Simulation of Quasi-Linear Mesoscale Convective Systems in Northern China: Lightning Activities and Storm Structure

Quasi-linear mesoscale convective systems (QLMCSs), which generally last several hours (typically longer than 10 hours) and cover hundreds of miles, are composed of several convective cells arranged almost in a line. QLMCSs are capable of causing a plethora of different severe weather types, including strong wind, hail, microbursts, and torrential rain; moreover, they are responsible for a large percentage of lightning events, which pose great danger to the public (Feng et al., 2009). Therefore, from the last decade on, much effort has been made to understand the characteristics of QLMCSs, including the distribution of their morphologies, the condi- tions of their formation, their types of organization, and their characteristics of evolution (e.g., Smull and Houze, 1985; Rutledge et al., 1988; Parker and Johnson, 2000; Zhu and Chen, 2003; Li et al., 2012).

Many case studies of QLMCSs have focused on specific features of the squall line. (Weisman et al., 1988) found that within the squall line there is a narrow band of intense thunderstorms along the boundary line that separates the rain-cooled air from relatively warm air. (Chong et al., 1987) indicated that the precipitation of the squall line stretches over a very wide band, with the anvil typically spreading to the rear side of the system. (Weisman and Rotunno, 2004) and (Stensrud et al., 2005) showed that the strength and longevity of squall lines are associated with the storm-generated cold pool and environmental shear. Moreover, the distribution of the morphologies of QLMCSs has also been discussed, based on radar-observed characteristics. For instance, (Parker and Johnson, 2000) proposed that QLMCSs have different organizational modes, such as convective lines with leading, trailing, and parallel stratiform clouds, and pointed out that the location of stratiform precipitation of every QLMCS is roughly in accordance with the advection of hydrometeors implied by the mean upper- and mid-tropospheric storm-relative winds.

Although many features of QLMCSs have been revealed, their lightning activities are relatively poorly understood. (Mazur and Rust, 1983) may have been the first scientists to research the cloud-to-ground (CG) lightning characteristics of a QLMCS, and found the highest concentration of CG flashes to be located in convective regions. Following that pioneering work, increasing efforts have since been made to study the lightning characteristics of QLMCSs. Storm structures and lightning activities have been described based on Doppler radar and CG lightning observations, and most case studies have shown that numerous negative CG strokes are clustered within and near the convective line, while most positive CG strokes would be located underneath the stratiform region (Rutledge and MacGorman, 1988; Carey et al., 2003; Lang et al., 2004b; Lu et al., 2009). Some studies have considered that perhaps the advection of charged particles from the convective line and the generation of charge in the original position might account for the occurrence of positive CG strokes in the stratiform region (Nielsen et al., 1994). In addition, in recent years, the evolution of the total lightning structure of QLMCSs has also been investigated by using total lightning detection systems and radar observations (e.g., Lyons et al., 2003; Lang et al., 2004a; Carey et al., 2005). (Carey et al., 2005) established a comprehensive model of the total lightning structure of a QLMCS, which possibly explains how the very-high-frequency lightning structure is related to the dynamical and precipitation structures. (Ely et al., 2008) analyzed the total lightning structure during the lifetime of a QLMCS using three-dimensional total lightning data and composite radar reflectivity, and suggested that the lightning pathway extends from the convective line into the stratiform region at a relatively invariable altitude of 9 km. (Liu et al., 2011) also investigated lightning activities and radar reflectivity characteristics of a QLMCS over Beijing, China, based on data from the SAFIR 3000 lightning detection system and Doppler radar. The lightning morphology of QLMCSs has also been investigated. (Lu et al., 2009) analyzed the charge transfer and in-cloud structure of large-charge-moment positive lightning strokes in QLMCSs and proposed that most positive CG flashes in MCSs initiate in the convective region, whereas they produce strokes in the stratiform region. Moreover, (Lu et al., 2013) investigated the spatial correlation between sprites and in-cloud lightning flash structure in QLMCSs and found that the large-scale structure of sprites could be affected by the in-cloud geometry of positive charge removal.

