Locating Parent Lightning Strokes of Sprites Observed over a Mesoscale Convective System in Shandong Province,China

Anjing HUANG,Gaopeng LU,Hongbo ZHANG,Feifan LIU,Yanfeng FAN,Baoyou ZHU,Jing YANG,and Zhichao WANG

1Key Laboratory of Middle Atmosphere and Global Environment Observation(LAGEO),Institute of Atmospheric Physics,Chinese Academy of Sciences,Beijing 100029,China

2University of Chinese Academy of Sciences,Beijing 100049,China

3Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters,Nanjing University of Information Science and Technology,Nanjing 210044,China

4Key Laboratory of Meteorological Disaster of Ministry of Education,Nanjing University of Information Science and Technology,Nanjing 210044,China

5School of Earth and Space Sciences,University of Science and Technology of China,Hefei 230026,China

6State Key Laboratory of Severe Weather,Chinese Academy of Meteorological Sciences,Beijing 100081,China

7Atmospheric Observation Center of Beijing Meteorological Bureau,Beijing 100031,China

ABSTRACT In this paper,we report the location results for the parent lightning strokes of more than 30 red sprites observed over an asymmetric mesoscale convective system(MCS)on 30 July 2015 in Shandong Province,China,with a long-baseline lightning location network of very-low-frequency/low-frequency magnetic field sensors.The results show that almost all of these cloud-to-ground(CG)strokes are produced during the mature stage of the MCS,and are predominantly located in the trailing stratiform region,which is similar to analyses of sprite-productive MCSs in North America and Europe.Comparison between the location results for the sprite-producing CG strokes and those provided by the World Wide Lightning Location Network (WWLLN) indicates that the location accuracy of WWLLN for intense CG strokes in Shandong Province is typically within 10 km,which is consistent with the result based on analysis of 2838 sprite-producing CG strokes in the continental United States.Also,we analyze two cases where some minor lightning discharges in the parent flash of sprites can also be located,providing an approach to confine the thundercloud region tapped by the sprite-producing CG strokes.

Key words:red sprites,positive cloud-to-ground strokes(+CGs),mesoscale convective system(MCS)

1.Introduction

Red sprites are transient,vertically structured optical emissions occurring in the mesospheric region that typically span the altitude range of 40–90 km above active thunderstorms(Sentman et al.,1995;Winckler,1995;Stanley et al.,1999),and are a dominant species of transient luminous events discovered successively since the first serendipitous observation over a distant thunderstorm by Franz et al.(1990).Observations of sprites have been conducted persistently and intensively from various platforms all over the world to understand their physical mechanism and the relationship with the structure and development of mesoscale convective systems(MCSs)as the most productive weather systems of sprites(Sentman and Wescott,1993;Boccippio et al.,1995;Lyons,1996;Neubert et al.,2005;Chen et al.,2008;Yang et al.,2008;Matsudo et al.,2009;Soula et al.,2009;Wang et al.,2015).

Studies over the past two decades have shown that red sprites are predominantly produced by energetic positive cloud-to-ground strokes(+CGs)(Bell et al.,1998;Williams,1998;Huang et al.,1999;Cummer and Lyons,2005),which transfer large amounts of electric charge from thunderclouds to the ground following the return stroke(Fuquay,1982;Gomes and Cooray,1998;Cummer and Lyons,2005).The sudden removal of thunderstorm charge drives the formation of optical emissions in the mesosphere via the tran-sient quasi-electrostatic field that exceeds the threshold for dielectric breakdown to initiate the streamer-type ionization(Pasko et al.,1997).The emergence of sprites could also be connected to the presence of irregularities in the mesosphere(e.g.,caused by gravity waves)(Sentman et al.,2003;Soula et al.,2015).Nevertheless,there is increasing interest in studying red sprites as a phenomenon that manifests the electromagnetic coupling between the troposphere and mesosphere.

Coordinated ground-based observations of sprites and their parent strokes indicate that sprites are generally displaced from the ground location of parent strokes,and the lateral offset can vary from several km up to 100 km(Sentman et al.,1995;Füllekrug et al.,2001;Soula et al.,2010;Lu et al.,2013).Numerous studies indicate that the occurrence of sprites is generally associated with the evolution of stratiform cloud(Lyons,1996,2006;Williams and Yair,2006;Soula et al.,2009;Lang et al.,2010);sprite-producing lightning flashes usually initiate in the convective region of MCSs and propagate into the stratiform regions to deposit the positive charge there to the ground(Lu et al.,2009,2013;Lang et al.,2010;van der Velde et al.,2010,2014;Soula et al.,2015).Lu et al.(2013)showed that the large-scale structure of sprites is affected by the morphology of positive charge removal in the thunderstorm,as also indicated by the numerical simulation of Asano et al.(2009).

Su et al.(2002)reported the first ground-based observations of sprites in mainland China.Since then,almost all sprite observations have been obtained in North China(e.g.,Yang et al.,2008,2013,2015;Wang et al.,2015),and the location information for the sprite-producing strokes is usually provided by operational lightning detection networks,whose performance(especially their detection efficiency and location accuracy)has not yet been systematically evaluated.Due to the limited efficiency of these networks,the observed sprites cannot be examined with the desired reliability,and the available data sources are insufficient to support investigations on the spatiotemporal relationship between sprites and parent lightning flashes(e.g.,Lu et al.,2013;Soula et al.,2017).Therefore,it remains necessary to construct a lightning detection system that can support the study of lightning effects in the upper atmosphere through the electromagnetic coupling between tropospheric thunderstorms and the mesosphere.

