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Long impulse currents associated with positive return strokes
\ PERGAMON
Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 582Ð588
Long impulse currents associated with positive return strokes Chandima Gomes\ Vernon Cooray Institute of High Voltage Research\ Uppsala University\ Sweden Received 7 April 0886 ^ accepted 09 March 0887
Abstract Long distant electric _elds "399Ð499 km#\ generated by 15 positive cloud!to!ground ~ashes\ were analysed[ These ~ashes consist of well detectable long impulse _elds subsequent to the initial peak[ These hook!shaped slow _elds are of considerable amplitude and have a mean duration of 0[13 ms[ The amplitude of the long impulse _eld and the initial peak of the _eld show an approximately linear relationship[ The long impulse current pertinent to positive return strokes which give rise to the measured long impulse _elds were estimated[ Flashes with these slow _elds lower a mean charge of 49 C within the _rst 2 ms "excluding the _rst 099 ms which contains the initial peak#\ whereas the maximum charge lowered is 013 C[ The mean of the ratio between the peak of the long impulse _eld and the initial peak is 30)[ We also estimated the _elds that will be generated by the long impulse currents at distances of 0999 km\ 2999 km and 4999 km from the strike[ The estimated peak magnetic _elds at 4999 km have a mean of 41 pT[ The peak magnetic _elds observed at distances of about 4999 km from positive lightning ~ashes\ which were associated with red sprites\ are in the same range as the peak magnetic _elds that we have calculated for the above 15 ~ashes[ Hence we conclude that the observed Q!bursts which coincide with the occurrence of red sprites are due to the long impulse currents of positive return strokes[ This slow _eld variation is rarely observed in connection with negative return strokes[ Even when it is present\ in the event of a negative return stroke\ the amplitude and the duration of the tail are much less than those of its counterpart in positive return strokes[ This explains why ionospheric lightning is predominantly associated with positive return strokes but not with negative return strokes[ Þ 0887 Elsevier Science Ltd[ All rights reserved[
0[ Introduction In general\ negative return stroke radiation _elds rise to their peak values in about a few microseconds[ After reaching the peak\ these _elds decrease and cross the zero line within about 49 ms[ The total duration of these radiation _elds is about 099 ms[ On the other hand Cooray and Lundquist "0871# and Cooray and Perez "0873#\ reported that many of the positive return stroke radiation _elds observed in Sweden do not follow this typical behaviour[ After 49Ð099 ms following the initial peak\ the _elds of the positive return strokes start to increase again[ This secondary increase lasts for about 199Ð499 ms at which time the _eld reaches a maximum[ Subsequent to this secondary peak\ the _eld decays and crosses the zero line in about 0Ð4 ms[ Henceforth\ we refer to this _eld component as Long Impulse Fields "LIF# and the return
Corresponding author[ Tel[ ] 9935 07 422525 ^ fax ] 9935 07 491508 ^ e!mail ] vernon[coorayÝhvi[uu[se
stroke current of the positive ground ~ash which gen! erates this _eld as Long Impulse Current "LIC#[ Such a _eld generated by a positive return stroke observed in Sweden is given in Fig[ 0[
Fig[ 0[ Flash no[ P959685[16[ Parameters Ein\ Eim\ T0 and T1 are described in the text[
S9906Ð8209:87:,*See front matter Þ 0887 Published by Elsevier Science Ltd[ All rights reserved PII ] S 0 2 5 3 Ð 5 7 1 5 " 8 7 # 9 9 9 2 8 Ð X
583
C[ Gomes\ V[ Cooray:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 582Ð588
In recent years\ after the discovery of red sprites\ a striated glow phenomenon occurring in the mid!latitude over mature and dissipating thunderstorms\ a signi_cant interest has developed in studies of the positive return stroke currents\ as they are associated with such pheno! mena "Boccippio et al[\ 0884 ^ Burke and Jones\ 0885#[ In this paper we present a quantitative analysis of LIFs and estimate the signatures of LICs pertinent to positive lightning ~ashes of a thunderstorm observed in Sweden[
1[ Experimental The measurements were conducted in Uppsala "48[7>N\ and 06[5>E#\ Sweden on 5 July 0885[ The data set is pertinent to a frontal thunderstorm which occurred in the daytime[ Some 72 cloud!to!ground ~ashes were recorded\ of which 30 were positive ~ashes[ Twenty!six of these positive ~ashes contained well detectable LIFs[ The antenna system used to capture the _elds is identical to that described previously by Cooray and Lundquist "0871#[ The vertical _eld was sensed by a ~at plate ante! nna[ After passing through a bu}er ampli_er\ the signal was directly fed through a properly terminated coaxial cable to a transient recorder[ The zero!to!peak rise time of the output of the antenna system for a step input voltage was a few hundred nanoseconds ^ the decay time constant of the system was about 14 ms[ The recording system is the same as that described previously by Cooray and Perez "0883#[ This system consists of a LeCroy tran! sient recorder with 0 megabyte of memory[ The sampling time was 9[4 ms with a pre!trigger delay time of 099 ms[ Some 49 Hz noise is superimposed on the observed wave forms but\ compared with the amplitudes of the _eld traces concerned in this study\ the e}ect of this back! ground noise is negligible[
