Understanding the Effects of Aerosols on Electrification and Lightning Polarity in an Idealized Supercell Thunderstorm via Model Emulation

Aerosol effects on the lightning intensity and polarity of a continental supercell storm were investigated using a three‐dimensional lightning scheme within the Weather Research and Forecasting model. We find that both intra‐cloud (IC) and cloud‐to‐ground (CG) flashes are enhanced by the increasing number of cloud condensation nuclei (CCN), especially the percentage of positive CG (+CG) strokes peaking at 42%. Electrical characteristics of the storm varied in different aerosol scenarios through microphysical processes. Added aerosols increase the number of cloud droplets and ice‐phase hydrometeors. The greater ice‐crystal concentration and larger graupel size ensure sufficient charge separation, leading to higher charge density and more lightning discharges. In addition, an inverted polarity charge structure with a strong positive‐charge region in the mid‐levels was formed mainly due to the positively charged graupel in the presence of higher supercooled cloud water content. Positive lightning channels originating from this positive‐charge region propagated to the ground, producing more +CG strokes. When the aerosol concentration was low, the charge density in the upper positive‐charge region was much lower due to smaller ice‐particle content. Consequently, there were barely any +CG strokes. Most of the negative CG flashes deposited positive charge in the lower negative‐charge region.

Aerosols can also influence the percentage of intra-cloud (IC) and cloud-to-ground (CG) flashes, as well as the percentage of positive/negative CG lightning (Guo et al., 2016;Murray et al., 2000).Positive CG (+CG) flashes can be correlated with storm severity and even tornado occurrence, although they only account for a small fraction of the total flashes that most storms produce (Carey et al., 2003;Schultz et al., 2011;Yuan et al., 2020).During the 2019-2020 Australian wildfire, Liu et al. (2021) found that added aerosols invigorate both negative CG (−CG) and positive intra-cloud (+IC) lightning in moist oceanic convection.However, Lyons et al. (1998) reported that thunderstorms generate a high fraction of lightning with positive polarity (+CG) during a pollution episode under exceptionally dry conditions over the central US.Fernandes et al. (2006) found an enhancement of +CG strokes in smoke-invigorated clouds in Brazil.A tripole charge configuration with a lower positive-charge center and no +CG flashes was observed by X. Qie et al. (2005) in a thunderstorm over the Tibetan Plateau.An inverted dipole with an additional negative-charge region below the main positive-charge center was proposed to explain the enhancement of +CG flashes in dust-ingested clouds over the Mediterranean Sea (Yair et al., 2021).The electrical processes under different aerosol conditions, especially the lightning polarity and its origins, vary in different studies.
Observing the details of in-cloud processes (e.g., graupel, snow, and ice crystals) is challenging, especially in terms of any causal effect.However, numerical simulations can be used to study aerosol effects on storm-scale electrification and lightning discharges (e.g., Khain et al., 2010;Mitzeva et al., 2006).Mansell and Ziegler (2013) and Tan et al. (2017) employed three-and two-dimensional models, respectively, to investigate the response of storm-scale electrical processes to aerosol concentration.Additionally, P. Zhao et al. (2015) used the Weather Research and Forecasting (WRF) model to investigate thunderstorm electrification under clean and polluted conditions, finding that elevated aerosols increased the cloud water content (CWC) and ice-phase particle concentration.More studies have been devoted to investigating the relationship between aerosols and lightning production.For instance, Shi et al. (2015) related the lightning flash rate to the ice-phase particle mass in thunderclouds, finding that an increase in aerosol concentration led to increases in charge separation and lightning flash rate.To compare the differences between the microphysics and electrification of polluted and pristine thunderclouds, Y. Wang et al. (2011) used the lightning potential index to represent lightning activity, which is linked to updrafts, ice-phase particles, and liquid water contents from WRF model simulations.A bulk lightning model was used by Sun et al. (2021) (hereafter referred to as Sun21) to estimate the flash origin density by reducing and redistributing charges throughout a cylindrical region after each discharge (Fierro et al., 2013).These simulations were mainly based on a simple empirical formula or bulk lightning parameterization.To investigate in detail the effects of aerosols on lightning intensity and polarity in thunderclouds, this study presents simulation results obtained using a model with explicit treatments of three-dimensional discharge processes.

