Journal of Atmospheric and Solar-Terrestrial Physicspeople.ee.duke.edu/~cummer/reprints/224_Lu18_JASTP_RocketTrig… · the indirect measurement of lightning currents with the B-dot

Measurement of continuing charge transfer in rocket-triggered lightning

with low-frequency

magnetic sensor at

close range

Gaopeng Lu a, c, d, *, Yanfeng Fan b, Hongbo Zhang a, Rubin Jiang a, d, Mingyuan Liu a,

Xiushu Qie a , d, Steven

A. Cummer e ,

Congzheng Han a, f, Kun Liu a, f

aKey

Laboratory of Middle Atmosphere and Global Environment Observa tion, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100029, China

bState Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, 100081, China

cState Key Laboratory of Numerical Mode ling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG) , Institute of Atmospheric Physics, Chinese Academy of

Sciences, Beijing, 100029, China

dCollaborative Innovation Center on Forecast and Evaluatio n of Meteorological

Disasters, Nanjing University of Information Science and Technology, Nanjing, Jiangsu,

210044, China

eElectrical and Computer Engineering Department, Duke University, Durham, NC, 27606, United States

fChengdu University of Information and Technology, Institute

of Electronic Engineering, Chengdu, Sichuan 610225, China

A R T I C L E

I N F O

Keywords:

Initial continuous current

Long continuing current

Rocket-and-wire triggered

lightning

Low-frequency magnetic sensor

A B S T R A C T

Based on the magnetic elds recorded with a compact low-frequency (LF) magnetic sensor deployed at 78 mfi

distance from the channel base, we reconstruct the time-resolved current waveform for the continuously dis-

charging processes

in classical rocket-and-wire triggered lightning ashes, including the initial continuous currentfl

(ICC) and long continuing current. Both the overall feature and the millisecond-scale slow variations (e.g.,

initial

current variation, ICC pulses and -components)

embedded in the channel-base current as measur ed with theM

conventional methods (such as the shunt

or Pearson coil) can be retrieved through

the numerical integral of close

LF magnetic signals. Despite the artifact caused by the magnetic elds radiated by the fast in-cloud processes, thefi

new approach has the advantage of

signi cantly reduced noise in

compariso n with the measurements of con-fi

ventional methods, and it is likely applicable to remotely measure the initial continuous current in upward

lightning from high objects and altitude-triggered lightning, as well as long continuing current in natural cloud-to-

ground (CG) lightning strokes that

occur at

suf ciently close range (e.g., within 100 m).fi

1. Introduction

During the classical rocket-and-wire triggered lightning where a

grounded metallic wire is unreeled from an ascending rocket (Newman

et al., 1967 Fieux et al., 1975 Fisher et al.,

1993 Lalande et al., 1998; ; ; ;

Zheng et al., 2013), when the upward leader (usually of positive polarity)

initiated from the wire undergoes a sustained development, the trig-

gering wire becomes a conduit where the electrical charge is

continu-

ously transported from the in-cloud reservoir to ground, forming a

characteristic process

called the initial continuous current (ICC) (Wang

et al., 1999). With typical amplitude of 20 300 A and a relatively long–

duration (typically longer than 100 ms), the ICC is usually responsible for

the major charge transfer in rocket-triggered lightning, and the total

charge transported by ICCs ranges between a few C and over 100

C

( ; ). It has been observed that the ICCHubert et al., 1984 Wang et al., 1999

is also present in altitude-triggered lightning (where the lower portion of

metallic wire is replaced with a nylon wire) (e.g., ) andZheng et al., 2013

upward lightning from tall objects (e.g., ;Miki et al., 2005 Diendorfer

et al., 2009 Zhou et

al., 2011; ).

In the rocket-triggered lightning experiment,

the ICC can be

directly

measured by applying a shunt (or a current transformer, such as Pearson

coil) installed

at the channel base (e.g., ;Wang et al., 1999 Biagi et al.,

2009 Yoshida et

al., 2010 Qie et al., 2011; ; ), which makes it possible to

precisely quantify the charge transfer from the thundercloud to ground.

