1.Key Laboratory of Middle Atmosphere and Global Environment Observation (LAGEO), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China 2.University of Chinese Academy of Sciences, Beijing 100049, China 3.Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing 210044, China 4.Key Laboratory of Meteorological Disaster of Ministry of Education, Nanjing University of Information Science and Technology, Nanjing 210044, China 5.School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, China 6.State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China 7.Atmospheric Observation Center of Beijing Meteorological Bureau, Beijing 100031, China Manuscript received: 2017-12-19 Manuscript revised: 2018-03-14 Manuscript accepted: 2018-04-20 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. Keywords: red sprites, positive cloud-to-ground strokes (+CGs), mesoscale convective system (MCS) 摘要:本文利用长基线闪电定位网中的超低频和低频磁天线观测到了2015年夏季中国山东省一次不对称中尺度对流系统(MCS)上空产生的30多次红色精灵(red sprite)瞬态发光事件,并得到了红色精灵母体闪电的自主定位结果。定位结果显示,几乎所有红色精灵母体地闪(CG)回击都产生在MCS的成熟期,主要位于MCS尾部层状云区,这和北美与欧洲对产生sprite的MCS的研究结果一致。对比红色精灵母体闪电的定位结果和全球闪电定位网(WWLLN)提供的定位数据,发现WWLLN对于山东省强地闪回击的定位误差在10公里以内,这和在美国大陆基于2838次红色精灵母体闪电的相关研究结果一致。此外,我们分析了两个可以定位舞蹈状红色精灵母体闪电中微小放电过程的个例,提供了一种估算母体闪电在雷暴云中总放电区域的方法。 关键词:红色精灵, 正极性地闪回击(+CGs), 中尺度对流系统(MCS)
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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 gamma-ray 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 SpriteCam 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. Figure2. 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.
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). Figure3. 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.
2 2.2. Location algorithm of sprite-producing +CG strokes -->
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 \begin{equation} \tau_{i,j^*}(x,y)=\dfrac{{\rm Dis}((x,y),(x_{\it i},y_{\it i}))-{\rm Dis}((x,y),(x_{\it j},y_{\it j}))}{c} , \ \ (1)\end{equation} 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× 108 m 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; (x i,y i) represents the location of reference station i while (x j,y j) represents location of varying station j. Hence, we need to solve a set of nonlinear equations given by \begin{equation} (x,y)={\rm argmin}\sum_{j=1}^N\|\tau_{i,j}(x,y)-\tau_{i,j^*}(x,y)\| . \ \ (2)\end{equation} 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.
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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 sprite-producing 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). 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. Figure6. 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.
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.
2 4.2. Comparison with radar observations -->
4.2. Comparison with radar observations
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). Figure7. Examination of SP+CG strokes (indicated by red plus signs) detected by LERP from 1355 UTC to 2000 UTC 30 July 2015 overlaid on the composite radar reflectivity from Jinan, Shandong Province. The SP+CG strokes shown in each panel occurred within one hour centered at the time shown in the corresponding panel.
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. Figure8. 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.
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 thunderstorm 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).
2 4.3. Comparison with cloud-top brightness temperature -->
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). Figure9. 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.
The cloud-top brightness temperature during the two-hour quiet period of sprite production (1725-1918 UTC) 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. Figure10. 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.
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 coming from the north had completely disappeared (or merged with the sprite-producing MCS). Most SP+CGs were located near the convective region. 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.
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APPENDIX A
3 WWLLN Accuracy for Sprite-producing Strokes -->
WWLLN Accuracy for Sprite-producing Strokes
From 2008 to 2013, ground-based sprite observations were implemented in the continental United States, and low-light-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. FigureA1. Instrumentation network for sprite observations in the continental United States during 2008-13. The low-light video cameras (SpriteCam) and low-frequency magnetic sensors wereinstalled 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.
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. FigureA2. (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 sprite-producing CG strokes for which the WWLLN location error is smaller than a given distance.
3 APPENDIX B -->
APPENDIX B
3 Confining the Size of Sprite-producing Lightning with Fast Discharges -->
Confining the Size of Sprite-producing Lightning with Fast Discharges
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 sprite-producing lightning. Therefore, it remains valuable to detect fast discharges in order to identify the thunderstorm region over which the red sprite is produced. FigureA3. 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 sprite-producing lightning flash. The legend shows the color scheme for the detection of lightning emissions at different times after the flash onset.
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