Correlation Between Total Lightning Activity and Precipitation Particle ...

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ACTA METEOROLOGICA SINICA

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Correlation Between Total Lightning Activity and Precipitation Particle Characteristics Observed from 34 Thunderstorms∗ ZHENG Dong1† (

), MENG Qing1 (

), ZHANG Yijun1 ( 3

and ZHONG Min (

), DAI Jianhua2 (

)

),

1 Laboratory of Lightning Physics and Protection Engineering, Chinese Academy of Meteorological Sciences, Beijing 100081 2 Shanghai Meteorological Center, Shanghai 200030 3 Hubei Provincial Meteorological Bureau, Wuhan 430074 (Received October 29, 2009; revised September 29, 2010)

ABSTRACT A total of 34 thunderstorms around Shanghai and Wuhan of China are analyzed in order to determine the relationship between total lightning activity and precipitation particle characteristics. Precipitation particle concentration data are obtained from the 2A12 product of TRMM/TMI (Tropical Rainfall Measuring Mission/TRMM Microwave Image) and lightning activity data are from the TRMM/LIS (Lightning Imaging Sensor) and SAFIR3000 (Surveillance et Alerte Founder par Interferometric Radioelectirque). On a spatial scale of 0.1◦ ×0.1◦ , a weak spatial relationship is found between total lightning and the vertically integrated content (VIC) of precipitation particles (cloud water, precipitation water, cloud ice, and precipitation ice). A strong power relationship is identified between the lightning density (D30 ; fl km−2 min−1 ), relative to a rainfall intensity threshold value of 30 mm h−1 , and the maximum rainfall intensity (Rmax ; mm h−1 ); the −0.18 obtained regression equation is Rmax = 23.10D30 + 11, with a correlation coefficient of 0.841. Lightning frequency shows a significant linear correlation with the contents and covering areas of precipitation particles (in which the VICs exceed threshold values). Furthermore, ice particles above the –10 ◦ C level exhibit a stronger correlation with lightning activity than those above the 0◦ C level or the integrated ice particles at all levels. The results demonstrate that the particles responsible for the most significant charging process and lightning activity are restricted by the threshold value of VIC among the particles, which reflects the demand of the charging process on dynamic characteristics. The obtained fitting equations can provide useful reference for assimilating lightning information into numerical prediction models so as to improve the reliability of forecast results. The particle products from the prediction models are also helpful in estimating the occurrence of lightning activity within 2–6-h periods. Key words: lightning activity, precipitation particles, correlation, TRMM Citation:

Zheng Dong, Meng Qing, Zhang Yijun, et al., 2010: Correlation between total lightning activity and precipitation particle characteristics observed from 34 thunderstorms. Acta Meteor. Sinica, 24(6), 776–788.

1. Introduction According to the non-inductive charging (NIC) mechanism (Takahashi, 1978; Jayaratne et al., 1983; Saunders et al., 1991; Saunders and Peck, 1998; Pereyra et al., 2000), the charging process and charge transfer among ice particles that occur via ice–ice collision are affected by factors such as temperature, liquid water content, relative humidity (Berkelis and List,

2001), and riming rate (Brook et al., 1997). The large ice-phase particles (e.g., graupel and hail) and small ice-phase particles (e.g., ice crystals) ultimately carry different polarities of charge. Because of the differences in the gravity and terminal fall velocity of these two size groups of particles, they separate from each other under the action of updraft and form different areas with contrasting polarities of charge. Lightning is thought to initiate in the region with

∗ Supported by the National Natural Science Foundation of China under Grant No. 41005006, the Special Projects for Public Welfare (Meteorology) of China Meteorological Administration under Grant No. GYHY200806014, the National Science and Technology Supporting Program under Grant No. 2008BAC36B04, and the New Meteorological Technology Promoting Program of China Meteorological Administration under Grant No. CMATG2008M20. † Corresponding author: [email protected].

