Charge analysis on lightning discharges to the ground in Chinese inland plateau (close to Tibet)

Since the summer of 1996, scientists from China and Japan have conducted a joint observation of natural cloud-to-ground lightning discharges in the Zhongchuan area that is located close to Qinghai-Xizang (Tibet) Plateau, China. It has been found that the long-duration of intracloud discharge processes, just before the first return stroke, lasted more than 120 ms for 85% of cloud-to-ground flashes in this area, with a mean duration of 189.7 ms and a maximum of 300 ms. We present the results of charge sources neutralized by four ground flashes and two intracloud discharge processes, just before the first return stroke, by using the data from a 5-site slow antenna network synchronized by GPS with 1 μs time resolution. The result shows that the altitudes of the neutralized negative charge for three negative ground flashes were between 2.7 to 5.4 km above the ground, while that of neutralized positive charges for one positive ground flash and one continuing current process were at about 2.0 km above the ground. The comparison with radar echo showed that the negative discharges initiated in the region greater than 20 dBZ or near the edge of the region with intense echoes greater than 40 dBZ, while positive discharge initiated in the weak echo region.


Introduction
The unusual characteristics of Chinese inland plateau, thunderstorms have been widely noticed in China since the 1980s (Wang et al., 1987;Liu et al., 1987Liu et al., , 1989)).This result was based originally upon observations made with a ®eld mill by noting the change of the ®eld when the thunderstorm was overhead.It was deduced that the charge structure of most storms in Gansu Province, located near the Qinghai-Xizang Plateau of China, was positively tripolar, i.e., an upper positive charge and a main negative charge below the positive.However another positive charge region comparable in amount to the upper positive charge region is widely distributed at the base of thundercloud.In 1989, Liu et al. (1989) found, using the recordings of E and DE measured by ®eld mills, that most of the intracloud discharges took place between the main negative charge region and the lower positive charge region instead of upper positive charge region.
To better understand the charge structure of thunderstorms and discharge features on Chinese Inland Plateau, scientists from China and Japan jointly conducted a multi-station simultaneous observation of natural lightning in the summer of 1996 in Zhongchuan Latitude 36°36¢N, Longitude 103°36¢E, Lanzhou which is also located in the verge of Qinghai-Xizang Plateau.Here we use lightning-caused ®eld changes on the surface to estimate the locations and magnitudes of charges neutralized by lightning discharge.
The multi-station measurement of lightning electric ®eld change is one of the most eective ways to study the charge structure of thunderstorms.Workman et al. (1942) made the ®rst time-resolved simultaneous measurement of electric ®eld change caused by lightning discharge at eight stations in New Mexico.The data were used to calculate the location of the charge center for individual strokes of discharges to the ground and for complete intracloud (IC) discharges.They found that both the negative and positive charges lay within a limited range of ambient cloud temperature between )5 °C and )25 °C, and were distributed horizontally within the storm.Later several other multi-station lightning studies were conducted to investigate the relative locations of charges involved in successive strokes of discharges to the ground (Reynolds and Neill, 1985;Ogawa and Brook, 1969;Krehbiel et al., 1979;Brook et al., 1982) or determine charge locations for ground ¯ashes as a whole (Barnard, 1951;Jacobson and Krider, 1976).In Florida, a large-area network of electric ®eld mills and other instruments were used to investigate the electrical structure of Florida thunderstorm (Jacobson and Krider, 1976;Maier and Krider, 1986;Krider, 1989;Koshak and Krider, 1989;Murphy et al., 1996).They found that the point charge (Q) ®ts cloud-to-ground (CG) ¯ashes and the point-dipole (p) model ®ts IC discharges in Florida.The Q-solutions tend to concentrate where the environmental air temperature are between )10 to )20 °C, or 6 to 8 km above sea level (asl).The p-vectors tend to be located at both above and below the Q-region and point toward the Qregion.A similar method was also employed to investigate the initial development of vertical intracloud lightning discharges (Liu and Krehbiel, 1985) and the location of pulses in preliminary breakdown processes (Ushio et al., 1996).
We report results of electric ®eld change measurements for lightning discharges made at ®ve surface stations during a thunderstorm.The measurements were of sucient accuracy and time resolution to allow the charge sources of individual strokes of ground discharges to be located.At the same time, a radar measurement was made so that the charge calculated could be related to the storm environment.In addition to providing basic data about ground discharges themselves, such data and study have an important bearing on our understanding of the electrical structure of plateau thunderstorms in China.

