Aug 20, 1976 - Department of Electrical Engineering, University of Florida, Gainesville, Florida ..... km and Q = 1 C. These curves provide a reasonable fit to the.
VOL. 81, NO. 24
JOURNAL OF GEOPHYSICAL RESEARCH
AUGUST 20, 1976
ElectricField Statisticsfor CloseLightning Return Strokes Near Gainesville, Florida J. A. TILLER, M. A. UMAN, Y. T. LIN, AND R. D. BRANTLEY Departmentof ElectricalEngineering,Universityof Florida, Gainesville,Florida 32611 E. P. KRIDER
Institute of AtmosphericPhysics,Universityof Arizona, Tucson,Arizona 85721
The salientpropertiesof the electricfield intensityfrom first and subsequent lightningreturn strokesin the 0- to 25-km distancerangenearGainesville,Florida, are presented,includingelectricfieldwaveshape versusdistance,initial peak risetime versusdistance,risetime histograms,initial peak magnitudeversus distance,normalized(to 100 km) initial peak magnitudehistograms,normalizedinitial peak magnitude versus rise time, ramp starting time versus distance, and field at 170 #s versus distance. The mean normalizedinitial peak field for first return strokeswas9.9 V/m and for subsequentstrokes,5.7 V/m. The maximum measuredvaluesof normalizedinitial peak field were about 30 V/m. The largestfield recorded at 170 •ts was about 25 kV/m generatedby a first stroke within 0.5 km. Return strokeswere found to lower a typical chargeof the order of 1 C in 170 •ts.
INTRODUCTION
interval betweenthe occurrenceof the lightningand the arrival of the first loud thunderclap (assumedto be associatedwith exhibited by lightning return strokes have recently been given the main channelnear the ground as opposedto branchesor by Fisherand Urnan [1972] and by Lin and Urnan[1973]. Data in-cloud channels). For this measurementa strip chart reon the magnitudeof the initial radiation field peakshave been corder was used to record both a pulse associatedwith the given by Lin and Uman [1973]. Most of these data are for return strokeelectricfield and the output of a thundermicrolightning in the 100-km range, although some data are pre- phone. Additionally, an observerwith a stopwatchsimultanesented for close strokes. In the present paper we extend the ously measuredthe time interval betweenthe observedlightwork of Fisherand Urnan[1972] and Lin and Urnan[1973] for ning and the associatedthunder. The typical distance-ranging error is estimatedto be +0.3 km, and the maximum possible return strokes within 25 km to include data on radiation field Statistical data on the initial electric radiation field rise time
rise time and peak value versusdistance,histogramsof peak field values normalized to 100 kin, histogramsof rise time values,data on normalizedpeak field versusrise time, data on electricfield magnitudeat 170 us (primarily electrostaticfield) versus distance, and information about electric field wave
shapeversusdistance. THE EXPERIMENT
The electric field measuring and calibration systemswere very similarto thosedescribedby Fisherand Urnan[1972].The return strokeelectricfield was detectedby a circularflat-plate antenna.The amplifiedreturn strokesignalwasusedto trigger a Tektronix 555 oscilloscope with a sweepspeedof 10 or 20 #s per division.The electricfield signalwas simultaneouslyfed to the input of a 2.5-#sdelay line, the delayedoutputgoingto the vertical input of the oscilloscope.The oscilloscope displaywas photographedwith a streak camera with a film speedof 0.05 m/s perpendicularto the sweep direction. The total system responseto a stepfunction input wasa 10-90% risetime of 0.2 #s with no overshootand an exponentialdecay with a time constant of I ms. The systembandwidth extended from less than I kHz
to about 2 MHz.
error
+0.7
kin.