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ZHENG Dong, MENG Qing, ZHANG Yijun, et al.

the largest electrical field and between the charge regions. The lightning channel may propagate in the cloud or toward the ground. Consequently, precipitation particles in cloud, especial ice particles in the mixed-phase region, are the main carriers of the charge and should have a close relationship with charging and discharging processes in a thunderstorm. For example, based on in situ observations, Takahashi et al. (1999) reported that the polarity of the charge carried by graupel changed at about the –11 ◦ C level. Coincident with the increase in the concentration of graupel particles, the charge amount increased by an order of magnitude. In the case that the concentration of graupel exceeded 1 per liter and the average charge of each particle reached tens of pC, lightning discharge was produced. The authors found the most active charging process at around the –20 ◦ C level, where graupel was concentrated. Based on an analysis of lightning activity and particle information obtained from multi-parameter radar, Dotzek et al. (2001) found that lightning activity was most likely to occur in regions where graupel particles accumulated, followed by regions where snow and small, dry hail particles accumulated during the development stage of a supercell thunderstorm. During the decaying stage of the storm, the main lightning activity was found in areas of hail and heavy rain. Carey and Rutledge (1996) reported that intracloud (IC) lightning activity increased exponentially with an increase in the volume of the region mainly occupied by graupel. A rapid decrease in cloud-toground (CG) lightning activity coincided with a decrease in the amount of hail and graupel. Studying the lightning activity and precipitation characteristics before and after the onset of the South China Sea (SCS) summer monsoon, Yuan and Qie (2008) reported that the flash rate of precipitation systems could be expressed as functions of maximum storm top height, maximum snow depth, and minimum polarization corrected temperatures (PCTs), respectively. Among them, the correlation between flash rate and PCTs was more significant, which also implies the close relationship between the lightning activity and ice particles. The charge that supports the initiation of light-

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ning or that is consumed by lightning discharge is carried mainly by ice particles. The charge quantity depends mainly on the quantity of ice particles and collisions among them. The collision efficiency is largely determined by the wind field in the cloud, which also influences the quantity of ice particles. The relationship between lightning activity and ice particles is expected to be relatively constant among different thunderstorms and regions, as reported previously. For example, based on 46000 radar scan data, Gauthier et al. (2006) reported a strong linear correlation between the vertically integrated content (VIC) of precipitation ice and CG lightning. The authors also found that the correlation is applicable to different thunderstorms and regions. Petersen et al. (2005) discussed the relationship between ice particles obtained from the TRMM (Tropical Rainfall Measuring Mission) satellite and lightning density in several different regions around the world, and found that the relationship was relatively stable over continents, oceans, and coastal areas. As the relationships between lightning activity and the parameters of precipitation particles become better defined, lightning information can be better incorporated into mainstream meteorological applications, including warning decision support systems and improved numerical weather prediction. In addition, by introducing the relationship, we can use the products about precipitation particles from numerical prediction models to forecast lightning activity over periods of 2–6 h (it remains difficult to directly couple the charging and discharging processes into numerical prediction models). The objective of this paper is to investigate the storm-scale relationships between total lightning activity (i.e., IC and CG lightning) and the characteristics of precipitation particles. A total of 34 thunderstorm events around Shanghai and Wuhan of China are selected for analysis. These thunderstorms were observed by the TRMM satellite and two SAFIR3000 (Surveillance et Alerte Founder par Interferometric Radioelectirque) systems. The study focuses on the stage when the TRMM satellite passed over the storms. The relationships are discussed based on precipitation particle data obtained from the in-

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verse products of TRMM Microwave Image (TMI) and total lightning observed by SAFIR3000 and Lightning Imaging Sensor (LIS). 2. Observation and data 2.1 Observation The TRMM satellite (Christian and Latham, 1998; Kozu et al., 2001; Wang, 2001; Fu et al., 2003) was launched on 28 November 1997. Its orbit altitude was increased from 350 to 403 km on 24 August 2001. The main mission of TRMM is to examine precipitation in tropical and subtropical regions. TMI, onboard the TRMM satellite, measures the intensity of radiation at five separate frequencies: 10.7, 19.4, 21.3, 37.0, and 85.5 GHz. Except for the 21.3-GHz channel, which has only vertical polarization, other channels have dual polarization (vertical and horizontal polarization). TMI has a swath width of 878 km at the surface. The 2A12 data inverted from TMI are used in this study. LIS, designed by the Global Hydrology and Climate Center (GHCC) Lightning Team, has a 2-ms time resolution with a 128×128 CCD (ChargeCoupled Device) matrix and a telescope lens. After the increase in orbit altitude, the field of view of LIS increases to 667 km and the view time for a given location is about 90 s, with a spatial resolution of about 3–6 km. According to Boccippio et al. (2002), the detection efficiency of LIS is about (93±4)% during the night and (73±11)% during the day. LIS records