Based on observed data from Doppler radar and lightning detection systems, the aforementioned previous studies have described the temporal evolution and spatial distribution characteristics of lightning activities, as well as the correlations between lightning activities and radar reflectivity associated with QLMCSs. However, there are still some uncertainties related to QLMCS characteristics due to the limitations of observations, especially with respect to the evolution of lightning activity and its relationship with QLMCS structures. Therefore, in order to improve our understanding of the lightning events associated with QLMCSs, the relationship between QLMCS structures and lightning activities should be investigated in detail through other methods, especially the connections among lightning activity, the wind field, CAPE, the temperature field, and so on. Recently, a numerical model was used to analyze the details of the correlations between the total lightning rate and the microphysics and kinematics in supercell storms (Kuhlman et al., 2006), and the results turned out to be credible. Therefore, the purpose of this paper is to investigate the structures and lightning activities of QLMCSs through high-resolution operational weather prediction model outputs, in which some of the high-resolution parameters and variables, such as wind speed, temperature, CAPE, and mixing ratios of hydrometeors, cannot otherwise be observed directly. Moreover, there is currently considerable controversy concerning how thunderstorms become electrified, although many researchers have accepted the mechanisms involving the interaction between updraft, precipitation, and cloud particles (Keighton et al., 1991). In this study, two QLMCS cases that occurred in northern China are simulated with the Weather Research and Forecasting (WRF) model. The mechanisms of lightning flashes associated with the QLMCSs are also analyzed. The simulation results are first compared with observations in section 3, to validate the simulation. Then, the lightning densities are calculated with the WRF model output based upon a new method, which is described in section 5.1. In sections 6.1 and 6.2, the relationships between lightning and horizontal wind structure, CAPE, and temperature are presented. The electrification mechanism of lightning flashes occurring in the QLMCSs is discussed in section 7, and finally the conclusions and a discussion are given in section 8.

The S-band Doppler radar reflectivity data from the CINRAD-SA (China Next Generation Weather Radar) of Beijing [(39.814^°N, 116.472^°E); triangle 1 in Fig. 1], Tianjin [(39.044^°N, 117.717^°E); triangle 2 in Fig. 1], and Shijiazhuang [(38.352^°N, 114.712^°E); triangle 3 in Fig. 1] and routine observations from the China Meteorological Administration are assimilated in the model to improve the initial conditions of the simulation. The radar reflectivity data of Beijing are also used to validate the simulation. Each of the three Doppler radars covers a radius of 230 km from its location and makes seven-level unique elevation scans (0.5^°-3.4^°) every six minutes.

In this paper, the lightning data from the SAFIR 3000 lightning detection system, which comprises three sensors about 120 km apart, with the center station located at the Beijing Meteorological Administration (locations represented by stars in Fig. 1b), are used to validate the simulation. The detection efficiency of the SAFIR 3000 lightning detection system is greater than 90% around the central regions of the network (Zheng et al., 2009), and the total lightning flash characteristics [intracloud (IC) and CG lightning] are obtained. A detailed introduction to the SAFIR 3000 detection system in China and the processing of its data can be found in (Liu et al., 2011). The SAFIR system is reported to have a high detection accuracy of 1 km (Mazur et al., 1997; Wang and Liao, 2006; Zheng et al., 2009; Liu et al., 2011). The total lightning information from SAFIR 3000 can be used to validate the calculated lightning density, in spite of its accuracy being lower than that of the LMA (lightning mapping array) and LDAR (lightning detection and ranging network) (Thomas et al., 2004; Carey et al., 2005; Ely et al., 2008). In calculation, the lightning radiation sources, when they occurred within 7 km in one second, were defined as one lightning flash, and the position of the first radiation was taken as the lightning's location. Therefore, in this paper, the lightning activity refers to the entire lightning flash.

Figure 1.  (a) The first nested grid and the distribution of routine observation stations (dots), rawinsonde stations (squares), and locations of Doppler radars (triangles) (1, Beijing station; 2, Tianjin station; 3, Shijiazhuang station). Panel (b) is the same as (a), but for the second nested grid, and also shows the three SAFIR 3000 lightning detection system stations around Beijing (stars).

Version 3.2 of the WRF model is used in this study. It is a non-hydrostatic and wholly compressible atmospheric model, and a terrain-following hydrostatic vertical pressure coordinate is used. A detailed description of the model is available at http://www.wrf-model.org/index.php. It is an accessible research tool and commonly used by many operational services for short- and medium-range weather prediction (Yair et al., 2010). In this paper, in an attempt to improve the model forecast, we use the 3D-Var (three-dimensional variational) analysis system, developed within the Advanced Regional Prediction System (ARPS) model (Xue et al., 2003) framework, to assimilate the surface and rawinsonde observations, and the data from CINRAD-SA. Both the reflectivity and radial velocity data from CINRAD-SA are used. Six-hourly NCEP-NCAR (National Centers for Environmental Prediction-National Center for Atmospheric Research) reanalysis data (1^°× 1^°) are used as the background and the model lateral boundary conditions. The 3D-Var system within the ARPS model has been proven to be very effective for initializing midlatitude thunderstorms in many studies (Hu et al., 2006a, b; Zhao and Xue, 2009), and the ARPS4WRF procedures of the ARPS model are used to produce the initial field directly used in the WRF model.

