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Characterization and Modeling of Lightning Processes with Emphasis on Compact Intracloud Discharges

Permanent Link: http://ufdc.ufl.edu/UFE0041368/00001

Material Information

Title: Characterization and Modeling of Lightning Processes with Emphasis on Compact Intracloud Discharges
Physical Description: 1 online resource (508 p.)
Language: english
Creator: Nag, Amitabh
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: characterization, cloud, electromagnetic, ground, lightning, modeling, pulses
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: CHARACTERIZATION AND MODELING OF LIGHTNING PROCESSES WITH EMPHASIS ON COMPACT INTRACLOUD DISCHARGES Electromagnetic signatures of different lightning processes in Florida are acquired and examined with emphasis on compact intracloud discharges (CIDs). CIDs are the strongest natural producers of HF-VHF radiation, and they are considered the prime candidate for proposed satellite-based VHF global lightning monitors. Based on experimental evidence of reflections in electric field and dE/dt records and modeling, we infer that CID is essentially a bouncing-wave phenomenon. A transmission line model of CIDs including multiple reflections is developed and used for testing the applicability of Hertzian (electrically short) dipole approximation to CIDs. The latter approximation was used to estimate electrical parameters of CIDs. CID peak currents were found to be comparable to those of first return strokes. The occurrence of preliminary breakdown pulse trains in different geographical locations and the role of the lower positive charge region (LPCR) in facilitating different types of lightning are examined. While the LPCR may serve to enhance the electric field at the bottom of the negative charge region and thereby facilitate the launching of a negatively-charged leader toward ground, presence of excessive LPCR may prevent the occurrence of negative cloud-to-ground flashes by 'blocking' the progression of descending negative leader from reaching ground. Natural lightning electric field waveforms simultaneously measured at Camp Blanding and in Gainesville (45 km apart) are examined. It is shown, via modeling, that the slow front in electric field at far distances is primarily due to the radiation field component, while at near distances it is composed of more or less equal contributions from all three components of electric field. For both experimental and model-predicted waveforms, the duration of the slow front appears to be similar at near and far distances from the lightning channel. Various features of positive lightning discharges, which are considerably less understood than their negative counterparts, are analyzed. Relative magnitudes of first and subsequent return-stroke current and field peaks in negative cloud-to-ground lightning are examined. The performance characteristics of the U.S. National Lightning Detection Network (NLDN) are evaluated using rocket-triggered lightning data.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Amitabh Nag.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Rakov, Vladimir A.
Local: Co-adviser: Uman, Martin A.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-10-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041368:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041368/00001

Material Information

Title: Characterization and Modeling of Lightning Processes with Emphasis on Compact Intracloud Discharges
Physical Description: 1 online resource (508 p.)
Language: english
Creator: Nag, Amitabh
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: characterization, cloud, electromagnetic, ground, lightning, modeling, pulses
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: CHARACTERIZATION AND MODELING OF LIGHTNING PROCESSES WITH EMPHASIS ON COMPACT INTRACLOUD DISCHARGES Electromagnetic signatures of different lightning processes in Florida are acquired and examined with emphasis on compact intracloud discharges (CIDs). CIDs are the strongest natural producers of HF-VHF radiation, and they are considered the prime candidate for proposed satellite-based VHF global lightning monitors. Based on experimental evidence of reflections in electric field and dE/dt records and modeling, we infer that CID is essentially a bouncing-wave phenomenon. A transmission line model of CIDs including multiple reflections is developed and used for testing the applicability of Hertzian (electrically short) dipole approximation to CIDs. The latter approximation was used to estimate electrical parameters of CIDs. CID peak currents were found to be comparable to those of first return strokes. The occurrence of preliminary breakdown pulse trains in different geographical locations and the role of the lower positive charge region (LPCR) in facilitating different types of lightning are examined. While the LPCR may serve to enhance the electric field at the bottom of the negative charge region and thereby facilitate the launching of a negatively-charged leader toward ground, presence of excessive LPCR may prevent the occurrence of negative cloud-to-ground flashes by 'blocking' the progression of descending negative leader from reaching ground. Natural lightning electric field waveforms simultaneously measured at Camp Blanding and in Gainesville (45 km apart) are examined. It is shown, via modeling, that the slow front in electric field at far distances is primarily due to the radiation field component, while at near distances it is composed of more or less equal contributions from all three components of electric field. For both experimental and model-predicted waveforms, the duration of the slow front appears to be similar at near and far distances from the lightning channel. Various features of positive lightning discharges, which are considerably less understood than their negative counterparts, are analyzed. Relative magnitudes of first and subsequent return-stroke current and field peaks in negative cloud-to-ground lightning are examined. The performance characteristics of the U.S. National Lightning Detection Network (NLDN) are evaluated using rocket-triggered lightning data.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Amitabh Nag.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Rakov, Vladimir A.
Local: Co-adviser: Uman, Martin A.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-10-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041368:00001


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1 CHARACTERIZATION AND MODELING OF LIGHTNING PROCESSES WITH EMPHASIS ON COMPACT INTRACLOUD DISCHARGES By AMITABH NAG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010

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2 2010 Amitabh Nag

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3 To my parents and Gurudev

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4 ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Vlad imir Rakov, for his patient guidance and support over the course of my graduate study. I am gr ateful for the comments and suggestions that I received from Dr. Martin Uman, Dr. Douglas Jo rdan, and Dr. Robert Moore. I would like to acknowledge the help and coopera tion of my colleagues and memb ers of the University of Florida, Lightning Research Group. Dimitris Tsalikis, Dr. Joseph Howard, Christopher Biagi, Dustin Hill, Michael Stapleton, and Keith Rambo have all contributed in various ways toward the completion of this study. Finally, I would like to thank my parents whose sacrifices, support, and blessings will always be the reason behind whatev er I achieve in life. They have motivated me and helped me stay focused over the past four years.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ........10 LIST OF FIGURES.......................................................................................................................14 ABSTRACT...................................................................................................................................31 CHAPTER 1 INTRODUCTION..................................................................................................................33 2 LITERATURE REVIEW.......................................................................................................36 2.1 Role of Lightning in the Global Electric Circuit........................................................... 36 2.2 Lightning Discharge Processes..................................................................................... 37 2.2.1 Cloud-to-Ground Discharges............................................................................ 38 2.2.1.1 Preliminary breakdown in ground discharges.................................... 43 2.2.1.2 Electric and magnetic field waveforms from natural negative first strokes................................................................................................. 46 2.2.2 Cloud Discharges.............................................................................................. 50 2.2.2.1 General information............................................................................ 50 2.2.2.2 Initial breakdown in cloud discharges................................................52 2.3 Lightning Initiation Mechanisms.................................................................................. 56 2.3.1 Conventional Breakdown.................................................................................. 57 2.3.2 Runaway Breakdown........................................................................................ 58 2.4 Rocket-Triggered Lightning.......................................................................................... 58 2.5 Compact Intracloud Discharges.................................................................................... 62 3 EXPERIMENTAL SETUP....................................................................................................67 3.1 The Lightning Observatory in Gainesville.................................................................... 67 3.2 Overview of Experiments............................................................................................. 68 3.2.1 Single-Station Experiment................................................................................ 68 3.2.2 Two-Station Experiment................................................................................... 70 3.2.3 Equipment......................................................................................................... 72 3.2.3.1 Fiber optic links.................................................................................. 72 3.2.3.2 Digital storage oscilloscopes.............................................................. 75 3.2.3.3 GPS time-stamping system................................................................. 80 3.2.3.4 Dedicated phone line.......................................................................... 81 3.3 Wideband Electric Field Measurements ....................................................................... 82 3.3.1 Theory............................................................................................................... 82 3.3.2 Antenna............................................................................................................. 83 3.3.3 Electric Field Measuring System fo r the Two-Station Experime nt (E1).......... 84

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6 3.3.4 Electric Field Measuring System for the Single-St ation Experiment (E2)....... 86 3.4 Electric Field Derivative Measurements....................................................................... 89 3.4.1 Theory............................................................................................................... 89 3.4.2 Antenna............................................................................................................. 89 3.4.3 dE/dt Measuring System for the Two-Station Experiment (dE1)..................... 90 3.4.4 dE/dt Measuring System for the Single-Station Experime nt (dE2)..................91 3.5 Magnetic Field Derivative Measuring System.............................................................. 92 3.5.1 Theory............................................................................................................... 92 3.5.2 Antenna............................................................................................................. 93 3.5.3 dB/dt Measuring System for the Single-Station and Two-Station Experime nts (dB).............................................................................................. 95 3.6 Narrowband HF Measuring System.............................................................................. 96 3.7 Narrowband VHF measuring system............................................................................ 97 3.8 Amplitude Calibration of Measuring Systems............................................................ 100 3.9 Time Delays Between Measurements.........................................................................102 3.10 Details of the Two-Station Experiment Configuration............................................... 103 4 COMPACT INTRACLOUD LI GHTNING DISCHARGES............................................... 109 4.1 Phenomenology........................................................................................................... 109 4.1.1 Experimental Data and Methodology............................................................. 109 4.1.2 Relation of Compact In tracloud Discharges to Other Types of Lightning..... 113 4.1.3 Different Types of Electric Field Waveforms................................................. 115 4.1.4 Source Heights................................................................................................ 120 4.1.5 Electric Field Waveform Characteristics........................................................ 123 4.2 Conceptual Mechanism and Modeling........................................................................ 127 4.2.1 Evidence of Reflections in CID Electroma gnetic Field Signatures................ 128 4.2.2 Bouncing-Wave Mechanism........................................................................... 133 4.2.3 Bouncing-Wave Model: Current Distribution along the Channel.................. 140 4.2.4 Bouncing-Wave Model: Electric Fields at 2 and 200 km............................... 143 4.2.5 Hertzian Dipole Approximation...................................................................... 146 4.2.6 Equivalent Current Sources to Repres ent Multiple Trave ling Waves in the Bouncing-Wave Model................................................................................... 147 4.2.7 Bouncing-Wave Model: Allowed Ranges of Variation of Input Parame ters. 152 4.2.7.1 Reflection coefficients...................................................................... 152 4.2.7.2 Propagation speed (v) and channel length ( h )................................155 4.2.7.3 Source height.................................................................................... 161 4.2.7.4 Distance............................................................................................ 161 4.2.7.5 Current waveshape............................................................................ 162 4.2.8 Testing the Validity of BouncingWave Model and Hertzian-Dipole Approxima tion Using Electric Fields Simultaneously Measured at Near and Far Distances by Eack [2004]..................................................................169 4.2.8.1 Bouncing-wave model...................................................................... 169 4.2.8.2 Hertzian dipole approximation.........................................................170 4.2.8.3 Discussion......................................................................................... 171 4.2.9 Discussion and Summary................................................................................172 4.3 Estimation of Electrical Parameters............................................................................177

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7 4.3.1 The Hertzian Dipole Approximation Approach.............................................. 178 4.3.2 Limits of Validity of the He rtzian Dipole Approximation.............................. 182 4.3.3 Electrical Parameters of CIDs.........................................................................190 4.3.4 Upper Bound on Electric Field Prior to CID..................................................194 4.3.5 Total Energy Dissipated by CIDs................................................................... 203 4.3.6 Discussion....................................................................................................... 207 4.4 Summary.................................................................................................................... .213 5 PRELIMINARY BREAKDOWN PULSE TR AINS IN NE GATIVE CLOUD-TOGROUND LIGHTNING AND IN ATTEMPTED LEADERS............................................ 219 5.1 Characterization of Microsecondand Submicrosecond-Scale Electric Field Pulses Prior to First Re turn-Stroke Waveforms..........................................................219 5.2 Attempted Leaders...................................................................................................... 230 5.3 Some Inferences on the Role of Lower Positive Charge Region in Facilitating Different Types of Lightning...................................................................................... 233 5.3.1 Introduction..................................................................................................... 233 5.3.2 Analysis and Discussion.................................................................................241 5.3.2.1 Generation of preliminary breakdown pulse train ............................ 241 5.3.2.2 Variations in occurrence of pr eliminary breakdown pulse train ...... 242 5.3.2.3 Type of discharge versus ma gnitude of lower positive charg e region................................................................................................ 244 5.4 Summary.................................................................................................................... .247 6 TWO-STATION MEASUREMENTS OF CLOUD-TO-GROUND LIGHTNING ELECTRIC FIELDS ............................................................................................................. 251 6.1 Introduction............................................................................................................... ..251 6.2 Measured Electric Field Waveforms........................................................................... 253 6.3 Transmission Line Model........................................................................................... 277 6.3.1 Channel-Base Current without Pronounced Slow Front................................. 280 6.3.2 Electric Fields Computed Using the Original Transmission Line Model ....... 280 6.3.3 Electric Fields Computed Using the Two-W ave Transmission Line Model.. 281 6.3.4 Electric Fields Computed Using the Three-Wave Transm ission Line Model..............................................................................................................282 6.3.5 Channel-Base Current with Pronounced Slow Front and Computed Electric Fields................................................................................................. 283 6.4 Discussion................................................................................................................. ..299 6.5 Summary.................................................................................................................... .303 7 CHARACTERIZATION OF POSITIVE CLOUD-TO-GROUND LIGHTNING.............. 311 7.1 Multiplicity............................................................................................................... ...311 7.2 Parameters of Return Stroke Electric Field and Field Derivative Wa veforms........... 318 7.2.1 Distance-Normalized Electric Field Peaks...................................................... 318 7.2.2 Risetime.......................................................................................................... 319 7.2.3 Slow Front and Fast Transition....................................................................... 328

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8 7.2.4 Zero Crossing Time........................................................................................329 7.2.5 dE/dt Waveform Characteristics..................................................................... 337 7.3 Peak Current............................................................................................................... .346 7.3.1 Peak Current Estimated by the Na tional Lightning Detection Network (NLDN)........................................................................................................... 346 7.3.2 Linear Regression Equations Relating NLDN Current s and DistanceNorm alized Fields........................................................................................... 346 7.3.3 Peak Currents Inferred from Measured Electric Field Peaks Using the Transmission Line Model ............................................................................... 351 7.4 Charge Transferred by Return Strokes........................................................................359 7.5 Ratio of Electric and Magnetic Field Peaks................................................................ 365 7.6 Leader Stepping.......................................................................................................... 365 7.7 Preliminary Breakdown Pulse Trains.......................................................................... 367 7.8 Bipolar Lightning Discharges..................................................................................... 369 7.9 Summary.................................................................................................................... .373 8 FIRST VERSUS SUBSEQUENT RETURN-STROKE CURRENT AND FIELD PEAKS IN NEGATIVE CLOUD-TO -GROUND LIGHTNING DISCHARGES.............. 386 8.1 Introduction............................................................................................................... ..386 8.2 Methodology............................................................................................................... 386 8.3 Instrumentation and Data............................................................................................ 388 8.3.1 Electric Field Measurements in Gainesville, Florida...................................... 388 8.3.2 Electric Field Measurements in Austria.......................................................... 390 8.3.3 Electric Field Measurements in Brazil............................................................ 390 8.3.4 Electric Field Measurements in Sweden......................................................... 391 8.3.5 Currents Estimated by Lightning Locating Systems.......................................391 8.4 Analysis and Discussion.............................................................................................392 8.5 Summary.................................................................................................................... .400 9 SUMMARY OF RESULTS AND RECOMMENDATIONS FOR FUTURE RESEARCH....................................................................................................................... ..404 9.1 Summary of Results.................................................................................................... 404 9.1.1 Compact Intracloud Discharges...................................................................... 404 9.1.2 Preliminary Breakdown in Cloud-to -Ground Flashes and in Attem pted Leaders............................................................................................................407 9.1.3 First Return Strokes in Nega tive Cloud-to-Ground Lightning....................... 408 9.1.4 Positive Cloud-to-Ground Lightning.............................................................. 409 9.1.5 Ratio of First versus Subsequent Return Stroke Intensities in Negative Cloud-to-Ground Discharges.......................................................................... 410 9.2 Recommendations for Future Research......................................................................411 APPENDIX A INVENTORY TABLE AND CATALOG OF 48 COMPACT INTRACLOUD DISCHARGE WA VEFORMS............................................................................................. 413

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9 B ELECTRIC FIELD DERIVATIVE WAVEFO RMS OF 27 POSITIVE RETURN STROKES........................................................................................................................ .....464 C NLDN RESPONSES TO ROCKET-T RIGGERED LIGHT NING AT CAMP BLANDING, FLORIDA, IN 2004, 2005, AND 2007......................................................... 478 C.1 Introduction............................................................................................................... ..478 C.2 Data and Methodology................................................................................................479 C.3 Results and Discussion................................................................................................ 480 C.3.1 Flash and Stroke Detection Efficiencies......................................................... 480 C.3.2 Location Accuracy.......................................................................................... 483 C.3.3 Peak Current Estimates................................................................................... 487 C.4 Summary.................................................................................................................... .491 LIST OF REFERENCES.............................................................................................................495 BIOGRAPHICAL SKETCH.......................................................................................................508

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10 LIST OF TABLES Table page 2-1 Characteristics of narrow bipolar electric field pulses and associated HF (3-30 MHz) radiation...................................................................................................................... .......653-1 A list of LOG sensors (see Figure 3-3) used in two-stati on and single-station experiments........................................................................................................................713-2 Digital storage oscilloscope used at the LOG prior to April 2008.................................... 763-3 Digital storage oscilloscopes us ed at the LOG after April 2008....................................... 783-4 Characterization and calibr ation factors of measuring systems at the LOG prior to April 2008 (Benton Hall)................................................................................................. 1033-5 Characterization and calibration factors of electric field and dE/dt measuring systems at the LOG after April, 2008 (Engineering Building)...................................................... 1043-6 Characterization and calibr ation factors of dB/dt measuring systems at the LOG after April, 2008 (Engineering Building)................................................................................. 1053-7 GPS locations, accurate to 2 m, of a ll antennas on the roof of the Engineering Building in 2008.............................................................................................................. 1054-1 Number of NLDN-located CIDs in different horizontal distance ranges........................ 1114-2 Influence of source height on the ratio of initial electric field peak to opposite polarity overshoot of CID electric fields......................................................................... 1614-3 Influence of distance on the ratio of initi al electric field peak to opposite polarity overshoot of CID electric fields....................................................................................... 1634-4 Parameters and k in Equation 4-9 yielding different values of current risetime (t1).... 1634-5 Combinations of reflection coefficients, propagation speeds, and channel lengths that produce distant CID electric fields that ar e consistent with experimental data for current risetime of 3 s....................................................................................................1654-6 Combinations of propagation speeds and channel lengths that produce distant CID electric fields that are consistent with experimental data for = 0 and current risetime of 2 s............................................................................................................... .1654-7 CID parameters for which electric fields at close and far distan ces that are based on the bouncing-wave model and Hertzian dipo le approximation best fit the fields measured by Eack in New Mexico..................................................................................172

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11 4-8 Comparison of electric fields based on the Hertzian dipole approxima tion and bouncing-wave model for a current risetime of 6 s for different combinations of reflection coefficients, current wa ve speeds, and channel lengths..................................1874-9 Comparison of electric fields based on the Hertzian dipole approximation and bouncing wave model for a current risetime of 3 s for different combinations of reflection coefficients, current wa ve speeds, and channel lengths..................................1884-10 Comparison of electric fields based on the Hertzian dipole approximation and bouncing wave model for a current risetime of 8.5 s for different combinations of reflection coefficients, current wa ve speeds, and channel lengths..................................1884-11 Parameters of nine located CIDs with ch annel lengths estimated using reflections in dE/dt waveforms and assumed propagation speed of 2.5 x 108 m/s................................1924-12 Peak current and charge transfer at 5 s scaled to different cha nnel lengths that were inferred for 9 CIDs using reflections in measured dE/dt waveforms and assumed propagation speeds........................................................................................................... 1934-13 Peak current and charge transfer at 5 s scaled to different channel lengths for 39 CIDs.................................................................................................................................1934-14 The maximum electric field at the su rface of each of the two oppositely charged spheres separated by a zero net charge region (Figure 4-42a) for different combinations of charge transfer and assumed volume charge density............................2045-1 Categorization of pulses according to normalized amplitude.......................................... 2205-2 Summary of occurrence of smaller and narrower pulses observed in the 12 cloud-toground discharges............................................................................................................ 2276-1 Summary of natural lightni ng fields simultaneously measured at Camp Blanding and in Gainesville, Florida......................................................................................................2556-2 Characteristics of electric field wavefo rms produced by negative first return strokes measured at near (Camp Blanding) and far (Gainesville) stations.................................. 2576-3 Initial (radiation) el ectric field peaks for each stroke in four flashes recorded at near (Camp Blanding) and far (G ainesville) stations..............................................................2596-4. The values of the parameters m, I0, n, 1, and 2 for different values of k, reproduced from Table II of De Conti and Visacro used in Equation 6-9 to produce current waveform shown in Figure 6-35.......................................................................... 2957-1 Summary of the positive and bipolar cloud-to-ground light ning data (a total of 54 flashes) recorded at the LOG. Data record ed is indicated by "Y" and not recorded by "N"...................................................................................................................................315

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12 7-2 Interstroke interval, distance between firs t and second strokes, and semi -major axis (SMA) length of NLDN 50% loca tion error ellipse for each stroke of 8 two-stroke positive flashes............................................................................................................... ..3187-3 Parameters of electric field waveforms produced by first and subsequent return strokes in positive lightning............................................................................................. 3207-4 Number of positive return strokes in different distance ranges and corresponding GM electric field peaks normalized to 100 km....................................................................... 3207-5 Risetimes of return stroke electric fi eld waveforms in different regions and in different seasons...............................................................................................................3267-6 Characteristics of the slow front and fast transition in positive and negative returns strokes in different regions............................................................................................... 3367-7 Zero-crossing time and opposite polarity ov ershoot relative to peak of the return stroke electric field waveform for different seasons in Florida and Japan......................3427-8 Number of positive return strokes in different distance ranges and corresponding GM current peaks....................................................................................................................3477-9 Number of negative return strokes in different distance ra nges and corresponding GM current peaks............................................................................................................. 3527-10 Summary of electric field change ( E ), charge transfer ( Q ), and average current ( Q/ t ) at different times ( t ) after the beginning of the return stroke field change for 17 first and 2 subsequent positive retu rn strokes.......................................................3627-11 Ratio of electric and magnetic field p eaks for the seven positive return strokes............. 3658-1 Summary of first to subsequent stroke el ectric field or current peak ratios estimated from differen t studies....................................................................................................... 3978-2 Summary of first to subsequent stroke electric field or current peak ratios for subsequent strokes following a previously-formed channel............................................ 3988-3 Summary of first to subsequent stroke electric field or current peak ratios for multiple-stroke flashes only............................................................................................. 3998-4 Summary of subsequent to first stroke electric field or current peak ratio estimated from differen t studies....................................................................................................... 4018-5 Summary of multiple-stroke flash charac teristics reported in different studies.............. 402A-1 Summary of horizontal dist ance (r), measured electric (Ep) and magnetic (Bp) field peaks, height (h), elevation angle ( ), inclined distance (R), and normalized electric field (EN) for 48 CIDs recorded at the LOG in 2008.......................................................413

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13 C-1 Summary of flashes and strokes recorded at Cam p Blanding during summers of 2004, 2005, and 2007, along with the corresponding NLDN detection efficiencies.......479

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14 LIST OF FIGURES Figure page 2-1 The left panel shows a simplified illustrati on of the global electric circuit. The right panel shows the Earth-atmosphere lossy capacitor system (not to scale). ......................... 372-2 Different types of lightning discharges..............................................................................392-3 Four types of cloud-to-g round lightning discharge........................................................... 402-4 Various processes comprising a ne gative cloud-to-ground lightning flash.......................412-5 Examples of electric field pulse waveforms characteristic of (a) preliminary breakdown in negative ground flashes, (b) th e active stage (in itial breakdown) in cloud flashes.......................................................................................................................442-6 Histogram of the ratio of preliminary brea kdown to first return stroke field peaks for individual flashes...............................................................................................................462-7 Typical vertical electric field intensity (left column) and azimuthal magnetic flux density (right column) waveforms for first (solid line) and subsequent (broken line) return strokes................................................................................................................. .....472-8 Electric field waveforms of (a) a first retu rn stroke, (b) a subsequent stroke initiated by a dart-stepped leader, and (c) a subsequent return stroke initiated by a dart leader, showing the fine structure both before and after the initial field peak.............................. 482-9 Occurrence statistics of electric field pulses in a cloud discharge..................................... 532-10 Electric field record of cloud flash 05/24/06_299............................................................. 552-11 Examples of (a) classical and (b) n arrow pulses in the early stage of cloud discharges...........................................................................................................................552-12 Histogram of total duration of unipolar and bipolar pulses in 12 selected cloud discharges...........................................................................................................................562-13 Submicrosecond-scale pulses that occurred in a cloud discharge..................................... 592-14 Sequence of events in classical trigge red lightning. The upward positive leader and initial continuous current cons titute the initial stage......................................................... 602-15 Narrow bipolar pulses recorded by th e Los Alamos Sferic Array (LASA).......................653-1 The Lightning Observatory on the roof of the Engineering Building on the University of Florida campus at Gainesville.....................................................................683-2 Google Earth image of the LOG in 2008........................................................................... 69

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15 3-3 Schematic showing positions of the different sensors at the LOG in 2008....................... 713-4 Block diagram of the si ngle-station experiment................................................................ 733-5 Block diagram of the two-station experiment.................................................................... 743-6 Frequency response of an Opticomm MMV-120C fiber-optic link used at the LOG.......753-7 Digitizing oscilloscopes inside the glass cupola at the LOG in August, 2008.................. 773-8 The GPS antenna used at the LOG....................................................................................803-9 An electric field antenna system........................................................................................ 823-10 An elevated flat plate antenna used for measuring wideband electric field at the LOG............................................................................................................................ .......853-11 Electronics inside a Hoffma n enclosure used in electric field measuring system (E1) at the LOG..........................................................................................................................873-12 Schematic of the high input-impedance amplifier used in electric field measuring system (E1) at the LOG..................................................................................................... 873-13 Frequency response of the high input-impedance amplifier used in electric field measuring system (E1) at the LOG.................................................................................... 883-14 Frequency response of the high input-impedance amplifier used in electric field measuring system (E2) at the LOG.................................................................................... 88 3-15 An electric field derivative antenna system...................893-16 Schematic of the amplifier used in dE/d t measuring systems (dE1 and dE2) at the LOG............................................................................................................................ .......913-17 Frequency response of the amplifiers used in dE/dt measuring systems (dE1 and dE2) at the LOG................................................................................................................ .923 A single-ended output coaxial loop antenna with both ends of the cable terminated in 50 ....................................................................................................................................943-19 Two loops (oriented north-south and eas t-west) of the magnetic field derivative antenna used at the LOG....................................................................................................963-20 Frequency response of the amplifiers used in dB/dt measuring systems, dB (N-S) and dB (E-W), at the LOG........................................................................................................973-21 Block diagram of the HF measuring system. The HF receiver had an overall gain of 31 (30 dB) at center frequency (5 MHz)............................................................................98

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16 3-22 Frequency response of the HF receiver used at the LOG..................................................983-23 Whip antenna used for the narrowband VHF measurement at the LOG........................... 993-24 Block diagram of the VHF measuring syst em. The VHF receiver had an overall gain of 27 (29 dB) at the cente r frequency (36 MHz)...............................................................993-25 Frequency response of the VHF receiver used at the LOG.............................................1003-26 The histogram of the ratio of electric to magnetic field peaks for 43 first return strokes in negative cloud-to-ground lightni ng, recorded in 2008 in Gainesville, Florida........................................................................................................................ ......1023-27 OR gate used to generate tr igger pulses at Camp Blanding............................................. 1073-28 Functional diagram of a one-shot circuit implemented using a CD74HC221 (monostable multivibrator) used to generate a 5 V, 462 s rectangular pulse which is fed into the telephone line................................................................................................ 1073-29 Trigger pulse from Camp Blanding recei ved at Gainesville via the AT&T BellSouth analog conditioned telephone line................................................................................... 1083-30 A block diagram schematically sh owing the two-station experiment............................. 1084-1 Electromagnetic signatures produced by a CID in Gainesville, Florida.......................... 1104-2 Geometrical parameters and equations used in estimating radiation source heights. See text for details........................................................................................................... .1124-3 Electric field and VHF (36 MHz) radi ation from a CID that was followed by a "normal" IC (from another experime nt in Gainesville, Florida)......................................1144-4 A CID that occurred during an eight-str oke negative CG, within horizontal distances of 7 to 8 km of all the CG strokes. (a ) Wideband electric field and VHF (36 MHz) radiation. (b) Plan view of NLDN-estimated relative positions of the CID (hollow circle) and return strokes (numbere d solid circles) of CG flash...................................... 1174-5 Wideband electric field reco rd (top) showing two CIDs that occurred 66 ms apart at a horizontal distance of 24 km from each other. Indivi dual CID signatures (bottom) displayed on expanded (10 and 5 s per di vision for CID 1 and CID 2, respectively) time scales.................................................................................................................... ....1194-6 Occurrence context of CIDs............................................................................................. 1204-7 Three types of CID elect ric field waveforms exhibiti ng (a) only radiation, (b) radiation and static field components (induc tion component is not apparent), and (c) only induction and static field components.....................................................................1214-8 Histograms of radiation source heights for 48 CIDs.......................................................123

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17 4-9 Histograms of electric fields peaks normalized to R = 100 km and = 0o for 48 CIDs.................................................................................................................................1254-10 Electric field waveform ch aracteristics for 48 CIDs........................................................1264-11 Signatures of a CID that transferred ne gative charge downward (or positive charge upward), recorded in Gainesville, Florida....................................................................... 1304-12 Signatures of a CID that transferred negative charge upward (or positive charge downward), recorded in Gainesville, Florida.................................................................. 1314-13 Characteristics of 5 MHz HF radiation signature for 31 CIDs........................................ 1354-14 Characteristics of 36 MHz VHF radiation signature for 52 CIDs................................... 1364-15 Histograms of the starting-time of (a) HF and (b) VHF radiati on signatures relative to the onset-time of the correspond ing electric field waveform...................................... 1374-16 Illustration of the bouncing-wave mechanis m for a CID current pulse with a peak of 50 kA and propagation speed v= 28 m/s injected at th e bottom of a 100 m long vertical conducting ch annel at t = 0.................................................................................1384-17 Currents associated with the bouncing-wave model........................................................ 1444-18 Geometrical parameters used in calculat ing the electric field at observation point P on perfectly conducting ground at horizontal distance r from the vertical CID channel extending between heights h1 and h2..................................................................1454-19 Electric fields predicte d by the bouncing-wave model.................................................... 1484-20 Electric fields at (a) 2 km and (b) 200 km computed using the Hertzian dipole approximation for a CID with a channel length of 100 m at a height of 15 km, excited by current waveform shown in Figure 4-17a for z = h1 + h/2 (in the middle of the channel)..................................................................................................................1494-21 Currents, electric fiel ds, electric field derivatives, and their components.......................1534-22 Currents, electric fiel ds, electric field derivatives, and their components.......................1544-23 Illustration of the reversal distance for electrostatic and induc tion field components. Inset shows the direction of the far ( < 35.3o) electric field vector for different combinations of charge polarity and direction of charge motion.................................... 1554-24 Combinations of propagation speed and channel length for which the ratio of initial electric field peak to opposite polarity overs hoot of model-predicted electric fields at 200 km attains 2.5 (the lowest value found in the experimental data) and 3.0 for a current risetime of 6 s and for (a) = 0 and (b) = -0.5............................................... 158

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18 4-25 Bouncing-wave model predicted electric fields at 200 km for different combinations of propagation speed and cha nnel length for a current rise time of 6 s and for (a) = 0 and (b) = -0.5............................................................................................................. 1594-26 Currents and corresponding electric fields for the same total cu rrent duration (30 s) and peak (50 kA), but different risetimes of 3, 6 and 9 s for = 0, h = 100 m, and v = 2 x 108 m/s................................................................................................................. 1664-27 Electric field waveforms at 200 km fo r different propagation speeds and channel lengths of (a) 100 m and (b) 500 m, fo r a current risetime of 2 s and = 0.................. 1674-28 Electric field waveforms at 200 km for di fferent combinations of propagation speed and channel length for a current risetime of 8.5 s and for (a) = 0 and (b) = -0.5....1684-29 Electric fields computed using the bounc ing-wave model (in red) overlaid with the fields measured by Eack (in blue) at (a) near and (b) far distances................................. 1734-30 Electric fields computed using the Hert zian dipole approximation (in red) overlaid with the fields measured by Eack (in blue) at (a) near and (b) far distances................... 1734-31 Bouncing-wave model-predicted electric field for a CID and current waveforms obtained by solving Equation 4-13 (blue line) and using the radiation field approximation (red line)..................................................................................................1814-32 Vertical electric fields for th e bouncing-wave model (solid line) for = 0, v = 2 x 108 m/s, RT = 6 s, and channel lengths of (a) 100, (b) 350, and (c) 700 m versus those for the Hertzian dipole approximation (dashed line)....................................................... 1844-33 Same as Figure 4-32, but for = -0.5 and channel lengths of (a) 100 and (b) 350 m, for both of which the Hertzian di pole approximation is acceptable................................ 1854-34 Comparison of the Hertzian dipole va lidity domain (combinations of propagation speed and channel length) with the "allowed" one for RT = 6 s and = 0................... 1864-35 Measured electric field a nd electric field derivative and inferred electrical parameters, each as a function of time, for a CID........................................................... 1894-36 Histogram of peak currents for 48 CIDs.......................................................................... 1954-37 Histogram of zero-to-peak current risetimes for 48 CIDs............................................... 1964-38 Histogram of 10-to-90% cu rrent risetimes for 48 CIDs.................................................. 1974-39 Histogram of charge transf erred at 5 s for 48 CIDs...................................................... 1984-40 Histogram of peak radiated power for 48 CIDs............................................................... 1994-41 Histogram of radiated en ergy at 5 s for 48 CIDs........................................................... 200

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19 4-42 Simplified charge configurat ion and electric field intens ity profile giving rise to a CID............................................................................................................................ .......2054-43 Ranges of dissipated energy and channel le ngth for typical first strokes in cloud-toground flashes, regular intrac loud flashes, and CIDs...................................................... 2144-44 NLDN-reported peak current versus peak current estimated using the transmission line model with v = 1.8 x 108 m/s for 48 CIDs................................................................ 2144-45 NLDN-reported peak current versus peak current estimated using the Hertzian dipole (HD) approximation for 48 CIDs..................................................................................... 2155-1 Electric field record of cloud-to-ground flash 05/24/06_1078 showing preliminary breakdown pulse train followed by two return strokes....................................................2215-2 Examples of (a) classical and (b) n arrow preliminary breakdown pulses in cloudto-ground discharges analyzed in this study.................................................................... 2235-3 Occurrence of pulses of different amplitude prior to the first stroke of cloud-toground flash whose electric field r ecord is shown in Figure 5-1..................................... 2245-4 Occurrence of pulses of different total dur ation prior to the firs t stroke of cloud-toground flash whose electric field r ecord is shown in Figure 5-1..................................... 2245-5 Histogram of pulse amplitude for four different types of pulses in cloud-to-ground flash whose electric field reco rd is shown in Figure 5-1................................................. 2255-6 Histogram of total pulse duration for f our different types of pulses in cloud-toground flash whose electric field r ecord is shown in Figure 5-1..................................... 2255-7 Histogram of total duration of unipol ar and bipolar pulses in 12 cloud-to-ground discharges.........................................................................................................................2265-8 Occurrence of pulses of different total dur ation in different part s (four quarters) of the preliminary breakdown pulse train fo r all 12 cloud-to-ground flashes combined..... 2265-9 Histogram of the total duration of pre liminary breakdown pulse trains for 12 cloudto-ground flashes..............................................................................................................2285-10 Ranges of variation (vertical bars) and m ean values (diamonds) of pulse duration in individual preliminary breakdown pulse trains................................................................ 2295-11 Ranges of variation (vertical bars) and mean values (diam onds) of interpul se interval in individual preliminary breakdown pulse trains........................................................... 2295-12 Electric field record of an attempted leader with no pulse activity following the preliminary breakdown pulse train.................................................................................. 231

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20 5-13 Typical (a) classical and (b) narrow pulses of a preliminary breakdown (PB) pulse train of an attem pted leader.................................................................................... 2345-14 Histogram of preliminary breakdown pulse train duration for attempted leaders. Note that a total of 35 preliminar y breakdown pulse trains were found in 33 electric field records........................................................................................................................ ......2355-15 Ranges of variation (vertical bars) and m ean values (diamonds) of pulse duration in individual preliminary breakdown pulse trains of attempted leaders.............................. 2355-16 Ranges of variation (vertical bars) and mean values (diam onds) of interpul se interval in individual preliminary breakdown pul se trains of attempted leaders.......................... 2365-17 The electric field record of the PB pulse train of a nega tive cloud-to-ground discharge that occurred on A ugust 1, 2008 in Gainesville, Florida at a distance of 28 km from the measuring station........................................................................................ 2405-18 A schematic illustration (left) of electric field enhancement and reduction effects of the lower positive charge region (+QLP) below the main negative charge region ( QN). Schematic representation of prelim inary breakdown stepping process (right, top) in negative ground flashes. A sketch of expected electric field record (right, bottom) of resultant wideband PB pulse train.................................................................. 2425-19 Percentage of flashes with detectable PB pulse train and altitudes of the upper cloud boundary (UCB), the main negative charge region (assumed to be between the 0oC and -15oC isotherms), and the lower cloud bound ary (LCB), each as a function of latitude..............................................................................................................................2455-20 Schematic representation of four types of lightning, AD, that may arise depending upon the magnitude of the LPCR..................................................................................... 2486-1 The electric field waveforms of th ree-stroke flash 073107_1252, measured at the near (top panel) and far (bottom panel) st ations both shown on a 140 ms time scale..... 2606-2 The electric field waveforms of si ngle-stroke flash 100407_360, measured at the near (top panel) and far (bottom panel) st ations both shown on a 100 ms time scale..... 2616-3 The electric field waveforms of a tw o-stroke flash 070508_008, measured at the near (top panel) and far (bottom panel) st ations shown on a 15 ms time scale....................... 2626-4 The electric field waveform of sixstroke flash 070608_020, measured at the near (top panel) station shown on a 450 ms time scale........................................................... 2636-5 The electric field waveforms of the first return stroke of flash 073107_1252, measured at the near (top panel) and fa r (bottom panel) stations shown on a 1 ms time scale..................................................................................................................... ....264

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21 6-6 The electric field waveforms of the fi rst return stroke of flash 100407_360, me asured at the near (top panel) and far (bottom panel) stations shown on a 1 ms time scale....... 2656-7 The electric field waveforms of the fi rst return stroke of flash 070508_008, measured at the near (top panel) and far (bottom panel) stations shown on a 2.5 ms time scale.... 2666-8 The electric field waveforms of the fi rst return stroke of flash 070608_020, measured at the near (top panel) and far (bottom panel) stations shown on a 2 ms time scale....... 2676-9 The initial rising portion of the first strokes of flash 073107_1252 at the near (blue line) and far (red line) stations overlaid for direct comparison, shown on a 30 s time scale..................................................................................................................................2686-10 The initial rising portion of the first strokes of flash 100407_360 at the near (blue line) and far (red line) stations overlaid for direct comparison, shown on a 50 s time scale..................................................................................................................................2686-11 The initial rising portion of the first strokes of flash 070508_008 at the near (blue line) and far (red line) stations overlaid for direct comparison, shown on a 50 s time scale..................................................................................................................................2696-12 The initial rising portion of the first strokes of flash 070608_020 at the near (blue line) and far (red line) stations overlaid for direct comparison, shown on a 100 s time scale..................................................................................................................... ....2696-13 The initial rising portion of the first stroke of flash 073107_1252 at the near (blue line, top panel) and far (red line, bottom) stations each shown on a 30 s time scale.... 2706-14 The initial rising portion of the first st roke of flash 100407_360 at the near (blue line, top panel) and far (red line, bottom) stat ions each shown on a 20 s time scale............ 2716-15 The initial rising portion of the first st roke of flash 070508_008 at the near (blue line, top panel) and far (red line, bottom) stat ions each shown on a 40 s time scale............ 2726-16 The initial rising portion of the first st roke of flash 070608_020 at the near (blue line, top panel) and far (red line, bottom) stat ions each shown on a 50 s time scale............ 2736-17 First positive stroke elect ric and magnetic field wavefo rms measured at 825 and 288 m at Camp Blanding, Florida, by Jerauld et al. [2009] on a 40-ms timescale................ 2746-18 Electric field of the first positive stroke measured in Gainesville, at a distance of 45 km by the Los Alamos Sferic Array (LASA).................................................................. 2756-19 Magnetic field measured at 288 m by Jerauld et al. [2009], overlayed with the electric field measured a distance of 45 km from th e first positive stroke...................... 276

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22 6-20 Ratio of near and far initia l (radiation) field peaks versus inverse ratio of near and far field distances for 8 negative return strokes recorded at Camp Blanding and in Gainesville. ......................................................................................................................2766-21 NLDN-estimated peak current versus initia l (radiation) field peak normalized to 100 km for 8 negative return str okes recorded at Camp Blanding (near station) and in Gainesville (far station).................................................................................................... 2776-22 Geometrical parameters used in calculat ing the electric field at observation point P on perfectly conducting ground at horizontal distance r fr om the vertical returnstroke channel extending between ground and height H.................................................2816-23 The channel-base current waveform give n by Equation 6-8 used to calculate return stroke electric fields for the one-wav e, two-wave and three-wave models..................... 2826-24 Electrostatic (red), inducti on (green), and radi ation (blue) components of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km from the lightning channel computed usi ng the original, one-w ave TL model for an assumed current-wave propa gation speed of 0.5 x 108 m/s and channel length of 4 km............................................................................................................................. .......2846-25 Electrostatic (red), inducti on (green), and radi ation (blue) com ponents of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km from the lightning channel computed usi ng the original, one-w ave TL model for an assumed current-wave propa gation speed of 1 x 108 m/s and channel length of 4 km... 2856-26 Electrostatic (red), inducti on (green), and radi ation (blue) components of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km from the lightning channel computed usi ng the original, one-w ave TL model for an assumed current-wave propa gation speed of 2 x 108 m/s and channel length of 4 km... 2866-27 Electrostatic (red), inducti on (green), and radi ation (blue) components of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km from the lightning channel computed usi ng the two-wave model for an assumed current-wave propagation speed of 0.5 x 108 m/s and channel length of 4 km............... 2876-28 Electrostatic (red), inducti on (green), and radi ation (blue) components of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km from the lightning channel computed usi ng the two-wave model for an assumed current-wave propagation speed of 1 x 108 m/s and channel length of 4 km.................. 2886-29 Electrostatic (red), inducti on (green), and radi ation (blue) components of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km from the lightning channel computed usi ng the two-wave model for an assumed current-wave propagation speed of 2 x 108 m/s and channel length of 4 km.................. 2896-30 Electric field components Eu and Ed due to the upward and downward moving current waves, respectively, along with the total electric field (Eu + Ed) at 500 m for

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23 current propagation sp eeds of (a) 0.5 x 108, (b) 1 x 108, and (c) 2 x 108 for the twowave model..................................................................................................................... .2906-31 Electrostatic (red), inducti on (green), and radi ation (blue) components of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km from the lightning channel computed usi ng the three-wave model for an assumed current-wave propagation speed of 0.5 x 108 m/s and channel length of 4 km............... 2916-32 Electrostatic (red), inducti on (green), and radi ation (blue) components of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km from the lightning channel computed usi ng the three-wave model for an assumed current-wave propagation speed of 1 x 108 m/s and channel length of 4 km.................. 2926-33 Electrostatic (red), inducti on (green), and radi ation (blue) components of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km from the lightning channel computed usi ng the three-wave model for an assumed current-wave propagation speed of 2 x 108 m/s and channel length of 4 km.................. 2936-34 Electric field components Eu, Ed, and Er due to the two incident current waves (upward and downward moving), ), and the ground reflected current wave, respectively, along with th e total electric field (Eu + Ed + Er) at 500 m for current propagation speeds of (a) 0.5 x 108, (b) 1 x 108, and (c) 2 x 108 for the three-wave model................................................................................................................................2946-35 Current waveform represented by Equation 6-9 with parameters given in Table 6-4.....2956-36 Electrostatic (red), inducti on (green), and radi ation (blue) components of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km computed using the one-wave model............................................................................... 2966-37 Electrostatic (red), inducti on (green), and radi ation (blue) components of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km computed using the two-wave model.............................................................................. 2976-38 Electrostatic (red), inducti on (green), and radi ation (blue) components of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km computed using the three-wave model............................................................................ 2986-39 Total electric fields at (a) 500 m and (b) 100 km for the one-wave (red line), twowave (green line), and three-wave (blue line) models for v = 108 m/s overlaid for direct comparison............................................................................................................. 3056-40 The return stroke electric fields at 100 km for the (a) two-wave and (b) three-wave models when the height of the junction poi nt is 20 m (red line) and 100 m (blue line) above ground....................................................................................................................3066-41 Contributions from upward (dotted curve) and downward (solid gray curve) waves to the model-predicted dE/dt waveform at 30 m calculated by Jerauld et al. [2007]

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24 using the two-wave model with dI/dt as input and current originat ing at a height of 6.5 m................................................................................................................................3076-42 Electric fields at 100 km calculated by Jerauld et al. [2007] using the singleand two-wave models, assuming propagation over a perfectly conducting ground............... 3086-43 Total electric fields at (a) 500 m and (b) 100 km for the one-wave (red line), twowave (green line), and three-wave (blue line) models for v = 108 m/s overlaid for direct comparison............................................................................................................. 3096-44 Electrostatic (red), inducti on (green), and radi ation (blue) components of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km computed using the three-wave model............................................................................ 3107-1 Histogram of the number of strokes pe r flash for 52 positive cloud-to-ground flashes in Florida..........................................................................................................................3127-2 Electric field record of a multiple-str oke positive cloud-to-ground flash in Florida with three return st rokes (RS) shown on a 75-ms time scale........................................... 3177-3 Histogram of the initial electric fiel d peak normalized to 100 km for 48 positive return strokes................................................................................................................. ...3217-4 Distance-normalized electric field peak versus distance from the measuring station for 48 positive return strokes...........................................................................................3227-5 Histogram of the zero-to-peak riseti me for 62 positive return strokes............................ 3247-6 Histogram of the 10-90% risetime for 62 positive re turn strokes.................................... 3257-7 Zero-to-peak risetime time versus the distance from the measuring station for 48 positive return strokes...................................................................................................... 3277-8 10-to-90% risetime time versus the di stance from the measuring station for 48 positive return strokes...................................................................................................... 3277-9 A typical slow front-fast transition sequen ce in a positive return stroke electric field waveform recorded on June 1, 2008 in Gainesville, Florida, shown on a 70 s time scale..................................................................................................................................3307-10 Histogram of the slow front duration for 62 positive return strokes. Statistics given are arithmetic mean (AM), geometric m ean (GM), minimum (min), and maximum (max) values for first and subsequent stro kes, as well as for all data combined............. 3317-11 Histogram of the slow front amplitude relative to peak for 62 positive return strokes... 3327-12 Histogram of the fast transition 10-to90% risetime for 62 positive return strokes........ 333

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25 7-13 Slow front duration versus the distance from the measuring station for 48 positive return strokes................................................................................................................. ...3347-14 Slow front amplitude relative to peak versus the distance from the measuring station for 48 positive return strokes...........................................................................................3347-15 Fast transition 10-to-90% risetime tim e versus the distance from the measuring station for 48 positive return strokes................................................................................ 3357-16 The electric field waveform of a positive re turn stroke that occurred at a distance of 157 km on May 5, 2008 in Gainesville, Florida, shown on a 2.5 ms time scale............. 3397-17 Histogram of the zero crossing ti me for 41 positive return strokes................................. 3407-18 Zero crossing time versus distance from the measuring station for 34 positive return strokes........................................................................................................................ ......3407-19 Histogram of the opposite polarity overshoot relative to peak for 31 positive return strokes........................................................................................................................ ......3417-20 Opposite polarity overshoot relative to peak versus distance from the measuring station for 27 positive return strokes................................................................................ 3427-21 A typical electric field de rivative (dE/dt) waveform of a positive return stroke in the dataset presented here shown on a 23 s time scale........................................................ 3437-22 Histogram of the peak electric field derivative normalized to 100 km for 27 positive return strokes................................................................................................................. ...3447-23 Peak dE/dt normalized to 100 km versus distance from the measuring station for 27 positive return strokes...................................................................................................... 3447-24 Histogram of the width of the dE/dt puls e at half peak value for 37 positive return strokes........................................................................................................................ ......3457-25 dE/dt half-peak width versus the distance from measuring stati on for 27 (out of 37) located positive return strokes.........................................................................................3457-26 Histogram of the NLDN-estimated peak currents for 48 positive return strokes. Statistics given are arithmetic mean (A M), geometric mean (GM), minimum (min), and maximum (max) values for first and subs equent strokes, as well as for all data combined..........................................................................................................................3477-27 NLDN-estimated peak current versus di stance from the measuring station for 48 positive return strokes...................................................................................................... 3487-28 NLDN-estimated peak current versus normalized electric field peak for 48 positive return strokes................................................................................................................. ...349

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26 7-29 NLDN-estimated peak current versus peak current estimated using Equation 7-2 (with E being negative). ...................................................................................................3527-30 Normalized electric field peak versus distance from the measuring station for 116 negative return strokes.....................................................................................................3527-31 NLDN-estimated peak current versus distance-normalized electric field peak for 116 first and subsequent ne gative return strokes.................................................................... 3537-32 NLDN-estimated peak current versus measured electric field peak for 48 positive and 116 negative return strokes....................................................................................... 3547-33 The NLDN-estimated peak currents versus peak currents estimated using the transmission line model for assume d return-stroke speeds of (a) 108 m/s, (b) 1.5 x 108 m/s, (c) 1.8 x 108 m/s, and (d) 3 x 108 m/s for 75 negative subsequent return strokes........................................................................................................................ ......3567-34 The NLDN-estimated peak currents versus peak currents estimated using the transmission line model for assume d return-stroke speed of 1.8 x 108 m/s for (a) 41 negative first return strokes and (b) 48 positive return strokes........................................ 3587-35 Measurements of electric field changes ( E) at times t = 0.5 ms, 1.0 ms, and 1.5 ms after the beginning of the return stroke............................................................................ 3617-36 Histograms of charge transfer within (a) 0.5 ms, (b) 1 ms, and (c) 1.5 ms of the beginning of the return stroke field change..................................................................... 3637-37 Charge transfer at 1.5 ms versus the distance from the measuring station for 19 positive return strokes...................................................................................................... 3647-38 Electric field (integrated dE/dt) signature of the return stroke of a single-stroke positive flash that apparently involved a stepped leader shown on a 600s time scale..................................................................................................................................3677-39 Electric field signature of preliminary breakdown (PB) pulse train having the same initial polarity as the following return str oke (RS) of a positive flash on a 20-ms time scale..................................................................................................................................3697-40 Electric field signature of preliminary breakdown pulse train ha ving initial polarity opposite to that of the following return st roke of a positive flash on a 65-ms time scale..................................................................................................................................3707-41 Electric field record of bi polar flash composed of three negative strokes followed by a positive stroke and then by a negative one recorded in Gainesville, Florida, on October 5, 2007................................................................................................................3727-42 Electric field waveforms of individual retu rn strokes of the five-stroke bipolar flash shown in Figure 7-41....................................................................................................... 373

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27 7-43 Electric field record of a three-str oke bipolar cloud-to-g round flash with two negative and one positive return strokes (RS), shown on a 404-ms time scale............... 3747-44 Electric field waveforms of the first (t op panel) and second (bottom panel) return strokes of a two-stroke flash, each show n on a 300 s time scale. The interstroke interval was 19 ms........................................................................................................... 3787-45 Electric field waveforms of the first (t op panel) and second (bottom panel) return strokes of a two-stroke flash, each show n on a 500 s time scale. The interstroke interval was 79 ms........................................................................................................... 3797-46 Electric field waveforms of the first (t op panel) and second (bottom panel) return strokes of a two-stroke flash, each show n on a 300 s time scale. The interstroke interval was 8.5 ms.......................................................................................................... 3807-47 Electric field waveforms of the first (t op panel) and second (bottom panel) return strokes of a two-stroke flash, ea ch shown on a 300 s time scale................................... 3817-48 Electric field waveforms of the first (t op panel) and second (bottom panel) return strokes of a two-stroke flash, ea ch shown on a 300 s time scale................................... 3827-49 Electric field waveforms of the first (t op panel) and second (bottom panel) return strokes of a two-stroke flash, ea ch shown on a 200 s time scale................................... 3837-50 Electric field waveforms of the first (t op panel) and second (bottom panel) return strokes of a two-stroke flash, ea ch shown on a 300 s time scale................................... 3847-51 Electric field waveforms of the first (t op panel) and second (bottom panel) return strokes of a two-stroke flash, ea ch shown on a 250 s time scale................................... 3858-1 Typical electric field record of a multiple-stroke negative cloud-to-ground flash in Florida with three return strokes......................................................................................3898-2 Histogram of the ratio of the first-to-subs equent-return-stroke electric field peak for multiple stroke negative cloud-to-ground lightni ng flashes in (a) Florida, (b) Austria, (c) Brazil, and (d) Sweden............................................................................................... 3928-3 Histogram of the ratio of the subsequent-t o-first-return-stroke electric field peak for multiple stroke negative cloud-to-ground lightni ng flashes in (a) Florida, (b) Austria, (c) Brazil, and (d) Sweden............................................................................................... 3938-4 Geometric mean (GM) electric field peak s for strokes of different order estimated from different studies, labeled A, B, C, D, E, and F........................................................ 394B-1 Electric field derivative waveform of a positive return stroke that occurred on December 16, 2007, at 06:50:27 (UTC) at a distance of 38 km, shown on a 30-s time scale..................................................................................................................... ....464

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28 B-2 Electric field derivative waveform of a positive return s troke that occurred on December 16, 2007, at 06:55:35 (UTC) at a distance of 7.8 km, shown on a 30-s time scale..................................................................................................................... ....464B-3 Electric field derivative waveform of a positive return stroke that occurred on December 16, 2007, at 07:02:55 (UTC) at a distance of 8.5 km, shown on a 25-s time scale..................................................................................................................... ....465B-4 Electric field derivative waveform of the (a ) first return stroke and (b) second return stroke (of a two-stroke positive flash) that occurred on January 22, 2008, at 23:55:10 (UTC), shown on a 30-s time scale............................................................................... 465B-5 Electric field derivative waveform of a positive return stroke that occurred on January 23, 2008, at 02:35:47 (UTC) at a dist ance of 8.4 km, shown on a 20-s time scale..................................................................................................................................466B-6 Electric field derivative waveform of a positive return stroke that occurred on January 23, 2008, at 02:56:28 (UTC) at a dist ance of 64 km, shown on a 35-s time scale..................................................................................................................................467B-7 Electric field derivative waveform of a pos itive return stroke that occurred on April 26, 2008, at 22.16.22 (UTC) at a distance of 98 km, shown on a 40-s time scale........ 467B-8 Electric field derivative waveform of a pos itive return stroke that occurred on April 26, 2008, at 22.26.10 (UTC) at a distance of 94 km, shown on a 35-s time scale........ 468B-9 Electric field derivative waveform of a positive return stroke that occurred on May 18, 2008, at 17:27:12 (UTC) at a distance of 84 km, shown on a 40-s time scale........ 468B-10 Electric field derivative waveform of a positive return stroke that occurred on May 18, 2008, at 19:07:38 (UTC) at a distance of 72 km, shown on a 30-s time scale........ 469B-11 Electric field derivative waveform of a positive return stroke that occurred on May 18, 2008, at 21:25:29 (UTC) at a distance of 49 km, shown on a 40-s time scale........ 469B-12 Electric field derivative waveform of a pos itive return stroke that occurred on June 1, 2008, at 19:35:47 (UTC) at a distance of 72 km, shown on a 30-s time scale.............. 470B-13 Electric field derivative waveform of a pos itive return stroke that occurred on June 1, 2008, at 21:23:41 (UTC) at a distance of 31 km, shown on a 30-s time scale.............. 470B-14 Electric field derivative waveform of the (a ) first return stroke and (b) second return stroke (of a two-stroke positive flash), that occurred on June 2, 2008, at 23:06:25 (UTC), shown on a 50-s time scale............................................................................... 471B-15 Electric field derivative waveform of a pos itive return stroke that occurred on June 9, 2008, at 20:27:05 (UTC) at a distance of 101 km, shown on a 30-s time scale............ 472

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29 B-16 Electric field derivative waveform of a pos itive return st roke that occurred on August 13, 2008, at 21:23:59 (UTC) at a distance of 20 km, shown on a 40-s time scale........ 472B-17 Electric field derivative waveform of a pos itive return stroke that occurred on August 13, 2008, at 22:08:10 (UTC) at a distance of 23 km, shown on a 30-s time scale........ 473B-18 Electric field derivative waveform of a pos itive return stroke that occurred on August 13, 2008, at 22:11:17 (UTC) at a distance of 28 km, shown on a 40-s time scale........ 473B-19 Electric field derivative waveform of a pos itive return stroke that occurred on August 14, 2008, at 12:52:06 (UTC) at a distance of 42 km, shown on a 60-s time scale........ 474B-20 Electric field derivative waveform of a pos itive return stroke that occurred on August 14, 2008, at 13:27:12 (UTC) at a distance of 25 km, shown on a 40-s time scale........ 474B-21 Electric field derivative waveform of a pos itive return stroke that occurred on August 23, 2008, at 20:47:43 (UTC) at a distance of 42 km, shown on a 50-s time scale........ 475B-22 Electric field derivative waveform of a pos itive return stroke that occurred on August 23, 2008, at 21:01:46 (UTC) at a distance of 42 km, shown on a 40-s time scale........ 475B-23 Electric field derivative waveform of a pos itive return stroke that occurred on August 24, 2008, at 21:53:34 (UTC) at a distance of 35 km, shown on a 40-s time scale........ 476B-24 Electric field derivative waveform of the (a ) first return stroke and (b) second return stroke (of a two-stroke positive flash) that occurred on November 30, 2008, at 16:03:52 (UTC) at a distance of 41 km, shown on a 30-s time scale............................ 476C-1 Histogram of Camp Blanding triggered lig htning return-stroke peak currents, I, for 2004, 2005, and 2007.......................................................................................................481C-2 NLDN stroke detection effi ciency as a function of peak current measured at Camp Blanding...........................................................................................................................482C-3 Plot of NLDN stroke locations for 18 strokes in 10 flashes triggered during 2004, 2005, and 2007 at Camp Blanding................................................................................... 484C-4 Histogram of the NLDN absolute location errors. Corresponding st atistics are also given.................................................................................................................................485C-5 NLDN absolute location error vers us Camp Blanding peak current...............................488C-6 NLDN absolute location error versus the number of reporting NLDN sensors.............. 488C-7 NLDN 50% error ellipse semi-major axis length versus Camp Blanding peak current.. 489C-8 NLDN absolute location error plotted ve rsus NLDN 50% error ellipse semi-major axis length........................................................................................................................490

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30 C-9 NLDN-reported peak current versus peak current directly me asured at Camp Blanding...........................................................................................................................491C-10 Histograms of (a) signed and (b) absolute NLDN peak current estimation errors, given as a percentage of the direct ly measured Camp Blanding current ( I% = 100 I/ICB, where I = INLDN ICB)..................................................................................493C-11 Number of reporting NLDN sensors versus Camp Blanding peak current for 18 strokes detected by multiple sensors and 5 strokes detected by a single (Ocala) sensor...............................................................................................................................494

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31 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CHARACTERIZATION AND MODELING OF LIGHTNING PROCESSES WITH EMPHASIS ON COMPACT INTRACLOUD DISCHARGES By Amitabh Nag May 2010 Chair: Vladimir A. Rakov Cochair: Martin A. Uman Major: Electrical and Computer Engineering Electromagnetic signatures of different lightning processes in Florida are acquired and examined with emphasis on compact intracloud discharges (CIDs). CIDs are the strongest natural producers of HFVHF radiation, and they are considered the prime candidate for proposed satellite-base d VHF global lightning monitors. Based on experimental evidence of reflecti ons in electric field and dE/d t records and modeling, we infer that CID is essentially a bouncing-wave phenomenon. A transm ission line model of CIDs including multiple reflections is developed and used for testing the applicability of Hertzian (electrically short) dipole appr oximation to CIDs. The latter approximation was used to estimate electrical parameters of CIDs. CID peak currents were found to be comparable to those of first return strokes. The occurrence of preliminary breakdown pulse trains in different geographical locations and the role of the lower positive charge region (L PCR) in facilitating different types of lightning are examined. While the LPCR may serve to enhance the electric field at the bottom of the negative charge region and thereby facilitate the launching of a nega tively-charged leader toward

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32 ground, presence of excessive LPCR may prevent the occurrence of negative cloud-to-ground flashes by blocking the progression of des cending negative leader from reaching ground. Natural lightning electric field waveforms si multaneously measured at Camp Blanding and in Gainesville (45 km apart) ar e examined. It is shown, via m odeling, that the slow front in electric field at far distances is primarily due to the radiation field co mponent, while at near distances it is composed of more or less equal contributions from all three components of electric field. For both experimental and model-predicte d waveforms, the duration of the slow front appears to be similar at near and fa r distances from the lightning channel. Various features of positive lightning disc harges, which are considerably less understood than their negative counterparts, are analyzed. Relative magnitudes of first and subsequent return-stroke current and field peaks in nega tive cloud-to-ground lightning are examined. The performance characteristics of the U.S. National Lightning Detection Network (NLDN) are ev aluated using rocket-triggered lightning data.

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33 CHAPTER 1 INTRODUCTION Lightning is a transi ent, high-current electrical discharge that transfers charge between the atmosphere and the Earth or between different parts of the atmosphere. The primary sources of lightning are clouds termed cumulonimbus, commonly referred to as thunderclouds [Uman, 1987]. Lightning was present on Earth long before human life evolved and it may even have played a crucial role in the e volution of life on our planet. Each year some 25 million cloud-toground lightning discharges occur in the United States alone. Lightning strikes involve the formation of channels carrying tens of kiloam peres of electric current with channel peak temperatures of the order of 30,000 K. Thus, lightning strikes have far-reaching and often disastrous consequences affecting essential se rvices such as aviation, power transmission and distribution, communication, as we ll as the day-to-day human life. It has been recently established that the rate of light ning incidence (and the global electr ic circuit in general) can be significantly influenced by change s in Earths climate. On the other hand, lightning activity may have important consequences to life on Earth, fo r example, via changing the global balance of NOx (nitrogen oxides, mainly nitric oxide, NO, and nitrogen dioxide, NO2) which largely controls the amount of ozone in the atmosphere [ Rakov and Uman 2003]. Lightning is the second most effective weathe r-related killer in the United States. According to the US National Oceanographi c and Atmospheric Administration (NOAA) publication Storm Data, the annual average numbe r of lightning-related deaths in the United States between 1965-95 is 85. Also, about 300 indivi duals are injured by lightning each year in the United States. The recent Sago coal-mine explosi on in West Virginia l eading to the death of 12 miners in January 2006 and many California wildfires causing immense damage to property and wildlife are believed to have been cause d by lightning. Lightning and other effects of

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34 thunderstorms have been a major concern for the aviation industry. A typical commercial plane is struck by lightning once a year on average [ Rakov and Uman 2003, Ch. 10]. There were two well documented cases where lightning was initiate d by large rockets launched from Earth, the Saturn V vehicle of NASAs Apollo 12 and US Air Forces Atlas-Centaur 67. The latter suffered damage that led to the loss of the vehicle a nd its payload. More recently, in 2006 the launch of NASAs Atlantis had to be dela yed due to lightning strike to the launch pad. According to the Electric Power Research Institute (EPRI), lightni ng is a major cause (40-50%) of electric service interruptions, resulting in $50 million per year in damage and restoration expenses. Lightning is involved in 5% of all US resi dential-property-damage insuran ce claims, including those from tens of thousands of home fires, with tota l claims of over one b illion dollars annually. Over the years, a large number of studies have been conducted to measure and model various features and effects of lightning discha rges, which served to improve our understanding of the physics of the lightning proc esses and the role of lightning in the global circuit. Lightning Locating Systems (LLSs) such as the North Am erican Lightning Detect ion Network (NALDN), monitor, report, and archive th e occurrence of lightning on continental and regional scales. The information available from the LLSs can be used to study the occurrence of lightning discharges and examine the existence of any trend in its long-term variation. In fact, LLSs (along with satellites) have become an indispensable tool in studying global lightning activity. However, LLSs are still evolving via the incorporation of newly acquire d knowledge about lightning [e.g. Cummins et al ., 2006]. Different types of lightning di scharges produce unique electro magnetic signatures that can be measured and studied to obtain insight into the processes involved in the discharges. Many of these processes remain poorly understood. The pu rpose of this dissert ation is to examine

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35 measured electromagnetic signatures of different lightning processes with an aim to improve our understanding of the physical proc esses involved, infer various pa rameters of these processes, and develop models that can be us ed to describe their salient prope rties. Chapter 2 gives a review of the existing literature concerni ng lightning that is relevant to this dissertation. Chapter 3 gives a detailed description of the experiments and in strumentation at the In ternational Center for Lightning Research and Testing (ICLRT) with emphasis on the Lightning Observatory in Gainesville (LOG). The main goals of this dissertation are listed below. Discuss the phenomenology, newly proposed-mechanism, models, and electrical parameters of Compact Intracloud Discharges. Characterize preliminary breakdown pulse trains in negative cloud-to -ground lightning and in attempted leaders and qualitatively exam ine the inferred dependence of lightning type on the magnitude of the lower positive charge region. Examine the fine structure of electric field waveforms produced by first return strokes in negative cloud-to-ground lightning in experimental data and via modeling. Characterize in detail various features of positive and bipolar cloud-to-ground lightning discharge. Examine the relative magnitudes of first and s ubsequent return stroke electric field and current peaks in negative cloud-to-ground lightning. The atmospheric electricity sign convention according to which a downward-directed electric field (or field change) vector is considered to be positive is used throughout this dissertation except in Sections 4.2 and 4.3. The physics sign conve ntion according to which a downward-directed electric field (o r field change) vector is consider ed to be negative is used in these two Sections.