Model Description and Experiment Design
We used the electrified WRF model version 4.3.1 (WRF-ELEC; Fierro et al., 2013) coupled with a sophisticated three-dimensional lightning scheme (MacGorman et al., 2001;hereafter M01).The model includes a double-moment microphysics scheme and an explicit charging parameterization (Mansell et al., 2005).
The National Severe Storms Laboratory bulk microphysics scheme (Mansell et al., 2010) assumes gamma size distribution and predicts both mass and number concentrations for six hydrometeor species (cloud droplets, raindrops, graupel, snow, hail, and ice crystals).Mansell et al. (2010) provide further descriptions of the scheme.Only details relevant to this work are presented here.The cloud nucleation is predicted following Twomey (1959).The activated aerosols are represented by cloud condensation nuclei (CCN), and their bulk concentration is prescribed by Equation 1: where CCNC is the assumed CCN concentration, S is the supersaturation, and k = 0.6 is the exponent in Twomey (1959) CCN relationship.The number of un-activated CCN is tracked, with the model depleting local CCN either in the cloud or at the cloud base when droplets are activated (Mansell & Ziegler, 2013).Droplet condensation growth is treated explicitly (i.e., no saturation adjustment), which can leave residual supersaturation.Cloud droplet nucleation, deposition, evaporation, condensation, ice multiplication, freezing and melting, riming, sublimation, cloud ice nucleation and aggregation, and conversions between hydrometeor species are all included in the microphysical processes.High-density frozen drops (e.g., small hail) fall in the graupel SUN ET AL. 10.1029/2023JD039251 3 of 23 category because graupel particle density can be predicted within the allowed range (300-900 kg m −3 ).Collected low-density snow and ice crystals are assumed to add to the graupel volume at the minimum density allowed for graupel (Mansell et al., 2010).
Electrification parameterizations (Mansell et al., 2005) consist of non-inductive charge separation, which is independent of the ambient electric field transfer charge between graupel and small ice and snow particles.The non-inductive charging is based on the riming accretion rate (RAR; Saunders & Peck, 1998).The mean separated charge (δq) is calculated for rebounding collisions between graupel-hail and snow-cloud ice (Fierro et al., 2013), using the non-inductive critical charging curve as a function of temperature and RAR: where B, a, and b are subjected to crystal size; D n,I is the diameter for the cloud ice (or snow) category;   and   are the mass-weighted mean terminal fall speeds for graupel and cloud ice (or snow), respectively; and q ± (RAR) is the charge separation as a function of RAR.The critical RAR curve defines the positive and negative graupel charging zones, which is a piece-wise continuous function given by Mansell et al. (2005): where s(T) is the polynomial fit as a function of temperature T: (5) Inductive charge separation (i.e., electric field-dependent) in rebounding graupel-droplet is also considered.Following a set of tests, Mansell et al. (2010) found that the rate of inductive charging is much weaker than noninductive charge separation, but it is important for the formation of lower-charge regions.The electric field potential is solved using the "black box multigrid" elliptic equation solver (Dendy & Moulton, 2010).
The lightning model used in this study differs from that used by Fierro et al. (2013).We use an explicit three-dimensional scheme (M01) for discrete lightning discharges.This scheme considers the discharge process as individual flashes (i.e., IC and CG flashes) rather than a bulk process across the domain of simulation (i.e., Ziegler & MacGorman, 1994, hereafter ZM94;Fierro et al., 2013).Currently, the M01 scheme is less practical for real-time use because it is more time consuming than the ZM94 scheme (about 3 times more) for comparable flash density.Breakdown is initiated when the electric fields exceed a height-dependent threshold E init provided by Dwyer (2003).After that, the starting point is selected randomly among grid points with |E| > E init -δE init , where δE init = 10 kV m −1 .The M01 scheme propagates an explicit channel parallel and antiparallel in a time step from the point of initiation.The lightning channel at each end initially stops at points where the ambient magnitude falls below a fixed threshold [set to 90% of E init , as in Fierro et al. (2015)].A channel end is terminated if it reaches the ground.Others are allowed to extend to all contiguous points having |ρ| > |ρ chan | and |ϕ| > |ϕ end |, where ρ is the net charge density at a grid point, ρ chan is the minimum value of charge density for a point to be involved in channels, and ϕ and ϕ end represent the ambient electrical potential at a grid point and at the channel end before development, respectively.All grid points satisfying these criteria can become involved in discharging processes.The proportion of the available charge density neutralized by individual flashes is set to 30% [as in M01].The lightning model computes flash rates, the flash extent density (FED), and lightning channel counts (LCCs) of total lightning activity (IC and CG strokes).In the present study, the FED is the total number of flashes developing into the grid column.The LCC represents the integration of all positive or negative channel counts at a given altitude in each column every time step.