A two-nested grid system with a center located at (116.5^°N, 39.8^°E) is used in this study. The first (outer) system extends 1482 km in an east-west direction and 1380 km in a north-south direction, with grid spacing of 3 km (coverage area shown in Fig. 1a). The second (inner) system extends 582 km in the east-west direction and 480 km in the north-south direction, with grid spacing of 1 km (coverage area shown in Fig. 1b). There are 35 vertical levels, with the top at 50 hPa. The convection is simulated explicitly with this grid spacing in the model; no cumulus parameterization is needed. Based on a comparison with different experiments, the cloud microphysics in the model is configured to use the Single Moment Six-Species (WSM-6) microphysics parameterization (Hong and Lim, 2006). In this scheme, water substances can be divided into six forms: vapor, cloud water, rain, ice, snow, and either graupel or hail. We use the rapid radiative transfer model longwave radiation scheme (Mlawer et al., 1997) and a new 4th-order shortwave scheme. The Monin-Obukhov scheme is used to simulate surface layer fluxes, while the Yonsei University scheme is used to simulate boundary layer fluxes (Hong et al., 2006).

Severe QLMCSs occur frequently in North China every summer. In this study, we select two typical cases of the region for detailed study. The first is a leading line with a trailing stratiform MCS (TS) that occurred on 13 June 2010, and the second is a linear system with parallel stratiform MCS (PS) that occurred on 1 August 2009. Hereafter, the 13 June 2010 case is referred to as Case 1, and the 1 August 2009 case is referred to as Case 2.

Figure 2.  Evolution of the QLMCS on 13 June 2010 (Case 1): (a) low-level radar reflectivity (dBZ) from the CINRAD-SA Doppler radar in Beijing; (b) track of the storm (solid line represents the leading line linked by low-level reflectivity over 35 dBZ); (c) evolution of lightning rate within 15 min.

Figure 3.  As in Fig. 2, but for the evolution of the QLMCS on 1 August 2009 (Case 2).

Figure 2 illustrates the evolution of the reflectivity (Fig. 2a), the track of the QLMCS (Fig. 2b), and the temporal evolution of the lightning rate for Case 1 (Fig. 2c). The first echo on Beijing's radar appeared at 0600 UTC (not shown), and then the formation stage was characterized by rapid radar-echo growth in terms of areal extent and reflectivity intensity. More thunderstorm cells formed at 1100 UTC and the leading line of the convective region formed at 1200 UTC, with the reflectivity increasing rapidly. The QLMCS moved southeastward at a speed of approximately 33 km h^-1 during this stage. At about 1300 UTC, the QLMCS developed into a squall line composed of several convective cells aligned linearly at the front, and a developing stratiform region at the back, almost 7 h after the time of the first echo. A new supercell storm formed in the mature stage, which merged with the mother cells at 1400 UTC, and meanwhile the stratiform region behind the convective line extended approximately 75 km. Next, the QLMCS moved southeastward at an increased speed of approximately 48 km h^-1. During the latter period of the mature stage (soon after 1430 UTC), the reflectivity began to decrease and the reflectivity of the leading line decreased obviously at 1500 UTC. At 1700 UTC, the thunderstorms split into three cells and disappeared quickly. Figure 2c shows the lightning rate increased slowly in the initial stage of the QLMCS. From 1100 UTC, the increase of the lightning rate became faster than in the initial stage, and two small peaks of lightning rate occurred at 1145 and 1215 UTC, before it gradually decreased. Subsequently, the lightning rate again increased rapidly and reached a maximum at about 1400 UTC. Between the period of maximum and minimum lightning rate (1400-1500 UTC), the total lightning rate decreased sharply. After 1500 UTC, the lightning rate varied slightly before the QLMCS dissipated.

Figure 3 shows the evolution of the reflectivity (Fig. 3a), the track of the QLMCS (Fig. 3b), and the temporal evolution of the lightning rate of Case 2 (Fig. 3c). Unlike Case 1, several isolated convective areas formed at 0700 UTC, and then grew with increasing reflectivity intensity before finally merging to form a QLMCS at 0900 UTC. Compared with Case 1, the QLMCS of Case 2 was smaller in range and weaker in intensity, and the stratiform precipitation was narrower. Similar to Case 1, the QLMCS in Case 2 also moved southeastward. The lightning rate was at its maximum at 1200 UTC, then weakened, and two weak peaks appeared during the decaying stage. Both QLMCSs originally formed to the northwest of Beijing and moved from the northwest to the southeast. Based on the radar and lightning information, the complete lifetime of both QLMCSs is divided into three typical stages: the formation stage, the mature stage, and the dissipation stage.

In the simulation, Case 1 is initialized from 0600 UTC to 1800 UTC on 13 June 2010, while Case 2 is simulated from 0600 UTC to 1800 UTC on 1 August 2009. Both simulations cover from the formation stage to the dissipation stage. The large time step of the integration is 15 s, and the time step ratio is 3. The save interval is 15 minutes for both runs. On the 3 km and 1 km grid, both CINRAD-SA full-volume reflectivity and radial velocity data are assimilated at 6-min time intervals beginning at 0600 UTC and continuing for 5 h.