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36 CHAPTER 2 LITERATURE REVIEW This chapter presents a review of the exis ting literature concer ning lightning that is relevant to this dissertation. S ection 2.1 presents a brief intro duction to the physics of natural lightning, both cloud and cloud-to-ground types. S ection 2.2 presents a brief review of the mechanis m of lightning initiation in thundercloud s. Rocket-triggered ligh tning and the Compact Intracloud Discharge are discussed, re spectively, in Sections 2.3 and 2.4. 2.1 Role of Lightning in the Global Electric Circuit The conductivity of atmosphere at sea level is 10-14 S/m and it increases rapidly with altitude. In the region of the atmo sphere 60 km or so above the sea level, free electrons are major contributors to the conductivity. This region is sometimes referre d to as the electrosphere [e.g., Chalmers, 1967]. It is usually assumed that under quasi-static conditions, the electrosphere is conductive enough to consider it an equipotential region. The potenti al of the electrosphere is positive with respect to the Earth, its magnitude being about 300 kV. According to the "classical" view of atmospheric electricity, the Earth-atmosphere system can be crudely modeled as a lossy spherical capacitor [e.g., Uman 1974], with the inner and outer shells consisting of the Earths surface and the electrosphere, respectively (see Fi gure 2-1). According to this model, the Earths surface is negatively charged, having a total magnitude of roughly 5 x 105 C, while an equal positive charge is distributed throughout the atmosphere [ Rakov and Uman 2003]. The capacitor is lossy because the atmosphere is weakly-c onducting. The charge on the Earth's surface would thus disappear (if not re-supplie d) in about 10 minutes. Thunders torms (lightning discharges), which primarily transfer negative charge to Earth, therefore, serve to recharge the Earth. There are, on average, 2000 thunderstorm s in progress at any time over about 10% of the Earth's

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37 Figure 2-1. The left panel shows a simplified illust ration of the global elec tric circuit. Adapted from Pierce [1974]. The right panel shows the Earth-atmosphere lossy capacitor system (not to scale). surface. There are other contri butors to the global electric circuit [see, for example, Rakov and Uman 2003] that are not considered here. 2.2 Lightning Discharge Processes Uman [1987] defines lightning as a transient, high-current electrical discharge that transfers charge between the atmo sphere and the Earth or between different parts of the atmosphere. The most common sources of lightning are the electric charge regions located in ordinary thunderstorm (cumulonimbus) clouds. The charge structure of a cumulonimbus can be approximated as a vertical tripole consisting of three charge centers, main positive at the top, main negative in the middle, and an additional smaller positive at the bottom. The tw o upper charges, located respectively at heights of about 12 and 7 km for Florida [ Krehbiel, 1986], are usually specified to be equal in magnitude (typically some tens of coulombs) and therefor e form a dipole. The magnitude of the lower positive charge (probably about 10 C or less), located approximately at a height of about 2 km, is

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38 significantly smaller than that of the dipole charges. These cloud charge locations (which vary from one geographical region to another) and ma gnitudes have been estimated by a variety of remote [e.g., Krehbiel, 1986] and in situ methods [e.g., Simpson and Scrase 1937]. Two primary mechanisms that attempt to explain the cl oud electrification pro cess are the convection mechanism and the graupel-ice mechanism. In th e convection mechanism th e electric charges are supplied by external sources such as fair-weather space charge and corona near ground and cosmic rays at the cloud top. Organized convectio n provides large-scale charge separation. There is no role for precipitation in forming the dipole charge structure. This mechanism was supported by Vonnegut [1953, 1994], Wilson [1956], and Moore and Vonnegut [1977] among others. The graupel-ice mechanism explains the process of cloud electrificati on by collisions between precipitation particles (graupel) and cloud particles (small ice crys tals). The presence of water droplets is necessary for significant charge transfer [ Reynolds et al ., 1957, Takahashi 1978, Jayaratne et al. 1983]. The large-scale separation of char ged particles is provided by the action of gravity. Around 75% of lightning discharges occur within the cloud and include intracloud, intercloud and cloud-to-air discha rges. Cloud discharges are often referred to as ICs. Lightning discharges involving charge tr ansfer to the ground constitu te around 25% of all lightning discharges and are called cloud-to-ground discharges, often referred to as CGs. Figure 2-2 shows the various types of lightning discharges. 2.2.1 Cloud-to-Ground Discharges Cloud-to-ground discharges or CGs, as the name suggests, involve char ge transfer between cloud and ground via a high conductivity chan nel. The overall cloud-to-ground lightning discharge, often term ed ground flash, consists of t ypically three to five com ponent strokes or just

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39 Figure 2-2. Different types of lightning discharges. Taken from Schoene [2007]. strokes [ Rakov and Uman 2003]. Each stroke is composed of a leader/return stroke sequence. Cloud-to-ground discharges can be classified in to four types (Figure 2-3) according to the polarity of the charge transferre d to ground and the direction of pr opagation of the initial leader. Types (a) and (b) effectively lowe r negative charge to ground, while types (c) and (d) effectively lower positive charge to ground. Downward ne gative lightning comprises about 90% of all cloud-to-ground flashes, while downward positiv e lightning accounts for only about 10% of cloud-to-ground discharges. Upward negative an d positive lightning is relatively rare as compared to the other two categories and are usually observed on tall structures or short structures on mountain tops. The various processes associated with a negative cloud-to-ground lightning flash are shown in Figure 2-4. A downwardnegative cloud-to-ground stroke is composed of a downwardmoving leader and an upward-moving return stroke. Leader initiati ng the first stroke in a flash exhibits stepping and is preceded by the initial or preliminary breakdown, which can be defined as the in-cloud process that initi ates or leads to the initiation of the downward-moving stepped

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40 Figure 2-3. Four types of cloud-to-gr ound lightning discharge. Taken from Rakov and Uman [2003]. leader. The stepped leader serves to form a ne gatively charged plasma channel extending from the cloud toward the ground at an average speed of 2 x 105 m/s. As the leader approaches ground, one or several upward leaders, having positive charge, are initiated from the ground or from grounded objects (e.g., trees or other structures) and one of these upward leaders attaches to a branch of the downward-moving stepped leader at tens of meters above the ground surface. Once the two leaders have connect ed, a large surge of current, known as the first return stroke, travels at about one third to one half the speed of light (with speed gene rally decreasing with increasing height) from the ground toward the cloud charge source along the plasma channel neutralizing the negative leader charge. When the first-return stroke reaches the cloud, in-cloud discharge activity known as J (for junction) and K-processes occur in the cloud. The J-processes

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41 Figure 2-4. Various processes comprising a negative cloud-to-ground ligh tning flash. Adapted from Uman [1987]. result in redistribution of cloud charge in respon se to the preceding return-stroke and lasts for tens of milliseconds. K-processes are transients that occur during the slower J-process. Following this in-cloud activity, often a new lead er, known as a dart or dart-stepped leader, follows the path of the previous lead er channel at an average speed of 106-107 m/s and does not exhibit stepping. As the dart or dart-stepped leader approaches ground, an attachment process similar to that for the first stroke takes place. However, the attachment process for subsequent strokes occurs over a shorter di stance, takes less time and typically occurs when the upward leader is less than 10 meters in height. This is followed by the subsequent return-stroke wave that again neutralizes the leader charge deposited al ong the channel. The peak currents associated with the first and subsequent return str okes are about 30 kA and 15 kA, respectively.

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42 Downward-positive flashes (type c), accounti ng for roughly 10% of the total cloud-toground discharges, transport positive charge from cloud to ground. The leader/return stroke process in downward positive discharges is similar to that of negative flashes. However, the peak currents and charge transfers associated with positive first strokes can be much higher than for negative first strokes. The highest directly m easured lightning currents and the largest charge transfers to ground are thought to be associated with positive lightning [ Goto and Narita 1995]. Also, single-stroke positive flas hes are much more common than single-stroke negative flashes. Positive lightning has been found to be related to sprites which occur in the middle atmosphere [ Boccippio et al. 1995]. Positive lightning can be the dom inant type of lightning during the dissipating stage of thunderstorms and during the cold season. Positive lightning discharges are characterized in Chapter 7 of this dissertation. Upward lightning discharges (types b and d) are thought to occur only from tall objects (higher than 100 m or so) or from objects of m oderate height on mountain tops. The initiation mechanism involved in an upward discharge is completely different from that in a downward flash. The first leader in an upward flash is initiated from the ground-based object and moves towards the cloud. This upward directed leader bridges the gap between the object and the cloud charge source or in-cloud discharge channel, forming a continuous pa th to ground through which a current, with a magnitude of typically several hundred amperes las ting for several hundred milliseconds called the initial continuous current (ICC), flows. This process is followed by subsequent dart leader/return stroke sequences which are sim ilar to subseque nt strokes of downward flashes. It may be mentioned here that rocket-triggered lightning (discussed in Section 2.4) is similar in phenomenology to the upward lightning discharge initiated from tall grounded objects.

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43 Lightning discharges (flashes) that transfer to ground both positive and negative charges are termed bipolar lightning discharges. These disc harges have not been well studied. The sparse data on bipolar lightning indicate that the majority of bipolar flashes is initiated by upward leaders from tall objects, events ca lled "natural upward lightning" [ Berger 1978]. In the data of Berger [1978], obtained between 1963 and 1973 at Mount San Salvatore in Switzerland, bipolar flashes accounted for 72 out of 1196 observed flashes (6 percent). Rakov [2005], based on a review of literature, states that bipolar flashes may not occur less often than positive flashes, at least when tall objects are involved, with bipol ar flashes constituting 6 to 14% of summer lightning in Europe and the United States a nd 3 to 33% of winter lightning in Japan. Jerauld et al. [2009] examined one unusual lig htning flash, producing two ch annel terminations on ground and containing two strokes that lowered positive charge followed by four strokes that lowered negative charge. That bipolar light ning flash is the first well docum ented description of a natural downward bipolar lightning flash. Bi polar lightning discharges are ex amined in Chapter 7 of this dissertation. 2.2.1.1 Preliminary breakdown in ground discharges In the electric field records of some cloud-to -ground discharges, a bi polar pulse train with pulses having the same initial polarity as the foll owing return-stroke, durations of the order of tens of microseconds and preceding the first-return stroke pulse typically by tens of milliseconds is commonly attributed to preliminary breakdown. The preliminary breakdown involves the formati on of one or more channels in the cloud. In the latter case, the channels extend in seemingly random directions from the cloud charge source, with one of them evolvi ng into the stepped leader that bridges the cloud charge source and the ground [e.g., Rakov and Uman 2003, Ch. 4]. The preliminary breakdown process in ground flashes sometimes produces a train of rela tively large microsecond-scale electric field

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44 Figure 2-5. Examples of electric field pulse waveforms charac teristic of (a) preliminary breakdown in negative ground flashes, (b) th e active stage (in itial breakdown) in cloud flashes. The waveforms have been recorded, from a distant storm, by D.E. Crawford at Camp Blanding, Florida. Adapted from Rakov [1999]. pulses, as illustrated in Figure 2-5a. The pulses are typically bipolar with the polarity of the initial half-cycle being the same as that of the following return-stroke pulse. The characteristic features of preliminary-breakdown pulse trains in negative clo ud-to-ground flashes (based on information found in the literature) are as follows: Duration of the pulse train: The entire duration of the preliminary-breakdown pulse train is of the order of 1 ms [e.g., Rakov, 1999]. Regularity of pulses in a train: This is a subjective feature, but it has been noted by many researchers. According to Kitagawa and Brook [1960] and Weidman and Krider [1979], regularity of preliminary-breakdown pulses and uniformity of time in tervals between them in the case of cloud-to-ground flashe s is higher than for cloud flashes. Overall pulse shape: Individual preliminary-br eakdown pulses in the train are bipolar, as reported by many investigators [e.g., Kitagawa 1957; Clarence and Malan 1957; Kitagawa and Kobayashi 1959; Kitagawa and Brook 1960; Krider and Radda, 1975; Weidman and Krider 1979; Beasley et al. 1982; Gomes et al. 1998; Rakov 1999]. Polarity of the initial half cycle: The initia l polarity of bipolar pul ses in the train of a negative cloud-to-ground flash is the same as that of negative return-stroke pulses [e.g., Weidman and Krider 1979]. For the atmospheric electricity sign convention [e.g., Rakov and Uman, 2003, pp. 8-9] this polarity is positive. In contrast, for the initial breakdown in (a) ( b )

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45 cloud flashes, the dominant polarity of the initial half cycle of individual pulses is negative [e.g., Rakov, 1999]. Overall pulse duration: According to Rakov et al. [1996], the typical total duration of individual pulses in the trai n is in the range of 20 to 40 s. In contrast, for the preliminary breakdown in cloud flashes the typical total pulse duration is 50 to 80 s. Interpulse interval: The typical time interval be tween individual pulses in the train is 70 to 130 s, versus 600 to 800 s for initial breakdown in cloud flashes [ Rakov et al. 1996]. The percentage of flashes exhi biting detectable preliminary breakdown pulse trains varies from less than 20% to 100% [e.g., Clarence and Malan 1957; Gomes et al. 1998; Nag and Rakov, 2008]. The time interval between the pulse train and the return-stroke waveform is typically a few tens of milliseconds. The amplit ude of the preliminary breakdown pulses can be comparable to, or even exceed, that of the first re turn stroke pulse, which makes them capable of producing significant electromagnetic interference to the functioning of various airborne and ground-based circuits. The statistical distribution of the ratios of electric fi eld peaks of the initial half-cycle of the larg est preliminary breakdown pulse in a train and the corresponding first return-stroke pulse for 59 flashes analyzed by Nag [2007] is shown in Figure 2-6. (Those flashes occurred at distance ranging from a few to a bout 100 km.) The geometric and arithmetic means of the ratio are 0.45 and 0.62, respectively, with minimum and maximum values being 0.16 and 5.1, respectively. About 19% of the 59 preliminary breakdown pulse trains contain pulses whose peaks are greater than those of the corresponding first return str okes, although this percentage might be somewhat influenced by local noise level. Nag and Rakov [2008] identified and examined lightning events exhibiting pulse trains that are characteristic of prelimin ary breakdown in negative cloud-t o-ground discharges, but are not followed by return stroke waveforms. They referred to these events as attempted first cloud-toground leaders". Preliminary breakdown in negative cloud-to-ground lightning and attempted leaders are examined in detail in Chapter 5 of this dissertation.

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46 AM = 0.62 GM = 0.45 Min = 0.16 Max = 5.1 n = 59 Preliminary Breakdown to First Re turn Stroke Field Peak Ratio 00.250.51248 Occurrence 0 5 10 15 20 25 30 Figure 2-6. Histogram of the ratio of preliminary breakdown to first return stroke field peaks for individual flashes. Adapted from Nag [2007]. 2.2.1.2 Electric and magnetic field waveform s from natural negat ive first strokes Several studies have been conducted to examine first stroke electric fi elds in the range of tens to hundreds of kilometers [e.g. Weidman and Krider 1978 in Florida and Arizona and Cooray and Lundquist 1982 in Sweden]. Figure 2-7 shows t ypical electric and magnetic fields at distances ranging from 1 to 200 km fr om negative return strokes, published by Lin et al. [1979], which are drawings based upon many measurements obtained in Florida. The initial peak (when discernible) of the fields at each distance is essentially due to the radiation component and decreases inversely with distance in the absence of significant propagation effects [ Lin et al., 1980]. After some tens of microseco nds, the electric and magnetic fields within a few kilometers are dominated by the electrostatic and magne tic induction components, respectively. Beyond 50 km or so, the both the electric and magnetic fiel d waveshapes are bipolar and dominated by their respective radiation components.

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47 Figure 2-7. Typical vertical elec tric field intensity (left column) and azimuthal magnetic flux density (right column) waveforms for first (solid line) and subsequent (broken line) return strokes (leader waveforms not show n) at distances of 1, 2, 5, 10, 15, 50, and 200 km. Adapted from Lin et al. [1979].

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48 Figure 2-8. Electric field waveforms of (a) a first re turn stroke, (b) a subsequent stroke initiated by a dart-stepped leader, and (c) a subsequent return stroke initiated by a dart leader, showing the fine structure both before and af ter the initial field peak. Each waveform is shown on two time scales, 5 s per division (labelled 5) and 10 s per division (labeled 10). The fields are normalized to a distance of 100 km. Leader pulses (L), slow front (F), and fast transiti on (R) are indicated. Adapted from Weidman and Krider [1978]. The fine structure in the elec tric field waveforms of first and subsequent return strokes (Figure 2-8), was examined by Weidman and Krider [1978]. First-stroke fi elds can be separated temporally into two phases. The first one is the so-called initial slow front, or simply slow front, described by Weidman and Krider [1978] as an initial portion or front which rises slowly for 2 8 s to about half the peak field amplitude. The second part which follows the slow front is

PAGE 49

49 an abrupt transition to peak, t ypically referred to as the fast transition, having a 10-90% rise time of 0.2 s or less when the field propagation was over seawater, according to Weidman and Krider [1978]. [ Weidman and Krider 1980 give a 10-90% rise time of 0.1 s over seawater]. The shape of the slow front is typically concave, although Weidman and Krider [1978] do report some convex shaped fronts. The relative amplitude of the slow front and total peak field for first strokes is reported by Weidman and Krider [1978] to be 0.4-0.5, while Cooray and Lundquist [1982] and Master et al. [1984] give ratios of about 0.4 and 0.3, respectively. The corresponding first-stroke slow front durations are 4, 2.9, and 5 s, respectively. Weidman and Krider [1978] report that subse quent return strokes pr eceded by dart leaders also exhibit slow fronts, although they are generally smaller than t hose of first strokes, with the front amplitude to total field peak ratio being about 0.2. These subsequent return stroke field fronts are also of shorter duration, having a mean of 0.6 0.9 s. Interestingly, subsequent return strokes preceded by dart leaders were reported to have fast transitions to peak field similar to those of first strokes, indicati ng that the primary distinction be tween first and these subsequent return strokes fields is the slow front. Finall y, slow fronts from subsequent strokes preceded by dart-stepped leaders are also reported by Weidman and Krider [1978] to have front amplitude to peak field ratios similar to those of first strokes, but a mean duration of 2.1 s, in between those of first (mean of 4 s) and subsequent return strokes preceded by dart leaders (mean of 0.6 0.9 s). The origin of the slow-front current in first strokes has long been a ma tter of discussion. It has often been attributed to the presence of an upward connecting leader [e.g., Rakov and Uman 2003, p. 144]. Weidman and Krider [1978] noted that the shapes and relative amplitudes of the fronts and fast transitions in the current waveforms are surpri singly similar to those in the

PAGE 50

50 radiated fields (currents and fi elds being measured in differe nt studies). On the other hand, there are experimental data [ Willett et al. 1989a], although for triggered-lightning strokes, which suggest that radiation field waveforms can exhibit pronounced slow fronts without similar features in corresponding current waveforms. Ot her mechanisms of slow-front production have been considered by Weidman and Krider [1978], Thottappillil and Uman [1993], and Cooray et al. [2004]. According to Jerauld et al. [2007] the source of the slow fronts observed in the currents and in the distant radiati on fields of natural first stroke s is likely to be a pair of microsecond-scale current waves, each having a peak of up to some tens of kiloamperes, propagating in opposite directions from the junction of the descending and upward connecting leaders at a speed on the order of 108 m/s. In Chapter 6 of this dissertation results of the two-station measurem ents of natural and triggered lightning discharges ar e described. Return-stroke wave forms measured simultaneously at close (less than 1 km from the lightning chan nel) and distant (about 45 km from the lightning channel) stations are examined in order to gain additional insights into the origin of the slow front in return-stroke field waveforms. 2.2.2 Cloud Discharges 2.2.2.1 General information Cloud discharges or ICs, cons tituting approxima tely thr ee-quarters of all lightning discharges, do not contact ground. ICs have been less well studied than CGs because of the difficulty of securing photographic records of in -cloud channels and inability to obtain direct measurements of currents and charge transfers associated with ICs. Ground-based singleand multiple-station electric field measurements, as well as VHF lightning-channel imaging have been the primary means of studying ICs.

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51 In general, cloud discharges are most likely to begin in the high elec tric field region near the upper boundary of the main negative charge bridging the main negative and upper positive charge regions. However, they have been f ound to occur between the main negative charge region and the lower positive charge region (sometimes in hybrid flashes), in which case they are referred to as inverted intracloud discharges [ Qie et al 2005, Tassendorf et al. 2007]. Cloud discharges can be viewed as bei ng composed of an early or active stage and a late or final stage. The beginning of a cloud discharge is typically marked by the largest microsecond scale pulses in its wideband electric fi eld record. According to Villanueva et al. [1994], the larger pulses tend to occur early in a flash and presumably are re lated to the flash initiating breakdown process. These early stage pulses are often referred to as initial-breakdown pulses. The transition from the early stage to the late stage of a cloud discharge is thought to be related to the disintegration of the channel existing between the main nega tive and upper positive charge regions. The late stage, also called the J-stage, is physically similar to the J-process (junction process) in ground discharges. In the late stage, charge transp ort supposedly takes place from remote sources in the main negative charge regi on to the partially (or completely) neutralized negative charge center from where the negative channel originated during the initial stage. Various transient processes occu rring during the late stage are referred to as K-processes. Kitagawa and Brook [1960] portrayed the electric fi eld signature of cloud lightning discharges as being composed of three stages, initial, very active and fina l. However, the threestage structure was later replaced by the pres ently accepted two-stage model (described above) proposed by Villanueva et al. [1994]. Villanueva et al. analyzed microsecond-scale pulses in wideband electric field records of cloud flashes in Florida and New Mexico acquired using a 12bit digitizing system with a 500 ns sampling inte rval. The average of the peak-to-peak amplitude

PAGE 52

52 of the five largest pulses in a flash was found. All pulses with peak-to-peak amplitude greater than 50% of the average amplitude were labeled large pulses, pulses with amplitudes between 25% and 50% of the average amplitude were labeled medium pulses, and pulses between 12.5% and 25% of the average amplitude were labe led small pulses. The results of the analysis showed that about 60% and 50% of the large pul ses occurred within the first 20 ms and 5 ms, respectively, of the flash suggesting that the large pulses were associated with the initialbreakdown process. Occurrence statistics of pulses in one of the electric field records in this study is shown in Figure 2-9. Bodhika et al. [2006] conducted a similar study of cloud flashes recorded in Sri Lanka and reporte d that about 80% of electric fiel d pulses occurred in the early stage of the flash thus supporti ng the two stage structure of cloud discharges proposed by Villanueva et al. [1994]. However, in both the above cited studies, pulses that were smaller than 12.5% of the average amplitude [in some flashes there were hundreds of them, Villanueva et al. 1994] were not included. 2.2.2.2 Initial breakdown in cloud discharges Preliminary breakdown, often called initial br eakdown, m ay be viewed as an in-cloud process that precedes and leads to the initiation of both cloud discharges and downward cloud-toground discharges. Cloud discharges can be viewed as being composed of an early (or active) stage having a duration of some tens to a few hun dreds of milliseconds and a late (or final) stage that constitutes the remainder of the flash. In ge neral, cloud discharges ar e most likely to begin with a negatively charged channel extending in an intermittent manner with an average speed of the order of 105 m/s. Overall, the early-stage processes in cloud lightning are probably similar to the initial breakdown and ste pped leader processes in ne gative cloud-to-ground lightning. The largest microsecond-scale electric field pul ses tend to occur at the beginning of a cloud discharge [ Villanueva et al. 1994]. These pulses, in analogy to the preliminary breakdown

PAGE 53

53 Figure 2-9. Occurrence statistics of electric field pul ses in a cloud discharge. a. (i) Overall electric field record and hist ograms of occurrence of (ii) large, (iii) medium, and (iv) small electric field pulses in different part s of this record for cloud flash 64 on day 231 in 1991 at Kennedy Space Center, Florida. b. Same as (a) but for the first 25 ms of the flash. Adapted from Villanueva et al [1994]. pulses in ground flashes (described in Section 2.2.1.1), are usually referre d to as initial or preliminary breakdown pulses. These pulses are e ither relatively slow-rising, wide bipolar waveforms with several small pulses superimposed on the initial half cycl e or relatively narrow or smooth singly-peaked or multiply-peaked bipolar waveforms [ Rakov, 2006] as illustrated in Figure 2-5b. The initial pol arity of the bipolar electric field puls es in cloud discharges is usually opposite to that of the preliminary-breakdown pul ses in negative cloud-to-ground discharges, the latter pulses being usually of the same polarity as that of the following return-stroke pulse. Individual pulses in the early stage of cloud discharges are characterized by a typical total ( i ) ( iv ) ( iii ) ( ii ) ( iv ) ( iii ) ( ii ) ( i ) (a) (b)

PAGE 54

54 duration of 50-80 s and the typical time interval between pulses is 600-800 s [ Rakov et al. 1996]. Kitagawa and Brook [1960] reported that cloud-flash pul ses appeared in groups separated by intervals ranging from 0.3 to 10 ms. Nag et al. [2009] examined microsecondand submic rosecond-scale pulses in electric field records of cloud discharges acquired in summer 2006, in Gainesville, Florida and included all detectable pulses, including the smaller pulses ignored by Villanueva et al. [1994] and Bodhika et al. [2006], in the initia l stage of cloud discharges. Figur e 2-10 shows an example of the measured electric field waveform of a cloud discharg e in their data set. In addition to classical initial breakdown pulses (see Figu re 2-11a) having durations of the order of tens of microseconds, narrow pulses, having durations equal to or less than 4 s (see Figure 2-11b), were also observed. Nag et al. [2009] found that the majority of pulses in the early stage of cloud discharges are typically small in both amplitude and duration. Further, they found that the amplitudes of these most common pulses are 50% or less than that of the largest pulse, and their durations are less than or equal to 4 s. In contrast, total durations of classical initial breakdown pulses in cloud flashes ar e thought to be considerably l onger, typically some tens of microseconds. Figure 2-12 shows th e distribution of total durations of pulses in their 12 cloud flashes. One can see from this Figure that 85 % (1125 out of 1323) of the pulses had durations less than or equal to 4 s, of which 70% (783 out of 1125) were bipolar, and that 26% (338 out of 1323) of the pulses had durations less than 1 s. The arithmetic mean pulse duration was 3.5 s, which is outside the 50 s range of typical durations usua lly given for classical initial breakdown pulses in cloud discharges [e.g., Rakov and Uman 2003]. The discrepancy is apparently due to the inclusion of smaller pulses by Nag et al. [2009] that were ignored in

PAGE 55

55 Figure 2-10. Electric field record of cloud flash 05/24/06_299. Taken from Nag et al. [2009]. Figure 2-11. Examples of (a) cl assical and (b) narrow pulse s in the early stage of cloud discharges. Taken from Nag et al. [2009].

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56 Figure 2-12. Histogram of total duration of uni polar and bipolar pulses in 12 selected cloud discharges. Adapted from Nag et al. [2009]. previous studies. In Weidman and Krider's [1979] study only a few (2 out of 137) negative pulses had durations less than 10 s. 2.3 Lightning Initiation Mechanisms One of the less understood areas in lightning research is th e initiation mechanism of a downward lightning discharge. This is mainly be cause of the fact that the maximum electric fields typically measured in thunderclouds are 1 to 2 x 105 V/m, which is an order of magnitude lower than the expected air brea kdown field of the order of 106 V/m. Also, there is a lack of optical records due to the in-cloud nature of this process. The detailed physics involved in the initiation of lightning is not yet understood. It may be thought of as a process which results in the formation of the first plasma channel within th e cloud that may lead to either a cloud or a ground discharge depending on the configurations of ch arges involved and region of the cloud in which the breakdown is taking place. Mean duration = 3.5 s N = 1323 N BP = 945 N UP = 378Duration ( s) 01248163264128264 Number of Pulses 0 50 100 150 200 250 300 350 400 450 500 550 Bipolar (BP) Unipolar (UP)

PAGE 57

57 Over the years a number of theories have been proposed in order to explain the physics behind the initiation mechanism of lightning. In this section, a brief review of the proposed lightning initiation mechanisms th at involve either conventional or runaway air breakdown is presented. Both of these two mechanisms attempt to explain the formation of an ionized region, sometimes referred to as lightning seed, in the cloud that is capable of locally enhancing the electric field at its extremities thus leading to th e formation of a self-propagating leader channel. 2.3.1 Conventional Breakdown According to the conventiona l breakdown mechanism lightning is initiated via the emission of positive corona from the surface of precipitation partic les, highly deformed by strong electric fields in the case of raindrops, coupled with some mech anism whereby the electric field is locally enhanced to suppor t the propagation of corona streamers. The most detailed hypothetical scenario of light ning initiation via conventiona l breakdown is described by Griffiths and Phelps [1976b] who consider a system of positiv e streamers developing from a point on a hydrometeor where the electric field exceeds the corona onset value of 2.5 to 9.5 x 105 V/m (2.5 to 9.5 kV/cm). The developing streamers are as sumed to form a conical volume that grows longitudinally. The ambient electric field in th e thundercloud required to support the propagation of corona streamers, E0, was found by Griffiths and Phelps [1976a] from laboratory experiments to be 1.5 x 105 V/m (1.5 kV/cm) at about 6.5 km and 2.5 x 105 V/m (2.5 kV/cm) at about 3.5 km. If the ambient electric field is higher than E0, the streamer system will intensify, carrying an increasing amount of positive charge on the prop agating base of the cone and depositing an equally increasing amount of negative charge in th e conical volume. As a result, an asymmetric conical dipole is formed, which presumably can se rve to enhance the existing electric field at the cone apex [ Rakov, 2006].

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58 Another hypothetical mechanism proposed by Nguyen and Michnowski [1996] involves a bidirectional streamer development assisted by a ch ain of precipitation particles, as opposed to the propagation of positive streamers alone. 2.3.2 Runaway Breakdown Gurevich et al. [1999] suggested that r unaway electrons ma y play an important role in lightning initiation. Energy gained by a runaway electron from the electric field between collisions with air particles, must be more th an it looses in a collision. The runaway breakdown mechanism is associated with a current pulse having an amplitude of 100-200 A leading to the formation of a field-enhancing io nized region (lightning seed) by a cosmic ray particle with an energy of 1016 eV [ Gurevich et al. 2003]. The current pulse is pr edicted to generate a bipolar electric field pulse w ith a characteristic fu ll width of 0.2-0.4 s [ Gurevich et al., 2002] which is more than an order of magnitude shorter th an the shortest preliminary breakdown pulses, including so-called narro w bipolar pulses [e.g., Rakov, 2006] (see Section 2.5) that have characteristic full widths of a few tens of microseconds. Submicrosecond-scale electric field pulses some what similar to the lightning initiation pulses predicted by Gurevich et al. [2002, 2003] have been observed as a part of preliminary breakdown in cloud and ground discharges by Gurevich et al. [2003] and by the University of Florida Lightning Research Group (see Figure 2-13) [ Rakov and DeCarlo 2005; Rakov 2006]. However, the relation between the ru naway breakdown mechanism proposed by Gurevich et al. [1999] and the occurrence of multiple submic rosecond-scale pulses is still unclear. 2.4 Rocket-Triggered Lightning The rocket-and-wire technique is a method of artificially initia ting a cloud-to-ground lightning flash. The technique involves launching a small rocket that extends upward a thin conducting wire, which can be gr ounded or ungrounded. If the wire is grounded, the flash is

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59 Figure 2-13. Submicrosecond-scale pulses that occurred in a cloud discharge. Taken from Rakov and DeCarlo [2005] and Rakov [2006]. usually referred to as classical triggered lightning. The primary distinction between natural cloud-to-ground lightning (described in Section 2 .2.1) and classical rocket-triggered lightning is that the stepped-leader/first-ret urn-stroke sequence in natural li ghtning is replaced by initial stage (the upward positive leader, involving destruction of the triggering wire, and initial continuous current) in classical triggere d lightning. In fact, the phenom enology of classical triggered lightning is similar to that of upward li ghtning initiated by tall grounded objects [ Rakov and Uman 2003, Ch. 6]. The rocket is typically constr ucted from fiberglass or plasti c and is about 1 m in length. The triggering wire is Kevlar-reinforced copper or steel of diameter a bout 0.2 mm and the spool can be mounted on either the rocket or the gr ound. The rocket is laun ched when thunderstorm conditions are deemed adequate, although these conditions may vary by region. The sequence of

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60 Figure 2-14. Sequence of events in classical tr iggered lightning. The upward positive leader and initial continuous current constitute the initia l stage. Adapted from Rakov et al. [1998]. events in classical triggered li ghtning is shown in Figure 2-14. Under favorable conditions, i.e., when the measured static electric field on gr ound is sufficiently high (less than -5 kV/m for negative charge overhead), a rocket trailing a wire is launched. The average speed of the rocket is about 200 m/s, and when the rocket reache s about 300 m, a positively-charged upward leader (assuming a negative cloud charge source overhead) is initiated fr om the upper end of the wire. This leader has an average speed of about 105 m/s. The upward leader current vaporizes the triggering wire and the gap between the bottom of the leader and the ground is bridged by a plasma channel. The upward leader leads to establishing the initial continuous current (ICC)

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61 which has a duration of some hundreds of millis econds. The combined upward-leader and ICC processes are referred to as the initial stage (IS) of rocket-triggered lightning, which is similar to the initial stage in upward flashes initiated from tall towers [ Miki et al. 2005]. After a no-current interval of some tens of milliseconds, a downw ard-propagating negatively-charged dart leader may traverse the gap between cloud and ground at an average speed of about 107m/s. When this dart leader makes contact with ground, an upward return stroke wave propagates up towards the cloud at a speed of the order of 108 m/s. After an interval of typically some tens of milliseconds, more strokes may follow. These leader/return-str oke sequence are thought to be very similar to subsequent dart-leader/retur n-stroke sequences in na tural negative lightning [e.g., Fisher et al., 1993]. Triggering with an ungrounded wire, having a ga p of some hundreds of meters or more between the bottom of the conducting wire a nd ground, is usually refe rred to as altitude triggered lightning. In cases where th e gap is only a few meters or le ss, it is typically not referred to as altitude triggering. The primary difference between classical and alt itude triggered lightning techniques is that the latter is capable, to a degree, of reproducing a st epped leader followed by a first return stroke, whereas the classical me thod is not. In both cases, usually negative cloud charge is lowered towards ground. In altitude triggering, the bottom of the conducting triggering wire is typically isolated fr om a grounded intercepting wire by insulating Kevlar cable. The grounded intercepting wire and insu lating Kevlar cable typically have lengths on the order of some tens and hundreds of meters, respectively. Unintentional altitude tr iggering can also occur as a result of accidental breakage of the wire dur ing classical triggering. Since the triggering wire is ungrounded, the presence of a strong electric field (due to the overhead cloud charge source) results in the initiation of a bi directional (positive charge up a nd negative charge down) leader

PAGE 62

62 from opposite ends of the wire. When contac t is made between the downward-stepped and upward-connecting leaders, the return stroke is initiated. However, th is return stroke is dissimilar from both natural first and subsequent strokes, as well as strokes in classical-triggered lightning. The current waveform measured at ground appears to be chopped soon af ter reaching its peak value, and its width is appreciably smaller than that of the following return strokes. This phenomenon is presumably due to the return st roke front (having a speed on the order of 108 m/s) catching up with the upward-moving leader tip (which is st ill propagating towards the cloud at a speed of about 105 m/s) after 10 s or so, producing an oppos ite-polarity downward-moving reflected current wave that chops the current waveform measured at ground. This return stroke is referred to as an initial-stage return stroke [ Rakov and Uman 2003]. The leader/returnstroke sequences that follow this initial-stage stroke are thought to be sim ilar those in classical triggered lightning. Although the altitude-triggering techniqu e reproduces some features observed in natural stepped leader s and first return strokes, the complexity of the triggering process (e.g. the bidirectional le ader and the reflected initial-sta ge return stroke wave) often makes it difficult to interpret the resulting data. Details of observations from altitude-triggered lightning can be found in Laroche et al [1991], Lalande et al [1998], Rakov et al [1998], Chen et al [2003], and Saba et al [2005]. 2.5 Compact Intracloud Discharges Cloud lightning discharges that produce both (1) single, usually solitary bipolar electric field pulses having typical full widths of 10 to 30 s and (2) intense HF-VHF radiation bursts (much m ore intense than those from any othe r cloud-to-ground or normal cloud discharge process) are referred to as Comp act Intracloud Discharges (CIDs) These discharges were first reported by Le Vine [1980] and later characterized by Willett et al. [1989b] and Smith et al. [1999, 2004], among others. Most of the reported elec tric field signatures of these discharges are

PAGE 63

63 produced by distant (tens to hundreds of kilomete rs) events and hence ar e essentially radiation. The radiation field pulses produced by CIDs are referred to as Narrow Bi polar Pulses (NBPs). Close waveforms that are dominated by the indu ction and electrostatic field components were reported before this study only once [ Eack 2004]. Both polarities of the initial half-cycle of the NBPs have been observed, with negative pola rity (atmospheric electricity sign convention, according to which a downward-dire cted electric field vector is assumed to be positive) being more frequent. The term "CID" was coined by Smith et al. [1999] who inferred that the spatial extent of these discharges must be relativel y small, 300 to 1000 m. CIDs tend to occur at relatively large altitudes, t ypically more than 10 km [ Smith et al. 2004], while Light and Jacobson [2002] reported that CIDs often produced no optical emission observable by FORTE satellite. A recent summary of ground-based a nd space observations of CIDs is given by Hamlin et al. [2009]. Le Vine [1980], who used an electric field measur ing system triggered when the associated HF-VHF signal, in the range from 3 to 300 MHz, exceeded a relatively high threshold level, reported observations of narrow bipolar electric field pulses that have been recorded in conjunction with their associated HF-VHF radiat ion. The initial polarity of the bipolar pulses was negative (atmospheric electricity sign convention) that is, opposite to th at of electric field pulses due to return strokes in negative cloudto-ground lightning. The pulse amplitudes were of the order of one-third those of the return stroke peaks reco rded at about the same time. Le Vine [1980] attributed the observed narrow bipolar pulses accompan ied by strong HF-VHF radiation to K processes, a hypothesis not c onfirmed by subsequent studies. Willett et al. [1989b], working at KSC in 1985 and 1987, obtained recordings of both electric field (E) and electric fi eld derivative (dE/dt) for narrow bipolar pulses. Their measuring

PAGE 64

64 system was triggered by the output of an HF recei ver that could be tuned to any center frequency between 3 and 18 MHz. Both polarities of the initial half-cycle of the narrow bipolar pulses were observed, with negative polarity (atmospheric electricity sign c onvention) being more frequent. For 18 waveforms, Willett et al. [1989b] estimated arithmetic mean values of E and dE/dt peaks normalized to 100 km of 8 V/m and 20 V/m/ s, respectively. Both values are comparable to their counterparts for first return strokes observed in the same experiment. The overall pulse width was 20 to 30 s. Spectral analysis indicated that the sources of the narrow bipolar pulses radiated much more strongly than first re turn strokes at frequencies from 10 to at least 50 MHz. At 18 MHz the energy-spectral density (measured in (V m-1 Hz-1)2) for these pulses was nearly 16 dB higher than that for first return strokes at the same distance. Smith et al. [1999], who used a multiple-station electri c field change measuring system in concert with an HF (3 to 30 MHz) time-of-a rrival (TOA) lightning locat ing system, presented a detailed characterization of the narrow bipolar pu lses in three thunderstorm s at distances greater than 80 km in New Mexico and west Texas, incl uding locations of their sources in the cloud. The characteristics of the 24 narrow bipolar electric field pulses (see for example, Figure 2-15) and associated HF (3 to 30 MHz) radiation studied by Smith et al. [1999] are summarized in Table 21. Smith et al. [1999] reported that the pul se peaks were comparable to those of return-stroke waveforms. Nearly all pulses studied by Smith et al. [1999] were the only events within the field record having a length of typically 4 to 10 ms. The HF (3 to 30 MHz) emissions associated with narrow bipolar pulses had a durat ion of only a few microseconds and were typically 10 times more powerful than the HF emissions fr om normal lightning discharges. CIDs have recently attracted considerable attention because (a) they are likely to be the strongest natural producers of HF-VHF radiation [e.g., Thomas et al. 2001], (b) they are

PAGE 65

65 Figure 2-15. Narrow bipolar pulses recorded by the Los Alamos Sferic Array (LASA). (a) Narrow positive bipolar pulses (positive NBPs ) from a discharge that occurred 32 km northwest of Tampa, Florida. Physics sign convention is used here. (b) Narrow negative bipolar pulses (negative NBPs) from a discharge that occurred in Oklahoma. Adapted from Smith et al. [2002]. Table 2-1. Characteristics of narro w bipolar electric fi eld pulses and associated HF (3-30 MHz) radiation reported by Smith et al. [1999]. Electric Field Pulse Characteristics Mean Std. Dev. Risetime (10-90 percent) 2.3 0.8 s Half-peak width 4.7 1.3 s Pulse duration 25.8 4.9 s Initial peaka 9.5 3.6 V m-1 Opposite polarity overshoota -3.9 1.6 V m-1 Ratio of initial peak to opposite polarity overshoot 2.7 Ratio of peaks for narrow bipol ar pulses and return-stroke pulses 0.71 Ratio of peaks for narrow bipolar pulses and cloud-flash pulses 2.6 HF Radiation Characteristics Mean Std. Dev. Duration 2.8 0.8 s Peakb 2.4 1.1 mV m-1 Ratio of peaks for narrow bipol ar pulses and return-stroke pulses 9.9 Ratio of peaks for narrow bipolar pulses and cloud-flash pulses 29 a Normalized to 100 km; physics sign convention. b Normalized to 10 km and 1 kHz bandwidth. Time, s (b) (a) 34 Hz 0.5 MHz, ~ 1 ms Time, s

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66 considered the prime candidate for proposed sate llite-based VHF global li ghtning monitors [e.g., Wiens et al. 2008] and (c) they are thought to invol ve the runaway elec tron breakdown [e.g., Gurevich and Zybin 2004; Gurevich et al. 2004; Tierney et al. 2005]. Watson and Marshall [2007] used the original tr ansmission line (TL) model [ Uman et al., 1975] and a modified TL model with an exponent ially increasing current along the channel to compute electric field signatures at horizontal distances of a few and 200 km and compare them with corresponding measured waveforms reported by Eack [2004]. Both models can successfully match the two-station field measurements. The exponentially increasing current was assumed by Watson and Marshall to correspond to the runway breakdown process. The original TL model was also employed by Le Vine [1980]. In Chapter 4 of this dissertation, new experime ntal data that are needed for testing the validity of various models of CID are presente d. Further, we propose a conceptual mechanism for this phenomenon and present a model based on this mechanism for computing electromagnetic field signatures of CIDs. Elect rical parameters of CIDs are also inferred.

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67 CHAPTER 3 EXPERIMENTAL SETUP 3.1 The Lightning Obser vatory in Gainesville Measurements of electrom agnetic signals from lightning discharges have been performed in Gainesville, on the University of Florida cam pus, since 2004. Over the years the experimental setup has undergone upgrades, modifications, expansions, and relocation. From 2004 to 2007 the instrumentation was located on th e roof and in a closet on the third floor of Benton Hall (29 38 37.77 N, 82o 20 50.00 W), a three-storey building on the University of Florida campus. In 2004, the experimental setup was operated by Brian DeCarlo. The experimental setup in 20052007 is described in detail in Nag [2007]. In 2004 and 2005, the system included only wideband electric field measurements. In 2006 and 2007, th e measurement station was gradually expanded to include, in addition to wideband electric fiel d, electric field deriva tive (dE/dt), narrowband high frequency (HF) and very high frequenc y (VHF) measurements. In March 2008 the experimental setup was relocate d to the roof of the five-s torey New Engineering Building (Building # 33) on the University of Florida campus and named the Lightning Observatory in Gainesville (LOG) (29o 38 32.27 N 82o 20 49.70 W). The Lightning Observatory (see Figure 3-1), where all instrumentation is presently loca ted, includes a glass c upola providing over a 180 degree unobstructed view of the horizon. The cupol a houses digitizing osci lloscopes, with the sensors being located nearby on the roof. In April-May 2008, addi tional electric field and dE/dt antennas, a new magnetic field deri vative (dB/dt) antenna, and an x-ray sensor were added to the existing experimental setup. Figure 3-2 show s the Google Earth image of the LOG in 2008. Approximate locations of different sensors ar e shown with different symbols on the image.

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68 Figure 3-1. The Lightning Observatory on the roof of the Engineering Building on the University of Florida campus at Gainesville. 3.2 Overview of Experiments 3.2.1 Single-Station Experiment The purpose of this experime nt was to obtain correlated wideband elec tric field, electric field derivative, magnetic field derivative, and narrowband very high frequency signatures (labeled E2, dE2, dB, and VHF, respectively, in Figures 3-2 and 33) of cloud and ground lightning discharges. Note that prior to April 2008, a narrowband high frequency (HF) measurement system was also a part of this expe rimental setup. It is not shown in Figures 3-2 and 3-3, which are for post-April 2008. The measur ing system settings allowed one to detect

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69 Figure 3-2. Google Earth image of the LOG in 2008. Approximate locations of different sensors are shown with different symbols on the image. E1, E2, dE1, dE2, dB, VHF, and Xray are the electric field (t wo-station experiment), elec tric field (single-station experiment), electric fiel d derivative (two-station expe riment), electric field derivative (single-station experiment), magne tic field derivative (both experiments), VHF (single-station experiment) and x-ra ys (single-station experiment) sensor, respectively. Also shown is th e location of the GPS antenna. electromagnetic signals from light ning discharges occurring at distances ranging from a few to about 100 km from the measuring station. Th e primary focus was on studying preliminary breakdown pulse trains in negative cloud-to-g round discharges and compact intracloud discharges (CIDs). In addition, co rrelated wideband electric field, and electric and magnetic field derivative measurements of positive, bipolar, and negative cloud-to-ground lightning from thunderstorms in and around Gainesville were al so acquired. In May 2008, an x-ray sensor provided by Dr. J. Dwyer of the Florida Institu te of Technology was installed for measuring N GPS dB (N-S & E-W) E1 dE1 VHF X-rays E2 dE2

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70 high-energy radiation from close (within 1 km) cloud-to-ground lightning. X-ray measurements (none were acquired as of Novemb er 2008) are outside the scope of this dissertation and will not be further discussed here. Figure 3-3 schematically shows positions of the different sensors used in this experiment. These sensors, grouped by experi ment, are listed in the Table 3-1. Figure 3-4 shows the block diagram of the single-station experiment. 3.2.2 Two-Station Experiment This experime nt was designed to measure fiel d waveforms (primarily radiation) at the Gainesville station due to natura l and rocket-triggered lightning at Camp Blanding, Florida. The Gainesville and Camp Blanding measuring stations are 45 km apart. The measuring system at Gainesville is externally triggered in synchroni zation with the triggering of the Camp Blanding system. An AT&T BellSouth analog conditioned telephone line was used to transmit a trigger pulse generated at Camp Blanding (near station) in response to lightning stri kes on-site or in its immediate vicinity, to Gainesville (distant station). The transmission time of the trigger pulse from Camp Blanding to Gainesville was meas ured in 2007 (when the measuring station was located at Benton Hall) and in 2008 (after relocation to the Engineering Building) and was found to be approximately 29 ms in both cases. This means that the lightning event producing the trigger at Camp Blanding triggers the system in Gainesville with a 29-ms delay. The effect of the transmission delay of the trigger pulse is c ountered by choosing the pretrigger time of the oscilloscope to be greater than this transmission delay. This experiment enables simultaneous measur ements of near (hundreds of meters from lightning channel) and distant (a bout 45 km from lightning channel) fields from the same cloudto-ground discharge. A detailed description of the configuration of the twostation experiment is given in Section 3.14. The experimental setup incl uded electric field, electric field derivative,

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71 Figure 3-3. Schematic showing positions of the di fferent sensors at the LOG in 2008. The use of sensors in different experiment s is indicated in Table 3-1. Table 3-1. A list of LOG sensors (see Figure 33) used in two-stat ion and single-station experiments. Two-station experiment Single-station experiment (stand-alone mode) Remarks 1. E1 1. E2 Wideband vertical electric field 2. dE1 2. dE2 Electric field derivative 3. dB (N-S) 3. dB (N-S) Magnetic fiel d derivative (north-south component) 4. dB (E-W) 4. dB (E-W) Magnetic fiel d derivative (eas t-west component) 5. VHF Narrowband (36 MHz) VHF radiation 6. X rays NaI x-ray detector E1 dE1 X-rays dE2 E2 GPS dB (N-S & E-W) N VHF Glass Cupola

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72 and magnetic field derivative measurements labe led E2, dE2, and dB, respectively, in Figures 32 and 3-3, which show positions of the corresponding sensors. These sensors are listed in Table 3-1. Figure 3-5 shows the block diagram of the tw o-station experiment. 3.2.3 Equipment The equipment used in the two experime nt s discussed in Sections 3.2.1 and 3.2.2, included sensors, fiber optic links, di gital storage oscilloscopes, GPS time stamping system, and a dedicated phone line. The sensors used for each measurement are described in Sections 3.3 to 3.7. The characteristics of the other equipment us ed are described in the following subsections. 3.2.3.1 Fiber optic links Opticomm MMV-120C fiber-optic links are being used at the LOG. The Opticomm MMV-120C fiber-optic links utilize frequency m odulation (FM) with a carrier frequency of 70 MHz and operate at an optical wavelength of 1310 nm. The Opticomm links were intended by the manufacturer to be used as video fiber-opt ic links and therefore had an input and output resistance of 75 (the standard resistance for video equipment). However, they were modified to match the performance characteristics (imp edance and bandwidth) required for lightning experiments at the ICLRT at Camp Blanding, Flor ida. The transmitter has an input impedance of 68 k and the receiver has an output impedance of 50 The bandwidth (-3 dB) of the link is from DC to 30 MHz, as specified by the manufactu rer. The manufacturer li sts the signal-to-noise ratio to be about 67 dB, however this value is ac quired using the short-haul RS-250C standard in which the signal is low-pass filter ed with a cut-off frequency of about 5 MHz. Thus, 67 dB may not be an accurate representation of the true signal-to-noise ratio ove r entire bandwidth. In practice, the signal-to-noise ratio over the entire bandwidth is several dB lower than the value obtained under the short-haul RS-250C standard.

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73 Figure 3-4. Block diagram of th e single-station experiment.

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74 Figure 3-5. Block diagram of the two-station experiment.

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75 Opticomm MMV-120CFrequency (Hz) 100101102103104105106107108 Gain (dB) -12 -10 -8 -6 -4 -2 0 2 Figure 3-6. Frequency response of an Opticomm MMV-120C fiber-optic link used at the LOG. The Opticomm links utilize 62.5/125 m (core/cladding) graded index multi-mode fiberoptic cable with ST connectors purchased from Fi ber Instrument Sales, Inc. Figure 3-6 shows the measured frequency response for an Opticomm MMV-120C fiber-optic link (with a 50 m long fiber) used at the LOG. The Opticomm links were calibrated using a 100 Hz, 1 V peak-to-peak square wave. 3.2.3.2 Digital storage oscilloscopes Four digital storage oscillosc opes (shown in Figure 3-7) we re used at the LOG in 2008. The various characteristics of each of the osc illo scopes are given below. Specific oscilloscope configurations are given in Tables 3-2 and 3-3. LeCroy WavePro 7100: The LeCroy WavePro 7100 is a four-channel DSO with a maximum bandwidth of 1 GHz at a maximum sampling rate of 10 GHz with an 8-bit vertical resolution. The maximum sampling rate is 20 GHz when ope rating in the 2-channel mode. The WavePro 7100 is capable of recording 24 megabyte per channel when all four channels are in use. Hence

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76 Table 3-2. Digital storage oscilloscope used at the LOG prior to April 2008. DSO Type Experiment Measurements Record length (ms) Pretrigger time (ms) Sampling rate (MHz) Trigger mode and input Comment LeCroy 7100 Singlestation/Twostation experiment E, dE/dt, HF, VHF 480 100 100 Threshold trigger on E/Threshold trigger on signal from Camp Blanding Used for both experiments, manually switched between triggering modes with an 8-bit resolution (that is one byte required to store each sample) the total record length is 24 megasamples for each of the 4 channels. At a maximum sampling rate of 10 GHz, the maximum record length is 2.4 ms. The Wa vePro 7100 uses the Microsoft Windows 2000 Professional (SP 4) operating system and has a flat panel touch-screen display. The processor memory is 1024 MB and the processor speed is 1.7 GHz. The recorded data can either be stored on the internal hard drive of the oscilloscope or on an external hard disk via USB port. LeCroy WavePro 7100A: The LeCroy WavePro 7100A is an advanced version of the LeCroy WavePro 7100 with an extended memory option. Like the WavePro 7100, the WavePro 7100A is a four-channel DSO with a maximum bandwidth of 1 GHz at a maximum sampling rate of 10 GHz with an 8-bit vertical resolution. The maxi mum sampling rate is 20 GHz when operating in the 2-channel mode. The WavePro 7100 is capable of recording 50 megabytes per channel when all four channels are in use. Hence with an 8-bit resolution the total record length is 50 megasamples for each of the 4 channels. At a maximum sampling rate of 10 GHz, the maximum record length is 5 ms. The WavePro 7100A uses the Microsoft Windows XP Professional (SP 2) operating system and has a flat panel touch-sc reen display. The processor memory is 1.98 GB and the processor speed is 2.8 GHz. The recorded da ta can either be stored on the internal hard drive of the oscilloscope or on an external hard disk via USB port.

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77 Figure 3-7. Digitizing oscillos copes inside the glass cupola at the LOG in August, 2008. LeCroy LT344Waverunner: The LeCroy LT344 is a four channel DSO with a maximum bandwidth of 500 MHz at a maximum sampling rate of 500 MHz with 8-b it vertical resolution. The LT344 is capable of a maximum record lengt h of one megabyte per ch annel when all four channels are in use. Since a sample is recorded with 8-bit resolu tion, one byte is required to store each sample; hence the total record length is on e megasample per channel. At the maximum

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78 Table 3-3. Digital storage oscilloscopes used at the LOG after April 2008. DSO Type Experiment Measurements Record length (ms) Pretrigger time (ms) Sampling rate (MHz) Trigger mode and input Comment Lecroy LT344 Singlestation experiment E, dE/dt, VHF 10 4 100 Threshold trigger on E or VHF Used after April, 2008 LeCroy 7100 Twostation experiment E, dE/dt 480 100 100 Width trigger on signal from CB Used also for the singlestation experiment prior to August, 2008 LeCroy 7100A Singlestation experiment E, dE/dt, dB/dt (two components), VHF 240/500 80/100 100 Threshold trigger on E or VHF Added in August, 2008 Yokogawa DL716 Twostation experiment E, dE/dt, dB/dt (two components) 3206 1280 10 Threshold trigger on LeCroy 7100 trigger-out Used after May, 2008 sampling rate of 500 MHz, the maximum record le ngth is 2 ms. Typically the LT344 is not used to acquire a single continuous record but rath er is used in segmented memory mode. In segmented memory mode, the acquisition memory is divided into multiple segments and a separate trigger is required to re cord each segment. For example, if five segments are used, the acquisition memory is divided into 200 kilo samples per segment per channel. Segmented memory mode is useful when acquisition memory is limited and multiple events are to be recorded with the duration of each event being ve ry small relative to th e time between events. Segmented memory mode is ideal for recordin g the electric and magnetic field waveforms (or their time-derivatives) from individual return strokes. The input resistance of each LT344 channel can be set to 50 or 1 M either AC or DC coupled. Each channel can be set from 2 mV per division to 10 V per division with a maximum RMS input vol tage of 5 V and 280 V

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79 when 50 and 1 M input resistances are used, respectivel y. In addition, each channel can be individually configured with an internal lo w pass filter of 25 MHz or 200 MHz (-3 dB). The LT344 is equipped with a PCMCIA Type III slot, which is used to add storage such as a hard drive or a compact flash card wh ich come in a variety of size s. A 128 MB compact flash card was used in the LT344; hence a maximum of 32 wa veforms could be stored if one megabyte was used per channel and all four channels were in use for each acquisition. Waveforms can be moved to and from the DSO over a 10Base-T Ethern et connection or the GP IB bus using LeCroy Scope Explorer software. Yokogawa DL716: The Yokogawa DL716 is a 16 channel DS O with a maximum bandwidth of 4 MHz (-3 dB) and a maximum sampling rate of 10 MHz, with 12-bit vertical resolution. The DL716 is capable of a maximum record length of 16 megasamples per channel when all 16 channels are used simultaneously. At the ma ximum sampling rate of 10 MHz, the maximum record length is 1.6 s when all 16 channels are us ed. Therefore, the DL716 is ideal for recording a continuous full-flash record of lightning electr ic and magnetic fields. Each DL716 channel can be set from 5 mV per division to 20 V per division with a maxi mum peak-to-peak input voltage range of 250 V. The input resistance of each channel is 1 M shunted with 30 pF of input capacitance, either AC or DC coupled. In addi tion, each channel can be individually configured with an internal low-pass filter having a -3 dB cutoff at 500 Hz, 5 kHz, 50 kHz, or 500 kHz. The DL716 is equipped with 9.2 GB of intern al storage and many acquired waveforms can be stored in the digitizer itsel f. The DL716 is also equipped with an external SCSI hard disk connector so that more storage can be added. Waveforms can be moved to and from the DL716 over a 10Base-T Ethernet c onnection using the File Transfer Protocol (FTP).

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80 Figure 3-8. The GPS antenna used at the LOG. The DL716 can be triggered by any of the 16 cha nnels or by an external TTL level trigger input. One major disadvantage of the DL716 is that, for long records (several hundred milliseconds or more), it takes up to 15 minutes to write the data from memory to disk. During this interval, the digitizer ca nnot trigger and hence no new lightning data can be recorded. 3.2.3.3 GPS time-stamping system This system consisted of a GPS antenna (shown in Figure 3-8), the GPS-ACU/2K m anufactured by Trimble and a PC card, the bc 627-AT manufactured by Datum Inc. The antenna and card tracked the GPS time in UT C format which was displayed on a PC via a software interface. The bc627-AT was connected to the trigger out of an oscilloscope. Any lightning event recorded by the oscilloscope genera ted an output trigger, causing the GPS card to trigger at the same instant and produce a timestamp.

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81 As stated in Section 1, prior to March 2008, the instrumentation was located on the third floor and roof of Benton Hall. At that time, th e GPS system PC was housed inside an electrical closet alongside electrical and communication junction boxes of the building. Spurious signals, probably from these junction boxes, often coupled to the GPS syst em producing timestamps that did not correspond to lightning flashes. In fact, timestamps were produced even when there was no nearby thunderstorms. However, since relocation of the instrumentation to the Engineering Building in March 2008, spurious timestamps have no longer been generated. The GPS timestamps generated by our system were co mpared with those generated by the National Lightning Detection Network (NLDN) for the same lightning events and it was found that for 43% of the events, NLDN times were within 10-m s of our GPS time stamps, for 71% they were within 40 ms and for 99% within 80 ms. The co rrectness of our event matching with NLDN data was verified using inter-stroke intervals in multip le stroke CGs and intervals between individual pulses produced by ICs. 3.2.3.4 Dedicated phone line A dedicated phone line, a condi tioned line provided by AT&T/Bellsouth, is being used to provide a link between Camp Blanding and Gainesvill e. This link is a four-wire line that enables transmission of a trigger pulse from Camp Bla nding to Gainesville and vice versa. The line has a characteristic impedance of 600 and a frequency bandwidth from 300 Hz to 3 KHz. Currently, the link is being used to transmit trigger pulse s generated at Camp Blanding in response to rocket-triggered or natural on-site events to Gain esville. The transmission delay of a pulse from Camp Blanding to Gainesville (45 km apart) is about 29 ms. The link is being used in the twostation experiment.

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82 3.3 Wideband Electric Field Measurements The various measure ments in the experiments discussed in Section 3.2 are described in the following sections. 3.3.1 Theory Lightning discharges, both cloud and cloud-to-g round, have durations that ma y extend to a second or more. However, the individual physical pr ocesses in a particular discharge can vary on microsecond and even submicrosecond tim e scales. Lightning processes can produce electromagnetic signatures in the range from a few hertz (long contin uing currents) to 1020 Hz (hard x-rays) [ Rakov, 2008]. Figure 3-9. An electric field an tenna system. Adapted from Uman [1987]. A sensor that is commonly used to measur e the lightning wideband electric field is a metallic flat plate antenna. Figure 3-9 shows an example of flat plate antenna system. Ca is the capacitance between the antenna plate and the ground, and R0 terminates the coaxial cable in its characteristic impedance. C is the integrating capacitor and R is the relatively large resistor (usually input resistance of associated elec tronics) that provides a discharge path for the capacitor C, so that the output voltage in response to a step-function excitation decays exponentially with a time constant = RC. The value of should be chosen such that it is much larger than the variation tim e of the signal of interest. Vout Coaxial C

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83 In order to satisfy boundary conditions on the surface of a perfect conductor, the electric field vector on the surface of sensing plate wi ll only have a vertical component. The charge Q induced on the antenna plate having a surface area A is given by Equation 3-1, which follows from the boundary condition on the normal component of electric field on the surface of a good conductor ( 0 s E where s is the surface charge density assumed to be constant). 0()() QtAEt (3-1) Any change in the vertical electric field E on th e antenna plate will cause a change in Q. The resultant short-circuit current I is given by: 0()() () dQtdEt ItA dtdt (3-2) Therefore, the voltage across the resistor R and capacitor C in Figure 3-9 (assuming that R >> 1/ C and Ca << C) and hence the output voltage (Vout) is given by Equation 3-3. 0 01( ) ()t out A Et VItd CC (3-3) Thus, the output voltage is direct ly proportional to the vertical component of electric field at the position of the antenna (assuming that the antenna does not significantly dist ort the electric field to be measured). 3.3.2 Antenna Circular flat plate antennas such as th e one shown in Figure 3-10 were used to measure wideband electric field at the L OG. The sensing plate of each an tenna (made of aluminum) was raised above the roof of the bu ilding by mounting it on a vertical me tallic (galvanized iron) pole. The sensing plate and the vertical pole were separated by a 1.5 cm long PVC insulator. The pole was fastened to a metallic (aluminum) base wh ich was connected to a nearby conductor of the

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84 lightning protective system of the building. Signal from the antenna (voltage between the sensing plate and grounded pole) was relayed via a double-s hielded and sleeved RG -223 coaxial cable to the electronics inside a Hoffman box (a shielding metallic enclos ure) placed at the antenna base. Raising the flat plate enhances the electric field relative to that in the absence of the antenna. This field enhancement (geometrical "gain") along with any electronic gain increases the sensitivity of the system for the same area of the fl at plate. All elevated flat plate antennas used at the LOG were calibrated with respect to a standard flat-plate antenna placed essentially flush with ground (roof surface). Addition al field enhancement factor due to presence of the building was also taken into account. 3.3.3 Electric Field Measuring System fo r the Two-Station Experiment (E1) This electric field m easuring system include d a circular flat plat e antenna which had a diameter of 44.6 cm and an area of 0.156 m2. The flat plate was mounted on a metallic pole, so that it was at a height of 1.71 m above the roof of the building. The antenna was followed by an integrating capacitor (1.94 nF) and a unity gain high input impedance amplifier placed inside a Hoffman box (see Figure 3-11). The signal from the antenna and associated electronics was transmitted to a LeCroy digitizing oscilloscope which sampled at a rate of 100 MHz and a Yokogawa digitizing oscilloscope which sampled at a rate of 10 MHz. The -3 dB bandwidth of the electric field measuring system was from 16 Hz (determined by the RC time constant of 9.89 ms of the integrator) to 13 MHz (determine d by the -3 dB upper frequency response of the amplifier) or from 16 Hz to 4 MHz (the latter determined by the -3 dB upper frequency response of the Yokogawa oscilloscope). An Opticomm fi ber optic transmitter-recei ver pair along with a 51 m long 62.5 m multi-mode fiber with ST connectors was used to transmit the signal from the antenna and associated electronics to the digitizing oscilloscopes.

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85 Figure 3-10. An elevated flat plate antenna used for measuring wideband electric field at the LOG. Similar antennas were used for the dE/dt and narrowband HF measurements. Figure 3-12 shows a schematic of the unity gain high input impedance amplifier circuit. It consisted of an AD825 operational amplifier whic h was used to implement a voltage follower. The input impedance of the amplifier was 5.1 M and the output impedance of the feedback circuit, and hence of the amplifier, was a fr action of an Ohm. The RC time constant of the antenna system was equal to 9.89 ms. The output of the amplifier was connected to the input of an Opticomm MMV-120C transmitter terminated in 50 Two 12 V batteries (placed inside the Hoffman box) were used, one to power the Op ticomm MMV-120C transmitter, and the other to power the amplifier. The amplifier ground was at 6 V above the ne gative battery terminal in order to bias the AD825 operational amplifier w ith V. Since the amplifier ground was 6 V Circular sensin g plate Metallic pole Metallic enclosure (Hoffman box) Antenna b ase PVC insulator

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86 above the common ground, a separate 12 V battery wa s required to power it. The relay circuit of the amplifier block was however powered by the same 12 V battery as the Opticomm MMV120C transmitter. The frequency res ponse of the amplifier with a 50 load is shown in Figure 313. In order to eliminate ground loops, all electron ic components were isolated from each other and the metal box by pieces of plastic and Styrofoam. 3.3.4 Electric Field Measuring System for the Single-Station Experiment (E2) The electric field measuring system used for th is experiment was similar to the one used in the two-station experiment. However, a 10.4 nF in tegrating capacitor followed by a unity gain amplifier (based on an AD825 operational amp lifier) with an input impedance of 1 M was used. The frequency response of the amplifier with a 50 load is shown in Figure 3-14. The -3 dB bandwidth of the electric field measuring system was from 15 Hz (determined by the RC time constant of 10.4 ms of the integrator) to 12 MHz (determined by the -3 dB upper frequency response of the amplifier). The circular flat plat e electric field antenna had a diameter of 50.3 cm and an area of 0.199 m2. The flat plate was mounted on a metall ic pole, so that it was at a height of 1.62 m above the roof of the building. An Op ticomm fiber optic transmitter-receiver pair along with a 51 m long 62.5 m multi-mode fiber was used to transmit the signal from the antenna and associated electroni cs to LeCroy digitizing oscillos copes sampling at a rate of 100 MHz. Note that while the electric field measuring sy stems at the LOG did not have any electronic gain, there were geometrical gains due to the antennas being located on top of a building and because the sensing plates were elevated above the roof level. Amplitude calibration of the measuring systems is discussed in Section 3.12. Tables 3-4 and 3-5 summarize the characteristics of the electric field measuring systems along with their calibration factors.

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87 Figure 3-11. Electronics inside a Hoffman enclosure used in electri c field measuring system (E1) at the LOG. Figure 3-12. Schematic of the high input-impedance amplifier used in electric field measuring system (E1) at the LOG. 62.5 m multi-mode fiber 12 V battery powering the O p ticomm transmitte r 12 V battery powering the amplifier High input impedance amplifier Opticomm MMV-120C transmitter Integrating capacitor From antenna To oscilloscope

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88 Amplifier for E1 Frequency (Hz) 100101102103104105106107108 Gain (dB) -6 -4 -2 0 2 Figure 3-13. Frequency response of the high inpu t-impedance amplifier used in electric field measuring system (E1) at the LOG. Amplifier for E2 Frequency (Hz) 100101102103104105106107108 Gain (dB) -6 -4 -2 0 2 Figure 3-14. Frequency response of the high inpu t-impedance amplifier used in electric field measuring system (E2) at the LOG.

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89 3.4 Electric Field Deriva tive Measurements 3.4.1 Theory Figure 3-15 shows the configuration for a flat plate antenna system acting as an electric field derivative (dE/dt) sensor. In this case, it follows from Equa tion 3-2 that the output voltage across the resistor R is given by Equation 3-4. 0()outdEt VIRAR dt (3-4) Figure 3-15. An electric field deriva tive antenna system. Adapted from Uman [1987]. Equation 3-4 represents the ideal time domain res ponse of a flat plate dE/dt antenna. The output voltage of the antenna is direc tly proportional to the vertical component of the electric field derivative at ground. Further, the out put voltage is directly proportional to the area of the antenna and the resistance between the antenna pl ate and ground. The antenna capacitance Ca [of about 80 pF, Jerauld 2007] does not affect the amplitude of the output voltage of the ideal (R << 1/ Ca or f << 1/(2 RCa), where f = /2 ) dE/dt measuring system. For dE/dt measurement systems at the LOG, R = 50 so that the limiting frequency f << 40 MHz. 3.4.2 Antenna Circular flat plate antennas similar to the one describe d in Section 3.3.2 and shown in Figure 3-10 were used to m easure electric field derivative at the LOG. Specific dimensions are given in Sections 3.4.3 and 3.4.4. Vout Coaxial C

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90 3.4.3 dE/dt Measuring System for th e Two-St ation Experiment (dE1) This dE/dt measuring system included a circular flat plate antenna having a diameter of 46.5 cm and an area of 0.170 m2. The flat plate was mounted on a me tallic pole, so that it was at a height of 1.33 m above the roof of the building. The antenna was followed by an amplifier with a gain (ratio of output to input voltage) of 8.89 placed inside a Ho ffman box. The signal from the antenna and associated electronics was transmitte d to a LeCroy digitizing oscilloscope which sampled at a rate of 100 MHz and a Yokogawa digi tizing oscilloscope which sampled at a rate of 10 MHz. The upper limit of the frequency bandwidth of the dE/dt measuring system was 17 MHz (determined by the -3 dB upper frequency re sponse of the amplifier) or 4 MHz (determined by the -3 dB upper frequency response of the Yokogawa oscilloscope). An Opticomm fiber optic transmitter-receiver pair along with a 51 m long 62.5 m single-mode fiber with ST connectors was used to transmit the signal from the antenna and associated electr onics to the digitizing oscilloscope. Figure 3-16 shows a schematic of the amplifier circuit. It consisted of a THS4215, an ultralow-distortion, high-speed operational amplifier which was used to implement a non-inverting amplifier. The input and output impedan ces of the amplifier were equal to 50 The amplifier was powered by a 12 V battery placed inside the Hoffman box. The frequency response of the amplifier with a 50 load is shown in Figure 3-17. The output of the amplifier is connected to the input of an Opticomm MMV-120C transmitter terminated in 50 Note that the THS4215 has a closed loop output re sistance of a fraction of an Ohm. Hence the total output resistance of the amplifier circuit as shown in Figure 3-16 is approximately 50 The load impedance for this circuit is the input impedance of the Opticomm transmitter (50 shunt resistance). The output resistance of the amplifier and the input resistan ce of the Opticomm form a voltage divider that

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91 reduces the overall gain of the am plifier by half. Hence, the overal l gain of the amplifier circuit loaded by the 50 input impedance of the Opticomm is 8.89, as stated in the previous paragraph. In order to eliminate ground loops, all electronic components in the Hoffman box were isolated from each other and the me tal box by pieces of plastic and Styrofoam. 3.4.4 dE/dt Measuring System for the Single-Station Experiment (dE2) W ith the exception of the antenna, all aspects of the dE/dt measuring system used for this experiment (including amplifier ch aracteristics) were the same as those used in the two-station Figure 3-16. Schematic of the amplifier used in dE/dt measuring systems (dE1 and dE2) at the LOG. Note that the overall gain of the amplifier circuit loaded by the 50 input impedance of the Opticomm is 8.89. experiment. In the single-station experiment, the circular flat plate dE /dt field antenna had a diameter of 50.3 cm and an area of 0.199 m2. The flat plate was mounted on a metallic pole, so that it was at a height of 1.7 m above the roof of the buildi ng. The upper limit of the frequency bandwidth of the dE/dt measurement was 17 MH z which was determined by the -3 dB upper frequency response of the amplifier. Note that in addition to the electronic gain of 8.89, the dE /dt measuring systems at the LOG had geometrical gains (field enhancements) due to the ante nnas being located on top of a building and because the sensing plates were el evated above the roof level. The amplitude

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92 Amplifiers for dE1 and dE2 Frequency (Hz) 100101102103104105106107108 Gain (dB) 13 14 15 16 17 18 19 20 Figure 3-17. Frequency response of the amplifiers used in dE/dt measuring systems (dE1 and dE2) at the LOG. calibration of the measuring systems is discussed in Section 3.12. Tables 3-4 and 3-5 summarize the characteristics of the dE/dt measuring systems along with their calibration factors. 3.5 Magnetic Field Derivative Measuring System 3.5.1 Theory To measure the m agnetic field from lightning a loop of wire can be used as an antenna. According to Faraday's law a changing magnetic field passing through an open circuited loop of wire will induce a voltage at the terminals of th e wire. The voltage magnit ude at the terminals of the wire is given by Equation 3-5. ()n outdBt VA dt (3-5) where A is the area of the loop and Bn(t) is the normal component of magnetic flux density passing through the loop, cosnBB where B is the total magnetic flux density and is the angle between the B vector and the normal to the loop. Th e output voltage is proportional to the

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93 time derivative of the magnetic field passing through the loop ( ()ndBt dt ). In the following the subscript n in Bn is dropped to simplify notation. 3.5.2 Antenna At the LOG, we used a square coaxial-cab le loop antenna with a single-ended output, which means that the output voltage is taken from only one end of the cable. The antenna was developed by George Schnetzer [ Jerauld 2007]. Each end of the cable was terminated in its characteristic impedance of 50 Figure 3-18 shows (a) the diagram and (b) equivalent circuit of a single-ended output coaxial-cable loop antenna with both ends of the cable terminated in 50 The 50 termination on the end of the cable at which the output voltage is measured is physically the input resistance of an amplifier. The other end of the cable is terminated by soldering a 50 resistor between the inner conductor and the outer sh ield. This soldering is located at the base of the antenna. Note that current is induced on both the inner conductor and the outer shield by either an exte rnal electric or magnetic field. Due to the current induced in the shield, unwanted magnetic field will necessarily be induced perpendicular to the loop. This induced magnetic field will distort the external magnetic field to be measured. Therefore, a small gap is placed in the shield to inhibit any shie ld current and hence prevent any unwanted magnetic fields from the shield. This gap is placed at th e top of the loop, as shown in Figure 3-18. The expressions for the ideal tim e-domain output voltage, Vout, and -3 dB upper frequency response, 0, of a single ended coaxial-cable loop an tenna are given by Equations 3-6 and 3-7. 1( ) 2load out looploadRA dBt V RRdt (3-6) 0 loopload loop R R L (3-7)

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94 Figure 3. (a) Diagram and (b) equivalent circuit of a single-ended output coaxial loop antenna with both ends of the cable terminated in 50 Adapted from Jerauld [2007]. For a loop terminated in 50 at both ends, Rload is 100 Lloop is the inductance of the loop, which is determined by the geometry of the antenna. Rloop is the total resistance of the loop antenna including the inherent resistance of the inner conducto r and any externally added resistance. Rloop affects both the gain and the bandwidth of the antenna and is determined by the desired characteristics of the antenna. If no ex ternal resistance is added to the antenna, Rloop is the resistance of the inner conductor of the cable which is nearly zero (can be neglected). At the LOG, two square single-ended co axial-cable loop antennas of area 0.533 m2 terminated in 50 were used to measure dB/dt. The an tennas were arranged in an orthogonal crossed-loop pair (as shown in Figure 3-19) individual antenna planes being oriented in northsouth and east-west directions a nd labeled dB (N-S) and dB (E-W ), respectively. An external (a) (b)

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95 resistance (Rloop) of 1410 was used. Rload, as stated previously, was 100 due to the 50 terminations at each end of the cab le. The inductance of this loop (Lloop) is approximately 4 H [Jerauld, 2007]. The upper limit of the frequency bandw idth of the antenna was calculated using Equation 3-7 to be about 61 MHz. 3.5.3 dB/dt Measuring System fo r the Single-Station and Tw o-Station Experiments (dB) The output of each antenna loop was c onnected to an amplifier with 50 input resistance and a gain of 145. The amplifiers were impl emented using OPA657, which is a low noise operational amplifier. The frequency re sponse of one such amplifier with a 50 load is shown in Figure 3-20. The signals from the two loops and associated electronics placed inside a Hoffman box were transmitted to two channels of a LeCroy digitizing oscilloscope, which sampled at a rate of 100 MHz, and a Yokogawa digitizing oscilloscope, which sampled at a rate of 10 MHz. In order to elimin ate ground loops, all electronic co mponents were isolated from each other and the metal box by pieces of plastic and Styrofoam. Note that the magnetic field measuring systems, dB (N-S) and dB (E-W), were used in both experiment s discussed in Section 3.2. The upper limit of the frequency bandwid th of the dB/dt measurements was 15 MHz (determined by the -3 dB upper frequency response of the amplifier in cas e of the single-station experiment) or 4 MHz (determined by the -3 dB upper frequency response of the Yokogawa oscilloscope in case of the two-station experiment). Opticomm fiber optic transmitter-receiver pair along with a 51 m long 62.5 m multi-mode fibers with ST connectors is used to transmit the signal from the antenna and associated electr onics to the digitizing os cilloscopes. Table 3-6 summarizes the characteristics of the dB/dt measuring systems along with the associated amplitude calibration factors de termined using Equation 3-6.