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information on lightning flashes, including the time, position, and radiation energy, among other factors. The SAFIR3000 uses interferometric technology to locate the three-dimensional position of lightning radiation sources produced by breakdown processes in the very-high-frequency (VHF; 110–118 MHz). At the same time, low-frequency (LF; 300–3 MHz) sensors help to discern CG flashes. The detected VHF sources are associated with a flash when they are separated by less than 7 km in space and less than 100 ms in time. The detection of CG return strokes is grouped into a CG flash considering a multiplicity delay of 0.5 s within a radius of 7 km. This study employs the SAFIR3000 systems established in Shanghai and Wuhan. The positions of the relevant substations are shown in Fig. 1. The systems were produced and installed by Vaisala Inc., and operated by local meteorological bureaus. Each system comprises three substations and one central station. The detection efficiency is ∼90% within or near the network, and the location accuracy is < 2 km within 200 km. The SAFIR system has been operated in many different countries. Previous studies have reported that it provides high-quality flash information and shows high reliability and represents good values (e.g., Kawasaki et al., 1994; Mazur et al., 1997; Lee et al., 2000; Wang and Liao, 2006; Dr¨ ue et al., 2007). This study analyzes 34 thunderstorms that occurred around the Shanghai district during 2005–2007 and around the Wuhan district during 2006–2007. The

Fig. 1. Sketch maps showing locations of the substations of SAFIR3000 systems in (a) Shanghai and (b) Wuhan. Solid circles indicate locations of the Shanghai and Wuhan radars.

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relevant orbit data for TRMM are listed in Table 1. The analyzed region is centered by radar with a radius of 200 km (locations of Shanghai and Wuhan radars are marked in Fig. 1 as solid circles). All the Table 1. Date and time when the TRMM satellite passed over the thunderstorms and the corresponding orbit number Place

Date and time Year

Around Shanghai 2005

2006

2007

Around Wuhan

2006

2007

Day/Month, Hour: minute 27/06, 15:19 05/07, 11:49 08/07, 10:39 08/07, 13:55 09/07, 09:43 30/08, 07:28 21/04, 08:46 06/08, 03:24 10/08, 04:19 31/05, 18:56 28/06, 09:20 08/07, 00:07 10/07, 03:09 20/07, 18:33 02/08, 11:24 04/08, 14:26 05/08, 10:14 15/08, 09:08 29/08, 02:39 23/06, 06:06

Orbit number 43403 43525 43571 43573 43586 44395 48043 49709 49770 54362 54792 54942 54975 55141 55339 55372 55385 55540 55754 49023

05/07, 22:52

49221

26/07, 26/07, 04/08, 30/05, 31/05, 18/06, 18/06, 22/06,

08:22 13:16 08:14 19:51 00:45 10:23 15:17 08:19

49539 49542 49679 54347 54350 54637 54640 54698

24/06, 29/06, 11/07, 24/07, 21/08,

08:07 10:02 03:50 16:27 06:48

54729 54808 54991 55202 55632

thunderstorms occurred within the observation ranges of LIS and TMI. There is no restriction on the style or development stage of the thunderstorms when the thunderstorm processes are selected for analysis. 2.2 Data We first give a brief introduction on production of the TRMM/TMI 2A12 data. The inversion algo-