In this section, the simulation results are validated using the observations. Since most of the lightning flashes occurred in the mature stage of the QLMCSs, our validation focuses mainly on the simulations during the mature period. The simulated reflectivity of Case 1 and Case 2 is shown in the right column of Fig. 4, and the corresponding observations are depicted in the left column.

Figure 4.  Low-level radar reflectivity (dBZ) observed by the CINRAD-SA Doppler radar in Beijing (left column), and the WRF-derived reflectivity (right column) on 13 June 2010 (Case 1) and 1 August 2009 (Case 2).

The radar observations show that the linear and high reflectivity region (>45 dBZ) had formed and advanced to the south edge of Beijing at 1300 UTC in Case 1 (Fig. 4a). An individual thunderstorm can be identified near the north of Tianjin with a reflectivity value greater than 45 dBZ (labeled "A" in the figure). The leading line of the convection region and storm A both propagated southeastward during the period 1300-1400 UTC, with the reflectivity intensity of the leading line increasing and the reflectivity intensity of storm A decreasing. The stratiform region at the back of the convective line extended approximately 75 km at 1400 UTC. The model forecast at 1300 UTC 13 June 2010 also depicts a linear and high reflectivity region near the south edge of Beijing, and the location error between the simulation and observation is less than 10 km. Although the simulated coverage area of high reflectivity near the north of Tianjin differs from the observation, storm A can be identified in Fig. 4b. Moreover, the moving direction of the simulated QLMCS is also southeastward. At 1400 UTC, the forecast of the location of the leading line of convection compared to the observed location is quite close. In some locations, the position error is less than 10 km. Although the simulated reflectivity of storm B is higher than observed, the position matches the observed area very well.

From the observed reflectivity in Fig. 4e, it can be seen that a linear intense reflectivity region (leading line) had formed around Beijing at 1000 UTC in Case 2, with maximum reflectivity greater than 45 dBZ, and the stratiform region extending about 10 km. The leading line of the convective region had moved southeastward by 1200 UTC, while the stratiform region had extended significantly parallel to the convective line. Figures 4f and 4h show that the simulation depicts the main trend and evolution of the QLMCS, albeit the simulation covers a larger region than that of the observation.

In addition, comparing the simulated surface wind fields with surface observations, as well as the wind field, temperature, and relative humidity with typical soundings, we find that the simulation successfully depicts the main characteristics of the QLMCS. Taken together, as mentioned above, the model prediction shows excellent agreement with observations, and thus the simulation can be used for further analysis.

Figure 5.  Scatter plots of the domain-wide maximum for the simulated (a) graupel flux at the -15^°C level (m s^-1) (Flux 1 represents), (b) vertical integral of graupel, snow, and cloud ice (kg) (Flux 2 represents), (c) precipitation ice mass (kg) and (d) non-precipitation ice mass (kg) versus observed flash-rate density (flashes per 15 min) for Cases 1 and 2.

(Barthe et al., 2010) suggested that an attractive way to predict lightning flashes in numerical models is to rely on the relationship between model parameters and flash rate. The noninductive charging process is induced by the collision between graupel and ice crystals (or snow crystals) in the region of supercooled liquid water. Therefore, the electric charge buildup rate of a thunderstorm is directly proportional to the concentrations of the interactive particles. (McCaul et al., 2009) proposed a useful method to estimate the total flash rate based on the resolved upward flux of graupel in the mixed-phase region at -15^°C and the gridded vertical integral of graupel, snow, and cloud ice. The results showed that the method could simulate lightning information of a spring supercell and squall line that occurred in the United States. Based on the calculation methods of lightning density in (McCaul et al., 2009), scatter plots of the domain-wide maximum for the simulated graupel flux at the -15^°C level and vertical integral of graupel, snow, and cloud ice versus observed flash-rate density for Case 1 and Case 2 are shown in Figs. 5a and b, and the correlation coefficient is also calculated. The correlation coefficient between the upward flux of graupel in the mixed-phase region at -15^°C and the observed flash-rate density is 0.39. The correlation coefficient between the observed flash-rate density and the vertical integral of hydrometeors is 0.38. From the scatter plot (Figs. 5a and b) and correlation coefficient, the observed lightning flash events and the mixing ratio of graupel at the -15^°C mixed-phase region and vertical integral of hydrometeors are poorly correlated. Therefore, in order to improve the ability to predict the lightning region associated with QLMCSs, necessary modifications are made to the lightning calculation method.

Based on previous published work, we know that the lightning flash rate has a good relation with the amount of precipitation ice mass in deep atmospheric convection (MacGorman and Rust, 1999). The relationship between precipitation ice mass and lightning flash density is relatively invariable between land, ocean and coastal regimes (Petersen et al., 2005). Subsequently, (Deierling et al., 2008) found that precipitation and non-precipitation ice mass above the melting level both show a good relationship with total lightning activity (correlation coefficients exceed 0.9 and 0.8, respectively) in different thunderstorms in the United States. Moreover, the relationship remains relatively unchanged in different regions. The above relationships have also been found by other investigators.