In this paper,we present the location results of parent strokes for about three dozen sprites observed over an asymmetric MCS in Shandong Province on 30 July 2015,with a long-baseline lightning location network developed with the main objective to study the lightning effects in near-Earth space.A description of the lightning location network and the associated location algorithm is presented in section 2.In section 3,we preliminarily examine the sprite observations on 30 July and the synoptic background for the parent thunderstorm.The location results of sprite-producing strokes are examined in section 4 through comparison with composite radar reflectivity and the cloud-top brightness temperature;the location accuracy of World Wide Lightning Location Network(WWLLN)(Rodger et al.,2006;Hutchins et al.,2012)with respect to sprite-producing lightning strokes in Shandong Province is also analyzed.In section 5,we present the location results of fast discharges during the parent lightning flashes for two “dancing sprite”events,and discuss the possibility to better confine the thunderstorm region over which the sprite is produced by detecting fast discharges.

2.Measurements and data

Since August 2014,a low-light-level video recording system(referred to as SpriteCam,which consists of a Watec 902H2 Ultimate video camera equipped with a Computar F1.2/8 mm TV lens,and the field-of-view is estimated to be about 56°)similar to that used by Lu et al.(2013)has been installed at a site(Fig.1)in the suburban area of Yancheng,Jiangsu Province,to observe transient luminous events produced by thunderstorms in East China(at a range up to 500 km).The frame rate is 30 frames per second(or 60 interlaced fields per second),and the video image is stamped with GPS time of millisecond accuracy.Due to the relatively serious haze weather that usually persists overnight,the observations of sprites are not as frequent as those from stations located at similar latitude in the continental United States(e.g.,Li et al.,2012;Lu et al.,2013).In addition to the SpriteCam system,several low-frequency(3–340 kHz)magnetic sensors are installed at several sites(Fig.1),forming a regional lightning location network that can locate the parent stroke of sprites with accuracy on the order of several kilometers.

Fig.1.Overview of the observation network.The locations of low-frequency magnetic field measurement stations(BEIJ for Beijing,XINZ for Xinzhou in Shanxi Province,HEFE for Hefei in Anhui Province,and BINZ and WEIH for Binzhou and Weihai in Shandong Province)are indicated by red squares,and the low-light video system(SpriteCam)installed at Yancheng station(Jiangsu Province)is marked by the black pentagram.The dashed circles mark the 300-km and 500-km detection ranges of the SpriteCam.The radar data used in this paper are from the weather radar located in Jinan,and the weather balloon sounding data are obtained in Zhangqiu,Shandong Province.

During the summer of 2015,SpriteCam registered a total of 46 sprites that were produced over three nights,as listed in Table1.In particular,a total of 38sprites were recorded on30 July,which is probably the most productive sprite-producing weather system ever reported in China.There are four sprites that seem to be produced by the current surge during the long continuing current initiated by a weak return stroke(e.g.,Lu et al.,2013),and thus the parent stroke(which usually precedes the observation of sprites by a few to several tens of ms)is difficult to discern from the associated sferic signal.According to the associated broadband magnetic field,all the sprite-producing strokes were of positive polarity,transferring positive charge from thunderclouds to the ground.

The radar data used for our analysis are from the weather radar located in Jinan(36.803°N,116.781°E),and the detection range of the radar is estimated to be 340 km.Our analyses mainly refer to the Principal User Processor products and composite reflectivity from radar observations every 6 min.We also use the global infrared cloud image data of the National Centers for Environmental Prediction/Climate Prediction Center(NCEP/CPC)to obtain the cloud-top brightness temperature from the fusion of the data products from GOES,METEOSAT,and Google Mobile Services;the spatial resolution of this dataset is 4 km and the temporal resolution is 30 min.The composite radar reflectivity data and cloud-top temperature data are used to describe the structure and evolution of the MCS(e.g.,Soula et al.,2009).Moreover,our analyses also refer to the atmospheric circulation at 500 hPa,700 hPa and 850 hPa,the ground truth in Shandong Province,and sounding profiles from Zhangqiu(36.72°N,117.53°E)(http://weather.uwyo.edu/upperair/sounding.html).

2.1.Long-baseline lightning location network

The Lightning Effects Research Platform(LERP)was developed with the main goal to investigate the lightning effects in near-Earth space,such as transient luminous events(Boccippio et al.,1995;Soula et al.,2010),terrestrial gammaray flashes(Fishman et al.,1994;Connaughton et al.,2010),and thunderstorm-induced effects on the lower ionosphere(e.g.,Shao et al.,2013;Yu et al.,2015,2017).The platform consists of a long-baseline lightning detection network as well as several research facilities that are designed to capture the lightning effects in the mesosphere,including Sprite-Cam used in this paper.The sferic signals of LERP stations are continuously recorded and saved,making it possible for a posteriori analysis to identify weak lightning signals through careful inspection.In the future,the LERP network will be supplemented with ultra-low frequency magnetic sensor that will enable us to measure the impulse charge transfer of individual cloud-to-ground(CG)strokes(Cummer and Lyons,2005;Lu et al.,2013),which is unavailable for present lightning location networks.