To investigate in detail the effect of aerosols on lightning discharges in thunderclouds, an outbreak supercell thunderstorm with a large amount of convective available potential energy was chosen and simulated.This storm occurred in western Texas on 2 June 1995, significantly intensifying on the immediate cool side of the outflow boundaries (Gilmore & Wicker, 2002;hereafter GW02).The present study therefore only included supercells on the cool side.Figure 1 shows the thermodynamic profile used for simulations, taken from Fierro et al. (2006).Gilmore (2000) provides details of this storm.The purpose for choosing this profile is to provide a suitable thunderstorm environment so that the aerosol effects on electrification and lightning polarity can be investigated.
Simulations were performed in a 400-km × 400-km domain, with a constant grid spacing of 1 km in the horizontal.The vertical grid had 61 vertical levels, with the top set to 20 km.Each simulation was run for 240 min, with a 5-s time step.Although the storm did not dissipate after 240-min simulation, the lightning flash rate and +CG flashes did increase in the polluted run, which is sufficient for our analysis.Convection was initiated by a thermal bubble having a perturbation of +2.5 K.The dominant CG polarity of the storms observed on 2 June 1995 depends on the local environment (GW02).Therefore, we designed all sensitivity experiments using a horizontally homogeneous environment in this study instead of a heterogeneous one (Fierro et al., 2006), with the purpose of examining aerosol impacts on lightning polarity.Besides the continental case [900 × (ρ air /ρ 0 ) cm −3 , where ρ 0 = 1.225 kg m −3 , and ρ air is air density, hereafter Ctrl run], additional simulations were designed based on the Ctrl run by changing CCN concentrations to 350 × (ρ air /ρ 0 ) cm −3 (i.e., clean run) and 1,400 × (ρ air /ρ 0 ) cm −3 (i.e., polluted run) in the initial conditions.There were no observations of IC lightning from the National Lightning Detection Network for this case (Fierro et al., 2006).The variation of CG lightning flashes observed in actual storms was only reproduced in the Ctrl run.Simulated flashes were dominated by negative polarity, consistent with the lightning behaviors before crossing the boundaries.The convective characteristics (e.g., 40-dBZ echo-top height) of the simulated storms in the Ctrl case were also similar to observations (GW02).
For comparison, the CCN concentration in the clean run was selected according to simulation tests conducted by Mansell et al. (2010).This concentration can promote large cloud droplet diameters to sustain an effective collision-coalescence process.The initial number concentration for the polluted case was set following Mansell et al. (2005), which was higher than the number concentration in the Ctrl run.The high prescribed CCN concentration guaranteed small droplets that could efficiently hinder the warm-rain process in the model (Dye et al., 1974;Mansell et al., 2005).

Aerosol Effects on Convection and Microphysics
To investigate whether increasing the CCN concentration changes convection, Figure 2 shows the spatial distribution of radar reflectivity during different stages of the storm for different aerosol scenarios.Based on the characteristics of reflectivity and lightning activity (van den Broeke et al., 2008;Liu et al., 2021;Lu et al., 2022;C. Zhao et al., 2022), the different stages of storm development, that is, initial (Figures 2a, 2d Figure 2 also depicts FED at different times.The spatial distribution of simulated lightning was consistent with that of radar reflectivity at the different stages.Lightning was concentrated in areas where the radar echo was greater than 40 dBZ.FEDs were enhanced as the CCN concentration increased.We further examined convective intensities for the different runs by comparing profiles of radar reflectivity and vertical velocity (Figure 3).The maximum updraft speed above 10 km (Figure 3a) and the 55-dBZ echo volume (Figure 3b) were significantly increased in the polluted case, indicating much stronger convection.