Experiment
A map of measurement network is shown in Fig. 1.Five stations covered an area of 10 ´10 km 2 in Zhongchuan, northwest of Lanzhou, at the eastern edge of Qinghai-Xizang Plateau.The altitude of this area was about 2 km above sea level.The central station was the A-station known as Shanzidun.There were no high buildings or trees around.The development of storms over the network was monitored and recorded by a 5-cm wavelength radar, which was located at about 60 km southeast of A-station, about 2129 m above sea level.The Cartesian coordinates of the radar station were (10.9 km, )58.6 km).
During the 1996 experiment, the electric ®eld and ®eld changes generated by cloud-to-ground lightning discharges were recorded by the 5-station slow antenna system and ®eld mills separately.The data presented were mainly from the slow antenna system with a time constant of about 5 s and a bandwidth of 0.2 Hz to 2 MHz.The output of slow antenna was digitized at a sampling frequency of 1 MHz and an amplitude resolution of 12 bits.The data were recorded by a PC with a recording length of 1 M words for each lightning discharge.The signals from dierent stations were synchronized by GPSs with 1 microsecond time resolution.In addition to the slow antenna and ®eld mill sensors, three all-sky video cameras were mounted at station A, station B and station C to photograph the lightning channel and determine the horizontal location of ground ¯ashes.

Charge model and analysis method
In this study, we used a point charge model to determine the location in cloud and the magnitude of charge center neutralized by ground lightning ¯ashes, through simultaneous measurements of the electric ®eld change at ®ve stations.For a charge Q brought to earth by ground lightning, the ®eld changes at ith station is given by where the x; y; z are coordinates of point charge Q; x i , y i are the coordinate of ith station; R i is the distance between Q and the ith station.e 0 is the permittivity of vacuum (which is essentially equal to the permittivity of atmospheric air).All are in mks units.To determine x; y; z and Q of ground lightning discharge, four independent measurements are sucient in principle.The use of an overdetermined data set serves to improve the accuracy and also make possible to calculate a quantitative error estimation.
Neutralization or rearrangement of charge by intracloud processes which neutralize both positive and negative charges in the cloud, is usually modeled by means of discrete models, utilizing two point charges of equal and opposite charge value.When the spacing between the two charges is not large, the ®eld changes at the ground approaches that of a point dipole, given by where p QD Ri p x ĩx p y ĩy p z ĩz is the dipole moment vector, and R i is the distance between the center of point-dipole (x; y; z) and observer (x i ; y i ).The model has six unknown parameters.The point-dipole charge model is widely used when the number of observation stations is limited.
If p is set in spherical coordinate system, then where h is elevation angle of p, with the vertically upward direction denoted as 0°; / is its azimuth with north is denoted as 0°and it increases clockwise.In this expression the six unknown parameters are (x; y; z; p; h; /).The numerical method used here is the nonlinear least square ®tting as described by Krehbiel et al. (1979).It consists of performing a nonlinear least square ®t of the data to the charge model, deriving a Chi-square estimate of the `goodness of ®t'.The function to be determined, for the point charge model, is the reduced Chi-square where DE mi is the electric ®eld change measured at the i th station, and DE i x; y; z is the ®tted value of the ®eld change as calculated from the model, r 2 i is the estimated variance of the measurement in DE mi due to experimental errors, r i was estimated at 10% in the calculations, m is the number of degrees of freedom, n±m, where n is the number of independent station points (here 5) and m is the number of unknowns.The best result is de®ned as that which minimizes the deviation between the observed and ®tted values, as measured by the Chisquare (v 2 ) statistic of goodness of ®t.The uncertainty of the results can be derived from the error matrix, which is the inverse of the curvature matrix of v 2 hypersurface in x, y, z, and Q space.