The radio frequency lightning signals(sferics)recorded for locating lightning discharges with the time difference of arrival(TDOA)technique(e.g.,Li et al.,2017)are measured with a pair of magnetic sensors(with 3-dB bandwidth of 6–340 kHz)oriented east–west and north–south,respectively(Zhang et al.,2016).The signals from the magnetic sensor are recorded continuously at 1 MHz,and all the scientific data from LERP are synchronized with GPS time(with 50-ns precision).

Figure 2 shows the broadband magnetic sferic signals recorded at the six LERP stations shown in Fig.1 for a+CG stroke producing a prompt sprite on 30 July 2015,which was not detected by WWLLN.The lightning signals at all stations are normalized by the peak value for the comparison.Generally speaking,as the distance from the lightning stroke to the low-frequency station increases,the time-of-arrival difference between the ground wave and the( first)ionosphere reflection becomes smaller,and the dominance of the ground wave also declines.However,as shown in the figure,at a range up to 565 km(at XINZ station)from the lightning stroke,the peak lightning signal is still dominated by the ground wave,which is ideal for accurately locating the sprite producing lightning strokes examined in this paper.

Fig.2.Broadband magnetic fields measured at six stations(at distances ranging from 165 km to 565 km)shown in Fig.1 for the causative CG lightning stroke associated with a prompt sprite recorded at 1514:59 UTC 30 July 2015.For comparison,all the magnetic fields are normalized by the peak value,and the ground wave and the( first)ionospheric reflection in the signal are indicated.

Table 1.List of sprite observations in the summer of 2015 from the low-light-level imaging system(SpriteCam)located in Yancheng,Jiangsu Province.An SP+CG is defined as a lightning stroke that produces a sprite either through the impulse charge transfer following the return stroke,or through the M-component superimposed on the long continuing current after the return stroke.

The lightning location results of LERP are compared with the WWLLN,which mainly detects lightning sferics in the 6–22-kHz band(Hutchins et al.,2012).Based on the sprite observations in a six-year period from 2008 to 2013 at multiple sites in the United States(Lu et al.,2013),we evaluate the location accuracy of WWLLN with respect to 2838 sprite-producing strokes through comparison with the National Lightning Detection Network(NLDN)(Cummins et al.,1998),whose lightning location accuracy has been shown to be better than 1 km in the continental United States(e.g.,Jerauld et al.,2005;Biagi et al.,2007;Nag et al.,2011).In most cases,WWLLN can locate the sprite-producing lightning strokes with accuracy better than 10 km(see Appendix A for details).As shown in Table 1,WWLLN has a relatively high detection efficiency(typically ＞70%)for the sprite-producing lightning strokes in Shandong Province.In contrast,the detection efficiency of WWLLN for lightning strokes with peak current stronger than?130 kA is estimated to be＞35%(Abarca et al.,2010).Therefore,WWLLN seems to be more sensitive to lightning strokes with relatively large impulse charge moment changes(so,with a high potential for producing sprites).

2.2.Location algorithm of sprite-producing+CG strokes

Regional lightning detection networks composed of multiple stations mostly adopt the TDOA algorithm with the least-squares method to determine the lightning location(Lewis et al.,1960;Li et al.,2017).We use the TDOA algorithm to obtain the optimal solution by consecutively searching in the solution space(e.g.,Ziskind and Wax,1988),and the signals received by at least three stations are needed to locate one lightning discharge.

For a lightning electromagnetic pulse,the time of arrival at the first station is t1,at the second station is t2,and so on till tN.Then,we can calculate the time delay of the same event at two stations.By assuming that our system has j stations and choosing one station as the base station,we can obtain(j?1)time differences by τi,j=ti? tj,where i is the index of the base station and j is the iteration indexes for the rest.If we denote the latitude and longitude of lightning to be x and y,respectively,then position(x,y)for the time-delay estimation is

where Dis()is the distance between two locations on Earth’s surface(and the curvature of Earth is taken into account),and the constant c represents velocity of light(2.99792458×108m s?1).The asterisk j of τi,j?(x,y)represents that station j keeps changing with respect to the reference station i.Correspondingly,(x,y)represents location of lightning;(xi,yi)represents the location of reference station i while(xj,yj)represents location of varying station j.Hence,we need to solve a set of nonlinear equations given by

There are several methods to solve this equation set.Generally,in order to ensure the resolution is convergent after repeated iteration,we can assign multiple initial values randomly,and then solve the equations through the gradient descent method to obtain the global optimal solution.This method generally can achieve good results in the two dimensional space,but the computation efficiency is relatively low.An alternative method is to divide the whole space with appropriate discrete intervals,and then choose the calculated point of Eq.(2)with minimum error.Specifically,we apply an optimization method of lightning location based on the grid search,which can quickly search the candidate target regions by using the multi-dimensional spatial data index(Qin,2014): firstly,obtain the target area through rapid searching of data in hyperspace;then,compare the error of each Support Vector Machine classifier stored in the target candidate region to locate lightning,so that we can meet the requirements of real-time performance and good positioning accuracy.