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rithm used for TMI, the Goddard Profiling (GPROF) algorithm, was developed by Kummerow et al. (1994, 1996, 2001). Large numbers of hydrometeor profiles were generated using the Goddard Cumulus Ensemble (GCE) model (Tao and Simpson, 1993) to simulate typical precipitation cases. The radiation transfer model was then used to simulate the upward radiation brightness temperature of the profiles. An independent cloud-radiation dataset was compiled, including four styles of hydrometeors (cloud water, precipitation water, cloud ice, and precipitation ice), surface rainfall, and the vertical latent-heat profile over the sea. Based on the different weight of each profile in the dataset, Bayesian technology was used to construct a precipitation profile similar to that observed as the inversion result and to generate the 2A12 data. The concentrations (unit: g m−3 ) of cloud water, precipitation water, cloud ice, and precipitation ice in 2A12 were separated at 14 levels for altitudes ranging from the ground to 18 km. Previous studies that used 2A12 data or compared 2A12 data with other data or numerical model results for China (e.g., Huang et al., 2004; Li and Wu, 2005; Feng et al., 2007; Liu and Fu, 2007) reported that the concentration data for the four hydrometeors are largely reliable in the China region. In this study, we calculate the VICs of the four hydrometeors, i.e., the concentration of precipitation particles is integrated in the vertical direction and the total content per unit area (unit: kg m−2 ) is obtained. Considering that the effects of the precipitation particles on charging vary with position in the thunderstorm, the VICs of the particles are calculated at all levels, above the 0 ◦ C level, and above the –10 ◦ C level. The height of the temperature level is obtained from the soundings prior to the analysis time. The main analysis is described in three sections below. In Section 3.1, the spatial correlation between lightning density and the VICs of particles is synthetically analyzed with a grid size of 0.1◦ ×0.1◦ ; this is referred to as spatial correlation. Section 3.2 focuses on the correlation between the relative lightning density (as defined in Section 2) and the maximum surface rainfall intensity. The correlations between lightning frequency per minute and the contents (unit: kg) and

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covering areas (unit: km2 ) of the particles are analyzed in Section 3.3. An analysis grid size of 0.01◦ ×0.01◦ is used in Sections 2 and 3. Particle concentration data are interpolated to grid-point values by a bilinear interpolation. To ensure the accuracy of the interpolation at the margins of the analysis region, the spatial region used in the interpolation process is larger than the analysis region. During the analysis process, it is found that the SAFIR3000 has higher location accuracy in the twodimensional plane than the LIS does. In the process of selecting thunderstorms for analysis, it is found that the lightning radiation dots (LRDs) located by the SAFIR3000 always show a close correspondence with regions of strong radar reflectivity (observed by radar) and high concentrations of ice particles (observed by TRMM/TMI or TRMM/PR (Precipitation Radar)). However, some of the lightning activities observed by LIS are found to be located apart from the thunderstorms. This finding may be related to the respective location methods. The length of a single lightningdischarge event is typically in the order of tens of kilometers. LIS only estimates the average position of the lightning based on the optic radiation received by the CCD matrix (128×128) in its field of view (> 600 km); i.e., LIS locates an event with a long length in a relatively small and coarse grid. The SAFIR3000 uses interferometric technology to locate the position of the VHF source for which the center frequency is 114 MHz. The dots located by SAFIR3000 usually represent the mean position of a breakdown event with a short length. Previous studies have demonstrated the reliability of the detection accuracy of the SAFIR3000 (Kawasaki et al., 1994; Mazur et al., 1997; Lee et al., 2000; Wang and Liao, 2006; Dr¨ ue et al., 2007; Zheng et al., 2009). However, in the present study, LIS shows a higher detection efficiency than SAFIR3000 does. During the present analysis process, it is found that when the thunderstorm is near the center of the SAFIR3000 network, SAFIR3000 and LIS observe similar amount of lightning activity; however, when the thunderstorm is far from the SAFIR3000 network, SAFIR3000 observes much fewer lightning discharges than LIS does.