Data and results
In this section we present results of a detailed analysis of electric ®eld measurements for cloud-to-ground lightning ¯ashes.The ¯ashes were produced by a storm on August 12, 1996, that developed from the west of D station and then moved southeast.The ®rst cloud-toground ¯ash was observed at 16:18:36 (Beijing Time) at three stations (C, D and E stations).29 cloud-to-ground lightning ¯ashes were produced by the storm during 1 h and 17 min following the ®rst ¯ash including 9 positive and 20 negative ¯ashes.To be analyzed here are ¯ash 11, ¯ash 12, ¯ash 13 and ¯ash 22 including three negative (lower negative charge to the ground) and one positive (lower positive charge to the ground) discharges.These ¯ashes were selected for analysis because each produced large but unsaturated amplitude recordings at all the ®ve measurement stations.
Electric ®eld measurements obtained for Flash 12 occurred at 16:42:20, are shown in Fig. 2. The upward or positive change shows that it was a negative ground ¯ash.The magnitude of the total ®eld change ranged from 68.4 V/m at A station to 230.7 V/m at D station.This ¯ash occurred 20 km west and 3 km north of the A-station according to the all-sky video camera at three stations.
The ¯ash consisted of three individual strokes to the ground, and each stroke was characterized by a leader and return stroke change, the latter of which appears as a positive step labeled R1, R2 and R3.The positive electric ®eld change before the ®rst return stroke (R1) lasted about 200 ms.Generally, a stepped leader progresses to the ground at a speed of 10 5 m/s and leaves a weak ionized channel behind for ®rst return stroke.Assuming that the stepped leader travels about 3 to 6 km distance from cloud to the ground, the time of progression is about 30 to 60 ms.This indicates that the electric ®eld changes prior to the ®rst return stroke here were not completely produced by the stepped leader, but the initial part was produced by a long-duration intracloud discharge process.Because of this event, it was hard to distinguish the start of the stepped leader from the preceding intracloud activity.Subsequent strokes of the ¯ash were initiated by dart-type leaders which are typically less than 3 ms in duration.Only the change caused by return stroke was considered when the ®rst return stroke was analyzed, and the change produced by stepped leader was neglected, while the electric ®eld change produced both by return stroke and The long-duration intracloud discharge process before the ®rst return stroke was a very common event over the Chinese Inland Plateau.Twenty one out of 29 cloud-to-ground ¯ashes in this thunderstorm were preceded by a long-duration intracloud discharge process which usually lasted for 120 ms±300 ms.The electric ®eld change produced by the intracloud discharge process was usually rising and the discharge was well underway when ®rst return stroke occurred.
To study the characteristics of intracloud discharge process just before the ®rst return stroke, the electric ®eld changes were divided into four stages labeled `a' to `e' as shown in Fig. 2. They were ®tted by using a pointdipole charge model.
Figure 3 shows the recorded electric ®eld changes for ¯ash 11 occurred at 16:39:41.The ¯ash produced two strokes to the ground labeled R1 and R2.A complete waveform of the intracloud discharge process just before R1 was observed at E-station, and it lasted about 200 ms.Other stations did not record the complete waveform of intracloud discharge.The intracloud discharge process of this ¯ash will not be discussed here.
Figure 4 shows the electric ®eld change at ®ve stations produced by the negative cloud-to-ground ¯ash 22, and occurred at 17:24:22.This ¯ash produced only one stroke to the ground which is labeled R. The weak step change followed return stroke R characterized by slow change corresponding to `K' events in the cloud.Just before the return stroke, positive ®eld changes were observed at four stations including station A, B, C, and D, while negative ®eld changes were observed at station E. The duration of intracloud discharge process just before R1 was about 240 ms.The opposite polarity of the intracloud discharge was caused by dierent distances from the discharge sources to the stations.
Figure 5 shows a positive cloud-to-ground ¯ash 13, which occurred at 16:44:44.The waveform could be divided into three dierent parts: a±e, e±f and f±g as shown in Fig. 5.The electric ®eld change during e±f interval was produced by a return stroke, and that of f±g  interval, which is 300 ms in duration, was produced by a long continuing current event.The ®rst part (a±b±c±d±e) lasted for about 210 ms, which corresponded to a longduration intracloud discharge.