However, one major problem is that the channel-base current spans a

wide dynamic range (from a few A

for the initial current pulses to tens of

kA for the return strokes) so that the conventional measurement is usu-

ally set with a bias toward the return strokes typically with peak

current

* Corresponding author. Key Laboratory of Middle Atmosphere and Global Environment Observation, Institute of Atmospheric Physics, Chinese Academy of Sci-

ences, Beijing 100029, China.

E-mail address: [email protected] (G. Lu).

Contents

lists available at ScienceDirect

Journal of Atmospheric and Solar-Terrestrial Physics

journal homepage:

www.elsevier.com/locate/jastp

https://doi.org/10.1016/j.jastp.2018.02.0 10

Received 10 November 2017; Received in revised form 8 February 2018; Accepted 25

February 2018

Available online 18 May 2018

1364-6826/ 2018 Published by Elsevier Ltd.©

Journal of Atmospheric and Solar-Terrestrial Physics 175 (2018) 76 86–

in excess of 10 kA (e.g., ; ), and thus weakYang et al., 2010 Lu et al., 2014

current pulses during the initial stage of

triggered lightning and small

variations superimposed on the initial

continuous current usually cannot

be precisely measured.

Also, for the current measurement with either shunt or Pearson coil, it

is required that the current ows along the desired path to groundfl

(usually the lightning rod that is grounded). Therefore, for the altitude-

triggered lightning where the triggering wire is not grounded and thus

the lightning charge transfer usually does not follow the lightning rod

( ; ; ), or upwardPinto et al., 2005 Saba et al., 2005 Zheng et al., 2013

lightning from high objects with a complicated grounding structure (e.g.,

Miki et al., 2005 Zhou et al., 2011 Lu et al., 2013 Wang et al., 2016; ; ; ), the

measurement of channel-base current requires substantially more efforts.

Therefore, the new technique is desired to improve the capability to

quantitatively measure the

initial continuous current in situations where

the lightning current ows through an unexpected strike point, such asfl

the indirect measurement of lightning currents with the -dot sensor asB

described by .Romero et al. (2012)

In this paper, we applied the method described by Fan et al. (2017b)

to reconstruct the current waveform of continuously discharging pro-

cesses in rocket-triggered lightning by measuring the

low-frequency (LF)

magnetic elds with a compact sensor deployed at 78 m distance fromfi

the channel base. These processes include the ICC present in nearly all

the rocket-triggered lightning, and the long continuing current that is

essentially the same as that in

the natural

cloud-to-ground (CG) lightning

strokes. The numerical integral of magnetic signals recorded at close

range is applied to retrieve the

time-resolved waveform of long

continuing current as measured by a

shunt at the channel base. One

prominent advantage of this method, in

addition to its portability to

implement and the wide range of deployment, is that the background

noise in the retrieved

current waveform is considerably reduced so that

the relatively slow

variations (such as -components with timescalesM

typically longer than 200 μs) as weak as a few hundred mA can be readily

resolved.

2. Measurement and data

The measurements examined in this

paper

were conducted during the

SHandong Arti cially Triggered Lightning Experiment (SHATLE) infi

summer of 2014 ( ). As shown in a, two magneticQie et al., 2011 Fig. 1

sensors

were deployed at distances of 78 m (on the roof of control room)

and 970 m (at

the main observation building), respectively, from the

lightning triggering site. The two induction coils of magnetic sensor

(made of one layer of solenoid varnished copper wire

winding around a

ferrite

rod with 1-cm diameter and 20-cm length) at 78 m range were

oriented in azimuthal and vertical direction (relative to

the lightning

channel), respectively; the

coils

of magnetic sensor at the main obser-

vation site were

oriented in north-south and east-west direction,

respectively. The channel-base current of classical rocket-triggered

lightning was measured

with both a

5-m shunt (with bandwidth ofΩ

0 3.2 MHz) and a Pearson

coil (with bandwidth of 0.9 Hz 1.5 MHz),– –

which have different measurement ranges of 8 A to 2 kA and 40 A to

30 kA, respectively.