The maximum uncertaintyin the derivedelectricfield values due to systemcalibration errors and errors in data analysisis estimatedto be + 15%. Measurementsof initial peak risetime made at 20 #s per division are accurateto typically +0.5 #s andat 10#s per divisionto +0.3 #s. All risetime measurements were 'zero' to peak and were made in the same manner as thoseof Fisherand Uman [1972] and Lin and Uman [1973]. The zero time of the return stroke field was chosen at the 'break-
point' shownin Figure I if the field slopeprior to that point was not appreciable.Otherwise,the zero time was chosenat a point of relativelysmall field slope.Most of the uncertaintyin the measurement of the rise time was in the determination
of
the zero time, sincethe beginningof the return stroke wave form was often not well defined and sinceonly 2.5 #s of the signalwas recordedprior to the occurrenceof the triggerlevel field. Krider and Radda [1975] have noted that for 52 first return strokesnear Kennedy SpaceCenter, Florida, inclusion of the slow field change before the breakpoint resultedin an approximatedoubling of the risetime from the valuesfound in this paper and in the papers by Fisherand Urnan [1972] and Lin and Uman [1973]. Although initial peaks from strokes at all distancesare referredto in this paper as radiation field peaks,our computer
All data were collectedeither on the Universityof Florida campusor at the Gainesville airport. The data presentedare showthat roughly25%of th,e initial peakmagnifrom 16 thunderstormperiodsoccurringon 14 different days calculations tude of strokes at I km and 50% of the initial peak magnitude during the summersof 1973 and 1975. Although most of the at 0.5 km are electrostatic and induction fields(seeFigure 3 of activity was due to small convectivestorms, some data were Uman et al. [1975a] for a samplecalculationand for a definitaken during the movementof small organizedsystems. The strokes were distance ranged by measuring the time tion of radiation, induction, and electrostaticfields). Some subsequentreturn strokesmight be expectedto have the characteristics
Copyright¸ 1976by the AmericanGeophysicalUnion. 4430
of first return strokes. This is the case if the
TILLER ET AL.' LIGHTNING RETURN STROKES
4431
Figure 3 shows electric field rise time histograms for first and subsequentreturn strokes.Figures3a and 3b contain data
T .•..•-(INITIAL PEAK) 5V/mh
from two different
1973 thunderstorms
within 25 km of a data-
taking site. Most lightningflashesusedin thesedata samples were not distance ranged. Figure 3c includes only distanceranged strokesfrom 1973 and 1975.As is evident from Figure
•5=EAKPO•N• ) D=lSkm 3•m/
D=100 km
3, the mean electric field rise time for first return strokes is
2.0 V/m
T •
D-Skm
larger than the mean rise time for subsequentstrokes, an observationfirst made by Fisherand Uman [1972]. In a Pennsylvaniastudy,Fisherand Uman [1972] found a mean risetime
of 3.6 #s with a standard deviation of 1.8 #s for 26 first return strokescloser than 25 km. For 26 subsequentreturn strokes the mean rise time was 3.1 #s with a standard deviation of 1.9 #s. For a closestorm (less than 10 km) at Kennedy Space Center, Lin and Uman [1973] reporteda mean risetime of 4.0 #s with a standard deviation of 2.2 #s for 12 first strokes. Eighty-threesubsequentreturn strokeshad a mean risetime of 1.2 #s with a standard deviation of 1.1 #s. Data recorded at Kennedy Space Center from five storm systemsduring the summer of 1971 [Lin and Uman, 1973; Uman et al., 1973] and two storm systemsduring the summer of 1974 show typical rise times of 1 #s. It appears that individual thunderstorms produce return strokes with different mean electric field rise
_•
•øølV/m
•
5o•/m
IO•m
times. I0000
'
(BREAKPOINT
REFERENCE
V/m
LINE)
Data on the initial peak electric field versusdistanceare given in Figure 2b. The data show a general increasein the value of the initial peak field with decreasingdistance,as is
predictedby the inverserelationshipbetweenthe radiation field and the distance [McLain and Uman, 1971]. Theoretical
Fig. 1. Typical electricfield wave forms at variousdistances.Both first and subsequentstroke data were usedto obtain the wave forms. Hence the wave form• are smaller in magnitude than typical first return strokesand larger than typical subsequentreturn strokes.
0 62
•k
subsequent str•ketakesa differentchannelthantheprevious
ß qpe o
oeo ß oo.olt,o o
Actual wave forms are found in the work of Fisher and Uman
[1972] and Uman et al. [1975b]. The electricfield ri•e times plotted in Figure 2a range from 0.8 to 5.3 •s and appear to be uncorrelatedwith stroke dis-
tance.•irst and subsequent returnstrokerisetimesfor distanceslessthan about 2 km may constitutea biasedsample becausethe initial radiation field peak is di•cult to identify in the presenceof the large induction and electrostaticfields associatedwith very closereturn strokes.The exceptionoccurs when the initial peak has a relatively rapid rise time and/or a
relativelysharp initial peak. For the majority of very close forms
a rise time measurement
was not
o 8
![ i , , i !! , !! , i [, , i i , FIRST
Idealized electric field waves shapesderived from the distance-ranged data are drawn in Figure 1. The wave shape parame[ersdiscussedin the paper are definedin the figure.