Lightning charge locations and magnitudes
The structure of the ground stroke charges for each of the ¯ashes studied is summarized in Figure 6.The small circles denoted the size of spherical volumes which would have contained the individual stroke charges at the uniform density of 20 C/km 3 .The charge values, goodness of ®t, and other relative information are summarized in Table 1.The magnitude of charge lowered by discrete negative ground strokes ranged from a maximum of 5.44 C to a minimum of 2.74 C, and was much less than that lowered by positive stroke.First strokes tended to be more energetic than subsequent ones, although the dierence was not large.The charge neutralized by individual negative ground strokes was of small magnitudes.The total charge lowered to the ground by one negative ¯ash was no more than 11.0 C. The magnitude of charge lowered by discrete negative ground strokes is in good agreement with that reported by Krehbiel et al. (1979), however, the total charge lowered by one ¯ash is about 4 times less than that reported by Krehbiel et al. (1979).The uncertainties given for the various charge center results in Table 1 are too small in view of the relatively large distance of the ¯ashes from the measurement network.This may result from the fact that the Chi-square values are small due to having only one redundant station.
The centers of the negative charge neutralized by discrete strokes were located between 2.74 km to 5.41 km above the ground.The horizontal location of ¯ash 12 was in good agreement with that determined by all-sky video camera at three stations.The charge centers for the ground strokes of ¯ashes 12 and 11 developed horizontally northeast or southwest in the Fig. 6.The structure of the ground stroke charges for each of the ¯ashes.The small circles denote the size of spherical volumes which would have contained the individual stroke charges at the uniform density of 20 C/km 3 cloud, which was 4.6 km for ¯ash 12 and 5.5 km for ¯ash 11, respectively.This indicated that the lightning channel was mainly extended horizontally.
The center of charge neutralized by ¯ash 13 was 1.73 km above the ground.The `+c' in Table 1 is associated with a long post-stroke continuing current event.Since the continuing current ¯owed to the ground following the return stroke channel, it can also be ®tted with a point charge model.The altitude of the charge neutralized by continuing current was 1.60 km above the ground which was close to that of the return stroke.The electric charge lowered to the ground by positive discharge is much greater than that lowered by negative discharge.The charge lowered to the ground by the positive ¯ash was 68.13 C including the return stroke and continuing current, which was seven times greater than that released by negative ¯ashes.The electric charge transported by continuing current in 300 ms was 26.46 C, corresponding to an average current of 88.2 A. This result is smaller than that obtained by Brook et al. (1982) in Japanese winter thunderstorms, whose result for positive ground ¯ashes was 200 A to 40 kA.This disagreement may be attributed to the dierence in center locations of the neutralized charge.Positive discharge occurred in Japanese winter thunderstorms initiated in the upper positive charge region, while that initiated in a lower positive region for Chinese inland plateau thunderstorms.
In addition to the ground stroke results, the ®eld changes caused by intracloud discharge process just before R1 have been analyzed to determine the dipolar rearrangement of charge that accompanied this process.The ®eld changes were divided into several intervals, and were analyzed by using the point dipole charge model as a series of ®eld changes, each beginning at the starting point of intracloud discharge process.Since ®ve stations were not enough to determine the six unknown parameters in the point dipole model, we calculated other ®ve unknowns for certain h, say 10°, then repeated the calculation by increasing 10°until h 90 .In this way, the freedom is 0, and as a result the uncertainty increased.After nine repeat calculations, we chose a group of result with the best goodness of ®t and the least error as the ®nal result for the location of dipole and its dipole moment.The detailed information of the result is presented in Table 2.The total elapsed time from the beginning of intracloud discharge process to the time at which the ®eld change was measured is given in the second column of Table 2.The dipole moment neutralized by a±b part for ¯ash 12 was 2.98 C km with an altitude of 2.6 km.The dipole moment neutralized by a±c part was 8.41 C km with an altitude of 2.27 km, while those for a±d part were 12.09 C km and 2.31 km, respectively.The total dipole moment neutralized by intracloud discharge process (a±f ) was 13.4 C km with a center altitude of 2.0 km.The position of point dipole of whole intracloud discharge process (a±f part), projected in x-z and y-z panel, is illustrated in Fig. 7.
The intracloud discharge process just before R1 for ¯ash 13 started with a±b part, whose dipole moment was 6.4 C km, and the corresponding altitude was 3.1 km; the neutralized dipole moment for a±c was 12.9 C km with an altitude of 3.4 km; the center location of the dipole moment neutralized by a±d was 2.7 km with the dipole moment of 20.7 C km.The discharge altitude during the whole intracloud discharge process, a±f, had hardly changed, and the dipole moment increased to 29.8 C km.Its position projected in x-z and y-z panel also is illustrated in Fig. 7.
According to these results, it is shown that the central location of dierent phases of intracloud discharge process did not change greatly, so the channel should be established before point b.Then the discharge was stable and the discharge channel would not be changed greatly.A further study on the progression of initial streamer before point b would be of great signi®cance when sucient data are available.
The data listed in Table 2 were selected from nine groups of results which were calculated by using dierent elevations increasing from 10°to 90°with an increment of 10°.Actually the results were very close for both ¯ashes when h 10 ; 20 ; 30 and 40°respectively, which indicated that intracloud discharge process just before R1 developed nearly vertically.