2[ Theory and analysis Wait "0859# provided a mathematical treatment of the propagation of ELF components within the EarthÐiono! sphere waveguide[ The results of this mathematical treat! ment could be used to understand how the signature of the LIFs of positive return strokes change as they propagate di}erent distances over the surface of the Earth[ In the mathematical derivation given by Wait "0859#\ the Earth was assumed to be a perfect conductor and the ionosphere was considered to be a homogeneous conductor for ELF frequencies[ The e}ective conduc! tivity of the ionosphere is taken as o9vr\ where o9 is the permittivity of free space and vr is a parameter which has a daytime value of 0[1×094 s−0[ The daytime height of the lower edge of the ionosphere is taken as 69 km[ According to Wait "0859#\ when the current moment of the source that gives rise to the ELF component is a
Dirac delta function\ the vertical electric _eld\ E"t#\ of the zero!order waveguide mode\ at the ground at a distance r from the source\ is given by E"t#
0:1
0 1
m
c 1 1r 1p h
p9 2:1
b
¦
$ 01 01 0 1 01 % Pa
0 ct? t? t? − P b 7 r b r
8 ct? 1 t? Pc ¦ = = = u"t?# 017 r b
"0#
where P9 is unity b
Pa"t#
Pb"T#
r 10 1h vr
01 0 1
0 0 0− 0 1 e 3T −0 1T T2:1 1
T
Pc"T# −
e0− 3T1 0
2:1
3 T
2:1
e03T1− 0
1p0:1 0 e rfc 1 T 1T0:1
0 1
t? t−r:c where c is the speed of light in free space and u"t?# is the Heaviside unit step function[ Once the response for the delta function is known\ the response corresponding to an arbitrary source current moment can be derived from the convolution theorem[ For the _eld calculations\ we employed the positive return stroke model of Cooray "0884#[ The basic concepts of this model are as follows[ The total charge brought to ground by the return stroke is initially stored on the corona sheath of the leader channel[ As the return stroke front surges upwards\ the corona sheath collapses drai! ning its charge into the highly conducting return stroke core[ Consequently\ each point of the leader channel was treated as a current source that injects a current into the return stroke[ Subsequently\ this corona current travels along the return stroke core to ground at the speed of light[ Since neither the temporal variation nor the spatial dependence of the corona current in positive return stro! kes is known\ their nature was inferred by appealing to the available experimental observations on positive return strokes and long sparks[ Measured current wav! eforms due to positive return strokes "Berger et al[\ 0864# have an initial fast rising portion that takes a few micro! seconds\ a relatively slow decaying part that takes some few tens of microseconds\ and a very slow varying sec! ondary peak that lasts for several hundred microseconds "return strokes with long continuing currents are not considered#[ Cooray "0884# considered this as evidence for the existence of three distinct regions in the corona sheath*a hot region "innermost region of the corona
C[ Gomes\ V[ Cooray:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 582Ð588
sheath# which is neutralised almost immediately by a {return stroke| like neutralisation process\ an inter! mediate region which is neutralised slowly by radial nega! tive streamers originating from the central core\ and a third region "outermost region of the corona sheath# which is neutralised very slowly by corona discharges and ion transport[ He represented the corona current generated by these three regions by three exponential functions with di}erent decay time constants[ The mag! nitudes of these time constants were evaluated by appeal! ing to experimental data on long sparks and comparing the model simulations with the observed properties of positive return strokes[ Since it is the charge and the time constants of the current component from the outermost sheath which are responsible for the amplitude and the duration of the slow tail "i[e[ the ELF component of the radiation _eld#\ we changed these parameters to get an exact _t to the slow tails of the measured positive return strokes[ For a given set of model parameters\ the vari! ation of the model simulated current moment as a func! tion of time was evaluated and that was combined with eqn "0# through the convolution theorem to calculate the distant ELF _eld "or LIFs#[ This procedure was repeated by changing the model parameters until a match was obtained between the model simulated and the measured LIFs[ In estimating this best _t it was necessary for us to pinpoint the location of the peak of LIF which\ some! times\ was oblique due to the various _ne structures superimposed on the _eld[ Thus\ there is some sub! jectivity involved in its estimation[
3[ Results and discussion The 15 ~ashes with LIFs used in this study were located between 399 km and 499 km from the measuring station\ with most of them clustering around 349 km[ Hence\ in the calculations we considered r 349\999 m for all of these ~ashes[ This choice does not in~uence the calculated peak LICs and the corresponding charge transport by more than 4)[ Several examples of the measured and the model simu! lated LIFs together with the corresponding positive return stroke current waveforms are depicted in Figs 1Ð 3[ In the calculations\ we did not attempt to simulate the VLF component of the _eld "i[e[ the initial peak# because eqn "0# is valid only in the ELF region[ Therefore\ the model parameters that in~uence the VLF component including the initial peak were not changed from one example to another[ This is the reason why the initial peak of the calculated current waveform does not change from one example to another[ By integrating these cur! rent waveforms\ we estimated the total charge component that was brought down to ground during the _rst 2 ms of these return strokes[ In this estimation\ however\ we excluded the _rst 099 ms\ which includes the initial peak[
584