STROKES
o 75 FIRST RETURN STROKES ß 16:3 SUBSEQUENT RETURN STROKES
RESULTS AND DISCUSSION
stroke wave
RETURN
6
u; 5
strokesin the flashand henceis initiated by a steppedor a dart steppedleader rather than a dart leader.Bra•tley et al. [1975] found that between15 and 30%of Florida flasheshad spatially separatechannels.In the presentwork we do not distinguish betweensubsequentstrokesinitiated by dart leadersand those taking separatechannels. All return stroke electricfieldsobservedand analyzedin the present study are of a sign consistentwith the lowering of negativechargefrom cloud to ground.
return
FIRST
ß 151 SUBSEQUENT RETURN STROKES
STROKE
THEORY
•t•e[t • SUBSEQUEN STROKE THEOR
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DISTANCE,
.
.
12
km
.
14
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i
16
i
,
18
,
20
possiblebecausethe peakscould not be identified.Subsequent Fig. 2. (a) Electricfield risetime versusdistance.(b) Initial peak stroke initial peaks were generally easierto identify than first magnitudeversusdistance.The theoretical curves of part (b) were stroke peaks becauseof their faster rise times and smaller calculatedby usingan inversedistancerelationshipand the normaoverall field change. lized initial peak field meansfor first and subsequentstrokes.
4432
TILLER ET AL.: LIGHTNING RETURN STROKES
FIRST STROKES
(A) 8/16/7:5 MEAN :$.7• s
I0
1622-1705 EDST
70 STROKES 20
FIRST RETURN
SUBSEQUENTSTROKES
--
ZO '
76 STROKES
MEAN=2.5Ats S.D.:0.8 •as
STROKES
'
,
,
8
75 STROKES
6
S.D.,6.8 V/m
MEAN,9.9
V/m
-
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SUBSEQUENT RETURN STROKES
(B) 8/19/75 50 20
STROKES
MEAN,2.7/as ,0.9•s
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15:58-1558 EDST --
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MEAN;2.1,•s
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15
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NORMALIZED INITIAL PEAK FIELD, V/m
2o
0 CiD 1.0 2D
14
I0
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(C) ALL 1973 AND 1975 DISTANCE-RANGED DATA
62 STROKES MEAN::5.0,as S.D.:1.2,as
16
:9
.
.
20
m
MEAN,5.7 V/m S.O.,4.5 V/m
S.D.,0.9•s .
i i i--i i i
165 STROKES
m u. 18 o
0
" 0.0
i I 1.0 2.0 $.0 4.0
5.0 6.0 7.0
Fig. 4. Histogramsof normalized initial peak electric field. The initial peak fieldswerenormalizedto a distanceof 100km by usingan inversedistancerelationship.
ELECTRIC FIELD RISE TIME,
Fig. 3. Histogramsof electricfield risetime. Data in parts(a) and (b) were taken during two periodsof closethunderstormactivity and include rise times from flashesthat were not distanceranged.All rise timesin part (c) are from distance-ranged flashes.
given in Figure 4, and their distant peak field means are smaller. For lightning distancerangedat lessthan 10 km from a Kennedy Space Center station the normalizedinitial peak field mean of 12 first return strokes was 19.8 V/m; for 83 0
curvesfor theradiationfieldpeakaredrawnasfunctfons of
60 FIRST RETURN
STROKES
ß 146 SUBSEQUENT RETURN STROKES
distancein Figure 2b by using the normalized first and sub32 ' ' ' 0 ' ' sequentstrokemeansof Figure 4 (9.9 and 5.7 V/m at 100km, 30 respectively).Figure 2b alsoshowsthat, in general,first return stroke peak fields tend to be larger than subsequentreturn 2B 0 stroke peak fields. Biasesprobably exist in the data of Figure 2b. The reason • 24 ß for the relatively small number of first and subsequentreturn > o o strokepeaksplotted for distanceslessthan 2 km is the sameas • 22 o that discussedfor Figure 2a. The selectionof only fast risetime tu o •- 20 data for strokesat distanceslessthan 2 km may biasthe initial peakdistribution,althoughthe informationcontainedin Fig• 18ß ß o o0 ß ure 5 would indicate that this is probably not the case. For ,,• 16 ß ß very closethunderstormsthe oscilloscope trigger levelwas set D-ß relatively high, so that the high-frequencynoise associated ,4. .o o with closeleader and interstroke processes would not trigger ,9, 12ß oßo o o_ . N • ß the oscilloscope.Therefore it is possiblethat thesevery close ß I=' 8 n,,ß ß o o o thunderstormsproducedsmall return strokeswhich were not recorded. Return strokeswhose fields were tens of volts per / 0 _ e ß ß 0 / meter often could not be analyzed becausethe oscilloscope vertical scalewas set for much larger fields,or the fieldswere not recordedbecausethe minimum triggeringlevelwas limited by the roughly10 V/m ambient60-Hz signal.At all distances, wave forms occurred which were off scaleon the oscilloscope and hence could not be analyzed. o I 2 3 4 5 6 Histogramsof the initial peak fieldsnormalizedto 100 km ELECTRICFIELD RISETIME,•t are shownin Figure 4. Lin and Urnan[1973]reportednormalFig. 5. Normalized initial peak electricfield versuselectricfield ized initial peak fields for three isolated Florida thunder- rise time. The initial peak •elds were normalizedto a distanceof l• storms. Their close peak field means are larger than those km by usingan inversedistancerelationship.