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This discrepancy arises because LIS has a larger observation region than SAFIR3000. Furthermore, because LIS receives an optical signal in high altitude, the detection efficiency shows little change with changing distance from the point under the satellite to the edge of the field of view. SAFIR3000 receives VHF signals, whose intensity decays with distance. In addition, at least two substations are needed to determine the position of a discharge event. These conditions mean that the detection efficiency of SAFIR3000 decreases with increasing distance between the thunderstorm and the center of the SAFIR3000 network. In a previous study on a thunderstorm around Wuhan, Zheng et al. (2010) compared the CG lightning data detected by an CG lightning location network and the total lightning data detected by an SAFIR3000 network, revealing that the ratio of CG to total lightning was reasonable when the convective regions that produced the main lightning activity were located within or near the SAFIR3000 network, but was unreasonable (the ratio was larger than normal, and even approached one) when the convective regions moved away from the SAFIR3000 network. Consequently, in Section 3.1 (spatial correlation analysis), the lightning data observed by SAFIR3000 are used to confirm the location accuracy. In Sections 2 and 3 (which consider lightning frequency), lightning observed by LIS is used to ensure reliable detection efficiency because the analysis is conducted on the storm scale and some lightning activities occur away from the network. 3. Analysis and results 3.1 Spatial correlation between lightning activity and particle VICs There exists no clear definition regarding the position of an IC lightning event. Here, we regard the first LRD of an IC lightning event observed by SAFIR3000 as the position of that event. This approach is taken because this position is usually the closest to the initial position of the lightning. The position of CG lightning is taken as that where the return stroke reaches the ground. The total lightning data are chosen within a period of 5 min before and after the TRMM

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satellite is directly over the main body of the thunderstorm. The lightning density (unit: fl km−2 min−1 ) is calculated for an analysis grid size of 0.1◦ ×0.1◦ . Six function relationships are taken into account: linear function, power function, logarithmic function, hyperbolic function, exponential function, and negative exponential function. The VICs of the particles are the independent variable and the lightning density is the dependent variable. During the analysis process, grid points without lightning or particles are not considered. The spatial correlations between particle VIC and total lightning density are generally not significant, although the exponential relationship is better than the relationships obtained for other functions and is statistically significant at the 0.01 level (F -test). Figure 2 shows scatter plots and fitting curves (the optimal relationship is shown in each case) for lightning density versus the four types of particles. Table 2 lists

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the analysis results regarding the exponential relationship, including the calculated integration levels with the best correlation, correlation coefficients, and regression equations. Among the liquid phase particles, the VIC of cloud water above the 0 ◦ C level and the VIC of precipitation water at all levels show stronger relationships with lightning density than that of water at other levels. Among the ice particles, the VICs of cloud ice and precipitation ice above –10 ◦ C show the strongest relationships with lightning density. This result reflects the fact that the main charging activity is generated in the mixed-phase regions where the temperature is below –10 ◦ C, as described by the NIC mechanism. 3.2 Correlation between lightning activity and maximum surface rainfall The maximum rainfall intensity in a thunderstorm is usually of concern in terms of hazard

Fig. 2. Scatter plots and fitting curves (the exponential function shows the best correlation, see Table 2) of the density of total lightning observed by SAFIR3000 vs. (a) VIC of cloud water, (b) VIC of precipitation water, (c) VIC of cloud ice, and (d) VIC of precipitation ice.

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Table 2. Spatial exponential relationship between the VICs of precipitation particles and lightning density Hydrometeors

Levels of

Correlation

the best

coefficient

Regression equation

correlation Above 0 ◦ C

0.401

DSL=1.68 × 10−3 exp(4.85VICcldWater0 )