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96 Figure 3-19. Two loops (oriente d north-south and east-west) of the magnetic field derivative antenna used at the LOG. 3.6 Narrowband HF Measuring System The narrowband HF measuring system included an elevated flat plate antenna, similar to the one described in Section 3.7.2, followed by an HF receiver having center frequency at 5 MHz (with a -3 dB bandwidth of 4.7 MHz to 5.4 MHz) and an overall gain (ra tio of output to input voltage) of 31. The electronics we re placed inside a Hoffman box at the base of the antenna. The signal from the antenna and associated elec tronics was transmitted to a LeCroy digitizing oscilloscope which sampled at a rate of 100 MHz. An Opticomm fiber optic transmitter-receiver pair along with a 51 m long 62.5 m single-mode fiber with ST connectors was used to transmit the signal from the antenna and associated electr onics to the digitizing oscilloscope. Figure 3-21 shows the block diagram of the HF measuring sy stem. The HF receiver consisted of two single stage amplifiers and a passive bandpass filter. The amplifiers were implemented using the THS4211 operational amplifier an d were powered by two 12 V batteries placed inside the Crossed loop dB/dt antenna Hoffman box

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97 Amplifiers for dB (N-S) and dB (E-W) Frequency (Hz) 100101102103104105106107108 Gain (dB) 14 15 16 17 18 19 20 21 22 23 Figure 3-20. Frequency response of the amplifiers used in dB/dt measuring systems, dB (N-S) and dB (E-W), at the LOG. Hoffman box. The filter circuit was connected be tween the two amplifier blocks in order to reduce DC offset that is introduced by the high gain amplifiers. The frequency response of the HF receiver (amplifier-filte r-amplifier configuration) is shown in Figure 3-22. The sensing circular flat plate of the HF measuring system had a diameter of 50.3 cm and an area of 0.199 m2. The plate was elevated, so that it was at height of 1.62 m above the roof of the building. No absolute amplitude calibration for the narrowband HF measuring system was attempted, since it was not essential for the purpose of this experiment. 3.7 Narrowband VHF measuring system The narrowband VHF measuring system included a whip antenna, followed by a VHF receiver having center frequency at 36 MHz (with a -3 dB bandwidth of 34 MHz to 38 MHz) and an overall gain (ratio of output to input voltage) of 27. The whip antenna had a length of 67 cm

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98 Figure 3-21. Block diagram of the HF measuring system. The HF receiver had an overall gain of 31 (30 dB) at center frequency (5 MHz). HF receiverFrequency (MHz) 02468101214 Gain (dB) -30 -20 -10 0 10 20 30 Figure 3-22. Frequency response of the HF receiver used at the LOG. and was mounted on top of a 3.26 m tall metallic pol e attached to the parapet on the western side of the roof, as shown in Figure 3-23, so that the tip of the antenna was at a height of about 4 m above the roof level. The sensing section of the whip was insulated by a thin plastic disc from the grounded section (portion below the insulator in Figure 3-23). The electronics were placed in a Hoffman box located on the roof surface near the antenna. The signal was transmitted from the antenna and associated electroni cs via 42 meters of double shielded and sleeved RG-223 coaxial cables to a LeCroy digitizing oscilloscope which sampled at a rate of 100 MHz. Figure 3-24

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99 Figure 3-23. Whip antenna used for the narrowband VHF measurement at the LOG. Figure 3-24. Block diagram of the VHF measur ing system. The VHF receiver had an overall gain of 27 (29 dB) at the center frequency (36 MHz). VHF whip antenna Metallic mounting pole Insulato r

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100 VHF receiver Frequency (MHz) 02 04 06 08 0 Gain (dB) -20 -10 0 10 20 30 Figure 3-25. Frequency response of the VHF receiver used at the LOG. shows the block diagram of the VHF measuring system. The VHF receiver consisted of two dual stage amplifiers and passive bandpass filters Each amplifier consisted of two THS4211 operational amplifiers and was powered by a 12 V battery placed in the Hoffman box. The filter circuit was connected between the two amplifier bl ocks in order to reduce DC offset that is introduced by the high gain amplifiers. The freq uency response of the VHF receiver (amplifierfilter-amplifier configuration) is shown in Figure 3-25. No absolute amplitude calibration of the narrowband VHF measuring system was attempted, since it was not essential to the purpose of this work. 3.8 Amplitude Calibration of Measuring Systems As stated in section 3-1, th e antennas of the LOG were located on the roof of Benton Hall (a 12 m tall building) from 2004-2007. In 2008, the antennas were relocated to the roof of the five-storey Engineering Building, which is 23 m ta ll. Further, the sensing plate of each electric field and dE/dt antenna was elevated above the roof surface. Both these factors, that is, the height

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101 of the building and the elevation of the antenna sensing plates serve to enhance the measured electric field and, in effect, introduce an addi tional gain in the syst em. The enhancement of electric field due to the presence of the buildi ng was estimated using results of finite difference time domain (FDTD) calculations of Baba and Rakov [2007] and Baba [personal communication, 2009]. The enhancement factor fo r Benton Hall is about 1.2 and that for the Engineering Building is about 1.4. Each of the elevated flat plate antennas us ed at the LOG was calibrated experimentally (using simultaneously measured lightning electric fields) with respect to another flat plate antenna placed essentially flush with the roof surface. The enhan cement factors for all electric field and dE/dt antennas along with overall calibration factors for different measurements at the LOG in 2008 are listed in Tables 3-4 and 3-5. Note that the gains due to the building height, elevation of sensing plates, and el ectronic amplifiers (if any) are all multiplicative factors to the measured fields. The presence of tall building ha s essentially no effect on the gain of the dB/dt measuring system, the amplitude calibration fact or for which was estimated using Equation 3-6. Table 3-7 gives the GPS locations, accurate to 2 m, of all antennas on the roof of the Engineering Building in 2008. In order to check the calibration of the meas uring systems, we computed the ratio of the electric to magnetic field peaks for 43 first return strokes in negative lightning at distances ranging from 8 to 67 km. The return-stroke initial field peaks (esse ntially radiati on) are produced by sources near ground (typically within 100 m), so that the elevation angle, 0, and the expected ratio of electric to magnetic field peaks is the speed of light. (This method is described in Chapter 4.) Figure 3-26 shows the histogram of th e ratio of electric to magnetic field peaks for

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102 GM = 2.97 x 108 m/s N = 43E/B (x 108m/s) 2.52.62.72.82.93.03.13.23.33.43.5 Number 0 2 4 6 8 10 Figure 3-26. The histogram of the ratio of elect ric to magnetic field peaks for 43 first return strokes in negative cloud-t o-ground lightning, recorded in 2008 in Gainesville, Florida. 43 first return strokes in negative cloud-to-grou nd lightning. We found that the 43 ratios were within % of the speed of light with th e arithmetic mean being 0.99c, which gives us confidence in our electric and magnetic field measurements. 3.9 Time Delays Between Measurements For all measuring systems (with the exception of the narrowband VHF system) at the LOG, equal length (51 m) optical fiber cables of the same specification and manufacturer were used. Hence time delays between various measur ements were negligible (less than a few nanoseconds). For the VHF measuring system, on the other hand, a 42.7-m long double-shielded and sleeved coaxial cable was used. The end-to-end (from the input of the electronics at the antenna to the oscilloscope input) traversal time for a VHF signal was measured to be 0.31 s. Traversal time through a 51 m long optical fiber at the speed of light was 0.17 s. The end-toend traversal time through a fiber optic link and associated elect ronics for the electric field

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103 Table 3-4. Characterization and calibration factors of measuring systems at the LOG prior to April 2008 (Benton Hall). Measuring system E1 dE1 Experiment Both Both Antenna Description Elevated fl at plate Elevated flat plate Elevation of sensing plate a bove the roof (m) 1.71 m 1.33 m Diameter of plate (cm) 44.6 46.5 Antenna plate area, A, (m2) 0.156 0.170 Integrating capacitance, C, (nF) 1.94 Resistance, R 5.1 M (see Figure 3-12) 50 (see Figure 3-16) Gain due to elevation of sensing plate, Gp 15.3 9.1 Electronic gain, Ge 1 8.89 Relationship between measured voltage and field (Field = K x Vout) 0()out peCV Et GGA V/m 0()out peV dEt dtGGAR V/m/ s Calibration factor without building enhancement effect, K 91.8 m-1 164.2 m-1 s-1 Gain due to presence of building, Gb 1.2 1.2 Overall calibration factor, Kt = K/Gb 76.5 m-1 136.9 m-1 s-1 measuring system (E2) was measured to be 0.3 s. Hence, the time delay between the VHF signal and electric field signal (E2) was 10 ns (the narrowband VHF signal lagged the electric field signal by 10 ns). 3.10 Details of the Two-Station Experiment Configuration As discussed in Section 3.2.2, this experi ment was designed to measure distant field waveforms at the LOG and close ones at Camp Blanding due to natura l and rocket-triggered lightning at Camp Blanding. An AT&T BellSouth analog conditioned telephone line was used to transmit a trigger pulse generated at Camp Blanding (near station) in resp onse to lightning strikes on-site or in its immediate vicinity to Gainesvi lle (distant station). Th e frequency bandwidth of this line, according to the provide r specifications was from 300 Hz to 3 kHz and its characteristic impedance was 600 In case of lightning on-site (either na tural or rocket-triggered), a trigger pulse is generated in the Launch Control at Camp Blanding via an OR gate. There are two inputs to the OR gate, trigger pulse due to detected optic al signals (in case of onsite natural lightning),

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104Table 3-5. Characterization and calibration factors of electric field and dE/dt measur ing systems at the LOG after April, 2008 (Engineering Building). a From 08/19/08 to 11/30/08, Ge for E2 was 1.4, and th e overall calibration factor Kt was 273.8 m-1. Measuring system E1 dE1 E2 dE2 Experiment Two-station Two-stat ion Single-station Single-station Antenna Description Elevated flat plate Elevated flat plate Elevated flat pl ate Elevated flat plate Elevation of sensing plate above the roof (m) 1.71 1.33 1.62 1.70 Diameter of plate (cm) 44.6 46.5 50.3 50.3 Antenna area, A, (m2) 0.156 0.170 0.199 0.199 Integrating capacitance, C, (nF) 1.94 10.4 Resistances 5.1 M (see Figure 3-10) 50 (see Figure 3-13) 1 M (see Section 3.7.4) 50 (see Figure 3-13) Gain due to elevation of sensing plate, Gp 15.3 9.1 11 13.1 Electronic gain, Ge 1 8.89 1 8.89 Relationship between measured voltage and field (Field = K x Vout) 0()out peCV Et GGA V/m 0()out peV dEt dtGGAR V/m/ s 0()out peCV Et GGA V/m 0()out peV dEt dtGGAR V/m/ s Calibration factor without building enhancement effect, K 91.8 m-1 164.2 m-1 s-1 536.7 m-1 97.5 m-1 s-1 Gain due to presence of building, Gb 1.4 1.4 1.4 1.4 Overall calibration factor, Kt = K/Gb 65.6 m-1 117.3 m-1 s-1 383.3a m-1 69.6 m-1 s-1

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105 Table 3-6. Characterization and calibration factors of dB/dt measuring systems at the LOG after April, 2008 (Engineering Building). Table 3-7. GPS locations, accurate to 2 m, of all antennas on the roof of the Engineering Building in 2008. Measurement Antenna GPS location (2008) E1 29.64248 N -82.34714 W dE1 29.64244 N -82.34714 W E2 29.64214 N -82.34715 W dE2 29.64209 N -82.34714 W dB (N-S) and dB (E-W) 29.64246 N -82.34711 W VHF 29.64234 N -82.34715 W Measuring system dB (N-S) dB (E-W) Experiment Both Both Antenna Description Loop Loop Antenna area, A, (m2) 0.533 0.533 Resistances Rload = 100 Rloop = 1410 (see Figure 3-15) Rload = 100 Rloop = 1410 (see Figure 3-15) Electronic gain, Ge 145 145 Relationship between measured voltage and field (Field = K x Vout) (2) ()out loopload eloadVRR dBt dtGRA T/s (2) ()outloopload eloadVRR dBt dtGRA T/s Calibration factor without building enhancement effect, K 0.391 m-2 0.391 m-2 Gain due to presence of building, Gb Overall calibration factor, (K t = K/Gb) 0.391 m-2 0.391 m-2

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106 and trigger pulse due to current sensed by the curre nt-viewing resistor (shunt ) at the base of the launcher (in case of rocket-trigg ered lightning), as shown in Fi gure 3-27. The output of the OR gate is a 3.15 V, 200 s TTL pulse. This pulse is transmitted via a fiber optic link to the Office Trailer at Camp Blanding where it triggers a one-shot monostable ci rcuit. The one-shot circuit is implemented using the CD74HC221, which is a high-speed CMOS logic dual monostable multivibrator whose schematic is shown in Figure 3-28. The output of the one-shot circuit is a 5 V, 462 s rectangular pulse. This pulse is fed into the Camp Bla nding end of the AT&T BellSouth analog conditioned telephone line termin ated in its characteristic impedance (600 ). This pulse undergoes some distortion due to th e characteristics of th e phone line (see Figure 329) and arrives at Gainesville (receiving) end in about 29 ms. The phone line is terminated in its characteristic impedance at the Gainesville end. This pulse was used to trigger the measuring systems at the LOG. The transmission delay of the trigger pulse from Camp Blanding to Gainesville was estimated by measuring the round trip time of a test pulse from Camp Blanding to Gainesville and back. The one way transmissi on delay is half the round trip time. A block diagram of the two-station experiment is shown in Figure 3-30. During thunderstorms near both Gainesville and Camp Blanding, it was found that higher frequency noise pulses were often coupled to the phone line causing it to generate spurious triggers. In order to alleviate th is problem two steps were taken. Firstly, a low pass filter with a 3 dB cut-off frequency of 1.5 kHz was installed at the Gainesville end of the line. Secondly, instead of triggering the LeCroy oscilloscope on a rising pulse e dge (level trigger), a more selective pulse-width trigger was chosen. The os cilloscope triggered only when it sensed at its input a pulse whose width is greater than 350 s at a voltage level of 702 mV, which is a characteristic feature of the actual trigger pulse received at Gainesville (see Figure 3-29). These

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107 steps have reduced the problem of spurious triggers greatly, however, on rare occasions some spurious pulses did trigger the measuring system s of the two-station experiment at the LOG. Figure 3-27. OR gate used to generate trigger pulses at Camp Blanding. Figure 3-28. Functional diagram of a one-s hot circuit implemented using a CD74HC221 (monostable multivibrator) used to generate a 5 V, 462 s rectangular pulse which is fed into the telephone line.

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108 Figure 3-29. Trigger pulse from Camp Blanding received at Gain esville via the AT&T BellSouth analog conditioned telephone line. Figure 3-30. A block diagram schematically showing the two-station experiment.

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109 CHAPTER 4 COMPACT INTRACLOUD LI GHT N ING DISCHARGES Cloud lightning discharges that produce both (1) single, usually solitary bipolar electric field pulses having typical full widths of 10 to 30 s and (2) intense HF-VHF radiation bursts (much more intense than those from any other cloud-to-ground or nor mal cloud discharge process) are referred to as Compact Intracloud Discharges (CIDs). These discharges were first reported by Le Vine [1980] and later characterized by Willett et al. [1989b] and Smith et al. [1999, 2004], among others as discussed in Chapter 2 (Section 2.5). In this Chapter, we present and characterize new experimental data, propose a conceptual mechanism for this phenomenon, and present a model based on this mechanism for computing electromagnetic field signatures of CIDs. Electrical parameters of CIDs are also inferred. 4.1 Phenomenology In this Section, we present new experimental da ta that are needed for testing the validity of various models of this phenomenon. Electric field waveform characteristic s, source heights, and context of occurrence of CIDs are examined. The atmospheri c electricity sign convention according to which a downward-direct ed electric field (or field cha nge) vector is considered to be positive is used in this Section. 4.1.1 Experimental Data and Methodology We examine wideband electric fields, electric field derivatives (dE/dt), magnetic field derivatives (dB/dt), and narrowband VHF (36 MH z) radiation bursts produced by 157 CIDs. The initial polarity of dist ant (essentially radiation) wideband electric field pulses produced by 156 of these CIDs was negative (opposite to that of negative return strokes) One relatively close waveform did not exhibit the radiation field pulse, with only induction and static field components being evident (see Figure 4-7c). All the 157 events transported negative charge

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110 Figure 4-1. (a) Wideband electric field, (b) electric field derivative (dE/dt), (c) integrated magnetic field derivative (d B/dt), and (d) narrowband VHF (36 MHz) radiation burst produced by a CID in Gainesville, Florida. From Ez/B = 2.24 x 108 m/s, and r = 17.2 km, the source height h = 15 km. upward (or lowered positive charge ). The data were acquired in August-September, 2008 at the LOG using instrumentation described in Chapte r 3. Typical measured waveforms for one CID are shown in Figure 4-1. We also recorded, ove r the same time period, 4 CIDs whose distant electric field waveforms had initial positive polarity. These four transported negative charge downward (or raised positive charge) and are no t further considered in this Section. CIDs were identified by their intense VHF ra diation signature and characteristic wideand field (NBP or, in one case, its close-range c ounterpart) and field derivative waveforms. Different triggering schemes were employed in acquiring the data an alyzed in this Chapter. For 80 events the system was triggered on VHF only. The trigger threshold was empirically set at a relatively high level so as to minimize triggers on cloud-to-ground lightning (those were less

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111 Table 4-1. Number of NLDN-located CIDs in different horizontal distance ranges. Distance Range (km) 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-135 0-135 Number of events 5 20 21 24 18 36 13 13 150 a Number of events used in Sections 4.1.4 and 4.1.5 0 14 8 10 6 3 6 1 48 a149 events were identified by the NLDN as cloud discharges and 1 even t as positive CG. than 6% of all triggers). For 77 events the syst em could also trigger on wideband electric field, but the VHF threshold was always exceeded. Thus, we assume that for all the 157 events analyzed here our measuring system was triggered on VHF. The sample of 157 was formed by manually searching all our strong-VHF records for characteristic CID wi deband field and field derivative signatures (see Figure 4-1) and accepting only those with electric field peaks greater than 1.5 times the background noise level. Ther e were many strong VHF producers that did not satisfy the latter criterion, which probably introduced some amplitude bias, as discussed in Section 4.1.5. GPS timestamps were used to obtain NLDN-estim ated locations for selected events. Out of 157 CIDs, 149 (95%) were correctly identified as cloud discharges and located by the NLDN. The distances of these events from the measur ement station ranged from 5 to 132 km. One CID was misidentified by the NLDN as a positive CG at 38 km with an estimated peak current of 24 kA. Seven CIDs were not detected by the NLDN. Table 4-1 gives the number of located events in different distance ranges. Simultaneous measurements of electric a nd magnetic radiation fi eld pulses produced by CIDs and NLDN-reported horizontal distances to these discharges can be used to obtain estimates of source heights. Fo r a vertical source a bove perfectly conducting ground (see Figure 4-2), the ratio of the ve rtical component of electric field intensity (Ez) and the azimuthal component of magnetic flux density (B) on the ground surface is given by [e.g., Baum, 2008]

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112 Figure 4-2. Geometrical parameters and equations used in estimating radiation source heights. See text for details. coszE c B (4-1) where c is the speed of light, so that the elevation angle can be found as 1cos()z E cB The source height can be estimated as tan hr where r is the horizontal distance of the source from the field measuring st ation. This approach is valid for a vertical radiator and for early-time field measurements for which t<< R/c [Baum, 2008], where R is the inclined distance from the measuring station to th e source, this distance being given by 22Rhr For R = 15 30 km, R/c = 50 100 s, while t (NBP risetime) is typically a few microseconds. In order to check if our height-estimation method is influenced by calibration of our field measuring systems, we computed Ez/B ratios for 43 first return strokes in negative lightning at distances ranging from 8 to 67 km. The return-stroke initial field peaks (esse ntially radiati on) are produced

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113 by sources near ground (typically within 100 m), so that 0 and expected ratio Ez/B c. We found that the 43 ratios were with in % of the speed of light with the arithmetic mean being 0.99c, which gives us confidence in our el ectric and magnetic field measurements. For estimating source heights we selected 48 CIDs with NLDN-reported distances ranging from 12 to 89 km, whose electric field peaks we re greater than 2.5 times the background noise level (in order to reduce the peak-measurement error). Each of these 48 CIDs was reported by 4 to 22 (11 on average) NLDN sensors with a length of the semi-major axis of 50% location error ellipse ranging from 400 m to 4.9 km (mostly 400 m, so that the median was as small as 400 m). Measured waveforms including electric field, dE /dt, dB/dt, and narrowband VHF (36 MHZ) for these 48 CIDs are shown in Appendix A. 4.1.2 Relation of Compact Intracloud Disc harges to Other Types of Lightning It is generally thought that CIDs occur in isolation (within seve ral hundred microseconds to a few milliseconds) or at the beginning of ordinary cloud discharges [e.g., Smith et al., 2004]. Krehbiel et al. [2008] reported a CID that occurred 800 ms prior to a gigantic jet. The majority (72%; actually 72.6%, but set at 72 % to assure that all the percentages add to 100%) of CIDs examined here appeared to occur in isolation; that is, th ere was no other lightning process occurring prior to or following the CIDs w ithin the length of the record (500 ms with a 100 ms pretrigger). About 24% of CIDs were f ound to occur prior to, dur ing, or following cloudto-ground (CG) or normal IC lightning discharges. Specifically, 18% (28 out of 157) of CIDs accompanied ordinary cloud discharges. NLDN locations were available for 8 IC flashes in all of which CIDs preceded IC impulsive processes. Five CIDs preceded IC impulsive processes by 5.3 to 67 ms with horizontal separation distances being 1 km or less. Seven CIDs were within 10 km of ICs, and one beyond 25 km. An example of wide band electric field and VHF radiation from a CID followed by a cloud (IC) flash is shown in Figure 4-3. Further, 6% (9 out of 157) of the

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114 Figure 4-3. Electric field and VHF (36 MHz) radiation from a CID that was followed by a "normal" IC (from another experiment in Gainesville, Florida). Inset shows the CID signature on an expa nded (5 s per division) time scale. No NLDN locations are available.

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115 CIDs appeared to occur in association with CG flashes. NLDN locations were available for 7 CG flashes. In three cases, CIDs were found to precede CGs by 72 to 233 ms, while in four cases, they occurred during or after CGs. In three cases, CIDs were found to occur within 5 km of CG strokes and in seven cases they were within 20 km. Figure 4-4a shows the wideband electric field and VHF radiation from an eight-stroke CG ( only the second through seventh strokes were recorded by our system), with a CID occurring be tween the third and fourth strokes at horizontal distances of 7 to 8 km from all strokes of this flash. Plan view of NLDN locations of this CID and the CG strokes is shown in Fi gure 4-4b. Interestingly, locations of seven out of eight strokes are within less than 1 km of each other, while one stroke (of order 4) which was immediately preceded by the CID, created a new termination on ground, about 3 km away from other strokes of the flash. We also observed (for the first time) thr ee sequences of two CIDs (4% of all CIDs analyzed here), with time interv als within the pairs being 43, 66 and 181 ms. These intervals are comparable to interstroke intervals in CG flas hes. The horizontal separation distances were 16, 24, and 11 km, respectively. The CIDs in the fi rst pair were found to occur successively at heights of 18 and 15 km. Electric field record of one of the "multiple" CID events (the second pair) is shown in Figure 4-5. The occurrence context of CIDs is summarized in Figure 4-6. It is presently not clear how CIDs influence (if at all) the ordinary lightning processes. 4.1.3 Different Types of Electric Field Waveforms The electric field associated with lightning discharges is often viewed as being composed of the electrostatic, inducti on, and radiation field component s. At larger distances (beyond several tens of kilometers) and at early times the radiation component is generally the dominant one. As distance decreases, relative contributions of th e other two components increase. Most of

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116 the CID waveforms found in the literature are essentially radia tion (NBP pulses), with closer waveforms that exhibit both radiation and elec trostatic field components being exceedingly rare. Only seven were recorded within 15 km and five within 10 km [Eack, 2004]. Only one waveform [Eack, 2004, Figure 4-1] dominate d by induction and electr ostatic field components (no radiation field component is disc ernible) is found in the literature. In Figures 4-7a-c, we present three types of CID electric field waveforms recorded in Gainesville, Florida. CID that produced the essent ially radiation field si gnature, shown in Figure 4-7a, was located at a horizontal distance of 40 km, and for the event shown in Figure 4-7b the distance was 9.4 km. In the latter case, note an el ectrostatic field change of about 6 V/m after the radiation pulse (induction field component might be significant too, but is difficult to identify). NLDN did not detect the CID whose electric field signature is shown in Figure 4-7c, but its parent thunderstorm was observed to be overhead. For this even t, the static and induction components are dominant and the radiation comp onent is undetectable (negligible). Results presented in Figures 4-7a-c are consistent with experimental [Eack, 2004] and model-predicted [Watson and Marshall, 2007] waveforms found in the literature, with the type of waveform shown in Figure 4-7c being previously observed, as noted above, only once. Note that for a short vertical dipole at relati vely large elevation angle above ground (see Figure 4-2) the radiation field peak on the one hand and induction and sta tic field changes on the other hand are expected to have opposite polarities. Specifically it follows from equation (A.38) of Uman [1987, p. 329] for the electric field at perfectly conducting groun d due to a differential ve rtical dipole that the opposite polarities are expected for > 35.3o, which translates to r < 21 km if source height h = 15 km.

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117 Figure 4-4a. Wideband electric fiel d and VHF (36 MHz) radiation from a CID that occurred during an eight-stroke negative CG, within horizontal distances of 7 to 8 km of all the CG strokes. Only the second through seventh strokes were recorded by our measurement system. The CID height above ground was estim ated to be about 14 km. Note that the VHF radiation produced by the CID is much larger than that produced by the CG strokes (RS2 to RS7). Inset shows the CID wideband electric field signature on an expanded time scale.

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118 Figure 4-4b. Plan view of NLDN-estimated rela tive positions of the CID (hollow circle) and return strokes (numbered solid circles) of CG flash whose wideband and VHF signatures are shown in Figure 4-4a. The semi-major axis (SMA) lengths of NLDNreported 50% location error ellipses for each of the return strokes and the CID are also given. Strokes 1 to 3 o ccurred before the CID and strokes 4 to 8 after it. Arrows indicate changes in plan-view location from strokes 1-3 to the CID, then to stroke 4 (new termination on ground), and to strokes 5-8.

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119 Figure 4-5. (top) Wideband electric field record showing two CIDs that occurred 66 ms apart at a horizontal distance of 24 km f rom each other. The height of CID 2 above ground was estimated to be about 17 km, while the height of CID 1 is unknown. (bottom) Individual CID signatures displayed on expanded (10 and 5 s per division for CID 1 and CID 2, respectively) time scales.

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120 Figure 4-6. Occurrence context of CIDs. Of the 157 CID signatures examined here, 151 were of type (a), 5 of type (b), and 1 of type (c), where (a), (b), and (c) are the three part s of Figure 4-7. Unfort unately, no source heights could be estimated for waveforms of types (b) and (c). 4.1.4 Source Heights Smith et al. [2004] used two methods to estimate CID heights above ground. One was based on measuring delays of ionosphere and gr ound-ionosphere reflectio ns with respect to direct-path wave in VLF/LF ground-based (LASA) field records. The other one employed FORTE satellite VHF records showing direct -path and ground-reflec tion signals. The groundbased estimates were on average 1 km higher than the satellite estimates, the latter being considered by Smith et al. as more accurate. The distribution of source heights for 48 CIDs inferred here using the method described in Section 4.1.1 is shown in Figure 4-8. Table A-1 in Appendix A gives the horizontal distance and

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121 Figure 4-7. Three types of CID electric field waveforms exhib iting (a) only radiation, (b) radiation and static field components (induc tion component is not apparent), and (c) only induction and static field components. Note that for the geometry shown in Figure 4-2, the radiation fiel d peak on the one hand and induction and static field changes on the other are expected to have opposite polarities when > 35.3o. Assuming a source height of 15 km and using NLDN-estimated distances, we found = 21o and 58o for (a) and (b), respectively. Of 157 CID signatures, 151 were of type (a), 5 of type (b), and 1 of type (c).

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122 height information for each of these 48 CIDs. The minimum and maximum source heights were 8.8 and 29 km, respectively. The geometric mean was 16 km and median was 15 km, the latter being similar to the median source height of 13 km reported for the same NBP initial polarity by Smith et al. [2004]. The majority of height values in Smith et al.'s study (based mostly on events in the vicinity of Florida) were between 3 a nd 20 km, although some heights were as large as about 30 km. Note that the height s larger than 15 to 20 km are lik ely to be above the upper cloud boundary and therefore appear unr ealistic. There are two primary sources of error in our estimated source height: elevation angle error and distance error. The angle error is primarily due to inaccuracies in the measurement of the el ectric field peak because of the presence of background noise. The distance error can be esti mated using NLDN-reported 50% location error ellipses. As these two types of errors are uncorre lated, the total height error for each of the 48 CIDs may be taken as the square root of the sum of the squares of th e two individual error components. The median height error was estimat ed to be % (error range was from 5 to 23%), which does not explain the apparently unr ealistic source heights. There are nine CIDs whose estimated heights are greater than 20 km in our dataset. We found them unremarkable in all respects, except for their height. All nine were isolated and occurred at horizontal distances ranging from 32 to 63 km. Jacobson and Heavner [2005] found that less than 20% of their CIDs observed in Florida were at altitudes ranging from 15 to 20 km, and very few occurred above 20 km. They stated that their altitude measurement uncertainties were less th an 2 km, so it is likely that at least some of their events were truly occurring above the nomin al tropopause, whose altitude they estimated to be about 15 km. It is possible that the CIDs observed at heig hts greater than 20 km were associated with convective surges overshooting the tropopause and penetrating deep into the

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123 Source height (km) 03691215182124273033 Occurrence 0 2 4 6 8 10 12 With IC (N = 8) With CG (N = 4) Multiple ( N = 3) Isolated ( N = 33) GM = 16 km N = 48 Figure 4-8. Histograms of radiat ion source heights for 48 CIDs. stratosphere [e.g., Romps and Kuang, 2009]. Darrah [1978] observed tropopause overshoots up to 5 km in severe storms. We wonder if at least some of the CIDs in ferred to occur well above the cloud top (in the stratosphere) could be associ ated with gigantic jets. Krehbiel et al. [2008] described gigantic jets as resembling negative upward leaders exhibiting impulsive rebrightening and extending from cloud tops to the ionosphere. 4.1.5 Electric Field Wavefo rm Characteristics For the subset of 48 CIDs, we estimated elect ric field peaks normalized, assuming inverse distance dependence, to R = 100 km and to = 0o as

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124 cos0 () 100cosNoR EE (4-2) Normalization to = 0o corresponds to h = 0, but at 100 km the result is essentially the same for median h = 15 km. The distribution of normalized electric field peaks is shown in Figure 4-9. The geometric mean is 20 V/m, which is considerably larger than the initial electric field peak at 100 km for negative first return strokes (6 V/m in Florida [Rakov and Uman, 2003]). We found that the normaliz ed electric field peak tends to increase with horizontal distance (determination coefficient = 0.59). This sugge sts that our sample is biased toward larger peaks, with the bias increasing with increasing distance. Indeed, the geometric mean normalized electric field peak for horizontal distance ra nges of 10-30 km, 30-50 km, and 50-70 km were found to be 15 V/m (N = 22), 23 V/m (N = 16), a nd 31 V/m (N = 9), respectively. One CID that occurred at 89 km had a normalized electric field peak of 35 V/m. This amplitude bias was apparently introduced by the requirement to have sufficiently pronounced field signatures for estimating source heights. Note that even for the smallest distances, 10 to 30 km, the source strength (15 V/m) is considerably higher than that for first return strokes in negative CGs (6 V/m). Willett et al. [1989b] reported an arithmetic mean di stance-normalized NBP initial peak of 8.0 5.3 V/m at 100 km for 18 Florida CIDs that occurred in a storm at a distance of 45 km (no distances for individual events were available). Further, Smith et al. [1999] found a mean of 9.5 3.6 V/m at 100 km for 24 CIDs at horizontal di stances ranging from 82 to 454 km (there might have been significant propagation e ffects) in New Mexico and West Texas. Our arithmetic mean ( standard division) is 21 8.9 V/m at 100 km for all the 48 events and 15 3.4 V/m for 22 events within 10-30 km.

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125 Electric field peak normalized to 051015202530354045 Occurrence 0 4 8 12 16 20 With IC (N = 8) With CG (N = 4) Multiple (N = 3) Isolated (N = 33) GM = 20 V/m N = 48 R = 100 km and = 0o Figure 4-9. Histograms of electric fields peaks normalized to R = 100 km and = 0o for 48 CIDs. Figure 4-10a and 10b show distributions of the total pu lse duration (including the overshoot) and the total width of the initial half-cycle, respectively, for the 48 CIDs. The total durations range from 9.6 to 38 s with ar ithmetic and geometric means of 24 and 23 s, respectively. The total width of the initial half-cycle ranges from 2.8 to 13 s with arithmetic and geometric means being 6.1 and 5.7 s, respectively. Smith et al. [1999] found the arithmetic mean total pulse duration to be 26 4.9 s, which is similar to our estimate. Figure 4-10c shows the distribut ion of the ratio of initial el ectric field peak to opposite polarity overshoot for the 48 CIDs. The ratio ra nges from 3.5 to 17 with arithmetic and

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126 N = 48 AM = 24 s GM = 23 sTotal pulse duration (s) 0510152025303540 Occurrence 0 2 4 6 8 10 12 14 (a) Total width of initial half cycle (s) 02468101214 Occurrence 0 2 4 6 8 10 12 14 16 18 N = 48 AM =6.0 s GM =5.6 s(b) N = 48 AM = 6.1 GM = 5.7Ratio of initial electric field peak to opposite polarity overshoot 357911131517 Occurrence 0 5 10 15 20 25 (c) Figure 4-10. (a) Total pulse duration including overshoot, (b) total width of initial half-cycle, and (c) ratio of initial electric field peak to opposite polarity overshoot for 48 CIDs.

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127 geometric means being 6.1 and 5.7, respectively. Willett et al. [1989b] reported the arithmetic mean ratio to be 8.8 5.2 for 18 events and 9.1 2.0 for 6 events in two different storms in Florida, while Smith et al. [1999] found the arithme tic mean ratio to be 2.7 for 24 CIDs in New Mexico and West Texas. Our estimate is between the previously reported values. 4.2 Conceptual Mechanism and Modeling As discussed in Chapter 2, Watson and Marshall [2007] used the origin al transmission line (TL) model [Uman et al., 1975] and a modified TL model w ith an exponentially increasing current along the channel to compute electric fiel d signatures at horizontal distances of a few and 200 km and compare them with corresponding measured waveforms reported by Eack [2004]. Both models can successfully match the two-station field measurements. The exponentially increasing current was assumed by Watson and Marshall to correspond to the runaway electron breakdown process. The original TL model was also employed by Le Vine [1980]. In all the modeling studies to date the TL was assumed to be energized at one end with the other end being terminated in its characteristic impedance, so that the travelling wave is totally absorbed there. A good agreement with measurements was achieved fo r currents and speeds comparable to those of return strokes in cloud-to-ground lightning; that is, for curre nt peaks of some tens of kiloamperes, durations of some tens of microseconds, and speeds of the order of 108 m/s. In this Section, we propose a conceptual mechanism for the CID phenomenon and present a model based on this mechanism for computing el ectromagnetic field signatures of CIDs. The model is used to determine "allowed" (consistent with experimental data) ranges of effective current reflection coefficients at channel ends propagation speed, channel length, and current risetime. Additionally, the Hertzian dipole approx imation and testing model validity against twostation measurements of Eack [2004] are considered. The physic s sign convention according to

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128 which a downward-directed electric field (or field change) vector is considered to be negative is used in this Section and in Section 4.3. The data used in this Section were acquire d in summers of 2007 and 2008 in Gainesville, Florida (at the LOG), and include wideband electric fields, elect ric field derivatives (dE/dt), magnetic field derivatives (dB/dt), and narrowband VHF (36 MHz) radiation bursts produced by CIDs. For some events we also have narrowband HF (5 MHz) radiation records. A total of 220 CIDs (including 212 dE/dt signatures) were examined in this Section. The instrumentation used to acquire the data is described in Chapter 3. Phenomenological characteristics of 157 CIDs acquired in August-September of 2008 at the LOG are discussed in Section 4.1. 4.2.1 Evidence of Reflections in CID Electromagnetic Field Signatures Hamlin et al. [2007] reported that 12% of their CI Ds each showed evidence of one currentpulse reflection, which appeared as a secondary puls e after the initia l peak in their distant electric field waveforms. They interpreted the secondary pu lse as a signature of re flection of the current pulse off the "far end" of the CID channel and used this feature to estimate CID channel lengths. The average time interval between the primary a nd secondary electric field peaks was 6.7 s with a standard deviation of 2.7 s. The upper bound on the channel length (determined assuming that the current wave tr avelled at the speed of light) wa s found to be about 2 km. In the following, we will present experimental evidence of multiple (up to 7) reflections from both ends of the CID channel. Our pulse detection e fficiency was considerably higher than Hamlin et al.'s, because, in addition to electric fields, we used our dE/dt records. We found that Hamlin et al.s secondary peak is actually a hi gher-order one and therefore woul d result in an overestimate if used for calculating radiator length. Also, electric field peaks of the same polarity as that of the main pulse occur at the time when the current fron t is in the middle of the channel, in contrast

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129 with Hamlin et al.s [2007] assumption that they occur at th e time of first reflection at the far end of the channel. In Figure 4-11 we present (a) electric fiel d, (b) dE/dt, and (c) VHF radiation burst produced by one of the CIDs in our data set. For this event, the initial polarity of NBP (see Figure 4-11a) is the same as that of negative re turn strokes and consistent with motion of positive charge upward (or negative charge downward). The duration, about 16 s, is typical for NBPs (10 to 30 s on average). A superposition of electric field, dE/dt, a nd VHF signatures is shown in Figure 4-11d. A typical event w ith initial polarity consistent with motion of negative charge upward is shown in a similar format in Figure 412, with HF signature additionally presented in Figure 4-12c. Both events occurred at unknown di stances, but their fields are clearly dominated by the radiation field component. At least one secondary peak (l abeled S4) having the same polarity as the primary peak and multiple shoulders (labeled S1-S3 and S5) are se en in Figure 4-11a. We observed one or more secondary peaks in 34 (15%) of 220 CID electri c field records, while in 186 (85%) cases no secondary peak could be identified. Following Hamlin et al. [2007], we measured time intervals between the primary and first clear secondary peak (S4 in Figure 4-11a) of the same polarity in electric field records of 34 CIDs. They ranged be tween 1.0 s to 5.8 s with a mean of 3.2 s. The latter is about a fact or of two shorter than Hamlin et al.'s mean of 6.7 s. In dE/dt signatures, secondary peaks (see Figu re 4-11b) appear as pronounced oscillations after the initial opposite polarity (negative) overshoot. There are five pronounced cycles in Figure 4-11b, whose positive half-cycles are labele d S1 to S5. The first three of them correspond to shoulders S1 to S3 and the following one to the secondary peak S4 in Figure 4-11a. Note that peaks in electric field waveform correspond to lo cal "zeros" in dE/dt wave form (and vice versa),

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130 Figure 4-11. (a) Electric field, (b) dE/dt, and (c) VHF radiation signature s of a CID that transferre d negative charge downward (or positive charge upward), recorded in Gainesville, Florida. The event occurred at an unknown distance. The three signatures are overlaid in (d) for direct comparison. S1-S5 are five secondary peaks a ppearing as pronounced osci llations in (b) and mostly as shoulders in (a). Electric field and dE/dt wave forms have been low-pass filt ered to accentuate reflection signatures.

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131 Figure 4-12. (a) Electric field, (b) dE/dt, and (c) HF of a CID that tr ansferred negative charge upward (or positive charge dow nward), recorded in Gainesville, Florida. The even t occurred at an unknown distance. The el ectric field, dE/dt, and VHF signatures are overlaid in (d) for direct comparison.

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132 as seen in Figure 4-11d where the two waveforms (as well as the VHF radiation signature) are superimposed. We found multiple secondary p eaks (oscillations) in 32 (15%) of 212 dE/dt records. Factors that can make reflections undetectable in the remaining 85% include a relatively small magnitude of the incident wave, relatively long radiating channel, relatively large losses along the channel, and a relatively small (in absolu te value) current refl ection coefficients at channel ends. It is important to note that lowe r-order reflections (duri ng the primary portion of the overall electric field or dE/dt waveform), while being undetectable, do influence the magnitude of the overall waveform (see Figure 422b). It is likely that the 15% of waveforms showing pronounced reflections correspond to shor test CID channels. The average time interval between consecutive peaks of the same polarity in dE/dt signatures ranged from 0.84 to 1.8 s (with a mean of 1.2 s). We will show later, vi a modeling, that the multiple peaks (oscillations) in dE/dt waveforms are due to reflections at either end of CID channel, with time interval between consecutive peaks (oscillation period) being equal to the roundtrip time along the channel. One-half of the peri od is the channel traversal time. Interestingly, the period of oscillations remains more or le ss constant (see Figure 4-11b), impl ying that the radiator length remains fixed during the bouncing-wave process. A round trip time of 1 s corresponds, for example, to a propagation speed of 2 x 108 m/s and a channel length of 100 m. Figures 4-13a and 4-13b show the histogram of the total duration of 5 MHz HF radiation signature in our dataset and the sc atter plot of the total duration of HF radiation signature versus total duration of the correspondi ng electric field waveform of 31 CIDs, respectively. The AM and GM durations of the 5 MHz HF radiation burst are 5.8 and 5.3 s, respectively. Figures 414a and 4-14b show the histogram of the total duration of 36 MHz VHF ra diation signature in our dataset and the scatter plot of the total dur ation of VHF radiation signature versus total

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133 duration of the corresponding electric field wave form of 52 CIDs, respectively. The AM and GM durations of the 36 MHz VHF ra diation signature are both 11 s. In our data, the VHF signature usually begins at about the same time as the electr ic field and dE/dt signatures, and all three have comparable durations. In contrast, the correspon ding HF signature in our data (see Figure 4-12c) began, on average, 1.7 s after the electric fiel d, dE/dt, and VHF signatures did. Figures 4-15a and 4-15b, respectively, show histograms of the starting-time of HF and VHF radiation signatures relative to the onset -time of the corresponding electric field waveform. An apparent delay in the onset of HF rela tive to VHF may be related to the production of longer streamers (associated with lower frequency fi elds) at later times. There appear s to be some structure in the VHF radiation waveforms in Figures 4-11c and 4-12d, but we could not uniquely relate this structure to features of corresponding electric fi eld or dE/dt waveforms. 4.2.2 Bouncing-Wave Mechanism Based on the evidence of multiple reflections, we postulate that the compact intracloud discharge is essentially a bounc ing-wave phenomenon. It can be viewed as beginning with injection of current pulse at one end of a relatively short cond ucting channel (this channel could be created by the runaway electron breakdown process [e.g., Tierney et al., 2005, Gurevich and Zybin, 2004, Gurevich et al., 2004]), which is reflected multiple times successively at either end of the channel until it is attenuated and absorbed, depending upon the conditions along the channel and boundary conditions at channel ends, re spectively. The concept is illustrated by four schematic snapshots in Figure 4-16. Figure 4-16a shows a CID current pulse (similar to that inferred by Watson and Marshal [2007]) with a peak current of 50 kA, total durat ion of 30 s (much longer than expected time needed to traverse the channe l), and risetime of 6 s (som ewhat shorter than 9 s in Watson and Marshals pulse, but more consistent with experimental data, as shown in Section 4.2.7), injected

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134 at the bottom of a 100 m long vertical c onducting channel at t = 0. The pulse (i0) travels upward at an assumed speed of 2 x 108 m/s (similar to that inferred by Watson and Marshal [2007]), so that the front of this pulse will reach the top of the channel at t = 0.5 s. The instant just before the pulse hits the top is schematically shown in pa rt A of Figure 4-16b. At the top of the channel, the current pulse in general will "see" an impedance discontinuity and hence will be partly reflected. The front of the current pulse (scaled according to the reflection coefficient at the top of the channel) will move downward. This is shown in part B of Figure 4-16b. The downward motion of the current pulse front will continue ti ll t = 1 s at which time it will hit the bottom of the channel where it will be reflected again a nd begin travelling upward (C in Figure 4-12b). The second reflection at the top and resultant downw ard moving wave are depi cted in part D of Figure 4-16b. Note that while the initial parts of the current pulse front have already experienced multiple reflections at the top and bottom of the channel, later portions of the front (total front duration is 6 s) are still making their first trip upward or did not even en ter the bottom of the channel. At t = 30.5 s, the last point on the tail of the originally injected current pulse will reach the top. After t = 0.5 s, in addition to the upward-moving incident wave (i0), different portions of the pulse will be travelling either downward or upward after being reflected from the top or the bottom of the channel, respectively. Howeve r, with each successive reflection and traversal of the channel, the current pulse will be dimini shed due to partial abso rption at the channel end and attenuation along the channel. The multiple curre nt reflections are illustrated in Figure 4-16c where reflection coefficients at the top (t) and bottom (b) of the channel were assumed to be equal to -1. One of the features of CIDs is very strong HF -VHF radiation. It is generally thought that HF-VHF radiation is produced due to electrical breakdown of virgin air. The CID mechanism

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135 HF radiation signature duration, s 024681012 Occurrence 0 2 4 6 8 10 12 14 16 N = 31 AM = 5.8 s GM = 5.3 s Min= 1.2 s Max = 11 s (a) N = 31Total duration of electric field pulse, s 04812162024 HF radiation signature duration, s 0 4 8 12 16 20 24 (b) Figure 4-13. (a) Histogram of th e total duration of 5 MHz HF ra diation signature and (b) total duration of HF radiation signature versus total duration of the corresponding electric field waveform for 31 CIDs.

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136 N = 52 AM = 11 s GM = 11 s Min = 6.2 s Max = 19 sVHF radiation signature duration, s 68101214161820 Occurrence 0 2 4 6 8 10 12 14 16 (a) N = 52Total duration of electric field pulse, s 05101520253035 VHF radiation signature duration, s 0 5 10 15 20 25 30 35 (b) Figure 4-14. (a) Histogram of the total duration of 36 MHz VHF ra diation signature and (b) total duration of HF radiation signature versus total duration of the corresponding electric field waveform for 52 CIDs.

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137 HF start time with respect to electric field waveform, s 012345 Occurrence 0 2 4 6 8 10 12 N = 31 AM = 1.7 s Median = 1.4 s Min = 0.59 s Max= 5.3 s (a) N = 52 AM = 0.14 s Median = 0.17s Min = 1.4 s Max = 1.7 sVHFstart time with respect to electric field waveform, s 1.5 1.0 0.50.00.51.01.52.0 Occurrence 0 5 10 15 20 25 30 35 (b) Figure 4-15. Histograms of the st arting-time of (a) HF and (b) VHF radiation signa tures relative to the onset-time of the corres ponding electric field waveform.

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138 Figure 4-16a. A CID current pulse with a peak of 50 kA, total dur ation of 30 s and zero-to-peak risetime of 6 s, injected at the bottom of a 100 m long ve rtical conducting channel at t = 0. The inset shows the initial 2.5 s of the incident current waveform and first four reflections occurring at A, B, C, and D. Vertical arrows indicate times at which reflections begin. The wave makes two round trips (experiences four reflections) during initial 2 s, six round tr ips (12 reflections) during th e current risetime (6 s), and 30 round trips (60 reflections) during th e entire current duration (30 s). In practice, due to attenuation along the channel and absorption at channel ends, higherorder reflections will be progressively less pronounced, so that less than 10 reflections are expected to be detectable in the dE/dt waveforms and even less in electric field signatures.

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139 Figure 4-16b. Schematic representation of the bouncing-wave mechanis m of CID for channel length h = 100 m and propagation speed v= 28 m/s. Current-wave duration is much longer than the channel traversal time Straight arrows represent current waves on CID channel and bracket-shaped arrows re present the process of wave reflection at the ends. If b = t = 1 (short-circuit conditions), it is the same wave bouncing between the ends. If b = t = -1 (open-circuit conditions ), the wave changes polarity each time it hits the end. If b = t = -0.5, the current wave changes polarity and is reduced in magnitude by a fact or of 2 at each end. If t = 0, the wave is fully absorbed at the top end. For | t | < 1 and | b | < 1 partial absorption ta kes place at the top and bottom, respectively. It is expected that reflected current waves will reduce current at each end, while corresponding voltage will be enhanced there. As a result, coronalike electrical breakdown (shown by broken li nes) may occur at the channel ends. Breakdown associated with the incident wave, i0, is not shown here. Figure 4-16c. Illustration of the multiple current reflections with reflection coefficients at the top (t) and bottom (b) of the channel assume d to be equal to -1.

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140 described above implies that HF-VHF radiation will be produced (1) when the front of current pulse moves upward along the channel for the first time (actually creates that channel) and (2) at either end of the channel when current reflecti ons are produced there. Re flections of different portions of current pulse may result in coronalike electrical breakdown (represented by broken lines in Figure 4-16b) at channel extremities, because a reduction of current is accompanied by an increase of line charge density and associated voltage (voltage doubles at an open circuit end and increases by a factor of 1.5 if the current reflection coefficient = -0.5). This breakdown at both channel ends is likely to produce an in tense burst of HF-VHF radiation which is a characteristic feature of CIDs (see Figure 4-11c). The proposed s cenario also helps explain the "noisiness" of dE/dt waveforms compared to corresponding electric field waveforms, a CID feature first noticed by Willett et al. [1989]. 4.2.3 Bouncing-Wave Model: Current Di stribu tion along the Channel We consider a vertical channel whose bottom and top ends are at heights of h1 and h2, respectively. The assumption that the CID channel is generally vertical is supported by large magnitudes of the vertical component of elect ric field measured at ground level [see, for example, Willett et al., 1989; Smith et al., 1999, and Section 4.1] that are comparable with or exceeding those of first return strokes. The larger the deviation of the ch annel from vertical, the smaller the vertical component of electric field at ground level. For a horizontally oriented channel this field component at ground level is close to zero. Additionally, the observed occurrence of CIDs between horizonta lly extensive charge layers [e.g., Rison et al., 1999] and their relatively short channels ar e probably consistent with more or less vertical orientation. We do not consider here the process of creation of the CID channel. The presence of conducting channel in the cloud is evidenced by pronounced VLF/LF field waveforms. We assume that the channel is energized by injection of a current wave at its bottom end. The transmission line (TL)

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141 model that relates the longitudinal current i(z,t) at any height z and any time t to the current at the channel origin (which in our case is at h1) is given by: 1 1(,)(, -) zh iztiht v (4-3) In order to account for the multiple reflecti ons that take place at the channel ends (as described in Section 4.2.2) we speci fy two equivalent current sources, iu(h1,t) and id(h2,t) (see Section 4.2.6, Equations 4-7 and 4-8), connected at the bottom and at the top of the channel, respectively. iu(h1,t) accounts for the incident wave and all reflections at h1; it propagates upward. id(h2,t) accounts for all reflections at h2 and propagates downward. One can compute partial electric fields at observation point P due to each of these two curr ents. The total electric field at P due to a current wave originating at h1 and undergoing multiple reflections at both channel ends is given by the superposition of th ese two electric field components (see Section 4.2.6). Let us consider the event illustrated in Figur e 4-16. A current pulse with a peak of 50 kA, total duration of 30 s, a nd risetime of 6 s (see Figure 4-16a), is injected at th e bottom of a 100 m long vertical channel. We assume that the bottom of the channel is at an altitude of 15 km and that negative charge is transferred upward. The pulse travels upwards at an assumed speed of 2 x 108 m/s. The round-trip time for the current puls e along the channel from bottom to top and back is 1 s. Let the current reflection coefficients at the bottom and the at top of the channel be equal to -0.5. Note that in our m odel the reflection coefficients, for simplicity, account for both absorption at channel ends and attenuation along the channel. So, they should be viewed as effective reflection coefficients. Figure 4-17a shows the currents computed using Equations 4-7 and 4-8 (Section 4.2.6), at the bottom (z = h1), middle (z = h1 + h/2) and top (z = h2) of the 100 m long channel. Peak

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142 currents at these heights are 40, 34, and 32 kA, re spectively. They are not much different from each other (currents at the ends are within less than 20% of the current in the middle). A threedimensional plot of current as a function of bot h time and height is shown in Figure 4-17b. Note that the incident current wave peak is 50 kA, while the equivalent curre nt distribution along the channel peaks at 32 to 40 kA, due to reflections (absorption at the ends). Further, the overall current waveshapes at these three positions along the channel are similar. Half-peak widths are 7.0 s, 8.2 s, and 8.6 s, respectively, although the waveforms in the middle and at the top are shifted by 0.25 and 0.5 s, respectively, from th e waveform at the bottom. Figure 4-17c shows the total current (including reflections, if any) al ong the channel at t = 0.5, 4, 8, and 16 s after the incident current wave starts moving upwards from the bottom of the channel. Note that at t = 8 s (not far from the current peak) the distri bution of current along the channel is essentially uniform. The current distribution along the CID channel is not much different from uniform, as expected for a Hertzian (electrically short) dipol e, because of relatively short channel length, relatively long current waveforms, and relatively high propagation speed. In Section 4.3, we will show that at least some CIDs can be approximated by vertical Hertzian dipoles. This approximation will enable us to simplify the field equations and use measured fields to infer various electrical parameters of CIDs (within this approximation, th e propagation speed and reflection coefficients are not input parameters an d the current waveshape is the same as that of the time integral of NBP). In Section 4.2.5, we compute CID electric fi eld waveforms using the Herztian dipole approximation and compare them with their counterparts computed using the bouncing-wave model in Section 4.2.4.

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143 4.2.4 Bouncing-Wave Model: Electr ic Fields at 2 and 200 km The general time-domain equation for co mputing the vertical electric field dEz due to a vertical differential current element idz (vertical dipole of length dz carrying a uniform current i(t)) at a height h above a perfectly conducting ground plane for the case of an observation point P on the plane at a horizontal distance r from the dipole is given by [e.g., Uman, 1987]: 22 22 2 54 2 3 0 0() (,) 1(2)()(2)() (,)[(,)(,)] 2()()()t zRz dizt hrRzhrRzr c dErtdzizdiztdzdz RzccRzccRzdt (4-4) where 0 is the electric permittivity of free space, R is the inclined distance from the dipole to the observation point, which is given by 22Rzr From Equation 4-4 for the geometry shown in Figure 4-18, the total el ectric field at the observation point for a finite-length channel w hose lower and upper ends are at altitudes of h1 and h2, respectively, is given by: 2 122 22 2 542 3 0 0() (,) 1(2)()(2)() (,)[(,)(,)] 2()()()h t z hRz dizt hrRzhrRzr c E rtdzizd iztdz dz RzccRzccRzdt (4-5) Where h2 is a function of time during the first traversal of the channel. Figure 4-19a shows the electros tatic, induction, radiation el ectric field components, and total electric field predicted by our model at a horizontal distan ce of 2 km. Current distribution shown in Figure 4-17 was used in the calculati ons. As expected, the static and induction components are dominant at 2 km (radiation near ly along the axis of the vertical dipole is negligible). Figure 4-19b shows the total electric field (essentially the same as its radiation

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144 Figure 4-17. (a) Currents computed using Equati ons 4-7 and 4-8 (Section 4.2.6), at the bottom (z = h1), middle (z = h1 + h/2) and top (z = h2) of the channel for a CID characterized by h1 = 15 km, h = 100 m, v= 28 m/s, t = b = -0.5, Ip = 50 kA, and current risetime = 6 s. Peak currents at these three heights are 40, 34, and 32 kA, respectively. They are not much different from each other (currents at the ends are within less than 20% of the current in the middle). (b) A threedimensional plot of current as a function of both time and height. Note that the in cident current wave peak is 50 kA (as shown in Figure 3a), while the equivalent current distribution along the channel p eaks at 32 to 40 kA, due to reflections (absorption at the ends). (c) Th e total current (including reflec tions, if any) along the channel at t = 0.5, 4, 8, and 16 s after the incident current wave starts moving upwards from the bottom of the cha nnel. Note that at t = 8 s (not far from the current peak) the distribut ion of current along the cha nnel is essentially uniform. (a) (b) (c)

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145 Figure 4-18. Geometrical parameters used in calculating the elect ric field at observation point P on perfectly conducting ground at horizontal distance r from the vertical CID channel extending between heights h1 and h2. See text for details. component) at a horizontal distance of 200 km. At least two secondary peaks can be seen in the electric field waveform shown in Figure 4-19b. Figure 4-19c shows the el ectric field derivative at 200 km, in which one can discern four cycles of oscillations after the primary cycle. The time interval between consecutive maxima in the dE /dt signature is 1 s which corresponds to the round trip time of the current puls e along the channel, that is, from bottom to top and back. The half period (0.5 s) is the travel time of the current pulse in one direction. In Section 4.2.7, we used our bouncing-wave model to compute distant electric field waveforms and compare them with measurements. We varied model parameters, such as current wave propagation speed, channel le ngth, current reflection coeffici ents, and current risetime, in order to examine effects of these variations on fields predicted by our model. We found that that model-predicted fields are consis tent with experimental data onl y for relatively narrow ranges of

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146 these parameters. Specifically, we estimated that the effective current reflection coefficients (assumed to be the same) at channel ends should be approximately in the range of 0 to -0.5, the wave propagation speed ranges from about 0.3 to 3 x 108 m/s, and the channel length is less than about 1000 m. The lower bound on channel length was assumed to be about 100 m, based on observed reflection signatures in dE/dt records. Influence of cu rrent risetime on field waveforms was also examined, and it was found to be typically in the range from about 2 to 8.5 s. We also determined the "allowed" combinations of parameters. In Section 4.2.8, we test th e validity of the bouncing-wave model using electric fields simultaneously measured at near and far distances by Eack [2004]. A good match between model-predicted fields and the e xperimental data is obtained for a peak current of 75 kA, current risetime of 5.2 s, propagation speed of 1.4 x 108 m/s, channel length of 650 m, and current reflection coefficients at channel ends equal to zero. 4.2.5 Hertzian Dipole Approximation Equation 4-4 also applies to a ve rtical dipole of finite length h, provided that h is very short compared to the shor test significant wavelength (Hertzian dipole approximation). For a vertical Hertzian dipole we can replace dz with h in (2) to get: 22 22 2 54 2 3 0 01(2) (2) (/) (,)[ (/) (/) ] 2t zhrh hrhrhditRc Ert iRcd itRc Rc Rc R d t (4-6) Note that the current in Equa tion 4-6 is the same everywhe re along the dipole (independent of z). In Figures 4-20a and b we compare electric field waveforms at r = 2 km and r = 200 km, respectively, computed using the Hertzian dipole approximation (Equa tion 4-6) with their counterparts computed using the bouncing-wave model. The Hertzi an dipole, assumed to be 100 m in length and located at a he ight of 15 km above ground, was excited by the current found for the middle of the channel (z = h1 + h/2) using the bouncing wave m odel (see Figure 4-17a).

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147 Figure 4-20c shows the dE/dt waveforms computed using the Hertzian dipole approximation and the bouncing wave model. Clearly, the fields co mputed using the Hertzi an dipole approximation closely match those based on the bouncing-wave model. Note, howev er, that for longer channels, slower speeds, and shorter current risetimes, th e Hertzian dipole appr oximation may not be applicable. Limits of validity of the Hertzian di pole approximation in terms of these parameters are discussed in Section 4.3. In Section 4.2.8, we test th e validity of the Hertzian dipole approximation using electric fields simultaneously measured at near and far distances by Eack [2004]. A good match between model-predicted fields and the e xperimental data is obtained for a peak current of 74 kA, current risetime of 9 s, and channel length of 500 m. The CI D parameters providing a good match with the experimental data for the Hertzian dipole approximation are not much different (particularly the peak current) from those for the bouncing-wave model (see Section 4.2.4). 4.2.6 Equivalent Current Sources to Represent Multiple Traveling Waves in the BouncingWave Model An elevated vertical lightning channel is m odeled as a transmission line with impedance mismatch at either end. As a result, reflectio ns are produced when the travelling current pulse hits channel ends. We assume that the line is uniform and that any losses along the line are accounted for in the reflection coeffi cients at the ends. So, the reflect ion coefficients used in this Chapter are effective reflection coefficients Although there will likely be a corona-like discharge (a nonlinear process) at either end of the line, we assume the effective reflection coefficients to be constant. Th e distribution of curre nt along the channel ca n be expressed in terms of the incident current, i0(t), channel length, h, current wave speed, v, and effective current reflection coefficients at the top, t, and the bottom, b, of the channel. The initial part

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148 Figure 4-19. (a) Electrostatic, i nduction, radiation electric field components, and total electric field predicted by the bounc ing-wave model at a horizontal distance of 2 km. As expected, the static and induction compon ents are dominant at this distance. (b) Total electric field (essentially the same as its radiation component) at a horizontal distance of 200 km. At least two secondary peaks can be seen in the elect ric field waveform. (c) The electric fiel d derivative at 200 km, in which one can discern four cycles of oscillations af ter the primary cycle. The time interval between consecutive maxima in the dE/dt signature is 1 s which corresponds to the round trip time of the current pulse along th e channel, that is, from bottom to top and back. The half period (0.5 s) is the travel time of the current pu lse in one direction.

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149 Figure 4-20. Electric fields at (a) 2 km a nd (b) 200 km computed using the Hertzian di pole approximation for a CID with a chann el length of 100 m at a height of 15 km, excited by current waveform shown in Figure 4-17a for z = h1 + h/2 (in the middle of the channel). The current peak, Ip, is 34 kA. The dE/dt signatur e is shown in (c). Electric fields and dE/dt computed using the bouncing wave model and pres ented in Figure 4-19 are al so shown for direct comparison. A good match is evident in each of the three panels.

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150 (first half a microsecond for, say, h = 100 m and v = 2 x 108 m/s) of the incident current is associated with the creation of CID channel (probably via runaway el ectron breakdown [e.g., Tierney et al., 2005; Gurevich and Zybin, 2004, Gurevich et al., 2004]) and the later part with the polarization of the create d channel in the cloud electric field. In the model considered here we assume that the channel is alrea dy created and an incident current i0(t) is injected at the bottom of the channel. Then the sum of upward-travelling current waves (incident wa ve and all reflections from the bottom) is given by: 11 22 22 101010101 1,3,5,...24 ( 1 ) (,)(,)(,)(,)... (,)nn utbtbtb nhhn h ihtihtiht iht iht vv v (4-7) Similarly, for the sum of downward-travelling current waves (all reflections from the top) we have 1 22 202 2,4,6,...(1) (,)(,)nn dtb nnh ihtiht v (4-8) These two expressions specify equivalent curr ent sources connected at the channel ends. The two sources launch current waves toward each other and the total current at any position z along the channel can be obtained by appropriately shifting and combining iu(h1,t) and id(h2,t). For example, at 1222hh zhh 112()(,)(,) 222udhhh ihihtiht vv The total current and its two components in the middle of the channel are shown in Figure 4-21a. Additionally, in Figure 4-22b we show the incident current (i0), the sum of all reflections (ir), and the total current (itotal) in the middle of the channel. Note that while the incident current moves upward along the channel, the sum of all the reflections c ontains both upward and downward moving components. Field components and total fields at 200 km corresponding to currents

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151 shown in Figures 4-21a and 4-22a are presented in Figures 4-21b and 4-22b and field derivatives are shown in Figures 4-21c and 4-22c. For compu ting the currents and fields shown in Figures 421 and 4-22 we used h = 100 m, v = 2 x 108 m/s, and = -0.5. We now introduce sign conventions used in this study. As noted in Section 4.1, for a short vertical dipole at relati vely large elevation angle above ground (see Figure 4-23) the radiation field peak on the one hand and induction and sta tic field changes on the other hand are expected to have opposite polarities. Specifically it follows from equation (A.38) of Uman [1987, p. 329] for the electric field at perfectly conducting groun d due to a differential ve rtical dipole that the opposite polarities are expected for > 35.3o, which translates to r < 21 km if source height h = 15 km. The horizontal distance r at which the stat ic and induction componen ts change direction is equivalent to the well known [e.g., Rakov and Uman, 2003; Ch. 3] reversal distance for the electrostatic field due to an elevated finite-l ength vertical dipole. We assume that a positive charge moving in the positive z direction (vertically upward) constitutes a positive current. After the first reflection from the top of the channel, th e current is flipped in polarity (due to negative current reflection coefficient). After the next reflection from the bottom of the channel, the polarity will be flipped again. Hence, iu, the sum of upward-travelling current waves (incident wave and all reflections from the bottom), is positive, while id, the sum of downward-travelling current waves (all reflections from the top), is negative. At far distances (for < 35.3o), the electric field change is e ssentially equal to its radiation field component. Motion of positive charge upward (or negative charge moving downward) produces a radiation electric field change (initi al peak) directed downwar d as shown in Figure 423 (inset). The opposite is true, that is the radiation electric fiel d is directed upward, for motion of positive charge downward (or negative char ge moving upward). At close distances (for >

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152 35.3o), motion of positive charge upward (or ne gative charge moving downward) produces electrostatic and induction fiel d changes directed upward and ra diation electric field change directed downward. According to the physics sign convention [e.g., Rakov and Uman, 2003; Ch. 1], a downward directed electric field vector is assume d to be negative. We use the physics sign convention in Sections 4.2 and 4.3. 4.2.7 Bouncing-Wave Model: Allowed Ranges of Variation of Input Parameters We have used our bouncing-wave model to co mpute distant electric field waveforms and compare them with measurements. The model i nput parameters, current wave propagation speed, channel length, effective current reflection coefficients, source height, and current risetime were allowed to vary. We found that model-predicted fi elds are consistent with experimental data only for relatively narrow ranges of these parameters. 4.2.7.1 Reflection coefficients The current reflection coefficient at either cha nnel end is expected to be between -1 and 0. Positive reflection coefficients imply that the equivalent impedance of surrounding medium is lower than the characteristic impedance of current-carrying channel, which is physically unreasonable. As the magnitude of the reflecti on coefficient increases the amplitudes of the secondary peaks in the electric field waveform become larger. As a result, the number of secondary peaks discernible in the electric fi eld waveform increases with increasing the reflection coefficient magnitude. If we limit the number of secondary pe aks detectable in the electric field waveform to three, then effectiv e current reflection coeffi cients (for simplicity accounting for both absorption at th e ends and attenuation along the channel) should be in the range from -0.5 to 0. Note that in our dataset, 85% of the electric field waveforms do not exhibit any secondary peaks and in the remaining 15% typi cally only one secondary peak is observed. It

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153 Figure 4-21. (a) Th e total current (itotal) and its upward (iu) and downward (id) components in the middle of the channel, (b) the total elect ric field and its comp onents corresponding to currents shown in (a), and (c) corre sponding electric field derivatives.