The frequency response measured in the laboratory for the magnetic

sensors

used

in the observation, including the induction coil and ampli-

fying circuit, is plotted in b (e.g., ); the phaseFig. 1 Fan et al., 2017b

response of

sensor has not been quanti ed yet. The

3-dB bandwidth offi

the magnetic sensor is 6 330 kHz, and the sensor behaves roughly as a–

d /d sensor below 6 kHz. Therefore, the relatively fast processes withB t

time scales shorter than 100 μs in the triggered lightning (such as, leader

stepping, process, and return stroke) are mainly characterized by theK

B-sensor part; the relatively slow processes with time scales longer than

1

ms, such as continuing current (tens to hundreds of milliseconds)

( ;

; ), initialWilliams and Brook, 1963 Fisher

et al., 1993 Miki et

al., 2005

magnetic sensor is relatively high (e.g., ), the measurementLu et al.,

2016

data recorded in summer of 2014 is subject to a saturation for fast

magnetic pulses (e.g., with timescales less than 100 μs) with magnitude

greater than approximately 65 nT. In this paper, we mainly present the

results for two rocket-triggered lightning ashes

on August 18 andfl

August 23, respectively.

Fig. 2a shows the channel-base current measured for the triggered

lightning at 04:17:18 UTC on August 18 (the snapshot image of this event

is shown in the inset of

a), which was relatively complicated byFig. 1

comprising six

subsequent strokes with peak current ranging between

2 kA and 18 kA. As the channel-base current for

this event spans a broad

range from

~10 A to 20 kA, we plot

the time-resolved current waveform

in logarithmic scale by combining the measurements of channel-base

current with shunt and Pearson coil, respectively (namely replacing the

saturated portion

of shunt measurement with the Personal coil mea-

surement during the

same time period). It can be clearly seen that the

noise level of channel-base current measured during the SHATLE mea-

surement is about 8 A. The rst long excursion of ~230 ms duration wasfi

the initial continuous current (ICC) typical to classical rocket-triggered

lightning, which transferred a total of 18.4 C negative charge to

ground; the second long excursion

of ~260 ms after the sixth stroke was

caused by a long continuing current superposed with several millisecond-

Fig. 1.

(a) Sketch of magnetic eld measurements during the SHandong Arti-fi

ficial Triggered Lightning Experiment (SHATLE) during summer of 2014. (b)

Frequency response of the low-frequency magnetic eld sensor from the cali-fi

bration in the laboratory, showing that the magnetic sensor works as

a sensorB

between 6 kHz

and 340 kHz, and approximately as a dB/dt sensor below 6 kHz.

G. Lu et al. Journal of Atmospheric and Solar-Terrestrial Physics 175 (2018) 76 86–

( ;

; ), initialWilliams and Brook, 1963 Fisher

et al., 1993 Miki et

al., 2005current and -component (typically longer than 2 ms) ( ),M Qie et al., 2014are primarily measured by the d /dt portion. As the sensitivity of ourB

scale variations called -components (e.g., ;M Rakov et al., 1995 Thottap-pillil et al., 1995 Campos et al., 2007; ),

similar to a triggered lightning

77

Fig. 2.

(a) Time-reso lved current waveform (absolute value in

the logarithmic scale) combined from the measurement with

shunt

and Pearson coil for the triggered lightning at 04:17:18

UTC on August

18, 2014, which contained the initial contin-

uous c urrent and six subsequent strokes, with the last stroke

followed by

a long continuing

current. (b) Time-resolved

current

waveform (absolute value in logarithmic scale)

measured with a 5-m shunt at the channel base for theΩ

rocket-triggered lightning at 16:29:52 UTC on August 23,

2014,

which only contained the initial continuous current. We

can see that the noise level of channel-base current is

approximately 8

A.


Fig. 3. Channel-base current

(panel a) and magnetic elds (panels b and c for 78

m and 970 m distance, respectively) measured for the initial continuous currentfi

during the triggered lightning

ash at 04:17:18 UTC on August 18, 2014.fl

78

flash examined by .Zhou et al. (2013)

The initial continuous current shown

in a, as the only case ac-Fig. 2

quired during the summer campaign in 2014 without saturation in the

magnetic eld recorded at 78 m range, has been

examined byfi Fan et al.