Precipitation water

All levels

0.436

DSL=11.63 × 10−3 exp(7.54 × 10−2 VICprecipWater ) − 0.01

All water

All levels

Cloud water

Cloud ice Precipitation ice

0.436

DSL=11.53 × 10−3 exp(7.01 × 10−2 VICWater ) − 0.01

Above

–10◦ C

0.342

DSL=12.59 × 10−3 exp(0.33VICcldIce−10 ) − 0.01

Above

–10◦ C

0.421

DSL=12.34 × 10−3 exp(0.06VICprecipIce−10 ) − 0.01

–10◦ C

All ice Above 0.415 DSL=12.33 × 10−3 exp(0.05VICIce−10 ) − 0.01 −2 −1 Note: DSL is the density (unit: fl km min ) of the total lightning observed by SAFIR3000. The unit of VIC is kg m −2 . The subscript “cldWater” in the regression equation denotes cloud water; “precipWater” denotes precipitation water; “Water” denotes all liquid water (cloud water plus precipitation water); “cldIce” denotes cloud ice; “precipIce” denotes precipitation ice; “Ice” denotes all ice particles (cloud ice plus precipitation ice). The subscripts “0” and “–10” denote the temperature levels above which the VICs of the particles are calculated. The absence of a subscript number indicates that the VIC of the particles is calculated at all levels.

mitigation. Previous studies have reported strong relationships between lightning frequency and rainfall intensity in a time sequence (e.g., Zhou et al., 1999; Chang et al., 2001; Pessi et al., 2004). However, lightning frequency is strongly influenced by the size and intensity of the thunderstorm. In turn, thunderstorm size shows a relatively weak relationship with maximum rainfall intensity. Therefore, the correlation between lightning frequency and rainfall intensity reported in previous case studies lacks universal significance. In this section, a new parameter, relative lightning density (unit: fl km−2 min−1 ), is introduced. The relevant equation can be written as Dr = F/Ar ,

(1)

where Dr is lightning density (D) relative to a certain threshold value of rainfall intensity (subscript r), F is the frequency of lightning over the entire thunderstorm calculated over 1 min, and Ar is the area (A) of the region in which the rainfall intensity exceeds the threshold value r. The correlation between Dr and maximum rainfall intensity Rmax (unit: mm h−1 ) is analyzed in this section. This approach helps to eliminate the influence of uncertain or unknown factors on the lightning distribution in thunderstorms. It also connects the lightning activity caused by strong dynamic and microphysical processes with the strong rainfall region, which is also caused by strong dynamic and microphysical processes. Therefore, this correlation should be universal.

The analysis is based on a 0.01◦ ×0.01◦ grid. Because the analysis is performed on the storm scale, a fine grid is beneficial to the fine region choice of the thunderstorms and the calculation of the content of particles under the condition of the threshold value; the same grid is used in Section 3.3. Lightning data observed by LIS are used in the analysis. The threshold values of rainfall intensity are chosen from 0 to 50 mm h−1 at intervals of 5 mm h−1 . The six function relationships mentioned above are taken into account here. For a threshold value of 30 mm h−1 (20 thunderstorms produced rainfall exceeding this threshold value when the TRMM satellite passed overhead), the strongest correlation is obtained for all function relationships. Furthermore, the power relationship performs the best among the six functions, yielding a correlation coefficient of 0.841 and a regression equa−0.18 tion of Rmax = 23.10D30 +11. The obtained F test value of 43.579 is much larger than the value of F0.01,1,18 (= 8.285), which indicates that the correlation is significant at the 0.01 level. The scatter plot and fitting curve corresponding to the regression equation are shown in Fig. 3. 3.3 Correlations between lightning activity and the contents and covering areas of precipitation particles This section introduces the threshold values of the particle VICs. We now focus on the relationship between the frequency of total lightning in the entire

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4. Conclusions and discussion

Fig. 3. Power function relationship between the lightning density relative to a rainfall intensity threshold value of 30 mm h−1 and the maximum rainfall intensity. Lightning data were observed by LIS.

thunderstorm and the contents and covering areas of those precipitation particles for which the VICs exceed the relevant threshold values. The calculation is performed in an analysis grid of 0.01◦ ×0.01◦ , using lightning data observed by LIS. Again, the six function relationships mentioned above are taken into account. The results show that the correlation is adequately described by a linear relationship; consequently, only the results of linear correlations are reported here. The analysis reveals that significant relationships exist between lightning frequency and the contents and covering areas of particles only in the case that suitable threshold values are chosen for particle VICs. The correlations weaken in the case with the chosen threshold value larger or smaller than the optimal value. The analysis process is not described here. Figure 4 and Table 3 show the best correlations based on the suitable threshold values of the VICs of precipitation ice. For a certain threshold value, the contents or covering areas of the ice particles above the –10 ◦ C level exhibit a stronger relationship with lightning frequency than the case in which ice particle content is integrated for all levels or the case in which the ice particles are above the 0 ◦ C level. Table 3 lists the linear fitting formulas used to calculate the lightning frequency by using the contents and covering areas of the particles for which VIC values exceed the optimal value.