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154 Figure 4-22. (a) The incident current (i0), the sum of all reflections (ir), and the total current (itotal) in the middle of the channel, (b) the el ectric field components and the total field corresponding to currents shown in (a), and (c) corresponding electric field derivatives. Note that while the incident current moves upward along the channel, the sum of all the reflections contains bot h upward and downward moving components.

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155 Figure 4-23. Illustration of the re versal distance for electrostatic and induction fi eld components. Inset shows the direction of the far ( < 35.3o) electric field vector for different combinations of charge polarity and direc tion of charge motion. In case of bipolar electric field signature (d ominated by its radiation component) the direction of electric field vector refers to the initial half cycle. is likely that actual current reflec tion coefficients are close to -1 while the effective values are lower in absolute value due to our lumping of losses along the channel at the channel ends and combining those losses with absorption there. It is important to note that reflections do influence the overall field waveform, even when they ar e not detectable. All the field calculations presented in this Appendix were performed for two values of (assumed to be the same at both channel ends), 0 and -0.5. 4.2.7.2 Propagation speed (v) and channel length ( h ) The ratio of initial electric field peak to opposite polarity overshoot fo r distant CID electric field waveforms ranges from 2.5 to 14 in studies of Willett et al. [1989, Table 1] and Smith et al. [1999, Table 2] In our data the ratio varies from 3.5 to 17 (see Section 4.1.5). Either decreasing

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156 the current wave speed or increas ing the channel length serves to decrease this ratio. Hence the smallest observed ratio (2.5) can be used to establish a lower bound for propagation speed and an upper bound for channel length; that is, "allowed combinations of these two parameters. We additionally show results for the ratio equal to 3. The upper bound for speed is the speed of light, and the lower bound for channel length was set to be about 100 m. In Section 4.3 it is sh own that for 9 located CIDs for which we were able to estimate (assuming a speed of 2.5 x 108 m/s) channel lengths usi ng oscillations in their measured dE/dt signatures, CID channel lengths range from 108 to 142 m. For a longer channel, the current wave will generally be more attenuated while traversing it, and hence the reflected wave will be less pronounced. Thus it is logica l to assume that the 9 events with most pronounced reflections are associated with the shortest channels. Note that, for all 32 CIDs (discussed in Section 4.2.1), including the 9 located ones, whose dE/dt signatures showed multiple secondary peaks (oscillations), CID channel lengths range from 84 to 181 m, for an assumed speed of 2 x 108 m/s. The latter speed was consid ered to be the lower bound for the events with measured channel traversal times, since for lower speeds th e channel length would become unreasonably small. We first present field calculations that were performed using the incident current wave shown in Figure 4-16a. Its zero-topeak risetime is 6 s and its total duration is 30 s. Influence of current risetime will be examined later in this Appendix. Figures 4-24a and b, show for = 0 and = -0.5, respectively, different combinations of propagation speed and channel length for which the ratio of initia l electric field peak to opposite po larity overshoot of model-predicted electric fields at 200 km attains 2.5 (the lowe st value found in the expe rimental data) and 3.0 (included for comparison). It can be seen from Figure 4-24a that the largest allowed (within our

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157 model) value of channel length h for = 0 is about 1000 m. A larger h would result in a speed greater than 3 x 108 m/s, which is not allowe d. For the ratio equal to 3, the largest allowed h = 750 m. For = -0.5, one can see from Figure 4-24b th at the upper bound for channel length is about 500 m (not much different for ratios of 2.5 and 3). Also, it can be seen from Figures 4-24a and b that for the lowest assumed value of channe l length (100 m), the lowest allowed values of propagation speed are about 0.3 x 108 m/s and 0.7 x 108 m/s for = 0 and = -0.5, respectively. Allowed channel lengths for different values of propagation speed are tabulated in Figures 4-24a and b. The overall upper bounds on h for = 0 and for = -0.5 are 1000 and 500 m, respectively. Note that h/v (channel traversal time), which yi elds the ratio = 2.5, is almost constant and equal to about 3.6 s and 1.7 s for = 0 and = -0.5, respectively. These longest allowed traversal times are about 0.6 and 0.3 tim es the current zero-to-peak risetime of 6 s. Transformations of distant electric field waveforms in response to variations in h and v are illustrated in Figure 4-24 for a current risetime of 6 s. In each panel of this figure, the fields are shown for fixed values of and h and variable v. Figures 4-25a and b show, for = 0 and = -0.5, respectively, the model predicted electric fi elds at 200 km (the source current is described in Section 4.2.3 and shown in Figure 4-16a) for four different propagation speeds and for two values of h. The latter are the assumed absolute lower bound (100 m) and the upper bound for each of the values of (see Figure 4-24). For both values of reflection coefficient and for h = 100 m, one can see that electric field waveforms for all four propagation speeds appear to be consistent with experimental data (ratio 2.5). However, the electric field waveforms for the upper bounds of channel lengths ( h = 500 m for = -0.5 and h = 1000 m for = 0) are inconsistent with experi mental data (the ratio 2.5 condition is not satisfied), except for the upper bound on the propagation speed (3 x 108 m/s).

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158 Figure 4-24a. Combinations of propagation speed and channel length for which the ratio of initial electric field peak to opposite polar ity overshoot of model-predicted electric fields at 200 km attains 2.5 (the lowest value found in the experimental data) and 3.0 for a current risetime of 6 s and = 0. The area limited by the v = 3 x 108 m/s, h = 0.1 km, and Ratio = 2.5 lines defines the domain of "allowed" combinations of v and h. Figure 4-24b. Same as Figure 4-24a, but for = -0.5.

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159 Figure 4-25a. Bouncing-wave model predicte d electric fields at 200 km for different combinations of propagation speed and channel length for a current risetime of 6 s (the source current is described in Sec tion 4.2.3 and shown in Figure 4-16a) and = 0.

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160 Figure 4-25b. Same as Figure 4-25a, but for = -0.5.

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161 Table 4-2. Influence of source height on the ratio of initial electric field peak to opposite polarity overshoot of CID electric fields. The fields were calculated using the bouncing-wave model for r = 200 km and current risetime of 6 s. Reflection Coefficient Current Wave Speed (m/s) Channel Length (m) Source Height (km) Ratio 5 3.0 15 3.1 0.7 x 108 100 25 3.1 5 2.4 15 2.5 = -0.5 3 x 108 500 25 2.6 5 2.7 15 2.7 0.3 x 108 100 25 2.7 5 2.7 15 2.6 = 0 3 x 108 1000 25 2.5 4.2.7.3 Source height Smith et al. [2004] reported the median CID sour ce heights to be 13 km and 15 km, respectively (see also Section 4.1). The range of variation in our da ta is from 8.8 to 29 km. In our calculations we assumed a typical source height of 15 km. The rati o of the initial peak to the opposite polarity overshoot of the model-predicted waveforms of CIDs at a particular distance changes with altitude (as shown in Table 4-2) However, the changes are relatively small and the upper bounds on channel length at different speeds remain essentially the same for different altitudes. For example, all other parameters remaining constant, the upper bounds on channel length at a distance of 200 km, for = 0 and v = 3 x 108 m/s is about 1100 m for an altitude of 5 km, and about 1000 m for both 15 and 25 km. 4.2.7.4 Distance The ratio of the initial peak to the opposite polarity overshoot of the model predicted waveforms of CIDs at a particular height changes with distance (a s shown in Table 4-3). This, in turn, would change the upper bound on channel le ngth at different speeds. However, these

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162 changes are relatively small. For example, all other parameters remaining constant, the upper bounds on channel length for a source height (altitude) of 15 km, = 0 and v = 3 x 108 m/s are 900, 1000, and 1100 m for distances of 50, 200, and 400 km, respectively. Similarly, for = -0.5 and v = 3 x 108 m/s, the upper bounds on channel length is about 600 m for 50 km and about 500 m for both 200 and 400 km. 4.2.7.5 Current waveshape The expression for the current injected at the bo ttom end of the CID channel used in all our computations is an asymmetric Gaussian pulse with total duration t2 and zero-to-peak risetime of t1. The expression for i0(t) is given by: 2 1 2 1(()) 1 0 (()/) 1 () {tt ttk A ett it A ett (4-9) where k=(t2-t1)/t1, and is a parameter that, along with k, controls the shape of the Gaussian pulse and causes current to approach zero at t = 0 and t = t2. In computing electric fields we have used a current pulse with a peak (A) of 50 kA and total duration (t2) of 30 s. In the following, we will examine the influence of current risetime (t1), assuming that the total duration (t2) of current pulse remains the same at 30 s. The values of the parameters and k yielding different values of t1 are given in Table 4-4. In our model, for shorter lengths and higher spee ds, the total width of the initial half-cycle of the CID electric field signature tends to become equal to the risetime of the incident current pulse. This is clearly seen in Figure 4-25a where all field wa veforms were computed for the same current risetime of 6 s. Electric field signatures produced by cu rrents having the same total duration (30 s) and peak (50 kA), but different risetimes, 3, 6 and 9 s, are shown in Figure 4-26, for = 0, h = 100 m and v = 2 x 108 m/s. The total width of the initial half-cycles of the electric field signatures are 3.4, 6.4, and 9.3 s, respectively. In our experimental data, the

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163 Table 4-3. Influence of distance on the ratio of initial electric field peak to opposite polarity overshoot of CID electric fields. The fields were calculated using the bouncing-wave model for h = 15 km and current risetime of 6 s. Reflection Coefficient Current Wave Speed (m/s) Channel Length (m) Distance (km) Ratio 50 3.2 200 3.1 0.7 x 108 100 400 3.0 50 3.0 200 2.5 = -0.5 3 x 108 500 400 2.4 50 2.7 200 2.7 0.3 x 108 100 400 2.7 50 2.3 200 2.6 = 0 3 x 108 1000 400 2.6 Table 4-4. Parameters and k in Equation 4-9 yielding different values of current risetime (t1). The total duration of current pulse t2 remains the same and equal to 30 s. Current Risetime (s) k = (t2-t1)/t1 2 50/t2 14 3 32/t2 9 6 15/t2 4 8.5 10/t2 2.53 9 10/t2 2.33 total width of the initial half cycle ranged from 2. 8 to 13 s with a geometric mean of 5.6 s. We assumed that the initial half-cycle duration is unlik ely to be less than 2.5 s and used this as an additional criterion in determin ing allowed combinations of h and v. From Figure 4-26 one can see that the ratio of the initial field peak to the opposite polarity overshoot decreases with increasing current risetime. The ratios for current risetimes of 3, 6 and 9 s are 8.5, 4.0, and 2.3, respectively. For a current risetime of 8.5 s the ratio is 2.5, which is the minimum allowed value assumed in our study. Since we assume that the lower bound on channel length is 100 m, and increasing the channe l length causes a decrease in the ratio (Figure

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164 4-24), a current risetime longer than 8.5 s would result in an el ectric field waveform that is inconsistent with experimental data for any channel length equal to or greater than the lower bound, when the propagation speed is 2 x 108 m/s. In fact, for propagation speeds of 0.7 x 108 m/s to 3 x 108 m/s, the ratio remains approximately 2.5 (varies from 2.47 to 2.55), when the current risetime is 8.5 s. Tables 4-5 and 4-6 list the allowed combinations of reflection coefficients, propagation speeds, and channel lengths that produ ce distant field waveforms that are consistent with experimental data for current risetimes of 2 and 3 s. The following criteria were used in determining allowed combinations: (1) the ratio of initial peak to opposite polarity overshoot is equal to or greater than about 2.5 (2) the total width of initial half cycle is equal to or greater than about 2.5 s, and (3) the overall shape of the initial half cycle is consistent with observed ones. For longer risetimes, the range of allowed h-v combinations was determined by the ratio (criterion 1). For shor t risetimes and shorter channel lengths, the range of allowed h-v combinations was determined by the total width of the initial half cycle (criterion 2). Criterion 3 was the primary one for short rise times and longer channel lengths. In this latter cas e, the initial half cycle exhibited flattening (s ee Figure 4-27b) that is not consis tent with experimental data, for all speeds other than the speed of light. Note that for a current risetime of 2 s and = -0.5, no combination of parameters produced wavefo rms consistent with experimental data. Transformations of distant electric fi eld waveforms due to variations in h and v are illustrated in Figure 4-27 and 4-28 for current risetimes of 2 and 8.5 s, respectively. Figures 427a and b show, for h = 100 m (the lower bound on channel length, see Table 4-6) and h = 500 m (the upper bound on channel length, see Tabl e 4-6), respectively, the model predicted electric fields at 200 km (the source current is described in Se ction 4.2.3 and shown in Figure 416a) for different propagation speeds and = 0. For h = 100 m, one can see that electric field

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165 waveforms for all propagation speeds, except for 3 x 108 m/s (which violates criterion 1 described above), appear to be consistent with experimental data. However, the electric field waveforms for the upper bound on channel length ( h = 500 m) are inconsistent with experimental data (violate criterion 3) for all propaga tion speeds, except for 3 x 108 m/s. For a current risetime of 8.5 s, electric field waveforms for = 0 (Figure 4-28a) and -0.5 (Figure 428b) appear to be consistent with experiment al data for propagation speeds ranging from about 108 to 3 x 108 m/s only for h = 100 m. Table 4-5. Combinations of reflection coefficien ts, propagation speeds, and channel lengths that produce distant CID electric fields that ar e consistent with experimental data for current risetime of 3 s. Reflection Coefficient Current Wave Speed (m/s) Channel Length (m) 1.1 x 108 ~100 2 x 108 ~100-175 = -0.5 3 x 108 ~100-275 0.4 x 108 ~100 0.7 x 108 ~100-200 1 x 108 ~100-250 2 x 108 ~100-500 = 0 3 x 108 ~100-800 Table 4-6. Combinations of propagation speeds and channel lengths th at produce distant CID electric fields that are consistent with experimental data for = 0 and current risetime of 2 s. No combination produced waveforms consistent with experimental data for = -0.5. Reflection Coefficient Current Wave Speed (m/s) Channel Length (m) 0.6 x 108 ~100 0.7 x 108 ~100-125 1 x 108 ~100-200 2 x 108 ~100-300 = 0 3 x 108 ~200-500

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166 Figure 4-26. Currents (a) and corres ponding electric fields (b) for the same total current duration (30 s) and peak (50 kA), but differe nt risetimes of 3, 6 and 9 s for = 0, h = 100 m, and v = 2 x 108 m/s.

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167 Figure 4-27. Electric field waveforms at 200 km for different propagation speeds and channel lengths of (a) 100 m and (b) 500 m, fo r a current risetime of 2 s and = 0.

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168 Figure 4-28. (a) Electric field waveforms at 200 km for different combinations of propagation speed and channel length for a current risetime of 8.5 s and = 0. (b) Same as in (a), but for = -0.5.

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169 4.2.8 Testing the Validity of Bouncing-Wave Mo del and Hertzian-Dipole Approximation Using Electric Fields Simultaneously Mea sured at Near and Far Distances by Eack [2004] 4.2.8.1 Bouncing-wave model Here, we use the simultaneously measured near and far electric field signatures of one CID reported by Eack [2004] to test the validity of bouncing-wave model. This same event was previously used for testing th e validity of other models by Watson and Marshal [2007]. The CID transferred negative charge upwar d (or positive charge downward) We use the trial and error approach to determine a combination of CID pa rameters, including the current peak, the current zero-to-peak risetime (RT), the propagation sp eed (v), current reflection coefficient ( ), and the channel length ( h), for which the bouncing-wave model predicted electric fields best match the measured electric fields at both near and far distances from the discharge. The CID channel was assumed to be vertical. Electric field signatures of this CID, measured at Los Alamos (near station) and Socorro (far station), New Mexico, are shown in Figure 1 of Eack [2004] and reproduced in Figure 4-29 of this Chapter. Horizontal distances were es timated, using Los Alamos Sferic Array (LASA) measurements and a time-of-arriv al (TOA) method, to be 2.8 km from the Los Alamos station and about 200 km from the Socorro station with a stated error of km. The CID height was estimated to be of 11.6 km above mean sea le vel. The height above local terrain should be smaller by about 2 km [Smith et al., 2004]; that is, about 9.6 km. The CID height was estimated by measuring delays of ionosphere and ground-ionosphere reflections with respect to direct-path wave in VLF/LF ground-based (LASA) field records. Smith et al. [2004] estimated errors of this method relative to another, more accurate method that employed FORTE satellite VHF records showing direct-path and ground-re flection signals. The ground-base d estimates were on average 1 km higher than the satellite estimates. After removal of the 1-km bias, the LASA height

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170 estimates were within 1 km of satellite estimates. Thus, the height of the CID in question is 9.6 1 = 8.6 km with a random error of km. In summary, uncertainties in distance of the CID in question are 0.8 to 4.8 km and 198 to 202 km from the Los Alamos and Socorro station, respectively, and uncertainties in height are 7.6 to 9.6 km above ground level. We include these uncertainties in our search for CID parameters that provide best match between model-predicted and measured electric field waveforms at both near and far distances. Figures 4-29a and b show the model predicted electric fields overlai d with the measured ones at near and far distances, respectively. A reasonably good match between calculated and measured fields was obtained for a peak current of 75 kA, RT = 5.2 s, v = 1.4 x 108 m/s, = 0, h = 650 m, horizontal distances of 2.3 and 200 km from the near and far stations, respectively, and the height of the bottom of the CID channe l of 7.8 km above ground level. The CID current pulse was assumed to be injected at the bottom e nd of the CID channel and to travel upward. The expression for the current waveform is given in Section 4.2.7 (Equation 4-9). The values of and k (parameters that control the sh ape of the Gaussian current puls e) along with the best-fit values of peak current, RT, v, and h are given in Table 4-7. 4.2.8.2 Hertzian dipole approximation Here, we use the two-station data of Eack [2004] to test the validity of the vertical Hertzian dipole approximation. In contrast with the bouncing-wave model, v and are not parameters of the Hertzian dipole approximation. The testing procedure used here is similar to that described above for the bouncing -wave model. Figure 4-30 shows electric fields based on the Hertzian dipole approximation overlaid with the experimental data at near and far distances. A reasonably good match between calculated and measured fields was obtained for a peak current of 74 kA, RT = 9 s, h = 500 m, horizontal distances of 2.4 and 200 km from the near and fa r stations, respectively, and the height of CID

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171 channel of 7.2 km above ground level. The expressi on for the current waveform injected is given in Section 4.2.7 (Equation 49), with the values of and k along with the best-fit peak current, RT, and h being given in Table 4-7. 4.2.8.3 Discussion The Gaussian current pulse that we used for testing the Hertzian dipole approximation is the same as that employed by Watson and Marshall [2007] for modeling the same CID. They were unable to obtain a good match with Eack's near field data using th e transmission line model and assuming that the stated horizontal distance, 2.8 km, is exact. As shown in this Appendix, both the close and distant fields can be reason ably well reproduced by the bouncing-wave model (which for = 0 reduces to the tran smission line model used by Watson and Marshall [2007]) when the uncertainties in the estimated horizon tal distances and source height are taken into account. We now compare, with reference to Table 47, parameters for which predictions of the bouncing-wave model and Hertzian dipole approximation best fit the two-sta tion data of Eack [2004]. The channel lengths that fit Eack's two-station data for the bouncing-wave model and Hertzian dipole approximation are similar, 650 m and 500 m, respectively, and both are within the corresponding allowed ranges. The peak curre nts predicted by both m odels are almost the same (75 kA for the bouncing-wave model and 74 kA for the Hertzian dipole approximation). Note that our peak-current estimates of 74-75 kA are similar to that (74 kA) of Watson and Marshall (based on the TL model) and apprec iably higher than that (29 kA) of Eack (based on the assumption that the near field peak is due to induction field compone nt only). Our predicted zero-to-peak current risetime of 9 s for the Hert zian dipole approximation is larger than that (5.2 s) for the bouncing-wave model and is close to the upper limit (8.5 s) of the range of allowed values. The source heights for which a r easonably good match with two-station data is

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172 obtained for the bouncing-wave model and Hertzian dipole approximation are similar, 7.8 and 7.2 km, respectively, although the la tter is slightly outside the range of uncertainty (7.6 9.6 km) in this parameter. Table 4-7. CID parameters for which electric fiel ds at close and far distances that are based on the bouncing-wave model and Hertzian dipo le approximation best fit the fields measured by Eack [2004]. Bouncing-Wave Model Hertzian Dipole Approximation Parameters Best-fit value Allowed range Best-fit value Allowed range Peak current, kA 75 74 Zero-to-peak current risetime, s 5.2 2.5 8.5 9 2.5 8.5 Total Current duration (t2), s 36 36 (see Equation 4-9) 18.1/t2 10.25/t2 k (see Equation 4-9) 5.92 3 Propagation speed, m/s 1.4 x 108 0.3 3 x 108 Current reflection coefficient 0 -0.5 0 Channel length, m 650 100 1000 500 100 550 Distance from near station, km 2.3 0.8 4.8 2.4 0.8 4.8 Distance from far station, km 200 198 202 200 198 202 Height of the channel above ground, km 7.8 (lower end) 7.6 9.6 7.2 7.6 9.6 4.2.9 Discussion and Summary Smith et al. [1999] estimated the CID channel leng ths to range from 300 to 1000 m. In estimating the lower bound, they considered two oppositely charged spherical regions, immediately adjacent to each othe r, with the CID channel extendi ng between the centers of the two spheres (see Section 4.3 for more details) The lower bound on channel length was found by comparing the maximum electric field (at the poin t of contact of the spheres), for the average charge estimated from observations, with the conventional breakdown electr ic field in the cloud

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173 Figure 4-29. Electric fields computed using the bouncing-wave model (in red) overlaid with the fields measured by Eack [2004, Figure 1] (in blue) at (a ) near and (b) far distances. Figure 4-30. Electric fields computed using the Hertzian dipole approximation (in red) overlaid with the fields measured by Eack [2004, Figure 1] (in blue) at (a) near and (b) far distances.

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174 (of the order 106 V/m). The upper bound on channel length of 1000 m was apparently based on the median duration of 3.2 s of HF radiation produced by CIDs [Smith, 1998] and the upper limit for the propagation speed of 3 x 108 m/s. Our channel lengths estimated from channel traversal times measured in dE /dt records are smaller than Smith et al.'s lower bound of 300 m, with the corresponding charge c onfiguration being discussed in Section 4.3. The upper bound on CID channel length estimated in this study (s ee Section 4.2.7) by comparing bouncing-wave model predicted electric fields to experi mental data is the same as that of Smith et al. [1999]. Using the upper bound on channel length and the mean duration (10-to-90%) of 13.7 s of CID dipole moment change, Smith et al. [1999] calculated the propagation speed of the current wave to be 7.3 x 107 m/s. According to the bouncing-wave mechanism proposed in this Chapter, the average propagation speed inferred by Smith et al. [1999], who essentially assumed that the total duration of the CID electric field pulse is equal to one channel traversal time, must be an underestimate, although it is within the range of allowed values (see Section 4.2.7). Eack [2004] erroneously used the dipole approx imation to infer the propagation speed for CIDs from his two-station electric field meas urements. In doing so, he estimated the dipole moment change, p, from a close field record, which at later times is dominated by the electrostatic field component. From the electrostatic field change, Ees, measured at distance r, the dipole moment change is 3 04espEr (4-10) This step is fine, but then Eack substituted the resultant p value into the equation for dipole moment change in terms of the radiation electric field change, Er, at distance r (much larger than r in Equation 4-10), 2 04( )r p crEtdtdt, (4-11)

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175 where c is the speed of light (speed at which an electromagnetic wave propagates from the source to the observer), which he labeled as "v" and misinterpret ed as the propagation speed of the CID current wave along the channel. The propagation speed along the channel is not a parameter of the dipole approximation and, hence, it cannot be derived from this approximation. In fact, solving Equation 4-11 for c should yield 3 x 108 m/s, and any deviation from this value (Eack computed 1.5 x 108 m/s, on average) should be viewed as being due to inadequacy of employed model and/or measurement errors. Further, Eack used his misinterpreted propagation speed and the total duration of the CID electric field pulse to estimate the CID channel length. The resultant (incorrect) averag e channel length for seven CIDs was 3.2 km (larger than the upper bound estimated in Section 4.2.7). Hamlin et al. [2007] inferred that the s econdary peak (of the same polarity as the preceding primary peak) in CID electric field signatures was due to reflection of the current wave from the far end of the channel. They used an assumed propagation speed of 3 x 108 m/s and the time difference between the primary and secondary peaks to estimate the upper bound on channel length, which was found to be 2 km. However, as found from modeling (s ee Section 4.2.4), the secondary peaks observed by Hamlin et al. [2007] actually occur at the time when the current front is in the middle of the cha nnel, after being reflected from its far end. More importantly, the secondary peak, occurring several microseconds af ter the primary peak, results from one of the higher-order reflections from the far end of the channel, as evident from comparison of electric field and dE/dt signatures in Figure 4-11. It follows that Hamlin et al.'s channel lengths are overestimates. In Section 4.2.7, we estimated the upper bound on channel length to be about 1000 m. Longer channels would result in distant el ectric field waveforms that are inconsistent with experimental data.

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176 Watson and Marshall [2007] used the original tr ansmission line (TL) model [Uman et al., 1975] and a modified TL model with an exponent ially increasing current along the channel to compute electric field signatures at horizontal distances of 2.8 and 200 km and compare them with corresponding measured waveforms reported by Eack [2004]. Both models can, in principle, successfully match the two-station field measurements (for the TL model after a slight change in distance from the close station). Th e exponentially increasing current was assumed by Watson and Marshall to correspond to the runaway electr on breakdown process. They estimated the propagation speed and channel length to be 6 x 107 m/s and 630 m, respectively, for the exponentially increasing current model. For the TL model (constant amplitude of current wave) they estimated a speed of 2 x 108 m/s and a channel length of 500 m. Watson and Marshall's estimates of propagation speed and channel length are within the range of allowed values found in Section 4.2.7. In this study, we assume that the shortest CID channel length is about 100 m and show, via comparison of bouncing-wave model predictions with measurements, that the upper bound on channel length is approximately 1000 m. Thus compact intracloud discharges are indeed "compact". The uniqueness of CIDs is apparently related to the fact that a short conducting channel (its length is primarily determined by the spatial extent of high-fi eld region) is created faster (on a submicrosecond time scale) than th e cloud electric field can polarize this channel (make it nearly equipotential). This mismatch resu lts in a transient, bounci ng-wave process in the channel. The polarization rate s hould be primarily determined by the conductivity of the channel, which for a "lightning seed" created via a runawa y electron breakdown proce ss is expected to be of the order of 10-4 S/m [Solomon et al., 2001]. It is possible that the bouncing waves serve to maintain channel conductivity. As evidenced by a more or less constant period of oscillations

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177 (see Figure 4-11b), the channel length remains consta nt in the later part of the discharge. This short and fixed channel length property (alt hough there should be co rona-like streamers developing from channel ends) implies that CI Ds cannot pervade large cloud volumes and tap remote charge reservoirs, which is consistent with the fact that the majority CIDs tend to occur in isolation from any other lightning activity. On the other hand, CI Ds apparently can and do cause charge redistribution in the cloud, which may facilitate or contribute to initia tion of "normal" IC discharges or influence development of CG discharges [e.g., Rison et al., 1999; Thomas et al., 2001; Krehbiel et al., 2008; Section 4.1]. 4.3 Estimation of Electrical Parameters In Section 4.2 we showed that the current distribution along the CID channel is often not much different from uniform, because of relatively short channel length, h, relatively long current waveform, and relatively high propagation speed, v. This observation suggests that at least for some "allowed" combinations of v and h, we can reasonably approximate the CID channel by a vertical Hertzian dipole. This appr oximation will enable us to simplify the field equations and use measured fields to infer vari ous parameters of CIDs. Within the Hertzian dipole approximation, the propagation speed is not an input parameter and the current waveshape is the same as that of the time integral of CID radiation field signature, which is often referred to as the narrow bipolar pulse or NBP. In this Section, we determine the limits of va lidity of the Hertzian dipole approximation as applied to CIDs, and use this approximation to in fer the peak current, current risetime, charge transfer, radiated power, and ra diated energy for the 48 located CIDs studied in Section 4.1. Additionally, we estimate the uppe r bound on cloud electric field pr ior to CID and total energy dissipated by this type of lightning. The physics sign convention according to which a

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178 downward-directed electric field (o r field change) vector is consider ed to be negative is used in this Section. 4.3.1 The Hertzian Dipole Approximation Approach Equation 4-4 also applies to a ve rtical dipole of finite length h =h2 h1, provided that h is very short compared to th e shortest significant wavelength (Hertzian or electrically short dipole approximation). For exam ple, for a dipole of length, h = 500 m can be considered Hertzian if >>500 m. This means that the above a pproximation is valid for frequencies f << 600 kHz. From Equation 4-4 for the geometry shown in Figure 4-18, the tota l electric field at the observation point for a vertical He rtzian dipole we can write: 22 22 2 54 2 3 0 01(2) (2) (/) (,)[ (/) (/) ] 2t zhrh hrhrhditRc Ert iRcd itRc Rc Rc R d t (4-12) where 22 R hr Note that current i in Equation (3) varies only as a function of time, with all the geometrical parameters being fixed. In Section 4.3.2, we will show that the vertic al Hertzian dipole approximation is consistent with the CID bouncing-wave model for a reasonab ly large subset of "allowed" combinations (established in Sect ion 4.2.7) of v and h. Equation 4-12 can be expressed as a second order differential equation: 222222 54232 0(2)(2) [] 2zdE hhrhrdirdi i dtRcRdtcRdt (4-13) where arguments of Ez and i have been dropped to simplify notation. For known Ez and the geometrical parameters ( h, h, and r) this equation can be numerically solved for i We employed the Runge-Kutta method of order three (with four stages and an embedded second-order method, also known as the BogackiShampine method [ Bogacki and Shampine 1989]) to solve Equation (4) for i using measured electric fields Ez (which had a better signal-to-

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179 noise ratio than the measured electric field derivative waveform s) of 48 located CIDs that occurred at horizontal distances r ranging from 12 to 89 km and heights h ranging from 8.8 to 29 km (Section 4.1). The initial and final values of current used to solve Equation 4 were required to be zero, and the error tolerance of the numerical solution was set to 10-6. Channel lengths h for 9 CIDs were estimated from reflections in el ectric field derivative (dE/dt) waveforms and assumed propagation speeds covering the entire ra nge of their allowed values (see Section 4.2). For the remaining 39 CIDs there were no reflecti on signatures observed, a nd a reasonable value of h = 350 m was assumed. This value is consistent with the Hertzian dipole approximations for speeds in the range of 2 to 3 x 108 m/s. We also consid ered other values of h, which are consistent with the Hertzian dipo le approximation. Note that for Ez measured at far distances, the peak current can also be estimated analytically using the radiation field approximation, given by: 22 232 0() 2zdE hrdi dtcRdt (4-14) In order to illustrate this, an electric fi eld waveform (shown in Figure 4-31a) computed using the current waveform show n in Figure 4-31b (black line) and the bouncing-wave model for a CID occurring at a height of 15 km and a horizontal distance of 200 km was used in both Equation 4-13 and the radiation field approximati on (Equation 4-14) to solve for current. Results are presented in Figure 4-31b, al ong with the current used compute the elect ric field shown in Figure 2a. One can see from Figure 4-31b that the three current waveforms are very similar to each other. For the 9 CIDs with reflection signatures in dE/dt wave forms, occurring at horizontal distances ranging from 19 to 89 km, the radiatio n field approximation estimated current peaks were, on average, 17% greater than those obtained by numerically solving Equation 4-13. The differences in peak ranged from 7% to 21% for 8 CIDs and for one CID with a poor signal-tonoise ratio it was 47%.

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180 The charge transferred up to time t can be obtained by integrati ng the current with respect to time: 0()tQid (4-15) Further, the source current can be used to find th e radiation components of E and H and hence the Poynting vector, total radiated power and energy. The magnitude of the Poynting vector, which has the meaning of the radi ated power density, can be obtained as: SEH (4-16) where 2 01 sin 4 hdi E cRdt and 1 sin 4 hdi H cRdt [e.g., Uman, 1987]. After substituting the latter two field expressions in Equation 4-16 we get 2 3 01sin 4()hdi S cRdt (4-17) The total radiated power, obtained by integr ating Equation 4-17 over a spherical surface of radius R whose center is at the position of the dipo le, is (presence of ground is not taken into account): 2 2 2 2 3 00 0sin 6()radhdi PSRdd cdt (4-18) where and are the polar and azimuthal angles of th e spherical coordinate system. The total energy dissipated up to time t can be obtained by integrating the radiated power with respect to time: 0()t radWPd (4-19) Note that since di dt is inversely proportional to h, S Prad, and W are each independent of h.

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181 Figure 4-31. (a) Bouncing-wave mode l-predicted electric field for a CID occurring at a height of 15 km and a horizontal distance of 200 km ( h = 100 m, v = 2 x 108 m/s, = 0) and (b) current waveforms obtained by solving Equation 4-13 (blue line) and using the radiation field approximation (red line) with the electric field shown in (a) as an input. Also shown is the current waveform (b lack line) used to compute the electric field in (a).

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182 4.3.2 Limits of Validity of the He rtzian Dipole Approximation In this Section, we compared electric fiel ds produced at 200 km by a typical CID at a height of 15 km having a current zero-to-peak risetime RT of 6 s computed using the vertical Hertzian dipole approximation with their c ounterparts predicted by the bouncing-wave CID model (see Section 4.2). Calculations were perf ormed for different combinations of effective current reflection coefficients at channel e nds, channel lengths, and propagation speeds, each within the bounds ("allo wed" ranges) established in Secti on 4.2.7. The Hertzian dipole was excited by the current found for the middle of the channel ( z = h1 + h/2 ) using the bouncing wave model (see Equations 4-7 to 4-9 and Tabl e 4-4 of Section 4.2). The bouncing-wave model predicted waveforms were used as the ground-trut h, and electric field waveforms based on the Hertzian dipole approximation with initial p eaks within about 15% of ground-truth peaks were considered as confirming the validity of the approximation. The influence of RT was also considered. Figure 4-32 shows the electric fields for the Hertzian dipole approximation (dashed line) and bouncing-wave model (solid line) for = 0, v = 2 x 108 m/s, RT = 6 s, and channel lengths of 100, 350, and 700 m. While the Hertzian dipole approximation is acceptable for the lengths in the range of 100-350 m, it is not fo r 700 m. Figure 4-33 shows the elec tric fields for the Hertzian dipole approximation (dashed line) and bouncing-wave model (solid line) for = -0.5, v = 2 x 108 m/s, RT = 6 s, and channel lengths of 100 and 350 m. In both cases the Hertzian dipole approximation is acceptable. The results are summarized and compared with the "allowed" ranges of variation of v and h in Figure 4-34, from which one can see that the Hertzian dipole approximation is consistent w ith the bouncing-wave model for a reasonably large subset of "allowed" combinations of propagation speed an d channel length. Specifically, it can be seen from Figure 4-34 that for = 0 the Hertzian dipole approximation is valid for h ranging from

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183 about 100 to 550 m and for speed s ranging from about 0.7 x 108 m/s to 3 x 108 m/s, while the "allowed" ranges are from about 100 to 1000 m for h and from about 0.3 x 108 m/s to 3 x 108 m/s for v. For = -0.5, the Hertzian dipole approxima tion is valid for the entire "allowed" domain (from about 100 to 500 m for h and about from 0.7 x 108 m/s to 3 x 108 m/s for v; see Figure 4-24b of Section 4.2.7). Note that for RT = 6 s h/ v (channel traversal time), for which the Hertzian dipole approximation is acceptable, is almost constant and equal to about 1.9 s and 1.7 s for = 0 and = -0.5, respectively. Channel length values for which the Hertzian dipole approximation is valid (initial peaks within about 15% of bouncing-wave model predicted peaks) for different values of propagation speed and for RT = 6 s are given in Table 4-8. Note that the errors for the opposite polarity overshoot were larger, so the Hertzian dipole ap proximation may be invalid at later times after the initial half cycle, whose duration in our data set varies from 2.8 to 13 s with a GM of 5.6 s. Since the errors at later times (during the NBP opposite polari ty overshoot) are larger, the waveforms for the various parameters shown in Figure 4-35 (and discussed in Section 4.3.3) may be invalid at those times. Additionally, for some of the electric field waveforms after the initial half cycle and particularly towards the tail of the opposite polari ty overshoot the signal-to-noise ratio was poor. This is why, we limited our estimate s of charge transfer an d energy to the initial 5 s of the process. Note that the peak current, current risetimes, and peak power are generally unaffected by the uncertainties encountered at later times. We now consider the influe nce of zero-to-peak risetime, RT. In Section 4.2 it was determined that the CID current risetime is likely to be in the range from about 2 to 8.5 s. For RT = 2 s, the Hertzian dipole approximation is not valid fo r any allowed combination of parameters. For RT = 3 s, the approxi mation is valid when v = 2 to 3 x 108 m/s and h = 100 to

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184 Figure 4-32. Vertical electric fields fo r the bouncing-wave mode l (solid line) for = 0, v = 2 x 108 m/s, RT = 6 s, and channel lengths of (a) 100, (b) 350, and (c) 700 m versus those for the Hertzian dipole approximation (dashed line). The Hertzian dipole approximation is acceptable for channel lengths in the range of 100-350 m, but not for 700 m.

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185 Figure 4-33. Same as Figure 4-32, but for = -0.5 and channel lengths of (a) 100 and (b) 350 m, for both of which the Hertzian dipole approximation is acceptable. 200 m (channel traversal time, h/ v = 0.3 to 1 s) for both = 0 and = -0.5. For RT = 8.5 s, the approximation is valid for h = 100 m and for v = 1 to 3 x 108 m/s (channel traversal time, h/ v = 0.3 to 1 s), which cover the enti re range of "allowed" values for both = 0 and = -0.5. Channel length values for which the Hertzian dipole approximation is valid (initial peaks are within about 15% of bouncing-wave model predicted peaks) for different values of propagation speed are given in Table 4-9 for RT = 3 s and in Table 4-10 for RT = 8.5 s. In summary, the shorter the current risetime, the smaller the Hertzi an dipole domain relative to the allowed one, as expected.

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186 Figure 4-34. Comparison of the Hertzian dipole validity domain (combinations of propagation speed and channel length) with the "allowed" one for RT = 6 s and = 0. See text for details.

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187 Table 4-8. Comparison of electric fields ba sed on the Hertzian dipole approximation and bouncing-wave model for a current risetime of 6 s for different combinations of reflection coefficients, current wave speeds, and channel lengths. Combinations of speed and channel length in italics are considered to be consistent with the Hertzian dipole approximation. Reflection Coefficients Current Wave Speed (m/s) Channel Length (m) Difference in initial peak (%) Difference in opposite polarity overshoot (%) 100 8.7 58 0.7 x 108 125 15 37 100 3.2 48 1 x 108 170 13 39 100 -0.76 -1.9 2 x 108 350 15 39 100 -1.3 -1.9 = -0.5 3 x 108 500 14 45 0.3 x 108 100 51 1.1 100 7.4 -1.4 135 15 -0.77 0.7 x 108 250 61 1.6 100 2.7 -1.7 170 11 -0.7 190 15 -0.3 1 x 108 350 60 1.6 100 -0.62 -1.9 350 13 -1.0 375 15 -0.9 2 x 108 700 63 1.8 100 -1.3 -1.9 500 12 -1.1 550 15 -0.89 = 0 3 x 108 1000 60 1.6

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188 Table 4-9. Comparison of electric fields ba sed on the Hertzian dipole approximation and bouncing wave model for a current risetime of 3 s for different combinations of reflection coefficients, current wave speeds, and channel lengths. Combinations of speed and channel length in italics are considered to be consistent with the Hertzian dipole approximation. Reflection Coefficients ( ) Current Wave Speed (m/s) Channel Length (m) Difference in initial peak (%) Difference in opposite polarity overshoot (%) 1.1 x 108 100 19 52 100 4.4 66 150 14 56 2 x 108 175 21 51 100 0.49 44 225 14 56 = -0.5 3 x 108 275 21 61 0.4 x 108 100 127 -0.5 100 42 -1.4 0.7 x 108 200 164 1.0 100 20 -1.7 1 x 108 250 127 0.60 100 2.5 -2.4 2 x 108 175 15 -1.2 100 0.09 -2.4 = 0 3 x 108 250 15 -0.58 Table 4-10. Comparison of elect ric fields based on the Hertzi an dipole approximation and bouncing wave model for a current risetime of 8.5 s for different combinations of reflection coefficients, current wave speeds, and channel lengths. Combinations of speed and channel length in italics are considered to be consistent with the Hertzian dipole approximation. Reflection Coefficients ( ) Current Wave Speed (m/s) Channel Length (m) Difference in initial peak (%) Difference in opposite polarity overshoot (%) 1 x 108 100 0.17 -1.4 2 x 108 100 -1.4 -1.9 = -0.5 3 x 108 100 -1.7 -1.9 1 x 108 100 0.07 -1.6 2 x 108 100 -1.4 -1.9 = 0 3 x 108 100 -1.6 -1.9

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189 Figure 4-35. (a) Measured electric field, (b ) measured electric field derivative, (c) in ferred current, (d) inferred charge tra nsferred, (e) inferred radiated power, and, (f) inferred ra diated energy, each as a function of time, for a CID that occurred at a horizontal distance of 50 km, at an inferred height of 16 km, and had an inferred channel leng th of 103 m (v = 2.5 x 108 m/s).

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190 4.3.3 Electrical Parameters of CIDs Of the 48 located CIDs studied in Section 4.1, for 9 events, we were able to estimate channel lengths using reflection signatures in their measured dE/dt signatures and assumed speeds within their limiting values of 2 x 108 and 3 x 108 m/s. Speeds lower than 2 x 108 m/s are not considered, since for measured traversal ti mes they would result in unreasonably small radiator lengths. For v = 2.5 x 108 m/s (average speed value), th e channel lengths for the nine events range from 108 to 142 m. These events oc curred at horizontal distances of 30 to 89 km and estimated heights of 8.8 to 19 km, and had electric field peaks normalized to 100 km ranging from 14 to 35 V/m. Figure 4-35 shows the measured electric field and electric field derivative along with the inferred current, ch arge transferred, and radiated power and energy, each as a function of time, for one such event. Vertical a rrows indicate reflection signatures in the dE/dt waveform. The estimated channel length (for v = 2.5 x 108 m/s) was 138 m. Table 4-11 summarizes the estimated parameters for all th e 9 events. The geometric mean (GM) peak current is 143 kA with a range 87 to 259 kA. The current zero-topeak risetimes range from 3.0 to 9.5 s with a GM of 5.4 s. Note that one out of nine values of RT, 9. 5 s, is larger than the estimated upper limit of 8.5 s. The charge transf er for the first 5 s ranges from 79 to 496 mC with the GM being 303 mC. The GM peak radiated power and energy radiated for the first 5 s are 29 GW (ranging from 12 to 70 GW) and 24 kJ (ranging from 7.5 to 52 kJ), respectively. We now discuss uncertainties in estimated parameters for the 9 events. For the lower bound on speed (2 x 108 m/s), all radiator lengths (86 to 114 m) are near the assumed lower bound, 100 m (Section 4.2.7), which is expected because reflection signatures should be pronounced only for the shortest channe ls. For the upper bound on speed (3 x 108 m/s), the channel lengths would in crease by a factor of 1.5 to range from 129 to 171 m. Since the inferred peak current and charge transfer are inversely proportional to channel length within the Hertzian

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191 dipole approximation (see Section 4.3.1), these two parameters would de crease by a factor of 1.5. Thus, the uncertainty in our current and ch arge transfer estimates for the 9 events is 25% for the assumed v = 2.5 x 108 m/s. The current risetimes, peak power, and energy values, on the other hand, are independent of ch annel length (and hence of assu med speed) and will remain the same as those for 2.5 x 108 m/s. Table 4-12 summarizes the peak current and charge transfer at 5 s each scaled to different channel lengths (inf erred using measured channel traversal times and different assumed propagation speeds) for the 9 CIDs. Note that since all h values are less than 200 m (even for v = 3 x 108 m/s), all nine events can be reasonable approximated by Hertzian dipo les for almost the enti re "allowed" range of current zero-to-peak risetimes (a bout 2 to 8.5 s). As a result, the inferred current risetimes (ranging from 3 to 9.5 s with the GM being 5.4 s) should be close to their true values, confirming our assumed typical ze ro-to-peak risetime of 6 s. For the remaining 39 events, which did not ex hibit reflection signatures, the electrical parameters were estimated for three assumed valu es of channel length, 170, 350, and 500 m, for which the Hertzian dipole approximation is valid (for RT = 6 s) if the implied propagation speeds are 108, 2 x 108, and 3 x 108 m/s, respectively. CID electrical parameters for h = 170 m, 350 m, and 500 m are compared in Table 4-13. The geometric mean values of peak current for the assumed channel length values of h = 170 m, 350 m, and 500 m were 132, 64, and 45 kA, respectively. The corresponding geometric mean charge transf ers at 5 s were 293, 142, and 100 mC. Note that for the 39 events the Hertzi an dipole validity domain is smaller than the "allowed" domain. As a result, we cannot assi gn any specific uncertainty to the estimated parameters in this case.

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192Table 4-11. Parameters of nine located CI Ds with channel lengths estimated using re flections in dE/dt waveforms and assumed propagation speed of 2.5 x 108 m/s. Event ID Distance (km) Radiator Height (km) Electric Field at 100 km (V/m) Radiator Length (m) Peak Current (kA) Zero-toPeak Current Risetime (s) 10-90% Current Risetime (s) Charge Transfer at 5 s (mC) Peak Power (GW) Energy at 5 s (kJ) 082408_427 19 15 14 138 140 7.9 3.9 243 18 17 083008_09 89 19 35 108 197 3.8 1.5 496 70 52 083008_31 52 16 28 138 259 5.9 3.4 441 28 39 083008_45 50 16 30 128 142 3.4 1.5 412 50 40 083008_52 50 17 30 139 148 3.0 1.4 493 59 50 091008_138 33 16 14 134 118 9.5 4.9 79 12 9.1 091008_140 36 13 22 142 104 4.7 1.6 272 28 23 091008_161 30 10 21 123 157 6.9 3.6 412 36 25 091008_176 43 8.8 16 113 87 7.0 3.9 230 12 7.5 AM 45 14 24 129 150 5.8 2.9 342 35 29 GM 41 14 22 129 143 5.4 2.6 303 29 24 Min 19 8.8 14 108 87 3.0 1.4 79 12 7.5 Max 89 19 35 142 259 9.5 4.9 496 70 52

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193 Table 4-12. Peak current and charge transfer at 5 s scaled to di fferent channel lengths that were inferred for 9 CIDs using reflections in measured dE/dt waveforms and assumed propagation speeds. h m Peak current, kA Charge Transfer at 5 s, mC v, m/s AM GM Min Max AM GM MinMax AM GM MinMax 2 x 108 (lower bound) 103 103 86 114 188 179 108 324 427 379 98 621 3 x 108 (upper bound) 155 154 129 171 125 119 72 216 285 253 65 414 2.5 x 108 (average) 129 129 108 142 150 143 87 259 342 303 79 496 Table 4-13. Peak current and char ge transfer at 5 s scaled to different channel lengths for 39 CIDs. Peak current, kA Charge Transfer at 5 s, mC h m v (allowed) m/s AM GM Min Max AM GM Min Max 170 108 142 132 68 328 327 293 45 706 350 2 x 108 69 64 33 160 159 142 22 343 500 3 x 108 48 45 23 112 111 100 15 240 Figures 4-36 to 4-41 show histograms for the peak current, zero-to-peak current risetime, 10-to-90% current risetime, charge transfer at 5 s, peak radiated power, and energy at 5 s, respectively, for all 48 events, in cluding 9 events with channel le ngths estimated from reflection signatures (for an assumed propagation speed of 2.5 x 108 m/s) and 39 events with an assumed channel length of 350 m (implied v 2 x 108 m/s). The minimum, maximum, arithmetic, and geometric mean values for each parameter are gi ven for the 9 and 39 events individually and for all 48 events combined. As noted earlier, curren t risetimes, peak radiat ed power and radiated energy are independent of channel length, while peak current and charge transfer can be scaled to other channel lengths, provided that they are cons istent with the Hertzian dipole approximation. For the 39 CIDs, the geometric mean values of current zero-to-peak risetime and 10-to90% current risetime are 4.9 and 2.5 s, respectiv ely. The geometric mean peak radiated power,

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194 and energy radiated for the first 5 s are 28 GW and 32 kJ, respectively. For all 48 events, GM values of peak current, zero-to-peak current risetime, 10-to-90% current risetime, and charge transfer for the first 5 s are 74 kA, 5.0 s, 2.5 s, and 164 mC, respectively. The corresponding geometric mean peak radiated power, and energy ra diated for the first 5 s are 29 GW and 31 kJ. Note that in the distributions of peak current and charge transfer at 5 s (Figures 4-36 and 4-39, respectively) the 9 CIDs with reflection signatures constitute the tail of the histogram, which is related to their shorter inferred channel length s. Overall, the CID current parameters are comparable to their counterparts for first return strokes in cloud-to-gr ound lightning, while their peak radiated electromagnetic power a ppears to be considerably higher. 4.3.4 Upper Bound on Electric Field Prior to CID In this Section, we will consider the CID as a discharge between two spherical charge regions. Such simplified configuratio n is similar to that employed by Cooray [1997] for studying regular cloud discharges. For a CI D current pulse with a peak current of 50 kA, total duration of 30 s, and zero-to-peak risetime of 6 s [see Secti on 4.2.3] the total CID charge transfer (which is the time integral of current), Q is 0.44 C. Let us consider two spherical volumes, one containing +0.44 C of charge and the other -0 .44 C of charge, each with a uniform volume charge density, v, of 20 nC/m3 (absolute value) [e.g., Rakov and Uman 2003; Section 3.2.5]. Then, from 34 3vQb the radius, b of each sphere is 174 m. Let us assume that the vertical distance between the surfaces of these spherical volumes is 100 m (assumed to be approximately equal to the shortest CID channel length), as sh own in Figure 4-42a, and that the medium outside the charged spheres contains zero net charge. Presence of ground and other charges in the cloud is neglected. The 100-m assumption allows us to obtain the upper bound on electric field (all

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195 N = 48 Peak Current, kA 04080120160200240280320 Occurrence 0 2 4 6 8 10 12 14 Figure 4-36. Histogram of peak currents for 48 CIDs. For 9 events with reflection signatures, channel lengths were inferred using cha nnel traversal times measured in dE/dt waveforms and assumed propagation speed of 2.5 x 108 m/s. For the other 39 events an assumed channel leng th of 350 m (implied v 2 x 108 m/s) was used. Statistics given are the arithmetic mean (AM), geom etric mean (GM), minimum value (min), and maximum value (max) for the 9 and 39 events individually and for all data combined. CIDs with reflection signatures CIDs without reflection signatures All CIDs AM, kA 150 69 84 GM, kA 143 64 74 Min, kA 87 33 33 Max, kA 259 160 259 N 9 39 48

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196 N = 48 Zero to Peak Risetime, s 012345678910 Occurrence 0 2 4 6 8 10 Figure 4-37. Histogram of zero-to -peak current risetimes for 48 CIDs. See also caption of Figure 4-36. CIDs with reflection signatures CIDs without reflection signatures All CIDs AM, s 5.8 5.2 5.3 GM, s 5.4 4.9 5.0 Min, s 3.0 2.3 2.3 Max, s 9.5 9.5 9.5 N 9 39 48

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197 N = 48 10 to 90% Risetime, s 0123456 Occurrence 0 2 4 6 8 10 12 14 Figure 4-38. Histogram of 10-to-9 0% current risetimes for 48 CIDs. See also caption of Figure 4-36. CIDs with reflection signatures CIDs without reflection signatures All CIDs AM, s 2.9 2.7 2.7 GM, s 2.6 2.5 2.5 Min, s 1.4 1.1 1.1 Max, s 4.9 5.7 5.7 N 9 39 48

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198 N = 48 Charge Transfer at 5 us, mC 080160240320400480560640 Occurrence 0 2 4 6 8 10 12 Figure 4-39. Histogram of charge transferred at 5 s for 48 CIDs. See also caption of Figure 436. CIDs with reflection signatures CIDs without reflection signatures All CIDs AM, mC 342 159 193 GM, mC 303 142 164 Min, mC 79 22 22 Max, mC 496 343 496 N 9 39 48

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199 N = 48 Peak Radiated Power, GW 020406080100120 Occurrence 0 2 4 6 8 10 12 14 16 18 20 Figure 4-40. Histogram of peak radiated power for 48 CIDs. See also caption of Figure 4-36. CIDs with reflection signatures CIDs without reflection signatures All CIDs AM, GW 35 38 37 GM, GW 29 28 29 Min, GW 12 9.6 9.6 Max, GW 70 124 124 N 9 39 48

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200 N = 48 Radiated Energy at 5 us, kJ 020406080100120140 Occurrence 0 2 4 6 8 10 12 14 Figure 4-41. Histogram of radiated energy at 5 s for 48 CIDs. See also caption of Figure 4-36. other conditions being the same, larger separations between the spheres will result in lower electric fields). For each sphere, the electric field intensity at any point at a distance r from the center of the sphere can be obtained using Gauss's law as 0 3 2 0 3 3{v vr rb E b rb r (4-20) CIDs with reflection signatures CIDs without reflection signatures All CIDs AM, kJ 29 43 40 GM, kJ 24 32 31 Min, kJ 7.5 4.0 4.0 Max, kJ 52 146 146 N 9 39 48

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201 For the positively charged sphere v is positive and the electric fi eld is directed radially outward, while for the negatively charged one it is negative and directed radially inward. For the configuration shown in Figure 4-42 a, the total electric field at a ny point along the line joining the centers of the two spheres is gi ven by superposition of the fiel d contributions (both directed upward) from the two spheres. The total electric field intensity prof ile (solid line) and contributions from the individual spheres (broke n line) are shown in Figure 4-42b. Inside each of the charged spheres, the electric field intensity increases almost linearly with distance from 2 x 104 V/m at the center to a maximum of 1.8 x 105 V/m at the surface. Outside the charged spheres, the electric field intensity is minimum (1.6 x 105 V/m) at a point equidistant from the two spheres. A CID channel is likely to be form ed primarily between the two spherical volumes of charge, where the net electric charge is assume d to be zero and the electric field intensity is near its highest values. We will now examine dependence of electric field profile on charge transfer and volume charge density by using the peak currents for the nine events summari zed in Table 4-11, but keeping the same current waveshape (risetime of 6 s and total duration of 30 s). In Section 4.3.3, we estimated the channel lengths for the nine located CIDs using channel traversal times measured in dE/dt waveforms and assumed propagation speed of 2.5 x 108 m/s to range from 108 to 142 m. The inferred peak currents ranged fr om 87 kA to 259 kA, with the geometric mean being 143 kA. The total charge transferred (over 30-s cu rrent duration) for p eak currents of 87, 143, and 259 kA are 0.77 C, 1.3 C, and 2.3 C, respec tively. For a total char ge transfer of 1.3 C and assumed volume charge densities of 2 nC/m3, 20 nC/m3, and 200 nC/m3, the radii of the spherical charge regions are 533 m, 247 m, and 115 m, respectively. The ma ximum electric field intensities (occurring between the sp heres, on their surfaces) are 6.9 x 104, 2.8 x 105, and 1.1 x

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202 106 V/m, respectively. The maximum electric field va lues for different combinations of charge transfer and assumed charge density are summ arized in Table 4-14. Additionally given are minimum and average electric fields between the spherical charge regions and estimated electric potential difference between them. Excep t for the probably unrealistically high v = 200 nC/m3 cases (for which maximum fields range from 7.3 x 105 V/m to 1.4 x 106 V/m), the maximum electric field for all combinations of Q and v considered does not exceed 3.5 x 105 V/m, which is less than the conventional breakdown electric field in the cloud (of the order 106 V/m) and is generally of the order of 104 to 105 V/m. These maximum electric field estimates are for h = 100 m. All other conditions be ing the same, the maximum electric field will decrease with increasing h. If the two spherical charge regi ons were in direct contact ( h = 0) the total electric field profile would have maximum at the point of contact that is given by max 23 0002 2 344vb Qp E bb (4-21) where p = 2 Qb is the dipole moment change for charge transfer Q over a distance of 2 b. Smith et al. [1999] used such a configur ation to impose a lower bound on CID channel length, which they assumed to extend between the centers of th e charged spheres. In doing so, they computed Emax for their average measured dipole moment change, p = 0.38 C km, and different b and compared those field values with electric fields measured in thunderclouds. For b = 50 m (corresponds to their channel length of 100 m), they found Emax = 2.7 x 107 V/m, which is about an order of magnitude greater than the conventional breakdown electric field in the cloud, and concluded that such a short channel was phys ically unrealistic. Our estimated CID channel lengths of the order of 100 m suggest that Smith et al.'s configuration, in which two oppositely charged regions are in direct contact, is inconsis tent with at least some experimental data. In

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203 order to explain such short channel lengths, the charged regions should be separated by a region of essentially zero net charge (w hich can be created due to mixi ng) or by a region of very low charge density compared to the charged regions. 4.3.5 Total Energy Dissipated by CIDs In this Section, we estimate the total ener gy dissipated by a CID with reference to the charge configuration shown in Figure 4-42a. If we assume that a CID neutralizes all the charge in each of the two spherical regions, the total energy dissipated will be equal to the total electrostatic energy stored in this charge configuration. One can find the total electrostatic energy as the sum of the electrostatic energies require d to individually assemble the two uniformly charged spheres (self electrostatic energy [ Cooray 1997]) and the electrost atic energy due the two spherical charge regions being placed in relatively close proximity to each other (mutual electrostatic energy). The self electrostatic energy, W1, of a uniformly charged sphere of radius b containing charge Q can be readily found as [ Cheng, 1993]: 2 1 03 20 Q W b (4-22) This equation can be obtained by integrating the electrostatic energy density, 2 02eE W where E is given by Equation 4-20 for r b, over the spherical volume. Estimation of the mutual electrostatic energy, W2, is more complicated and requires additional simplifying assumptions. We will replace the two spherical charge regions with their equivalent point charges of magnitude +Q and Q located at corresponding sphere cente rs, so that they are separated by distance (2 b + h). This approximation is similar to that employed by Cooray [1997] for

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204Table 4-14. The maximum electric field at the surface of each of the two oppositely ch arged spheres separa ted by a zero net cha rge region (see Figure 4-42a) for different comb inations of charge transfer and assumed volume charge density. The distance h between the surfaces of char ged spheres is assumed to be 100 m. Also given are the minimum and average electric fields, potential difference between the spheres, the total electrostatic energy and its compone nts. See text for details. Peak Current, kA Total Charge Transfer (Q ), C Volume Charge Density (v), nC/m3 Radius of Spherical Charge Regions (b), m Maximum Electric Field Between Spheres (Emax), V/m Minimum Electric Field Between Spheres (Emin), V/m Average Electric Field, Eav = (Emax + Emin )/2, V/m Potential Difference Between Spheres, V Eav h, (V) External Energy, (Q V), J Self ( Internal) Electrostatic Energy (W1), J Mutual Electrostatic Energy (W2), J Total Energy (W = 2W1 + W2), J Total Energy (W = 2W1 + Q V), J 2 375 4.6 x 104 4.4 x 104 4.5 x 104 4.5 x 106 2.0 x 106 2.8 x 106 2.1 x 106 7.7 x 106 7.6 x 106 20 174 1.8 x 105 1.6 x 105 1.7 x 105 1.7 x 107 0.7 x 107 6.1 x 106 3.9 x 106 1.6 x 107 1.9 x 107 50 0.44 200 81 7.3 x 105 4.7 x 105 6.0 x 105 6.0 x 107 2.6 x 107 1.3 x 107 6.7 x 106 3.3 x 107 5.2 x 107 2 451 5.7 x 104 5.5 x 104 5.6 x 104 5.6 x 106 4.3 x 106 7.1 x 106 5.3 x 106 2.0 x 107 1.9 x 107 20 210 2.3 x 105 2.1 x 105 2.2 x 105 2.2 x 107 1.7 x 107 1.5 x 107 1.0 x 107 4.1 x 107 4.7 x 107 87 (Min) 0.77 200 97 9.1 x 105 6.4 x 105 7.8 x 105 7.8 x 107 6.0 x 107 3.3 x 107 1.8 x 107 8.4 x 107 1.3 x 108 2 533 6.9 x 104 6.7 x 104 6.8 x 104 6.8 x 106 8.8 x 106 1.6 x 107 1.2 x 107 4.5 x 107 4.1 x 107 20 247 2.8 x 105 2.6 x 105 2.7 x 105 2.7 x 107 3.5 x 107 3.5 x 107 2.4 x 107 9.4 x 107 1.1 x 108 143 (GM) 1.3 200 115 1.1 x 106 8.4 x 105 1.0 x 106 1.0 x 108 1.3 x 108 7.5 x 107 4.4 x 107 1.9 x 108 2.8 x 108 2 649 8.6 x 104 8.4 x 104 8.5 x 104 8.5 x 106 2.0 x 107 4.4 x 107 3.4 x 107 1.2 x 108 1.1 x 108 20 301 3.5 x 105 3.3 x 105 3.4 x 105 3.4 x 107 7.8 x 107 9.4 x 107 6.7 x 107 2.6 x 108 2.7 x 108 259 (Max) 2.3 200 140 1.4 x 106 1.1 x 106 1.3 x 106 1.3 x 108 3.0 x 108 2.0 x 108 1.2 x 108 5.3 x 108 7.0 x 108

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205 Figure 4-42. (a) Simplified charge configuration giving rise to a CID. The CID channel length, h = 100 m, is assumed to be approximately equal to the distance between the two charged regions. The electric field vector points upward and is assumed to be positive. (b) The electric field intensity as a function of z for x = 0 that is produced by each of the two charged regions (broken line) shown in (a) and the total electric field profile (solid line). Field and electrosta tic energy values for this and other configurations are gi ven in Table 4-14. studying the energy dissipated by regular cloud di scharges. The mutual electrostatic energy W2 of these two point charges is given by [ Cheng, 1993]: 2 2 04(2) Q W bh (4-23) Thus, the total electrostatic energy W of the overall charge co nfiguration, and hence the energy dissipated by a resultant CID can be found as 122 WWW (4-24) Estimates of energy dissipated by a CID havi ng a 100 m long channel for different values of total charge transfer Q (estimated for a fixed current waveshape and different peak currents)

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206 and volume charge density v are given in Table 4-14. The assumed volume charge density v is used to compute b in Equation 4-22 for a given Q For a charge transfer of 0.44 C (peak current of 50 kA), the total dissipated energy values are 7.7 x 106, 1.6 x 107, and 3.3 x 107 J for charge densities of 2, 20, and 200 nC/m3, respectively. For a charge density of 20 nC/m3 and charge transfers ranging from 0.44 C to 2.3 C the energy values range from 1.6 x 107 to 2.6 x 108 J. The corresponding energy per unit length ranges from 1.6 x 105 to 2.6 x 106 J/m. It follows from Equations 4-22 to 4-24 that, all other conditions remaining the same, the mutual electrostatic energy W2 due to the two equivalent point charges and hence the total electrostatic energy of the charge configuration shown in Figure 4-42a decreases with increasing the CID channel length. Thus, th e values of total CID energy given above for the lower bound on channel length of 100 m should be viewed as the upper bound. For a CID current pulse with a peak of 50 kA described in Section 4.2.3, assumed v = 20 nC/m3, and channel lengths of 350, 500, and 1000 m, the total electrostatic energy values will be 1.47 x 107, 1.42 x 107, and 1.35 x 107 J, respectively, versus 1.6 x 107 J for h = 100 m. In our calculations of electr ostatic energy, we have neglec ted the effect of ground. This simplifying assumption should not introduce a si gnificant error because (1) CIDs occur at relatively large altitudes, typically greater than 10 km [ Smith et al., 2004; Section 4.1] and (2) W2 is inversely proportional to the distance between equivalent point charges. Indeed, the mutual electrostatic energy between a char ge and its image separated by more than 20 km is at least an order of magnitude smaller than that between the two actual ch arges separated by less than 1.4 km (the limiting case in Table 4-14; h = 100 m). This is true even for CID channel lengths of 1000 m in which case the two equi valent point charges represen ting the actual charges are separated by le ss than 2.3 km.