Also based on previous published work, simulated ice-phase particles in a thunderstorm can be classified into precipitation ice mass (graupel and precipitation snow) and non-precipitation ice mass (ice and non-precipitation snow). (Petersen et al., 2005) showed that both non-precipitation and precipitation ice mass above the -10^°C isotherm within regions of radar reflectivity greater than 18 dBZ possess a good relationship with lightning flash density. In this study, in order to estimate lightning density more effectively, the precipitation ice mass is computed from the model output by vertically integrating the mass of precipitating ice between the -10^°C and -50^°C isotherm within regions of radar reflectivity greater than 35 dBZ. The non-precipitation ice mass is computed by vertically integrating the mass of non-precipitating ice from the -10^°C isotherm to the model top and within regions of radar reflectivity greater than 20 dBZ. Figures 5c and d present scatter plots of the domain-wide maximum for the simulated precipitation ice mass and non-precipitation ice mass versus the observed flash-rate density for Case 1 and Case 2. The correlation coefficient between the maximum observed flash-rate density and simulated maximum precipitation ice mass is 0.71. The correlation coefficient between the maximum observed flash-rate density and simulated maximum non-precipitation ice mass is 0.62. Therefore, both the precipitation and non-precipitation ice correlate well with the observed lightning flash rate. Thus, the regression equation derived by fitting the observed lightning flash events and both the precipitation and non-precipitation ice is used to predict the lightning regions.

From the finding in Fig. 5c, we propose that the functional relationship between precipitation ice mass and lightning density can be described by the linear equation \begin{equation} \label{eq1} F_1=4.5\times 10^{-5}\left[\int_{-10{ c}}^{-50{ c}}(\rho\times\Delta x\times \Delta y\times \Delta z\times q_{ p})dz\right]-27.3 , (1)\end{equation} where F₁ is flashes per km² per 15 min (save interval is 15 min in the model); ρ is the density of air; ∆ x, ∆ y and ∆ z are the grid spacings in the x, y and z directions, respectively; and q _p is the mixing ratio of precipitating ice. \([\int_-10 c^-50 c(\rho\times\Delta x\times\Delta y\times\Delta z\times q_ p)dz]\) is the precipitation ice mass in our study. From the findings in Fig. 5d, we also propose the functional relationship between non-precipitation ice mass and lightning density can be described by the linear equation \begin{equation} \label{eq2} F_2=2.7\times 10^{-4}\left[\int_{-10}(\rho\times\Delta x\times\Delta y\times\Delta z\times q_{ np})dz\right]-41.3 . (2)\end{equation} Both regressions are found to be significant at the greater than the 99% confidence level.

Both precipitation and non-precipitation ice mass possess good relationships with the lightning density (Table 1), and thus they are both used for its estimation. Accordingly, we construct a blended WRF lightning threat index that retains F₁ and F₂. This is a similar approach to what (McCaul et al., 2009) did in their lightning prediction scheme. Our goal is to offer an alternative, which has the possible advantage of using the integrated precipitating ice in our formulation over a layer rather than using model output values at a particular layer. Therefore, this lightning threat index is similar to the lightning potential index (LPI), which also integrates over a layer, but just within the convective region. Both the schemes from (Yair et al., 2010) and (McCaul et al., 2009) used the vertical velocity as an estimation factor. In contrast, our scheme does not use the vertical velocity as an estimation factor directly. Instead, term F₁ includes the effects of the vertical velocity, because both the vertical velocity and the terminal velocity of the ice particle are calculated when determining the precipitating ice particles. Both F₁ and F₂ are calibrated against the maximum lightning density, and their peaks should be coincident in space and time. Therefore, any weighted combination of the two designed WRF lightning threat indexes in this study is also properly calibrated. Based on the results of sensitivity tests of the effects of various weight choices on the maximum lightning densities and the areal coverage, we suggest that a workable weighted combination equation is \begin{equation} F=0.6F_{1}+0.4F_{2} .(3) \end{equation}

Equations (1-3) are used to compute the lightning density and estimate the location of lightning flashes based on the output of the WRF model. The calculated lightning densities are compared with observations in the following section.

The calculated lightning density with the simulated precipitation and non-precipitation ice mass in this study is named the PNP. In this section, the observed lightning densities from the SAFIR 3000 lightning detection system in Beijing are used to validate the PNP. The LPI, defined by (Yair et al., 2010), is also used for the validation. The PNP and LPI, as well as the observed lightning densities in Case 1 and Case 2, are shown in Fig. 6. The PNPs of Case 1 and Case 2 from the WRF model are plotted in the middle column of Fig. 6, and the corresponding LPI and observed lightning density are plotted in the right and left column, respectively.