,o oo 81- o -- '• o.. •,, lr c• o
'
'1
TILLER ET AL.: LIGHTNING RETURN STROKES
subsequentreturn strokesit was 13.7 V/m. For a radar-ranged 110-km thunderstorm which produced 700 strokes, Lin and Uman [1973]found first and subsequent returnstroke-normalized peak field meansof 2.0 and 1.9 V/m, respectively.About 350 first return
strokes from
a 195-km
thunderstorm
4433
to 5 0 64
FIRST
RETURN
STROKES
ß 121 SUBSEQUENT RETURN STROKES
had a
normalizedpeak field mean of 5.9 V/m; about 750 subsequent return strokeshad a mean of 5.2 V/m. Kalakowskyand Lewis [1967] reportedthat of half a million electricfield wave forms recordedin New England over a 30-month period, only 27 strokes(about 0.005%) had normalizedinitial peak fieldsover 16 V/m. The largestpeak was 47 V/m. All of the 27 strokes were from single-strokeflashesand typically were associated with cold fronts or squall lines. Thirteen of the 27 strokes loweredpositivecharge.In view of the above, it appearsthat differentthunderstorms can producedifferentinitial peak field distributionsand hencethat the histogramsof Figure 4 represent the compositecharacteristicsof 16 thunderstorms,each having potentially different return stroke properties. Figure5 showsa plot of electricfield risetime versusnormalized initial peak field. The data presentedrepresentonly distance-rangedlightningflashes.As is shownin the figure, data pointsappearto be random, and no correlationbetweenelectric field rise time and the normalized initial peak field is
E 104 o
)0
Q=3C, H=5km O=lC,
H=7km
z I0 3 0 0
o
o
o
ß
8ß ß
o o
ß o
0
o ß
uJ i02
ß
.: ß oø ß
o
o
ß o
ß
evident.
Many electric field wave forms exhibit a discontinuityin slope(the ramp startingtime identifiedin Figure 1) followed by a regionof roughlyconstantslope.To our knowledge,this featureof the electricfield has not beenidentifiedpreviouslyin the literature. Ramp starting time is plotted in Figure 6 as a functionof distance.Although the data sampleis not large,the ramp starting time appearsto increasewith distance.For distancesless than 2 km and greater than 12 km the wave forms do not have a clearly defined ramp starting point. In about half of the intermediaterange data analyzedthere was no observableramp startingtime. With someimagination,a ramp starting time can be identified at 5-10 #s for some strokesin the 0.5- to 2-km range, but the identificationis not definiteenoughto plot in Figure 5. Distant wave formseither do not haverampsor haverampssosmallthat positiveidentificationof the ramp startingpoint is not possible.As is shown in Figure1, the high-frequency fluctuationson theelectricfield wave form usually decreaseafter the ramp begins. The electric field intensity 170 #s after the breakpoint is plottedas a functionof distancein Figure 7. Biaseswhich may exist in the data are the same as those considered
in the
discussionof Figure 2b. Our computercalculationsshowthat 90% or more of the field at 170 #s in the 0- to 20-km distance 0
20
ß 59
FIRST
RETURN
SUBSEQUENT
STROKES
RETURN
STROKES
80 •
70
uJ 60 •'
oeooe
50
_z 40 ß
•- 3o •
•'
20
0
2
4
6
8
I0
12
14
16
18
2:0
DISTANCE, km
Fig. 7. Electricfield intensityat 170#s versusdistance.The curves representthe electric field changesoccurringwhen a 5-km uniformly chargedline of 3.0-C charge(line chargedensityof 6.0 X 10-4 C/m) and a 7-km line of I-C charge(line chargedensity1.4 X 10-4 C/m) are lowered to ground.
