thunderstorm Electrification and Precipitation Study. Atmos. Res., 76, 247271.

    • Search Google Scholar
    • Export Citation
  • Saunders, C. P. R., H. Bax-Norman, C. Emersic, E. E. Avila, and N. E. Castellano, 2006: Laboratory studies of the effect of cloud conditions on graupel/crystal charge transfer in thunderstorm electrification. Quart. J. Roy. Meteor. Soc., 132, 26532673.

    • Search Google Scholar
    • Export Citation
  • Schultz, C. J., W. A. Petersen, and L. D. Carey, 2009: Preliminary development and evaluation of lightning jump algorithms for the real-time detection of severe weather. J. Appl. Meteor. Climatol., 48, 25432563.

    • Search Google Scholar
    • Export Citation
  • Stolzenburg, M., and T. C. Marshall, 1994: Testing models of thunderstorm charge distributions with Coulomb’s law. J. Geophys. Res., 99 (D12), 25 92125 932.

    • Search Google Scholar
    • Export Citation
  • Stolzenburg, M., T. C. Marshall, W. D. Rust, E. C. Bruning, D. R. MacGorman, and T. Hamlin, 2007: Electric field values observed near lightning flash initiations. Geophys. Res. Lett., 34, L04804, doi:10.1029/2006GL028777.

    • Search Google Scholar
    • Export Citation
  • Takahashi, T., 1978: Riming electrification as a charge generation mechanism in thunderstorms. J. Atmos. Sci., 35, 15361548.

  • Tessendorf, S. A., L. J. Miller, K. C. Wiens, and S. A. Rutledge, 2005: The 29 June 2000 supercell observed during STEPS. Part I: Kinematics and microphysics. J. Atmos. Sci., 62, 41274150.

    • Search Google Scholar
    • Export Citation
  • Tessendorf, S. A., S. A. Rutledge, and K. C. Wiens, 2007: Radar and lightning observations of normal and inverted polarity multicellular storms from STEPS. Mon. Wea. Rev., 135, 3682–3706.

    • Search Google Scholar
    • Export Citation
  • Thomas, R. J., P. R. Krehbiel, W. Rison, S. J. Hunyady, W. P. Winn, T. Hamlin, and J. Harlin, 2004: Accuracy of the lightning mapping array. J. Geophys. Res., 109, D14207, doi:10.1029/2004JD004549.

    • Search Google Scholar
    • Export Citation
  • Wang, P. K., and H. R. Pruppacher, 1977: Acceleration to terminal velocity of cloud and raindrops. J. Appl. Meteor., 16, 275280.

  • Weinheimer, A. J., 1987: The electrostatic energy of a thunderstorm and its rate of change. J. Geophys. Res., 92 (D8), 97159722.

  • Weiss, S. A., D. R. MacGorman, and K. M. Calhoun, 2012: Lightning in the anvils of supercell thunderstorms. Mon. Wea. Rev., 140, 20642079.

    • Search Google Scholar
    • Export Citation
  • Wiens, K. C., S. A. Rutledge, and S. A. Tessendorf, 2005: The 29 June 2000 supercell observed during STEPS. Part II: Lightning and charge structure. J. Atmos. Sci., 62, 41514177.

    • Search Google Scholar
    • Export Citation
  • Williams, E. R., 1985: Large-scale charge separation in thunderclouds. J. Geophys. Res., 90 (D4), 60136025.

  • Williams, E. R., and R. M. Lhermitte, 1983: Radar tests of the precipitation hypothesis for thunderstorm electrification. J. Geophys. Res., 88 (C15), 10 98410 992.

    • Search Google Scholar
    • Export Citation
  • Williams, E. R., C. M. Cooke, and K. A. Wright, 1985: Electrical discharge propagation in and around space charge clouds. J. Geophys. Res., 90 (D4), 60596070.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 2777 1144 298
PDF Downloads 1367 324 18