Our analysis shows that the charge transported during this time to ground does not exceed about 4 C[ We have also calculated the electric _elds generated by these return strokes at 0999\ 2999 and 4999 km[ Several examples of such _eld signatures are shown in Figs 1Ð3[ As described later\ these calculations made it possible for us to compare our results with some of those available in the literature[ In Table 0\ we have tabulated the values of various measured and calculated parameters such as the initial peak of the measured _eld "Ein#\ the peak of the LIF "Eim#\ the time from the initial peak to the peak of LIF peak "T0#\ the time from the initial peak to the zero!crossing of the LIF "T1# and the charge transported to ground by the LIC for the 15 return strokes "these parameters are shown in Fig[ 0#[ In addition\ the peak values of the LIFs at 0999\ 2999 and 4999 km "Exxxx#\ together with the peak value of the magnetic _eld of the LIFs at 4999 km "M4999#\ are also given in this table[ The last row of the table gives the mean value of these various parameters[ The mean charge lowered during the _rst 2 ms after the initial peak is 49 C\ whereas the mean of the peak LIC "Iim# is 27[1 kA[ The mean duration of the LIF "T1# is 0[13 ms and the mean rise time "T0# of that is 9[21 ms[ In seven ~ashes the Eim ] Ein ratio was equal to or more than 49)\ while the mean of this value is 30)[ Note that\ in the case of the initial peak of the measured _eld "Ein#\ propagation e}ects have not been taken into account\ in the given values[ For the initial peak of nega! tive return strokes\ the propagation of 349 km\ over land of conductivity 9[990Ð9[994 S:m\ will result in a reduction in amplitude of 19Ð29) "Cooray\ 0876#[ The estimated electric _eld at 4999 km "E4999# has a mean amplitude of 05 mV:m while the horizontal mag! netic _eld\ calculated by assuming the _elds to be radi! ation _elds\ at the same distance "M4999# has a mean peak value of 41 pT[ The full!width of the LIF at this distance is 4Ð09 ms[ We have made this calculation in order to compare our results with those of Boccippio et al[ "0884# which are pertinent to red sprites[ They have observed that most of the red sprites occur subsequent to positive return strokes\ which are associated with Q!burst events in the ELF Schumann resonance band[ The amplitudes of the Q!bursts which they measured at about 4999 km from the mesoscale convective systems which initiated red sprites are in the same range as of our estimation[ With these results\ we may conclude that all or some of the 15 positive return strokes we have considered in this study\ are associated with subsequent red sprites[ Figure 4 shows the estimated magnetic _elds of the 15 ~ashes at 4999 km as a function of the charge brought to ground by the corresponding LICs[ The values of these magnetic _elds are comparable to the peak values of Q!bursts associated with positive return strokes that gave rise to red sprites at similar distances "Boccippio et al[\ 0884#[ The authors of the last reference found that most of the positive return strokes with initial peak currents larger
585
C[ Gomes\ V[ Cooray:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 582Ð588
Fig[ 1[ Flash no[ P959685[00[ "a# Measured electric _eld "0# and calculated _eld "1# ^ "b# channel base current that was employed to calculate the _eld ^ "c# calculated _eld at 0999 km "0# and calculated _eld at 2999 km "1# ^ "d# calculated _eld at 4999 km[
Fig[ 2[ Flash no[ P959685[06[ "a# Measured electric _eld "0# and calculated _eld "1# ^ "b# channel base current that was employed to calculate the _eld ^ "c# calculated _eld at 0999 km "0# and calculated _eld at 2999 km "1# ^ "d# calculated _eld at 4999 km[
C[ Gomes\ V[ Cooray:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 582Ð588
586
Fig[ 3[ Flash no[ P959685[31[ "a# Measured electric _eld "0# and calculated _eld "1# ^ "b# channel base current that was employed to calculate the _eld ^ "c# calculated _eld at 0999 km "0# and calculated _eld at 2999 km "1# ^ "d# calculated _eld at 4999 km[
than a certain threshold gave rise to red sprites[ Since their peak current estimation was based on the initial peak of radiation _elds\ their results indicate that positive return strokes generating radiation _eld peaks larger than a certain threshold are capable of generating red sprites[ However\ Fig[ 5 shows the relationship between the initial peak of the radiation _eld and the amplitude of the LIF of the measured electric _elds[ The two parameters are approximately linearly correlated[ Thus\ one can expect the peak amplitude of the LIC to increase linearly with the initial return stroke peak current of positive return strokes[ Since the peak of LIC increases almost linearly with the charge brought to ground by the LIC "Fig[ 6#\ it is reasonable to expect a linear correlation between the initial peak current and the total charge brought to ground by the LIC[ If this is true\ the results of Boccippio et al[ "0884# suggest that red sprites are generated by positive return strokes with LICs that transport charge magnitudes larger than a certain threshold[ This sugges! tion is further strengthened by the fact that the estimated duration of the LICs is about a few milliseconds and the red sprites are generated within 1Ð2 ms after the initiation of positive return strokes[ The results of this study further support the concept originally set forth by Wilson "0845# for the mechanism of the triggering of sprites\ in which the rapid removal of a large positive charge from a vertically extensive charge layer stresses the mesosphere to dielectric breakdown[