Height of the lightning charge
From our analysis, it is clearly shown that the charge centers for the individual negative ground strokes were located between 3 to 6 km above the ground, while that for positive ground stroke was at about 2 km above the ground.These two charge regions were the main sources contributing to cloud-to-ground discharge.Although ¯ash 13 was the only positive ¯ash to the ground we analyzed, the location of intracloud discharge process just before R1 supported this result.In the 1980s, we used the ®eld changes as the storm approached and receded from the ®eld mill stations to infer that the large positive charge region was located at the base of the thundercloud (Wang et al., 1987;Liu et al., 1987).
Although our data covered only one thunderstorm and four ground ¯ashes, these new results and the ®eld mill data of the previous years are consistent.
In contrast, Brook et al. (1982) found that the positive ground ¯ashes initiates in upper positive charge region in the winter thunderstorms of Japan.The occurrence of positive ground ¯ashes is a consequence of the wind shear.The shear provides a horizontal displacement between the charge regions that helps to ensure that an initiating positive streamer will continue down to ground rather than into the negative charge region that would normally be located directly below it.They suggested that positive ground ¯ashes should appear at a threshold shear value in the cloud layer of about 1.5 m/s/km.The variations in charge sources corresponding to positive ground ¯ash between Japan and Chinese Inland Plateau may result from the dierences in charge structures of thunderstorm which depend on the season, meteorological conditions and other factors.
7 Relation to storm structure As described earlier, a 5-cm wavelength radar was operated during the observations, and atmospheric sounding data were obtained from 0700 (Beijing Time) measurements.The positive and negative charge centers for individual ground strokes were located at 2 km and 3±6 km above the ground, respectively.At these elevations the environmental clear air temperature at the time of sounding ranged between )2 and )15 °C for negative charges, and +5 °C for positive charges.The cloud base was close to the ground.All negative charges are con®ned to the cold part of the cloud (below 0 °C).This result is consistent with earlier studies in New Mexico (Krehbiel et al., 1979) and in Florida (Jacobson and Krider, 1976).They found the charges neutralized by negative ground ¯ashes were located in the temperature zone between )5 and )25 °C.
Figure 8 shows the RHI radar echo obtained closest to four ¯ashes, respectively.The clear air temperature at 0700 is also shown to the right of each radar echo as reference.Charge sources for the individual ground strokes of these ¯ashes coincided reasonably well with Fig. 7.The projected position in x-z and y-z panel for intracloud discharge process just before ®rst return stroke of ¯ash 12 and ¯ash 13 the radar echoes and accordingly were superimposed on them.We contoured the radar data at 10 dBZ, 20 dBZ and 40 dBZ levels.The good agreement suggests that the model we used here is reasonable.All negative ¯ashes were initiated in the region greater than 20 dBZ or near the edge of the region with intense echo greater than 40 dBZ except the ®rst return stroke in ¯ash 12, while the location of positive ¯ash was in the echo region with 10 dBZ which was 84 km away from the radar.These results agree with previous results obtained by comparing the data from radar echo with DF data (Ge et al., 1992).They found that negative ground ¯ashes occurred often near, but not in, the strong echo center, and there was a positive correlation between the rate of the negative ground ¯ashes and radar area of the intensity greater than 30 dBZ, while positive ground ¯ashes usually occurred in weak echo region and the ¯ash rate decreased with the increase of storm intensity.
The horizontal locations of intracloud discharge process just before R1 indicate that the centers of the dipole moment were at about 74 km away from the radar station.Referring to the radar echo at 16:44 shown in Fig. 8, we can see that the dipole moment centers fall between the positive and negative charge center.These along with the ground discharge of ¯ash 13 con®rm again the existence of the lower positive charge region and the reliability of these results.