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207 The total electrostatic energy of the charge configuration shown in Figure 4-42a can be alternatively estimated as the su m of energies stored inside th e two spheres and energy stored between them. The internal energy can be comput ed as the volume integral of energy density, 2 02 E, which is different from the self energy W1 in that E within each sphere should additionally include the contributi on from the other sphere. As a zero approximation, we neglect this difference and assume that the internal energy is not much different from self energy W1 (the larger the separation between the spheres the sm aller the difference). We will roughly estimate the external energy as the product of charge transfer Q and potential difference V between the surfaces of the two spheres, with V being found as the average electric field intensity Eav between the spheres times the distance h between their surf aces. Values of Eav, V and the total energy, W = 2 W1 + Q V are given in Table 4-14. The total electrostatic energy values estimated using the two different approaches are fairly similar, particularly for lower (2 and 20 nC/m3) values of v. As expected, the GM electromagnetic energy of 31 kJ ra diated during the first 5 s (s ee Figure 4-41) is much lower than the total CID energy estimates based on electrostatic considerations (see Table 4-14). 4.3.6 Discussion Smith et al. [1999], using distant (essentia lly radiation) electric fi eld signatures of 15 CIDs from thunderstorms in New Mexico and west Texas, estimated the mean CID dipole moment change to be 0.38 C km. The minimum and ma ximum values were 0.26 and 0.80 C km. The mean dipole moment change duratio n (10-90%) for the 15 CIDs was 13.7 s. They also inferred that CID channel lengths should be in the range of 300 to 1000 m. Using the mean dipole moment change (0.38 C km) and the limiting channel lengths we estimate the range of charge transfers for their CIDs to be 0.38 C to 1.27 C. Our estimated charge transfers for the first 5 s

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208 are of the order of tens to hundreds of millicoulombs (see Tables 4-11, 4-12 and 4-13, and Figure 10) and are apparently consistent with Smith et al.'s values which correspond to the mean charge transfer time of 13.7 s. Eack [2004], using simultaneous measurements of electric fields at near and far distances for seven CIDs, estimated that, on average, a CI D transferred 0.3 C over a distance of 3.2 km. These results are based on a value of speed deri ved from the misinterpreted dipole approximation equation (see Section 4.2.9) and, therefore, are invalid. For one event produced by a New Mexico thunderstorm, Eack also estimated the peak curren t of 29 kA from the measured predominantly induction electric field peak (assu ming a uniform current over the entire channel length). For the same event, Watson and Marshall [2007], using the transmission line model, inferred a considerably larger p eak current of 74 kA, which is about the same as our estimates based on both the bouncing-wave model and Hertzi an dipole approximation (see Section 4.2.8). For downward negative lightning, Berger et al [1975] reported a median total charge transfers of 5.2 C and 1.4 C for first str okes and subsequent strokes, respectively. Schoene et al. [2009] reported the geometric mean charge transfer within 1 ms after the beginning of the return stroke for 151 negative rocket-triggered lightning strokes (which are similar to subsequent strokes in natural lightning) to be 1.0 C. Us ing in-situ measured el ectric field profiles, Maggio et al. [2009] estimated the average (p robably arithmetic mean) charge transferred by 29 IC flashes to be 17.6 C. Thus, charges transferred by individual CG strokes and by regular ICs are considerably larger than those transferred within the first 5 s by CIDs. Rakov et al. [1998], from two-station measurements of electric and magnetic fields of a dart-stepped leader in triggered-lightning, estima ted that the formation of each leader step is associated with a charge of a few millicoloum bs and a current of a few kiloamperes. From

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209 measurements of electric field pul ses radiated by leader steps of first strokes in natural lightning, Krider et al. [1997] inferred that the minimum charge i nvolved in the formation of a step is 1-4 mC and the peak step current is at least 2-8 kA. The charge transfers for cloud-to-ground lightning leader steps are one to two orders of magnitude smalle r than those transferred during the first 5 s by CIDs. Our estimated CID peak currents of tens to hundreds of kiloamperes are at least an order of magnitude grea ter than those expected for leader steps. Note that the stepformation process is thought to occu r on a time scale of the order of 1 s, and typical step lengths are 10 and 50 m for dart-stepped and st epped negative leaders, respectively [ Rakov and Uman 2003]. Krider et al. [1968] estimated the peak input power per unit channel leng th for a natural lightning first stroke to be 7.8 x 108 W/m. Jayakumar et al. [2006] estimated the mean value of peak input power per unit length for tr iggered-lightning strokes to be 9.6 x 108 W/m. Krider and Guo [1983] and Krider [1992] estimated the wideband radi o-frequency electromagnetic power radiated by a subsequent return st roke at the time of the electric field peak to be 3 to 5 GW. The average zero-to-peak risetime of the subs equent-stroke field waveforms was 2.8 s, so that the radiating channel length at the time of field p eak was probably some hundreds of meters, which is comparable to the channel length for CIDs. Our arithmetic mean peak radiated power (wideband) of 37 GW found for 48 CIDs is about an order of magnitude higher than the above estimates for subsequent return strokes. For first strokes, Krider and Guo [1983] estimated an arithmetic mean peak electromagnetic power of 20 GW, which is still lower than our estimate for CIDs. Rison et al. [1999] and Thomas et al. [2001] each reported the peak radiated power in the narrowband VHF (60-66 MHz) frequency range of the Lightning Mapping Array (LMA) for one

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210 New Mexico CID to be greater than 100 kW and greater than 300 kW, resp ectively. Source peak powers radiated at 60-66 MHz by "normal" lightning processes ranged from 1 W (minimum locatable value) up to 10-30 kW [ Thomas et al. 2001]. Rison et al [1999] stated that the peak VHF radiation from CIDs was typically 30 dB (a factor of 1000) stronger than that from other lightning processes. Assuming a potential difference of 108-109 V between the earth and a cloud charge source, Uman [1987] estimated from electrostatic considerat ions the input energy for lightning leaderreturn stroke sequences lowering 5 C of charge from a height of 5 km to ground to range from 1 to 10 x 105 J/m. Hence the total energy for a 5 km long channel would be in the range of 5 to 50 x 108 J. For the same assumed channel length and charge transfer and using the concepts of self and mutual electrostatic energy, Cooray [1997] estimated that the en ergy dissipated by a typical first leader-return str oke sequence is 5.5 x 108 J. For cloud discharges occurring between two vertically separated spherical ch arge regions and neutralizing ch arges ranging from 1 to 8 C, Cooray [1997] found the dissipated energy to range from about 2.5 x 108 to 18 x 108 J. We estimated the energy dissipated by CIDs having a channel length of 100 m and neutralizing total charges in the range of 0.44 to 2.3 C, to be in the range of 7.7 x 106 to 5.3 x 108 J. For a 1-C charge transfer, the CID energy is 5.3 x 107 J, which is about a factor of 5 smaller than 2.5 x 108 J estimated by Cooray for regular cloud discharges. As stat ed in Section 4.3.5, all other conditions remaining the same, for channel lengt hs greater than 100 m th e total electrostatic energy of the configuration shown in Figure 4-42a and hence the energy dissipated by CIDs will be lower. Our estimates of CID energy per unit channel leng th (based on values in the next to last column of Table 4-14 and h = 100 m) range from 7.7 x 104 to 5.3 x 106 J/m. Interestingly, the

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211 input energy per unit length for a natu ral lightning first stroke of 2.3 x 105 J/m reported by Krider et al. [1968] is within this range. For triggered lightning strokes, Jayakumar et al. [2006] estimated the mean value of input energy per unit length for 36 triggered-lightning strokes to be 3.6 x 103 J/m, which is more than an order of magnitude smaller than the lower bound estimated here for CIDs. Cooray [1997] estimated the energy dissipated by a typical first leader return stroke sequence to be 5.5 x 108 J for a 5-km long channel, which corresponds to 1.1 x 105 J/m. Assuming that the first stroke channel length ranges from 5 to 8 km [e.g., Rakov and Uman 2003] and Cooray's value of energy per unit length, we estimated the total energy range to be from 5.5 to 8.8 x 108 J. As noted above, Cooray [1997] estimated the dissipated energy for regular cloud discharges to be about 18 x 108 J for a charge transfer of 8 C. The corresponding channel length was 2.5 km. Taking the charge transfer of 8 C as typical for cloud discharges we estimate the energy per unit channel length to be 7.2 x 105 J/m. Using this latter value and the range of IC channel leng ths of 2 to 5 km [e.g., Shao and Krehbiel 1996], we estimate the IC energy range of 1.4 to 3.6 x 109 J. Using median charge transfers and average in-cloud potentials, Maggio et al. [2009] estimated the energy dissipat ed by 16 IC flashes to be 1.5 x 109 J per flash, which is near the lower bound of our range. Chan nel lengths for CIDs ar e within the range of 100 m to 1000 m (see Section 4.2). As seen in Table 4-14, the energy dissipated by a CID with h = 100 m and v = 20 C/m, dissipating 1.3 C of charge, is about 108 J, or 106 J/m. Using this energy per unit length and the rang e of channel lengths, we estimate the range of total energy dissipated by CIDs to be 108 to 109 J. Figure 4-43 summarizes the ranges of total energy dissipated by first strokes in cloud-to-ground discharges, regular intracloud discharges, and CIDs along with corresponding ranges for channel length. It appears that CIDs do not tend to surpass

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212 either cloud-to-ground first strokes or regular cloud discharges in terms of energy. Hence, the labels like "energetic intracloud discharges" [e.g., Eack, 2004; Smith et al. 2004] and "highenergy discharges" [ Watson and Marshall 2007] that are sometimes used to refer to CIDs are probably not justified. As seen in Figure 4-43, th e most distinctive feature of CIDs (besides their very intense HF-VHF radiation) is their small spatial extent. Figure 4-44 shows the NLDN-reported peak curre nt versus peak current estimated using the Hertzian dipole (HD) approxi mation for 48 CIDs. For 9 events, channel lengths were inferred using channel traversal times measured in dE/d t waveforms and assumed propagation speed of 2.5 x 108 m/s. For the other 39 events, an assumed ch annel length of 350 m (w hich implies that v 2 x 108 m/s) was used. The majority of NLDN-repor ted peak currents are considerably smaller than those predicted by the Hertzian dipole ap proximation. Some discrepancy is expected because NLDN-reported peak currents are assumed to be proportional to peak fields, which is a reasonable approximation for return strokes, while for the Hertzi an dipole approximation, which applies to electrically short ra diators, the peak of radiati on electric field component is proportional to the peak of current time derivative (d i /dt) (see Equation 4-13) It follows that the CID current peak is proportional to the peak of the integral of radiation electric field, which occurs at the time of field zero-crossing. In or der to examine this discrepancy further, we computed CID peak currents using measured elec tric field peaks and the transmission line model [ Uman and McLain 1969] with v = 1.8 x 108 m/s. The assumed value of speed provides a good match between NLDN-reported peak currents and those estimated using the TL model for negative first and subsequent re turn strokes (see Chapter 7, Figure 7-33). Thus, the TL-model based calculations presented here simulate, to some extent, NLDN peak current estimates. The results are shown in Figure 4-45. Clearly, the di screpancy between the TL-model predictions and

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213 NLDN-reported values is appreciably smaller th an in Figure 4-44, but there seem to be additional factors that make NLDN-reported curr ents underestimates. One of these factors is field attenuation due to its propagation over lossy ground. It is seen in Figure 4-45 that the discrepancy tends to increase with increasing the p eak current. Events with larger peak currents are reported by a larger number of NLDN stations and, hence, their NLDN-reported current is more influenced by more strongly attenuated contributions from dist ant stations. The NLDN current estimation procedure does include comp ensation for far field propagation effects. However, if this compensation is not sufficient, the NLDN-reported peak current will be an underestimate. The 48 CIDs were reported by 4 to 22 (11 on average) NLDN stations, so that contributions from distances up to 625 km were included, while the distances for our TL model estimates were considerably smaller, ranging from 12 to 89 km. Another f actor is the significant elevation of CIDs above ground. CIDs typically occur at heights greater than 10 km and hence radiation field peaks at relatively close distances can be significan tly reduced relative to the case of sources near ground level, which is assume d in the NLDN field-to-current conversion equation. This can additionally contribute to underestimation of CID peak currents by the NLDN. 4.4 Summary Compact Intracloud Discharges (CIDs) are cl oud lightning discharges that produce single bipolar electric field pulses (socalled Narrow Bipolar Pulses or NBPs) having typical full widths of 10 to 30 s and intense HF-VHF radiation bursts (much more intense than those from any other cloud-to-ground or norma l cloud discharge process). We examined wideband electric fields, electric and magnetic field derivatives, and narrowband VHF (36 MHz) radiation bursts produced by 157 CIDs. These lightning events appear to be the strongest natural producers of HF-VHF radiation. The initial polarity of di stant wideband electric field pulses produced by

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214 Figure 4-43. Ranges of dissipated energy and channel length for t ypical first strokes in cloud-toground flashes, regular intrac loud flashes, and CIDs. Charge transfers were assumed to be 5 C, 8 C, and 1.3 C for these th ree types of discharges, respectively. Peak Current Based on HD Approximation, kA 050100150200250300 NLDN Reported Peak Current, kA 0 50 100 150 200 250 300 9 events with h estimated from channel traversal times 39 events with assumedh = 350 m Figure 4-44. NLDN-reported peak current versus peak current estimated using the transmission line model with v = 1.8 x 108 m/s for 48 CIDs. Hollow and solid circles represent the two subsets of events identified in Figure 15.

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215 Peak Current Based on TL Model, kA 020406080100120140 NLDN Reported Peak Current, kA 0 20 40 60 80 100 120 140 9 events with h estimated from channel traversal times 39 events with assumedh = 350 m Figure 4-45. NLDN-reported peak current versus peak current estimated using the Hertzian dipole (HD) approximation for 48 CIDs. Fo r 9 events (hollow circles), channel lengths were inferred using channel traversa l times measured in dE/dt waveforms and assumed propagation speed of 2.5 x 108 m/s. For the other 39 events (solid circles) an assumed channel length of 350 m (with implied v 2 x 108 m/s) was used. these CIDs was negative (opposite to that of ne gative return strokes). NLDN located 150 of the 157 CIDs at distances ranging from 5 to 132 km from the measurement station and correctly identified 149 (95%) of them as cloud discharg es. Different types of electric field waveforms arepresented and discussed. The majority (about 72%) of CIDs appeared to occur in isolation from any other lightning process, while about 24% were found to occur prior to, during, or following CG or normal IC lightning. About 18% were associated with cloud flashes and 6% with ground ones. In three cases tw o CIDs occurred within 43, 66, and 181 ms of each other (the first documented "multiple" CIDs), with a total of 4% of CIDs occurring in pairs. For 48 CIDs, the geometric means of source height and electr ic field peak normalized to 100 km and zero elevation angle were estimated to be 16 km a nd 20 V/m, respectively. The geometric means of

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216 total pulse duration, width of initial half-cycle, an d ratio of initial electr ic field peak to opposite polarity overshoot were 23 s, 5.6 s, and 5.7, respectively. We examined the electric field derivative (d E/dt) signatures of 212 CIDs in Florida and found multiple secondary peaks (osc illations), which are indicativ e of reflections, in 15% of them. It is likely that the waveforms showing pronounced reflections correspond to shortest CID channels. The shortest radiat ing channel length appears to be about 100 m. Based on the experimental evidence of multiple reflections and m odeling, we infer that the CID is essentially a bouncing-wave phenomenon. Some tens of reflecti ons may occur at both radiating-channel ends. It is possible that the bouncing waves serve to maintain channe l conductivity. Only higher-order reflections (in the later portion of the waveform) are de tectable (if at all) in either electric field or dE/dt waveforms, while the undetectable lower-ord er reflections do influence the magnitude of the primary signature. In about 85% dE/dt signatures no reflections were observed. Factors that can make reflections undetectable include a rela tively small magnitude of the incident wave, relatively long radiating channel, relatively large losses along the ch annel, and a relatively small (in absolute value) current reflection coeffici ents at channel ends. Reflections at channel extremities may result in corona-like electrical breakdown there, because a reduction of current is accompanied by an increase of line charge dens ity and associated voltage (voltage doubles at an open circuit end and increases by a factor of 1.5 if the current reflection coefficient = -0.5). This breakdown at channel ends is likely to produce intense bursts of HF-VHF radiation and increase "noisiness" of dE/dt signatures, whic h are characteristic feat ures of CIDs. Thus, reflections are responsible for the fine structur e of wideband electric field and dE/dt waveforms and, by inference, for noisiness of dE/dt waveforms and for accompanying HFVHF radiation bursts.

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217 We modeled the CID as a wave traveling on an elevated vertical transmission line. In order to account for multiple reflections that take place at the channel ends we specified two equivalent current sources, connected at the bottom and at the top of the channel. By comparing modelpredicted electric fields with measurements we estimated that effective current reflection coefficients at channel ends should be in the ra nge of 0 to -0.5, that the wave propagation speed ranges from 0.3 to 3 x 108 m/s, and channel length is less than 1000 m. In these calculations, we assumed that the current wave had a risetime of 6 s and a total duration of 30 s. Influence of current risetime on field waveform s was also examined, and it was found to be typically in the range from about 2 to 8.5 s. The current dist ribution along the CID channel is often not much different from uniform, as expected for a Hert zian (electrically shor t) dipole, because of relatively short channel length, relatively long cu rrent waveform, and relatively high propagation speed. Both the bouncing-wave model and the He rtzian-dipole approximations are capable of reproducing two-station CID elect ric field measurements of Eack [2004]. We estimated electrical parame ters of 48 located CIDs using their measured electric fields and vertical Hertzian dipole a pproximation. This approximation is consistent with the bouncingwave model for a reasonably large subset of allowed combinations of propagation speed and channel length. For example, for current zero-topeak risetime RT = 6 s and propagation speed v = 2 x 108 m/s the allowed range of channel length, h, is from 100 to 700 m, with the Hertzian dipole approximation being valid for h up to 375 m. For nine events, we estimated CID channel lengths from channel traversal times measured in dE/dt waveforms and assumed propagation speeds of 2 x 108 m/s and 3 x 108 m/s, which cover the entire ra nge of allowed values. For v = 2.5 x 108 m/s, the channel lengths for these nine events ranged from 108 to 142 m. The corresponding geometric mean values of peak current, zero-to-peak current risetime, 10-to-90%

PAGE 218

218 current risetime, and charge transfer for the fi rst 5 s are 143 kA, 5.4 s, 2.6 s, and 303 mC, respectively. The geometric mean peak radiated power, and energy radiated for the first 5 s are 29 GW and 24 kJ, respectively. For the remaining 39 events, there were no reflection signatures observed, and h was assumed to be 350 m, for which the Hertzian dipole approximation is valid for speeds in the range of 2 to 3 x 108 m/s. In this case, geometric mean values of peak current, zero-to-peak current risetime, 10-to-90% current risetime, and charge transfer for the first 5 s are 64 kA, 2.5 s, and 142 mC, respectively. Th e geometric mean peak radiated power, and energy radiated for the first 5 s are 28 GW a nd 32 kJ, respectively. Radiated power and energy are independent of h, while peak current and charge transf er can be scaled to other channel lengths, provided that they are consistent with the Hertzian dipole approximation. For the 39 events, we additionally considered h = 170 m, which is consistent with v 108 m/s, and h = 500 m, which is consistent with v = 3 x 108 m/s. For all 48 events, GM values of peak current, zero-to-peak current risetime, 10-to-90% current risetime, and charge transfer for the first 5 s are 74 kA, 5 s, 2.5 s, and 164 mC, respectively. The geometric mean peak radiated power, and energy radiated for the first 5 s are 29 GW and 31 kJ, respectively. Overall, the estimated CID current waveform parameters are comparable to their counterparts for fi rst strokes in cloud-toground lightning, while their peak radiated electromagnetic power appears to be considerably higher.

PAGE 219

219 CHAPTER 5 PRELIMINARY BREAKDOWN PULSE TRAINS IN NE GATIVE CL OUD-TO-GROUND LIGHTNING AND IN ATTEMPTED LEADERS In this chapter preliminary breakdown (PB) pulse trains are char acterized in detail. Additionally, lightning events exhibiting pulse trains that are characteristic of preliminary breakdown in negative cloud-to-gro und discharges, but are not followed by return stroke waveforms are analyzed. Further, relationship between the lower positive charge region (LPCR) in thunderclouds (see Chapter 2) and the occurrence of PB pulse trains is examined. Assuming that the preliminary breakdown pul se train is a manifestation of interaction of a downwardextending negative leader channel with the lower positive charge region, the inferred dependence of lightning type on the magnitude of this charge region is qualit atively examined. Finally a set of conceptual scenarios for the occurrence of PB pulse trains are proposed that can be tested by future observations. 5.1 Characterization of Microsecondand Sub microsecond-Scale Electric Field Pulses Prior to First Return-Stroke Waveforms Microsecondand submicrosecond-scale pulses in electric fi eld records of cloud-to-ground lightning discharges acquired in summer 2006, in Gainesville, Florida were examined. A total of 12 ground flashes were analyzed in detail, with the electric field record length being 96 or 200 ms and sampling interval being 4 or 10 ns. Only pulses prior to the first return stroke in each flash were examined. 93% (655 out of 706) of thes e pulses were associated with the preliminary breakdown pulse train. The majority of them we re relatively small in amplitude and duration. The peak-to-peak amplitude of each bipolar pulse and zero-to-peak amplitude of each unipolar pulse in a particular cloud-to-ground discharge was normalized with respect to that of the largest preliminary breakdown pulse (which was also the larg est pulse prior to the fi rst return stroke) in that flash. Pulses were classified into four different categories depending upon the value of their

PAGE 220

220 normalized amplitude as shown in Table 5-1. The time at which the first return stroke occurred was relabeled as the zero of the time scale (t=0) and positions of all other pulses on the time axis were determined with respect to it. Only pul ses with peak-to-peak amplitudes equal to or exceeding twice that of the local average noise level were considered. The electric field record of each prelimin ary breakdown pulse train was examined using different time windows (mostly tens of microseconds). Overall preliminary breakdown pulse train duration is defined as the time interval between the peaks of the first and last pulses in the train. Pulses were considered as not belonging to the pulse train if they were separated from the last pulse of the train by at leas t 2 ms. Pulse duration is defined as the full width of the pulse, and interpulse interval is defined as the time inte rval between the peaks of two consecutive pulses. Further, in order to examine th e occurrence of pulses in different parts of preliminary breakdown pulse trains, each pulse train was divided into four quarters, and the number of pulses within each quarter was counted. Table 5-1. Categorization of pulses according to normalized amplitude. Normalized Pulse Amplitude Category 0.25 Very Small > 0.25 and 0.5 Small > 0.5 and 0.75 Medium > 0.75 and 1.0 Large For each of the 12 cloud-to-ground discharges th e following characteristics were examined: Occurrence of pulses of different amplitude versus time prior to the first return stroke. Occurrence of pulses of different total duration versus time. Statistical distribution of pulse amplitude. Statistical distribution of total pulse duration. Figure 5-1 shows an example of the measured electric field wavefo rm of a cloud-to-ground discharge (flash 05/24/06_1078). In addition to classical pr eliminary breakdown pulses (see Figure 5-2a) having durations of the order of te ns of microseconds, previously not reported

PAGE 221

221 Figure 5-1. (a) Electric fiel d record of cloud-to-ground flas h 05/24/06_1078 showing preliminary breakdown pulse train followed by two return strokes. Note that the return-stroke peaks are smaller than those of some preliminary-breakdown pulses. (b) The preliminary breakdown pulse train shown on a 1.05 ms time scale. (b) (a)

PAGE 222

222 narrow pulses with durati ons less than or equal to 4 s (see Figure 5-2b) were also observed. Figures 5-3 to 5-6 show results of the analys is for the flash presented in Figure 5-1. The overwhelming majority (about 93%) of the 706 pulses in the 12 cloud-to-ground discharges examined in this study were associated with the preliminary breakdown pulse trains typically occurring tens of milliseconds before the first re turn-strokes of the flashes and lasting for a few milliseconds, as seen in Figures 5-3 and 5-4. Typi cally, the majority of pulses in a flash were found to be small or very small in amplitude and to have durations less than or equal to 4 s. Also, pulses with durations less than or equal to 4 s (including submicrosecond-scale pulses) were found to occur both before and after the la rgest pulse in the preliminary breakdown pulse train. Table 5-2 summarizes the occurrence of sma ller and narrower pulses in the 12 selected cloud-to-ground discharges. It was found that, for individual flashes, 57 to 98% of the pulses belonged to the small and very small amplitude cat egories. Further, 22 to 89% of the pulses had durations less than or equal to 4 s. Figure 5-7 shows the distribution of total durations of pulses in all the 12 cloud-to-ground flashes. It can be seen from this Figure that 78% (553 out of 706) of the pulses had durations less than or equal to 4 s, of which 87% (479 out of 553) were bipolar, and that 22% (157 out of 706) of the pulses had durations less than 1 s. The arithmetic mean pulse duration was 4.7 s, which is outside the 20 s range of typical dur ations usually given for classical preliminary breakdow n pulses in ground discharges [e.g., Rakov and Uman 2003]. A moderate linear correlation was found betw een the amplitude and duration of pulses. Figure 5-8 shows the occurrence of 655 pulse s in four quarters of the preliminary breakdown pulse train for all the 12 cloud-to-gro und flashes. The majority (532 of 655 or 81%) of the preliminary breakdown pulses occur during the fi rst half of the pulse train. Also, 87% (129

PAGE 223

223 Figure 5-2. Examples of (a) classical and (b ) narrow preliminary breakdown pulses in cloudto-ground discharges analyzed in this study. of 148) of the pulses with to tal durations greater than 4 s occur during the firs t half of the pulse train. Figure 5-9 shows the histogram of the total duration of 655 prelim inary breakdown pulse trains in 12 cloud-to-ground flashes. The range of variation and arithmetic mean of total pulse train durations are 1.1.0 ms a nd 3.4 ms, respectively. Figures 5-10 and 5-11 show ranges of variation (vertical bars) of pulse duration and interpul se interval in individual pulse trains,

PAGE 224

224 N = 97 NL = 1 NM = 1 NS = 3 NVS = 92 Time (ms) -50-45-40-35-30-25-20-15-10-50 Number of Pulses 0 20 40 60 80 100 120 Large (L) Medium (M) Small (S) Very Small (VS) Figure 5-3. Occurrence of pulses of different amp litude prior to the first stroke of cloud-toground flash whose electric field record is shown in Figure 5-1. Inset shows the occurrence of pulses of different amplitude between -19.5 ms and -14 ms using bin size of 500 s. N = 97 N (<1 ms) = 13 N (1-4 ms) = 69 N (>4 ms) = 15 Time (ms) -50-45-40-35-30-25-20-15-10-50 Number of Pulses 0 20 40 60 80 100 120 Submicrosecond 1-4 microseconds Above 4 microseconds Figure 5-4. Occurrence of pulses of different total duration prior to the first stroke of cloud-toground flash whose electric field record is shown in Figure 5-1. Inset shows the occurrence of pulses of different total dur ation between -19.5 ms and -14 ms using bin size of 500 s. Time (ms) -19-18-17-16-15-14 Number of Pulses 0 5 10 15 20 25 30 Time (ms) -19-18-17-16-15-14 0 5 10 15 20 25 30 Number of Pulses

PAGE 225

225 N = 97 NBP = 85 NUP = 12 Normalized Amplitude 0.00 0.25 0.50 0.75 1.00 Number of Pulses 0 20 40 60 80 100 Positive Bipolar Negative Bipolar Positive Unipolar Negative Unipolar Figure 5-5. Histogram of pulse amplitude for four different ty pes of pulses in cloud-to-ground flash whose electric field reco rd is shown in Figure 5-1. N = 97 NBP = 85 NUP = 12 Durations (ms) 01248163264 Number of Pulses 0 10 20 30 40 50 60 Positive Bipolar Negative Bipolar Positive Unipolar Negative Unipolar Figure 5-6. Histogram of total pul se duration for four different t ypes of pulses in cloud-to-ground flash whose electric field reco rd is shown in Figure 5-1.

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226 Mean Duration = 4.7 s N = 706 NBP= 626 NUP= 80Duration ( s) 01248163264 N um b er o f P u l ses 0 50 100 150 200 250 300 350 Bipolar (BP) Unipolar (UP) Figure 5-7. Histogram of total duration of unipolar and bipolar pul ses in 12 cloud-to-ground discharges. Normalized Time 0.000.250.500.751.00 Number of Pulses 0 50 100 150 200 250 300 Submicrosecond (N = 128) 1-4 microseconds (N = 379) Above 4 microseconds (N = 148) N = 655 Figure 5-8. Occurrence of pulses of different total duration in diffe rent parts (four quarters) of the preliminary breakdown pulse train for all 12 cloud-to-ground flashes combined.

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227 Table 5-2. Summary of occurrence of smaller and narrower pulses observed in the 12 cloud-toground discharges. Number of pulses in the Small and Very Small categories (%) Number of pulses having durations less than or equal to 4 s (%) Flash ID Total Number of Pulses Bipolar UnipolarTotal Bipolar Unipolar Total 05/24/06_224 169 141 (83) 23 (14) 164 (97) 127 (75) 22 (13) 149 (88) 05/24/06_228 27 19 (70) 6 (22) 25 ( 93) 7 (26) 4 (15) 11 (41) 05/24/06_1078 97 83 (86) 12 (12) 95 ( 98) 70 (72) 12 (12) 82 (85) 05/28/06_1152 23 13 (57) 0 (0) 13 (57) 5 (22) 0 5 (22) 05/28/06_1360 41 35 (85) 1 (2.4) 36 (88) 33 (80) 1 (2.4) 34 (83) 06/01/06_21 44 38 (86) 2 (4.6) 40 (91) 29 (66) 2 (4.6) 31 (71) 06/02/06_120 25 19 (76) 2 (8.0) 21 (84) 8 (32) 1 (4.0) 9 (36) 06/02/06_139 72 58 (81) 6 (8) 64 (89) 58 (81) 6 (8.3) 64 (89) 06/02/06_207 48 36 (75) 6 (13) 42 ( 88) 34 (71) 6 (13) 40 (83) 06/02/06_212 65 48 (74) 9 (14) 57 ( 88) 43 (66) 9 (14) 52 (80) 07/15/06_23 73 58 (79) 11 (15) 69 ( 95) 52 (71) 9 (12) 61 (84) 07/17/06_54 22 14 (64) 2 (9.1) 16 (73) 13 (59) 2 (9.1) 15 (68) Total 706 562 (80) 80 (11) 642 (91) 479 (68) 74 (10) 553 (78) respectively. All the pu lse trains were found to have mini mum pulse durations less than 1.5 s (see Figure 5-10). The range of va riation and the arithmetic mean of pulse durations for all 12 pulse trains were found to be 0.5 s and 4.8 s, respectively. The mean duration is significantly less than th e lower bound of the 20 s range of typical durations previously reported for classical preliminary breakdown pulses [ Rakov and Uman 2003]. In the study of Weidman and Krider [1979], the minimum duration of such classical pulses was between 10

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228 and 15 s. Interestingly, if all pulses with durations equal to or less than 4 s in our dataset were excluded, the mean duration of the remaining 108 (out of a total of 655) pulses would be 16 s, which is closer to, but still outside of the 20 s range for classical pulses. For interpulse intervals (see Figure 5-11), the range of variation and arithmetic mean are 0.6 s and 65 s, respectively. The previously reported typical values of inte rpulse interval, presumably for larger pulses, are in the range of 70 s [ Rakov and Uman 2003]. It appears that in previous studies of preliminary breakdown pulse trains, sm aller (and narrower) pulses were arbitrarily disregarded, which led to biases toward larger average pulse durati ons and longer average interpulse intervals. AM = 3.4 ms GM = 3.2 ms N = 12 Pulse-Train Duration ( ms ) 0123456 Number of Events 0 1 2 3 4 5 Figure 5-9. Histogram of the total duration of preliminary breakdown pulse trains for 12 cloudto-ground flashes.

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229 Individual Pulse-Train Rank (by increasing mean pulse duration) 123456789101112 Pulse Duration ( s) 0 10 20 30 40 50 Mean Value Mean = 4.8 s Range = 0.5 49 s N = 12 Figure 5-10. Ranges of variation (v ertical bars) and mean values (diamonds) of pulse duration in individual preliminary breakdown pulse trains. 123456789101112 Interpulse Interval ( s) 1 10 100 1000 Mean Value Mean = 65 s Range = 0.6 1585 s N = 12Individual Pulse-Train Rank (by increasing mean interpulse interval) Figure 5-11. Ranges of variation (vertical bars) and mean valu es (diamonds) of interpulse interval in indivi dual preliminary breakdown pulse trains.

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230 5.2 Attempted Leaders In this Section lightning events exhibiting pulse trains that are characteristic of preliminary breakdown in negative cloud-to-gro und discharges, but are not followed by return stroke waveforms were identified and examined. It was assumed that these lightning events are manifestations of the initiation of downward nega tive stepped leaders that fail to propagate all the way to the ground. We refer to these events as attempted first cloudto-ground leaders. In a total of 2475 electric field reco rds of lightning events acquired (using a sampling interval of 4 or 10 ns) in Gainesville, Florida, in 2006, we found 35 waveforms in 33 of these records that satisfied the criteria (which are the characteristic feat ures of preliminary breakdown pulse trains in negative cloud-to-ground flashes) set for atte mpted cloud-to-ground leaders. The electric field record of an attempted lead er is shown in Figure 5-12. Preliminary breakdown pulse trains of a ttempted cloud-to-ground leaders typically contained two types of pulses, larger classical pulses (see for example, Figure 5-13a) with durations of the order of tens of microseconds and narrow pulses (see for example, Figure 513b) whose durations were a few microseconds, with many being in the 1 to 2 s range. Almost half (46%) of the pulse trains were found to ha ve minimum pulse duratio ns in the range of 1 s. Smaller and narrower pulses tended to occur at the onset and toward the end of each pulse train. In addition to bipo lar pulses with positive (atmospheric electricity sign convention) initial half-cycle, negative unipolar and ne gative (initial half-cycle) bipol ar pulses were sometimes seen toward the end of the train. Characteristics of preliminary breakdown pul se trains in attempted leaders can be summarized as follows: (1) The range of variatio n and arithmetic mean of total durations of pulse trains are 0.8.9 ms and 2.7 ms, respectively, with 74% of the pulse trains having total durations less than or equal to 3 ms (see Fi gure 5-14). (2) The range of variation and the

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231 Figure 5-12. (a) Electric field reco rd of an attempted leader with no pulse activity following the preliminary breakdown pulse train. (b) Preliminary breakdownlike pulses of the attempted leader shown in (a).

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232 weighted arithmetic mean of individual pulse durations are 1 s and 17 s, respectively (see Figure 5-15). (3) The range of variation and the we ighted arithmetic mean of interpulse intervals are 1 530 s and 73 s, respectively (see Figure 5-16). In Section 5.1.1, the arith metic mean pulse duration and inte rpulse interval for preliminary breakdown pulse trains in cloud-to-ground discharges were found to be 4.8 and 65 s, respectively, versus 17 and 73 s for attempted cloud-to-ground leaders. This implies that preliminary breakdown pulse trains in ground discha rges contain a larger fraction of narrow ( 4 s) pulses than the pulse trains in attemp ted cloud-to-ground lead ers. Both classical (having durations of tens of microseconds) and narrow pulses were found in both types of pulse trains. However, submicrosecond-scal e pulses were only observed in preliminary breakdown pulse trains of ground discharges.Some of the isolat ed short-duration discharges which have been observed by Maier et al. [1996] and Krehbiel et al. [2003] who used VHF timeof-arrival lightning mapping systems and by Defer et al. [2001] who used a VHF interferometric lightning mapper, might be attempted cloud-to-ground l eaders, similar to thos e considered in this study. It is possible that some of the attempted l eaders could also be classified as inverted intracloud flashes, occurring between the main negative and lower positive charge regions. In this latter case, the lower positive charge can be viewed as blocking the progression of descending negative leader from reaching ground and thus converting the potential cloud-toground flash to an intracloud one. Whatever th e scenario, characteristics of preliminary breakdowntype pulses that were at tributed to attempted leaders were indicative of a cloud-toground flash. Another possible interpretation of the observed pulse trains is a unique discharge

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233 process in the cloud that may or may not be followed by formati on of a stepped-leader channel terminating (or not terminating) on ground. Since the preliminary breakdowntype pulses cons idered here have the same polarity as return stroke pulses in negative cloud-to-ground flashes and durations of the initial half cycle of these two types of pulses may be comparable (a few tens of microseconds), some of the attempted cloud-to-ground leaders can be miscla ssified by the NLDN as low-intensity negative cloud-to-ground discharges. If it is assumed that about 25% of the 2475 records examined here were due to negative cloud-to-g round flashes, and that 25% of these cloud-to-ground flashes had peak currents equal to or less than 10 kA, the expected number of low-intensity ( 10 kA) negative cloud-to-groun d events would be 155. If the NLDN recorded all these 155 negative cloud-to-ground events plus all 35 attempted l eaders (all assumed to have NLDN intensities 10 kA), about 18% of reported low-intensity cloud-to -ground flashes would be misclassified events. 5.3 Some Inferences on the Role of Lower Positive Charge Region in Facilitating Different Types of Lightning 5.3.1 Introduction The gross charge structure of a normal thund ercloud can be viewed as a vertical tripole consisting of three charge centers (regions), main positive at the top, main negative in the middle, and an additional positive below the main negative [Williams, 1989]. The magnitudes of the main positive and negative charges are typically some tens of coulombs, while the lower positive charge is probably 10 C or less. The negativ e charge region is apparently related to the 10 to -25oC (0 to -15oC in earlier studies) temperature range while the lower positive charge is typically found just below the freezing level. Fo ur different hypotheses re garding the origin of the lower positive charge region (LPCR) are reviewed by Rakov and Uman [2003, p. 88]. The LPCR can be associated with (a) graupel, which, according to the graupel-ice cloud

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234 Figure 5-13. Typical (a) classical and (b) narrow pulses of a preliminary breakdown (PB) pulse train of an attempted leader. (b) (a)

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235 Figure 5-14. Histogram of preliminary breakdown pulse train duration for attempted leaders. Note that a total of 35 preliminary breakdow n pulse trains were found in 33 electric field records. Figure 5-15. Ranges of variation (v ertical bars) and mean values (diamonds) of pulse duration in individual preliminary breakdown pulse trains of attempted leaders.

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236 Figure 5-16. Ranges of variation (vertical bars) and mean values (diamonds) of interpulse interval in individual prel iminary breakdown pulse trains of attempted leaders. electrification mechanism, charges positively at temperatures warmer than the reversal temperature, (b) positive charge deposited in the cloud by lightning, (c) corona at ground surface, and (d) positive screening layer at the lower cloud boundary. In this paper, we assume that the charge that is produced by corona at ground under thunderclouds and subsequently carried by updraft into the cloud is a signifi cant contributor to the LPCR. Chauzy and Soula [1999] have provided a quantitative evidence (the other three hypothetical scenarios remain largely qualitative) for the corona orig in. They estimated, from measurements and modeling, that a significant portion (some tens to few hundred coul ombs) of positive charge produced by corona at ground level could be transferred to an altitude of 1000 m (the upper limit of their computational domain) over an area of 10 x 10 km2 for the entire thundersto rm lifetime. Chauzy and Soula noted that some positive charge will be carried by updrafts from 1000 m to higher altitudes. They concluded that the corona-produced charge can account for the formation of the LPCR, as earlier suggested by Malan [1952].

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237 Whatever the source of the LPCR, it is genera lly thought that the LPCR serves to enhance the electric field at the bottom of the negative ch arge region and thereby facilitate the launching of a negatively-charged leader toward ground [e.g., Clarence and Malan, 1957; Ogawa, 1993; Tessendorf et al., 2007]. On the other hand, the presence of excessive lower positive charge in thunderclouds over the Tibetan Plat eau has been reported to prev ent the occurrence of negative cloud-to-ground discharges and facilitate intracloud di scharges between the main negative and lower positive charge regions [Qie et al., 2005]. Thus, electric breakdown between the main negative and lower positive charge regions may result in either a cloud-to-ground (CG) or an intracloud (IC) flash. Bipolar pulse trains in wideband electric fiel d records typically occurring a few tens of milliseconds (sometimes considerably less) prio r to the first return-stroke pulse and having overall duration of a few milliseconds are ofte n attributed to preliminary breakdown (PB) process [e.g., Brook, 1992; Heavner et al., 2002]. The amplitude of largest pulses in PB pulse trains can be comparable to or even exc eed that of the first return-stroke pulse [Gomes et al., 1998; Schulz and Diendorfer, 2006; Nag and Rakov, 2009]. These pulse trains are examined in Section 5.1. However, in many cases (at least in some locations, as discussed below) the first return-stroke pulse is not preceded by a detectable PB pulse train. Electric field pulse trains that are characteristic of preliminary breakdown in negative CG discharges but are not followed by return-stroke waveforms have been identified and examined in Section 5.2. These trains were attributed to attempted cloud -to-ground leaders. Some of the attempted leaders examined in Section 5.2 could also be classified as inverted intracloud flashes, occurring between the main negative an d lower positive charge regions. In that case, the lower positive charge can be viewed as blocking the progression of descending negative

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238 leader from reaching ground and thus converting the potential CG flash to an intracloud (or cloud-to-air) one. The relationship between t ype of lightning discharge and cloud charge structure, with emphasis on blue and gi gantic jets, was recently studied by Krehbiel et al. [2008] (see also commentary by E.R. Williams, on pp. 216-217). PB pulse trains were observed to occur at the beginning of electrostatic field changes produced by stepped leaders [e.g., Beasley et al., 1982], which implies that, when they do occur, they have something to do with initia tion of appreciable charge transfer. Beasley et al. [1982, Fig. 26] reported that PB pulses in Florida were radiated between altitudes of 4 to 6 km and their VHF sources appeared to propagate downward, apparently from the lower boundary of main negative charge region toward and into the LPCR. Similar downward progression was also reported by Heavner et al. [2002]. Further, Schonland [1956], working in South Africa, attributed the initial (faster, bright er, and heavily branched) stage of the leader, this initial stage being the same as the PB discussed here, to accumulations of positive space charge near the cloud base. Thus, it is likely that the PB pulse train is a manifestation of interaction of a downward-extending negative lead er channel with the LPCR. An attempt was made to obtain estimates of source heights of individual PB pulses using simultaneous measurements of electric and magne tic radiation fields of PB pulse train. This method is described in Chapter 4 (Section 4.1.4). Un fortunately, for the PB pulse trains analyzed in Sections 5.1 and 5.2 of this Chapter, magnetic field measurements were not available. So, a negative cloud-to-ground discharge (that occurred in August, 2008 in Gainesville, Florida) in which a PB pulse train preceded the first return stroke was selected for the purpose. The first pulse of the PB pulse train occu rred 7.31 ms prior to the first stroke. The NLDN located the first stroke at a distance of 27.8 km from the measur ing station. The PB pulse train (electric field

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239 record of which is shown in Figure 5-17) consiste d of five detectable pulses. The second pulse of the train, which occurred 7.14 ms prior to the fi rst stroke, was detected by the NLDN as a cloud discharge at a distance of 28.5 km from the measuring station. The other four pulses in the train were not detected by the NLDN. The electric field waveforms of the second, third, and fifth pulses in the train had better signa l-to-noise ratio relative to th e other two pulses (as seen in Figure 5-17) and hence were selected for analysis to estimate their source heights. It was assumed that all pulses occurred at the same horizontal distance of 28.5 km as the second pulse for which NLDN-estimated distance was available. The source heights for the second, third, and fifth pulses were inferred to be 6.5 km, 7.1 km, and 5.8 km, respectively. The inferred source height of the third pulse is 600 m higher than th at of the second pulse. The inferred source height for the fifth pulse is 700 m lower than that of the second pulse in the train and 1300 m lower than that of the third, which probably indicates a downward progres sing channel. However, the sample of three pulses in one PB train is too small to make any conclusions. There are two primary sources of error in our estimated source heights: elevati on angle error and distance error as discussed in Chapter 4 (Section 4.1.4). The me dian height error for the three PB pulses was estimated to be %. Further, an unknown erro r was introduced due to the assumption that all PB pulses in the train occurred at the same horizontal distance from the measuring station, as distances for individual pulses were not availabl e. The differences in source heights of the three PB pulses (ranging from 600 m to 1300 m) are less than the hei ght estimation error of % (ranging from 1100 m to 1350 m). In or der to use this method of height estimation effectively for determining source heights of PB pulses and exam ining direction of channel progression, height estimation errors have to be of the order of hundr eds of meters or less so that locations of individual PB pulse sources (whi ch probably occur within a few hundred meters of each other)

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240 Figure 5-17. The electric field record of the PB pulse train of a negative cloud-to-ground discharge that occurred on A ugust 1, 2008 in Gainesville, Florida at a distance of 28 km from the measuring station. The PB pulse train consisted of five detectable pulses with the signal-to-noise ratio for the second, third, and fifth pulses being better that the first and fourth pulses in the train. can be accurately estimated. Distant electric and magnetic field measurements (in which the field change is essentially radiation) of PB pulses with high signalto-noise ratio with each pulse preferably occurring at a known horizontal distance is required to obtain reliable results using this method. In this study, we examine variations in occu rrence of PB pulse trains in CG flashes. Assuming that the PB pulse train is a manifestation of interaction of a downward-extending negative leader channel with the LPCR, we qualitatively examine the inferred dependence of lightning type on the magnitude of this charge re gion. The result is a set of conceptual scenarios that can be tested by future observations. 2n d pulse 3r d pulse 5t h pulse

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241 5.3.2 Analysis and Discussion 5.3.2.1 Generation of preliminary breakdown pulse train Figure 5-18 (left panel) shows the vertical components of electric field vectors, EN and ELP, due to the main negative and lower positive cloud charge regions, respectively. Between the negative and positive charge regions, EN and ELP are in the same direction and hence electric field is enhanced due to the presence of the LPCR. On the other hand, in the region below the LPCR EN and ELP are in opposite directions and hence the field is reduced. It follows that a descending leader originating at the lower bounda ry of main negative charge region would be initially accelerated and then (a fter traversing the LPCR) decelerat ed due to the presence of the LPCR. This scenario appears to be consistent with description of type leader [Schonland, 1956], which exhibits a higher speed near the cl oud base and a lower speed at lower altitudes (although it does accelerate near gro und). The initial part of the type leader is associated with pronounced electric field pulses, which are the same as the PB pulses considered here. In the following, we assume that the PB pulse train occurs when a descending negative leader encounters a significant LPCR and con tinues to propagate through it in a primarily downward direction. The negative leader is ste pped, and the presence of positive space charge along its path is expected to intensify the steps, compared to the case of stepping in the absence of ambient space charge. When the LPCR is small or absent, the initiation of negative leader is essentially not assisted by the LPCR (such init iation would generally re quire a stronger negativecharge source) and no appreciable pulse train is produced. In this view, the occurrence of pronounced PB pulse train can be used as a proxy of existence of significant LPCR. The initial polarity of PB pulse s in negative ground discharges is the same as that of the following return-stroke pulse. In effect, both types of pulses (negative return-stoke pulse and PB

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242 Figure 5-18. (left) A schematic illustration (not to scale) of electric field enhancement and reduction effects of the lower positive charge region (+QLP) below the main negative charge region (-QN). The main positive charge regi on is not shown. Arrows indicate the direction of vertical components of electric field vectors. The to tal electric field is enhanced, (EN+ELP), between the negative and positive charge regions and reduced, (EN-ELP), below the positive charge region. (ri ght, top) Schematic representation of preliminary breakdown stepping process in negative ground flashes. Negatively sloped arrow indicates the overall downward extension of negatively charged channel through the LPCR. Three steps giving rise to current (and light) pulses are shown. Each current pulse originates at the tip of downward-extending channel and propagates upward (positively-sloped arrows ). (right, bottom) A sketch of expected electric field record of resu ltant wideband PB pulse train. pulses) are due to a recoil process occurring when the negative leader channel comes in contact with ground (return-stroke pulse) or with progressively lower layers of the LPCR (PB pulses). Conceptually, th e recoil process in the case of PB should be similar to the stepformation process optically observed in rocket-triggered lightning by Wang et al. [1999]. Based on this analogy, we schematically show in Figure 5-18 (right panel) the PB stepping process in the cloud and resultant el ectric field pulse train. 5.3.2.2 Variations in occurrence of p reliminary breakdown pulse train As noted in Nag and Rakov [2008], PB pulse trains are dete cted prior to the first returnstroke pulse in only about 18% of CG fl ashes in Florida. On the other hand, Schulz and Diendorfer [2006], who used a 12-bit measuring system set up at an electromagnetically quiet site in Austria, reported considerably larger percentage of ground fl ashes showing PB pulse trains. In their data set, 89% of 92 negative multiple-stroke flashes and 71% of 94 negative

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243 single-stroke flashes (that is, 80% of 186 negative CG flashes) had detectable PB pulse trains. Further, Gomes et al. [1998] reported that essent ially all electric field records of 41 negative CG flashes acquired in Sweden, contained detectab le PB pulse trains, while the corresponding percentage for Sri Lanka was only 19%. It is important to note that the same instrumentation and methodology were used in both Sweden and Sri Lanka. Ogawa [1993] reported that 32 out of 89 (36%) CG flashes in Kyoto, Japan had electric field signatures indicative of PB pulse trains. Clarence and Malan [1957] found that out of their total 407 first-stroke electric field waveforms recorded at Johannesburg, South Africa, 16% were preceded by so-called fast type leaders (exhibiting pronounced PB pulses). They also observed slow type leaders that were characterized by small PB pulses and constituted 21% of their data set. If we combine both fast and slow type leaders, the percentage of flashes with detectable PB pulses in South Africa will be 37%. Recently, Makela et al. [2008] reported that at least 90% of CG flashes in southwest Finland exhibited PB pulse trains. Percentage of flashes with dete ctable PB pulse trains as a fu nction of latitude is shown in Figure 5-19a and discussed next. If the PB pulse tr ain were indeed an indication of the presence of a significant LPCR in the thundercloud, the detec tion of PB pulse trains in the majority of negative ground discharges in Sweden, Finland, and Austria compared to just about 20% of negative ground discharges in Florida and Sri Lanka, 16 to 37% in South Africa, and 36% in Japan could be interpreted as being due to the more frequent presence of a significant LPCR at higher latitudes than at relative ly low ones. This could be due to more intense corona at ground (which we assume to be a significant, if not dom inant, source of the LPCR) at higher latitudes. This hypothesis is consistent with the work of Chauzy and Soula [1999] who used measured electric fields and numerical modeling to esti mate the amount of charge produced by corona

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244 during thunderstorms in Florida (lower latitude) and in southwes tern France (higher latitude). The corona-produced positive charge at ground level over a 10 x 10 km2 area varied from 63 to 124 C (94 C on average) in Florida and from 106 to 362 C (214 C on average) in southwestern France; that is, the average positive charge at the higher-latitude locati on was found to be more than twice larger than at the lower-latitude one (although the higher terrain is France could have also been a factor). Further, it is known that th e height of the main nega tive charge region, shown to be between the 0oC and -15oC isotherms in Figure 5-19b, above ground tends to be smaller at higher latitudes [e.g., Rakov and Dulzon, 1984], as seen in Figure 5-19b. This can increase electric field at ground and make positive corona production at ground more efficient (due to the cubic dependence of corona current on surf ace electric field) at higher latitudes. 5.3.2.3 Type of discharge versus magnitude of lower positive charge region We now discuss four conceptual scenarios (sho wn in Figure 5-20, left panel) that may arise depending upon the magnitude of the LPCR when a negative leader channel extends downward from the negative charge region. Examples of e xpected electric field signatures for these scenarios are shown in the right panel of Figur e 5-20. The field signatur es were recorded in Gainesville, Florida, and interpreted as resulting from proposed scenarios, although no information on cloud charge structure was available. When the magnitude of LPCR is abnormally large, say, comparable in magnitude to that of main negative charge, as shown in Figure 5-20A (left panel), inverted IC di scharges are expected to occur. This type of discharge bridging the main negative and abnormally large lower positive charge regions have been reported by Qie et al. [2005]. In this scenario, a descending negative leader would likely change its direction of propagation to predominantly horizontal [Coleman et al., 2008], interact with the LPCR, and be unable to forge its way to ground. The result is an inverted IC flash. VHF imaging presented by Tessendorf et al. [2007] indicates that the LPCR

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245 Figure 5-19. (a) Percentage of flashes with detectable PB pulse train and (b) altitudes of the upper cloud boundary (UCB), the main negative charge region (assumed to be between the 0oC and -15oC isotherms), and the lower cloud boundary (LCB) [Rakov and Dulzon, 1984], each as a function of latitude. The altitudes are averages for the Northern Hemisphere in July, but assumed to be applicable, as a first approximation, to the Southern Hemisphere as well. Note that the lower percentage of flashes with detectable PB pulse train appears to be associated with highe r altitude of main negative charge region above ground and vice versa. appears to be vertically deeper and to have a larger horizontal extent when such IC flashes occur. An example of expected electric field signature of such a discharge is shown in Figure 5-20A (right panel), which exhibits a PB pulse train followed by static field change some tens of milliseconds in duration, indicative of an invert ed IC flash (attempted cloud-to-ground leader; Section 5.2). If the lightning ch annel emerges from the cloud, it can be viewed as an "air discharge" or even as a "spide r" lightning, if it develops over a large distance near the cloud base.

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246 Figure 5-20B (left panel) shows the scenar io where the magnitude of the LPCR is somewhat smaller than in scenario A. Similar to scenario A, a negatively-charged leader channel extending vertically from the main negative charge region would become predominantly horizontal, but would eventually make terminat ion on ground. In this case, the discharge can be viewed as a hybrid flash (an IC followed by a CG). Such flashes (with IC durations ranging from a few tens to over 100 ms) were examined by Coleman et al. [2008]. The electric field signature expected for this type of discharge is shown in Figure 5-20B (right panel), which shows a PB pulse train followed by a field chan ge characteristic of a cloud di scharge lasting for about 50 ms, followed by the first return stro ke waveform of a CG flash. If the magnitude of the lower positive charge relative to the main negative charge is even smaller, as shown in Figure 5-20C (left panel), the descending ne gative leader would traverse the positive charge region and continue to propagate in a predominantly vertical direction to ground. The electric field signature expect ed to be produced in this case is shown in Figure 5-20C (right panel). It exhibits a PB pulse train and stepped-leader wavefo rm followed by the first return stroke (RS) waveform. Leader duration, found as th e time interval between PB and RS, is about 20 ms. Negative stepped leaders that are characterized by very short (a few milliseconds) durations and, by inference, very high speeds (~106 m/s versus typical ~105 m/s) also belong to this category. In this latter case, the lower positive charge is either entirely consumed by the negative leader or whatever remains of it is in capable of decelerating th is leader. Very fast stepped leaders, which are probably associated with very strong negative-charge sources, were observed in different geographica l locations, in different seasons, and both over water and over land [e.g., Clarence and Malan, 1957; Heavner et al., 2002; Frey et al., 2005]. In Florida, only

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247 about 5% of stepped leaders are shorter than 5 ms suggesting that such ve ry fast stepped leaders are relatively rare. Figure 5-20D (left panel) shows the scenario when the LPCR is insignificant. This scenario is similar to scenario C, except for the LPCR playing essentially no role in negative leader initiation. The electric field signat ure produced in this case is exp ected to be that of a stepped leader/return stroke sequence not preceded by a detectable PB pulse trai n, as shown in Figure 520D (right panel). 5.4 Summary Lightning events exhibiting pulse trains that are characteristic of preliminary breakdown in negative cloud-toground discha rges, but are not followed by re turn stroke waveforms, are assumed to be manifestations of attempte d cloud-to-ground leaders. Preliminary breakdown pulse trains in negative cloud-to-ground discharg es and in attempted leaders were examined. Both classical (having durations of tens of microseconds) and n arrow (having durations of a few microseconds) pulses were found in both type s of pulse trains. However, submicrosecondscale pulses were only observed in preliminar y breakdown pulse trains of ground discharges. The arithmetic mean pulse duration and interpulse in terval for preliminary breakdown pulse trains in cloud-to-ground discharges were found to be 4.8 and 65 s, respectively, versus 17 and 73 s for attempted cloud-to-ground leaders. This implies that preliminary breakdown pulse trains in ground discharges contain a larger fraction of narrow ( 4 s) pulses than the pulse trains in attempted cloud-to-ground leaders. The majority of pulses occurring in PB pulse tr ains prior to the first return stroke in cloudto-ground discharges are typically small in bot h amplitude and duration. Amplitudes of these most common pulses are 50% or less than that of the largest pulse, and their durations are less than or equal to 4 s. A significant fraction (22%) of exam ined pulses had total durations less

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248 Figure 5-20. (left) Schematic re presentation of four types of lightning, AD, that may arise depending upon the magnitude of the LPCR. Th e charge configuration in each of the scenarios represents only its vertical profile (no lateral boundaries are shown). Arrows indicate the direction of prop agation of negative leader. (right) The corresponding examples of e xpected electric field signatures. The field waveforms are from four different thunderstorms reco rded at some tens of kilometers in Gainesville, Florida, using the same instru mentation with a decay time constant of 10 ms. PB = preliminary breakdown pulse tr ain; RS = return-stroke waveform.

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249 than 1 s. The largest pulses in the preliminary breakdown pulse train can exceed in magnitude the following first return-stroke pulse Pulses with larger durations (>4 s) tend to occur earlier in the train. Almost half (46%) of the PB pulse trains in attempted leaders were found to have minimum pulse durations in the range of 1 2 s Smaller and narrower pul ses tended to occur at the onset and toward the end of each pulse trai n. In addition to bipolar pulses with positive (atmospheric electricity sign convent ion) initial half-cycle, negativ e unipolar and negative (initial half-cycle) bipolar pulses were sometimes seen to ward the end of the train. It is possible that some of the attempted leaders could also be classified as invert ed intracloud flashes, occurring between the main negative and lower pos itive charge regions. In this latter case, the lower positive charge can be viewed as blo cking the progression of descending negative leader from reaching ground and thus convertin g the potential cloud-toground flash to an intracloud one. The PB pulse train appears to be generate d when a negatively-charged channel extends downward from the main negative charge region and encounters an appreciable LPCR. When the LPCR is small no PB pulse train may be produced. In this view, the fact that in some negative CG flashes no PB pulse train is de tectable could be due to insigni ficant LPCR. It appears that at higher latitudes a larger pe rcentage of CG discharges exhibit de tectable PB pulse trains than at lower latitudes. This implies th at a significant LPCR (or its portion originating from corona at ground) is present in thunderclouds more often at higher latitudes than at relatively low latitudes. While the LPCR may serve to enhance the electric field at the bottom of the negative charge region and thereby facilitate the launching of a negativelycharged leader toward ground, presence of excessive LPCR may prevent the oc currence of negative CG flashes by blocking

PAGE 250

250 the progression of descending negative leader from reaching ground. Four conceptual lightning scenarios are inferred that may arise depending upon the magnitude of the LPCR.

PAGE 251

251 CHAPTER 6 TWO-STATION MEASUREMENTS OF CL OUD-TO-GROUND LIGHTNING ELECTRIC FIELDS 6.1 Introduction In this chapter, the fine structure of elect ric field waveforms produced by first return strokes in negative cloud-to-ground lightning is examined. As discus sed in Chapter 2, the initial rising part of return stroke electric field waveforms can be separated into two phases. The first one is the so-called initial slow front or simply slow front, described by Weidman and Krider [1978] as an initial portion or front, wh ich for first strokes rises slowly for 2 8 s to about half the field peak. The second part which fo llows the slow front is an abrupt transition to peak, typically referred to as the fas t transition. The latter, according to Weidman and Krider [1978], has a 10-to-9 0% risetime of 0.2 s or less for first strokes, when the field propagation was over seawater. [Weidman and Krider, 1980 give a 10-to-90% risetime of 0.1 s for propagation over seawater]. The shape of the slow front is typically concave, although Weidman and Krider [1978] do report some convex slow fronts. Return-stroke models [e.g., Rakov and Uman, 1998] are used to relate the channel base current to the current distribution along the channel, which, in turn, can be used to calculate return-stroke electric and magnetic fields. Specifically, the tr ansmission line (TL) model [Uman and McLain, 1969] has been demonstrated to work reasonably well in reproducing both close [e.g., Schoene et al., 2003] and relatively distant [e.g., Willett et al., 1988] fields for the first few microseconds of strokes in rocket-triggered light ning (which are thought to be similar to natural negative lightning subs equent strokes). The slow-front current in firs t strokes has often been attributed to the presence of an upward connecting leader [e.g., Rakov and Uman, 2003, p. 144]. Weidman and Krider [1978] noted that the shapes and relative amplitudes of the fronts and fast tran sitions in the current

PAGE 252

252 waveforms are surprisingly similar to those in th e radiated fields (currents and fields being measured in different studies), perhaps indicating that the TL model, with the equivalent current waveforms starting at ground level and propagati ng upward, might be applicable to computing both the slow front and fast transition of natura l-lightning first-stroke fi elds. On the other hand, there are experimental data [Willett et al., 1989a, p. 13,283], although for triggered-lightning strokes, which suggest that radiation field waveforms can exhibit pronounced slow fronts without similar features in co rresponding current waveforms. Weidman and Krider [1978] considered the possibility that the slow front in radiation field waveforms of return strokes is due to an upward connecting discharge. They estimated that such a discharge would appear to have a length in excess of 100 m and a peak current of the order of 10 kA or more. According to Thottappillil and Uman [1993], who examined measured curr ent and electric field waveforms of negative return strokes from rocket-triggered ligh tning, the slow front at the beginning of the return stroke current waveform could be due to an upward propagati ng positive streamer or streamers, and not due to the return stroke. Using the modified Diendorfer-Uman model, they showed that a better agreement between initial peaks of calculate d and measured radiation fields of a rocket-triggered lightning return stroke w ith a current waveform containing a slow front could be obtained if the return stroke velocity was assumed to increase exponentially with height. Cooray et al. [2004] used the travelling current s ource type model and associated the slow front in the incident channel base curren t waveform with the upw ard connecting leader. Jerauld et al. [2007], showed, using an unusual trigge red-lightning stroke, that both close and distant fields can be predic ted by a version of the TL model in which both the slow-front and fast-transition currents are gene rated at the junction point of the upward and downward leaders and propagate away from that point, a model that is more physically reasonable than the model

PAGE 253

253 assuming that the current is genera ted at ground level. According to Jerauld et al. [2007] the source of the slow fronts observed in the currents and in the distant radia tion fields of natural first strokes is likely to be the slow fronts in a pair of microsecond-scale current waves propagating in opposite directions from the junction of the descending and upward connecting leaders at a speed on the order of 108 m/s. The current waves have magnitudes of up to some tens of kiloamperes. However, Jerauld et al. assumed that the initial downward wave exhibits no reflection at ground whic h is unrealistic [e.g., Rakov et al., 1998]. In this chapter we examine the shapes and relative magnitudes of slow fronts and fast transitions in electric field waveforms of first return stro kes in negative cloud-to-ground lightning measured simultaneously at two stations, one at about 45 km (far station), and the other at hundreds of meters to a few k ilometers (near station) from the lightning channel. We examine, via modeling, whether electric field waveform s can exhibit pronounced slow fronts without similar features in corresponding current waveform s. Further, model predicted return stroke electric field waveforms produced at close and far distances due to two current waves moving in opposite directions (up and down) from a junc tion point tens of meters above ground are presented. The effect of reflection of the downw ard moving wave from ground is also examined. 6.2 Measured Electric Field Waveforms In 2007 and 2008, five natural negative cl oud-to-ground lightning discharges were simultaneously measured at Camp Blanding and in Gainesville, Florida, which are 45 km apart. Table 6-1 summarizes the data available at both stations. The Camp Bl anding data was acquired and provided by Joseph Howard, Dus tin Hill, and Christopher Biag i. Flash identification (ID) numbers for both Camp Blanding and Gainesville stations are given. In this chapter, flashes are referred to by their Gainesville flash ID. Note that the electric field waveform of the first return

PAGE 254

254 stroke in flash 100507_470 was saturate d at the far (Gainesville) stat ion due to its relative large magnitude and is not examined here any further. The return stroke electric field at the near station is expected to be dominated by its electrostatic component, while that at the far st ation is expected to be essentially radiation. Figures 6-1 to 6-4 show the overall electric field records of the f our flashes obtained at the two stations. Note that for flash 070608_020, which contai ned six return strokes, only the first and the third strokes were recorded at Gainesville. The electric field waveforms of the first leaderreturn stroke sequence of each flash measured at the near and far stations are shown in Figures 65 to 6-8. Figures 6-9 to 6-12 show initial rising po rtions of the first str okes at the two stations overlaid for direct comparison. The electric field waveforms were amplitude normalized by setting the radiation field peak s of corresponding retu rn strokes at the two stations to be approximately equal to unity. It can be seen fr om Figures 6-9 to 6-12 that the initial rising portions of the near and far field return stroke wa veforms for all four first strokes are generally in good agreement with each other up to the init ial (predominantly radiation) field peaks. Characteristics of the first return stroke elec tric field waveforms at the two stations are summarized in Table 6-2. The AM and GM zero-topeak risetimes for the four first strokes were 7.2 s and 6.6 s, respectively, at the near statio n, and 7.0 s and 6.5 s, respectively, at the far station. The AM and GM 10-to-90% risetimes for the four first strokes were 4.9 s and 4.6 s, respectively, at the near station, and 4.0 s and 3.6 s, respectively, at the far station. Out of the four first strokes, three strokes displayed the two distinct phases of th e slow front and fast transition while for the first stroke of flash 070608_020, a distinct slow front phase is not seen probably due to overlap with the final leader step, as seen in Figure 6-16. Figures 6-12 to 6-16 show the magnitudes of the radiation field peak, sl ow front, and fast transition for each return

PAGE 255

255 Table 6-1. Summary of natural lightning fields simultaneously measured at Camp Blanding and in Gainesville, Florida. a Determined using the time of arrival (T OA) technique accurate to about 100 m. [Howard, 2009 and Hill, 2009, personal communication]. b Determined using NLDN-estimated locations. The values in the parentheses indi cate the semi-major axis lengt h of the NLDN 50% location error ellipse (the median location error). c Saturated. stroke in the dataset presented here. For two first return strokes (in flashes 073107_1252 and 070508_008, shown in Figures 6-13 and 6-15, respectively) the slow front appears to be concave at both the near and far stations, while fo r one first strokes (in flash 100407_360, shown in Figures 6-14), the slow front appears to be convex at both stations. Note that for flash 100407_360, the small change in slope from the re latively slow convex potion of the return stroke waveform to the fast rising portion was used to determine the duration and magnitude of the slow front. The AM and GM slow front dura tions for the three first strokes were 4.6 s and 4.3 s, respectively, at the near station, and 4.3 and 4.0 s, respec tively, at the far station. The amplitude of the slow front was, on average, 47% of the peak at the near station and 35% of the peak at the far station. The AM and GM 10-to-90% risetimes for the fast transition were both 0.6 s at the near station versus 0.9 s at the far stati on. From the above discussion it is evident that the overall field waveform characteristics of first re turn strokes up to the radiation field peak are Camp Blanding Gainesville Distance (for first stroke), km Flash ID Measuring station TOAa NLDNb E dE/dt Flash ID Distance (for first stroke), km E dE/dt MSE 07-05 E4 508 263 (400) Y Y 073107_1252 46 Y Y MSE 07-06 E4 979 704 (400) Y Y 100407_360 46 Y Y MSE 07-07 E4 834 Y Y 100507_470 45 Yc Y MSE 08-01 E11 and E18 81 and 667 3604 and 2962 (400) Y Y 070508_008 48 Y Y MSE 08-02 E18 1520 (500) Y Y 070608_020 46 Y Y

PAGE 256

256 similar for near (where the electric field is dominated by its electrostatic component) and far (where the electric field change is essentially radiation) distances. Similar field waveform characteristics have been reported from single-station measurements at distances ranging from 1 to 200 km for negative first return strokes by other researchers. Master et al. [1984] reported the AM zero-to-p eak and 10-to-90% risetimes for 105 first strokes in negative cloud-to-ground disc harges in Florida to be 4.4 s and 2.6 s, respectively. Their AM slow front duration was 2.9 s. Weidman and Krider [1978] reported the AM slow front duration for 62 negative firs t return strokes in Florida to be 4 s. Cooray and Lundquist [1982] found the AM duration of the slow front for negative first strokes in Sweden to be 5 s. The AM 10-to-90% risetime of the fast transition for negative first strokes in Florida was reported to be 0.97 s and 0.2 s by Master et. al [1984] and Weidman and Krider [1978], respectively. The AM slow front magnitude rela tive to peak for negative first strokes was reported to be 28%, 41%, and 50% by Master et al. [1984], Cooray and Lundquist [1982], and Weidman and Krider [1978], respectively. These values are comparable to the AM value of 47% (near station) and 35% (far station) found for return strokes in our dataset. Jerauld et al. [2009], who examined electric and magne tic fields from an unusual cloud-toground lightning flash containing two positive strokes followed by four negative strokes, compared the magnetic field of their first positiv e stroke measured at 288 m (see Figure 6-17) to the electric field measured a distance of 45 km by the Los Alamos Sferic Array (LASA) (see Figure 6-18). They found the close and distant waveforms to be remarkably similar during the slow front and the fast transition, up to the time of the return stroke peak as seen in Figure 6-19. For each stroke in the four flashes recorded at both near and far stations, Table 6-3 gives the measured initial (radiation) field peaks along with the NLDN-estimated peak currents. The

PAGE 257

257 Table 6-2. Characteristics of el ectric field waveforms produced by negative first return strokes measured at near (Camp Blanding) and far (Gainesville) stations. far field distance is approximately 45 km. The near field distance for the first strokes of flashes 073107_1252 and 100407_360 were determined using the Camp Blanding multiple-station network and the time of arrival (TOA) technique by Howard [2009, personal communication] and are accurate to about 100 m. The second and third strokes of flash 073107_1252 were most likely along the same channel as the first stroke (NLDN-estimated locations for the three strokes are within 900 m of each other) and hence were at the same distance from the near field measuring station. For flash 070508_008, the distan ce was estimated using the TOA technique by Hill [2009, personal communication], while for flash 070608_020, this technique did not yield accurate results. Flashes 070508_008 and 070608_020 were probably either at the edge of the Camp Blanding field measuring network or ou tside its perimeter. Note that TOA and NLDNestimated distances are in reasonabl e agreement for flashes 073107_1252 and 100407_360, while for flash 070508_008, they are different. The reason for this discrepancy in presently Zero-to-peak risetime, s 10-90% risetime, s Slow front duration, s Slow front magnitude relative to peak, % Fast-transition 10-90% risetime, s Flash ID Near Far Near Far Near Far Near Far Near Far 073107_1252 (Figure 6-1) 6.6 6.4 3.7 2.4 6.0 5.3 43 18 0.4 1.1 100407_360 (Figure 6-2) 3.9 3.7 2.8 2.6 2.7 2.3 49 44 0.9 0.7 070508_008 (Figure 6-3) 6.1 6.5 5.2 4.0 5.0 5.3 49 44 0.5 0.9 070608_020 (Figure 6-4) 12.3 11.4 8.0 7.0 Sample Size 4 4 4 4 3 3 3 3 3 3 AM 7.2 7.0 4.9 4.0 4.6 4.3 47 35 0.6 0.9 GM 6.6 6.5 4.6 3.6 4.3 4.0 47 33 0.6 0.9

PAGE 258

258 unknown. In this chapter, NLDN-estimated locati ons, which are probably accurate to about 200 m [Nag et al., 2008], are used for flashes 070508_008 and 070608_020. The radiation field component of vertical electric field is approximately inversely proportional to distance. As a resu lt, the ratio of near and far in itial (radiation) field peaks is expected to be close to the inverse ratio of near and far fiel d distances. However, one can see from Table 6-3 that out of the 8 negative return strokes recorded at th e two stations, the two ratios are equal for only one event (str oke 3 of flash 073107_1252). Figure 6-20 shows the scatter plot for ratio of near and far initial (radia tion) field peaks versus i nverse ratio of near and far field distances. This deviat ion from the expected inverse pr oportionality dependence of the radiation field peak on distance may be attributed to contribut ions from electrostatic and induction field components to the measured init ial field peak at the near station and to propagation effects. Also, the initial field peak at the near stati on is often not well defined (see, for example, Figures 6-14 and 6-16). The scatter plot for NLDN-estimated peak curr ent versus initial (radiation) field peak normalized to 100 km for 8 negative return strokes recorded at Ca mp Blanding (near station) and Gainesville (far station) is s hown in Figure 6-21. Note, that for the third stroke in flash 073107_1252, whose NLDN-estimated peak current is 19 kA the initial field peak normalized to 100 km obtained from both near and far field me asurements is equal to 5.2 V/m and hence the corresponding points in the plot overlap. One can see from Figure 6-21 that the scatter for the normalized initial field peaks at the near station is larger than that at the far station. This further points to the fact that the measured initial fi eld peak at the near station is affected by uncertainties in identifying those peaks in electric field waveforms and contributions to the peaks from electrostatic and in duction field components.