range is electrostatic.If we assume that the leader charge lowered to ground in the first 170 #s of the return stroke is uniformlydistributedwith height,the electrostaticfieldchange is [ Urnan, 1969]
E = (pL/2•reo)[D-•-
(H ø'+ Dø')-•/ø']V/m
(1)
wherepL is the chargeper unit lengthloweredto ground,H is the vertical channellength, D is the horizontal distancefrom the channelbaseto the observationpoint, and e0is the permittivity of free space.The electricfield changefrom (1) is plotted in Figure 7 for both H = 5 km, the approximate height of the freezinglevel, and a total chargeQ = pLH of 3.0 C and H -- 7 km and Q = 1 C. Thesecurvesprovide a reasonablefit to the first and subsequent strokedata, respectively.For a fixed• an increaseor decreasein the channelheight has little effect on the electricfield changewithin about I k m but resultsin an increaseor decrease,respectively,in the field changeat greater distances,the effect increasingwith distance.Thus, for example, if the measureddistantfield changesfrom first strokes are larger than the typical changesbecauseof data-taking biases,a moreadequatetheoreticalcurvecouldbe obtainedby usinga channelwith the sameuniform chargedensitybut with a length lessthan 5 km and hencea total chargeof lessthan 3 C. The choiceof a uniform charge distribution as the-return
strokefieldsourceisby nomeansunique.For example,a field
IO O 0
I
I
I
I
I
2
3
4
I
I
I
I
I
I
5
6
7
8
9
I0
II
DISTANCE, km
Fig. 6. Ramp starting time versusdistance.
changesimilarto the 3-C field changeplotted in Figure 7 can be producedby simply placinga 3-C point chargeat a height of 2 km. Or it can be producedby a chargedistributionof 1 C located near heightsof 0.5 and 6 km. Leader chargedensities
4434
TILLER ET AL.: LIGHTNING RETURN STROKES
which decreaseexponentiallyfrom the ground upward have beenpostulatedon physicalgrounds[e.g., Bruceand Golde, 1941]. If this is the case,sincethe chargemodelsdiscussed above require a rough chargesymmetryabout the channel midpoint in order to fit the experimentaldata, there apparently must be an additional chargesourcenear the channel top. The channeltop chargemight be due to both the charge effectivelylowered to ground when the return stroke current pulse(and charge)propagatesfrom ground to cloud and the residualcloud chargedrainedto ground in the time after the return stroke arrivesat the channeltop. No matter what the exact distribution
of the lowered return
strokechargemight be, the experimentaldata of Figure 7 are consistentwith a typicalchargemagnitudeof the order of I C being lowered to ground in a time of 170 #s, first strokes usuallyloweringmore chargethan subsequent strokes.Berger and Vogelsanger[1965] made direct current measurementson towersstruckby lightningin Switzerlandand found that for strokeswith peak currents over 10 kA the median charge lowered in I ms was about 5 C for first strokes and about 2 C
peak field as a function of distance. Since the vertical data spreadis much lessthan might be expectedgiventhe data of Figures2b and 7, it is evidentthat the electrostaticvalue at 170 #s dependson the magnitudeof the initial radiationfield peak. It followsthat the initial part of the return strokecurrent wave shapewhich is responsiblefor the initial radiationfield peak is relatedto the chargeloweredin 170#s. The chargeinvolvedin the upward-propagatingreturn stroke current wave shapeis certainlyrelated to the initial peak current and is responsible for part of the 170-#selectrostaticvalue, the remainingcharge transferbeingdue to chargeinitially storedin the air around the leaderand drainagefrom residualchargeat the channel top. First strokeshave larger ratios of electrostaticfield to initial peak field than do subsequentstrokes,particularlyfor distanceswithin a few kilometers.The implication of this observationis that first strokeshave relativelylarger and/or longer-durationreturn strokechannelcurrentsafter peak current and/or havemore chargestoragearoundthe leaderchannel than do subsequentstrokes. Berger et al. [1975] have reportedthat firstreturnstrokecurrentsmeasuredat the lightning channelbaseexhibit about twice the time to half of the peak current as subsequentreturn strokes.