We use the parallel matching TDOA algorithm in this paper based on the original TDOA algorithm to search for the optimal position that meets the error requirement according to the arrival time difference of lightning pulse measurements from the detection network(with at least four stations).The CUDA computing architecture is adopted to enable the use of a graphical processing unit(GPU)to conduct the parallel calculation.Different from a central processing unit(CPU),which gives priority to execute interactive instructions with relatively weak operation ability,a GPU uses multi-adder and multi-core computing to calculate the simple algorithm with a single core.The evaluation of Qin(2014)shows that a GPU-based lightning location algorithm is about 4000 times faster than the same algorithm running on a CPU.We can utilize each thread to calculate the time difference from one discrete point to every station and then add the modular.By comparing all threads,the smallest one is selected,and its discrete point coordinate input will be considered as the location point.In particular,we apply the parallel reduction algorithm(Harris,2007)to obtain the final thread with the smallest error.By requiring the synchronous lightning sferics recorded at four or more stations used to locate a lightning discharge,we apply the method of Qin(2014)to evaluate the location accuracy of LERP to be better than 6 km in the region of interest.

3.Overview of thunderstorm and sprite observations

In this section,we examine the synoptic background for the evolution of the MCS on 30 July 2015,which had a life span of more than 12 hours and a horizontal dimension in excess of 200 km.On the morning of 30 July,due to the southwest flow from the northern periphery of a subtropical anticyclone over the western Pacific and west trough in the Sichuan basin,moderate to intense convective precipitation appeared over a large range in Shandong Province,which is a typical mesoscale convective process seen in the North China Plain region.The dominant system of the large-scale circulation background was a forward-tilting trough,which often produces instability precipitation.There was strong convergence between the west of Shandong and the south of Henan.

The MCS on 30 July began with several small convective cells that first appeared at about 0520 UTC near Yantai,which then kept growing until forming an elongated convective line over eastern Shandong Province.The development of thunderstorms was accompanied by the southwestward motion of the low center from northwest of Hebei Province to the junction of Shandong Province.When the low center reached Shandong,the sprite-producing thunderstorm moved to central Shandong,and merged with another southbound thunderstorm.At about 1130 UTC,a stream of downdrafts occurred on the vertical wind profile,and the vertically integrated liquid water content reached 62 kg m?2,indicating that the thunderstorm had strong precipitation potential.As the MCS evolved while moving south,the leading convective line grew stronger on the western wing and the trailing stratiform precipitation region dominated on the eastern side,giving the MCS an asymmetric structure(Houze et al.,1990,Fig.8).

The balloon sounding at 0000 UTC in Zhangqiu,Shandong Province is shown in Fig.3,and several indices derived from the sounding are listed in Table 2.There was a relatively unstable atmospheric stratiform condition with a relatively high CAPE value of 2057.68 J kg?1,and the precipitable water for the entire sounding also reached a high value of 61.14 mm(mean seal level,msl),which indicates that the atmospheric environment provided a favorable condition for MCS development.

Table 2.Key parameters derived from the balloon sounding in Zhangqiu,Shandong Province,on 30 July 2015.The station elevation is 77.0 m(above mean seal level).

Fig.3.Skew-T log-P diagram based on the weather balloon sounding in Zhangqiu,Shandong Province,at 0000 UTC 30 July 2015.The blue line shows the path of air parcel,which reflects the variation of temperature for the air parcel with pressure(or height);the black line shows the variation in the vertical distribution for the atmospheric temperature and humidity above the sounding area.

Figure 4a shows the location of 22 sprite-producing+CG(SP+CG)strokes(colored from blue to red according to the time of occurrence)detected by WWLLN on 30 July.For comparison,we also plot the WWLLN-detected parent strokes for seven sprites observed on 29 July and 2 August,respectively,showing that the SpriteCam at Yancheng station is able to record sprites at ranges up to about 500 km.As shown in the figure,the SP+CG strokes on 30 July generally exhibited a tendency to move southwestward;as the sprite production appeared to be very active after 1500 UTC,we select the composite radar reflectivity(Fig.4b)and the cloudtop brightness temperature(Fig.4c)at about 1530 UTC for a brief discussion on the development of thunderstorm.The SP+CG strokes detected by WWLLN within one hour centered at the image time are shown in the figure.

As indicated by Fig.4b,the radar reflectivity indicates that,upon the active period of sprite production(after 1500 UTC),in addition to the sprite-producing MCS that generally moved southwestward,there was a smaller thunderstorm to the north that approached while migrating southeastward;the image of cloud-top brightness temperature(Fig.4c)shows that the two thunderstorms had merged well by 1530 UTC.By comparing Figs.4b and c,we can see that the coldest region(with cloud-top temperature colder than?210 K)corresponds to the convective region of the MCS,and the coldest temperature usually indicates the highest altitude(Soula et al.,2009).

We divide the lifetime of the MCS into three stages based on the radar reflectivity.At about 1410 UTC,the updraft occurred and the strongest reflectivity echo reached 60 dBZ,indicating that the thunderstorm had reached the mature stage.Thereafter,the strongest echo decreased below 55 dBZ,while the convective region(contoured by reflectivity≥30 dBZ)kept broadening and became more organized.The range of convective region and precipitation began to decline at 1740 UTC,which marks the onset of the dissipation stage.The sprite-producing thunderstorm completely died out at about 0310 UTC on 31 July.

Fig.4.(a)Overview of lighting strokes detected by WWLLN in association with the sprites observed on 29 July(black squares),30 July(colored plus signs),and 2 August(black circles)during the summer of 2015.(b)Comparison between SP+CGs(within one hour centered at the image time)with the composite radar reflectivity at 1528 UTC 30 July.(c)Comparison between SP+CGs(within one hour centered at the image time)with the cloud-top brightness temperature at 1530 UTC 30 July.