Figure 6.  (a) 15-min averages of observed lightning density [km^-2 (15 min)^-1] (left column), and (b) PNP- (middle column) and (c) LPI-predicted lightning density (right column) for Case 1 and Case 2.

In Case 1, the observed lightning flashes mainly occurred along the adjacent area of Beijing and Tianjin at 1300 UTC, and then the lightning region moved southeastward, being mainly located over central Tianjin and to the south of Beijing at 1400 UTC. Both the PNP and LPI present the main trend and locations of actual lightning activities, and the errors of lightning location between the calculated region (including the PNP and LPI) and the observed one are less than 30 km. Moreover, using our method, the lightning flash region is more similar to the observed one in size. In Case 2, possibly due to the low detection efficiency, only one band of the lightning region, along the adjacent area of Beijing and Tianjin, was detected. In both the PNP and LPI, two lightning regions are clear: one near the north boundary of Beijing, and the other corresponding to the observed lightning region. The southern branch of the calculated lightning region in both methods presents the main trend and locations of actual lightning, with the errors of lightning location at less than 30 km. It should be noted that the lightning region estimated by the PNP is superior in size to that of the LPI. From the lightning distribution and radar reflectivity in Case 1 and Case 2, the simulation and observation both show that the lightning mainly occurred in strong radar echoes, and was located entirely in the convective cores in the mature stage. The leading line of the convective region was formed and the frequency of lightning increased. When the frequency of lightning decreased, the MCS dissipated (figures not shown).

The lightning area fractions according to observations and both estimation methods are shown in Fig. 7. The lightning area fraction is the ratio of the area coverage between lightning and radar echo. In Case 1 (Fig. 7a), the PNP and LPI both reflect the maximum of the actual lightning area fraction; however, the weak maximum in the subsequent period is missed by both methods. In Case 2, the estimate using the PNP is also better than that using the LPI for the maxima of actual lightning area fraction. Taking all of the above into account, it is clear that, compared with the LPI, the PNP is more suitable for the simulated cases, and the estimation with the PNP reflects the main characteristics of the lightning event. However, it should be noted that the LPI may also be a suitable scheme for forecasting the lightning density over North China. Moreover, Fig. 7 shows that the LPI and w² (the square of vertical velocity) featured very similar trends, and the non-precipitating ice also featured a similar trend as the w². The precipitating ice, which is vital in triggering lightning events, is not so sensitive to the variation of the vertical velocity. Therefore, in the PNP scheme, the influence of the vertical velocity and the distribution of various particles are also taken into consideration to a suitable extent.

In order to analyze the dynamic and thermodynamic structures of the lightning flash region and find the parameters favorable for the formation of lightning flash in QLMCSs, lightning flashes are superposed on the horizontal wind field, CAPE, and temperature field. The cross sections of dynamic and microphysical fields between the lightning region and non-lightning region are also shown.

Figure 8 shows the total lightning distribution corresponding to the horizontal wind near the surface and the -15^°C level in the mature stage (1400 UTC 13 June 2010 and 1200 UTC 1 August 2009) in Case 1 and Case 2. (Petersen et al., 2005) proposed that lightning bears a close relationship with the large-sized precipitation ice in the mixed-phase region at -15^°C, and thus the horizontal wind fields at -15^°C levels are shown in this section. From Figs. 8a and c, strong convergence occurs at lower levels ahead of the QLMCS, while divergence appears in the stratiform region, which is located at the rear of the QLMCS. Most lightning flashes are located on the right side and at the front of the QLMCS, where the surface wind field converges obviously. Very few lightning flashes initiate in the stratiform region. Compared to previous studies, (Liu et al., 2011) also showed that most lightning occurs at the front of QLMCSs, based on the analysis of a QLMCS that passed over Beijing. However, (Ely et al., 2008) found that a small quantity of lightning can appear in the stratiform region, and suggested that charge advection of small ice crystals is the predominant mechanism for the charge structure of the stratiform region.

Figure 7.  Time series plots of area fractions of observed lightning density (Obs) (red dotted line), PNP-predicted lightning density (PNP) (green line), and LPI-predicted lightning density (LPI) (yellow line), non-precipitation ice mass predicted lightning density (No Pre) (blue line), precipitation ice mass predicted lightning density (Pre) (black line), and the time series plots of the average square of the vertical velocity (w²) (purple dotted line) in (a) Case 1 and (b) Case 2.

Figure 8.  Lightning flash regions (colored) and surface horizontal wind (m s^-1) in (a) Case 1 and (c) Case 2. Lightning flash regions (colored) and wind field at the -15^°C level in (b) Case 1 and (d) Case 2.