PAGE 259

259 Table 6-3. Initial (radiation) electri c field peaks for each stroke in four flashes recorded at near (Camp Blanding) and far (Gainesville) sta tions. Also given are the NLDN-estimated peak currents, ratios of near and far field peaks, a nd inverse ratios of near and far field distances. Flash ID Stroke order NLDNestimated peak currents (absolute values), kA Near field distance, m NLDNestimated far field distance, km Initial (radiation) field peak at near station, kV/m Initial (radiation) field peak at far station, V/m Ratio of near and far field peaks Inverse ratio of near and far field distances 1 41.3 46 3.65 25.18 145 91 2 12.9 46 1.13 7.36 154 91 073107_ 1252 3 19.4 508a 46 1.02 11.30 91 91 100407_ 360 1 92.3 979a 46 5.28 42.47 124 47 1 30.6 3604b (400) 48 0.08 16.74 5 13 070508_ 008 2 11.5 611b (1000) 45 1.18 9.29 127 74 1 133.1 1520b (500) 46 3.17 69.83 45 30 070608_ 020 3 22 3225b (400) 48 0.52 11.72 45 15 a Determined using the time of arrival technique [Howard, 2009], accurate to about 100 m. b Determined using NLDN-estimated locations. The values in the parentheses indicate the semi major axis length of the NLDN 50% location er ror ellipse (the medi an location error).

PAGE 260

260 Figure 6-1. The electric field waveforms of three-stroke flash 073107_1252, measured at the near (top pane l) and far (bottom pa nel) stations both shown on a 140 ms time scale. 1 s t RS 2 n d RS 3 r d RS 1 s t RS 2 n d RS 3 r d RS Distant Electric Field (46 km) Close Electric Field (508 m)

PAGE 261

261 Figure 6-2. The electric field waveforms of single-stroke flash 100407_360, measured at the near (top panel) and far (bottom pa nel) stations both shown on a 100 ms time scale. Close Electric Field (979 m) Distant Electric Field (46 km)

PAGE 262

262 Figure 6-3. The electric field waveforms of a two-stroke flash 070508_008, measured at th e near (top panel) and far (bottom pan el) stations shown on a 15 ms time scale. Distan ce indicated is for the first stroke only. Close Electric Field (3.0 km) Distant Electric Field (48 km) 1 s t RS 2nd RS 1 s t RS 2 n d RS

PAGE 263

263 Figure 6-4. The electric field waveform of six-stroke flash 070608_020, measured at the near (top panel) station shown on a 450 ms time scale. Only the first and third return strokes were recorded at the far station, the electric field waveforms of which are shown in the bottom panels each on a 40 ms time scale. Distant Electric Field (48 km) 5 t h RS 6 t h RS Close Electric Field (1.5 km) Distant Electric Field (46 km) 1 s t RS 2 n d RS 3 r d RS 1 s t RS 3 r d RS 4 t h RS

PAGE 264

264 Figure 6-5. The electric field waveforms of the first return stroke of flash 073107_1252, measured at the near (top panel) and far (bottom panel) stations shown on a 1 ms time scale. Close Electric Field (508 m) Distant Electric Field (46 km)

PAGE 265

265 Figure 6-6. The electric field waveforms of the first return stroke of flash 100407_360, m easured at the near (top panel) and f ar (bottom panel) stations shown on a 1 ms time scale. Close Electric Field (979 m) Distant Electric Field (46 km)

PAGE 266

266 Figure 6-7. The electric field waveforms of the first return stroke of flash 070508_008, m easured at the near (top panel) and f ar (bottom panel) stations shown on a 2.5 ms time scale. Close Electric Field (3.0 km) Distant Electric Field ( 48 k m )

PAGE 267

267 Figure 6-8. The electric field waveforms of the first return stroke of flash 070608_020, m easured at the near (top panel) and f ar (bottom panel) stations shown on a 2 ms time scale. Close Electric Field (1.5 km) Distant Electric Field ( 46 km )

PAGE 268

268 Figure 6-9. The initial rising por tion of the first strokes of flash 073107_1252 at the near (blue line) and far (red line) stations overlaid for direct comparison, shown on a 30 s time scale. Figure 6-10. The initial rising portion of the fi rst strokes of flash 100407_360 at the near (blue line) and far (red line) stations overlaid for direct comparison, shown on a 50 s time scale.

PAGE 269

269 Figure 6-11. The initial rising portion of the fi rst strokes of flash 070508_008 at the near (blue line) and far (red line) stations overlaid for direct comparison, shown on a 50 s time scale. Figure 6-12. The initial rising portion of the fi rst strokes of flash 070608_020 at the near (blue line) and far (red line) stations overlaid for direct comparison, shown on a 100 s time scale.

PAGE 270

270 Figure 6-13. The initial rising portion of the fi rst stroke of flash 073107_1252 at the near (blue line, top panel) and far (red line, bottom) stations each shown on a 30 s time scale. EP, ESF, and EFT are the magnitudes of the radiati on field peak, slow front and fast transition, respectively. Near Station Far Station

PAGE 271

271 Figure 6-14. The initial rising portion of the fi rst stroke of flash 100407_360 at the near (blue line, top panel) and far (red line, bottom) stations each shown on a 20 s time scale. EP, ESF, and EFT are the magnitudes of the radiati on field peak, slow front and fast transition, respectively. The change in slope from the relatively slow convex potion (partly concave at the near st ation) of the return stroke waveform to the fast rising portion was used to determine the dura tion and magnitude of the slow front. Near Station Far Station

PAGE 272

272 Figure 6-15. The initial rising portion of the fi rst stroke of flash 070508_008 at the near (blue line, top panel) and far (red line, bottom) stations each shown on a 40 s time scale. EP, ESF, and EFT are the magnitudes of the radiati on field peak, slow front and fast transition, respectively. Near Station Far Station

PAGE 273

273 Figure 6-16. The initial rising portion of the fi rst stroke of flash 070608_020 at the near (blue line, top panel) and far (red line, bottom) stations each shown on a 50 s time scale. EP, is the magnitudes of the radiation field peak. A distinct slow front phase is not seen probably due to overlap with the final l eader step, as seen in the distant electric field waveform. Near Station Far Station

PAGE 274

274 Figure 6-17. First positive stroke electric and magnetic field wa veforms measured at 825 and 288 m at Camp Blanding, Florida, by Jerauld et al. [2009] on a 40-ms timescale. Only the east-west component of the magnetic fields was measured. Taken from Jerauld et al. [2009].

PAGE 275

275 Figure 6-18. Electric field of the first positive stroke measured in Gainesville, at a distance of 45 km by the Los Alamos Sferic Array (LASA) The waveform is displayed on (a) 2-ms, (b) 1.5-ms, and (c) 500-ms timescales. The amplitude of the waveform has been normalized to its initial peak. Time zero corresponds to the beginning of the fast transition. Data provided courtesy of Los Alamos National Laboratories (LANL). Taken from Jerauld et al. [2009].

PAGE 276

276 Figure 6-19. Magnetic field measured at 288 m by Jerauld et al. [2009], overlayed with the electric field measured a distance of 45 km from the first positive stroke. Time zero corresponds to the beginning of the fast tr ansition. The distant field was measured by the Los Alamos Sferics Array (LASA) a nd is provided courtesy of Los Alamos National Laboratories (LANL). Taken from Jerauld et al. [2009]. N = 8Inverse Ratio of Near and Far Field Distance 020406080100120140160 Ratio of Near and Far Field Peaks 0 20 40 60 80 100 120 140 160 Figure 6-20. Ratio of near and far initial (radiati on) field peaks versus in verse ratio of near and far field distances for 8 negative return st rokes recorded at Camp Blanding and in Gainesville.

PAGE 277

277 N = 8Initial Field Peak Normalized to 100 km, V/m 0102030405060 NLDN Peak Current, kA 0 20 40 60 80 100 120 140 Camp Blanding (Near station) Gainesville (Far station) Figure 6-21. NLDN-estimated peak current versus in itial (radiation) field peak normalized to 100 km for 8 negative return str okes recorded at Camp Blanding (near station) and in Gainesville (far station). Note that for the third stroke in flash 073107_1252, whose NLDN-estimated peak current is 19 kA, the initial field peak normalized to 100 km obtained from both near and fa r field measurements is equal to 5.2 V/m and hence the corresponding points in the plot overlap. 6.3 Transmission Line Model The transmission line (TL) model [Uman and McLain, 1969] for return strokes involves a current wave injected at the bottom of the li ghtning channel travelling upward at constant velocity v without attenuation or di stortion. For the TL model the longitudinal current i(z,t) at any height z and any time t is related to the current at the chan nel origin (which in this case is at ground level) is given by Equation 6-1 and illustrated in Figure 6-22. (,)(0, -)z iztit v (6-1) Modifications to the TL m odel include a linear [MTLL, Rakov and Dulzon, 1987] and exponential [MTLE, Nucci et al., 1988] current decay with height, represented by equations 6-2 (MTLL) and 6-3 (MTLE), respectively.

PAGE 278

278 (,)(1)(0, -)zz iztit Hv (6-2) (,)(0, -)zz izteit v (6-3) H in Equation 6-2 is the assumed channel height and in Equation 6-3 is the assumed decay height constant. The overall electric field wave forms at close distances are best reproduced by the MTLL model. However, for the initial few microseconds all three models predict essentially the same fields. In this chapter, we use the original TL m odel to compute near and far electric field waveforms of return strokes with focus on their initial rising portion for the purpose of trying to understand better the slow-front and fast transition processes. In a ddition, we extend the original, one-wave TL model to include two and three current waves. The two-wave model [e.g., Jerauld et al., 2007] involves two initial curr ent waves assumed to originate from a lumped current source at some height above ground (assumed here to be the junction point of the downward and upward leaders) and propagate in both dir ections (up and down), at constant speeds vu and vd, respectively, away from the junction point without attenuation or di stortion. It is usually assumed that the amplitude of the upward wave is equal to that of the downward wave, and that the downward-moving wave is absorbed at gr ound. The three-wave model introduced here, additionally accounts for the refl ection at ground of the downward wave, with this reflected wave travelling up the channel (toward the j unction point and beyond) at constant speed vr. The amplitude of the reflected current wave, ir, is related to that of th e downward (incident) current wave, id by Equation 6-4. ir = id (6-4)

PAGE 279

279 where is the current reflection coefficient at gr ound, assumed to be constant. If the lightning channel below the junction point is modeled as a transmission line, having characteristic impedance Zd and is terminated at ground in a grounding impedance Zg, then is given by Equation 6-5. dg dg Z Z Z Z (6-5) Note that is positive for the case of Zd > Zg and negative for the case of Zd < Zg. Here, is assumed to be positive, because the characteristic impedance of a lightning channel is thought to be on the order of 1 k Rakov and Uman, 2003], while Zg is likely to be on th e order of tens to hundreds of ohms (depending on grounding conditions at the strike point). We assume here that vd, vu, and vr are all equal to each ot her. If the speed of ir is assumed to be higher than the speed at which the current iu moves upward from the junction point, the ground reflected wave will "catch up" with iu and get reflected off the impedance discontinuity at the front, with the resultant second reflecti on moving downward. This scenario introduces additional complications in the model and is not further considered here. The general time-domain equation for co mputing the vertical electric field dEz due to a vertical differential current element idz (channel segment of length dz carrying a uniform current i(t)) at a height z above a perfectly conducting ground plane for the case of an observation point P on the plane at a horizontal distance r from the dipole is given by [e.g., Uman, 1987]: 22 22 2 54 2 3 0 0() (,) 1(2)()(2)() (,)[(,)(,)] 2()()()t zRz dizt zrRzzrRzr c dErtdzizdiztdzdz RzccRzccRzdt (6-6)

PAGE 280

280 where 0 is the electric permittivity of free space, R is the inclined distance from the dipole to the observation point, which is given by 22Rzr From Equation 6-6 for the geometry shown in Figure 6-22, the total electric field at the observation point for a finite-lengt h channel whose lower and upper e nds are at altitudes of z = 0 and z = H, respectively, is given by: 22 22 2 542 3 0 00() (,) 1(2)()(2)() (,)[(,)(,)] 2()()()Ht zRz dizt zrRzzrRzr c E rtdzizd iztdz dz RzccRzccRzdt (6-7) 6.3.1 Channel-Base Current without Pronounced Slow Front The Heidler function [Heidler, 1985] is used to represen t the channel-base current waveform not containing a pronounced slow fr ont in this Chapter, and is given by: 20 1 1(0,) 1() ()n t nt I ite t (6-8) where I0 = 26 kA, = 0.5, n = 3, 1 = 4 s, and 2 = 6 s. The current waveform is shown in Figure 6-23 and has a peak of about 15 kA and a zero-to-peak risetime of 5.4 s. 6.3.2 Electric Fields Computed Using the Original Transmission Line Model Figures 6-24a and b show the electrostatic, i nduction, and radiation co mponents of electric field and the total electric field up to 10 s at 500 m and 100 km, respectively, from the lightning channel computed using the original TL model and the current shown in Figure 6-23. For the purpose of comparison of electric field and curr ent waveshapes, the total electric field and current waveforms are overlaid (with the current scal ed so that its peak is equal to the electric field peak) in Figures 6-24c and d for distances of 500 m and 100 km, respectively. Note that the

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281 Figure 6-22. Geometrical parameters used in calculating the elect ric field at observation point P on perfectly conducting ground at horizontal distance r from the vertical return-stroke channel extending between ground and height H. electric field peak at 500 m, pr edicted by the TL model, is not c onsistent with the experimental data. The current wave is assumed to travel upward along the 4 km long channel at an assumed speed of 0.5 x 108 m/s. The electric field at 500 m fr om the channel is dominated by its electrostatic component, while that at 100 km from the channel is essentia lly radiation. Figures 6-25 and 6-26 show the model predicted electri c fields at 500 m and 100 km for current-wave speeds of 1 x 108 m/s and 2 x 108 m/s, respectively. 6.3.3 Electric Fields Computed Using th e Two-Wave Transmission Line Model Figures 6-27a and b show the electrostatic, i nduction, and radiation co mponents of electric field and the total electric field up to 10 s at 500 m and 100 km computed using the two-wave TL model which considers two current waves movi ng in opposite directions from the junction point at height h = 20 m above ground. The chan nel length is 4 km. The speed of both the upward and downward moving current waves is assumed to be 0.5 x 108 m/s. For the purpose of comparison of waveshapes, the tota l electric field and current wa veforms are overlaid (with the

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282 Figure 6-23. The channel-base current waveform given by Equation 6-8 used to calculate return stroke electric fields for the one-wave, two-wave and three-wave models. The parameters chosen are I0 = 26 kA, = 0.5, n = 3, 1 = 4 s, and 2 = 6 s. The current has a peak of about 15 kA and a zero-to-peak risetime of 5.4 s. current scaled so that its peak is equal to th e electric field peak) in Figures 6-27c and d for distances of 500 m and 100 km, respectively. Figu res 6-28 and 6-29 show the model-predicted electric fields at 500 m and 100 km when the speed of both current waves is 1 x 108 m/s and 2 x 108 m/s, respectively. The individual field co ntributions due to the upward and downward moving current waves along with the total electric field at 500 m for current propagation speeds of 0.5 x 108, 1 x 108, and 2 x 108, are shown in Figure 6-30a, b, and c, respectively. 6.3.4 Electric Fields Computed Using th e Three-Wave Transmission Line Model Figures 6-31a and b show the electrostatic, i nduction, and radiation co mponents of electric field and the total electric field up to 10 s at 500 m and 100 km computed using the three-wave TL model which considers two currents moving in opposite directions from the junction point at a height h of 20 m above ground and the ground reflected wave moving upward from ground. The channel length is 4 km. The speed of all three current waves is assumed to be 0.5 x 108 m/s. For the purpose of comparison of waveshapes, th e total electric field and current waveforms are overlaid (with the current scaled so that its peak is equal to the el ectric field peak) in the Figures

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283 6-31c and d for distances of 500 m and 100 km, respectively. Figures 6-32 and 6-33 show the model-predicted electric fields at 500 m and 100 km when the speed of both current waves is 1 x 108 m/s and 2 x 108 m/s, respectively. The individual fiel d contributions due to the two incident current waves (upward and downward moving), and the ground reflected current wave along with the total electric field at 500 m for current propagation speeds of 0.5 x 108, 1 x 108, and 2 x 108, are shown in Figure 6-34a, b, and c, respectively. 6.3.5 Channel-Base Current with Pronounced Sl ow Front and Computed Electric Fields An expression for first return stroke current proposed by De Conti and Visacro [2007] is used to represent the channel-base current waveform containing a pronounced slow front in this Chapter, and is given by: 201 1 1(0,) 1() ()k k kn t m kk n k k kt I it e t (6-9) where 1 12 21[()]n kk k k kkn ke The values of the parameters m, I0, n, 1, and 2 for different values of k are taken from Table II of De Conti and Visacro [2007] and given here in Table 6-4. This current waveform has a pronounced sl ow front and is shown in Figure 6-35. The electric field waveforms at 500 m computed using the on e-wave, two-wave and threewave models are shown in Figures 6-36a, 6-37a and 6-38a, respectively. Current-wave speed is assumed to be 108 m/s and the channel length is 4 km. For the two-wave and three-wave models, the height of the junction point is assumed to 20 m. The electric field waveforms at 100 km computed using the one-wave, two-wave and th ree-wave models are shown in Figures 6-36b, 637b, and 6-38b, respectively.

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284 Figure 6-24. Electrostatic (red), induction (green), and radiati on (blue) components of electric field and the total electric f ield (magenta) up to 10 s at (a) 500 m and (b) 100 km from the lightning channel computed us ing the origin al, one-wave TL model for an assumed current-wave propagation speed of 0.5 x 108 m/s and channel length of 4 km The total electric fields are overlaid with current waveforms scaled so that its peak is equal to the el ectric field peak (though at r = 500 m, the electric field peak occurs after 10 s and is not consistent with experimental data), for direct comparison of the initial risi ng portions for distances of (c) 500 m and (d) 100 km. Cha nnel-base current waveform is given by Equation 6-8. (a) (b) (c) (d) r = 500 m One-wave model v = 0.5 x 108 m/s Scaled current Total field and scaled current are almost indistinguishable Total field r = 500 m r = 100 km Total field r = 100 km Electrostatic field Electrostatic Induction Radiation

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285 Figure 6-25. Electrostatic (red), induction (green), and radiati on (blue) components of electric field and the total electric f ield (magenta) up to 10 s at (a) 500 m and (b) 100 km from the lightning channel computed us ing the origin al, one-wave TL model for an assumed current-wave propagation speed of 1 x 108 m/s and channel length of 4 km. The total electric fields are overlaid with current waveforms scaled so that its peak is equal to the electri c field peak, for direct comparison of the initial rising portions for distances of (c) 500 m and (d) 100 km. Channel-base curr ent waveform is given by Equation 6-8. (a) (b) (c) (d) Electrostatic Induction Radiation One-wave model v = 1 x 108 m/s Scaled current Total field and scaled current are almost indistinguishable Total field r = 500 m r = 100 km Total field r = 100 km r = 500 m

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286 Figure 6-26. Electrostatic (red), induction (green), and radiati on (blue) components of electric field and the total electric f ield (magenta) up to 10 s at (a) 500 m and (b) 100 km from the lightning channel computed us ing the origin al, one-wave TL model for an assumed current-wave propagation speed of 2 x 108 m/s and channel length of 4 km. The total electric fields are overlaid with current waveforms scaled so that its peak is equal to the electri c field peak, for direct comparison of the initial rising portions for distances of (c) 500 m and (d) 100 km. Note that the portion of the predic ted electric field waveform after the peak in (a) and (c) at 500 m is inconsistent with experimental data. However, for the initial few microseconds (probably up to the peak) the predicted close fi elds are expected to be co rrect. Channel-base current waveform is given by Equation 6-8. (a) (b) (c) (d) One-wave model v = 2 x 108 m/s Scaled current Total field and scaled current are almost indistinguishable Total field r = 500 m r = 100 km Total field r = 100 km r = 500 m Electrostatic Induction Radiation

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287 Figure 6-27. Electrostatic (red), induction (green), and radiati on (blue) components of electric field and the total electric f ield (magenta) up to 10 s at (a) 500 m and (b) 100 km from the li ghtning channel computed using the two-wave model for an assumed current-wave propa gation speed of 0.5 x 108 m/s and channel length of 4 km. Th e total electric fields are overlaid with current waveforms scaled so that its peak is equal to the electric field peak (though at r = 500 m, th e electric field pea k occurs after 10 s), for direct compar ison of the initial rising portions for distances of (c) 500 m and (d) 100 km. The junction point is assumed to be at a he ight h of 20 m above ground. Channel-base current waveform is given by Equation 6-8. (a) (b) (c) (d) Two-wave model v = 0.5 x 108 m/s Scaled current Total field and scaled current are almost indistinguishable Total field r = 500 m r = 100 km Total field r = 100 km r = 500 m Electrostatic Induction Radiation

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288 Figure 6-28. Electrostatic (red), induction (green), and radiati on (blue) components of electric field and the total electric f ield (magenta) up to 10 s at (a) 500 m and (b) 100 km from the li ghtning channel computed using the two-wave model for an assumed current-wave propa gation speed of 1 x 108 m/s and channel length of 4 km. The total electric fields are overlaid with current waveforms scaled so that its peak is equal to the electric field peak, for direct comparison of the initial rising portions for distances of (c) 500 m and (d) 100 km. The junction poi nt is assumed to be at a height h of 20 m above ground. Channel-base current waveform is given by Equation 6-8. (a) (b) (c) (d) Two-wave model h = 20 m v = 1 x 108 m/s Scaled current Total field and scaled current are almost indistinguishable Total field r = 500 m r = 100 km Total field r = 100 km r = 500 m Electrostatic Induction Radiation

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289 Figure 6-29. Electrostatic (red), induction (green), and radiati on (blue) components of electric field and the total electric f ield (magenta) up to 10 s at (a) 500 m and (b) 100 km from the li ghtning channel computed using the two-wave model for an assumed current-wave propa gation speed of 2 x 108 m/s and channel length of 4 km. The total electric fields are overlaid with current waveforms scaled so that its peak is equal to the electric field peak, for direct comparison of the initial rising portions for distances of (c) 500 m and (d) 100 km. The junction poi nt is assumed to be at a height h of 20 m above ground. Note that the portion of the pred icted electric field waveform after the peak in (a) and (c) at 500 m is inconsistent with experimental data. However, for the in itial few microseconds (probably up to th e peak) the predicted close fields are expected to be correct. Channel-base cu rrent waveform is given by Equation 6-8. (a) (b) (c) (d) Electrostatic Induction Radiation Two-wave model h = 20 m v = 2 x 108 m/s Scaled current Total field and scaled current are almost indistinguishable Total field r = 500 m r = 100 km Total field r = 100 km r = 500 m

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290 Figure 6-30. Electric field components Eu and Ed due to the upward and downward moving current waves, respectively, along with the total electric field (Eu + Ed) at 500 m for current propagation sp eeds of (a) 0.5 x 108, (b) 1 x 108, and (c) 2 x 108 for the twowave model. (a) (b) (c) Two-wave model h = 20 m v = 0.5 x 108 m/s r = 500 m Two-wave model h = 20 m v = 1 x 108 m/s r = 500 m Two-wave model h = 20 m v = 2 x 108 m/s r = 500 m

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291 Figure 6-31. Electrostatic (red), induction (green), and radiati on (blue) components of electric field and the total electric f ield (magenta) up to 10 s at (a) 500 m and (b) 100 km from the li ghtning channel computed using the three-wave model for an assumed current-wave propa gation speed of 0.5 x 108 m/s and channel length of 4 km. Th e total electric fields are overlaid with current waveforms scaled so that its peak is equal to the electric field peak (though at r = 500 m, th e electric field pea k occurs after 10 s), for direct compar ison of the initial rising portions for distances of (c) 500 m and (d) 100 km. The junction point is assumed to be at a he ight h of 20 m above ground. Channel-base current waveform is given by Equation 6-8. (a) (b) (c) (d) Electrostatic Induction Radiation Three-wave model h = 20 m v = 0.5 x 108 m/s Scaled current Total field and scaled current are almost indistinguishable Total field r = 500 m r = 100 km Total field r = 100 km r = 500 m

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292 Figure 6-32. Electrostatic (red), induction (green), and radiati on (blue) components of electric field and the total electric f ield (magenta) up to 10 s at (a) 500 m and (b) 100 km from the li ghtning channel computed using the three-wave model for an assumed current-wave propa gation speed of 1 x 108 m/s and channel length of 4 km. Th e total electric fields are overlaid with current waveforms scaled so that its peak is equal to the electric field peak, for direct comparison of the initial rising portions for distances of (c) 500 m and (d) 100 km. The junction poi nt is assumed to be at a height h of 20 m above ground. Channel-base current waveform is given by Equation 6-8. (a) (b) (c) (d) Electrostatic Induction Radiation Three-wave model h = 20 m v = 1 x 108 m/s Scaled current Total field and scaled current are almost indistinguishable Total field r = 500 m r = 100 km Total field r = 100 km r = 500 m

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293 Figure 6-33. Electrostatic (red), induction (green), and radiati on (blue) components of electric field and the total electric f ield (magenta) up to 10 s at (a) 500 m and (b) 100 km from the li ghtning channel computed using the three-wave model for an assumed current-wave propa gation speed of 2 x 108 m/s and channel length of 4 km. The total electric fields are overlaid with current waveforms scaled so that its peak is equal to the electric field peak, for direct comparison of the initial rising portions for distances of (c) 500 m and (d) 100 km. The junction poi nt is assumed to be at a height h of 20 m above ground. Note that the portion of the pred icted electric field waveform after the peak in (a) and (c) at 500 m is inconsistent with experimental data. However, for the in itial few microseconds (probably up to th e peak) the predicted close fields are expected to be correct. Channel-base cu rrent waveform is given by Equation 6-8. (a) (b) (c) (d) Three-wave model h = 20 m v = 2 x 108 m/s Scaled current Total field and scaled current are almost indistinguishable Total field r = 500 m r = 100 km Total field r = 100 km r = 500 m Electrostatic Induction Radiation

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294 Figure 6-34. Electric field components Eu, Ed, and Er due to the two incident current waves (upward and downward moving), ), and the ground reflected current wave, respectively, along with th e total electric field (Eu + Ed + Er) at 500 m for current propagation speeds of (a) 0.5 x 108, (b) 1 x 108, and (c) 2 x 108 for the three-wave model. Three-wave model h = 20 m v = 0.5 x 108 m/s r = 500 m Three-wave model h = 20 m v = 1 x 108 m/s r = 500 m Three-wave model h = 20 m v = 2 x 108 m/s r = 500 m (a) (b) (c)

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295 Figure 6-35. Current waveform represented by Equa tion 6-9 with parameters given in Table 6-4. Table 6-4. The values of the parameters m, I0, n, 1, and 2 for different values of k, reproduced from Table II of De Conti and Visacro [2007], used in Equation 6-9 to produce current waveform shown in Figure 6-35. k I0k (kA) nk 1k (s) 2k (s) 1 2.8 2 1.2 100 2 4.8 3 3 100 3 2.9 5 4.8 25 4 4.1 7 6 60 5 16.7 36 6.6 44 6 11 2 100 600

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296 Figure 6-36. Electrostatic (red), i nduction (green), and radiation (blue) components of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km computed using the one-wave model. Cu rrent-wave speed is assumed to be 108 m/s and the channel length is 4 km. Channel-ba se current waveform is given by Equation 6-9. r = 500 m r = 100 km (a) (b) One-wave model v = 1 x 108 m/s Total field Electrostatic Induction Radiation

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297 Figure 6-37. Electrostatic (red), i nduction (green), and radiation (blue) components of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km computed using the two-wave model. Cu rrent-wave speed is assumed to be 108 m/s and the channel length is 4 km. The juncti on point is at a heig ht of 20 m. Channelbase current waveform is given by Equation 6-9. r = 500 m r = 100 km (a) ( b ) Two-wave model v = 1 x 108 m/s h = 20 m Total field Electrostatic Induction Radiation

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298 Figure 6-38. Electrostatic (red), i nduction (green), and radiation (blue) components of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km computed using the three-wave model. Current-wave speed is assumed to be 108 m/s and the channel length is 4 km. The juncti on point is at a heig ht of 20 m. Channelbase current waveform is given by Equation 6-9. r = 500 m r = 100 km (a) ( b ) Three-wave model v = 1 x 108 m/s h = 20 m Total field Electrostatic Induction Radiation

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299 6.4 Discussion From Figures 6-24 to 6-26 (original, one-wave TL model), 6-27 to 6-29 (two-wave model), and 6-31 to 6-33 (three-wave model) we can see that as expected, the return stroke electric field at 500 m for all three models is dominated by its electrostatic component, while that at 100 km is essentially radiation. The electric field peak at far distance (100 km) in creases with increasing current propagation speed for all three models. Also, at far dist ance current and total electric field waveshapes are almost identical for all thre e models and for all values of speed. Figures 639a and b show the tota l electric fields at 500 m and 100 km, respectively, for the one-wave, two-wave, and three-wave models for v = 108 m/s overlaid for direct comparison. At 100 km, the return stroke electric field peak for the one-wav e and two-wave models are approximately half of that for the three-wave model. This is due to the inclusion of the reflected wave from ground (see Figure 6-34) that is not part of the one-wave model and is neglected in the two-wave model. In order to avoid this discrepancy, the incident wa ves for the one-wave and two-wave models have to be adjusted to effectivel y account for the reflected wave at ground such that the modelpredicted electric fields can be directly compare d. Note that for all three models, for v = 2 x 108 m/s, the falling portion of the electric field waveform at 500 m after the peak is not consistent with experimental data. However, for the initia l few microseconds (probably up to the peak) the predicted close fields are expected to be correct As stated in Section 6.3, the overall electric field waveforms at close distan ces are best reproduced by the MTLL model. However, for the initial few microseconds the MTLL and TL models predict essentially the same fields. In all three models, no distinct slow front is seen in th e initial rising portion of the of return stroke electric field waveform for a ny considered value of speed. Next, we examine the effect of the variation in the height of the junction point from ground for the two-wave and three-wave models on the initial rising portion of the return stroke electric

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300 field waveform. Figure 6-40a shows the return stroke electric fields at 100 km for the two-wave model, when the height of the junction point is 20 m (red line) and 100 m (blue line) above ground. The current propagation speed is 108 m/s. The electric field ri setime appears to decrease from 5.1 to 4.2 s and the peak electric field increases from 3.04 to 3.49 V/m, due to the increase in the length of the channel below the junction point. Figure 6-40b shows the return stroke electric fields at 100 km for the three-wave mode l, when the height of the junction point is 20 m (red line) and 100 m (blue line) above gr ound. The current propagation speed is 108 m/s. The electric field waveforms are almo st indistinguishable from each other, and neither exhibits a distinct slow front in th e electric field waveform. Jerauld et al. [2007], showed, using an unusual trigge red-lightning stroke, that both close and distant fields can be predic ted by the two-wave model in which both the slow-front and fasttransition currents are generated at the junction point of the upward and downward leaders and propagate away from that point. They used the measured current waveform which consisted of a slow front fast transition sequen ce to produce dE/dt (at 30 m, see Figure 6-41) and electric field (at 100 km, see Figure 6-42) displaying the same f eatures. In the present study, we also used a two wave model to compute fields at the near and far distances and a current wave (given by Equation 6-8, see Figure 6-23) that did not co ntain a pronounced slow front. The resultant electric fields at near and far distances (see Figure 6-39) do not contain a slow front. Similar results are seen for the three-wave model, which is more realistic [e.g., Rakov et al., 1998] as it additionally accounts for the refl ection at ground of the downward current wave, with this reflected wave travelling up the channel (tow ard the junction point and beyond) at constant speed. Weidman and Krider [1978] noted that the shapes an d relative amplitudes of the fronts and fast transitions in the current waveforms are surprisingly similar to those in the radiated

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301 fields (currents and fields bei ng measured in different studies). On the other hand, there are experimental data [Willett et al., 1989a], although for triggered-lightning strokes, which suggest that radiation field waveforms can exhibit prono unced slow fronts without similar features in corresponding current waveforms. It is possible th at the physics of attachment process and the mechanism of the slow front/fast transition sequen ce generation is more complex than the simple models examined in this Chapter. In appears that a current containing a pronounc ed slow front is needed to produce slow fronts in electric field at both near and far distan ces. In order to demonstrate this, we used an expression for first return stroke current proposed by De Conti and Visacro [2007] which is given by Equation 6-9. From the electric field waveforms shown in Figures 6-36, 6-37, and 6-38 computed using the one-wave, two-wave, and three-wave models, respectively, for this channelbase current and for a current propagation speed of 108 m/s, it can be seen that for all three models the slow front in electric field is observed in both the n ear and far field waveforms. The total electric fields at 500 m and 100 km computed using the three models for v = 108 m/s are overlaid in Figures 6-43a and 6-43b, respectiv ely, for direct comparison. Apart from the difference in the return stroke electric field peak between the one-wave and two-wave models the on one hand and the three-wave model on the other hand (due to reasons discussed above), the characteristics of the slow front/fast transition sequences (duration of the slow front and its magnitude relative to peak) are also approximate ly the same in all three models. However, one can see from Figures 6-36b, 6-37b, and 6-38b, that th e slow front at 100 km is primarily due to the radiation field component, the contributions due to electrostatic and induction components being negligible, while at 500 m (see Figures 6-36a, 6-37a, and 6-38a), the slow front is composed of more or less equal (or comparab le) contributions from all three components of

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302 electric field. The electric field waveform at 500 m and 100 km computed using the three-wave model for v = 2 x 108 m/s are shown in Figures 6-44a and 6-44b, respectively. For v = 2 x 108 m/s the initial radiation field peak at 500 m is more pronounced than that for v = 108 m/s. The slow front duration at both 500 m and 100 km is 6.1 s. The amplitude of the slow front is 52% of the peak at 500 m and 44% of the peak at 100 km. For electric field waveforms of first return strokes measured at two-stati ons discussed in Section 6.2, the AM slow front duration for the three first return strokes at the near and far stations, were 4.6 and 4.3s, respectively. The amplitude of the slow front was, on average, 47% of the peak at the near station and 35% of the peak at the far station. The amplitude of the sl ow front relative to the peak was found to be similar in close and distant waveforms for tw o out of three first return strokes having a pronounced slow front. Note that there is some uncertainty invol ved in identifying the initial field peak at close distances to which the small differences may probably be attributed. The mechanism of formation of slow front in the current is probably related to the breakthrough phase of the attachment process by which the extending plasma channels of the upward and downward leaders make contact. This process begins when the relatively low-conductivity streamer zones ahead of the two propagating lead er tips meet to form a common streamer zone. The subsequent accelerated extension of the tw o relatively high-conductivity plasma channels toward each other takes place inside the common streamer zone. The break-through phase can be viewed as a switch-closing opera tion that serves to launch two return-stroke waves from the point of junction between two plasma channels [Rakov and Uman, 2003]. The transition from a low conductivity streamer zone to a highly conducting channel is likely to produce a slow front followed by a fast transition when current quickly rises to its peak value.

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303 6.5 Summary In this chapter we examine the shapes and relative magnitudes of slow fronts and fast transitions in electric field waveforms of first return stro kes in negative cloud-to-ground lightning measured simultaneously at two stations, one at about 45 km (far station), and the other at hundreds of meters to a few k ilometers (near station) from th e lightning channel. It was found that the overall field waveform characteristics of fi rst return strokes up to the radiation field peak are similar for near (where the electric field is dominated by its electrostatic component) and far (where the electric field is esse ntially radiation) distances. Th e radiation field component of electric field is expected to be inversely proportional to distance. However, the data examined here deviated from this expectation due to the measured initial field peaks at the near station being not so well defined and c ontributions from electrostatic and induction components. The return stroke slow front duration in close electric field waveform s, though not identical, is similar to that in distant electric field waveforms for experimental data. The amplitude of the slow front relative to the peak was found to be similar in close and distant waveforms for two out of three first return strokes having a pronounced slow front. We examined, via modeling, whether electr ic field waveforms can exhibit pronounced slow fronts without similar featur es in corresponding current wave forms. Three different models, the one-wave, two-wave and threewave, were used and close and di stant return stroke electric fields computed and examined. For all three models, the computed elect ric field waveforms do not exhibit distinct slow fronts. There are experimental data [Willett et al., 1989a], although for triggered-lightning strokes, which suggest that radiation field waveform s can exhibit pronounced slow fronts without similar features in corresponding current wavefo rms. It is poss ible that the physics of attachment process and the mechanis m of the slow front/fast transition sequence generation is more complex than the simple models examined in this Chapter. For an incident

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304 current wave containing a pronounced slow front, the duration of the slow front in modelpredicted electric fields and its magnitude relativ e to peak are approximately the same at near and far distances. The slow front at 100 km is pr imarily due to the radiation field component, the contributions due to electrosta tic and induction components being negligible. At 500 m the slow front is composed of more or less equal (or co mparable) contributions from all three components of electric field. It is likely that a slow front in return stroke current is responsible for a slow front in return stroke electric field. The mechanis m of formation of slow front in the current is probably related to the break-thr ough phase of the attachment process by which the extending plasma channels of the upward and downward leaders make contact.

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305 Figure 6-39. Total electric fields at (a) 500 m and (b) 100 km for the one -wave (red line), twowave (green line), and three-wave (blue line) models for v = 108 m/s overlaid for direct comparison. Channel-base curren t waveform is given by Equation 6-8. r = 500 m r = 100 km ( a ) ( b )

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306 Figure 6-40. The return stroke elec tric fields at 100 km for the (a) two-wave and (b) three-wave models when the height of the junction poi nt is 20 m (red line) and 100 m (blue line) above ground. The current propagation speed is 108 m/s. Channel-base current waveform is given by Equation 6-8. r = 100 km r = 100 km ( a ) ( b ) Electric fields for h = 20 m and h = 100 m are almost indistinguishable Three-wave model Two-wave model h = 100 m h = 20 m

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307 Figure 6-41. Contributions from upward (dotted cu rve) and downward (solid gray curve) waves to the model-predicted dE/dt waveform at 30 m calculated by Jerauld et al. [2007] using the two-wave model with dI/dt as input and current originat ing at a height of 6.5 m. The total field (sum of the two compone nts) is also shown (solid black curve). Taken from Jerauld et al. [2007].

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308 Figure 6-42. Electric fields at 100 km calculated by Jerauld et al. [2007] using the singleand two-wave models, assuming propagati on over a perfectly conducting ground. Integrated dI/dt was used as i nput to both models. Taken from Jerauld et al. [2007].

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309 Figure 6-43. Total electric fields at (a) 500 m and (b) 100 km for the one -wave (red line), twowave (green line), and three-wave (blue line) models for v = 108 m/s overlaid for direct comparison. Channel-base curren t waveform is given by Equation 6-9. r = 500 m r = 100 km (a) ( b ) Three-wave model Two-wave model One-wave model Three-wave model Two-wave model One-wave model

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310 Figure 6-44. Electrostatic (red), i nduction (green), and radiation (blue) components of electric field and the total electric field (magenta ) up to 10 s at (a) 500 m and (b) 100 km computed using the three-wave model. Current-wave speed is assumed to be 2 x 108 m/s and the channel length is 4 km. The junction point is at a height of 20 m. Channel-base current waveform is given by Equation 6-9. ESF EP ESF EP r = 500 m r = 100 km (a) ( b ) Three-wave model v = 2 x 108 m/s h = 20 m

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311 CHAPTER 7 CHARACTERIZATION OF POSITIVE CLOUD-TO-GROUND LIGHTNING Positive ligh tning discharges are considerably less understood than their negative counterparts (see Chapter 2). In this chapter, various features of positive cloud-to-ground lightning discharge, including multiplicity, parameters of return-stroke electric field waveforms, peak currents inferred from radiation electric fi eld peaks, charge transferred by return stroke, leader stepping, preliminary breakdown pulse tr ains, and occurrence with in otherwise negative cloud-to-ground flashes (which cons titutes a bipolar flas h) are examined. Presented here are 52 positive and 2 bipolar cloud-to-ground flashes r ecorded in 2007-2008 in Gainesville, Florida. Table 7-1 summarizes the positive and bipolar cl oud-to-ground lightning da ta recorded at the LOG. Of these 54 discharges, 41 occurred durin g the warmer (April-October) season and 13 during the colder (November-Feb ruary) season. We had GPS timing information for 45 positive flashes (containing 53 strokes) and 1 bipolar flash (1 positive return stroke). The National Lightning Detection Network (NLDN) located 52 (96%) out of 54 positive return strokes, of which 48 were correctly identified and 4 positive return strokes were misidentified as cloud discharges. NLDN-reported dist ances from the field measuring station (LOG) for the 48 correctly identified strokes ranged from 7.8 to 157 km and for 4 misidentified strokes from 1.8 to 5 km. 7.1 Multiplicity The term multiplicity is often used to denote nu mber of strokes per flash, not necessarily along the same channel to ground. Positive flashes are usually composed of a single stroke, whereas about 80% of negative flashe s contain two or more strokes [e.g., Rakov et al. 1994]. Multiple-stroke positive flashes do occur but they are relatively rare. Heidler et al. [1998], from electric field measurements in 199597 in Germ any, found that out of a total of 36 positive

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312 N = 52Number of Strokes per Flash 01234Number 0 5 10 15 20 25 30 35 40 45 42 (81%) 9 (17%) 1 (2%) Figure 7-1. Histogram of the number of strokes per flash for 52 positive cloud-to-ground flashes in Florida. flashes, 32 (89%) contained one stroke and 4 (10% ) contained two strokes. Out of the 52 positive cloud-to-ground flashes presented here 42 (81%) were single-str oke, 9 (17%) two-stroke, and 1 (2.0%) three-stroke flashes, as shown in Figure 7-1. The electric fiel d of the three-stroke flash is shown in Figure 7-2 (GPS timing information for this flash was not available and hence no NLDN data could be obtained). There were a tota l of 63 return strokes in 52 flashes with an average number of strokes per flash (multiplicity) of 1.2. For comparison, Rakov and Uman [1990b] reported an average multiplicity of 4.6 for 76 negative cloud-to-ground flashes in Florida. Note that for the dataset presented here, th e record length was either 240 ms with a pretrigger of 80 ms, or 500 ms with a pre-trigger of 100 ms. There is a small possibility that a subsequent stroke of a multiple-stroke positive flash triggered our field measuring system and, due to insufficient pre-trigger, the first stroke of the flash was missed. In order for this to happen,

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313 the field peak of the "missed" first stroke would have to be smaller than that of the subsequent stroke and it would have to occur at least 80 ms (the minimum pre-trigger time of our electric field records) prior to the subse quent stroke. Thus, some first return strokes in our dataset may actually be subsequent strokes, and some singl e stroke flashes may actually be multiple-stroke flashes. If that were the case, the calculated multiplicity of 1.2 would be an underestimate. We found that 13 out of 52 (25%) positive flas hes in our dataset were associated with (either preceded or followed by) intracloud discharges. However, this might be an underestimate due to the limited pre-trigger time an d record length, as discussed above. For 8 out of the 9 two-stroke flashes NLDN estimated locations for all strokes were available. These flashes occurred at distan ces ranging from 10 to 157 km from the field measuring station. Of these 8 flashes, the dist ance between the first and second strokes was less than 1 km for 1 flash, within 1 to 4 km for 3 flas hes, and within 10 to 15 km for 3 flashes. In one flash, the two strokes were separated by 29 km. Th e interstroke interval, distance between first and second strokes for each flash, and the semi-m ajor axis (SMA) length of NLDN 50% location error ellipse, which is defined as NLDN median lo cation error, for each stroke are given in Table 7-2. Figures 7-44 to 7-51 (at the end of this chapte r) show electric field re cords of the first and second return strokes for all eight located twostroke positive flashes. A second stroke that exhibits a wave shape similar to that of the co rresponding first stroke probably follows the same channel as the first one. Distance between stroke s being smaller than the largest NLDN median location error (SMA length) is also an indicati on of the two strokes sharing the same channel. Out of 8 two-stroke flashes, 3 contained str okes characterized by both similar electric field waveshapes and spatial separations that are sm aller than stroke location uncertainties. For

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314 example, in flash 06/02/08_431 (shown in Figure 7-37) for which the two strokes occurred within 83 ms and 222 m of each other (NLDN medi an location errors of 800 m and 500 m for the first and second stroke, respectiv ely) the second stroke likely followed the same channel as the first stroke. In one flash (05/ 16/08_49), field waveshapes were similar but separation (14 km) was much larger than median location errors (0.4 km). For 5 two-stroke flashes, different field waveshapes were accompanied by distances larger than location errors. Thus, only in one case out of eight the two criteria were inconsistent with each other. The issue of the number of channels to ground formed within a flash can, however, be only addressed conclusively when optic al records (video or still images) of the flash are available. Optical evidence of negative strokes following th e channel of preceding positive stroke in a bipolar flash in Florida has been reported by Jerauld et al. [2009]. Fleenor et al. [2009] observed four bipolar flashes (about 1% of the flashes in their dataset) in the Great Planes each of which had a positive first stroke that was followed by 1 (in 3 flashes) or 2 (in 1 flash) negative strokes. The intervals between the first and second strokes ranged from 43 ms to 348 ms. Two of their four negative second strokes followed the same channel to ground as the preceding positive first stroke. Examples of a positive subsequent stroke following the same channel as the preceding negative stroke have been previously reported fo r tower lightning and ro cket-triggered lightning. Janischewskyj et al. [1999] in Canada reported a flash that was initiated by an upward leader from the 553-m high Canadian National (CN) to wer in Toronto. The flash contained three strokes, the second of which was positive, fo llowing the same channel within at least 535 m above the tower top. The three cons ecutive return stroke peak currents, in stroke order, were -10.6 kA, +6.5 kA, and -8.9 kA. Jerauld et al. [2004] reported a triggered lightning flash containing both negative and positive strokes. Th e first stroke lowered negative charge to ground

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315 and the second stroke lowered positive charge via the same channel. The measured negative return stroke peak current was -11 kA and the positive +5 kA. The two return strokes were separated by about 58 ms. Table 7-1. Summary of the positive and bipolar cloud-to-ground lightning data (a total of 54 flashes) recorded at the LOG. Data record ed is indicated by "Y" and not recorded by "N". Flash ID Electric Field dE/dt dB /dt HF (5 MHz) VHF (36 MHz) 062007_00 Y N N N N 082407_286 Y Y N Y Y 082407_452 Y Y N Y Y 100507_186 Y Y N Y Y 100507_376 Y Y N Y Y 121607_49 Y Y N N N 121607_61 Y Y N Y Y 121607_63 Y Y N Y Y 011908_441 Y Y N N N 011908_481 Y Y N N N 012208_05 Y Y N Y Y 012208_06 Y Y N Y Y 012208_08 Y Y N Y Y 012208_10 Y Y N Y Y 012208_13 Y Y N Y Y 012208_14 Y Y N Y Y 012208_23 Y Y N Y Y 042608_00 Y Y N N Y 042608_01 Y Y N N Y 051608_27 Y Y N N Y 051608_29 Y Y N N Y 051608_31 Y Y N N Y 051608_47 Y Y N N Y 051608_49 Y Y N N Y 051808_86 Y Y N N Y 051808_88 Y Y N N Y 051808_106 Y Y N N Y 061008_05 Y Y N N Y 060108_131 Y Y N N Y 060108_208 Y Y N N Y 060108_215 Y Y N N Y 060208_431 Y Y N N Y 060908_700 Y Y N N Y

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316 Table 7-1. Continued Flash ID Electric Field dE/dt dB/dt HF (5 MHz) VHF (36 MHz) 080808_01 Y Y N N N 081308_31 Y Y N N Y 081308_40 Y Y N N Y 081308_41 Y Y N N Y 081308_57 Y Y N N Y 081308_58 Y Y N N Y 081408_84 Y Y Y N N 081408_85 Y Y Y N N 081408_87 Y Y Y N N 081408_90 Y Y Y N N 082308_173 Y N Y N Y 082308_338 Y N Y N Y 082308_339 Y N Y N Y 082308_343 Y N Y N Y 082308_344 Y N Y N Y 082308_345 Y N Y N Y 082308_346 Y N Y N Y 082308_348 Y Y Y N Y 082308_350 Y Y Y N Y 082408_783 Y Y Y N Y 113008_01 Y Y Y N N

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317 Figure 7-2. (a) Electric field re cord of a multiple-stroke positive cloud-to-ground flash in Florida with three return strokes (RS) shown on a 75-ms time scale. (b), (c), and (d). Electric fields of the first, second, and third return strokes, on a 1.5-ms time scale, respectively. GPS timestamps and NLDN inform ation were not available for this flash.

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318 Table 7-2. Interstroke interval, distance between first and second strokes, and semi-major axis (SMA) length of NLDN 50% loca tion error ellipse for each stroke of 8 two-stroke positive flashes. Flash ID Figure showing electric field waveforms Interstroke interval, ms Distance between first and second strokes, km SMA length for first stroke, km SMA length for second stroke, km Distance between strokes is smaller than largest SMA length Similarity of first and second stroke electric field waveforms 06/20/07_00 7-44 19 1.7 4.0 0.5 Y Y 01/22/08_05 7-45 79 12 0.7 0.4 N N 01/22/08_06 7-46 8.5 2.0 2.4 0.5 Y Y 05/16/08_49 7-47 116 14 0.4 0.4 N Y 06/02/08_431 7-48 83 0.22 0.8 0.5 Y Y 08/14/08_85 7-49 70 10 0.6 0.8 N N 08/23/08_350 7-50 201 29 0.5 0.4 N N 11/30/08_01 7-51 41 3.7 0.4 0.4 N N AM 77 9.1 1.2 0.5 GM 54 4.4 0.8 0.5 Min 8.5 0.22 0.4 0.4 Max 201 29 4 0.8 7.2 Parameters of Return Stroke Electri c Field and Field Derivative Waveforms The electric field and field derivative (dE/dt ) waveforms of positive return strokes were examined in detail. The various field waveform parameters of positive return strokes are discussed in the following Sections and summari zed in Table 7-3. Since not all the parameters could be measured in each waveform, samp le sizes in Table 7-3 are not the same. 7.2.1 Distance-Normalized Electric Field Peaks The measured initial electric field peak nor malized to 100 km for 48 positive return strokes located at distances of 7.8 to 157 km ranged from 4.34 to 66.3 V/m. The AM and GM fields were 21.7 V/m and 18.1 V/m, respectively. Note that the electric field change due to a positive return stroke is negative according to the at mospheric electricity sign convention. Only the magnitude of the electric field change is consid ered here. The histogram of the initial electric

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319 field peak normalized to 100 km for the 48 return strokes is shown in Figure 7-3. Cooray and Lundquist [1982] and Cooray et al. [1998] reported the AM electri c field peak normalized to 100 km to be 11.5 V/m and 13.9 V/m in Sweden and Denmark, respectively. These values are roughly 0.5 to 0.7 times of their coun terpart found in this study. Fi gure 7-4 shows the scatter plot for the distance-normalized electric field peak ve rsus distance from the m easuring station for the 48 positive return strokes in this dataset. Ideally, there should be no dependence. It can be seen in Figure 7-4 that even though the minimum normalized electric fiel d peak tends to increase with distance, the dependence is rather weak (deter mination coefficient = 0.20 ). The dependence of the minimum value on distance suggests a bias toward larger field peaks, which increases with increasing distance. Indeed, the GM normalized el ectric field peaks for distance ranges of 7.8-50 km and 64-157 km in this dataset are 14.8 V/m (N = 31) and 26.3 V/m (N = 17), respectively. Table 7-4 shows the number of posi tive return strokes in different distance ranges along with the GM electric field peak normalized to 100 km for each distance range. For negative lightning, Rakov and Uman [1990b] and Pavlick et al. [2002] found the GM electric field peak normalized to 100 km to be 5.9 V/m and 7.6 V/m for 76 and 178 first strokes, respectively, in Florida versus 19.8 V/m for 40 positive first strokes in this study. For 270 negative subsequent strokes, the GM electric fi eld peak normalized to 100 km was 2.9 V/m in Florida [Rakov and Uman, 1990a, b], while for the 8 positive s ubsequent strokes in the dataset presented here the value was 11.7 V/m. Note that even for distances less than 20 km (see Table 7-4) the GM electric field peak normalized to 100 km for positive strokes examined here is higher than for negative return strokes. 7.2.2 Risetime Histogram of the zero-to-peak risetime and 1090% risetime for 62 (out of the total of 63 return strokes recorded, the electric field waveform for one return stroke was saturated due to its

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320 Table 7-3. Parameters of electric field waveforms produced by first and subsequent return strokes in positive lightning. Parameter Sample size AM SD GM Median SD (logx) Range Initial electric field peak normalized to 100 km, V/m 48 21.7 13.2 18.1 19.5 0.275 4.34-66.3 Zero-to-peak risetime, s 62 7.77 3.76 6.92 7.19 0.213 2.26-21.1 10-to-90 percent risetime, s 62 4.02 2.12 3.40 3.71 0.279 0.36-10.4 Slow front duration, s 62 5.94 3.63 4.95 5.15 0.276 0.77-18.6 Slow front amplitude relative to peak, percent 62 39.4 15.0 36.7 36.7 0.167 14.1-79.4 Fast-transition 10-to-90 percent risetime, s 62 1.21 0.774 1.02 1.05 0.258 0.28-4.58 Zero-crossing time, s 41 53.6 42.9 42.1 42.7 0.299 11.3-197 Opposite polarity overshoot relative to peak, percent 31 15.6 9.49 13.0 14.3 0.273 4.13-43.6 Width of dE/dt pulse at half peak value, s 37 1.53 1.09 1.27 1.30 0.265 0.33-6.20 Peak electric field derivative normalized to 100 km, V/m/s 27 10.0 5.08 9.02 8.58 0.201 3.23-25.8 NLDN estimated peak current, kA 48 87.8 50.3 74.6 79.5 0.256 19.8-234 Table 7-4. Number of positive return strokes in different distance ranges and corresponding GM electric field peaks normalized to 100 km. Distance range, km 5-2020-40 40-60 60-80 80-100 100-160 0-160 Number of events 6 14 11 4 5 8 48 GM NLDN-estimated peak current, kA 10.8 17.3 14.4 23.8 23.0 30.1 18.1

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321 Electric Field Peak Normalized to 100 km (V/m) 010203040506070 Occurrence 0 2 4 6 8 10 Firststrokes, N = 40 Subsequent strokes, N =8 First return stroke Subsequent return stroke All AM, V/m 23.4 13.2 21.7 GM, V/m 19.8 11.7 18.1 Min, V/m 5.0 4.34 4.34 Max, V/m 66.3 20.3 66.3 N 40 8 48 Figure 7-3. Histogram of the in itial electric field peak norma lized to 100 km for 48 positive return strokes. Statistics given are arit hmetic mean (AM), geometric mean (GM), minimum (min), and maximum (max) values fo r first and subsequent strokes, as well as for all data combined.

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322 Distance, km 020406080100120140160180 Electric Field Normalized to 100 km, V/m 0 10 20 30 40 50 60 70 First strokes, N = 40 Subsequent strokes, N = 8 R2= 0.20 Figure 7-4. Distance-normalized el ectric field peak versus distance from the measuring station for 48 positive return strokes. Note that the electric field change due to a positive return stroke is negative according to th e atmospheric electricity sign convention. Only the magnitude of the electric fi eld change is shown in this plot. proximity to the measuring station) return stroke electric fields are shown in Figures 7-5 and 7-6, respectively. The zero-to-peak risetimes range from 2.26 to 21.1 s, with the arithmetic mean (AM) and geometric mean (GM) being 7.77 and 6.92 s, respectively. Rust et al. [1981] found the AM zero-to-peak risetime to be 6.9 s (which is similar to that found in this study) with a range of 4-10 s for 15 positive return strokes in the Great Plains, USA. Cooray and Lundquist [1982] found the AM zero to peak risetimes for 64 and 52 positive return strokes (from two different storms) in Sweden to be 13 and 12 s, respectively, each with a range of 5-25 s. For winter positive lightning in Japan, Ishii and Hojo [1989] found the zero to peak risetime for 123 return strokes to be in the range of 8-44 s with the AM being 21.2 s. For 32 strokes in summer, they reported the AM to be 13.2 s, which is shorter than that for winter positive lightning. Similarly, in the data presented here, for 45 return strokes in the warm (March to October) season, the AM and GM zero-to-peak ri setimes were 7.5 s and 6.8 s, respectively,

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323 which are shorter than the AM and GM zero-to-peak risetimes of 8.5 s and 7.4 s, respectively, for 17 return strokes that occurred during the cold (November-February) season. In the data presented here, the AM and GM 10-90% risetimes were 4.02 s and 3.40 s, respectively with a range of 0.36 to 10.4 s. Beasley et al. [1983] found the AM 10-90% risetime for 6 positive return strokes in Florida to be 2.7 s. The AM 10-90% risetimes in Sweden and for winter lightning in Japan were reported to be 6.2 s [Cooray, 1986a,b] and 8.7 s [Hojo et al. 1985], respectively. For return strokes in summer in Japan, Hojo et al. [1985] reported the AM risetime to be 6.7 s, which is shorter than that in winter. In the data presented here, for 17 return strokes that occurred during th e cold season the AM and GM 10-90% risetimes were 3.8 s and 3.1 s. For 45 return strokes in the warm seas on, the AM and GM 10-to-90% risetimes were 4.1 s and 3.5 s which are longer than those in winter. From the above discussion it appears that th e zero-to-peak and 10-to-90% risetimes for positive return strokes in Sweden and Japan are, in general, longer than those reported in this study for Florida and those reported by Rust et al. [1981] for the Grea t Plains. Table 7-5 compares the risetimes of positive return strokes in summer and winter in Florida with those in other regions. The scatter plot of the zero-to-peak and 10-to -90% risetimes versus distance for 48 positive return strokes (out of 62) located at distances ranging from 7. 8 to 157 km from the measuring station are shown in Figures 7-7 and 7-8. No corr elation between risetimes and distance is found (determination coefficients of 0.02 and 0.05, respectively). The AM zero-to-peak and 10-to-90% risetimes for 105 first strokes in negative cloud-toground discharges in Florida were reported by Master et al. [1984] to be 4.4 s and 2.6 s, respectively, which are shorte r than the corresponding values of 7.88 s and 4.03 s for 51

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324 positive first strokes for the dataset analyzed here. For 220 negative s ubsequent strokes in Florida, [Master et al., 1984] reported, the AM zero-to-peak and 10-to-90% risetimes to be 2.8 s and 1.5 s, respectively, versus 7.28 s and 3.95 s for 11 positive subsequent strokes analyzed here. In summary, it appears that electric field risetimes for positive subsequent return strokes are appreciably longer than for negative return strokes. Zero to Peak Risetime ( s) 0246810121416182022 Occurrence 0 5 10 15 20 First strokes, N = 51 Subsequent strokes, N = 11 First return stroke Subsequent return stroke All AM, s 7.88 7.28 7.77 GM, s 7.06 6.39 6.94 Min, s 2.26 3.58 2.26 Max, s 19.4 21.1 21.1 N 51 11 62 Figure 7-5. Histogram of the zero-to-peak risetime for 62 positive return strokes. Statistics given are arithmetic mean (AM), geometric m ean (GM), minimum (min), and maximum (max) values for first and subsequent stro kes, as well as for all data combined.

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325 10 to 90% Risetime, s 01234567891011 Occurrence 0 2 4 6 8 10 12 14 First strokes, N =51 Subsequent strokes, N =11 First return stroke Subsequent return stroke All AM, s 4.03 3.95 4.01 GM, s 3.40 3.41 3.40 Min, s 0.36 1.55 0.36 Max, s 9.41 10.40 10.4 N 51 11 62 Figure 7-6. Histogram of the 10-90% risetime for 62 positive retu rn strokes. Geometric mean (GM) value is given for all data combined (N = 62). Statistics given are arithmetic mean (AM), geometric mean (GM), minimum (min), and maximum (max) values for first and subsequent strokes, as well as for all data combined.

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326 Table 7-5. Risetimes of return stroke electric fiel d waveforms in differe nt regions and in different seasons. Parameter Reference and Location Season Sample size AM, s Remarks Summer 45 7.5 Present study, Florida Winter 17 8.5 Cooray and Lundquist [1982], Sweden Summer 64 and 52 12 and 13 Summer 32 13.2 Ishii and Hojo [1989], Japan Winter 123 21.2 Zero-topeak risetime Rust et al. [1981], Great Plains Summer 15 6.9 (a) The zero-to-peak risetime for positive return strokes in Sweden and Japan are, in general, longer than those reported in this study for Florida and those reported by Rust et al. [1981] for the Great Plains. (b) Zero-to-peak risetime for positive return strokes in summer is shorter than that for winter positive lightning. Summer 45 4.1 Present study, Florida Winter 17 3.8 Beasley et al. [1983], Florida Summer 6 2.7 Cooray [1986a,b], Sweden Summer 15 6.2 Summer 44 6.7 10-to90% risetime Hojo et al. [1985], Japan Winter 32 8.7 (a) The 10-to-90% risetime for positive return strokes in Sweden and Japan are, in general, longer than those reported in this study for Florida and those reported by Rust et al. [1981] for the Great Plains. (b) The 10-to-90% risetimes in summer are (i) longer than those in winter for positive return strokes in Florida, and (ii) shorter than those in winter for positive return strokes in Japan.

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327 R 2 = 0.02 Distance, km 020406080100120140160180 Zero to Peak Risetime, s 0 5 10 15 20 25 First strokes, N = 40 Subsequent strokes, N = 8 Figure 7-7. Zero-to-peak risetime time versus the distance from the measuring station for 48 positive return strokes. R 2 = 0.05 Distance, km 020406080100120140160180 10 to 90% Risetime, s 0 2 4 6 8 10 12 First strokes, N = 40 Subsequent strokes, N = 8 Figure 7-8. 10-to-90% risetime time versus th e distance from the measuring station for 48 positive return strokes.

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328 7.2.3 Slow Front and Fast Transition The initial rising portion of electric field wave form of positive return stroke (and negative return stroke as discussed in Chapter 2) is often viewed as being composed of initial relatively slow rising portion, called the slow front, and a portion showing a fast rise to peak, called the fast transition. A typical slow front-fast transition sequ ence in a positive return stroke electric field waveform is shown in Figure 7-9. The break-point between the slow front and fast transition was determined subjectively by examination of wave forms. The duration of the slow front for 62 positive return strokes in this dataset ranged from 0.77 s to 18.6 s. The AM and GM were 5.94 s and 4.95 s, respectively. Figure 7-10 and 7-11 show the histograms of the slow front duration and slow front amplitude relative to peak. The amplitude of the slow front in our dataset of 62 positive return strokes was on average 39.4 % (with a range of 14.1 to 79.4% and a GM of 36.7%) of the return stroke peak. The 10-90% risetime of the fast transition ranged from 0.28 to 4.58 s with AM and GM of 1.21 s and 1.02 s, respectively. The distribution of the fast transition 10-to-90% risetime is shown in Figure 7-12. Figures 7-13 and 7-14 show the scatter plots of the slow front duration and slow front amplitude relative to peak, respectively, versus distance for 48 positive return strokes (out of 62) located at distances ranging from 7.8 to 157 km from the measuring station. No correlation wa s found between these pa rameters and distance (determination coefficients of 0.003 and 0.02, for slow front duration and slow front amplitude relative to peak, respectively). Figure 7-15 shows the scatter plots of the fast transition 10-to90% risetime versus distance. It can be seen th at even though the minimum fast transition 10-to90% risetime tends to increase with distance, its dependence on distance for the sample of 48 positive return strokes is rather weak (determination coefficient = 0.26). Cooray and Lundquist [1982] reported the AM duration of the slow front (whose amplitude relative to the peak was on average 38% and within a range of 10-70%) to be 10 s.

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329 Cooray [1986a, b] found the 10-to-90% risetime of the fast transiti on to be in the range of 0.400.80 s (AM of 0.56 s). In Japan, Hojo et al. [1985] reported the AM duration of the slow front to be 19.3 s and Ishii and Hojo [1989] reported the AM 10-90% rise time of the fast transition to be 0.11 s. From the above discussion it can be seen that while the slow front duration for positive return strokes in Florida is, on average, shorter than that in Sweden and Japan, the 10-to90% risetime of the fast transition for positive return strokes in Florida is at least a factor of two longer than that in the othe r two geographical locations. For negative lightning, Master et al. [1984] reported the AM slow front duration for 105 first strokes in Florida to be 2.9 s, which is about half of that found for positive return strokes presented here. Similarly, Cooray and Lundquist [1982] found the AM durat ion of the slow front for negative first strokes in Sweden to be 5 s, wh ich is a factor of 2 sm aller than the AM value for positive return strokes reported by them. Weidman and Krider [1978] reported the AM slow front duration for 62 negative first return stroke s in Florida to be 4 s. The AM 10-to-90% risetime of the fast transition for negative first st rokes in Florida was repor ted to be 0.97 s and 0.2 s by Master et. al [1984] and Weidman and Krider [1978], respectively, both values being less than that found for positive discharges examined here. The AM slow front amplitude relative to peak for negative first strokes wa s reported to be 28%, 41% and 50% by Master et al. [1984], Cooray and Lundquist [1982], and Weidman and Krider [1978], respectively. These values are comparable to the AM value of 39.4% found for positive return strokes in our dataset. Table 7-6 summarizes the slow front-fast transition characteri stics in positive and negative return strokes in different regions. 7.2.4 Zero Crossing Time The histogram of the zero-crossing time (defined in Figure 7-16) for 41 positive return strokes (out of 62 examined, 21 return stroke waveforms did not exhibit zero crossing due to

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330 Figure 7-9. A typical slow front-fas t transition sequence in a positive return stroke electric field waveform recorded on June 1, 2008 in Gain esville, Florida, shown on a 70 s time scale. The discharge occurred at a distance of 72 km, so that the field waveform is dominated by its radiation component. r = 72 km

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331 Slow Front Duration ( s) 02468101214161820 Occurrence 0 5 10 15 20 25 30 First strokes, N =51 Subsequent strokes, N =11 First return stroke Subsequent return stroke All AM, s 6.06 5.36 5.94 GM, s 5.09 4.35 4.95 Min, s 0.77 2.02 0.77 Max, s 17.4 18.6 18.6 N 51 11 62 Figure 7-10. Histogram of the slow front duration for 62 positive return strokes. Statistics given are arithmetic mean (AM), geometric m ean (GM), minimum (min), and maximum (max) values for first and subsequent stro kes, as well as for all data combined.

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332 Slow Front Amplitude Relative to Peak (%) 01020304050607080 Occurrence 0 5 10 15 20 25 Firststrokes, N =51 Subsequent strokes, N =11 First return stroke Subsequent return stroke All AM, % 39.64 38.5 39.4 GM, % 36.67 37.1 36.7 Min, % 14.12 25.1 14.1 Max, % 79.43 56.9 79.4 N 51 11 62 Figure 7-11. Histogram of the slow front amplitude relative to peak for 62 positive return strokes. Statistics given are arithmetic mean (AM), geometric mean (GM), minimum (min), and maximum (max) values for first and subsequent strokes, as well as for all data combined.

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333 Fast Transition 10 to 90% Risetime ( s) 0.00.51.01.52.02.53.03.54.04.55.0 Occurrence 0 5 10 15 20 First strokes, N = 51 Subsequent strokes, N = 11 First return stroke Subsequent return stroke All AM, s 1.21 1.20 1.21 GM, s 1.01 1.08 1.02 Min, s 0.28 0.42 0.28 Max, s 4.58 2.06 4.58 N 51 11 62 Figure 7-12. Histogram of the fast transition 10-to-90% risetime for 62 positive return strokes. Statistics given are arithmetic mean (A M), geometric mean (GM), minimum (min), and maximum (max) values for first and subs equent strokes, as well as for all data combined.

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334 R 2 = 0.0003 Distance, km 020406080100120140160180 Slow Front Duration, s 0 5 10 15 20 First strokes, N = 40 Subsequent strokes, N = 8 Figure 7-13. Slow front duration versus the di stance from the measuring station for 48 positive return strokes. R 2 = 0.02 Distance, km 020406080100120140160180 Slow Front Amplitude Relative to Peak, % 0 20 40 60 80 100 First strokes, N = 40 Subsequent strokes, N = 8 Figure 7-14. Slow front amplitude relative to peak versus the distance from the measuring station for 48 positive return strokes.

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335 R 2 = 0.26 Distance, km 020406080100120140160180 Fast Transition 10 to 90% Risetime ( s) 0 1 2 3 4 5 First strokes, N = 40 Subsequent strokes, N = 8 Figure 7-15. Fast transition 10-to-90% risetime time versus the distance from the measuring station for 48 positive return strokes.