The long impulse _eld is rarely observed in connection with negative return strokes at the same range of distances[ In the 31 negative cloud!to!ground ~ashes which we recorded on the same day\ there were merely three _eld traces in which the LIF is detectable[ In these cases too\ the amplitude and the duration of the LIFs are much less than those of its counterpart in positive return strokes[ This fact further con_rms that the presence of a dominant long impulse current of a cloud!to!ground ~ash is an essential ingredient for the onset of a subsequent red sprite[ It is also obvious why ionospheric lightning is predominantly associated with positive return strokes but not with negative return strokes[
4[ Conclusions A large fraction of the positive cloud!to!ground ~ashes observed in Sweden lowers a considerable amount of charge to ground through a long impulse current "LIC# which lasts for about 9[4Ð2[9 ms[ the mean of the long impulse _eld "LIF# peak is more than 39) of the initial _eld peak of the return stroke[ the peak magnetic _elds observed at distances of about 4999 km from positive lightning ~ashes\ which were associated with red sprites\ are comparable with the peak magnetic _elds due to these LICs that we have calculated for the above 15 ~ashes[
587
C[ Gomes\ V[ Cooray:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 582Ð588
Table 0 Statistics of the _elds and currents due to the 15 positive return strokes
Flash ID
Charge "C#
Iim "kA#
Ein "V:m#
Eim "V:m#
Eim:Ein ")#
T0 "ms#
T1 "ms#
E0999 "mV:m#
E2999 "mV:m#
E4999 "mV:m#
M4999 "pT#
P959685[00 P959685[06 P959685[10 P959685[13 P959685[16 P959685[17 P959685[18 P959685[20 P959685[21 P959685[22 P959685[24 P959685[25 P959685[28 P959685[31 P959685[35 P959685[36 P959685[45 P959685[50 P959685[52 P959685[54 P959685[55 P959685[57 P959685[61 P959685[62 P959685[63 P959685[72 Mean
013 89 13 23 43 23 35 49 33 23 37 35 15 83 53 41 29 55 69 13 37 11 41 49 29 31 49
097[7 59[7 10[1 04[9 25[7 29[1 45[5 49[1 11[3 06[1 18[9 18[9 02[7 39[5 33[5 55[9 33[5 53[7 36[7 10[1 28[9 00[1 34[9 13[9 12[1 18[5 27[1
×6[5 5[3 1[5 0[3 2[3 2[5 4[1 6[1 1[3 2[5 1[5 1[9 0[3 2[7 3[7 5[1 1[3 4[5 3[9 2[9 4[9 1[5 3[5 2[1 2[9 1[3 3[9
3[7 1[5 0[9 9[5 0[2 0[5 2[1 1[1 0[9 9[5 0[1 0[1 9[5 0[1 0[7 2[5 9[7 2[9 1[9 0[9 0[7 9[3 1[9 9[7 0[9 0[1 0[5
³52 30 28 32 27 33 51 20 31 06 35 59 32 21 27 47 22 43 49 22 25 04 33 14 22 49 30
9[20 9[24 9[20 9[31 9[24 9[10 9[10 9[17 9[23 9[21 9[28 9[27 9[33 9[59 9[22 9[08 9[29 9[18 9[22 9[19 9[18 9[36 9[15 9[30 9[19 9[17 9[21
9[87 0[23 9[76 0[14 0[19 9[72 9[71 9[74 0[20 0[11 0[35 0[34 0[24 1[64 0[33 9[62 0[29 9[85 0[30 9[81 0[09 0[59 0[91 0[42 0[11 0[29 0[13
832 419 081 013 181 174 412 336 089 035 134 134 006 181 279 480 070 455 398 081 231 82 284 086 101 143 211
041 89 17 14 38 27 53 54 24 15 33 33 11 58 53 62 18 74 69 17 43 07 50 28 29 31 41
31 17 8 7 04 09 06 07 01 8 03 03 6 15 08 08 8 13 11 8 05 5 06 02 8 02 05
039 82 29 16 49 22 46 59 39 29 36 36 12 76 52 52 29 79 62 29 42 19 46 32 29 32 41
Iin ] Amplitude of the calculated long impulse current[ Ein ] amplitude of the initial peak ^ Eim ] amplitude of the impulse _eld ^ T0 ] time duration from the initial peak to the peak of the impulse _eld ^ T1 ] time duration from the initial peak to the zero!crossing time of the impulse _eld ^ E0999\ E2999\ E4999 ] calculated _elds due to the long impulse currents at 0999 km\ 2999 km and 4999 km respectively ^ M4999 ] calculated magnetic _eld at 4999 km[
Fig[ 4[ Correlation between the amplitude of the estimated mag! netic _elds at 4999 km and charge lowered by the LIC[
Fig[ 5[ Correlation between the amplitude of the LIF and initial peak of the measured _elds[ "Note that the propagation e}ects have not been taken into account in the case of the values of the initial peaks of the measured _elds[#
C[ Gomes\ V[ Cooray:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 582Ð588
588
Institute of High voltage Research[ The authors thank Prof[ Viktor Scuka for placing excellent research facilities at their disposal and Dr R[ Thottappillil for fruitful dis! cussions[ The comments made by Prof[ Alexander P[ Nickolaenko "one of the referees# helped us to improve the _nal version of the manuscript[ Financial assistance given by the IPPS of the International Science Programs\ Uppsala University\ and the Swedish Natural Science Foundation is gratefully acknowledged[ References
Fig[ 6[ Correlation between the peak LIC and the charge lowered by LIC[
Hence\ we conclude that the observed Q!bursts\ which coincide with the occurrence of red sprites\ are due to the long impulse currents of positive return strokes[ The LIC is very rarely observed in the _elds generated by negative cloud!to!ground lightning observed in Sweden[ This may be the reason it is that ionospheric lightning is pre! dominantly associated with positive return strokes but not with negative return strokes[ Acknowledgements The research work reported here was conducted within the framework of the lightning research program at the
Berger\ K[\ Anderson\ R[B[\ Kroninger\ H[\ 0864[ Parameters of lightning ~ashes[ Electra 79\ 12Ð64[ Boccippio\ D[J[\ Williams\ E[R[\ Heckman\ S[T[\ Lyons\ W[A[\ Baker\ I[T[\ Boldi\ R[\ 0884[ Sprites\ Q!bursts and positive ground ~ashes[ Science 158\ 0977Ð0980[ Burke\ C[P[\ Jones\ D[L[L[\ 0885[ On the polarity and continuing current in unusually large lightning ~ashes deduced from ELF events[ J[ Atmos[ Terr[ Phys[ 47\ 420Ð439[ Cooray\ V[\ 0876[ E}ects of propagation on the return stroke radiation _elds[ Radio Sci[ 11\ 646Ð657[ Cooray\ V[\ Lundquist\ S[\ 0871[ On the characteristics of some radiation _elds from lightning and their possible origin in positive ground ~ashes[ J[ Geophys[ Res[ 76 00\192Ð00\103[ Cooray\ V[\ Perez\ H[\ 0883[ Some features of lightning ~ashes observed in Sweden[ J[ Geophys[ Res[ 88\ 09\530Ð09\541[ Cooray\ V[\ 0884[ A model for positive return strokes[ Inst[ Phys[ Conf[ Ser[ No[ 032[ Wait\ J[ R[\ 0859[ On the theory of the slowtail portion of atmospheric wage forms[ J[ Geophys[ Res[ 54\ 0825Ð0835[ Wilson\ C[T[R[\ 0845[ A theory of thundercloud electricity[ Proc[ Roy[ Soc[ "A#\ 186Ð206[
Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 582Ð588
Long impulse currents associated with positive return strokes Chandima Gomes\ Vernon Cooray Institute of High Voltage Research\ Uppsala University\ Sweden Received 7 April 0886 ^ accepted 09 March 0887
Abstract Long distant electric _elds "399Ð499 km#\ generated by 15 positive cloud!to!ground ~ashes\ were analysed[ These ~ashes consist of well detectable long impulse _elds subsequent to the initial peak[ These hook!shaped slow _elds are of considerable amplitude and have a mean duration of 0[13 ms[ The amplitude of the long impulse _eld and the initial peak of the _eld show an approximately linear relationship[ The long impulse current pertinent to positive return strokes which give rise to the measured long impulse _elds were estimated[ Flashes with these slow _elds lower a mean charge of 49 C within the _rst 2 ms "excluding the _rst 099 ms which contains the initial peak#\ whereas the maximum charge lowered is 013 C[ The mean of the ratio between the peak of the long impulse _eld and the initial peak is 30)[ We also estimated the _elds that will be generated by the long impulse currents at distances of 0999 km\ 2999 km and 4999 km from the strike[ The estimated peak magnetic _elds at 4999 km have a mean of 41 pT[ The peak magnetic _elds observed at distances of about 4999 km from positive lightning ~ashes\ which were associated with red sprites\ are in the same range as the peak magnetic _elds that we have calculated for the above 15 ~ashes[ Hence we conclude that the observed Q!bursts which coincide with the occurrence of red sprites are due to the long impulse currents of positive return strokes[ This slow _eld variation is rarely observed in connection with negative return strokes[ Even when it is present\ in the event of a negative return stroke\ the amplitude and the duration of the tail are much less than those of its counterpart in positive return strokes[ This explains why ionospheric lightning is predominantly associated with positive return strokes but not with negative return strokes[ Þ 0887 Elsevier Science Ltd[ All rights reserved[
0[ Introduction In general\ negative return stroke radiation _elds rise to their peak values in about a few microseconds[ After reaching the peak\ these _elds decrease and cross the zero line within about 49 ms[ The total duration of these radiation _elds is about 099 ms[ On the other hand Cooray and Lundquist "0871# and Cooray and Perez "0873#\ reported that many of the positive return stroke radiation _elds observed in Sweden do not follow this typical behaviour[ After 49Ð099 ms following the initial peak\ the _elds of the positive return strokes start to increase again[ This secondary increase lasts for about 199Ð499 ms at which time the _eld reaches a maximum[ Subsequent to this secondary peak\ the _eld decays and crosses the zero line in about 0Ð4 ms[ Henceforth\ we refer to this _eld component as Long Impulse Fields "LIF# and the return
Corresponding author[ Tel[ ] 9935 07 422525 ^ fax ] 9935 07 491508 ^ e!mail ] vernon[coorayÝhvi[uu[se
stroke current of the positive ground ~ash which gen! erates this _eld as Long Impulse Current "LIC#[ Such a _eld generated by a positive return stroke observed in Sweden is given in Fig[ 0[
Fig[ 0[ Flash no[ P959685[16[ Parameters Ein\ Eim\ T0 and T1 are described in the text[
S9906Ð8209:87:,*See front matter Þ 0887 Published by Elsevier Science Ltd[ All rights reserved PII ] S 0 2 5 3 Ð 5 7 1 5 " 8 7 # 9 9 9 2 8 Ð X
583
C[ Gomes\ V[ Cooray:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 582Ð588
In recent years\ after the discovery of red sprites\ a striated glow phenomenon occurring in the mid!latitude over mature and dissipating thunderstorms\ a signi_cant interest has developed in studies of the positive return stroke currents\ as they are associated with such pheno! mena "Boccippio et al[\ 0884 ^ Burke and Jones\ 0885#[ In this paper we present a quantitative analysis of LIFs and estimate the signatures of LICs pertinent to positive lightning ~ashes of a thunderstorm observed in Sweden[
1[ Experimental The measurements were conducted in Uppsala "48[7>N\ and 06[5>E#\ Sweden on 5 July 0885[ The data set is pertinent to a frontal thunderstorm which occurred in the daytime[ Some 72 cloud!to!ground ~ashes were recorded\ of which 30 were positive ~ashes[ Twenty!six of these positive ~ashes contained well detectable LIFs[ The antenna system used to capture the _elds is identical to that described previously by Cooray and Lundquist "0871#[ The vertical _eld was sensed by a ~at plate ante! nna[ After passing through a bu}er ampli_er\ the signal was directly fed through a properly terminated coaxial cable to a transient recorder[ The zero!to!peak rise time of the output of the antenna system for a step input voltage was a few hundred nanoseconds ^ the decay time constant of the system was about 14 ms[ The recording system is the same as that described previously by Cooray and Perez "0883#[ This system consists of a LeCroy tran! sient recorder with 0 megabyte of memory[ The sampling time was 9[4 ms with a pre!trigger delay time of 099 ms[ Some 49 Hz noise is superimposed on the observed wave forms but\ compared with the amplitudes of the _eld traces concerned in this study\ the e}ect of this back! ground noise is negligible[