Summary and discussion
In this study we have presented the results of multistation electric ®eld measurements for four cloud-toground ¯ashes in one thunderstorm which occurred on August 12, 1996, in Zhongchuan area, on the edge of Qinghai-Xizang Plateau of China.The basic conclusions are summarized as follows: 1.One positive cloud-to-ground ¯ash (¯ash 13) consisted of only one return stroke which was followed by a long continuing current event.Negative ground discharges usually consisted of several return strokes.
The magnitude of charge ¯owing to the ground for three negative ground ¯ashes was about )10 C, while a charge of 68.31 C was transferred for the one positive ¯ash.The sources of charge for successive negative strokes of the ¯ashes to the ground developed over large horizontal distance (up to 5.4 km) within the cloud at almost a constant elevation.2. The sources of charge for three negative ground ¯ashes were con®ned between 2.74 to 5.41 km above the ground (2 km asl), while that for one positive ground stroke and one continuing current process occurred at about 2.0 km above the ground.3.In the Chinese Inland Plateau, cloud-to-ground discharges were preceded by a long-duration of intracloud discharges which lasted 120 ms to 300 ms for 85% of cloud-to-ground ¯ashes, with a mean duration of 189.7 ms.For the two analyzed cases, the central altitudes of the discharge, determined by using the point-dipole model, were about 2.3 to 3.4 km, and the dipole moments were between 13 to 30 C km with a charge structure of negative in the upper part and positive in the lower part.4. The comparison with radar echo shows that the negative discharges initiated in the region greater than 20 dBZ or near the edge of the region with intense echoes greater than 40 dBZ, while positive discharges initiated in a relatively weak echo region.
Although a discrete dipole model would have been a better method to analyze sources of charge neutralized by intracloud lightning discharges, here, because of the limited station number, we used a simpler model, i.e., the point dipole charge model.This model may cause signi®cant error when an intracloud discharge process is analyzed, especially if the charge neutralized by the lightning discharge was distributed in non-uniform or non-spherical distribution.Furthermore the thunderstorm was far from the network center, so the results may not be necessarily precise.Even if there were enough stations, one could not resolve the two charge centers in the cloud using the discrete dipole model due to the large distance of the ¯ash from the measurement stations.On the other hand, the results here are in good agreement with radar data and have a clear physical meaning, which indicate that the results are of a certain reliability.These results are from only four ground ¯ashes in one thunderstorm, and may not represent all lightning discharges in Chinese Inland Plateau.Perhaps these few ¯ashes are typical of a speci®c type of storm, weather pattern, season, and so on.Because the locations of positive charge sources are consistent with that of ®eld mill data in previous results (Wang et al., 1987;Liu et al., 1989), we suppose that there is a horizontally extensive positive charge region of large magnitude and wide dimension at base of the thunderstorm.The questions as to why a large number of positive charges exist at base of the cloud and why lower positive charges seem to be more eective in discharge processes in Chinese Inland Plateau remain unanswered.It could be some unknown electri®cation mechanisms exist in this area.

Fig. 1 .
Fig. 1.Map of the electric ®eld change measurement station.The coordinates of the radar station were (10.9 km, )58.6 km)

Fig. 2 .
Fig. 2. Electric ®eld change versus time for ¯ash 12, 16:42:20 (Beijing Time).Upward de¯ection indicate a decrease of negative charge overhead.Line segments before ®rst return stroke denote the dierent part of the preliminary breakdown process

Fig. 8 .
Fig. 8.The RHI radar echo obtained closest to four particular ¯ashes, numbered 11±13 and 22.The clear air temperature at 0700 is also shown on the right of each radar echo

Table 1 .
Location and magnitude of charges neutralized by return strokes and continuing current