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336 Table 7-6. Characteristics of the slow front and fast transition in posit ive and negative returns strokes in different regions. References and Location Sample size AM slow front duration, s AM slow front amplitude relative to peak, percent AM fasttransition 10to-90 percent risetime, s Remarks Positive return strokes Present study, Florida 62 5.94 39.4 1.21 Cooray and Lundquist [1982], Sweden 63 10 38 Cooray [1986a,b], Sweden 20 8.2 45 0.56 Hojo et al. [1985], Japan 19.3 Ishii and Hojo [1989], Japan 24 0.11 (a) The slow front duration for positive return strokes in Florida is, on average, shorter than that in Sweden and Japan. (b) The 10-to90% risetime of the fast transition in Florida is at least a factor of two longer than that in Sweden and Japan. Negative return strokes Master et al. [1984] 105 2.9 28 0.97 (N = 102) Cooray and Lundquist [1982], Sweden 83 5 (N= 82) 41 Weidman and Krider [1978], Florida 62 4.0 50 0.2 (N = 38) The slow front duration for positive return strokes in Florida and Sweden is, on average, longer for positive return strokes than for negative return strokes. them being relatively close to th e measuring station) in this da taset is shown in Figure 7-17. The values ranged from 11.3 to 197 s with the AM and GM being 53.6 s and 42.1 s, respectively. Figure 7-18 shows the scatter plot of the zero crossing time for 34 pos itive return strokes (out of 41) located at distances ranging from 18 to 157 km versus distance from the measuring station. No correlation between zero crossing time and distance is found (determination coefficient = 0.02). Ishii and Hojo [1989] found the AM zero-crossing tim e for 34 positive return strokes in

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337 summer and 89 positive return stroke s in winter at distances in the range of 100-300 km in Japan to be 151 s and 93 s, respectively. For 10 positiv e strokes that occurred during the cold season in our dataset and displayed zero-crossing, the AM and GM zero-crossing times were 52.7 s and 41.4 s, respectively, which are not much different from those for the overall sample. Figure 7-19 shows the histogram of the opposite polarity overshoot relative to peak for 31 positive return strokes (out of 41 exhibiting zero crossing, for 10 return stroke waveforms the opposite polarity overshoot was not measureable due to poor signal-to -noise ratio) in the dataset presented here. The overshoots were found to be from 4.13 to 43.6% of the return stroke peak with the AM and GM being 15.6% and 13.0%, resp ectively. The scatter pl ot of the opposite polarity overshoot for 27 positive re turn strokes (out of 31) located at distances ranging from 21 to 157 km versus distance from the measuring station is shown in Figure 7-20. No correlation between opposite polarity overshoot and distan ce is found (determination coefficient = 0.001). Ishii and Hojo [1989] found the opposite polarity overshoot to be, on average, 24% of the peak for 34 positive return strokes (in summer), and 40% of the peak for 89 positive return strokes (in winter), occurring at distances in the range of 100-300 km in Japan. For 178 negative return strokes in summer in Florida occurring at distances ranging from 50 to 250 km, Pavlick et al. [2002] reported the AM zero-crossing time to be 49.5 s and the opposite polarity overshoot to be, on average, 18. 5% of the peak. These values are similar to those of 53.6 s and 15.6% for positive return strokes examined in this study. Table 7-7 summarizes the zero crossing time and opposite polar ity overshoot relative to peak of the return stroke electric field waveform for different seasons in Florida and Japan. 7.2.5 dE/dt Waveform Characteristics The peak electric field deri vative (see Figure 7-21) normali zed to 100 km for 27 positive return strokes in our dataset wa s in the range of 3.23 to 25.8 V/m/ s with the AM and GM values

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338 being 10.0 V/m/s and 9.02 V/m/s, respectively. Fi gure 7-22 shows the histogram of the peak electric field derivative normalized to 100 km. Th e electric field derivati ve waveforms of the 27 positive return strokes located at distances ranging from 7.8 to 157 km are shown in Appendix B. The AM peak electric field derivative normali zed to 100 km for 22 posit ive return strokes in Denmark for propagation over salt water was reported by Cooray et al. [1998] to be 22 V/m/s, about a factor of 2 greater than our value. Figure 7-23 shows the scatte r plot of the distancenormalized peak electric field derivative for 27 positive return strokes versus distance from the measuring station. No correlation is found (determination coefficient = 0.01). The width of the dE/dt pulse at half peak value (defined in Figure 7-21) for 37 positive return strokes ranged from 0.33 to 6.2 s. The AM and GM were 1.53 s and 1.27 s, respectively. The histogram of the width of the dE /dt pulse at half peak value is shown in Figure 7-24. The AM width of the dE/dt pulse at half peak value for 21 positive return strokes in Denmark (for propagation over salt water) was reported by Cooray et al. [1998] to be 0.15 s, which is an order of magnitude shorter than that in our dataset. Figure 7-25 shows the scatter plot of the dE/dt half-peak width for 27 positive return strokes (out of 37) versus distance from the measuring station. It can be seen that even t hough the dE/dt half-peak width generally tends to increase with distance, its dependence on distance for the sample of 27 positive return strokes is rather weak (determination coefficient = 0.30). For negative lightning, Krider et al. [1996] reported the average peak electric field derivative normalized to 100 km fo r 63 negative return strokes in Florida to be 39 V/m/s, about four times larger than the average value for the positive return strokes examined here. The average width of the dE/dt pulse at half peak value for 61 return strokes in Florida (for propagation over salt water) was 0.1 s [Krider et al., 1996], which is about an order of

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339 magnitude shorter than that for positive lightning in the dataset presented here. From the above discussion it appears that the peak electric field derivative for positive return strokes in our dataset are smaller and the dE/dt half-peak widt h longer than those for both positive and negative return strokes reported in the literature. This could be due to field propagation effects over finitely conducting soil in our experiment. Figure 7-16. The electric field waveform of a positiv e return stroke that occurred at a distance of 157 km on May 5, 2008 in Gainesville, Florida, shown on a 2.5 ms time scale. The electric field waveform is dominated by its radiation component. Shown are the zerocrossing time ( Tzc), defined as the crossing of th e preceding background field level, and the opposite polarity overshoot ( Eos). r = 157 km

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340 Zero Crossing Time, s 020406080100120140160180200 Occurrence 0 2 4 6 8 10 12 14 First strokes, N = 32 Subsequent strokes, N = 9 First return stroke Subsequent return stroke All AM, s 57.8 38.8 53.6 GM, s 44.4 34.7 42.1 Min, s 13.7 11.3 11.3 Max, s 197 64.7 197 N 32 9 41 Figure 7-17. Histogram of the zero crossing time fo r 41 positive return strokes. Statistics given are arithmetic mean (AM), geometric m ean (GM), minimum (min), and maximum (max) values for first and subsequent stro kes, as well as for all data combined. Distance, km 020406080100120140160180 Zero Crossing Time, s 0 50 100 150 200 250 First strokes, N = 27 Subsequent strokes, N = 7 R2 = 0.02 Figure 7-18. Zero crossing time versus distance from the measuring station for 34 positive return strokes.

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341 Opposite Polarity Overshoot Relative to Peak (%) 051015202530354045 Occurrence 0 2 4 6 8 10 12 First strokes, N = 23 Subsequent strokes, N =8 First return stroke Subsequent return stroke All AM, % 13.6 21.5 15.6 GM, % 11.3 19.9 13.0 Min, % 4.13 8.03 4.13 Max, % 43.6 36.9 43.6 N 23 8 31 Figure 7-19. Histogram of the opposite polarity ov ershoot relative to peak for 31 positive return strokes. Statistics given are arithmetic mean (AM), geometric mean (GM), minimum (min), and maximum (max) values for first and subsequent strokes, as well as for all data combined.

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342 Distance, km 020406080100120140160180 Opposite Polarity Overshoot Relative to Peak, % 0 10 20 30 40 50 First strokes, N = 21 Subsequent strokes, N = 6 R2 = 0.001 Figure 7-20. Opposite polarity ove rshoot relative to peak versus distance from the measuring station for 27 positive return strokes. Table 7-7. Zero-crossing time and opposite polarity overshoot relative to peak of the return stroke electric field waveform for different seasons in Florida and Japan. References and Location Season AM zerocrossing time, s AM opposite polarity overshoot relative to peak, percent Remarks Positive return strokes Summer 53.9 (N = 31) 15.6 (N = 21) Present study, Florida Winter 52.7 (N = 10) 15.8 (N = 10) Summer 151 (N = 34) 24 (N = 34) Ishii and Hojo [1989], Japan Winter 93 (N = 89) 40 (N = 89) Zero-crossing times for positive return strokes in summer and winter in Florida are, on average, shorter than those in Japan. Negative return strokes Pavlick et al. [2002], Florida Summer 49.5 (N = 178) 18.5 (N = 178) Zero-crossing times for positive and negative return strokes in Florida are similar.

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343 Figure 7-21. A typical electric fiel d derivative (dE/dt) waveform of a positive return stroke in the dataset presented here shown on a 23 s time scale. Also shown are the peak electric field derivative (dEp) and the width of the pulse at half peak value (THPW).

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344 Peak dE/dt Normalized to 100 km, V/m/ s 0369121518212427 Occurrence 0 2 4 6 8 10 12 First strokes, N = 24 Subsequent strokes, N = 3 First return stroke Subsequent return stroke All AM, V/m/s 10.6 5.55 10.0 GM, V/m/s 9.61 5.42 9.02 Min, V/m/s 3.23 4.15 3.23 Max, V/m/s 25.8 7.12 25.8 N 24 3 27 Figure 7-22. Histogram of the peak electric fi eld derivative normalized to 100 km for 27 positive return strokes. Statistics given are arit hmetic mean (AM), geometric mean (GM), minimum (min), and maximum (max) values fo r first and subsequent strokes, as well as for all data combined. R 2 = 0.01 Distance, km 020406080100120140160180 Peak dE/dt Normalized to 100 km, V/m/ s 0 5 10 15 20 25 30 First strokes, N = 24 Subsequent strokes, N = 3 Figure 7-23. Peak dE/dt normalized to 100 km vers us distance from the measuring station for 27 positive return strokes.

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345 dE/dt Half Peak Width, s 01234567 Occurrence 0 2 4 6 8 10 12 14 16 First strokes, N = 31 Subsequent strokes, N = 6 First return stroke Subsequent return stroke All AM, s 1.52 1.59 1.53 GM, s 1.24 1.43 1.27 Min, s 0.33 0.67 0.33 Max, s 6.20 3.04 6.20 N 31 6 37 Figure 7-24. Histogram of the width of the dE/dt pulse at half peak value for 37 positive return strokes. Statistics given are arithmetic mean (AM), geometric mean (GM), minimum (min), and maximum (max) values for first and subsequent strokes, as well as for all data combined. R 2 = 0.30 Distance, km 020406080100120140160180 dE/dt Half Peak Width, s 0.0 0.5 1.0 1.5 2.0 2.5 3.0 First strokes, N = 24 Subsequent strokes, N = 3 Figure 7-25. dE/dt half-peak width versus the distance from measur ing station for 27 (out of 37) located positive return strokes.

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346 7.3 Peak Current 7.3.1 Peak Current Estimated by the National Lightning Detection Network (NLDN) The distribution of the NLDN-estimated peak currents for 48 positive return strokes (in 40 flashes) occurring at distances ranging from 7.8 to 157 km is shown in Figure 7-26. The peak currents range from 19.8 to 238 kA with the AM and GM being 87.8 kA and 74.6 kA, respectively. For 40 first strokes, the AM a nd GM peak currents were 93.4 kA and 78.9 kA, respectively, and for 8 subsequent strokes th e AM and GM values were 59.5 kA and 56.4 kA, respectively. Figure 7-27 show s the scatter plot for NLDN-estimated peak current versus distance from the measuring station for the 48 positive return strokes presented here. It can be seen that even though the minimum NLDN-estimat ed peak current tends to increase with distance, the dependence of the NLDN-estimated peak current on distance for the sample of 48 positive return strokes is rather weak (deter mination coefficient = 0.27). Table 7-8 gives the number of recorded strokes in different di stance ranges along with the GM NLDN-estimated peak current for each distance range. The GM peak current generally increases with increasing distance which suggests a bias to ward higher-intensity events, r ecorded from larger distances. Note that even for distances less than 20 km th e GM peak current is higher than for negative return strokes [Rakov and Uman, 2003]. 7.3.2 Linear Regression Equations Relating NLDN Currents and Distance-Normalized Fields According to the atmospheric electricity sign convention, for positive return strokes the electric field change is negative. The correspondi ng current is assumed here to be positive. The scatter plot of the NLDN-estimated peak current INLDN versus electric field peak normalized to100 km E is shown in Figure 7-28. The two parame ters appear to be linearly correlated (determination coefficient = 0.85), with the linear regression equation being given by

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347 Table 7-8. Number of positive return strokes in different distance ranges and corresponding GM current peaks. Distance range, km 5-2020-40 40-60 60-80 80-100 100-160 0-160 Number of events 6 14 11 4 5 8 48 GM NLDN-estimated peak current, kA 44.7 61.1 66.4 119 95.5 124 74.6 NLDN Estimated Peak Current (kA) 0306090120150180210240 Occurrence 0 2 4 6 8 10 12 14 16 First strokes, N =40 Subsequent strokes, N =8 First return stroke Subsequent return stroke All AM, A 93.4 59.5 87.8 GM, A 78.9 56.4 74.6 Min, A 19.8 28.2 19.8 Max, A 234 91.6 234 N 40 8 48 Figure 7-26. Histogram of the NLDN-estimated peak currents for 48 positive return strokes. Statistics given are arithmetic mean (A M), geometric mean (GM), minimum (min), and maximum (max) values for first and subs equent strokes, as well as for all data combined.

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348 Distance, km 020406080100120140160180 NLDN Peak Current, kA 0 50 100 150 200 250 First strokes, N = 40 Subsequent strokes, N = 8 R2 = 0.27 Figure 7-27. NLDN-estimated peak current versus distance from the measuring station for 48 positive return strokes. INLDN = 11.3 3.5E (7-1) where E is negative and in V/m and INLDN is positive in kA. Rakov et al. [1992b] used the electric fields measur ed at 5 km and directly measured currents for 28 negative triggere d-lightning strokes published by Willett et al. [1989a] to derive a regression equation that rela tes the negative subsequent return-stroke peak current I to the corresponding peak electric field E at distance D. I = 1.5 0.037ED (7-2) where E is positive and in V/m, d is in kilometers, and I is negative and in kA. For D = 100 km, Equation 7-2 reduces to I = 1.5 3.7E. Pavlick et al. [2002] used Equation 7-2 to estimate the peak currents from measured electric fields fo r 178 negative first return strokes occurring at distances ranging from 50 to 250 km. They fou nd the NLDN-reported peak currents to be, on average, 10% lower than thos e estimated using Equation 7-2.

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349 Electric Field Normalized to 100 km, V/m 70 60 50 40 30 20 100 NLDN Peak Current, kA 0 50 100 150 200 250 300 First strokes, N = 40 Subsequent strokes, N = 8 INLDN = 11.3 3.5E R = 0.85 48 positive return strokes Figure 7-28. NLDN-estimated peak current versus normalized electric field peak for 48 positive return strokes. Also shown is the regression equation line. Equation 7-2 (with E being negative) was formally applied he re to estimate peak currents for 48 (40 first and 8 subsequent) positive return stroke s from their measured electric field peaks. The scatter plot of the peak curre nt estimated from Equation 7-2 versus NLDN-estimated peak current is shown in Figure 7-29. The slanted (diagonal) solid line (slope = 1) is the locus of points for which the regression-equation-estimated peak current and the NLDN-estimated peak current are equal. For the sample of 48 positive return strokes, the points are approximately evenly scattered around this line. Also shown is the linear regression line (dashed) having a slope of 0.95 and determination coefficient of 0.85. The NLDN-reported peak currents were found to be, on average, 16% greater than those estimated using Equation 7-2. For comparison, we examined 116 negative return strokes that were recorded in August, 2008, during two thunderstorms in Gainesville, Florid a, using the same instrumentation as that

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350 employed for recording the positive returns stroke s discussed above. The negative return strokes (41 first strokes and 75 subsequent) occurred at distances ranging from 4 to 35 km (versus 7.8 to 157 km for the 48 positive strokes) from the fi eld measuring station and had NLDN estimated peak currents ranging from 4.7 to 154 kA (versus 19.8 to 238 kA for the 48 positive strokes). Figure 7-30 shows the scatter plot for NLDN-estim ated peak current versus distance from the measuring station for the 116 negative return strokes presented here. Note that while the peak currents for negative return strokes are assumed to be negative in Equation 7-2, only their magnitudes are shown in Figure 7-30. The dependence of the NLDN-estimated peak current on distance for this sample of negative return strokes is rather weak (determination coefficient = 0.32). However, there is a bias toward larger peak currents, which increases with increasing distance. Table 7-9 gives the number of recorded strokes in different distance ranges along with the GM NLDN-estimated peak current for each distance range. The scatter plot of the NLDN-estimated peak current INLDN versus electric field peak normalized to 100 km E for 116 negative return strokes is shown in Figure 7-31a. The two parameters are linearly correlated (determinati on coefficient = 0.95), the relationship being given by the following regression equation. INLDN = 2.29 3.06E (7-3) where E is positive and in V/m and INLDN is negative and in kA. The intercept (2.29) and slope (3.06) in Equation 7-3 can be compared to the those of Equation 7-1 (regression equation for 48 positive return strokes examined in this Chapter) and to those of Equation 7-2 for D = 100 (regression equation of Rakov et al. [1992b] for negative rocket-tri ggered lightning strokes). The values of corresponding regres sion equation parameters are si milar. The variation in the parameters may be due to physical differences between natural negative return strokes (Equation

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351 7-3), negative rocket-triggered lightning stroke s (Equation 7-2), and natural positive return strokes (Equation 7-1) or due to smaller sample sizes for Equations 7-1 and 7-2. Figure 7-32 shows the scatter plot of the NLDN-estimated peak current versus measured electric field for all strokes combined (a total of 164 return strokes, of which 48 are positive and 116 are negative). The combined regression equation is given by: INLDN = 7.81 3.58E (7-4) where E is positive for negative strokes and negative for positive ones and in V/m, and INLDN is negative for negative strokes and positive for positive ones and in kA. It is important to note that the NLDN fiel d-to-current conversion algorithm has been calibrated only for subsequent strokes [GM p eak current estimation error is about 20%, Jerauld et al., 2005, Nag et al., 2008]. Interestingly, th ere appears to be not much difference between first and subsequent strokes in Figures 7-29 and 7-31b. In fact, the slopes in regression equations for negative first strokes and negative subseque nt strokes given in Fi gure 7-31b are almost the same. This observation suggests that the NLDN pr ocedure to compensate for field propagation effects and find the average range-normalized signal strength (RNSS) works equally for both subsequent and first return strokes. 7.3.3 Peak Currents Inferred from Measured Electric Field Peak s Using the Transmission Line Model In this Section, we use the transmission line model [Uman et al., 1975] to infer peak currents from measured electric field peaks, NLDN reported distances, and assumed returnstroke speed. The relationship between the magnitudes of return-stroke peak current, I, and electric field peak, E, measured at distance D, based on the transmission line model, is given by [Rakov and Uman, 2003, Chapter 4].

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352 Table 7-9. Number of negative return strokes in different dist ance ranges and corresponding GM current peaks. Distance range, km 5-10 10-20 20-30 30-40 0-40 Number of events 26 80 3 7 116 GM NLDN-estimated peak current, kA 14.3 19.3 14.7 57.1 19.1 I = 1.5 0.037ED, kA 050100150200250300 NLDN Peak Current, kA 0 50 100 150 200 250 300 Positive first strokes,N = 40 Positive subsequentstrokes, N = 8 INLDN = 9.85 + 0.95I R2 = 0.85 Figure 7-29. NLDN-estimated peak current versus peak current estimated using Equation 7-2 (with E being negative). The solid line is th e diagonal with slope = 1 and the dashed line is the linear regression line. Distance, km 0510152025303540 NLDN Peak Current, kA 0 20 40 60 80 100 120 140 160 180 Firststrokes, N = 41 Subsequent strokes, N = 75 R2 = 0.32 Figure 7-30. Normalized electric field peak versus distance from the measuring station for 116 negative return strokes.

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353 Electric Field Normalized to 100 km, V/m 01020304050 NLDN Peak Current, kA 180 160 140 120 100 80 60 40 20 0 First strokes, N = 41 Subsequent strokes, N = 75 INLDN = 2.29 3.06E R = 0.95 (a) Electric Field Normalized to 100 km, V/m 01020304050 NLDN PeakCurrent, kA 180 160 140 120 100 80 60 40 20 0 First strokes, N = 41 Subsequent strokes, N = 75 Negative first strokes: INLDN= 1.29 3.03E R = 0.95 Negative subsequent strokes: INLDN= 2.56 3.04E R = 0.93 (b) Figure 7-31. (a) NLDN-estimated peak current vers us distance-normalized electric field peak for 116 first and subsequent negative return stro kes. Also shown is the regression line. (b) Same as in (a) but with individual re gression lines for 41 first and 75 subsequent strokes.

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354 I NLDN = 7.81 3.58E R = 0.96 N = 164Electric Field Normalizedto 100 km, V/m 80 60 40 20020406080 NLDN Peak Current, kA 300 200 100 0 100 200 300 Negative return strokes, N = 116 Positive return strokes, N = 48 Figure 7-32. NLDN-estimated peak current versus measured electric field peak for 48 positive and 116 negative return strokes. 022v EI cD (7-5) where o is the permittivity of free space, c is the speed of light, and v is the return stroke speed. Figure 7-33 shows scatter plot s for the NLDN estimated peak current magnitudes versus magnitudes of peak currents estimated (for di fferent values of v) using Equation 7-5 for 75 negative subsequent return strokes (discussed in Section 7.3.2). Return-stroke speeds were assumed to be 108 m/s (Figure 7-33a), 1.5 x 108 m/s (Figure 7-33b), 1.8 x 108 m/s (Figure 7-33c), and 3 x 108 m/s (Figure 7-33d). The slante d line (slope = 1) is the locus of points for which the transmission line model estimated peak current a nd the NLDN-reported peak current are equal. It can be seen that the overwhelming majority of the points are above this line for v =108 m/s and v = 1.5 x 108 m/s, and below it for v = 3 x 108 m/s. For v = 1.8 x 108 m/s the points are found to be

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355 scattered more or less evenly around the line. Thus, it appears that the NLDN-reported peak currents are equal to the transmission line model predicted peak curren ts (for the 75 negative subsequent return strokes) for an as sumed return stroke speed of 1.8 x 108 m/s. This suggests that the implied return-stroke speed in the NLDN fi eld-to-current conversion equation is 1.8 x 108 m/s, provided that the NLDN measured fi eld peak is consistent with ours. The NLDN uses the same field-to-current conversion procedure (and hence the same implied return-stroke speed) for negative first strokes and positive return strokes as it does for negative subsequent strokes. Therefore, for v = 1.8 x 108 m/s one should expect a good match between NLDN-reported currents and transmissi on line model predicted currents for negative first strokes and positive return strokes as well. Figures 7-34a and b show scatter plots of the NLDN-reported peak current versus the correspo nding peak current esti mated using Equation 75 for a return stroke speed of 1.8 x 108 m/s, for 41 negative first return strokes discussed in Section 7.3.2 and the 48 positive return strokes pr esented in Section 7.3.1, respectively. The solid slanted line (slope = 1) in both plots is the locus of points for which the transmission line model estimated peak current and the NLDN-reported peak current are equal. One can see from Figure 7-34a that for the 41 negative first return stro kes the NLDN-reported peak currents tend to be equal to the transmission line model predicted peak currents for the assume d return stroke speed of 1.8 x 108 m/s. However, for positive return stroke s (Figure 7-34b) most data points are above the diagonal (slope = 1 line). The relationship between the NLDN-reported peak current and the transmission line model estimated peak curren t for positive return strokes is given by the following regression equation: INLDN = 11.3 + 1.27 ITL (7-6)

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356 where INLDN and ITL are in kA. For comparison, a similar regression equation for negative first and subsequent strokes for an assumed return stroke speed of 1.8 x 108 m/s is: INLDN = -2.29 + 1.10 ITL (7-7) where INLDN and ITL are in kA. Note that Equations 7-6 can be derived from Equations 7-1 by using E = 0.36 ITL (ITL being positive and in kA and E being negative and in V/m), which is the relationship between electric field and current for the transmission line model for v = 1.8 x 108 m/s. Similarly, Equation 7-7 can be derived from Equations 7-3 using the same relation between E and ITL (ITL being negative and in kA and E being positive and in V/m). The discrepancy between negative first and subsequent strokes on the one hand and positive return strokes on the other hand suggests that the NLDN procedure to compensate for field propagation effects and find the average range-normalized signal strength (RNSS) works di fferently for these two groups of strokes. TL Model Estimated Peak Current, kA 020406080100 NLDN Peak Current, kA 0 20 40 60 80 100 (a) 75 negative subsequent strokes v = 1 x 108 m/s Figure 7-33. The NLDN-estimated peak currents versus peak currents estimated using the transmission line model for assume d return-stroke speeds of (a) 108 m/s, (b) 1.5 x 108 m/s, (c) 1.8 x 108 m/s, and (d) 3 x 108 m/s for 75 negative subs equent return strokes. Only the magnitudes of peak currents are considered.

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357 TL Model Estimated Peak Current, kA 020406080100 NLDN Peak Current, kA 0 20 40 60 80 100 (b) 75 negative subsequent strokes v = 1.5 x 108 m/s TL Model Estimated Peak Current, kA 020406080100 NLDN Peak Current, kA 0 20 40 60 80 100 (c) 75 negative subsequent strokes v = 1.8 x 108 m/s Figure 7-33. Continued

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358 TL Model Estimated Peak Current, kA 020406080100 NLDN Peak Current, kA 0 20 40 60 80 100 (d) 75 negative subsequent strokes v = 3 x 108 m/s Figure 7-33. Continued TL Model Estimated Peak Current, kA 050100150200250 NLDN Peak Current, kA 0 50 100 150 200 250 (a) 41 negative first strokes v = 1.8 x 108 m/s Figure 7-34. The NLDN-estimated peak currents versus peak currents estimated using the transmission line model for assume d return-stroke speed of 1.8 x 108 m/s for (a) 41 negative first return strokes and (b) 48 positive return strokes. Only the magnitudes of peak currents are considered.

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359 TL Model Estimated Peak Current, kA 050100150200250 NLDN Peak Current, kA 0 50 100 150 200 250 First strokes, N = 40 Subsequent strokes, N = 8 (b) 48 positive return strokes INLDN = 11.3 + 1.27ITLR = 0.85 v = 1.8 x 108 m/s Figure 7-34. Continued 7.4 Charge Transferred by Return Strokes The electric field change, E, at a horizontal distance r on perfectly conducting ground due to removal of a point charge, Q, from height H is given by [Rakov and Uman, 2003]. 03 22 22()QH E Hr (7-8) We will apply this point-charge model to positive return strokes to estimate the charge transfer, Q, from measured E, NLDN-reported r, and assumed H. As discussed in Chapter 2, the charge structure of a cumulonimbus can be approximated as a vertical tripole consisting of three charge centers, main positive at the top, main negative in the middle, and an additional smaller positive at the bottom. In Florida, the main positiv e and negative charges are located at heights of about 12 and 7 km [Krehbiel, 1986], respectively. We will assume that positive cloud to ground

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360 discharges originate in the main positive charge region and hence H = 12 km. Solving Equation 7-8 for Q we get: 03 22 22() Hr QE H (7-9) Charge transfer was estimated for 19 (17 fi rst and 2 subsequent) positive return strokes (occurring at distances ranging from 11 to 46 km ) within 0.5, 1, and 1.5 ms of the beginning of return stroke electric field change. Measurem ents of electric field changes (assumed to be essentially electrostatic) at these times are illust rated in Figure 7-35. The decay time constant of the field measuring system used to acquire the da ta was 10 ms, so that electrostatic field changes after 1.5 ms or so could be signi ficantly influenced by the instru mental decay. This is why we did not attempt to estimate char ge transfers over longer periods. Table 7-10 summarizes the values of charge transfer at different times. Histograms of charge transfers at diffe rent times are shown in Figure 7-36a-c The charge transfer in 0.5, 1, and 1.5 ranged from 1.67 to 26.5 C, 3.16 to 33.7 C, and 4.35 to 34.6 C, respectively, and the median charge transfer was 6.98 C, 12.2 C, and 13.2 C, resp ectively. These values are comparable to the median impulse charge (excluding continuing current) of 16 C for a sample of 26 positive return strokes reported by Berger et al. [1975] but considerably smaller than the median total charge transfer of 80 C. Total charge transfers of hundr eds of coulombs or more have been reported for positive discharges in Japanese winter thunderstorms [Goto and Narita, 1995]. As noted earlier, our electric field records were not suitable for estimating total charge transfers due to relatively short decay time constant of the measuring system The average currents (ratio of charge transfer and time) at 0.5 ms, 1 ms, and 1.5 ms vary fr om 3.34 to 53 kA, 3.16 to 33.7 kA, and 2.9 to 23.1 kA, respectively.

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361 Scatter plot for charge transfer at 1.5 ms versus the distance from the measuring station for 19 positive return strokes occurring at distances ranging from 11 to 46 km is shown in Figure 737. A weak dependence of charge transfer on di stance is found (determination coefficient = 0.29), with larger charge transfer s occurring in strokes at greater distances. However, the sample size of 19 strokes is rather small to draw any conclusions. Schoene et al. [2009] reported the charge transfer within 1 ms after the beginning of the return stroke for 151 negative rocket triggered lightning strokes at Camp Blanding, Florida. As stated in Chapter 2, rocket trigge red lightning strokes are similar to subsequent strokes in natural downward lightning. The minimum and maximum ch arge transfers within 1 ms after the beginning of the return stroke were 0.3 C and 8.3 C, respectively, with the AM and GM values being 1.4 C and 1.0 C, respectively. The mean valu es are about an order of magnitude smaller than the AM and GM values of 13.2 C and 10.7 C, respectively, for charge transfer within 1 ms for 19 positive return strokes in this study. Figure 7-35. Measurements of electric field changes ( E) at times t = 0.5 ms, 1.0 ms, and 1.5 ms after the beginning of the return stroke. r = 21 km

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362 Table 7-10. Summary of el ectric field change ( E), charge transfer ( Q), and average current ( Q/t) at different times ( t) after the beginning of the return stroke field change for 17 first and 2 subsequent positive return strokes. t = 0.5 ms t = 1.0 ms t = 1.5 ms Flash ID r km E V/m Q C Q/ t kA E V/m Q C Q/ t kA E V/m Q C Q/ t kA First Strokes 12/16/07_49 38 18.0 5.10 10.2 25.7 7.28 7.28 26.9 7.64 5.09 08/13/08_31 20 257 15.9 31.8 253 15.6 15.6 244 15.1 10.1 08/13/08_57 23 82.9 6.61 13.2 154 12.2 12.2 181 14.4 9.62 08/13/08_58 28 129 16.2 32.5 164 20.7 20.7 169 21.3 14.2 08/14/08_85 11 286 5.61 11.2 288 5.65 5.65 276 5.40 3.60 08/14/08_87 18 37.3 1.69 3.38 99.3 4.50 4.50 132 5.98 3.99 08/14/08_90 25 157 16.2 32.4 154 15.8 15.8 152 15.6 10.4 08/23/08_173 24 82.3 7.75 15.5 104 9.82 9.82 112 10.5 7.00 08/23/08_338 40 19.9 6.9 13.7 37.9 13.1 13.1 56 19.3 12.8 08/23/08_339 21 32.5 2.08 4.17 49.3 3.16 3.16 68.0 4.35 2.90 08/23/08_343 26 107 11.9 23.8 118 13.2 13.2 119 13.2 8.81 08/23/08_344 46 3.44 1.67 3.34 7.79 3.78 3.78 15.7 7.62 5.08 08/23/08_345 46 20.0 9.92 19.8 44.5 22.1 22.1 51.7 25.7 17.1 08/23/08_346 26 44.9 4.79 9.59 75.4 8.05 8.05 89.2 9.52 6.35 08/23/08_348 42 23.4 9.12 18.2 39.9 15.6 15.6 52.0 20.3 13.5 08/23/08_350 42 67.1 26.5 53.0 85.4 33.7 33.7 87.7 34.6 23.1 08/24/08_783 35 86.4 20.7 41.4 137 32.7 32.7 144 34.5 23.0 AM 30 85.5 9.92 19.8 108 13.9 13.9 116 15.6 10.4 SD 11 82.2 7.07 14.1 77.9 9.16 9.16 72.9 9.38 6.25 GM 28 52.9 7.47 14.9 79.5 11.2 11.2 92.5 13.1 8.71 Median 26 67.1 7.75 15.5 99.3 13.1 13.1 112 14.4 9.62 Minimum 11 3.44 1.67 3.34 7.79 3.16 3.16 15.7 4.35 2.90 Maximum 46 286 26.5 53.0 288 33.7 33.7 276 34.6 23.1 Subsequent Strokes 08/14/08_85 17 158 6.98 14.0 203 8.97 8.97 241 10.6 7.09 08/23/08_350 32 16.3 2.94 5.88 31.3 5.67 5.67 44.9 8.14 5.42

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363 Charge Transfer at 0.5 ms, C 0369121518212427 Number 0 1 2 3 4 5 First strokes, N = 17 Subsequent strokes, N = 2 (a) Charge Transfer at 1 ms, C 0369121518212427303336 Number 0 1 2 3 4 5 6 First strokes, N = 17 Subsequent strokes, N = 2 (b) Figure 7-36. Histograms of charge transfer with in (a) 0.5 ms, (b) 1 ms, and (c) 1.5 ms of the beginning of the return stroke field change.

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364 Charge Transfer at 1.5 ms, C 0369121518212427303336 Number 0 1 2 3 4 First strokes, N = 17 Subsequent strokes, N = 2 (c) Figure 7-36. Continued Distance, km 01020304050 Charge Transfer at 1.5 ms, C 0 5 10 15 20 25 30 35 40 Firststrokes, N =17 Subsequent strokes, N = 2 R 2 = 0.29 Figure 7-37. Charge transfer at 1.5 ms versus the distance from the m easuring station for 19 positive return strokes.

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365 7.5 Ratio of Electric and Magnetic Field Peaks The ratio of electric and magnetic field peaks can be used to estimate the source heights when the horizontal distance is known. This method is describe d in Chapter 4. The ratio was computed for seven positive return strokes in the dataset examined here. The return-stroke initial field peaks for these seven strokes were primaril y radiation. They occurred at distances ranging from 26 to 46 km. The ratios were within % of the speed of light with the AM and GM both being 1.01c. This is comparable to the ratio of the electric to magnetic field peaks for 43 first return strokes in negative lightning computed in Chapter 3. The ratios were within % of the speed of light with the AM being 0.99c. This suggests that the positive return-stroke initial field peaks are produced by sources near gr ound, so that the elevation angle, 0, and the expected ratio of electric to magnetic field peak is near the speed of light. Table 7-11 summarizes the ratio for the seven positive return strokes. Table 7-11. Ratio of electric and magnetic fiel d peaks for the seven positive return strokes. Flash ID Distance, km Electric field peak, V/m Magnetic field peak, T Ratio of electric and magnetic field peaks, m/s The ratio as a percentage of the speed of light 081408_84 42 159 0.553 2.87 x 108 0.96 082308_345 46 52.1 0.175 2.98 x 108 0.99 082308_346 26 62.2 0.190 3.27 x 108 1.09 082308_350 42 64.7 0.217 2.98 x 108 0.99 082408_783 35 59.7 0.208 2.87 x 108 0.96 113008_01 41 12.2 0.039 3.17 x 108 1.06 113008_01 44 9.80 0.031 3.16 x 108 1.05 7.6 Leader Stepping It appears that posi tive leaders can move through virgin air either continuously or intermittently (in a stepped fashion), as dete rmined from time-resolved optical images [Rakov and Uman, 2003, Chapter 5]. This is in contrast with negative leaders, which are always

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366 optically stepped when they propagate in virgin air. Further, distant (radiation) electric and magnetic field waveforms due to positive discha rges are less likely to exhibit step pulses immediately prior to the return-s troke waveform than are first strokes in negative lightning. Out of 63 positive return strokes (52 first strokes, 10 s econd strokes, and 1 third stroke) in the dataset presented here, 14 (27%) first strokes (see for example, Figure 7-2b) a nd 1 third stroke (see Figure 7-2d) were preceded by pronounced step pulses. Hojo et al. [1985] found that 26-30% of return stroke waveforms in Japanese thundersto rms in both summer and winter exhibited pulses indicative of a leader stepping process. The step pulses in the data set presented here were obs erved to start 74 to 626 s before the positive return-stroke pulse with the AM interval between pulse peaks being 20 s (ranging from 5.8 to 37 s). This is comparable to the average time interval of 17 s (ranging from 3 to 31 s) between leader pulses that occurred during the last 500 s prior to a positive return stroke examined by Kong et al. [2008]. Figure 7-38 shows an exampl e of electric field (integrated dE/dt) signature of one of the positive first stroke s in the dataset presente d here that apparently involved a stepped leader. For ste pped leader electric field pulses prior to negative return-stroke pulse, Krider et al. [1977] reported the AM in terpulse interval of 16 s and 25 s for Florida and Arizona, respectively. Cooray and Lundquist [1982] reported that the mean time interval between the electric field pulses just pr eceding return strokes in Sweden was 26 s for positive lightning versus 14 s in negative lightning. The reason for the occurrence of pulses indicat ive of stepping prior to the return-stroke pulse in some positive cloud-to-gro und discharges is not known. It could be associated with an upward connecting negative leader which may be launched in response to the non-stepped positive downward leader.

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367 Figure 7-38. Electric field (integra ted dE/dt) signature of the return stroke of a single-stroke positive flash that apparently involved a stepped leader shown on a 600s time scale. The electric field record of this flash was saturated. This flash was not detected by the NLDN. 7.7 Preliminary Breakdown Pulse Trains The first return stroke in a negative cloudto-ground lightning discha rge is thought to be preceded by the initial or preliminary breakdown, wh ich is defined as an in-cloud process that initiates or leads to the initiation of the downward-moving stepped leader [Rakov and Uman, 2003]. The preliminary breakdown process in ne gative ground flashes sometimes (in 18% of cases in Florida; see Chapter 5) produces a trai n of relatively large mi crosecond-scale electric field pulses whose initial polarity is the same as that of the following return-stroke pulse. The preliminary breakdown pulse train in negative cl oud-to-ground discharges may be viewed as a manifestation of interaction of a downward-exte nding negative leader channel with the lower positive charge region, as discussed in Chapter 5. The typical total pulse duration of individual Integrated dE/dt

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368 pulses in the train is 20 to 40 s with typical inter pulse interval in the range of 70 to 130 s [Rakov et al. 1996]. In the dataset presented here, only 5 (10%) out of 52 positive cloud-to-ground discharges had detectable preliminary breakdown pulse trains an example of which is shown in Figure 739. The mean total pulse duration of indi vidual pulses in the trains is 22 s with mean interpulse interval of 155 s. For preliminary breakdown pulse trains in positive cloud-to-ground discharges in Japane se winter storms, Ushio et al. [1998] reported a mean total pulse duration of 18 s and a mean interpulse interval of 54 s. In contrast with nega tive discharges, the initial polarity of preliminary breakdown pulses in positive discharges can be either the same as or opposite to that of the following retu rn-stroke pulse [see, for example, Ushio et al., 1998 and Gomes and Cooray, 1998]. Out of the 5 preliminary brea kdown pulse trains in the dataset presented here, pulses in four trains had the same initial polarity as that of the following returnstroke pulse, while pulses in one train had opposite polarity (see Figur e 7-40). There were no significant differences in the characteristics of the two types of pulse trains apart from their polarity. The preliminary breakdown pulse train with the same initial polarity as that of the following positive return stroke may be viewed as a manifestation of the interaction of a positive leader (moving downward from the upper positive char ge region) with the ma in negative charge region. On the other hand, according to Cooray and Scuka [1996], the opposite polarity preliminary breakdown in positive lightning takes place between the main negative and the lower positive cloud charge regions, similar to the pr eliminary-breakdown in negative lightning, but the negative charge is largely expended in neutralizing the lower positive charge. As a result, the vertical channel created by the preliminary breakdown process is "re-polarized" in the field of the main positive charge region and serves to launch a positive leader toward ground.

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369 Figure 7-39. Electric field signatu re of preliminary breakdown (PB) pulse train having the same initial polarity as the following return str oke (RS) of a positive flash on a 20-ms time scale. This flash occurred at a distance of 72 km from the measuring station and had an NLDN-estimated peak current of 146 kA. Inset shows initial part of the preliminary breakdown pulse train on a 1.5-ms time scale. 7.8 Bipolar Lightning Discharges Bipolar lightning discharge, as described in Chapter 2, is cloud-to-ground lightning that sequentially lowers both positive and negative char ge to ground. All bipolar lightning flashes can be divided into three categories, based on the ch aracteristics of the cu rrent polarity reversal [Rakov and Uman, 2003; Rakov, 2003, 2005]. A bipolar flash of Type 1 involves a current and charge polarity reversal duri ng the initial stage of a natural upward or a rocket-triggered (triggered using a small rocket trailing a grounded wi re) lightning discharge. This initial stage is characterized by a steady current flow of the order of 100 A for a time of the order of tenths of a second during and following the propagation of an upward-going leader toward and into the

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370 Figure 7-40. Electric field signatu re of preliminary breakdown pulse train having initial polarity opposite to that of the following return st roke of a positive flash on a 65-ms time scale. This flash occurred at a distance of 84 km from the measurement station and had an NLDN-estimated peak current of 139 kA. Inset shows initial part of the preliminary breakdown pulse train on a 1.6-ms time scale. cloud charge. Bipolar flashes of Type 2 is characte rized by different polarities of the initial-stage current and of the following return stroke or st rokes. A Type 3 bipolar flash involves return strokes of opposite polarity. Type 3 flashes can be grouped into two sub-categories, with Type 3a events being natural upward or rocket-triggered lightning discharges, while Type 3b events are natural downward cloud-to-ground flashes. Thus, types 1, 2, and 3a are all associated with natural upward or rocket-triggered lightning discharges, while Type 3b is the only natural downward cloud-to-ground bipolar light ning and is the type of bipolar lightning discussed in this Section.

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371 As noted in Section 2, ther e are two bipolar cloud-to-g round flashes in the dataset presented here. Figure 7-41 shows the electric fi eld signature of a bipol ar flash composed of three negative strokes followed by a positive stroke and then by a negative one. The interstroke interval between the third stroke (negative) and the fourth stroke (positive) was 69 ms and that between the fourth and the fifth (negative) st rokes was 20 ms. Figure 7-42 shows electric field waveforms of individual return strokes of this flash. No GPS timestamps (and hence no NLDN information) were available for this flash. It is not clear if the fourth (positive) stroke shared a channel with any of the negative strokes of the flash. The other bipolar flash (whose electric fiel d record is shown in Figure 7-43a) was composed of three strokes, the first and the th ird being negative and the second being positive. The interstroke interval between the first (negative, shown in Figure 7-43b) and second (positive, shown in Figure 7-43c) strokes was 130 ms and th at between the second and third (negative, shown in Figure 7-43d) strokes was 249 ms. The two negative str okes (the first and the third ones) were, therefore, separate d by 379 ms. The first stroke wa s preceded by a cloud discharge lasting for about 660 ms. Both the first and third strokes occurred at a dist ance of 46 km from the field measuring station (semi-major axis lengt h of NLDN 50% location error ellipse being 400 m for both strokes) and NLDN-estimated peak curr ents of 52 kA and 25 kA, respectively. The NLDN reported the third (positiv e) stroke as an intracloud disc harge at a distance of 39 km (semi-major axis length of 1.2 km). It appears that the second (positive) stroke formed a channel to ground different from that of the fi rst and third (negative) strokes. Jerauld et al. [2009] examined one natu ral bipolar lightning flas h, producing two channel terminations on ground and containing two strokes (strokes 1 and 2) that lowered positive charge to ground followed by four strokes that lowered negative charge. All stroke s occurred within 1

PAGE 372

372 km of a multiple-station electric field measuring network at Camp Blanding, Florida. Strokes 1 and 2 (both positive) were in separate channels, while strokes 3 to 6 (all negative) followed the same channel as stroke 2. The two positive leader/return-stroke sequences were separated in time by approximately 53 ms, followed by a negative le ader/return-stroke sequence approximately 526 ms later. The interstroke intervals for st rokes 3 to 6 were 280 ms, 260 ms, and 300 ms. The NLDN-estimated peak currents for the first five strokes of the flash were +50.7, +49.9. -14.2, 13.5,and -10 kA. The sixth stroke (nega tive) was not detected by the NLDN. Figure 7-41. Electric field record of bipolar flash composed of th ree negative strokes followed by a positive stroke and then by a negative one recorded in Gainesville, Florida, on October 5, 2007. GPS timestamps and NLDN info rmation were not available for this flash.

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373 Figure 7-42. Electric field waveform s of individual return strokes of the five-stroke bipolar flash shown in Figure 7-41. Strokes 1and 4 are s hown on a 150-s time scale, strokes 3 and 5 on a 100-s time scale, and stroke 2 on a 140-s time scale. 7.9 Summary Experimental data on positive and bipolar lightning acquired in Gainesville, Florida, in 2007-2008 are presented. Various features of positive discharge, including multiplicity, parameters of return stroke el ectric field waveforms, inferred currents, charge transferred by return stroke, leader stepping, and preliminar y breakdown pulse trains were examined. There were a total of 63 return-strokes in 52 positive flashes with an average multiplicity of 1.2. 1st RS 3rd RS 4th RS 2nd RS 5th RS (e) (c) (d) (b) (a)

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374 Figure 7-43. (a) Electric field r ecord of a three-stroke bipolar cloud-to-ground flash with two negative and one positive return strokes (RS) shown on a 404-ms time scale. (b), (c), and (d) Electric field waveforms of the first, second, and third return strokes, respectively, each shown on a 300-s time s cale. NLDN reported the positive stroke as an IC discharge at a distance of 39 km. Th e first and third stroke s both occurred at a distance of 46 km and had NLDN-estimated peak currents of 52 kA and 25 kA, respectively. Out of the 52 posit ive cloud-to-ground flashes presented here 42 (81%) were single-stroke, 9 (17% ) two-stroke, and 1 (2.0%) threestroke flashes. 89% of the positive return strokes were correctly identified by the NLDN. A second stroke that exhibits a waveshape similar to that of the corresponding fi rst stroke probably follows the same channel as the first one. Distance between strokes being sm aller than the largest NLDN median location error (SMA length) is also an indication of the two strokes sharing the sa me channel. Out of 8 NLDN-located two-stroke flashes, 3 contained strokes characterized by both similar electric field waveshapes and spatial separations that are smaller than stroke location uncertainties. 1st RS (b) (c) 2nd RS 3rd RS (d) (a)

PAGE 375

375 The GM electric field peak and electric field derivative peak, both normalized to 100 km, for 48 positive return strokes occurring at distances ranging from 7.8 to 157 km were 18.1 V/m and 9.02 V/m/s, respectively. The GM normalized el ectric field peak for distance ranges of 7.850 km and 64-157 km in this dataset are 14.8 V/m (N = 31) and 26.3 V/m (N = 17), respectively. The GM zero-to-peak risetime and 10-90% rise time for positive return strokes were 6.92 s and 3.40 s, respectively. Sim ilar values were reported by Rust et al. [1981] in USA and by Beasley et al. [1983] in Florida. The zero to peak and 10-90% risetimes for positive return strokes in Sweden and Japan were found to be, in general, longer than th ose reported for Florida and by Rust et al. [1981]. The GM slow front duration, slow front amplit ude relative to peak, and fast-transition 1090% risetime were 4.95 s, 36.7%, and 1.02 s, resp ectively. It was found that while the slow front duration for positive return strokes in Florid a is, on average, shorter than that in Sweden and Japan, the 10-90% risetime of the fast transition in Florida is at least a factor of two longer than that in the other two geographical locatio ns. The duration of the slow front for positive return strokes in Florida was found to be, on averag e, longer than that for negative first return strokes in Florida reported by Weidman and Krider [1978] and Master et al. [1984]. For positive return strokes examined here, the AM zero-crossing time was 53.6 s and the opposite polarity overshoot was, on average, 15.6% of the peak. These values are similar to those of 49.5 s and 18.5% reported by Pavlick et al. [2002] for negative return strokes in Florida. The NLDN field-to-current conversion algorith m has been calibrated only for negative subsequent strokes [GM peak current estimation error is about 20%, Jerauld et al., 2005, Nag et al., 2008]. Interestingly, for negative cloud-to-ground lightning, regression equations relating NLDN-estimated peak currents and measured electri c field peaks are not much different for first

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376 and subsequent strokes. This observation sugges ts that the NLDN procedure to compensate for field propagation effects and find the average range-normalized signal strength (RNSS) works equally for both subsequent and first return strokes. The discrepancy between regression equations for negative first and subsequent strokes on the one hand and positive return strokes on the other hand suggests that the NLDN procedure to compensate for field propagation effects and find the average RNSS works differently for these two groups of strokes. Charge transfer was estimated for 19 positive return strokes (occurring at distances ranging from 11 to 46 km) within 0.5 ms, 1 ms, and 1.5 ms after the beginning of return stroke electric field change. The median charge transfer within 0.5 ms, 1 ms, and 1.5 ms were estimated to be 6.98 C, 12.2 C, and 13.2 C, respectively. These valu es are comparable to the median impulse charge (excluding continuing current) of 16 C for a sample of 26 positive return strokes reported by Berger et al. [1975]. Schoene et al. [2009] reported the GM charge transfer within 1 ms after the beginning of the return stroke for 151 negative rocket tr iggered lightning strokes (considered similar to subsequent strokes in natural downward light ning) at Camp Blanding, Florida to be 1.0 C which is about an order of magnitude smaller th an the GM charge transf er within 1 ms of 10.7 C, found for positive lightning in our dataset. Positive leaders can move through virgin air either continuously or intermittently (in a stepped fashion), as determined from time-resolv ed optical images which is in contrast with negative leaders, which are always optically steppe d when they propagate in virgin air. Out of 63 positive return strokes (52 first strokes, 10 second strokes, and 1 third stroke) in the dataset presented here, 14 (27%) first strokes and 1 th ird stroke were precede d by pronounced step-like pulses. The AM interval between pulse peaks was found to be 20 s, which is similar to the

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377 average time interval of 17 s between leader pulses prior to a positive return stroke examined by Kong et al. [2008]. Preliminary breakdown pulses were identified an d examined. In the dataset presented here, only 5 (10%) out of 52 positive cloud-to-ground discharges had detectable preliminary breakdown pulse trains. The mean total pulse dura tion of individual pulses in the trains was 22 s with mean interpul se interval of 155 s. In contrast with nega tive discharges, the initial polarity of preliminary breakdown pulses in positive discharges can be either the same as or opposite to that of the following return-stroke pulse. Out of the 5 preliminary breakdown pulse trains in the dataset presented he re, pulses in four trains had the same initial polarity as that of the following return-stroke pulse, while pulses in one train had opposite polarity. There were no significant differences in the characteristics of the two types of pulse trains apart from their polarity. Two bipolar lightning discharges, which seque ntially lower both positive and negative charge to ground are examined. One of them was composed of three negative strokes followed by a positive stroke and then by a negative one. It is not clear if the fourth (positive) stroke shared a channel with any of the negative strokes of the flas h. The other bipolar flash was composed of three strokes, the first and the th ird being negative and the second being positive. NLDN reported the positive stroke in this flash as an intracloud discharge. It appears that the second (positive) stroke formed a channel to gr ound different from that of the first and third (negative) strokes.

PAGE 378

378 Figure 7-44. Electric field waveforms of the firs t (top panel) and second (bottom panel) return strokes of a two-stroke flash, each show n on a 300 s time scale. The interstroke interval was 19 ms. The NLDN-estimated distance between strokes was 1.7 km, and NLDN median location errors were 4.0 and 0.5 km for the first and second strokes, respectively. 1st RS INLDN = 116 kA r = 38 km 2nd RS INLDN = 28 kA r = 37 km

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379 Figure 7-45. Electric field waveforms of the firs t (top panel) and second (bottom panel) return strokes of a two-stroke flash, each show n on a 500 s time scale. The interstroke interval was 79 ms. The NLDN-estimated distance between strokes was 12 km, and NLDN median location errors were 0.7 and 0.4 km for the first and second strokes, respectively. 1st RS INLDN = 127 kA r = 85 km 2nd RS INLDN = 71 kA r = 80 km

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380 Figure 7-46. Electric field waveforms of the firs t (top panel) and second (bottom panel) return strokes of a two-stroke flash, each show n on a 300 s time scale. The interstroke interval was 8.5 ms. The NLDN-estimated distance between strokes was 2 km, and NLDN median location errors were 2.4 and 0.5 km for the first and second strokes, respectively. 1st RS INLDN = 145 kA r = 50 km 2nd RS INLDN = 45 kA r = 49 km

PAGE 381

381 Figure 7-47. Electric field waveforms of the firs t (top panel) and second (bottom panel) return strokes of a two-stroke flash, each show n on a 300 s time scale. The interstroke interval was 116 ms. The NLDN-estimated distance between strokes was 14 km, and NLDN median location error for both the first and second strokes was 0.4 km. 1st RS INLDN = 103 kA r = 129 km 2nd RS INLDN = 92 kA r = 125 km

PAGE 382

382 Figure 7-48. Electric field waveforms of the firs t (top panel) and second (bottom panel) return strokes of a two-stroke flash, each show n on a 300 s time scale. The interstroke interval was 83 ms. The NLDN-estimated di stance between strokes was 222 m, and NLDN median location errors were 0.8 and 0.5 km for the first and second strokes, respectively. 1st RS INLDN = 219 kA r = 157 km 2nd RS INLDN = 72 kA r = 157 km

PAGE 383

383 Figure 7-49. Electric field waveforms of the firs t (top panel) and second (bottom panel) return strokes of a two-stroke flash, each show n on a 200 s time scale. The interstroke interval was 70 ms. The NLDN-estimated distance between strokes was 10 km, and NLDN median location errors were 0.6 and 0.8 km for the first and second strokes, respectively. 1st RS INLDN = 101 kA r = 11 km 2nd RS INLDN = 61 kA r = 17 km

PAGE 384

384 Figure 7-50. Electric field waveforms of the firs t (top panel) and second (bottom panel) return strokes of a two-stroke flash, each show n on a 300 s time scale. The interstroke interval was 201 ms. The NLDN-estimated distance between strokes was 29 km, and NLDN median location errors were 0.5 and 0.4 km for the first and second strokes, respectively. 1st RS INLDN = 100 kA r = 42 km 2nd RS INLDN = 48 kA r = 32 km

PAGE 385

385 Figure 7-51. Electric field waveforms of the firs t (top panel) and second (bottom panel) return strokes of a two-stroke flash, each show n on a 250 s time scale. The interstroke interval was 41 ms. The NLDN-estimated distance between strokes was 3.7 km, and NLDN median location error for both the first and second strokes was 0.4 km. 1st RS INLDN = 69 kA r = 41 km 2nd RS INLDN = 60 kA r = 44 km

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386 CHAPTER 8 FIRST VERSUS SUBSEQUENT RETURN-STR OKE CURRENT AND FIELD PEAKS IN NEGATIVE CLOUD-TO-GROUN D LIGHTNING DISCHARGES 8.1 Introduction Return-stroke peak currents and electric a nd magnetic peak fields are often used to measure relative intensity of first and subsequent strokes. It is generally thought that for negative cloud-to-ground lightning discharges first strokes ar e typically a factor of 2 to 3 larger than subsequent strokes [e.g., Berger et al., 1975; Rakov et al., 1994; Cooray and Perez, 1994; Cooray and Jayaratne, 1994; Visacro et al., 2004]. In contrast, peak currents inferred from measured fields by lightning locating systems (LLS s) for first and subsequent strokes are often not much different from each other [e.g., Diendorfer et al., 1998; Rakov and Uman, 2003, Ch. 17]. In this Chapter, we examine relative intensities of first and subsequent strokes using electric field data acquired in Gain esville, Florida in 2006 (see Nag [2007] and Chapter 3), and compare the results with those of othe r lightning electric field meas uring studies in Austria, [Schulz and Diendorfer, 2006], Brazil [Oliveira et al., 2007], and Sweden [Schulz et al., 2008]. Additionally, we will consider results of recent LLS studies conducted in conjunction with video observations in USA [Biagi et al., 2007; Krider et al., 2007] and Brazil [Saba et al., 2006a]. In this Chapter, there are two Florida data sets, one acquired as a part of the pr esent study in 2006 in Gainesville, Florida, and the other [Rakov and Uman, 1990b] near Tampa, Florida, in 1979. Unless otherwise mentioned, the data set acquired in this study in 2006 is referred to as the Florida data set throughout this Chapter. 8.2 Methodology There are different approaches to estimating relative intensity of first and subsequent strokes. One approach is to form the ratio of geometric mean (GM), arithmetic mean (AM), or median intensities of first str okes and all subsequent strokes combined. This approach was used,

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387 for example, by Rakov and Uman [1990a, b] and Diendorfer et al. [1998]. Usually, intensities of strokes in single-stroke flashes are included, which results in a somewhat lower first-tosubsequent-stroke ratio than in the absence of singl e-stroke flashes, since strokes in single-stroke flashes are on average smaller than first strokes in multiple-stroke flashes. Another approach is to form the ratios for individual subsequent strokes and then find the AM, GM, or median of the resultant statistical distribution. This approach was employed, for example, by Thottappillil et al. [1992], Cooray and Perez [1994], and Cooray and Jayaratne [1994]. Clearly, the latter approach applies only to multiple-stroke flashes. For eith er of the two approaches, the use of GM (or median) values, as opposed to AM values, should probably be preferred, be cause distributions of current or field peaks or distributi ons of the ratios are close to log-normal. It is worth noting that subsequent strokes creating new terminations on ground are on average larg er than subsequent strokes following previously formed channels [Rakov et al., 1994], so that the occurrence of new channel terminations can potentially in fluence the field ratios examined here. In this Chapter, using our ow n measurements and data found in the literature we compiled statistical distributions of the ra tio of first to corresponding subseque nt return stroke electric field peaks and the ratio of subsequent to corresponding first return st roke field peaks for Florida, Austria, Brazil, and Sweden (additional informati on about data acquired in Austria, Brazil, and Sweden were provided by Schulz, Saba, and Thottappillil, respectively, via personal communication). Then the AM and GM for each of the two distributions were calculated. Ratios of AM (GM, median) first to AM (GM, median) subsequent stroke peak s were also computed, when possible. Further, we examined relative magn itudes of strokes of diffe rent order for Florida [Rakov and Uman, 1990; present study], Austria [Diendorfer et al., 1998; Schulz and Diendorfer, 2006], Brazil [Oliveira et al., 2007], and Sweden [Schulz et al., 2008]. For the present study in

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388 Florida, we normalized the electric field peak of each subsequent stroke in a particular flash with respect to the field peak of th e first return-stroke in that flash. Then, for each stroke order (sequential number of a stroke in a flash), the geometric mean of the normalized field peaks was calculated. For all the other studies, the GM fiel d peaks for subsequent strokes were normalized to the GM field peak for first strokes (including those in sing le-stroke flashes for data of Rakov and Uman [1990b] and Diendorfer et al. [1998]). Note that while computing the ratios for Florid a, Austria, Sweden, and Brazil, it has been assumed that for flashes having multiple ground term inations the distances from the antenna to all terminations are approximately the same. This assumption is justified when distances between different channel terminations of the same fl ash are small compared to the distance between them and the antenna. For the overwhelming major ity of flashes examined here the distances were larger than 20 km, which is much greate r than the geometric mean separation of 1.7 km between multiple channel terminations within a flash estimated in Florida by Thotappillil et al. [1992]. 8.3 Instrumentation and Data A brief description of the elec tric field measuring systems used in Gainesville, Florida (present study) and in Austria, Brazil, and Sweden and the data analyzed in this study is given below, followed by an overview of pertinent outp ut of lightning locating systems. Descriptions of instrumentation and data of other studies are available in the literature, in appropriate references provided in this Chapter. 8.3.1 Electric Field Measurements in Gainesville, Florida The electric field measuring system used to acquire the data analyzed in this study has been described in Nag [2007] and Chapter 3. Electric field si gnals from a flat-plate antenna and associated electronics were re layed to a digitizing oscillosc ope via a fiber-optic link. The

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389 Figure 8-1. (a) Typical electric field record of a multiple-stroke negative cloud-to-ground flash in Florida with three return strokes (RS) shown on a 150-ms timescale. (b) Electric field of the first return stroke, on an 80-ms timescale, of flash shown in Figure 8-1a. (c) Electric field of the second return stroke, on a 60-ms timescale. (d) Electric field of the third return stroke, on a 70-ms timescale. Initial (radiation) electric field peaks of return strokes of order 1, 2, and 3 are labeled as EP1, EP2, and EP3, respectively. Note that radiation field peaks seen in Figures 8-1b 8-1d are not resolved in Figure 8-1a. sampling interval was 10 ns. The measurement system had a useful frequency bandwidth of 16 Hz to 10 MHz. The record length was 200 ms. Using thunder ranging and the characteristic features of return-stroke electric field waveforms at known distances in the 50 to 250 km range [Pavlick et. al, 2002; Figure 5] we estimated that the majority of our records were due to lightning discharges occurring at distances ranging from a few to about a hundred kilometers from the field measuring station. An example of electric field record of multiple-stroke negative cloud-to-ground discharge in this dataset is shown in Figure 8-1. The data set consists of 176 multiple-stroke negative cloud-to-ground flashes recorded on July 15 and 17, 2006 in

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390 Gainesville, Florida. Each of the 176 records was examined to measure the amplitude of the initial (radiation) electric field peak (in digiti zer units) of individual return stroke waveform. Electric field peaks of subsequent strokes were no rmalized with respect to the electric field peak of the corresponding first stroke. It should be noted that the maxi mum number of strokes per flas h in the Florida data set is four, although some higher-order strokes were lik ely missed due to limited record length of 200 ms. Since higher order return strokes are expected to have somewhat smaller peak fields [Rakov and Uman, 1990b], the ratio of the first to subsequent return stroke field peaks based on this Florida data set should be viewed as a lower bound (the actual value can be somewhat higher). 8.3.2 Electric Field Measu rements in Austria The electric field measuring system used to acquire the data analyzed in this study has been described by Schulz and Diendorfer [2006]. The system could record fields continuously during the entire thunderstorm. A fi ber-optic link was used to rela y signals from a flat-plate antenna to a digitizing oscillos cope. The sampling interval was 200 ns. The measurement system had a useful frequency bandwidth of 350 Hz to 1.5 MHz. Electric field records of lightning discharges occurring at distances of 50 to 100 km from the field measuring station were included in the data set analyzed in this study. This data set consists of 81 multiple-stroke negative cloudto-ground flashes recorded during about one hour on July 11, 2005 in Bad Voeslau, Austria. Lightning locating system (ALDIS) data were used to normalize electric field peaks to 100 km. 8.3.3 Electric Field Measurements in Brazil The electric field measuring system used in Braz il was the same as that used in Austria and described above, but a double-shield ed coaxial cable instead of th e fiber optic link was used to transmit signals from the antenna to the digitizer. The data set analyzed in this study consists of 259 multiple-stroke negative cloud-to-ground flashe s occurring within 200 km of the field

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391 measuring station that were recorded during a bout one hour each on each February 11 and March 11, 2007 in So Jos dos Campos, Brazil. Electric field peaks were normalized to 100 km using lightning locating system (BrasilDat) data Additional information can be found in Oliveira et al. [2007]. 8.3.4 Electric Field Measurements in Sweden The electric field measuring system was the same as that used in Brazil, although the antenna was installed on the top of a building, while in Brazil (and in Austria) it was installed at ground level. A total of 93 multiple-stroke negative cloud-to-ground flashes occurring at distances ranging from 20 to 60 km on July 24, 2006 in Uppsala, Sweden, are analyzed in this study. Electric field peaks were normalized to 100 km using lightning locating system data. Additional information can be found in Schulz et al. [2008]. 8.3.5 Currents Estimated by Lightning Locating Systems Modern multiple-station lightning locating system s (LLSs) output a peak current estimate for each stroke using the measured magnetic ra diation field peaks and distances to the ground strike point reported by individual sensors. The field and curren t peaks are usually assumed to be proportional to each other. For data examined in this study, the magnetic-field-to-current conversion factor was 0.185 for the U.S. and Brazilian systems and 0.23 for the Austrian system, where the magnetic field was expressed in so-c alled LLP units. In the U.S. and Brazilian systems, a model was employed to increase the me asured field peak (normalized to 100 km) in order to compensate for its at tenuation due to propagation ov er finitely-conducting ground, while no such model was implemented in the Austrian system. In this study, we used only those LLSreported events confirmed by video records as having cloud-to-ground cha nnels, except for the Austrian LLS data for which no video records were available.

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392 8.4 Analysis and Discussion Figure 8-2 shows the distributions of the ratio of the first return stroke field peak to the corresponding subsequent return st roke field peak for Florida, Austria, Brazil, and Sweden. The arithmetic and geometric means of the ratio were, respectively, 2.1 and 1.7 for Florida, 2.3 and 1.6 for Austria, and 2.4 and 1.9 for either Brazil or Sweden. Thus, on average, the electric field peak of the first stroke is roughly 2 times larger than the field peak of the subsequent stroke. Distributions of the ratio of the subsequent to the corresponding first retu rn stroke field peaks, shown in Figure 8-3 are characterized by arithme tic and geometric means, respectively, of 0.75 Figure 8-2. Histogram of the ratio of the first-to-subsequent-returnstroke electric field peak for multiple stroke negative cloud-to-ground lightning flashes in (a) Florida, (b) Austria, (c) Brazil, and (d) Sweden.

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393 Figure 8-3. Histogram of the ratio of the subsequent -to-first-return-stroke electric field peak for multiple stroke negative cloud-to-ground lightning flashes in (a) Florida, (b) Austria, (c) Brazil, and (d) Sweden. and 0.58 for Florida, 0.87 and 0.64 for Austria, 0.69 and 0.53 for Brazil, and 0.64 and 0.52 for Sweden. The geometric mean electric field peaks for strokes of different order normalized (as described in Section 2 and in the caption of Fi gure 8-4) to the corresponding first stroke field peak from different studies in Florida, Austri a, Brazil, and Sweden are shown in Figure 8-4. Data of Rakov and Uman [1990b] were acquired using simultaneous single-station electric field and multiple-station TV records n ear Tampa, Florida, in 1979. The normalized field peaks for subsequent strokes in the 1979 and 2006 Florida data (see columns labeled A and B, respectively, in Figure 8-4) are found to be in good agreement, confirming the notion that the

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394 Figure 8-4. Geometric mean (GM) electric field peaks for strokes of different order estimated from different studies, labeled A, B, C, D, E, and F. For A, field peaks of subsequent strokes of different order are normalized to the electric field peak of the corresponding first return stroke and for B, C, D, E, and F the GM field peaks of subsequent strokes of different order are normalized to th e GM field peak for first strokes (including those in si ngle-stroke flashes for B and C). Sample size for strokes of order 12 in study D was as low as three (there were six in study E, and for study B the value is the average for 53 strokes of order 8 through 18). electric field (or current peak) of the first return stroke is appreciably larger than that of the subsequent stroke. In contrast, Diendorfer et al. [1998], who examined re turn strokes recorded by the Austrian lightning locating system (ALD IS), found the values of the field peaks (and ALDIS-reported peak currents, assumed to be propor tional to measured field peaks) of the first and subsequent strokes to be approximately equal (see columns labeled C in Figure 8-4). Further,

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395 Rakov and Uman [2003, Ch. 17] noted that similar first and subsequent stroke intensities were reported by the U.S. National Lightning Detect ion Network (NLDN) prior to its 2002 upgrade [Cummins et al., 2006]. Geometric mean values of the elec tric field peak for subsequent strokes of different order found from electric field meas urements in Austria (see columns labeled D in Figure 8-4) are generally larger that the corresponding values in other studies, except for those based on ALDIS data, particularly for stroke order 12. However, the later value may be unreliable due to the small sample size (there were only 3 strokes of order 12 in study D). We discuss next recent LLS studies conducted in conjunction with video observations. Saba et al. [2006a], using data from the Brazilian lightning locating system (BrasilDat), found the mean peak current of 55 first return stroke s (28.3 kA) to be 2.1 times the mean peak current of 193 subsequent return strokes (13.5 kA). The corresponding ratio of geometric mean values is 1.7. Note that Saba et al.s data are for strokes followed by continuing currents with durations ranging from 4 to 350 ms and are accompanied by high-speed (1000 frames per second) video records. The presence of continuing currents with durations down to a few milliseconds is unlikely to introduce any significant bias in LLS-inferred peak currents. Indeed, Shindo and Uman [1989] found that geometric me an electric field peak (nor malized to 100 km) for return strokes followed by questionabl e continuing currents with durations ranging from 1 to 10 ms was equal to that for regular subsequent return strokes (not followed by any continuing current). Biagi et al. [2007] examined post-2002-upgrade NLDN data (for 2003 and 2004) that were confirmed by ordinary video camera records in Arizona, Texas, and Oklahoma and reported the ratio of GM first to GM subsequent current peaks to be 1.3 and 1.2 in Arizona and Texas-Oklahoma, respectively. From a similar st udy in the Great Plains of eastern Colorado,

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396 western Kansas, and western Nebraska, the value of the ratio estimated from 2005 NLDN data is 1.3 [Krider et al., 2007]. Table 8-1 summarizes the values of first to s ubsequent stroke electr ic field (or current) peak ratio estimated in different studies. The ra tio varies from 1.0 to 2.5. The lowest value, 1.0, corresponds to the LLS study in Austria. The highest values, 2.3 to 2.5, correspond to direct current measurements on towers. Assuming that the radiation field peak is r oughly proportional to the product of the current and return-stroke speed, we infer th at the smaller ratio for fields than for currents implies a lower average return-stroke speed for first strokes than fo r subsequent strokes. This is consistent with optical speed measurements [Idone and Orville, 1982], who reported mean speeds of 9.6 x 107 m/s and 1.2 x 108 m/s for 17 first and 46 subsequent st rokes, respectively. The difference, though, is not very large. Alternatively, the higher ratios for directly m easured currents (relative to the ratios for fields) could be due to the lack of new channe l terminations for curr ents, since subsequent strokes in newly-formed channe ls are on average larger than those in previously-formed ones [Rakov et al., 1994]. However, the ratios do not change mu ch if the strokes in the newly-formed channels are excluded (see Tabl e 8-2): for Florida data of Rakov and Uman [1990a, b] the ratio of GM field peaks increases from 2.0 to 2.2 and for data of Biagi et al. [2007] and Krider et al. [2007] they remain unchanged at 1.3, 1.2 and 1.3 in Arizona, Texas-Oklahoma, and the Great Plains, respectively. Note that, the ratios in Table 8-1 calcula ted from LLS studies (ALDIS, BrasilDat, and NLDN), are for both multipleand single-stroke flashes combined. As noted in Section 2, this may result in some underestimation of the firstto-subsequent-stroke ratio, since strokes in

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397Table 8-1. Summary of first to subsequent stroke electric field or current peak ratios estimated from different studies. Reference(s) and location AM of first to subsequent stroke peak ratio Ratio of AM first to AM subsequent stroke peak GM of first to subsequent stroke peak ratio Ratio of GM first to GM subsequent stroke peak Ratio of median first to median subsequent stroke peak Number of subsequent strokes Number of first strokes Number of singlestroke flashes Stroke identification method Electric Field Rakov and Uman [1990a, b], Florida 1.9 2.0a 270 76 13 Electric field and TV records Diendorfer et al. [1998], Austria 1.0 1.0 53443 43133 24120 LLS reports Schulz and Diendorfer [2006], Austria 2.3 1.4 1.6 1.3 1.1 247 81 0 Oliveira et al. [2007], Brazil 2.4 1.7 1.9 1.7 1.8 909 259 0 Schulz et al. [2008], Sweden 2.4 2.0 1.9 1.8 2.0 258 93 0 Present study, Florida 2.1 1.7 1.7b 239 176 0 Electric field records Current Berger et al. [1975], Switzerland 2.5 135 101 ~50 Anderson and Eriksson [1980], Switzerland 2.3 2.3 114 75 Visacro et al. [2004], Brazil 2.5 2.5 59 31 15 Direct current measurements Saba et al. [2006a], Brazil 2.1c 1.7c 1.6c 193 55 16 Biagi et al. [2007], Arizona 1.5 1.3 1.2 1602 953 388 Biagi et al. [2007], TexasOklahoma 1.6 1.2 1.1 371 273 131 Krider et al. [2007], Great Plains 1.3 1.3 1.2 150 90 40 LLS reports confirmed by video records a For all subsequent strokes combined. For subsequent strokes following a previously-formed channel, Rakov et al. [1994] reported the ratio to be 2.2. b The median of the ratio of first to corresponding subsequent stro ke peak (in multiple stroke flashes), not the ratio of the med ians of the first and subsequent stroke peaks, as for other studies in this column. c For strokes followed by continuing currents with durations ranging from 4 to 350 ms.