2[ Theory and analysis Wait "0859# provided a mathematical treatment of the propagation of ELF components within the EarthÐiono! sphere waveguide[ The results of this mathematical treat! ment could be used to understand how the signature of the LIFs of positive return strokes change as they propagate di}erent distances over the surface of the Earth[ In the mathematical derivation given by Wait "0859#\ the Earth was assumed to be a perfect conductor and the ionosphere was considered to be a homogeneous conductor for ELF frequencies[ The e}ective conduc! tivity of the ionosphere is taken as o9vr\ where o9 is the permittivity of free space and vr is a parameter which has a daytime value of 0[1×094 s−0[ The daytime height of the lower edge of the ionosphere is taken as 69 km[ According to Wait "0859#\ when the current moment of the source that gives rise to the ELF component is a
Dirac delta function\ the vertical electric _eld\ E"t#\ of the zero!order waveguide mode\ at the ground at a distance r from the source\ is given by E"t#
0:1
0 1
m
c 1 1r 1p h
p9 2:1
b
¦
$ 01 01 0 1 01 % Pa
0 ct? t? t? − P b 7 r b r
8 ct? 1 t? Pc ¦ = = = u"t?# 017 r b
"0#
where P9 is unity b
Pa"t#
Pb"T#
r 10 1h vr
01 0 1
0 0 0− 0 1 e 3T −0 1T T2:1 1
T
Pc"T# −
e0− 3T1 0
2:1
3 T
2:1
e03T1− 0
1p0:1 0 e rfc 1 T 1T0:1
0 1
t? t−r:c where c is the speed of light in free space and u"t?# is the Heaviside unit step function[ Once the response for the delta function is known\ the response corresponding to an arbitrary source current moment can be derived from the convolution theorem[ For the _eld calculations\ we employed the positive return stroke model of Cooray "0884#[ The basic concepts of this model are as follows[ The total charge brought to ground by the return stroke is initially stored on the corona sheath of the leader channel[ As the return stroke front surges upwards\ the corona sheath collapses drai! ning its charge into the highly conducting return stroke core[ Consequently\ each point of the leader channel was treated as a current source that injects a current into the return stroke[ Subsequently\ this corona current travels along the return stroke core to ground at the speed of light[ Since neither the temporal variation nor the spatial dependence of the corona current in positive return stro! kes is known\ their nature was inferred by appealing to the available experimental observations on positive return strokes and long sparks[ Measured current wav! eforms due to positive return strokes "Berger et al[\ 0864# have an initial fast rising portion that takes a few micro! seconds\ a relatively slow decaying part that takes some few tens of microseconds\ and a very slow varying sec! ondary peak that lasts for several hundred microseconds "return strokes with long continuing currents are not considered#[ Cooray "0884# considered this as evidence for the existence of three distinct regions in the corona sheath*a hot region "innermost region of the corona
C[ Gomes\ V[ Cooray:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 582Ð588
sheath# which is neutralised almost immediately by a {return stroke| like neutralisation process\ an inter! mediate region which is neutralised slowly by radial nega! tive streamers originating from the central core\ and a third region "outermost region of the corona sheath# which is neutralised very slowly by corona discharges and ion transport[ He represented the corona current generated by these three regions by three exponential functions with di}erent decay time constants[ The mag! nitudes of these time constants were evaluated by appeal! ing to experimental data on long sparks and comparing the model simulations with the observed properties of positive return strokes[ Since it is the charge and the time constants of the current component from the outermost sheath which are responsible for the amplitude and the duration of the slow tail "i[e[ the ELF component of the radiation _eld#\ we changed these parameters to get an exact _t to the slow tails of the measured positive return strokes[ For a given set of model parameters\ the vari! ation of the model simulated current moment as a func! tion of time was evaluated and that was combined with eqn "0# through the convolution theorem to calculate the distant ELF _eld "or LIFs#[ This procedure was repeated by changing the model parameters until a match was obtained between the model simulated and the measured LIFs[ In estimating this best _t it was necessary for us to pinpoint the location of the peak of LIF which\ some! times\ was oblique due to the various _ne structures superimposed on the _eld[ Thus\ there is some sub! jectivity involved in its estimation[
3[ Results and discussion The 15 ~ashes with LIFs used in this study were located between 399 km and 499 km from the measuring station\ with most of them clustering around 349 km[ Hence\ in the calculations we considered r 349\999 m for all of these ~ashes[ This choice does not in~uence the calculated peak LICs and the corresponding charge transport by more than 4)[ Several examples of the measured and the model simu! lated LIFs together with the corresponding positive return stroke current waveforms are depicted in Figs 1Ð 3[ In the calculations\ we did not attempt to simulate the VLF component of the _eld "i[e[ the initial peak# because eqn "0# is valid only in the ELF region[ Therefore\ the model parameters that in~uence the VLF component including the initial peak were not changed from one example to another[ This is the reason why the initial peak of the calculated current waveform does not change from one example to another[ By integrating these cur! rent waveforms\ we estimated the total charge component that was brought down to ground during the _rst 2 ms of these return strokes[ In this estimation\ however\ we excluded the _rst 099 ms\ which includes the initial peak[