(2017b) to describe the method to reconstruct the time-resolved current

from the close magnetic

eld. In some cases, the saturated magneticfi

signal can be retrieved with the signal of vertical coil ( ),Fan et al., 2017b

but

this method is not applicable to all cases. Hence, it remains desirable

to reduce the gain

of magnetic sensor in the future measurement. In this

paper, we analyze a different case shown in

b (with saturation in theFig. 2

recorded magnetic eld during

the initial current variation, see b)fi Fig. 6

for

a triggered lightning ash that only contained an ICC lasting aboutfl

350 ms, over which there

were several variations and the total charge

transfer accumulated to 46.3 C. Moreover, the long continuing current

in a will also be examined

to

demonstrate the possible applicationFig. 2

of our method to reconstruct the current waveform for long continuing

current in natural lightning strokes that happen to strike the ground at

close range.

3. Method and evaluation

The case of triggered lightning analyzed by isFan et al. (2017b)

revisited here to describe the method to reconstruct the current along the

triggered lightning channel from

close magnetic measurement. aFig. 3

shows the time-resolved current waveform recorded for the initial

continuous current (ICC) of triggered lightning at 04:17:18 UTC

on

August 18, including the initial current pulses associated with the

inception of a sustained upward positive leader when the rocket reached

an altitude of 245 m (above the ground level, AGL). The subsequent

variation (referred to as

initial current variation, ICV) lasting ~20 ms is

typical to classical rocket-triggered lightning, which is linked to the

disintegration of triggering wire and the following reestablishment

of

lightning current ( ; ). The abruptWang et al., 1999 Rakov et al., 2003

enhancement of current near the end of initial continuous current (at

about 18.99 s) was an ICC pulse with a relatively

long timescale (~8 ms).

The total charge transfer during the initial continuous current was about

18.5 C.

The low-frequency magnetic elds recorded at 78 m and 970 m dis-fi

tance are plotted in b and c, respectively. As shown in the gures,Fig. 3 fi

the magnetic elds of initial

current pulses are particularly clear in thefi

signals recorded at 78 m range. These magnetic

eld pulses were inves-fi

tigated by , and they can

be best simulated as the radia-Lu et al. (2016)

tion from the downward propagation of current pulse generated at the

upper end of the ascending metallic wire ( ).Fan et al., 2017a

The initial current variation is rather complicated in this case, so as

the corresponding magnetic elds acquired at 78 m range. showsfi Fig. 4

the current waveform

of ICV ( a) and associated magnetic eldsFig. 4 fi

recorded at 78 m ( b) and 970 m ( c), respectively. The mag-Fig. 4 Fig. 4

netic signals recorded at two different distances are signi cantlyfi

different. The magnetic eld measured at 78 m range mainly exhibitsfi

millisecond-scale variations throughout the duration of ICV, while the

magnetic eld recorded at 970 m range exhibits a burst of fast pulsesfi

mainly during the early stage of ICV. This burst of magnetic pulses could

be

attributed to the step-like progression

of positive leader (Lu et al.,

2014), and it has been shown that these magnetic pulses are radiated

in

the vicinity of ascending positive

leader ( ).Zheng et al., 2018

During the rocket-triggered lightning

experiment at SHATLE, the

triggering wire usually has been unreeled over 100 m when the upward

positive leader becomes successful to launch the sequence of

initial

current pulses ( ; ). Before the ICC becomesLu et al., 2016 Fan

et al., 2017a

discernible (typically a

few ms after the inception of positive leader) in

the current measured at the channel base, the positive leader still pro-

gresses upward at a speed varying widely in the range of 2 104 m/s

to

2.1 105 m/s ( ; ). Consequently, for aBiagi et al., 2009 Jiang et al., 2013

vertical current ow with timescales longer than 1 ms, the magnetic eldfl fi

at 78 m range from the channel base is related to the current through the

Biot-Savart law. Based on the computation of magnetic eld radiated byfi

the current ow along the lightning channel, showedfl Fan et al. (2017b)


Fig. 4. Channel-base current (panel a) and magnetic elds (panels b and c for 78 m and 970 m distance, respectively) measured for the initial current variation (ICV)fi

of the triggered lightning at 04:17:18 UTC on August 18, 2014.