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398 Table 8-2. Summary of first to subsequent str oke electric field or current peak ratios for subsequent strokes following a previously-formed channel. Reference(s) and location Ratio of GM first to GM subsequent stroke peak for all subsequent strokes combineda Ratio of GM first to GM subsequent stroke peak for subsequent strokes following a previouslyformed channel Stroke identification method Rakov and Uman [1990a, b], Florida 2.0 2.2 Electric field and TV records Biagi et al. [2007], Arizona 1.3 1.3 Biagi et al. [2007], Texas-Oklahoma 1.2 1.2 Krider et al. [2007], Great Plains 1.3 1.3 LLS reports confirmed by video records a Taken from Table 8-1. Both subsequent stro kes following a previously-formed channel and those creating new termina tions on ground are included. single-stroke flashes are on average smaller than first strokes in multiple-stroke flashes. The ratios of GM first to GM subsequent curren t peaks estimated from NLDN data in TexasOklahoma and the Great Plains are, respectiv ely, 1.4 and 1.5, when only multiple-stroke flashes are considered (see Table 8-3), somewhat larger than 1.2 and 1.3, respectively, estimated for the case when both multipleand single-stroke flashes were combined (see Table 8-1). On the other hand, when single-stroke flashe s are excluded, the ratio of GM s for Arizona remains unchanged at 1.3. For the electric field measurements of Rakov and Uman [1990a, b] in Florida the ratio of GMs after excluding single-stroke flashes change d only slightly, from 2.0 to 2.1. Overall, the effect of excluding single-stroke flashe s appears to be relatively small. Table 8-4 summarizes the values of subsequent to first stroke electric field (or current) peak ratio estimated in different studies. All the geometric mean ratios and ratios of geometric means and medians are between 0.40 and 0.76, exce pt for those based on LLS reports, which range from 0.60 to 0.93. The arithmetic mean ratios and ratios of arithmetic means in Table 8-4 range from 0.48 to 0.87.

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399 Table 8-3. Summary of first to subsequent stroke electric field or current peak ratios for multiplestroke flashes only.a Reference(s) and location Ratio of AM first to AM subsequent stroke peak Ratio of GM first to GM subsequent stroke peak Ratio of median first to median subsequent stroke peak Number of subsequent strokes Number of first strokes Stroke identification method Rakov and Uman [1990a, b], Florida 2.0 (1.9) 2.1 (2.0) 270 63 Electric field and TV records Biagi et al. [2007], Arizona 1.3 (1.5) 1.3 (1.3) 1.3 (1.2) 1602 565 Biagi et al. [2007], TexasOklahoma 1.5 (1.6) 1.4 (1.2) 1.3 (1.1) 371 142 Krider et al. [2007], Great Plains 1.5 (1.3) 1.5 (1.3) 1.5 (1.2) 150 50 LLS reports confirmed by video records aValues in the parentheses are taken from Table 8-1 and correspond to both multipleand single-stroke flashes combined. It appears that the ratios are not mu ch influenced by the exclusion of single-stroke flashes. The question remains if the observed discrepa ncies are due to differences in lightning characteristics in different geographical locati ons or due to different instrumentation and methodologies involved. We will discuss each of these two possibilities below. From the methodology point of view, the NLDN (prior to the 2002 upgrade) and ALDIS results could be due to poor detection of relatively small subsequent strokes, rejection of the first stroke by the waveform discrimination algorithm a nd acceptance of the second stroke as the first stroke, and misclassification of a preliminary-breakdown pulse (associated with an in-cloud process; see Chapter 5) as the first return stro ke. More research is needed to quantify these effects. Also, the accuracy of first stroke peak current estimates derived from LLS data has not yet been confirmed by independent measurements [e.g., Krider et al., 2007]. Additionally, time resolution of video records (17 ms in Biagi et al. [2007] versus 1 ms in Saba et al. [2006a]) can play a role in detecting sm aller subsequent strokes. Saba et al. [2006b] estimated that 19% of the

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400 total number of strokes in their study would be missed if an ordinary video camera with 17 ms time resolution (inter-field interval) were used. On the other hand, the occurrence of larger th an first subsequent strokes can vary for different types of storms or fo r different locations. Table 8-5 presents a summary of percentages of multiple-stroke flashes with at least one subsequent stroke field peak greater than the first and percentages of subsequent strokes with field peak s greater than the first estimated in different studies. In Florida, Austria, Brazil, and Sweden, respectively, 21, 32, 20, and 18 % of the subsequent strokes were found to have field peaks greater than that of the first stroke. Percentages of flashes containing at least one subsequent stroke with field peak greater than that of the first stroke in these studies were 24, 49, 38, and 32%, respectively. Also given in Table 85 are the percentages estimated from earlier el ectric field measurements in Sri Lanka and Sweden and from LLS reports in Austria. The hi ghest percentages of flashes with at least one subsequent stroke field peak greater than the first were reporte d in Austria (49% for Schulz and Diendorfer [2006] and 51% for Diendorfer et al. [1998]). This possibly expl ains (at least in part) the smaller first-to-subsequent-stroke field peak ratio estimated from the Austrian studies compared to those for other regions in the wo rld. It is presently not known if the larger subsequent strokes in Austria are associated with new channel termin ations on ground or not. 8.5 Summary Relative magnitudes of electric field peaks of first and subsequent return strokes in negative cloud-to-ground lightning fl ashes recorded in Florida, Au stria, Brazil, and Sweden are analyzed in this study. On average, the electric fi eld peak of the first stroke is appreciably, 1.7 to 2.4 times, larger than the field peak of the subseq uent stroke (except for studies in Austria where the ratio varies from 1.0 to 2.3, depending on me thodology and instrumentation). Similar results were previously reported from electric field studies in Florida, Sweden, and Sri Lanka by Rakov

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401Table 8-4. Summary of subsequent to first stroke electric field or current peak ratio estimated from different studies. Reference(s) and location AM of subsequent to first stroke peak ratio Ratio of AM subsequent to AM first stroke peak GM of subsequent to first stroke peak ratio Ratio of GM subsequent to GM first stroke peak Ratio of median subsequent to median first stroke peak Number of subsequent strokes Number of first strokes Number of singlestroke flashes Stroke identification method Electric Field 0.52 0.49a 270 76 13 Rakov and Uman [1990a, b], Florida 0.49 0.47 270 63 0 Thottappillil et al. [1992], Florida 0.42b 199 46 0 Electric field and TV records Cooray and Perez [1994], Sweden 0.63 0.51 314 0 Cooray and Jayaratne [1994], Sri Lanka 0.55 0.43 284 81 0 Electric field records Diendorfer et al. [1998], Austria 1.0 1.0 53443 43133 24120 LLS reports Schulz and Diendorfer [2006], Austria 0.87 0.71 0.64 0.76 0.90 247 81 0 Oliveira et al. [2007], Brazil 0.69 0.59 0.53 0.58 0.55 909 259 0 Schulz et al. [2008], Sweden 0.64 0.51 0.52 0.56 0.50 258 93 0 Present study, Florida 0.75 0.58 0.57c 239 176 0 Electric field records Current Berger et al. [1975], Switzerland 0.40 135 101 ~50 Anderson and Eriksson [1980], Switzerland 0.43 0.43 114 75 Visacro et al. [2004], Brazil 0.40 0.40 59 31 15 Direct current measurements Saba et al. [2006a], Brazil 0.48d 0.60d 0.64d 193 55 16 Biagi et al. [2007], Arizona 0.65e 0.78 0.81 1602 953 388 Biagi et al. [2007], Texas-Oklahoma 0.63e 0.83 0.93 371 273 131 Krider et al. [2007], Great Plains 0.78f 0.78 0.81f 150 90 40 LLS reports confirmed by video records a For all subsequent strokes combined. For subsequent strokes following a previously-formed channel, Rakov et al. [1994] reported the ratio to be 0.46. b For all subsequent strokes combined. For subsequent strokes following a previously-formed channel, Thottappillil et al. [1992] reported the GM ratio to be 0.39 (176 events). c The median of the ratio of subsequent to corresponding first stroke peaks (in multiple-stroke flashes), not the ratio of the me dians of subsequent and first stroke peaks, as for other studies in this column. d For strokes followed by continuing currents with durations ranging from 4 to 350 ms. e For all subsequent strokes combined. For subsequent strokes following a previously-formed channel, Biagi et al. [2007] reported the ratio to be 0.61 and 0.59 for Arizona and Texas-Oklahoma, respectively. f For all subsequent strokes combined. For subsequent strokes following a previously-formed channel, Krider et al. [2007] reported the ratio of arithmetic means to be 0.75 and the ratio of medians to be 0.70.

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402 Table 8-5. Summary of multiple-stroke flash characteristics reported in different studies. Reference(s) and location Total number of flashes Percentage of flashes with at least one subsequent stroke field peak greater than the first Percentage of subsequent strokes with field peaks greater than the first Stroke identification method Thottappillil et al. [1992], Florida 46 33 13 Electric field and TV records Cooray and Perez [1994], Sweden 276 24 15 Cooray and Jayaratne [1994], Sri Lanka 81 35 12 Electric field records Diendorfer et al. [1998], Austria 15905 51 LLS reports Schulz and Diendorfer [2006], Austria 81 49 32 Oliveira et al. [2007], Brazil 259 38 20 Schulz et al. [2008], Sweden 93 32 18 Present study, Florida 176 24 21 Electric field records et al. [1994], Cooray and Perez [1994], and Cooray and Jayaratne [1994], respectively. For comparison, directly measured peak currents for fi rst strokes are, on averag e, a factor of 2.3 to 2.5 larger than those for subsequent strokes. [Berger et al., 1975; Anderson and Eriksson, 1980; Visacro et al., 2004]. The generally larger ratio for curr ents than for fields possibly implies a lower average return-stroke speed for first strokes than for subsequent strokes. There appear to be some differences between first versus subseq uent stroke intensities reported from different studies based on data reported by lightning locating systems (LLS s). The ratio of LLS-reported peak currents for first and subsequent strokes co nfirmed by video records is 1.7 to 2.1 in Brazil (for strokes followed by continuing currents with durations ranging from 4 to 350 ms), while in the U.S. (Arizona, Texas, Oklahoma, and the Great Plains) it varies from 1.1 to 1.6, depending

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403 on methodology used. Ratios involving arithmetic means are generally larger than those involving geometric means. The smaller ratios deri ved from the LLS studies are likely to be due to poor detection of relatively small subsequent strokes. The smaller values in Austria are possibly related (at least in part ) to the higher percentage (about 50% versus 24 to 38% in other studies) of flashes with at least one subsequent stroke greater than the first. The effects on the ratio of excluding single-stroke fl ashes or subsequent strokes in newly-formed channels appear to be relatively small. Additional data are needed to further clarify the issue of relative intensity of first and subsequent strokes in differen t geographical locations, as well as possible instrumental and methodol ogical biases involved.

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404 CHAPTER 9 SUMMARY OF RESULTS AND RECOMMENDATIONS FOR FU TURE RESEARCH 9.1 Summary of Results Measurements of electromagnetic signals from lightning discharges performed at the Lightning Observatory in Gainesville (LOG), on the University of Florida campus, in 2006, 2007, and 2008 are presented. In 2008, the experiment al setup included wideband electric field, electric field derivative (dE/dt ), magnetic field derivative (dB/dt), and narrowband very high frequency (VHF) measurements and was operated in either single-station or two-station mode. The single-station experiment was designed to obta in correlated wideband electric field, electric field derivative, magnetic field derivative, and narrowband VHF signatures of cloud and natural ground lightning discharges. The emphasis was on compact intracloud discharges, preliminary breakdown pulse trains, and positive cloud-to-gro und lightning. The two-station experiment was designed to measure far field waveforms (primarily radiation) at the Gainesville station due to natural and rocket-triggered lightning at Camp Bl anding, Florida, in conj unction with near field measurements there. The Gainesville and Camp Blanding measuring stations are 45 km apart. The data acquired were used to improve our understanding of the various lightning processes, infer parameters of these processe s, and develop models that can be used to describe and predict their salient properties. The primary results presen ted in this dissertation are briefly summarized below. 9.1.1 Compact Intracloud Discharges Compact Intracloud Discharges (CIDs) are cloud lightning discharges that produce single bipolar electric field pulses (socalled Narrow Bipolar Pulses or NBPs) having typical full widths of 10 to 30 s and intense HF-VHF radiation bursts (much more intense than those from any other cloud-to-ground or norma l cloud discharge process). We examined wideband electric

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405 fields, electric and magnetic fiel d derivatives, and narrowband VHF (36 MHz) radiation bursts produced by 157 CIDs. The majority (about 72%) of CIDs appeared to occur in isolation from any other lightning process, while about 24% we re found to occur prior to, during, or following CG or normal IC lightning. About 18% were associated with cloud flashes and 6% with ground ones. In three cases two CIDs occurred wi thin 43, 66, and 181 ms of each other (the first documented "multiple" CIDs), with a total of 4% of CIDs occurring in pairs. For 48 CIDs, the geometric means of source height and electr ic field peak normalized to 100 km and zero elevation angle were estimated to be 16 km a nd 20 V/m, respectively. The geometric means of total pulse duration, width of initial half-cycle, and ratio of initial electric field peak to opposite polarity overshoot were 23 s, 5.6 s, and 5.7, respectively. Based on the experimental evidence of multiple reflections and modeling, we infer that the CID is essentially a bouncing-wave phenomenon. Some tens of reflections may occur at both radiating-channel ends. It is possible that the bouncing waves serve to maintain channel conductivity. Only higher-order refl ections (in the later portion of the waveform) are detectable (if at all) in either electric field or dE/dt waveforms, while the undetectable lower-order reflections do influence the magnitude of the primary signature. In about 85% dE/dt signatures no reflections were observed. Reflections at channel extremities may result in corona-like electrical breakdown there, which is likely to produce intens e bursts of HF-VHF radiation and increase "noisiness" of dE/dt signatures, which are characteristic features of CIDs. We modeled the CID as a wave tr aveling on an elevated vertical transmission line. In order to account for multiple reflections that take place at the channel ends we specified two equivalent current sources, connected at the bottom and at th e top of the channel. By comparing electric fields predicted by this bouncingwave model with measurements we estimated that effective

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406 current reflection coefficients at channel ends should be in the ra nge of 0 to -0.5, that the wave propagation speed ranges from 0.3 to 3 x 108 m/s, and channel length is less than 1000 m. The lower bound on CID channel length appears to be a bout 100 m. Influence of current risetime on field waveforms was also examined, and it was found to be typically in the range from about 2 to 8.5 s. The current distribution along the CID channel is often not much different from uniform, as expected for a Hertzian (electrically short) di pole, because of relatively short channel length, relatively long current waveform, and relatively high propagation sp eed. We estimated electrical parameters of 48 located CIDs using their measur ed electric fields and ve rtical Hertzian dipole approximation. This approximation is consiste nt with the bouncing-wave CID model for a reasonably large subset of allowed combinati ons of propagation speed and channel length. For nine events, we estimated channel lengths from observed reflection signatures in measured dE/dt waveforms and assumed propagation speeds of 2 x 108 m/s and 3 x 108 m/s, which cover the entire range of allowed values. For v = 2.5 x 108 m/s (average value), the channel lengths for these nine events ranged from 108 to 142 m. For the remaining 39 events, there were no reflection signatures observed, and h was assumed to be 350 m, for which the Hertzian dipole approximation is valid for speeds in the range of 2 to 3 x 108 m/s. For all 48 events, GM values of peak current, zero-to-peak current risetime, 10-to-90% current risetime, and charge transfer for the first 5 s are 74 kA, 5 s, 2.5 s, and 164 mC, respectively. The geometric mean peak radiated power, and energy radiat ed for the first 5 s are 29 GW and 31 kJ, respect ively. Overall, the estimated CID current waveform parameters are comparable to their counterparts for first strokes in cloud-to-ground lightning while their peak radiated el ectromagnetic power appears to

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407 be considerably higher. Total ener gy dissipated by CIDs does not appear to be higher than that dissipated by first strokes in CG flashes or by regular IC flashes. 9.1.2 Preliminary Breakdown in Cloud-to-G round Flashes and in Attempted Leaders Lightning events exhibiting pulse trains that are characteristic of preliminary breakdown in negative cloud-to-ground discharges, but are not followed by return stroke waveforms, are assumed to be manifestations of attempted cloud-to-ground leaders. Preliminary breakdown (PB) pulse trains in 12 negative cloud-to-ground disc harges and in 33 attempted leaders were examined. Both classical (having durations of tens of microseconds) and narrow (having durations of a few microseconds) pulses were found in both types of pulse trains. However, submicrosecond-scale pulses were only observed in preliminary breakdown pulse trains of ground discharges. In fact, for cloud-to-ground discharges, a significan t fraction (22%) of examined pulses had total durations less than 1 s. The majority of pulses in PB pulse trains are typically small in both amplitude and duration. The largest pulses in the train can exceed in magnitude the following first return-stroke pu lse. About 19% of the 59 preliminary breakdown pulse trains were found to c ontain pulses whose peaks were greater than those of the corresponding first return strokes [Nag and Rakov, 2009]. Pulses with larger durations (>4 s) tend to occur earlier in the train. The PB pulse train appears to be generate d when a negatively-charged channel extends downward from the main negative charge region and encounters an appreciable lower positive charge region (LPCR). When the LPCR is sma ll no PB pulse train may be produced. In this view, the fact that in some negative CG flashes no PB pulse train is detectable could be due to insignificant LPCR. It was found that at higher la titudes a larger percentage of CG discharges exhibit detectable PB pulse trains than at lower latitudes. This implies that a significant LPCR is present in thunderclouds mo re often at higher latit udes than at relatively lo w latitudes. While the

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408 LPCR may serve to enhance the electric field at the bottom of the negative charge region and thereby facilitate the launchi ng of a negatively-charged leader toward ground, presence of excessive LPCR may prevent the occurrence of negative CG flashes by blocking the progression of descending negative leader from reaching ground. Four conceptual lightning scenarios are inferred that may arise depending upon the magnitude of the LPCR. 9.1.3 First Return Strokes in Ne gative Cloud-to-Ground Lightning Simultaneous measurements at Camp Blanding and in Gainesville were used to compare slow fronts in near and far electric field wavefo rms. A total of four first strokes in natural lightning were examined. For three of them the sl ow-front duration was similar at both stations, while for one first stroke a pronounced slow front was not observed. The amplitude of the slow front relative to the peak was f ound to be similar in close and di stant waveforms for two out of three first return strokes ha ving a pronounced slow front. The one-wave, two-wave, and three-wave tran smission line models were used to compute close and distant return stroke el ectric fields. For all three models, the computed electric field waveforms do not exhibit distinct slow fronts, if there is no similar feature in the causative current. For an incident current wave containing a pronounced sl ow front, the duration of the slow front in model-predicted elec tric fields and its magnitude relative to peak are approximately the same at near and far distances. The slow front at far distances (100 km) is primarily due to the radiation field component, with the cont ributions due to electrostatic and induction components being negligible. At ne ar distances (500 m), the slow front is composed of more or less equal (or comparable) contribu tions from all three components of electric field. It appears that a slow front in return stroke current is responsible for a slow front in re turn stroke electric field. The mechanism of formation of slow front in the current is probabl y related to the break-

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409 through phase of the attachment process by which the extending plasma channels of the upward and downward leaders make contact. 9.1.4 Positive Cloud-to-Ground Lightning Experimental data on 52 positive and 2 bipolar lightning flashes acquired in Gainesville, Florida, in 2007-2008 are presented. Various features of positive discharge, including multiplicity, parameters of return stroke electr ic field waveforms, inferred currents, charge transferred by return stroke, leader steppi ng, and preliminary breakdow n pulse trains were examined. There were a total of 63 return -strokes in 52 positive flashes with an average multiplicity of 1.2. Out of the 52 positive cloud-to-ground flashes, 42 (81%) were single-stroke, 9 (17%) two-stroke, and 1 (2.0%) th ree-stroke flashes. 89% of th e positive return strokes were correctly identified by the NLDN. The GM electric field peak and electric field derivative peak, both normalized to 100 km, for 48 positive return strokes occurring at distances ranging from 7.8 to 157 km were 18.1 V/m and 9.02 V/m/s, respectively. The GM zero-to-peak risetime and 10-90% risetime for positive return strokes were 6.92 s and 3.40 s, respectiv ely. The GM slow front duration, slow front amplitude relative to peak, and fast-transit ion 10-90% risetime were 4.95 s, 36.7%, and 1.02 s, respectively. The duration of the slow front for positive return strokes in Florida was found to be, on average, longer than that for negative fi rst return strokes in Florida reported by Weidman and Krider [1978] and Master et al. [1984]. The AM zero-crossing time for positive return strokes was 53.6 s and the opposite polarity overshoot was, on average, 15.6% of the peak. These values are similar to those, 49.5 s and 18.5%, reported by Pavlick et al. [2002] for negative return strokes in Florida. The median charge transfer within 0.5 ms, 1 ms, and 1.5 ms for 19 positive re turn strokes were estimated to be 6.98 C, 12.2 C, and 13.2 C, respectively.

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410 Out of 63 positive return stroke s (52 first strokes, 10 second st rokes, and 1 third stroke), 14 (27%) first strokes and 1 third stroke were preceded by pronoun ced step-like pulses. The AM interval between pulse peaks was found to be 20 s. Only 5 (10%) out of 52 positive cloud-to-ground discharges had detectable preliminary breakdown pulse trains. The mean total pulse dura tion of individual pulses in the trains was 22 s with mean interpul se interval of 155 s. In contrast with nega tive discharges, the initial polarity of preliminary breakdown pulses in positive discharges can be either the same as or opposite to that of the following return-stroke pulse. Out of the 5 preliminary breakdown pulse trains in the dataset presented he re, pulses in four trains had the same initial polarity as that of the following return-stroke pulse, while pu lses in one train had opposite polarity. Two bipolar lightning discharges, which sequentially lowered positive and negative charge to ground are examined. One of them was comp osed of three negativ e strokes followed by a positive stroke and then by a negative one. The other bipolar flash was composed of three strokes, the first and the third being negative and the second being positive. For this flash, both the first and third strokes occurr ed at a distance of 46 km from the field measuring station (semimajor axis length of NLDN 50% location error e llipse being 400 m for both strokes) and NLDNreported peak currents were 52 kA and 25 kA respectively. The NLDN reported the third (positive) stroke as an intracloud discharge at a distance of 39 km (semi-ma jor axis length of 1.2 km). It appears that the second (positive) stroke formed a channel to ground different from that of the first and third (negative) strokes. 9.1.5 Ratio of First versus Subsequent Return Stroke Intensities in Negative Cloud-toGround Discharges In collaboration with ALDIS (Austria), INPE (Brazil), and Uppsala University (Sweden), relative magnitudes of electric field peaks of first and subsequent return strokes in negative

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411 cloud-to-ground lightning flashes recorded in Fl orida, Austria, Brazil, and Sweden were analyzed. On average, the electric field peak of the first stroke is appreciably, 1.7 to 2.4 times, larger than the field peak of the subsequent stroke (except for studies in Austria where the ratio varies from 1.0 to 2.3, depending on methodology and instrumentation). Similar results were previously reported from electric field stud ies in Florida, Sweden, and Sri Lanka by Rakov et al. [1994], Cooray and Perez [1994], and Cooray and Jayaratne [1994], respectively. For comparison, directly measured peak currents for fi rst strokes are, on averag e, a factor of 2.3 to 2.5 larger than those for subsequent strokes. [Berger et al., 1975; Anderson and Eriksson, 1980; Visacro et al., 2004]. The generally larger ratio for curr ents than for fields possibly implies a lower average return-stroke speed for firs t strokes than for subsequent strokes. 9.2 Recommendations for Future Research Various types of lightning discharges have been characterized and modeled in this dissertation using data primarily obtained at the Lightning Observ atory in Gainesville (LOG). A few modifications and upgrades to the measuring station can be undertaken to further expand the scope of the experiments. Also, some of the models presented here can be improved. It is the authors opinion that the follo wing topics all warrant additi onal investigation, and a detailed study of each could yield important insight s into the lightning discharge process. High-speed video records: Optical re cords obtained using a high speed ( 1000 frames per second) video camera will help identify cha nnels to ground in both negative and positive cloud-to-ground lightning both of which were ex amined in this study. Optical images of positive (and bipolar) lightning channels are very rare. Further, high-speed video records can help one gain further insight into the attachment process in cloud-to-ground lightning. Multiple-station measurement of CIDs: Si multaneous measurement of CID wideband electric fields at multiple stations can be used to determine source locations using the time of arrival technique. Further, simultaneous close and distant field measurements of CIDs [e.g., Eack, 2004] are very rare, and can be used to te st theoretical models of this type of lightning discharge and gain further insi ght into its mechanism and parameters.

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412 Improvement of the bouncing-wave CID mode l: The bouncing-wave model presented in Chapter 4 considers both atte nuation along the CID channel a nd absorption at the channel ends as lumped at the channel ends. In order to make the model more realistic, attenuation of the current wave along the channel should be separated from absorp tion at channel ends. In other words, the current attenuation and re flection coefficients should be considered as separate model parameters. Additionally, the CID incident current can be represented by functions other than the Gaussian functi on used in Chapter 4 (e.g., Heidler function [Heidler, 1985]). Examination of two-station data for rocket -triggered lightning acquired in 2008 and 2009: Only natural lightning flashes simultaneously recorded at Camp Blanding and in Gainesville are considered in this dissertation. Twelve rock et triggered lightning flashes acquired simultaneously at the two stations in 2008 and 2009 are to be examined. Introduction of reflections from upward-moving front in the return-stroke model: In Chapter 6, a three-wave model for return st rokes, which considers two current waves moving in opposite directions (up and down) from an attachment point some tens of meters above ground and the reflection of the dow nward moving wave from ground, has been introduced. The speeds of all the three wa ves have been assumed to be equal. If the speed of the upward moving ground-reflected current wave is assumed to be higher than that at which the current front moves upward from the attachment point, the reflected wave will "catch up" with the origin al upward-moving current front and get reflected off the impedance discontinuity at the front, with the reflection moving downward. This scenario which is probably more realistic, is not considered in Chapter 6. Multiple reflections of the current wave in the return stroke channel along with current attenuation along the channel (such as that in the MTLL model) need s to be incorporated in the model. Evaluation of NLDN performance characteri stics using 2008 and 2009 rocket-triggered lightning data: Jerauld et al. [2005] examined the performa nce characteristics of the NLDN for the 2001-2003 period using rocket tr iggered lightning data acquired at Camp Blanding, Florida. Nag et al. [2008] extended their study us ing Camp Blanding data from 2004, 2005, and 2007 (there was no lightning tr iggering in 2006). Twelve flashes containing a total of 28 leader/r eturn stroke sequences were used for this purpose (see Appendix C). Rocket-triggered lightning data acquired at the ICLRT in 2008 and 2009 (98 strokes in 24 flashes) can be used for additional evaluation of the NLDN performance characteristics in Florida. Besides return strokes, NLDN detection efficiency, location accuracy, and current estimation errors should be evaluated for pulses occurring during the initial stage of rock et-triggered lightning.

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413APPENDIX A INVENTORY TABLE AND CATALOG OF 48 CO MPAC T INTRAC LOUD DISCHARGE WAVEFORMS Table A-1. Summary of horizontal distance (r), measured electric (Ep) and magnetic (Bp) field peaks, height (h), elevation angle ( ), inclined distance (R), and normalized electric field ( cos0 () 100cosNoR EE ) for 48 CIDs recorded at the LOG in 2008. Also given are the semi major axis (SMA) length of the NLDN 50% e rror ellipse, distance error ( 100%ESMA r r ), electric field peak measurement error (ME), and the total root mean square error ( 22 EEERMSrM ). Flash ID r, km SMA, km Ep, V/m Bp, T Ep/Bp, m/s h, km degrees R, km EN, V/m rE, % ME, % RMSE, % 082308_163 68 0.7 35.99 0.1248 2.89E+08 19 15.9 71 27 1.0 19 19 082308_164 64 2.3 64.08 0.2202 2.91E+08 16 14.1 66 44 3.6 10 11 082308_165 63 0.4 37.87 0.1347 2.81E+08 24 20.4 67 27 0.6 14 14 082308_174 62 0.6 53.02 0.1950 2.72E+08 29 25.0 69 40 1.0 13 13 082308_180 24 0.4 35.24 0.1483 2.38E+08 18 37.6 30 13 1.7 19 19 082308_207 12 0.4 42.89 0.2700 1.59E+08 19 58.0 22 18 3.4 16 16 082308_326 40 0.4 88.32 0.3057 2.89E+08 11 15.6 42 38 1.0 5 5 082408_364 38 0.6 48.83 0.1869 2.61E+08 21 29.4 44 24 1.6 14 14 082408_368 24 4.9 38.36 0.1505 2.55E+08 15 31.8 28 13 21 10 23 082408_370 38 0.5 40.93 0.1531 2.67E+08 19 27.0 43 20 1.3 17 17 082408_374 27 0.4 35.78 0.1499 2.39E+08 20 37.3 33 15 1.5 19 19 082408_378 37 0.4 54.00 0.2174 2.48E+08 25 34.1 44 29 1.1 13 13 082408_382 27 0.4 41.42 0.1496 2.77E+08 11 22.6 29 13 1.5 14 14 082408_386 32 0.4 55.76 0.2242 2.49E+08 22 34.0 39 26 1.2 10 10 082408_387 34 0.4 36.74 0.1623 2.26E+08 29 41.0 45 22 1.2 15 15 082408_394 35 0.6 66.08 0.2473 2.67E+08 18 27.0 39 29 1.7 8 9 082408_422_1 32 0.4 34.97 0.1339 2.61E+08 18 29.4 37 15 1.3 19 19 082408_422_2 17 0.4 40.61 0.1804 2.25E+08 15 41.4 23 13 2.3 16 16

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414Table A-1. Continued Flash ID r, km SMA, km Ep, V/m Bp, T Ep/Bp, m/s h, km degrees R, km EN, V/m rE, % ME, % RMSE, % 082408_427 19 0.4 45.45 0.1909 2.38E+08 15 37.5 24 14 2.1 15 15 082408_428 14 0.4 50.38 0.2363 2.13E+08 14 44.7 19 14 2.9 15 15 082408_429 13 0.4 45.73 0.2484 1.84E+08 17 52.2 21 16 3.1 12 12 082408_669 17 0.4 62.78 0.2502 2.51E+08 11 33.2 20 15 2.4 9 9 083008_09 89 0.6 38.11 0.1300 2.93E+08 19 12.2 91 35 0.7 18 18 083008_12 63 0.4 34.78 0.1248 2.79E+08 25 21.8 68 26 0.6 20 20 083008_16 49 0.6 41.42 0.1592 2.60E+08 28 29.9 57 27 1.2 17 17 083008_24 57 0.4 35.46 0.1201 2.95E+08 10 10.2 58 21 0.7 17 17 083008_31 52 0.6 49.96 0.1737 2.88E+08 16 16.5 55 28 1.1 13 13 083008_33 61 0.5 68.01 0.2324 2.93E+08 14 12.7 63 44 0.8 5 6 083008_45 50 0.4 54.15 0.1897 2.86E+08 16 17.9 53 30 0.8 10 10 083008_52 50 0.4 54.78 0.1926 2.84E+08 17 18.5 52 30 0.8 13 13 083008_61 12 0.4 54.47 0.2524 2.16E+08 11 44.0 16 12 3.4 13 13 083008_67 41 0.4 33.33 0.1157 2.88E+08 12 16.2 43 15 1.0 18 18 091008_120 21 0.4 71.31 0.2843 2.51E+08 13 33.3 25 21 2.0 9 9 091008_121 20 0.4 37.07 0.1525 2.43E+08 14 35.9 24 11 2.1 19 19 091008_123 19 0.4 73.64 0.3009 2.45E+08 13 35.4 23 21 2.1 11 11 091008_127 21 0.4 54.00 0.2139 2.52E+08 13 32.7 24 16 1.9 13 13 091008_128 17 0.5 45.99 0.2055 2.24E+08 15 41.8 23 14 2.9 12 12 091008_129 19 0.4 61.75 0.2385 2.59E+08 11 30.4 22 16 2.1 9 9 091008_132 19 0.4 50.90 0.1964 2.59E+08 11 30.3 22 13 2.1 14 14 091008_133 20 0.4 64.08 0.2391 2.68E+08 10 26.7 22 16 2.0 11 11 091008_135 18 0.4 34.27 0.1496 2.29E+08 15 40.2 24 11 2.2 20 20 091008_138 33 0.4 35.03 0.1293 2.71E+08 16 25.4 36 14 1.2 16 16 091008_140 36 0.4 53.99 0.1920 2.81E+08 13 20.4 38 22 1.1 13 13 091108_152 21 0.4 38.68 0.1512 2.56E+08 13 31.5 25 11 1.9 18 18 091108_161 30 0.4 70.79 0.2502 2.83E+08 10 19.4 31 24 1.3 8 8 091108_165 46 2.2 51.42 0.1911 2.69E+08 22 26.3 51 29 4.8 13 14

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415Table A-1. Continued Flash ID r, km SMA, km Ep, V/m Bp, T Ep/Bp, m/s h, km degrees R, km EN, V/m rE, % ME, % RMSE, % 091108_175 37 0.4 67.37 0.2310 2.92E+08 8.9 13.6 38 26 1.1 10 10 091108_176 43 0.4 35.58 0.1211 2.94E+08 8.8 11.7 44 16 0.9 16 16

PAGE 416

416 Figure A-1. CID 082308_163 shown on a 25 s time scale.

PAGE 417

417 Figure A-2. CID 082308_164 shown on a 25 s time scale.

PAGE 418

418 Figure A-3. CID 082308_165 shown on a 35 s time scale.

PAGE 419

419 Figure A-4. CID 082308_174 shown on a 20 s time scale. dE/dt is not available.

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420 Figure A-5. CID 082308_180 shown on a 50 s time scale. dE/dt is not available.

PAGE 421

421 Figure A-6. CID 082308_207 shown on a 35 s time scale. dE/dt is not available.

PAGE 422

422 Figure A-7. CID 082308_326 shown on a 25 s time scale. dE/dt is not available.

PAGE 423

423 Figure A-8. CID 082408_364 shown on a 30 s time scale.

PAGE 424

424 Figure A-9. CID 082408_368 shown on a 25 s time scale.

PAGE 425

425 Figure A-10. CID 082408_370 shown on a 25 s time scale.

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426 Figure A-11. CID 082408_374 shown on a 35 s time scale.

PAGE 427

427 Figure A-12. CID 082408_378 shown on a 35 s time scale.

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428 Figure A-13. CID 082408_382 shown on a 35 s time scale.

PAGE 429

429 Figure A-14. CID 082408_386 shown on a 45 s time scale.

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430 Figure A-15. CID 082408_387 shown on a 40 s time scale.

PAGE 431

431 Figure A-16. CID 082408_394 shown on a 25 s time scale.

PAGE 432

432 Figure A-17. CID 082408_422_1 shown on a 40 s time scale.

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433 Figure A-18. CID 082408_422_2 shown on a 50 s time scale. dE/dt is not available.

PAGE 434

434 Figure A-19. CID 082408_427 shown on a 35 s time scale.

PAGE 435

435 Figure A-20. CID 082408_428 shown on a 25 s time scale.

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436 Figure A-21. CID 082408_429 shown on a 30 s tim e scale. dE/dt is not available.

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437 Figure A-22. CID 082408_669 shown on a 40 s time scale.

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438 Figure A-23. CID 083008_009 shown on a 25 s tim e scale. VHF is not available.

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439 Figure A-24. CID 083008_012 shown on a 50 s tim e scale. VHF is not available.

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440 Figure A-25. CID 083008_016 shown on a 30 s tim e scale. VHF is not available.

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441 Figure A-26. CID 083008_024 shown on a 40 s tim e scale. VHF is not available.

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442 Figure A-27. CID 083008_031 shown on a 35 s tim e scale. VHF is not available.

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443 Figure A-28. CID 083008_033 shown on a 30 s tim e scale. VHF is not available.

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444 Figure A-29. CID 083008_045 shown on a 30 s tim e scale. VHF is not available.

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445 Figure A-30. CID 083008_052 shown on a 30 s tim e scale. VHF is not available.

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446 Figure A-31. CID 083008_061 shown on a 35 s tim e scale. VHF is not available.

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447 Figure A-32. CID 083008_067 shown on a 25 s tim e scale. VHF is not available.

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448 Figure A-33. CID 091008_120 shown on a 35 s tim e scale. VHF is not available.

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449 Figure A-34. CID 091008_121 shown on a 30 s tim e scale. VHF is not available.

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450 Figure A-35. CID 091008_123 shown on a 45 s tim e scale. VHF is not available.

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451 Figure A-36. CID 091008_127 shown on a 35 s tim e scale. VHF is not available.

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452 Figure A-37. CID 091008_128 shown on a 30 s tim e scale. VHF is not available.

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453 Figure A-38. CID 091008_129 shown on a 30 s tim e scale. VHF is not available.

PAGE 454

454 Figure A-39. CID 091008_132 shown on a 35 s tim e scale. VHF is not available.

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455 Figure A-40. CID 091008_133 shown on a 25 s tim e scale. VHF is not available.

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456 Figure A-41. CID 091008_135 shown on a 30 s tim e scale. VHF is not available.

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457 Figure A-42. CID 091008_138 shown on a 35 s tim e scale. VHF is not available.

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458 Figure A-43. CID 091008_140 shown on a 25 s tim e scale. VHF is not available.

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459 Figure A-44. CID 091108_152 shown on a 35 s tim e scale. VHF is not available.

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460 Figure A-45. CID 091108_161 shown on a 35 s tim e scale. VHF is not available.

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461 Figure A-46. CID 091108_165 shown on a 30 s tim e scale. VHF is not available.

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462 Figure A-47. CID 091108_175 shown on a 25 s tim e scale. VHF is not available.

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463 Figure A-48. CID 091108_176 shown on a 40 s tim e scale. VHF is not available.

PAGE 464

464 APPENDIX B ELECTRIC FIELD DERIVATIV E WAVEFORMS OF 27 POSI TIVE RETURN STROKES Figure B-1. Electric field derivative waveform of a positive return stroke that occurred on December 16, 2007, at 06:50:27 (UTC) at a di stance of 38 km, shown on a 30-s time scale. Figure B-2. Electric field derivative waveform of a positive return stroke that occurred on December 16, 2007, at 06:55:35 (UTC) at a distance of 7.8 km, shown on a 30-s time scale. Note that the initial (negative) peak may be slightly clipped (saturated), due to proximity of the flas h to the measuring station. r = 38 km r = 7.8 km

PAGE 465

465 Figure B-3. Electric field derivative waveform of a positive return stroke that occurred on December 16, 2007, at 07:02:55 (UTC) at a distance of 8.5 km, shown on a 25-s time scale. Figure B-4a. Electric field derivativ e waveform of the first return stroke (of a two-stroke positive flash) that occurred on January 22, 2008, at 23:55:10 (UTC) at a distance of 85 km, shown on a 30-s time scale. r = 8.5 km r = 85 km

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466 Figure B-4b. Electric field deriva tive waveform of the second retu rn stroke (of a two-stroke positive flash) that occurred on January 22, 2008, at 23:55:10 (UTC) at a distance of 80 km, shown on a 30-s time scale. Figure B-5. Electric field derivative waveform of a positive return stroke that occurred on January 23, 2008, at 02:35:47 (UTC) at a dist ance of 8.4 km, shown on a 20-s time scale. r = 80 km r = 8.4 km

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467 Figure B-6. Electric field derivative waveform of a positive return stroke that occurred on January 23, 2008, at 02:56:28 (UTC) at a dist ance of 64 km, shown on a 35-s time scale. Figure B-7. Electric field derivative waveform of a positive return stroke that occurred on April 26, 2008, at 22.16.22 (UTC) at a distance of 98 km, shown on a 40-s time scale. r = 64 km r = 98 km

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468 Figure B-8. Electric field derivative waveform of a positive return stroke that occurred on April 26, 2008, at 22.26.10 (UTC) at a distance of 94 km, shown on a 35-s time scale. Figure B-9. Electric field derivative waveform of a positive return stroke that occurred on May 18, 2008, at 17:27:12 (UTC) at a distance of 84 km, shown on a 40-s time scale. r = 94 km r = 84 km

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469 Figure B-10. Electric field derivative waveform of a positive return stroke that occurred on May 18, 2008, at 19:07:38 (UTC) at a distance of 72 km, shown on a 30-s time scale. Figure B-11. Electric field derivative waveform of a positive return stroke that occurred on May 18, 2008, at 21:25:29 (UTC) at a distance of 49 km, shown on a 40-s time scale. r = 72 km r = 49 km

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470 Figure B-12. Electric field derivative waveform of a positive return stroke that occurred on June 1, 2008, at 19:35:47 (UTC) at a distance of 72 km, shown on a 30-s time scale. Figure B-13. Electric field derivative waveform of a positive return stroke that occurred on June 1, 2008, at 21:23:41 (UTC) at a distance of 31 km, shown on a 30-s time scale. r = 72 km r = 31 km

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471 Figure B-14a. Electric field deriva tive waveform of the first re turn stroke (of a two-stroke positive flash), that occurred on June 2, 2008, at 23:06:25 (UTC) at a distance of 157 km, shown on a 50-s time scale. Figure B-14b. Electric field derivati ve waveform of the second return stroke (of a two-stroke positive flash), that occurred on June 2, 2008, at 23:06:25 (UTC) at a distance of 157 km, shown on a 20-s time scale. r = 157 km r = 157 km

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472 Figure B-15. Electric field derivative waveform of a positive return stroke that occurred on June 9, 2008, at 20:27:05 (UTC) at a distance of 101 km, shown on a 30-s time scale. Figure B-16. Electric field derivative waveform of a positive return stroke that occurred on August 13, 2008, at 21:23:59 (UTC) at a dist ance of 20 km, shown on a 40-s time scale. r = 101 km r = 20 km

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473 Figure B-17. Electric field derivative waveform of a positive return stroke that occurred on August 13, 2008, at 22:08:10 (UTC) at a dist ance of 23 km, shown on a 30-s time scale. Figure B-18. Electric field derivative waveform of a positive return stroke that occurred on August 13, 2008, at 22:11:17 (UTC) at a dist ance of 28 km, shown on a 40-s time scale. r = 23 km r = 28 km

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474 Figure B-19. Electric field derivative waveform of a positive return stroke that occurred on August 14, 2008, at 12:52:06 (UTC) at a dist ance of 42 km, shown on a 60-s time scale. Figure B-20. Electric field derivative waveform of a positive return stroke that occurred on August 14, 2008, at 13:27:12 (UTC) at a dist ance of 25 km, shown on a 40-s time scale. r = 42 km r = 25 km

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475 Figure B-21. Electric field derivative waveform of a positive return stroke that occurred on August 23, 2008, at 20:47:43 (UTC) at a dist ance of 42 km, shown on a 50-s time scale. Figure B-22. Electric field derivative waveform of a positive return stroke that occurred on August 23, 2008, at 21:01:46 (UTC) at a dist ance of 42 km, shown on a 40-s time scale. r = 42 km r = 42 km

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476 Figure B-23. Electric field derivative waveform of a positive return stroke that occurred on August 24, 2008, at 21:53:34 (UTC) at a dist ance of 35 km, shown on a 40-s time scale. Figure B-24a. Electric field deriva tive waveform of the first re turn stroke (of a two-stroke positive flash), that occurred on November 30, 2008, at 16:03:52 (UTC) at a distance of 41 km, shown on a 30-s time scale. r = 35 km r = 41 km

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477 Figure B-24b. Electric field derivati ve waveform of the second return stroke (of a two-stroke positive flash), that occurred on November 30, 2008, at 16:03:52 (UTC) at a distance of 44 km, shown on a 40-s time scale. r = 44 km

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478 APPENDIX C NLDN RESPONSES TO ROCKET-TRIGGERED LIGHTNING AT C AMP BLANDING, FLORIDA, IN 2004, 2005, AND 2007 C.1 Introduction The U.S. National Lightning Detection Network (NLDN) data are used in Chapters 4, 6, and 7 of this dissertation. Th e NLDN has been providing real-time, continental-scale lightning data since 1989. The NLDN data consists of, among other things, information about lightning type (cloud or ground), time of occurrence with nanosecond resolution, peak currents, number of detecting sensors, and location information includ ing associated uncertainties. The most recent network-wide NLDN upgrade that was completed in 2004 is described by Cummins and Murphy [2009]. Prior to the upgrade, the NLDN consisted of 106 sensors, including 63 LPATS III sensors, which provided only time of arrival information, and 43 IMPACT sensors, which provided both time of arrival and azimuth information. During the upgrade, all sensors in the NLDN were replaced with IMPACT-ESP sensor s having improved analog front-end circuitry, higher speed processor, and configurable wavefo rm criteria. The post-upgrade status of the network has been reported by Cummins et al. [2006]. Jerauld et al. [2005] examined the performance characteristics of the NLDN fo r the 2001-2003 period using rocket triggered lightning data acquired at Camp Blanding, Flor ida. Note that 2003 was essentially a postupgrade year for the Florida region. The NLDN pr opagation model, which is part of the NLDN field to current conversion procedure, was m odified on July 1, 2004 to provide a better match with Camp Blanding ground-truth data used in the evaluation performed by Jerauld et al. [2005]. In this Chapter, we use new rocket triggered lightning data obtained at Camp Blanding during the years 2004, 2005, and 2007 (there was no light ning triggering in 2006) to estimate the performance characteristics of the NLDN.

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479C.2 Data and Methodology During the summers of 2004, 2005, and 2007, a tota l of 18 negative flashes were triggered at the ICLRT. Of these 18, 12 flashes contained a total of 28 leader/return stroke sequences and 6 flashes consisted of initial stage only. The latter 6 are not considered in this study. A summary of Table C-1. Summary of flashes and strokes reco rded at Camp Blanding during summers of 2004, 2005, and 2007, along with the corresponding NLDN detection efficiencies. Year (Period) Number of Flashes Triggered Number of NLDN Detected Flashes NLDN Flash Detection Efficiency Number of Strokes Number of NLDN Detected Strokes NLDN Stroke Detection Efficiency 2004 (PreJuly 1, 2004) 2 2 100% 11 7 64% 2004, 2005 and 2007 (Post-July 1, 2004) 10 8 80% 17 11 65% 2004, 2005, and 2007 12 10 84% 28 18 64% the flashes and strokes recorded at Camp Blanding during the thr ee years is given in Table C-1. During the 2004 and 2007 seasons, an 11-meter tower launcher was used, while in 2005 an 8meter tall mobile launcher was used in addition to the tower launcher. Po sition of each launcher is known within a few meters. Lightning current wa s directly measured at the base of either launcher with a non-inductive current measuring re sistor (shunt). Different shunts were used in different years, but in all cases the bandwidth of the shunt exceeded 8 MHz. Lightning currents were transmitted to Yokogawa and LeCroy digi tizing oscilloscopes via fiber optic links. The Yokogawa oscilloscopes sampled at 2 MHz (-3 dB low pass filtered at 500 kHz) and the LeCroy oscilloscopes sampled at 20 MHz (-3 dB filte red at 5 MHz). Of the 12 triggered flashes considered here, 2 flashes (containing 11 stroke s) were triggered before July 1, 2004 (when the NLDN propagation model was modi fied) and 10 flashes (containi ng 17 strokes) were triggered

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480 after that date. Although the propagation model m odification does not aff ect flash or stroke detection efficiency, nor location errors, all the results are presented here for each of the two periods separately and for all data combined. The peak curren t distribution for all strokes recorded during 2004, 2005 and 2007 is given in Figure C-1. This dist ribution includes both strokes detected by the NLDN and those that we re not. The arithmetic mean (AM) and median peak currents are 14.1 kA and 11.3 kA, respectively and the minimum and maximum peak currents are 3.3 kA and 44.9 kA, respectively. Note that the distribution resembles a lognormal one, for which the median is thought to be better characteristic than the AM. Camp Blanding and NLDN events were correl ated using GPS (Global Positioning System) time stamps. The following NLDN performance ch aracteristics were determined: (1) flash detection efficiency, (2) stroke detection efficiency, (3) location errors, and (4) errors in peak current estimates. C.3 Results and Discussion C.3.1 Flash and Stroke De tection Efficiencies Table C-1 summarizes the NL DN flash and stroke detection efficiencies for 2004, 2005, and 2007. For all flashes triggered during this period, the flash detection efficiency was 84 % (10 out of 12), which is the same as reported by Jerauld et al. [2005] for 2001-2003. Note that, all strokes in classical triggered fl ashes are similar to subsequent strokes in natural lightning and hence the flash detection efficiency reported here is likely to be an underestimate of the true value for natural negative lightning flashes, since first strokes typically have larger peak currents than subsequent ones. The stroke detection e fficiency was 64% (18 out of 28) versus 60% reported by Jerauld et al. [2005]. The average stroke multiplicity for 2004, 2005, and 2007 (defined as the total number of strokes divided by the number of flashes triggered) at Camp Blanding was 2.3, versus 4.3 for 2001-2003. Figure C-2 gives the NLDN stroke detection

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481 Camp Blanding Peak Current [kA] 051015202530354045 Number 0 2 4 6 8 10 Pre-July 1, 2004, N = 11 Post-July 1, 2004, N = 17 Pre-July 1, 2004 Post-July 1, 2004 2004, 2005, and 2007 AM, kA 9.1 17.4 14.1 SD, kA 3.9 10.7 9.6 GM, kA 8.2 14.8 11.7 Median, kA 8.4 15.3 11.3 SD(log10I) 0.20 0.25 0.26 Min, kA 3.3 5.8 3.3 Max, kA 17.3 44.9 44.9 N 11 17 28 Figure C-1. Histogram of Camp Blanding triggered lightning return-s troke peak currents, I, for 2004, 2005, and 2007. Statistics given are the arithmetic mean (AM), standard deviation (SD), geometric mean (GM), median, standard deviation of the log10 of the parameter (SD(log10I)), minimum value (min), and maximum value (max) of peak currents for periods before and after July 1, 2004 and for all data combined.

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482 Figure C-2. NLDN stroke detection efficiency as a function of peak current measured at Camp Blanding. For each peak current range (bin size of 5 kA), the ratio given inside the column indicates the number of strokes detected by the NLDN (numerator) and the number of strokes recorded at Camp Bla nding (denominator), for that peak current range. The total number of strokes whose currents were measured at Camp Blanding is 28, of which 18 were detected by the NLDN. Pre-July 1, 2004 Cam p Blandin g Peak Current [ kA ] 051015202530354045 Stroke Detection Efficiency [%] 0 20 40 60 80 100 120 0/23/5 3/3 1/1 Post-July 1, 2004 Camp Blanding Peak Current [kA] 051015202530354045 Stroke Detection Efficiency [%] 0 20 40 60 80 100 120 0/0 1/42/4 4/5 1/1 1/1 0/0 0/02/2 2004, 2005, 2007 Camp Blanding Peak Current [kA] 051015202530354045 Stroke Detection Efficiency [%] 0 20 40 60 80 100 120 0/2 4/95/7 5/6 1/1 1/1 2/2 0/0 0/0

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483 efficiency as a function of peak current measured at Camp Blanding. For all data combined the stroke detection efficiency is 100% for stro kes above 20 kA, although the sample size (four strokes) is rather small. As the peak current de creases from 20 kA to 5 kA, the stroke detection efficiency decreases from 100 to 69%. Neither of the two strokes having peak currents less than 5 kA was detected by the NLDN. Similarl y, for the 2001-2003 data set examined by Jerauld et al. [2005], all six strokes having peak currents less than 5 kA were missed by the NLDN. C.3.2 Location Accuracy Figure C-3 shows a spatial distribution of NLDN stroke locations for 18 strokes in 10 flashes triggered at Camp Blanding duri ng 2004, 2005, and 2007. The origin (marked X) corresponds to the actual strike location that was known within a few meters, so that the horizontal and vertical axes correspond to the east-west (east being positive) and north-south (north being positive) location error components, respectively. The AM and median north-south location errors are 12.7 m and -8.5 m, respectively, while the AM and median east-west location errors are -7.1 m and -27.8 m, respectively. Figu re C-4 shows the histog ram of NLDN absolute stroke location errors for the 18 strokes shown in Figure C-3. The median absolute location error was 162 m with the largest error being 472 m. This is better than a median absolute location error of 600 m and a maximum of 11 km reported by Jerauld et al. [2005] for 95 Camp Blanding strokes located by the NLDN in 2001-2003. Figure C-5 shows the NLDN absolute location error plotted versus the peak current measured at Camp Blanding. Largest lo cation errors (> 300 m) correspond to strokes with peak currents less than 20 kA, although many st rokes in this peak current range were located with considerab ly smaller errors. Fi gure C-6 shows the NLDN absolute location error plotted versus the numbe r of NLDN sensors which were involved in the location solution. The number of reporting sensors ranges from 3 to 12. In general, location

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484 Figure C-3. Plot of NLDN stroke locations for 18 strokes in 10 flashes triggered during 2004, 2005, and 2007 at Camp Blanding. The origin (marked X) corresponds to the actual stroke location (lightning triggering locati on). The horizontal axis corresponds to the east-west component of the location error, with positive values corresponding to east. The vertical axis corresponds to the north-s outh component of the location error, with positive values corresponding to north. Statistics given are arithmetic mean (AM), median, and standard deviation (SD) for each location error component. PreJuly 1, 2004 PostJuly 1, 2004 2004, 2005, and 2007 N-S AM, m 32.9 -0.138 12.7 N-S SD, m 104 175 152 N-S Median, m -8.1 -75.0 -8.5 E-W AM, m -113.1 60.4 -7.1 E-W SD, m 194 152 190 E-W Median, m -45.1 50.9 27.8 N 7 11 18 East-West Distance [meters] -500-400-300-200-1000100200300400500 North-South Distance [meters] -500 -400 -300 -200 -100 0 100 200 300 400 500 Pre-July 1, 2004, N = 7 Post-July 1, 2004, N = 11 N S E W X

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485 Figure C-4. Histogram of the NLDN absolute loca tion errors. Corresponding statistics are also given. Pre-July 1, 2004 PostJuly 1, 2004 2004, 2005, and 2007 AM, m 194.2 206.6 201.8 SD, m 156.8 121.3 136.4 GM, m 135.1 162.3 151.2 Median, m 139.2 173.1 161.6 Min, m 33.7 23.4 23.4 Max, m 471.6 416.0 471.6 N 7 11 18 Absolute Location Error [meters] 050100150200250300350400450500 Number 0 1 2 3 4 Pre-July 1, 2004, N = 7 Post-July 1, 2004, N = 11

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486 errors seem to decrease as the number of repor ting sensors increases, although the dependence is characterized by a large scatter. The NLDN 50% error ellipse, calculated for each stroke location, is defined as a confidence region for which there is a 50% probabili ty that the actual stroke location lies within the area circumscribed by the ellipse, with the center of the ellipse being the most-probable (reported) stroke location. Hence the semi-major axis of the 50% ellipse is usually viewed as the median (50%) location error. Corresponding erro r ellipses for any probability level (e.g., 90%) can be derived by multiplying the semi-major and semi-minor axes of the 50% ellipse by an appropriate scaling factor. The two-dimensional Gaussian distribu tion of errors in latitude and longitude is based on the assumption that the random errors in sensor time and angle measurements are uncorrelated and their distributions are approximately Gaussian [Cummins et al., 1998]. Strokes located within a group of several sensors typi cally have relatively small, nearly circular error ellipses, whereas strokes detected by only two or three sensors typically have very large, elongated ellips es. A stroke detected by only two sensors, when that stroke is located near the line joining th e two sensors (base line), typically has an elongated ellipse whose major axis is along the base line. Figure C-7 shows the NLDN 50% semi-major axis lengths plotted versus peak current, measured at Camp Blanding. A semi-major axis length of 0.4 km was reported for majority of the strokes (13 out of 18). The largest semi-major axis length was 1.1 km for a stroke having peak current 13.3 kA Figure C-8 shows the NLDN absolute location error plotted versus NLDN 50% semi-major axis length. Strokes having absolute location errors less than 150 m are typically asso ciated with a semi-major axis length of 0.4 km. The largest absolute location error is associ ated with a semi-major axis length of 0.6 km. The slanted solid line (slope = 1) in Figure C-8 is the locus of points for whic h the NLDN 50% semi-major axis

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487 length and corresponding location er ror are equal, that is, repres ents the boundary of the 50% error ellipse. If the error ellipses are assumed to be nearly ci rcular, then data points below this line correspond to strokes with gr ound-truth locations enclosed by the 50% error ellipse and data points above it to ground-truth locations outside the 50% error ellipse. Data points below the dashed line (slope = 1.82) in Figure C-8 corre spond to strokes with ground-truth locations enclosed by the 90% error ellipse (assumed to be n early circular). It is cl ear from Figure C-8 that all strokes had groundtruth locations enclosed by the 50% error ellipse, which means that location errors in 2004, 2005, and 2007 were consid erably lower than pr edicted by the 50% and 90% NLDN error ellipses. C.3.3 Peak Current Estimates The NLDN-estimated peak current plotted versus peak current measured directly at Camp Blanding are shown in Figure C-9. The slanted solid line (slope = 1) is the locus of the points for which the NLDN peak currents and the Camp Bl anding peak currents are equal. For both periods, that is before and after the propagati on model was modified on July 1, 2004, there is a strong positive linear relationship between the m easured and NLDN-estimated peak currents. As seen in Figure C-9, the linear relationship seems to be stronger for the data acquired prior to July 1, 2004 although the sample size and range of current va riation are rather small. In fact, the mean values of the ratio ICB/INLDN are about 1.0 and 1.2 for the data acquired prior to and after July 1, 2004, respectively. For all data combined, the mean ra tio is about 1.1. This is to be compared to the mean ICB/INLDN ratio of 1.2 found for 2001-2003 by Jerauld et al. [2005]. The AM and median Camp Blanding peak curr ents for all 18 strokes are 17.4 and 14.3 kA, respectively, versus 16.3 and 12.7, respectively, fo r NLDN-estimated peak currents. Figures C10a and b, respectively, show the histograms for th e signed and absolute values of NLDN peak

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488 Cam p Blandin g Peak Current [ kA ] 01020304050 NLDN Absolute Location Error [meters] 0 100 200 300 400 500 Pre-July 1, 2004, N = 7 Post-July 1, 2004, N = 11 Figure C-5. NLDN absolute location error versus Camp Blanding peak current. Number of NLDN Reporting Sensors 12345678910111213 NLDN Absolute Location Error [meters] 0 50 100 150 200 250 300 350 400 450 500 Pre-July 1, 2004, N = 7 Post-July 1, 2004, N = 11 Figure C-6. NLDN absolute location error versus the number of reporting NLDN sensors.

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489 Camp Blanding Peak Current [kA] 05101520253035404550 NLDN Semi-Major Axis Length [km] 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Pre-July 1, 2004, N = 7 Post-July 1, 2004, N = 11 Figure C-7. NLDN 50% error ellipse semi-major axis length versus Camp Blanding peak current. current estimation errors as a percent of Camp Blanding peak current ( I% = 100 I/ICB, where I = INLDN ICB). The AM values of I% for pre-July 1, 2004, post-July 1, 2004, and both periods combined are 2.8%, -10%, and -5.1%, respectively. The corresp onding median values are 4.8%, -19%, and -1.2%. The AM and median NLDN-estimated peak current errors for all data combined are considerably lower (in absolu te value) than the corresponding values of -15% and -18% reported by Jerauld et al. [2005]. For absolute value of I% (see Figure C-10b), the AM values are 12%, 24%, and 19%, for pre-July 1, 2004, post-July 1, 2004, and both peri ods combined, respectively. The corresponding median values are 11%, 29%, and 20%. Jerauld at al. [2005] reported a median absolute error of 20% for all 2001-2003 strokes combined. The percen tage errors never exceeded in absolute value 41% for 2004, 2005 and 2007 versus 50% for 2001-2003.

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490 NLDN Semi-Major Axis Length [km] 0.00.20.40.60.81.01.2 NLDN Absolute Location Error [km] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 Pre-July 1, 2004, N = 7 Post-July 1, 2004, N = 11 Figure C-8. NLDN absolute location error plotte d versus NLDN 50% error ellipse semi-major axis length. The slanted solid line (slope = 1) is the locus of points for which the NLDN 50% semi-major axis length and corresp onding location error are equal. If the error ellipses are assumed to be nearly circ ular, then points below this line correspond to strokes with ground-truth locations enclosed by the 50% error ellipse and strokes above are outside the 50% error ellipse. Po ints below the dashed line (slope = 1.82) correspond to strokes with ground-truth loca tions enclosed by the 90% (assumed to be nearly circular) error ellipse.

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491 2004, 2005, 2007 N = 18 Camp Blanding Peak Current [kA] 05101520253035404550 NLDN Peak Current [kA] 0 5 10 15 20 25 30 35 40 45 50 Pre-July 1, 2004, N = 7 Post-July 1, 2004, N = 11 Figure C-9. NLDN-reported peak current versus peak current directly measured at Camp Blanding. The number of NLDN reporting sensors plotted against Camp Blanding peak current for 23 strokes (18 analyzed above pl us 5 reported by only one sensor and hence not located) is shown in Figure C-11. The 5 additional Camp Blanding strokes were detected by the NLDN sensor at Ocala, Florida, located 89 km from Camp Blanding. All thes e 5 strokes have peaks currents less than 12 kA. Interestingly, 6 other Camp Blanding strokes which had peak currents less than 12 kA were detected by 3 to 7 NLDN sensors. C.4 Summary We evaluated performance characteristics of the U.S. National Lightning Detection Network (NLDN) using rocket-triggered light ning data acquired in 2004, 2005, and 2007 (there was no lightning triggering at Camp Blanding in 2006) at Camp Blandi ng, Florida as the groundtruth. Twelve flashes, containing a total of 28 ne gative strokes, were triggered at Camp Blanding during these three years. The NLDN recorded 18 Camp Blanding strokes in 10 flashes. The

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492 resulting flash and stroke detection efficien cies are 84% and 64%, respectively. This is comparable to the results of Jerauld et al. [2005], who used triggered lightning data acquired in 2001-2003, also at Camp Blanding, Flor ida, and reported the same fl ash detection efficiency and a stroke detection efficiency of 60%. Note that, all strokes in classical triggered flashes are similar to subsequent strokes in natural lightning and hence the flash detection efficiency reported here is likely to be an underestimate of the true value for natural negative lightning flashes, since first strokes typically have larger peak currents than subsequent ones. The median absolute location error is 162 m and the largest error is 472 m wh ich is better than a median absolute location error of 600 m a nd a maximum of 11 km reported by Jerauld et al. [2005] for 95 Camp Blanding strokes (2001-2003) located by the NLDN. The arithmetic mean and median NLDN-estimated peak current errors for th e 18 negative strokes from 2004, 2005, and 2007 are about -5.1% and -1.2%, respectivel y, both being appreciably lower (in absolute value) than the corresponding values of -15% and -18% estimated by Jerauld et al. [2005]. The absolute value of median current estimation error in this st udy is 20%, which is the same as that in 2001-2003. The current estimation errors never exceeded in absolute value 50% in 2001-2003 and 41% in 2004, 2005, and 2007.

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493 Figure C-10. Histograms of (a) signed and (b) ab solute NLDN peak current estimation errors, given as a percentage of the direct ly measured Camp Blanding current ( I% = 100 I/ICB, where I = INLDN ICB). Corresponding statistics are given below each histogram. PreJuly 1, 2004 PostJuly 1, 2004 2004, 2005, and 2007 AM 2.8% -10.1% -5.1% SD 14.6% 24.8% 22.4% Median 4.8% -19.2% -1.2% Min -28.1% -40.5% -40.5% Max 20.6% 35.4% 35.4% N 7 11 18 PreJuly 1, 2004 PostJuly 1, 2004 2004, 2005, and 2007 AM 11.6% 24.2% 19.3% SD 9.4% 11.6 12.4% Median 11.4% 29.1% 19.9% Min 1.2% 4.4% 1.2% Max 28.1% 40.5% 40.5% N 7 11 18 I, [% of Camp Blanding Peak Current] -50-40-30-20-10010203040 Number 0 1 2 3 4 Pre-July 1, 2004, N = 7 Post-July 1, 2004, N = 11 (a) I, Absolute Value [% of Ca mp Blanding Peak Current] 01020304050 Number 0 1 2 3 4 5 6 Pre-July 1, 2004, N = 7 Post-July 1, 2004, N = 11 (b)

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494 Camp Blanding Peak Current [kA] 05101520253035404550 Number of Reporting NLDN Sensors 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Pre-July 1, 2004, N = 7 Pre-July 1, 2004, (Single Sensor Reports), N = 3 Post-July 1, 2004, N = 11 Post-July 1, 2004, (Single Sensor Reports), N = 2 Figure C-11. Number of reporti ng NLDN sensors versus Camp Blanding peak current for 18 strokes detected by multiple sensors and 5 strokes detected by a single (Ocala) sensor.

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508 BIOGRAPHICAL SKETCH Am itabh Nag received the Bachelor of T echnology in electronics and communication engineering from West Bengal University of Technology, Kolkata in June 2005. In August 2005, he was admitted to the Department of Electrical and Computer Engineering at the University of Florida as a Ph.D. student. He received the Master of Science and Ph.D. degrees in electrical engineering in May 2007 and May 2010, respec tively, from the University of Florida, Gainesville. From 2005 to 2010, he was a Research Assistant at the International Center for Lightning Research and Testing, University of Flor ida, where he was in charge of the Lightning Observatory in Gainesville. He has authored or coauthored more than 25 papers and technical reports on various aspects of lightning, with 7 fi rst-authored papers bei ng published in reviewed journals. His current research in terests include measurement, analysis, and modeling of electric and magnetic fields from cloud and ground light ning discharges, lightning detection and protection. He is a reviewer for various jour nals including the IEEE Transactions on EMC, Geophysical Research Letters, and Atmospheric Research and is a member of the Institute of Electrical and Electronic E ngineers, American Geophysic al Union, and American Meteorological Society.