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Our analysis shows that the charge transported during this time to ground does not exceed about 4 C[ We have also calculated the electric _elds generated by these return strokes at 0999\ 2999 and 4999 km[ Several examples of such _eld signatures are shown in Figs 1Ð3[ As described later\ these calculations made it possible for us to compare our results with some of those available in the literature[ In Table 0\ we have tabulated the values of various measured and calculated parameters such as the initial peak of the measured _eld "Ein#\ the peak of the LIF "Eim#\ the time from the initial peak to the peak of LIF peak "T0#\ the time from the initial peak to the zero!crossing of the LIF "T1# and the charge transported to ground by the LIC for the 15 return strokes "these parameters are shown in Fig[ 0#[ In addition\ the peak values of the LIFs at 0999\ 2999 and 4999 km "Exxxx#\ together with the peak value of the magnetic _eld of the LIFs at 4999 km "M4999#\ are also given in this table[ The last row of the table gives the mean value of these various parameters[ The mean charge lowered during the _rst 2 ms after the initial peak is 49 C\ whereas the mean of the peak LIC "Iim# is 27[1 kA[ The mean duration of the LIF "T1# is 0[13 ms and the mean rise time "T0# of that is 9[21 ms[ In seven ~ashes the Eim ] Ein ratio was equal to or more than 49)\ while the mean of this value is 30)[ Note that\ in the case of the initial peak of the measured _eld "Ein#\ propagation e}ects have not been taken into account\ in the given values[ For the initial peak of nega! tive return strokes\ the propagation of 349 km\ over land of conductivity 9[990Ð9[994 S:m\ will result in a reduction in amplitude of 19Ð29) "Cooray\ 0876#[ The estimated electric _eld at 4999 km "E4999# has a mean amplitude of 05 mV:m while the horizontal mag! netic _eld\ calculated by assuming the _elds to be radi! ation _elds\ at the same distance "M4999# has a mean peak value of 41 pT[ The full!width of the LIF at this distance is 4Ð09 ms[ We have made this calculation in order to compare our results with those of Boccippio et al[ "0884# which are pertinent to red sprites[ They have observed that most of the red sprites occur subsequent to positive return strokes\ which are associated with Q!burst events in the ELF Schumann resonance band[ The amplitudes of the Q!bursts which they measured at about 4999 km from the mesoscale convective systems which initiated red sprites are in the same range as of our estimation[ With these results\ we may conclude that all or some of the 15 positive return strokes we have considered in this study\ are associated with subsequent red sprites[ Figure 4 shows the estimated magnetic _elds of the 15 ~ashes at 4999 km as a function of the charge brought to ground by the corresponding LICs[ The values of these magnetic _elds are comparable to the peak values of Q!bursts associated with positive return strokes that gave rise to red sprites at similar distances "Boccippio et al[\ 0884#[ The authors of the last reference found that most of the positive return strokes with initial peak currents larger
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Fig[ 1[ Flash no[ P959685[00[ "a# Measured electric _eld "0# and calculated _eld "1# ^ "b# channel base current that was employed to calculate the _eld ^ "c# calculated _eld at 0999 km "0# and calculated _eld at 2999 km "1# ^ "d# calculated _eld at 4999 km[
Fig[ 2[ Flash no[ P959685[06[ "a# Measured electric _eld "0# and calculated _eld "1# ^ "b# channel base current that was employed to calculate the _eld ^ "c# calculated _eld at 0999 km "0# and calculated _eld at 2999 km "1# ^ "d# calculated _eld at 4999 km[
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Fig[ 3[ Flash no[ P959685[31[ "a# Measured electric _eld "0# and calculated _eld "1# ^ "b# channel base current that was employed to calculate the _eld ^ "c# calculated _eld at 0999 km "0# and calculated _eld at 2999 km "1# ^ "d# calculated _eld at 4999 km[
than a certain threshold gave rise to red sprites[ Since their peak current estimation was based on the initial peak of radiation _elds\ their results indicate that positive return strokes generating radiation _eld peaks larger than a certain threshold are capable of generating red sprites[ However\ Fig[ 5 shows the relationship between the initial peak of the radiation _eld and the amplitude of the LIF of the measured electric _elds[ The two parameters are approximately linearly correlated[ Thus\ one can expect the peak amplitude of the LIC to increase linearly with the initial return stroke peak current of positive return strokes[ Since the peak of LIC increases almost linearly with the charge brought to ground by the LIC "Fig[ 6#\ it is reasonable to expect a linear correlation between the initial peak current and the total charge brought to ground by the LIC[ If this is true\ the results of Boccippio et al[ "0884# suggest that red sprites are generated by positive return strokes with LICs that transport charge magnitudes larger than a certain threshold[ This sugges! tion is further strengthened by the fact that the estimated duration of the LICs is about a few milliseconds and the red sprites are generated within 1Ð2 ms after the initiation of positive return strokes[ The results of this study further support the concept originally set forth by Wilson "0845# for the mechanism of the triggering of sprites\ in which the rapid removal of a large positive charge from a vertically extensive charge layer stresses the mesosphere to dielectric breakdown[