Based on the precipitation particle concentration information obtained from the 2A12 product of TRMM/TMI and the total lightning activity observed by TRMM/LIS and SAFIR3000, 34 thunderstorms that occurred around Shanghai and Wuhan are analyzed in this study. The relationships between lightning activity and precipitation particle characteristics are identified. Main results are as follows: (1) The spatial relationships between total lightning density and the VICs of four kinds of precipitation particles (cloud water, precipitation water, cloud ice, and precipitation ice) are not significant when the analysis is performed on a spatial scale of 0.1◦ ×0.1◦ . Exponential relationships are established in describing the data when particle VICs are independent variables and lightning density is the dependent variable. The obtained regression equations are shown in Table 2. (2) A parameter, relative lightning density, is introduced in this study. A power relationship provides the best correlation between lightning density (with the threshold value of rainfall intensity at 30 mm h−1 ) and maximum rainfall intensity. The resulting regres−0.18 sion equation is Rmax = 23.10D30 +11, with a correlation coefficient of 0.841, where D30 represents the lightning density relative to a threshold value of 30 mm h−1 (unit: fl km−2 min−1 ) and Rmax is the maximum rainfall (unit: mm h−1 ). This relationship, based on the relative lightning density, should be relatively universal for different thunderstorms, compared with the relationships based on the lightning frequency. (3) Lightning frequency only shows a significant linear correlation with the contents and covering areas of precipitation particles for which VIC values exceed the suitable threshold values. Table 3 summarizes the results of this analysis and shows the regression equations. (4) Ice particles above the –10 ◦ C level show a stronger correlation with lightning activity than those above the 0 ◦ C level or the integrated ice particles at all levels. This is consistent with our understanding of the main charging regions based on the NIC mechanism, which states that charging activity occurs

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mainly in mixed-phase regions where the temperature is below –10 ◦ C.

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Analysis of a large number of observations reveals that a strong ice-phase process exists prior to the

Fig. 4. Scatter plots and fitting curves showing total lightning frequency observed by LIS vs. the covering areas and contents of precipitation particles for which VIC values exceed threshold values (TVs). Only the strongest linear relationship is shown in each case. The horizontal axis represents the area of cloud water above the 0 ◦ C level with TV = 0.3 kg m−2 (a1 ), the content of cloud water above the 0 ◦ C level with TV = 0.3 kg m−2 (a2 ), the area of precipitation water at all levels with TV = 4.0 kg m−2 (b1 ), the content of precipitation water at all levels with TV = 3.0 kg m−2 (b2 ), the area of all water at all levels with TV = 5.0 kg m−2 (c1 ), the content of all water at all levels with TV = 3.0 kg m−2 (c2 ), the area of cloud ice above the –10 ◦ C level with TV = 1.0 kg m−2 (d1 ), the content of cloud ice above the –10 ◦ C level with TV = 1.0 kg m−2 (d2 ), the area of precipitation ice at all levels with TV = 9.0 kg m−2 (e1 ), the content of precipitation ice above the –10 ◦ C level with TV = 3.0 kg m−2 (e2 ), the area of all ice above the –10 ◦ C level with TV = 7.5 kg m−2 (f1 ), and the content of all ice above the –10 ◦ C level with TV = 3.0 kg m−2 (f2 ).

