Review and evaluation of lightning return stroke models including some aspects of their application

Four classes of models of the lightning return stroke are reviewed. These four classes are: (1) the gas dynamic models; (2) the electromagnetic models; (3) the distributed-circuit models; and (4) the "engineering" models. Validation of the reviewed models is discussed. For the gas dynamic models, validation is based on observations of the optical power and spectral output from natural lightning. The electromagnetic, distributed-circuit, and "engineering" models are most conveniently validated using measured electric and magnetic fields from natural and triggered lightning. Based on the entirety of the validation results and on mathematical simplicity, we rank the "engineering" models in the following descending order: MTLL, DU, MTLE, BG, and TL. When only the initial peak values of the channel-base current and remote electric or magnetic field are concerned, the TL model is preferred. Additionally discussed are several issues in lightning return-stroke modeling that either have been ignored to keep the modeling straightforward or have not been recognized, such as the treatment of the upper, in-cloud portion of the lightning channel, the boundary conditions at the ground, including the presence of a vertically extended strike object, the return-stroke speed at early times, the initial bi-directional extension of the return stroke channel, and the relation between leader and return stroke models. Various aspects of the calculation of lightning electric and magnetic fields in which return stroke models are used to specify the source are considered, including equations for fields and channel-base current, as well as a discussion of channel tortuosity and branches.

[1]  Vernon Cooray Derivation of return stroke parameters from the electric and magnetic field derivatives , 1989 .

[2]  Nobuyuki Takagi,et al.  Oscillating bipolar electric field changes due to close lightning return strokes , 1983 .

[3]  Vladimir A. Rakov,et al.  Ratio of leader to return stroke electric field change for first and subsequent lightning strokes , 1990 .

[4]  Robert Meneghini,et al.  Simulation of radiation from lightning return strokes - The effects of tortuosity , 1978 .

[5]  M. Uman,et al.  Magnetic field of lightning return stroke , 1969 .

[6]  V. Rakov,et al.  Hl A MODIFIED TRANSMISSION LINE MODEL FOR LIGHTNING RETURN STROKE FIELD CALCULATIONS , 1999 .

[7]  Vernon Cooray,et al.  Propagation effects caused by a rough ocean surface on the electromagnetic fields generated by lightning return strokes , 1994 .

[8]  Martin A. Uman,et al.  Variation in light intensity with height and time from subsequent lightning return strokes , 1983 .

[9]  E. T. Pierce,et al.  The modeling of channel current in the lightning return stroke , 1977 .

[10]  G. N. Oetzel,et al.  Computation of the diameter of a lightning return stroke , 1968 .

[11]  Martin A. Uman,et al.  Currents in Florida lightning return strokes , 1973 .

[12]  R. B. Standler,et al.  Lighting return-stroke models , 1980 .

[13]  D. M. Le Vine,et al.  Electromagnetic fields radiated from a lightning return stroke - Application of an exact solution to Maxwell's equations , 1978 .

[14]  C. F. Wagner,et al.  Lightning Stroke , 1859, Electrical Engineering.

[15]  V. Rakov,et al.  New insights into lightning processes gained from triggered‐lightning experiments in Florida and Alabama , 1998 .

[16]  Vernon Cooray,et al.  Horizontal fields generated by return strokes , 1992 .

[17]  Vernon Cooray,et al.  Propagation effects on the lightning-generated electromagnetic fields for homogeneous and mixed sea-land paths , 1994 .

[18]  Farhad Rachidi,et al.  Electromagnetic fields radiated by lightning return strokes to high towers , 1998 .

[19]  M. Plooster,et al.  Shock Waves from Line Sources. Numerical Solutions and Experimental Measurements , 1970 .

[20]  R. D. Hill Analysis of irregular paths of lightning channels , 1968 .

[21]  Jeremy A. Landt,et al.  Three Dimensional Time Domain Modelling of Lightning , 1987, IEEE Transactions on Power Delivery.

[22]  M. Uman,et al.  The electromagnetic radiation from a finite antenna , 1975 .

[23]  Joseph E. Borovsky,et al.  Lightning energetics: Estimates of energy dissipation in channels, channel radii, and channel‐heating risetimes , 1998 .

[24]  K. M. L. Srivastava,et al.  Return stroke velocity of a lightning discharge , 1966 .

[25]  E. Philip Krider,et al.  The optical and radiation field signatures produced by lightning return strokes , 1982 .

[26]  M. Uman,et al.  The Lightning Discharge , 1987 .

[27]  Martin A. Uman,et al.  Effects of 200 km propagation on Florida lightning return stroke electric fields , 1976 .

[28]  C. Christopoulos,et al.  A nonlinear transmission line model of the lightning return stroke , 1988 .