79

that for current pulses

with

characteristics timescales 1 ms, the current

waveform along the lightning path can be reconstructed by numerically

integrating the magnetic signal recorded at 78 m range, i.e.,

' 0

d

d 'd ' (1)

where is the conversion coef cient

at time (which does

not vary(t) fi t

considerably with time when the channel length is more than 200 m),

and is the magnetic eld measured at 78 m range. The exact value ofB fi

should depend on the distance from the channel base, while it is

also

affected by many factors present in the eld experiment that are dif cultfi fi

to be considered in a

theoretical derivation. Therefore, in our work, we

determine the value of by comparing the measured channel-base cur-

rent and the numerical integral result of

close magnetic eld; for the vefi fi

cases of rocket-triggered lightning in SHATLE during 2014, there is

~0.00195 0.00005 A/nT ( ). Generally speaking, theFan

et al., 2017b

magnetic signal acquired by the sensor contains measurement noise

(from both data acquisition device and background), but the numerical

integral of this term typically goes to zero. Also, the DC offset in the

magnetic measurement is appropriately removed before the numerical

integral.

The waveform

of channel current retrieved from

the magnetic eldfi

shown in b using the

numerical integral described above is plottedFig.

3

in a. The major features present in the shunt measurement,Fig. 5

including all the millisecond-scale variations around the time with

abundant

de ections in the current

waveform,

are present in thefl

retrieved current waveform. The good consistency between the retrieved

current waveform and the measured channel-base current is largely

caused by that the ICC is mainly composed of

charge transfer processes

with time scales longer than 1 ms. The initial current pulses are not

retrieved as these pulses are of microsecond scale; for the impulsive

current pulses with relatively short time scales (e.g., 10 μs for the initial

current pulses), there is an approximately linear correlation between

channel-base current and magnetic eld measured with our sensor atfi

78 m distance ( ). As the initial current pulses do

notLu et al., 2016

contribute considerably to charge transfer, the total charge transfer

during the initial continuous current calculated from the retrieved cur-

rent waveform (about 18.45 C) is in good

agreement with the

measurement.

To quantitatively demonstrate that the noise level in the channel

current retrieved from the numerical integral of close magnetic eldfi

measurement is substantially reduced in comparison with the direct

channel-base current measurement, we performed the Fourier transform

of retrieved current waveform (e.g., ). Note that theRomero et al., 2012

numerical integral is also

applied to the component above 6 kHz,

and

therefore we need to compensate by dividing the result of Fourier

transform with the following factor

1

1 2j 6000(2)

As shown in b,

the result of Fourier transform

for the retrievedFig. 5

current waveform indicates that the reconstructed waveform is generally

consistent with the measurement below about 6 kHz. The at partfl

beginning approximately at 30 kHz is

from the background noise.

Therefore, from a technical perspective, the noise oor in the channel-fl

based

current retrieved from close magnetic eld is only about 1/10 offi

that for the

measurement with a shunt (namely the close magnetic eldfi

measurement can be used to detect the slow current variation as weak as

a few hundred mA).

We also applied the method described above to the magnetic eldsfi

measured at 970 m range, and the channel current cannot be recon-

structed with good consistency. The reason is that at a distance compa-

rable to or larger than the

vertical scale of lightning channel (about

several

hundred meters), in addition to the magnetic

eld from thefi

current along the vertical lightning channel, the magnetic signal received

by the sensor also contains a

signi cant portion of radiation eld fromfi fi

the in-cloud processes, such as -processes (as

shown in ).K Fig. 3


Fig. 5. (a) Waveform of

initial continuous current reconstructed from the low-frequency magnetic eld recorded at 78 m distance from the channel base. (b)

Fourierfi

transform of channel-base current from the measurement with

a shunt (black line) and the current waveform reconstructed from the integral of close magnetic eldfi