Figure 5 shows the composite image of 17 selected sprite events(with relatively dark background)observed between 1356 UTC and 1657 UTC on 30 July 2015.For the sprites observed after 1700 UTC,the parent lightning flash became closer to the observation site,and therefore the SpriteCam recorded the scattering light from the tropospheric lightning too.

4.Location of sprite-producing strokes

In this section,we examine the location results for the sprite-producing strokes on 30 July 2015 as provided by LERP.Most of these sprite-producing strokes were also detected by WWLLN,and therefore the performance of WWLLN in Shandong Province with respect to spriteproducing strokes is examined with this dataset.

4.1.Analysis of location results

With the broadband magnetic fields recorded at a minimum of five LERP stations,we locate the parent strokes for the sprites observed on 30 July 2015,and the results are listed in Table 3 in comparison with the detection results of WWLLN.The majority of sprites(22 events,or 65%of all the observations on 30 July)were observed during 1500 UTC to 1730 UTC,with an average time interval of 6 min 30 s between sprites,similar to the sprite-producing MCS examined by Wang et al.(2015).The time intervals between two successive sprites in this time period were much shorter(basically restricted in 10 min,and as short as 1 min 13 s)than other periods.By examining the LERP detection of SP+CG strokes during the entire sprite-producing period listed in Table 3,it is found that strokes missed by WWLLN are mainly during the mature stage of the MCS,and at the initial stage of the active sprite-producing period.None of the spriteproducing strokes between 1507 UTC and 1537 UTC was detected by WWLLN,and some of the SP+CGs during this period were actually relatively strong(in terms of the peak magnetic field received at Yancheng station).

Fig.5.Composite image of 17 selected sprites observed on the night of 30 July 2015,showing the main sky region with sprite production above the distant mesoscale convection system in Shandong Province.The red dashed line at the bottom marks the horizon(corresponding to the elevation angle of 0°),and the azimuth is the value clockwisely relative to true north.

With the location results of 22 sprite-producing strokes listed in Table 3 that were detected by both LERP and WWLLN,we evaluate the location accuracy of WWLLN with respect to strong CG lightning strokes in Shandong Province.Figure 6a shows a scatter plot of WWLLN lightning locations for the 22 SP+CGs relative to the locations(at the origin)determined by LERP.For most of these strokes,the WWLLN location is within 10 km of the LERP location;and interestingly,other strokes with relatively large location error(＞10 km)are all located by WWLLN to the northwest of LERP locations,which might imply a systematic location error(mainly in the east–west direction)of WWLLN in North China.

Figure 6b shows a histogram of the relative location errors for SP+CG strokes.With the LERP location as the ground truth,the mean and median WWLLN location error is 10.81 km and 6.35 km,respectively.As discussed in Appendix A,based on a total of 2838 lightning strokes associated with sprites observed in the continental United States,the mean and median location accuracy of WWLLN with respect to SP+CGs is estimated to be 7.48 km and 4.96 km,respectively.Therefore,there is no significant difference between the location accuracy of WWLLN for sprite-producing strokes in the United States and North China.

4.2.Comparison with radar observations

Fig.6.Analysis of the location error of WWLLN in Shandong Province with respect to sprite-producing lightning strokes(using the location results of LERP as the ground truth):(a)scatterplot of relative error with the location results of LERP at the origin(the black dashed circle marks the 10 km range);(b)histogram of total location error.

Table 3.Location of SP+CGs in comparison with those reported by WWLLN.In the second column,the value in parentheses is the peak magnetic field(units:nT)recorded at Yancheng station for the sprite-producing stroke.The bold records are SP+CGs of dancing sprites produced in one flash.

The locations of sprite-producing strokes detected by LERP are examined through comparison with observations of radar reflectivity from Jinan,Shandong Province.Figure 7 overlays the SP+CGs with the composite reflectivity over six selected time intervals,and the sprite-producing lightning strokes occurring within one hour centered at the image time are shown in the panel.Generally speaking,the sprite-producing strokes are located in the trailing stratiform regions,with reflectivity ranging from 20 dBZ to 40 dBZ,consistent with previous observations(e.g.,Lyons,1996;van der Velde et al.,2006;Lu et al.,2013).

As shown in Fig.7a,during the initial stage of sprite production,the SP+CGs are distributed near the southeastern boundary of the thunderstorm.After 1500 UTC,the thunderstorm evolved into the active stage of sprite production,and a total of 23 sprite events were observed until 1725 UTC(i.e.,approximately one sprite event observed every 6.5 min over 2.5 h).During the most active stage of sprite production,from 1507 UTC to 1555 UTC(with observations of nine sprites),the SP+CGs were mostly distributed at the center of the stratiform region;meanwhile,the thunderstorm developed a leading bow echo that moved southwestward,forming a leading-line trailing stratiform MCS(e.g.,Carey et al.,2005).As the MCS evolved,there was a tendency for the SP+CGs to move gradually southwestward along with the convective region,while the sprite production rate remained relatively high.Also,the SP+CG strokes remained located in the stratiform region of the MCS.