[29]  E. I. Dubovoy,et al.  Mesurements and numerical modeling of radio sounding reflection from a lightning channel , 1995 .

[30]  Vernon Cooray,et al.  Energy dissipation in lightning flashes , 1997 .

[31]  W. L. Taylor,et al.  A transmission line model with general velocities for lightning , 1977 .

[32]  Farhad Rachidi,et al.  On the Master, Uman, Lin, Standler and the Modified Transmission Line Lightning return stroke current models , 1990 .

[33]  M. Plooster,et al.  Numerical Model of the Return Stroke of the Lightning Discharge , 1971 .

[34]  M. Plooster,et al.  Numerical Simulation of Spark Discharges in Air , 1971 .

[35]  C. Leteinturier,et al.  Current and electric field derivatives in triggered lightning return strokes , 1990 .

[36]  Robert L. Gardner,et al.  Effect of the propagation path on lightning‐induced transient fields , 1981 .

[37]  Vladimir A. Rakov,et al.  Attachment process in rocket‐triggered lightning strokes , 1999 .

[38]  A. A. Few,et al.  Power spectrum of thunder , 1969 .

[39]  Gerhard Diendorfer,et al.  An improved return stroke model with specified channel-base current , 1990 .

[40]  Giuseppe Vecchi,et al.  Fractal approach to lightning radiation on a tortuous channel , 1994 .

[41]  Martin A. Uman,et al.  Peak power and energy dissipation in a single‐stroke lightning flash , 1968 .

[42]  Vernon Cooray,et al.  Effects of propagation on the rise times and the initial peaks of radiation fields from return strokes , 1983 .

[43]  Ashok K. Agrawal,et al.  Transient Response of Multiconductor Transmission Lines Excited by a Nonuniform Electromagnetic Field , 1980 .

[44]  R. L. Gardner,et al.  Reply to comments of Hill , 1987 .

[45]  James R. Wait Transient Fields of a Vertical Dipole Over a Homogeneous Curved Ground , 1956 .

[46]  C. E. R. BRUCE,et al.  The Lightning and Spark Discharges , 1941, Nature.

[47]  Gerhard Diendorfer,et al.  Extension of the Diendorfer-Uman lightning return stroke model to the case of a variable upward return stroke speed and a variable downward discharge current speed , 1991 .

[48]  M. Uman,et al.  Lightning return stroke current models with specified channel‐base current: A review and comparison , 1990 .

[49]  M. Rubinstein,et al.  An approximate formula for the calculation of the horizontal electric field from lightning at close, intermediate, and long range , 1996 .

[50]  Xuan-Min Shao,et al.  Radio interferometric observations of cloud‐to‐ground lightning phenomena in Florida , 1995 .

[51]  Richard E. Orville,et al.  A High-Speed Time-Resolved Spectroscopic Study of the Lightning Return Stroke. Part III. A Time-Dependent Model , 1968 .

[52]  M. V. Kostenko Electrodynamic characteristics of lightning and their influence on disturbances of high‐voltage lines , 1995 .

[53]  Richard E. Orville,et al.  An experimental test of the 'transmission-line model' of electromagnetic radiation from triggered lightning return strokes , 1988 .

[54]  Gerhard Diendorfer,et al.  Influence of channel base current and varying return stroke speed on the calculated fields of three important return stroke models , 1991 .

[55]  V. Rakov,et al.  Distribution of charge along the lightning channel : Relation to remote electric and magnetic fields and to return-stroke models , 1997 .

[56]  Matthew N. O. Sadiku,et al.  Elements of Electromagnetics , 1989 .

[57]  Richard E. Orville,et al.  A High-Speed Time-Resolved Spectroscopic Study of the Lightning Return Stroke: Part I. A Qualitative Analysis , 1968 .

[58]  Joseph E. Borovsky,et al.  An electrodynamic description of lightning return strokes and dart leaders: Guided wave propagation along conducting cylindrical channels , 1995 .

[59]  G. Vecchi,et al.  Lightning radiation field due to channel tortuosity and branching , 1997, 1997 Proceedings of International Symposium on Electromagnetic Compatibility.

[60]  C. Christopoulos,et al.  A model of the lightning channel, including corona, and prediction of the generated electromagnetic fields , 1990 .

[61]  Carl E. Baum,et al.  Analytic Return-Stroke Transmission-Line Model , 1987 .

[62]  M. Ianoz,et al.  Influence of a lossy ground on lightning-induced voltages on overhead lines , 1996 .

[63]  Farhad Rachidi,et al.  On the influence of elevated strike objects on directly measured and indirectly estimated lightning currents , 1998 .