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Fig. 4. (Continued.)

occurrence of lightning in convective clouds. The fact that ice particles are the main carriers of the charge indicates that ice particles and lightning activity should have a correlation in their spatial distributions. Actually, previous investigations have reported that the sites of convergence of ice particles generally coincide with strong lightning activity (e.g., Carey and Rutledge, 1996; L´opez and Aubagnac, 1997; Takahashi et al., 1999; Dotzek et al., 2001). However, the spatial

correlation between these two factors is relatively weak in the present study on a spatial scale of 0.1◦ ×0.1◦ . It might indicate that the amount of particles and amount of charge are weakly correlated in terms of their spatial distributions. We believe that dynamical processes (e.g., updraft or the wind field in the cloud) are responsible for the weak nature of the relationship, as such processes are expected to be the most important factor in controlling the environmental conditions

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Table 3. Correlations between lightning frequency and the contents and covering areas of precipitation particles restrained by the suitable threshold values of VIC Attributes

Area

Mass

Parameters

Cloud water

TV (kg m−2 ) Levels

0.3 Above 0 ◦ C level 0.817

Precipitation water 4 All levels

All water

Cloud ice

5 All levels

1.0 Above –10◦ C level 0.803

Precipitation ice 9.0 All levels

All ice 7.5 Above –10◦ C level 0.783

Correlation 0.766 0.765 0.783 coefficient Fitting FL=6.25×10−2 FL=1.89×10−2 FL=2.21×10−2 FL=4.92×10−2 FL=5.02×10−2 FL=5.16×10−2 equation ·A+14.93 ·A+7.65 ·A+8.44 ·A+7.39 ·A+9.82 ·A+12.07 TV (kg m−2 ) 0.3 3 3 1.0 3.0 3.0 Levels Above All levels All levels Above Above Above 0 ◦ C level –10 ◦ C level –10 ◦ C level –10 ◦ C level Correlation 0.817 0.777 0.774 0.793 0.764 0.770 coefficient Fitting FL=1.59×10−7 FL=2.29×10−2 FL=1.94×10−9 FL=3.06×10−8 FL=2.30×10−9 FL=1.86×10−9 equation ·M +15.83 ·M +5.89 ·M +4.30 ·M +8.12 ·M +9.87 ·M +7.87

Note: “TV” is the threshold value of the VIC of precipitation particles corresponding to the best correlation. “Levels” is the height ranges of precipitation particles considered in the calculation. In the equations, “A” is the area (km 2 ) of regions for which the VIC of the particle exceeds the threshold value; “M ” is the content (kg) of particles in regions for which the VIC of the particle exceeds the threshold value; “FL” is the lightning frequency per minute (unit: fl min −1 ) for the entire thunderstorm.

that influence the charging process and the transfer and distribution of particles (e.g., Boccippio, 2002; Ely et al., 2008; Deierling and Petersen, 2008; Zheng et al., 2009). Another explanation might be that the lightning initiation should have a closer relation with the distribution of electric field, but not with the charge considered in this paper. On the storm scale, lightning activity shows a significant relationship with particle content. The threshold values of the VICs of precipitation particles and the analyzed heights (e.g., the –10 ◦ C level) play important roles in the relationship between lightning activity and characteristics of precipitation particles (e.g., rainfall amount, the content and covering area of particles). This finding indicates that smaller regions with a larger number of particles (i.e., higher threshold values of the VICs of particles) may not encompass the total particles responsible for the most significant charging process and lightning activity. Similarly, the relationship between lightning activity and characteristics of precipitation particles is weak when the threshold values of VIC of particles are smaller than the optimal value or if there is no threshold value, as such particles do not necessarily represent the particles involved in both the charging process and lightning activity. Similarly, Deierling and Petersen (2008) reported that the updraft volume

in the charging zone (at temperatures colder than –5 ◦ C) with vertical velocities greater than either 5 or 10 m s−1 has the most significant relationships with total lightning activity. Therefore, the result regarding the dependence of the relationship between lightning activity and characteristics of particles on the threshold value of VIC may reflect the demand of the charging process on strong dynamic characteristics. In addition, the 34 thunderstorms occurred in different regions and were at different stages of development when observed by the TRMM satellite. Therefore, the results are universal only to a certain degree. The present results will be of use in assimilating lightning information into numerical prediction models to improve forecast results. Meanwhile, the particle products from the prediction models are also helpful in estimating lightning activity over the coming 2–6 h.

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