After 1725 UTC,there was a quiet period(i.e.,without sprite observation)of almost two hours,until 1918 UTC,when the SpriteCam did not record any sprites over the stratiform region of the MCS,albeit with some illuminations from lightning in distant thunderclouds triggered within the instrument.A similar quiescence in sprite production while a sprite-producing MCS evolved from the mature stage into the dissipation phase was also reported by Lu et al.(2013).Whether this is a common feature of sprite production in MCSs merits further investigation,and a relevant question is whether the evolution of MCSs into the dissipation stage is accompanied by the weakening of charge transfer to the ground by+CG strokes.

During the dissipation stage of the MCS,when the convective region significantly weakened,there were four sprites observed over the stratiform region,and the locations of SP+CGs were relatively scattered.Some of these sprites appeared to be very close,as the cloud illumination by the sprite-producing lightning was also recorded on video.

To gain a better understanding regarding the distribution of SP+CGs in the stratiform region of the MCS,we show the location of SP+CGs in a vertical cross-section of the thunder-storm along the black line in Fig.8a.As shown in Fig.8b,the strong updraft (as indicated by the relatively high radar reflectivity of＞35 dBZ)in the convective region is clear,and the altitude of convective cloud reaches 13 km while that of the stratiform echo maintains at around 10 km.The stratiform region of MCSs is a large pool of positive charge(Stolzenburg et al.,1998;Williams,1998),and the lightning flashes initiated in the convective region of an MCS help to transfer the positive charge from the stratiform region to the ground,thereby producing red sprites(Lu et al.,2009,2013).

4.3.Comparison with cloud-top brightness temperature

From the cloud-top brightness temperature,we can estimate the cloud top altitude as well as the associated vertical convection inside the thunderstorms(e.g.,Soula et al.,2009).Figure 8 compares the location of SP+CG strokes with the hourly images of cloud-top brightness temperature,which can reveal more comprehensive features of the MCS over a larger detection range.The SP+CGs occurring within one hour centered at the image time are shown in the corresponding panel.As shown in the figure,the SP+CG strokes are generally located in the relatively warm regions(220–230 K)of the thunderstorm,which is consistent with the observations of Savtchenko et al.(2009)and Soula et al.(2009)regarding several sprite-producing MCSs in Europe.

The hourly images of cloud-top brightness temperature clearly reveal the southwestward evolution of the MCS.The thunderstorm developed rapidly after 1400 UTC,and the boundary of convective cloud became distinct at about 1530 UTC.Meanwhile,the stratiform region expanded steadily until 1730 UTC,when the coldest cloud-top brightness temperature of 205 K(corresponding to a highest cloud top at about 16.7 km),and the thunderstorm area with cloud-top temperature of 220 K kept increasing;the vast majority of sprites observed on 30 July were produced during this period(e.g.,Soula et al.,2009).

The cloud-top brightness temperature during the two hourquiet period of sprite production(1725–1918UTC)does not show any noticeable difference from that during the active stage of sprite production(1500–1730 UTC).During this stage,several convection cells occurred in succession and eventually gathered into a convective core at around 1800 UTC,corresponding to the lowest cloud-top brightness temperature(201 K)and highest cloud top(16.7 km,msl).The reduction in cloud-top brightness temperature was likely due to the warm,moist air transferred from the western Pacific(with the thunderstorm moving southwestward)and the addition of southern cold air brought by the thunderstorm coming from the north.

The resurrection of sprite production during the dissipation stage of the MCS occurred over an extensive region in the stratiform region(Fig.9f),when the thunderstorm com-ing from the north had completely disappeared(or merged with the sprite-producing MCS).Most SP+CGs were located near the convective region.

Fig.8.Composite radar scan showing the vertical reflectivity structure(along the black line AB shown in Fig.8a)of the sprite-producing MCS at 1731 UTC 30 July 2015.The altitude is the value above the radar location.The sprite-producing strokes(indicated by red triangles)are all located in the stratiform region more than 150 km from the convective region.

Fig.9.Locations of SP+CG strokes detected by LERP(indicated by red plus signs)in comparison with the hourly images of cloud-top brightness temperature from 1430 UTC to 1930 UTC 30 July 2015.The SP+CG strokes shown in each panel occurred within one hour centered at the time shown on corresponding panel.

In summary,during the entire sprite-producing stage of the MCS,all but one of the SP+CG strokes were produced in the stratiform region,with composite radar reflectivity of 20–40 dBZ and cloud-top brightness temperatures of 220–230 K,which is consistent with the analyses of Soula et al.(2009)and Lu et al.(2013).Therefore,for the sprite-producing MCS on 30 July,the positive charge reservoir was also in the trailing stratiform region(Stolzenburg et al.,1998;Williams,1998).During the sprite-producing stage after about 1400 UTC,the trailing stratiform region expanded substantially in the rear of the convective core,and the sprite-producing rate remained relatively high until 1725 UTC.The subsequent quiet period of sprite production,until 1918 UTC,was accompanied by the weakening of the convective region(i.e.,the transition from the mature stage to the dissipation stage)and,meanwhile,the area of the stratiform region began to shrink,which is apparent in both the radar-observed reflectivity and cloud-top brightness temperature.