(blue line). (For interpretation of the references to color in this gure legend, the

reader is referred to the Web version of this article.)fi

80

Nevertheless, further theoretical and experimental studies are desired to

determine the range within which the method proposed in this paper is

applicable to reconstruct the channel-base current

waveform. As

mentioned earlier in this section, the magnetic eld measured at 970 mfi

distance from the channel distance is dominated by the radiation from

the in-cloud processes. For the magnetic eld measured at 970 m range,fi

the signal contains more de ections caused by

fast discharges.fl

4. Measurement of initial continuous current

In this section, we apply the method described above to reconstruct

the 350-ms long initial

continuous current shown in b. As shown inFig. 2

Fig. 6b, the magnetic signal recorded at 78 m distance is subject to

saturation for some part associated with the portion of initial continuous

current with magnitude up to about 2100 A. Therefore, we only analyze

the current measurement without saturated magnetic signals in associ-

ation. During the ICC, there are several distinct enhancements, including

the major current surge starting at about 52.65 s.

4.1. Reconstructed current waveform

With the method described in section , we numerically

integrate the3

current waveform (for the same time interval) measured at the channel

Fig. 6.

Measurement for the rocket-triggered lightning at 16:29:52 UTC on August 23, 2014: (a) the channel-base current measured with a 5-m shunt; and (b) theΩ

low-frequency (LF) magnetic eld measured at 78 m distance from the channel base. The magnetic

measurement is saturated at the interval (during the

initial currentfi

variation) marked by the thick gray line.

Fig. 7. Comparison between the shunt measurement of initial continuous cur-

rent and the current waveform reconstructed from the LF magnetic eld at 78 mfi

distance for the triggered lightning

at 16:29:52 UTC on

August 23, 2014. The

red color marks the segment of channel-base current

that is not reconstructed

due to the saturation of magnetic

signal measured at 78 m range. (For

inter-

pretation of the references to color in this gure legend, the reader is referred tofi

the Web version of this article.)


close magnetic elds recorded at 78 m range to reconstruct the currentfiwaveform along the lightning channel. For the convenience of

compar-

ison, we add an appropriate offset to the retrieved current waveform

shown in (and also for other retrieved current waveforms shown inFig. 7

this paper).

In general, the current waveform can be retrieved with fairly

good consistency with the channel-base current recorded with shunt,

including all the small millisecond-scale variations. During the initial

continuous current, the lightning channel remains illuminated and the

conductivity of lightning channel is very high (on the order of 10 4 s/m)

( ), and there

is no considerable attenuation

in the currentRakov, 1998

along lightning channel. Therefore, the current along the triggered

lightning channel should be almost equal to

the channel-base current as

measured by the shunt.

We also calculate the total charge transfer during the time interval of

numerical integral, which is 44.5 C according to the shunt measure-

ment, in good agreement with that (also 44.5 C) calculated with the

current waveform (for the same time interval) measured at the channelbase.

In the following section

,

we will examine the channel current4.2

waveform reconstructed for two major ICC variations indicated in Fig. 6

(as

ICC pulse and ICC pulse b, respectively).

4.2. Initial continuous current variations

We rst examine a large current pulse superposed on the ICC wave-fi

form that

appeared near 52.65 s in a (denoted as ICC pulse a). TheFig. 6

duration of this ICC variation pulse was longer than 10 ms, and it con-

tains multiple variations in the current waveform. a shows theFig. 8

magnetic signals recorded at 78 m distance from the channel base, and

we

can see that the initial part of this current pulse was superposed with a

long sequence of

microsecond-scale magnetic pulses, which could also be

observed in the magnetic eld recorded at 970 m (not shown).fi

81

As shown in b, the

current waveform reconstructed from theFig. 8

close magnetic eld is in excellent agreement with the measurement.fi

When we zoom in to

examine the reconstructed current waveform, we

can still identify some small

variations with amplitude of ~0.1 A that

might be associated with the aforementioned microsecond-scale mag-

netic pulses. However, since the current variation on this

magnitude

could not be identi ed from the measured channel-base current, wefi

cannot conclude whether the reconstructed small variations

are artifacts.

Figure 9 shows the current waveform reconstructed for another ICC

pulse at about 52.773 s in a (indicated as ICC pulse b). As shown inFig. 6

Fig. 8a, the magnetic eld recorded at 78 m distance exhibits a fast pulsefi

around the onset of the current enhancement, which is

similar to a case

examined

by , ). However, in our case examinedFan et al. (2017b Fig. 8

here, the

polarity of magnetic pulse appears to

be opposite to that asso-

ciated with ensuing current pulse. The presence of fast magnetic pulse in

the numerical integral of close

magnetic eld causes an artifact in thefi

reconstructed current waveform. Other than that, the general features,

including the rise time and magnitude of enhancement, are correctly

obtained.