The long impulse _eld is rarely observed in connection with negative return strokes at the same range of distances[ In the 31 negative cloud!to!ground ~ashes which we recorded on the same day\ there were merely three _eld traces in which the LIF is detectable[ In these cases too\ the amplitude and the duration of the LIFs are much less than those of its counterpart in positive return strokes[ This fact further con_rms that the presence of a dominant long impulse current of a cloud!to!ground ~ash is an essential ingredient for the onset of a subsequent red sprite[ It is also obvious why ionospheric lightning is predominantly associated with positive return strokes but not with negative return strokes[
4[ Conclusions A large fraction of the positive cloud!to!ground ~ashes observed in Sweden lowers a considerable amount of charge to ground through a long impulse current "LIC# which lasts for about 9[4Ð2[9 ms[ the mean of the long impulse _eld "LIF# peak is more than 39) of the initial _eld peak of the return stroke[ the peak magnetic _elds observed at distances of about 4999 km from positive lightning ~ashes\ which were associated with red sprites\ are comparable with the peak magnetic _elds due to these LICs that we have calculated for the above 15 ~ashes[
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Table 0 Statistics of the _elds and currents due to the 15 positive return strokes
Flash ID
Charge "C#
Iim "kA#
Ein "V:m#
Eim "V:m#
Eim:Ein ")#
T0 "ms#
T1 "ms#
E0999 "mV:m#
E2999 "mV:m#
E4999 "mV:m#
M4999 "pT#
P959685[00 P959685[06 P959685[10 P959685[13 P959685[16 P959685[17 P959685[18 P959685[20 P959685[21 P959685[22 P959685[24 P959685[25 P959685[28 P959685[31 P959685[35 P959685[36 P959685[45 P959685[50 P959685[52 P959685[54 P959685[55 P959685[57 P959685[61 P959685[62 P959685[63 P959685[72 Mean
013 89 13 23 43 23 35 49 33 23 37 35 15 83 53 41 29 55 69 13 37 11 41 49 29 31 49
097[7 59[7 10[1 04[9 25[7 29[1 45[5 49[1 11[3 06[1 18[9 18[9 02[7 39[5 33[5 55[9 33[5 53[7 36[7 10[1 28[9 00[1 34[9 13[9 12[1 18[5 27[1
×6[5 5[3 1[5 0[3 2[3 2[5 4[1 6[1 1[3 2[5 1[5 1[9 0[3 2[7 3[7 5[1 1[3 4[5 3[9 2[9 4[9 1[5 3[5 2[1 2[9 1[3 3[9
3[7 1[5 0[9 9[5 0[2 0[5 2[1 1[1 0[9 9[5 0[1 0[1 9[5 0[1 0[7 2[5 9[7 2[9 1[9 0[9 0[7 9[3 1[9 9[7 0[9 0[1 0[5
³52 30 28 32 27 33 51 20 31 06 35 59 32 21 27 47 22 43 49 22 25 04 33 14 22 49 30
9[20 9[24 9[20 9[31 9[24 9[10 9[10 9[17 9[23 9[21 9[28 9[27 9[33 9[59 9[22 9[08 9[29 9[18 9[22 9[19 9[18 9[36 9[15 9[30 9[19 9[17 9[21
9[87 0[23 9[76 0[14 0[19 9[72 9[71 9[74 0[20 0[11 0[35 0[34 0[24 1[64 0[33 9[62 0[29 9[85 0[30 9[81 0[09 0[59 0[91 0[42 0[11 0[29 0[13
832 419 081 013 181 174 412 336 089 035 134 134 006 181 279 480 070 455 398 081 231 82 284 086 101 143 211
041 89 17 14 38 27 53 54 24 15 33 33 11 58 53 62 18 74 69 17 43 07 50 28 29 31 41
31 17 8 7 04 09 06 07 01 8 03 03 6 15 08 08 8 13 11 8 05 5 06 02 8 02 05
039 82 29 16 49 22 46 59 39 29 36 36 12 76 52 52 29 79 62 29 42 19 46 32 29 32 41
Iin ] Amplitude of the calculated long impulse current[ Ein ] amplitude of the initial peak ^ Eim ] amplitude of the impulse _eld ^ T0 ] time duration from the initial peak to the peak of the impulse _eld ^ T1 ] time duration from the initial peak to the zero!crossing time of the impulse _eld ^ E0999\ E2999\ E4999 ] calculated _elds due to the long impulse currents at 0999 km\ 2999 km and 4999 km respectively ^ M4999 ] calculated magnetic _eld at 4999 km[
Fig[ 4[ Correlation between the amplitude of the estimated mag! netic _elds at 4999 km and charge lowered by the LIC[
Fig[ 5[ Correlation between the amplitude of the LIF and initial peak of the measured _elds[ "Note that the propagation e}ects have not been taken into account in the case of the values of the initial peaks of the measured _elds[#
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Institute of High voltage Research[ The authors thank Prof[ Viktor Scuka for placing excellent research facilities at their disposal and Dr R[ Thottappillil for fruitful dis! cussions[ The comments made by Prof[ Alexander P[ Nickolaenko "one of the referees# helped us to improve the _nal version of the manuscript[ Financial assistance given by the IPPS of the International Science Programs\ Uppsala University\ and the Swedish Natural Science Foundation is gratefully acknowledged[ References
Fig[ 6[ Correlation between the peak LIC and the charge lowered by LIC[
Hence\ we conclude that the observed Q!bursts\ which coincide with the occurrence of red sprites\ are due to the long impulse currents of positive return strokes[ The LIC is very rarely observed in the _elds generated by negative cloud!to!ground lightning observed in Sweden[ This may be the reason it is that ionospheric lightning is pre! dominantly associated with positive return strokes but not with negative return strokes[ Acknowledgements The research work reported here was conducted within the framework of the lightning research program at the
Berger\ K[\ Anderson\ R[B[\ Kroninger\ H[\ 0864[ Parameters of lightning ~ashes[ Electra 79\ 12Ð64[ Boccippio\ D[J[\ Williams\ E[R[\ Heckman\ S[T[\ Lyons\ W[A[\ Baker\ I[T[\ Boldi\ R[\ 0884[ Sprites\ Q!bursts and positive ground ~ashes[ Science 158\ 0977Ð0980[ Burke\ C[P[\ Jones\ D[L[L[\ 0885[ On the polarity and continuing current in unusually large lightning ~ashes deduced from ELF events[ J[ Atmos[ Terr[ Phys[ 47\ 420Ð439[ Cooray\ V[\ 0876[ E}ects of propagation on the return stroke radiation _elds[ Radio Sci[ 11\ 646Ð657[ Cooray\ V[\ Lundquist\ S[\ 0871[ On the characteristics of some radiation _elds from lightning and their possible origin in positive ground ~ashes[ J[ Geophys[ Res[ 76 00\192Ð00\103[ Cooray\ V[\ Perez\ H[\ 0883[ Some features of lightning ~ashes observed in Sweden[ J[ Geophys[ Res[ 88\ 09\530Ð09\541[ Cooray\ V[\ 0884[ A model for positive return strokes[ Inst[ Phys[ Conf[ Ser[ No[ 032[ Wait\ J[ R[\ 0859[ On the theory of the slowtail portion of atmospheric wage forms[ J[ Geophys[ Res[ 54\ 0825Ð0835[ Wilson\ C[T[R[\ 0845[ A theory of thundercloud electricity[ Proc[ Roy[ Soc[ "A#\ 186Ð206[