5.Detection of fast discharges in sprite producing flashes

The lightning mapping results based on the detection of very-high frequency(VHF)lightning emissions have been used to examine the spatial correlation between sprites and parent lightning flashes(e.g.,vander Velde et al.,2010,2014;Lu et al.,2013;Soula et al.,2017).However,the detection efficiency of VHF lightning mapping systems substantially depends on the distance from the network,and therefore it is not always feasible to determine the spatial structure of sprite-producing lightning flashes.Nevertheless,as the development of lightning channels in the horizontal charge layers in thunderclouds is sometimes accompanied by intermittent fast discharges(Lu et al.,2013,Fig.6)whose electromagnetic pulses could also be detected at a far distance,the overall structure of the parent flash might be confined by detecting these fast discharges with the same method used to locate the return strokes.In Appendix B,we present an example using a sprite-producing flash examined by Lu et al.(2013)to demonstrate the capability of fast discharge detections to delineate the overall spatial structure of the lightning flash,especially when the flash developed over a large extent.Also,due to the commonly observed lateral offset between sprites and their parent strokes(Füllekrug et al.,2001;S?o Sabbas et al.,2003;Lu et al.,2013,2016),the detection of small fast discharges helps to constrain the region of sprite production above thunderstorms.

Figure 10 shows two sprites,each composed of two elements appearing at different times and locations above the thunderstorm during the parent flash(also called“dancing sprites”).Dancing sprites can be produced by distinct CG strokes within the same parent flash(e.g.,Lu et al.,2013;Soula et al.,2017),or M-components superimposed on intense continuing current following a stroke(Cummer and Lyons,2005;Yang et al.,2015),or by both.In both cases,the various elements occurred with a different height for the top region,which suggests that the parent stroke associated with each element was likely at different ranges from the Sprite-Cam.

Figure 11 shows the broadband total magnetic field(which is calculated as the vector sum of two orthogonal components)recorded at Yancheng station(where the SpriteCam is also installed)in association with these two sprites events.The signals from fast discharges(including return strokes as well as relatively strong in-cloud lightning discharge events)produced in the same thunderstorm as the SP+CGs are indicated by demarcation of the peak.The lightning discharges located by WWLLN are also indicated,as are the inferred parent strokes of sprite elements.

Figure 12 shows the location of SP+CG strokes and fast discharges during the sprite-producing flashes in comparison with the image of cloud-top brightness temperature.The detection of fast discharges indicates that this sprite-producing fl ash has progressed into both the major MCS and the northern thunderstorm.

Fig.10.Composite image of different sprite elements(comprising the so-called “dancing sprite”)during two sprites observed at 1526:08 UTC and 1535:30 UTC,respectively,on 30 July 2015.The green element appeared prior to the purple one,and the red dashed line on the bottom marks the horizon.

Fig.11.Magnetic signals associated with two“dancing sprite”events at about(a)1526:08 UTC and(b)1535:30 UTC.The time window for the observation of individual sprite elements(indicated by SP-1 and SP-2,respectively)is indicated by red bars.

Fig.12.Comparison of cloud-top brightness temperature and SP+CG strokes(red plus signs)and other fast discharges(black multiplication signs)during the parent lightning flashes for the sprite event observed at(a)1530:08 UTC and(b)1535:29 UTC.

For the sprite observed at 1526:08 UTC,the parent strokes of both sprite elements(denoted as SP-1 and SP-2,respectively)were produced in the major MCS.Some fast discharges appear to be produced in the northern thunderstorm and were apparently separated from the sprite-producing CG strokes;they were likely associated with the spreading negative leaders during the latter half of the sprite-producing flash.Certainly,it is also likely that there were two lightning flashes occurring at almost the same time in different thunderstorms.For the sprite produced at 1535:30 UTC,the two elements(also denoted as SP-1 and SP-2,respectively)were produced respectively by two+CG strokes separated by nearly 200 km;as shown in Fig.12b,the parent stroke for the second element was located in the northern thunderstorm.

Fig.13.Comparison between the cloud-top brightness temperature and SP+CG strokes(red plus signs)and other fast discharges(black multiplication signs)detected during the parent lighting flash of two sprite events at(a)1526:08 UTC and(b)1535:30 UTC,showing that the detection of fast discharges can roughly depict the cloud region tapped by the sprite-producing stroke.

Similar to Fig.12,Fig.13 examines the location of SP+CG strokes and fast discharges during the spriteproducing flashes through comparison with the map of composite radar reflectivity.The radar-observed reflectivity better reveals that some fast discharges detected by LERP during the sprite-producing lightning were actually produced in the smaller thunderstorm to the north of the major MCS,and it seems there was no pathway for the negative lightning channel to extend from the major MCS to the southern thunderstorm.Although it remains likely that two lightning flashes occurred roughly at the same time without any physical connection in the two separate thunderstorms,another possibility should be mentioned.Yair et al.(2009)investigated the synchronicity of lightning activity in adjacent thunderstorm cells(Yair et al.,2006),proposing that the mutual electromagnetic coupling between remote thunderstorms could result in the lightning initiation due to the occurrence of lightning in an adjacent thunderstorm.

6.Conclusion

In this paper,we present results on the location of spriteproducing strokes for an asymmetric MCS in Shandong Province on 30 July 2015.A total of 38 red sprites(all produced by+CG strokes)were observed within about 6 h above this MCS,which is probably the most productive thunderstorm ever reported in association with sprite observations in China.Based on the broadband magnetic fields measured at six stations of LERP,we applied an optimization method of lightning location based on a grid search with CUDA parallel computing architecture to efficiently obtain the location of parent strokes(SP+CGs)for these sprites.The comparison between the location results of SP+CG strokes and that provided by the WWLLN indicated that the location accuracy of WWLLN for SP+CG strokes in Shandong Province is typically within 10 km,which is consistent with the result based on an analysis of more than 2800 SP+CG CG strokes in the continental United States.Also,the defection efficiency of WWLLN for the SP+CG strokes in Shandong Province was typically over 60%,which might be valid for SP+CG strokes in other regions of China.