5. Measurement of long continuing current

In some rocket-triggered lightning ashes and also lightning to highfl

objects, one of the subsequent return strokes will be followed by a long

continuing current (e.g., , ). In this section, weZhou et al., 2011 2013

applied our method to the long continuing current (i.e., the second long

excursion of

~270 ms

in a) that followed the sixth return stroke ofFig. 2

triggered lightning at 04:17:19 UTC on August 18, 2014, demonstrating

the likelihood of using numerical integral of close magnetic

elds tofi

remotely detect long continuing current in natural CG strokes.

Fig. 8. Measurement for a large current variation during the initial continuing current: (a) the magnetic eld measured at 78 m distance; (b) current waveform (withfi

offset) reconstructed from

the numerical integral of magnetic eld recorded at 78 m range in comparison with the channel-base measurement .fi


Fig. 9. Measurement

for another current variation during the initial continuous current: (a)

magnetic eld recorded at 78 m

range; (b) time-resolved current measuredfi

at

the channel base in comparison with the current waveform (with offset) reconstructed

from the numerical integral of magnetic eld recor ded at 78 m range.fi

82

The channel-base current and broadband magnetic elds recorded atfi

78 m for the long continuing current are plotted in a and b,Fig. 9

respectively. As shown in the gure, there are several -componentsfi M

superimposed on the long continuing current (e.g., Thottappillil

et al.,

1995 Flache et al., 2008 Zhou et al., 2013; ; ), leading to

current surges

with magnitude up to 1 kA. The magnetic signal recorded at 78 m was

saturated at

the moments corresponding to the return stroke (with peak

current of 19 kA) and the largest -component that peaks at aboutM

1400 A.

5.1. Reconstructed current waveform

Due to the saturation of magnetic pulse driven by the relatively strong

M-component

(with current peaking at 1.4 kA) at about 19.237 s, we

processed the magnetic signals measured at 78 m distance in two sepa-

rated time intervals divided by the -component that caused the satu-M

ration. The current waveform retrieved from the numerical integral of

several

fast pulses superposed on a millisecond-scale pulse, including one

relatively large pulse around the onset of the -component, which isM

interpreted as a -change. Due to the presence of this fast pulse, there isK

an artifact in the retrieved current waveform for the -componentM

( b).Fig. 12

Fig. 13 shows the measurements for an -component with a rela-M

tively complicated waveform by consisting of

three consecutive current

pulses (e.g., ). As shown

in a, there is noZhou et al., 2013 Fig. 13

discernible magnetic signal associated with the onset of rst currentfi

pulse, while the second current pulse appears to be initiated by a fast

K -process, similar to the case shown in a. Therefore, the LFFig. 12

magnetic signal recorded at 78 m distance is interesting in that it in-

dicates the

physical process leading

to -component as well as the directM

measurement of current enhancement at the channel base due to the

charge transfer in the -component.M

6. Discussions and summary

Fig. 10. Channel-base current (panel a) and magnetic eld measured at 78 m range (panel b) during

the long continuing current of triggered lightning at 04:17:18fi

UTC on August 18, 2014.


ration. The current waveform retrieved from the numerical integral ofclose magnetic signals is shown in . Again, the reconstructedFig.

11current waveform (with a signi cantly reduced noise level) is in goodfi

agreement with the measurement, including all the -components.M

Our method makes it possible to remotely measure the time-resolved

waveform of continuing current in natural cloud-to-ground (CG) light-

ning for which the

stroke location is usually unpredictable and thus the

direct measurement of channel-base current

is almost impossible. How-

ever, it should be noted that the treatment of continuing current in

nat-

ural CG strokes could be more

complicated than that in the rocket-

triggered lightning as investigated here. First of all, the stroke channel

of natural lightning usually contains some tortuosity even for the lowest

portion above the ground. Moreover, a precise estimation of distance

from the stroke channel is challenging. Further analyses are desired to

explore

the feasibility to use the dB/dt sensor as an effective tool to

remotely measure the continuing

current in natural CG strokes.