for subsequentstrokes.Bergeret al. [1975] report that first stroke 'impulse' currentshave median chargetransfersof 4.5 C; subsequentstroke impulse currentshave median charge Acknowledgments. This work was sponsoredin part by the Natransfersof 0.95 C. The impulse current is defined as the tional ScienceFoundation(GA-36835), the Officeof Naval Research 'rapidly changing'currentand thereforepresumablyoccursin (N00014-68-H-0173-0018, N00014-75-C-0143, and N00014-67-Aless than I ms. From measurements of the sum of the total
leader and return stroke electric field change produced by lightning in New Mexico storms,Brook et al. [1962] found the
mostfrequent firststrokecharge transfer to bebetween 3 and4
0209-0015),and the National Aeronauticsand SpaceAdministration (NGR-10-005-169). The work presentedrepresentsa portion of the first author'sMaster'sthesisin electricalengineeringat the University of Florida.
REFERENCES
C and the most frequentsubsequent strokechargetransferto be between 0.5 and I C.
Figure 8 gives the ratio of the field at 170 #s to the initial
Berger,K., and E. Vogelsanger,Messungenund Resultateder Blitzforschungder Jahre 1955-1963auf dem Monte SanSalvatore,Bull. Swiss Electrotech. Vet., 56, 2-22, 1965.
0 49
FIRST
RETURN
ß 109 SUBSEQUENT IOO
I
I
I
I
I
I
I
I
I
I
I
I
STROKES
RETURN I
I
I
I
STROKES I
I
I
Berger,K., R. B. Anderson,and H. Kroninger, Parametersof lightning flashes,Electra, 80, 23-27, 1975. Brantley,R. D., J. A. Tiller, and M. A. Uman, Lightningpropertiesin Florida thunderstormsfrom video tape records,J. Geoœhys. Res.,
--
80, 3402-3406, 1975.
--
.
.
-
.
-
Fisher, R. J., and M. A. Uman, Measured electric field rise times for
'0 0 O0
first and subsequentlightningreturn strokes,J. Geoœhys. Res., 77,
0
•
•o
.-o
o
z
Brook, M., N. Kitagawa, and E. J. Workman, Quantitativestudyof strokesand continuingcurrentsin lightningdischarges to ground,J. Geophys.Res., 67, 649-659, 1962. Bruce,C. E. R., and R. H. Golde, The lightning discharge,J. Inst. Elec. Eng., Part 2, 80, 487-520, 1941. 399-406, 1972.
Kalakowsky,C. B., and E. A. Lewis,VLF sfericsof very largevirtual sourcestrength,MF, LF, and VLF Radio PropagationConference, Publ. 36, pp. 228-245, Inst. of Elec. Eng., London, Nov. 1967. Krider, E. P., and E. J. Radda, Radiation field wave forms produced by lightningsteppedleaders,J. Geoœhys. Res.,80, 2653-2657, 1975. Lin, Y. T., and M. A. Uman, Electric radiation fields of lightning return strokesin three isolated Florida thunderstorms,J. Geophys.
ß
.
ß
o
.o "'o
øø•oo.d'ø_ o
oo.. o •"'. ' '•øø' o,._• . ß .•#o•o% ø' .•ß
ß•oß
-
00ß
ßo
ß ß
.
Res., 78, 7911-7915, 1973.
McLain, D. K., and M. A. Uman, Exact expressionand moment approximationfor the electricfield intensityof the lightningreturn stroke,J. Geophys.Res., 76, 2101-2105, 1971. Uman, M. A., Lightning,pp. 69, 85, 213,226, 227, McGraw-Hill, New York, 1969. Uman, M. A., D. K. McLain, R. J. Fisher, and E. P. Krider, Electric
0
-
ß ß
-
00ß
field intensityof the lightning return stroke,J. Geophys.Res., 78,
ß
ß
-
3525-3529, 1973.
O0
Uman, M. A., D. K. McLain, and E. P. Krider, The electromagnetic radiation from a finite antenna,Amer. J. Phys.,43, 33-38, 1975a.
Uman,M. A., R. D. Brantley,Y. T. Lin, J. A. Tiller, andE. P. Krider, O. I
I 0
I Z
s
i 4
•
I 6
I
I 8
I
I I I0
I I 12
I ! 14
t I t t 20 16 18
DISTANCE, km
Fig. 8. Ratio of the electricfield at 170 #s to the initial peak field versus distance.
Correlated electric and magnetic fields from lightning return strokes,J. Geoœhys. Res., 80, 373-376, 1975b.
(ReceivedFebruary 2, 1976; revised March 30, 1976; acceptedApril 6, 1976.)