Figure 9.  The lightning flash regions (white areas) and CAPE (J kg^-1) (color shaded) in (a) Case 1 and (b) Case 2. Lightning flash regions (white areas) and surface temperature (^°C) (color shading) in (c) Case 1 and (d) Case 2.

Figure 10.  Comparison of (a, b) vertical speed (color shading) (m s^-1), (c, d) radar reflectivity (color shading) (dBZ), (e, f) graupel mixing ratio (color shading) (g kg^-1), and (g, h) ice mixing ratio (color shading) (g kg^-1) between the lightning flash region and non-lightning flash region in Case 1 at 1400 UTC 13 June 2010. The left column represents lightning flash region, and the right column represents the non-lightning flash region. Black contour lines represent temperature (^°C).

Lightning is superposed on the CAPE field, as shown in Figs. 9a and b, and it reveals zones of intense CAPE located mainly in the direction of the QLMCS' movement; while in the stratiform region of the QLMCS, there are low CAPE zones due to the release of CAPE. Lightning events mainly occur in the regions with a large CAPE gradient.

In order to study the relationship between lightning activity and thermodynamic structure of QLMCSs, the lightning density is superposed on the surface temperature field, as shown in Figs. 9c and d. The distribution of lightning coincides with the area where the gradient of temperature is obvious. Ahead of the QLMCS are warm zones at the surface, while in the stratiform region of the QLMCS there are cold areas due to the evaporation of precipitation. Lightning events mainly occur at the rear of the warm regions.

As mentioned above, lightning events in QLMCSs mainly occur in regions with intense horizontal convergence and intense gradients of CAPE and temperature. In this section, the difference of vertical dynamic and microphysical characteristics between the lightning region and non-lightning region are discussed in detail.

According to the specific distribution of lightning locations, the typical lightning flashes region in Case 1 is located along 39.21^°N, spanning 115.5^°-117^°E, and the typical non-lightning region is located along 39.85^°N, spanning 116^°-117.5^°E. In Case 2, the typical lightning region is located along 38.8^°N, spanning 115^°-117^°E, and the typical non-lightning region is located along 39.8^°N, spanning 115.5^°-117.5^°E.

Figure 10 shows a comparison of the vertical speed, radar reflectivity, graupel mixing ratio, and ice mixing ratio between the lightning regions and non-lightning regions in case 1. The figures that show the same comparison in Case 2 are not included in this paper. Figures 10a and b show a comparison of the vertical speed between the lightning regions and non-lightning regions in Case 1. As can be seen, the lightning regions possess more intense ascending motion than the non-lightning regions in both cases; moreover, the vertical speeds in lightning regions are higher by one order of magnitude than those without lightning events. In Case 1, the maximum vertical velocity in the lightning region is greater than 30 m s^-1, while the maximum vertical speed is approximately 5 m s^-1 in the non-lightning region. In Case 2 (figures not shown), the maximum vertical speeds in the lightning and non-lightning regions are 14 m s^-1 and 4 m s^-1, respectively. At lower levels of the non-lightning regions, downward motions are dominant; whereas for the lightning regions, intense updrafts are obvious.

From the radar reflectivity comparison (Figs. 10c and d), it can be seen that the intensities of reflectivity in the lightning and non-lightning regions differ from each other slightly, and the maximum reflectivity in both instances is approximately 50 dBZ. However, the vertical ranges of the maximum reflectivity in the lightning and non-lightning regions are significantly different. The regions with the maximum radar reflectivity in the lightning regions extend from approximately 700 hPa to 250 hPa, while the corresponding regions fall within the vertical range of only 750-500 hPa in the non-lightning regions in Case 1 and Case 2.

Based on the above, it can be concluded that the storm structures of lightning regions and non-lightning regions in QLMCSs have significant differences. Figures 10e and f show comparisons of the mixing ratios of graupel between the lightning regions and non-lightning regions in Case 1. Figures 10g and h show comparisons of the mixing ration of ice between the lightning regions and non-lightning regions in Case 1.

Figures 10e and f show that the mixing ratios of graupel in the lightning regions are much larger than those in the non-lightning regions. In Case 1, the maximum graupel mixing ratio in the lightning region is greater than 8 g kg^-1 and has a larger coverage area; while in the non-lightning region, the maximum graupel mixing ratio is approximately 4 g kg^-1 and has a smaller coverage area. In Case 2 (figures not shown), the maximum graupel mixing ratios in the lightning and non-lightning regions are above 8 g kg^-1 and 2 g kg^-1, respectively. Moreover, many graupel particles in lightning regions reach a higher level (about 200 hPa) than those in non-lightning regions.

Figures 10g and h show a comparison of the ice particle mixing ratios between the lightning and non-lightning regions, from which it can be seen that the distributions of ice mixing ratio in both regions present no obvious differences. The majority of ice crystal is located in the vertical range of 300-200 hPa in both the lightning and non-lightning regions. Moreover, the ice particle mixing ratio in the non-lightning region covers a larger area than in the lightning region in Case 2 (figures not shown).