[64]  E. M. Bazelyan Waves of ionization in lighting discharge , 1995 .

[65]  R. Thottappillil,et al.  Comparison of lightning return‐stroke models , 1993 .

[66]  Vladimir A. Rakov,et al.  Characterization of vertical electric fields 500 m and 30 m from triggered lightning , 1995 .

[67]  D. W. Quinn Modeling of lightning , 1987 .

[68]  Vladimir A. Rakov,et al.  Treatment of retardation effects in calculating the radiated electromagnetic fields from the lightning discharge , 1998 .

[69]  R. D. Hill Channel heating in return‐stroke lightning , 1971 .

[70]  James R. Wait,et al.  Concerning the horizontal electric field of lightning , 1997 .

[71]  Vladimir A. Rakov,et al.  Some inferences on the propagation mechanisms of dart leaders , 1998 .

[72]  Vernon Cooray,et al.  Effects of propagation on the return stroke radiation fields , 1987 .

[73]  R. H. Golde,et al.  The lightning discharge , 1941 .

[74]  D. M. Le Vine,et al.  Comment on the transmission‐line model for computing radiation from lightning , 1992 .

[75]  Vladimir A. Rakov,et al.  On the empirical formula of Willett et al. relating lightning return‐stroke peak current and peak electric field , 1992 .

[76]  D. M. Le Vine,et al.  Radiation from lightning return strokes over a finitely conducting Earth , 1986 .

[77]  Louis Baker Return-Stroke Transmission Line Model , 1987 .

[78]  J. C. Willett,et al.  Submicrosecond intercomparison of radiation fields and currents in triggered lightning return strokes based on the transmission-line model , 1989 .

[79]  B. Schonland,et al.  The Lightning Discharge , 1956 .

[80]  Vernon Cooray,et al.  The effects of variation of current amplitude, current risetime, and return stroke velocity along the return stroke channel on the electromagnetic fields generated by return strokes , 1990 .

[81]  Martin A. Uman,et al.  Transient electric and magnetic fields associated with establishing a finite electrostatic dipole, revisited , 1991 .

[82]  M. Ianoz,et al.  On lightning return stroke models for LEMP calculations , 1988 .

[83]  Martin A. Uman,et al.  Lightning return stroke model with height‐variable discharge time constant , 1994 .

[84]  E. Philip Krider,et al.  The optical power radiated by lightning return strokes , 1983 .

[85]  Martin A. Uman,et al.  Electric fields preceding cloud‐to‐ground lightning flashes , 1982 .

[86]  Paul Krehbiel,et al.  An analysis of the charge structure of lightning discharges to ground , 1979 .

[87]  J. R. Grant,et al.  Characterization of Lightning Return Stroke Electric and Magnetic Fields From Simultaneous Two- Station Measurements (Paper 9C0949) , 1979 .

[88]  V. A. Rakov,et al.  LIGHTNING ELECTROMAGNETIC FIELDS: MODELING AND MEASUREMENTS , 1999 .

[89]  D. F. Strawe,et al.  Non-linear modeling of lightning return strokes , 1979 .

[90]  R. D. Hill Energy dissipation in lightning , 1977 .

[91]  S. Yokoyama,et al.  Winter lightning on Japan Sea coast-development of measuring system on progressing feature of lightning discharge , 1990 .

[92]  Martin A. Uman,et al.  Calculations of lightning return stroke electric and magnetic fields above ground , 1981 .

[93]  V. P. Idone,et al.  Microscale tortuosity and its variation as observed in triggered lightning channels , 1995 .

[94]  Vernon Cooray,et al.  A model for subsequent return strokes , 1993 .

[95]  Martin A. Uman,et al.  On the radiation field turn‐on term associated with traveling current discontinuities in lightning , 1990 .

[96]  R. L. Gardner,et al.  Lightning return stroke. A numerical calculation of the optical radiation , 1986 .

[97]  Vladimir A. Rakov,et al.  Observed leader and return‐stroke propagation characteristics in the bottom 400 m of a rocket‐triggered lightning channel , 1999 .

[98]  R. D. Hill Electromagnetic radiation from erratic paths of lightning strokes , 1969 .

[99]  P F Little,et al.  Transmission line representation of a lightning return stroke , 1978 .

[100]  David M. Le Vine,et al.  The influence of channel geometry on the fine scale structure of radiation from lightning return strokes , 1995 .

[101]  Jeremy A. Landt,et al.  Three-Dimensional Time Domain Modeling of Lightning , 1987, IEEE Power Engineering Review.

[102]  E. Philip Krider,et al.  On the electromagnetic fields, Poynting vector, and peak power radiated by lightning return strokes , 1992 .