5.2. M-components

The -component superimposed on the long continuing current canM

be well retrieved with our method. shows the reconstructionFig. 12

result for one -component that exhibits a relatively simple currentM

waveform. The magnetic eld recorded at 78 m distance ( a) showsfi Fig. 12

6. Discussions and summary

In this paper, we apply the method presented by toFan et al. (2017b)

reconstruct the channel current of rocket-triggered lightning on

the basis

of low-frequency magnetic elds recorded with a compact magneticfi

sensor at

78 m range. The main advantage

of this method to retrieve the

time-resolved current waveform with relatively long time

scale is that it

is a remote sensing approach that does

not require the current ow tofl

propagate through a desired location.

Provided that the magnetic sensor

is installed suf ciently close to the lightning channel, the currentfi

waveform could be

reconstructed through the numerical integral of

recorded magnetic signals.

This method is developed on the basis of two factors. First of all, the

noise present in

the magnetic eld measurement is of random distribu-fi

tion, and

the numerical integral of background

measurement almost goes

to zero. Therefore, the reconstructed current waveform is essentially

noiseless. Secondly, the main charge transfer contributing to the

continuing current usually has the time scale longer than 1 ms, and

therefore the associated lightning magnitude eld at 78 m range isfi

dominated by

the induction component ( ), which isFan et al., 2017b

approximately proportional to the current along the lightning channel.

In this paper, we examine both cases of initial continuous current

and

long continuing current with the close magnetic measurement. The same

83

Fig. 11. Comparison between the direct measurement of channel-base current and the current waveform (with offset) reconstructed from the magnetic eld recordedfi

at

78 m range for two segments of long

continuing current

separated by the largest -component (which caused the saturation of magnetic eld recorded at 78 mM fi

range) in a.Fig. 10


method has been applied by to the initial continuousFan

et al. (2017b)

current measured for other rocket-triggered lightning during summer of

2014, and

the

conversion coef cient is almost identical (with

variationfi

3%) for the lightning cases

at the

same range. Therefore, the recon-

struction result is reliable when the channel length is suf ciently longfi

(e.g., 200 m), and the moderate inclination

of lightning channel does

not considerably affect the conversion coef cient. This is very critical forfi

the practical application of this technique in the lightning measurement.

One drawback of our method is that the signals from in-cloud

processes

might cause some artifacts in the retrieved current waveform.

Our

method could also be applied to the altitude-triggered lightning

( ), where the lowest portion of triggering wire is nylonSaba et al., 2005

and thus the direct measurement of initial continuous current is almost

impossible. The measurement of altitude-triggered lightning has rarely

been reported except for a few cases where the downward leader

happened to strike the lightning rod (e.g., ). AlthoughZheng et al., 2013

Fig. 12. (a) Low-frequency magnetic signal recorded at 78 m distance from the channel base for an -component during the long continuing current of triggeredM

lightning at 04:17:18 UTC on August 18, 2014. (b) Time-resolved -component current measured at the channel base in comparison with the current waveform (withM

offset) retrieved from the numerical integral of magnetic signal shown in

panel a.

84

the actual stroke location is always displaced from the rod, the stroke

distance usually still satis es that assumption that

the inductionfi

component dominates the magnetic eld.fi

Also, the classical rocket-triggered lightning is similar to the upward

lightning initiated from tall buildings, where the ICC is also commonly

observed

( ; ). Although the situation isFlache et al., 2008 Zhou et

al., 2011

often

complicated

due to the actual geometry of structures, our method

is

probably suitable to remotely measure the initial continuous current of

upward lightning from tall buildings. As one step toward developing a

remote sensing method that is capable of

measuring continuing current

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Acknowledgment

This work was nancially supported by National Key Basic Researchfi

and Development Program (973) (2014CB441405), "The Hundred Tal-

ents Program" of Chinese Academy of Sciences (2013068), Natural

Sci-

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41605122). The data for the analyses in this paper are available upon

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Gaopeng Lu ( )[email protected]

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