In this study, two QLMCSs in northern China were simulated using the WRF model, which incorporated the 3D-Var of the ARPS model to assimilate the observed data. The simulations reproduced the general characteristics of convection, including surface horizontal wind, vertical evolution of temperature and humidity, as well as the radar reflectivity characteristics. Although the specific location of convection did not always correspond to the observations, the maximum location error was less than 50 km. As a result, the model predictions showed good agreement with the observations.

The main objectives of this work were to calculate the lightning density with simulations of the QLMCSs, and then investigate the relationship between the lightning locations and the dynamic and thermodynamic structures of QLMCSs in northern China. The main findings can be summarized as follows:

Most lightning takes place on the right side and at the front of the QLMCS where the surface wind field converges obviously; whereas, very few lightning flashes initiate in the stratiform region. Lightning events mainly occur in regions with a large CAPE gradient. The distribution of lightning coincides with the area where the gradient of temperature is large. Lightning events mainly occur behind the warm regions.

The lightning regions possess more intense ascending motion than the non-lightning regions; moreover, the ascending motion in lightning regions is generally one order of magnitude greater than that in non-lightning regions.The vertical ranges of maximum reflectivity stretch much higher in regions with lightning events than those without. Furthermore, the mixing ratio of graupel in lightning regions is much larger than that in non-lightning regions, mainly due to the obvious difference in ascending motion between the two regions. However, the distributions of the ice mixing ratio in lightning and non-lightning regions present no obvious differences since the ice parcel is a kind of small parcel that can be transported to higher levels of the troposphere by moderate or even weaker ascending motions.

Most previous studies have shown that the lightning flash rate bears a close relationship with cloud microphysics. Nowadays, cloud-resolving models such as the WRF model can simulate the temporal and spatial distributions of multiple species of hydrometeors with high resolution, which can then be used to estimate the lightning flash rate (McCaul et al., 2009; Yair et al., 2010). In this study, we developed a new method using the simulated precipitation ice mass and non-precipitation ice mass to establish the regression equation and estimate the lightning density effectively. According to the comparisons between simulations and observations, we conclude that the lightning rate can be credibly estimated by the simulated precipitation and non-precipitation ice masses. (Blyth et al., 2001) and (Latham et al., 2004) used analytic calculations and yielded the prediction that the lightning flash rate is roughly proportional to the product of the downward flux of graupel and the upward mass flux of non-precipitation ice mass. Our method further proves that there is a good correlation between the total lightning rate and the masses of precipitation and non-precipitation ice.

Based on the high resolution output of the WRF model, the relationships between storm structure and lightning activity in QLMCSs over China were investigated. In contrast to previous studies, we focused on the correlation between lightning flashes and the dynamic structure, including horizontal surface wind, CAPE, and temperature. The results showed that lightning flashes mainly initiate in the intense convergence region ahead of the QLMCS, in regions with a large gradient of CAPE, and in the regions behind the warm zones. Many previous observations have found that most lightning flashes are located in the convective reflectivity core (Carey et al., 2005; Ely et al., 2008; Liu et al., 2011), which in reality corresponds to the intense convergence region. The relationship between lightning flashes and CAPE proves that the locations of lightning flashes can be used to forecast the direction of the QLMCS' movement (CAPE is closely related to the path of the QLMCS). On the other hand, the lightning locations can reflect the position of the convective line and warm zone, and this could be used to improve prediction of severe QLMCS weather events, especially in regions with little or no radar coverage.

The cross section of vertical speed, radar reflectivity, graupel mixing ratio, and ice mixing ratio between the lightning and non-lightning region have also been discussed in this paper. The analysis showed that electrification, and hence the occurrence of lightning flashes, is correlated with wind field convergence, updraft volume, and the concentration of graupel. The results are in agreement with previous observational (Wiens et al., 2005) and modeling (Kuhlman et al., 2006) studies, which also show strong correlation between the lightning flash ratio and graupel and updraft volumes. Our study explored the differences between lightning and non-lightning regions in detail, the results of which enhance our understanding of lightning events. According to the noninductive charging theory, under favorable moisture conditions, intense convergence and updraft produce more graupel particles in the charging zone, thus leading to a greater number of collisions between graupel particles and ice (snow) crystals, which produce charge separation and subsequently result in increased lightning activity.

In this paper, the regression equation developed to forecast the lightning activities of QLMCSs was credible in the two cases, but it may need to be tuned based on additional case study results. The relationships between the lightning distribution and dynamic and microphysical fields have been analyzed indirectly by a regression relationship. This is the first step. In the future, we intend to investigate the relationship between three-dimensional lightning activity and storm structure more thoroughly based on more WRF simulations.