Analysis of SP+CG strokes located by LERP in comparison with radar composite reflectivity and NCEP/CPC images of cloud-top brightness temperature indicated that all these CG strokes were located in the trailing stratiform region of an elongated leading convective line.All the SP+CG strokes occurred in the thunderstorm region,with 15–35 dBZ reflectivity or 220–225 K cloud-top brightness temperature(e.g.,Soula et al.,2009).Most SP+CG strokes were produced during the mature stage of the MCS,which is consistent with previous studies(Savtchenko et al.,2009;Soula et al.,2009;Lu et al.,2013).

Examination of two cases of“dancing sprites”indicated that the detection of fast discharges in the parent lightning fl ashes of sprits might be helpful to constrain the in-cloud charge region tapped by SP+CG strokes,providing a method to confine the thunderstorm area over which red sprites might be produced.The two selected cases also reflect the findings of Yair et al.(2009)regarding the synchronized occurrence of lightning flashes in adjacent thunderstorm cells.

APPENDIX A

WWLLN Accuracy for Sprite-producing Strokes

Fig.A1.Instrumentation network for sprite observations in the continental United States during 2008–13.The low-light video cameras(SpriteCam)and low-frequency magnetic sensors were installed at several stations to investigate the correlation between transient luminous events and their parent lightning in the continental United States.This figure is revised based on Fig.1 of Lu et al.(2013)that is only for the observations in 2011.

From 2008 to 2013,ground-based sprite observations were implemented in the continental United States,and lowlight-level cameras were installed in several states to capture red sprites and other types of lightning-related transient luminous events over active thunderstorms(Li et al.,2012;Lu et al.,2013).During a six-year period,more than 4000 sprites were recorded,and the broadband sferics for the vast majority of these sprites were recorded near Duke University.As shown in Fig.A1,the parent strokes for a total of 2838 sprites were detected by both NDLN and WWLLN,providing an opportunity to evaluate the location accuracy of WWLLN with respect to SP+CG strokes with relatively high strength.As a commercial lightning detection network that provides data to many users in the United States,the performance of NLDN has been evaluated in different states by using triggered lightning data(e.g.,Nag et al.,2011).The average detection efficiency of lightning and return strokes has reached 93%and 76%respectively,and continues to increase(Biagi et al.,2007);plus,the typical location error is 600 m,while the error of relatively weak return strokes(6–10 kA)can reach 2 km(Jerauld et al.,2005).Therefore,the lightning location reported by NLDN was used as the ground truth in our analysis.

Figure A2 shows a histogram of the error for the WWLLN-detected lightning location(i.e.,the distance between the lightning locations detected by WWLLN and NLDN,respectively)with respect to 2838 sprite-producing strokes.The mean and median location error is 7.48 km and 4.96 km,respectively,and the distribution of WWLLN location error generally follows a log-normal distribution.Our results are generally consistent with Abarca et al.(2010)in so far as the location accuracy of WWLLN is typically better than 10 km in North America.

Fig.A2.(a)Statistical histogram of WWLLN location error for the parent CG of 2838 sprites detetcted by the SpriteCam network in the continental United States.(b)Percentage of spriteproducing CG strokes for which the WWLLN location error is smaller than a given distance.

APPENDIX B

Confining the Size of Sprite-producing Lightning with Fast Discharges

Fig.A3.Comparison between VHF sources detected by the lightning mapping array and the fast discharges detected by the network of low-frequency magnetic sensors for a sprite-producing lightning flash examined by Lu et al.(2013),showing that the detection of fast discharges can depict the overall spatial structure of a spriteproducing lightning flash.The legend shows the color scheme for the detection of lightning emissions at different times after the flash onset.

Figure A3 presents the results of fast discharge detection for a sprite-producing lightning flash examined by Lu et al.(2013).The VHF sources detected by the Oklahoma Lightning Mapping Array,along with the fast discharges detected by NLDN and a long-baseline lightning detection array operated by Duke University,are shown.Based on a comparison of the fast discharge sequences and the Lightning Mapping Array detection results,we can see that the detection of fast discharges roughly confines the spatial size of spriteproducing lightning.Therefore,it remains valuable to detect fast discharges in order to identify the thunderstorm region over which the red sprite is produced.

Acknowledgements.We thank Prof.Qinghe ZHANG,Shandong University(Weihai),and Mr.Shiwei FAN,Xiguan Elementary School of Dingxiang County(in Xinzhou,Shanxi Province),for hosting the broadband magnetic sensor as the key component of LERP in China.This work was supported by the National Key Basic Research and Development(973)Program of China(Grant No.2014CB441405),the Open Research Program of the Key Laboratory of Meteorological Disaster(Nanjing University of Information Science and Technology)of the Ministry of Education(Grant No.KLME1414),the National Natural Science Foundation of China(Grant No.41574179),the Natural Science Foundation of Excellent Youth Program of China(Grant No.41622501),and“The Hundred Talents Program”of the Chinese Academy of Sciences(Grant No.2013068).The authors also wish to thank WWLLN(http://wwlln.net),a collaboration of more 40 universities and institutions,for providing the lightning location data.