The cloud water number and ice-phase volume (i.e., ice crystals) also increased under polluted conditions.Figures 4-6 show the time-height variations of microphysical properties for different hydrometeors.For each quantity, properties were averaged horizontally over the entire region at a given altitude.The added CCN concentration increased the number of droplets while decreasing their radii.The droplet number concentration peaked below 3 km in the clean case, with higher values up to ∼8 km for the polluted case (Figures 4a and 4e).In the clean run, the largest cloud droplets (26.5 μm radius, Figure 7a) appeared around 9 km.Cloud droplets with maximum radius of 23.1 μm in the polluted run was smaller than in the clean case, appearing above 10 km.These smaller droplets suppressed the collection-coalescence process.The formation of more cloud droplets in the polluted run induced stronger convection, as previously discussed.As a result, more droplets lifted by stronger updrafts to higher levels increased the supercooled CWC and enhanced mixed-phase processes, leading to larger ice particle mixing ratios at upper levels (<−40°C, roughly 8-14 km, Figures 5b, 5d, and 5f).Rime splintering (i.e., the Hallett-Mossop process) can contribute to larger ice crystal number concentrations within a certain temperature range and is sensitive to the droplet size distribution (Mansell & Ziegler, 2013).Homogeneous freezing of cloud droplets from 8 to 14 km primarily led to an increase in ice particle content (Straka & Mansell, 2005).Table 1 summarizes the domain-averaged microphysical characteristics of different hydrometeors.These values were averaged over the entire simulation period.The ice crystal content was much greater under polluted conditions, with domain averages of 272.2 × 10 3 kg −1 for the polluted run and 37.5 × 10 3 kg −1 for the clean run.The mean-mass radius of ice crystals in the polluted run (21.9μm) was smaller than in the clean run (30.7 μm).The largest ice crystals in the polluted case appeared above 8.5 km, while in the clean case, they appeared around 8 km (Figure 7d).
Increasing the CCN concentration can effectively suppress the warm-rain processes (Figures 4d and 4f) due to the reduced conversion from smaller droplets to raindrops.Under polluted conditions, the rain water content was much less than that in the clean case.Compared to cloud droplets and ice crystals, graupel and snow particle contents were much less in the polluted case.Previous studies have reported that there could be more graupel in the mixed-phase region (e.g., Y. Wang et al., 2011; P. Zhao et al., 2015).However, other studies have found a decrease in the graupel content (e.g., Tan et al., 2017;Sun21).A possible explanation is that the additional mass is kept in droplets that freeze into ice crystals, reducing the net precipitation efficiency.Reduced raindrop freezing leads to a reduction in the graupel mass mixing ratio.The snow content is also reduced because of its similar growth process to graupel in simulations: collection of droplets or cloud ice (Mansell et al., 2010;Zrnic et al., 1993).The mean-mass radius of graupel for the polluted case was larger than in the clean case (Figure 7 and Table 1), mainly resulting from the lower number concentration.The difference in snow particle size between polluted and clean cases was small (Figure 7e).This is mainly because the collected snow particles were assumed to add to the graupel volume, resulting in a further decrease in snow content after 120 min (Figures 6a, 6c, and 6e).Small hail can be represented by frozen drops in the graupel category (Mansell et al., 2010).The change in hail content here was thus not significant with increasing CCN concentration.Figure 7f displays domain-averaged mean-mass

Aerosol Effects on the Evolution of Electricity
The vertical cross-section of the total net charge illustrates the charge structure at different stages of the simulations under clean, Ctrl, and polluted conditions (Figure 8).A charge configuration with negative charge below positive charge (i.e., a normal dipole) was seen in the clean run.Compared to the clean case, a significant inverted dipole (i.e., negative charge with positive charge below it) was simulated in the Ctrl and polluted runs.This inverted polarity charge distribution sustained a negative-charge region that later appeared beneath the main positive-charge region in the polluted case (Figure 8h).The charge density of the polluted run was greater than that of the clean run, with a maximum positive-charge density of more than +0.5 nC m −3 (Figure 8i).The peak charge density was about +0.1 nC m −3 in the clean run (Figure 8c).
To investigate the effect of aerosols on general electrical processes, Figure 9 shows the time evolution of the averaged non-inductive charging rate.Inductive charge separation was also considered, but its magnitude was around an order of magnitude lower than non-inductive charging so is not presented here.Figure 10 shows the time-height variation of the peak values of positive and negative charge density carried by graupel and cloud ice.
According to Saunders and Peck (1998), graupel particles gain positive charges from rebounding collisions in the presence of a higher supercooled liquid water content in the 9-13 km layer (<−40°C, Figure 9c).Under higher CCN conditions, graupel particles were charged positively within regions of higher CWC (8-10 km, Figures 9b  and 9c), and the reverse for cloud ice.The peak values of positive charge density were much higher than the negative charge density carried by graupel in the polluted case (Figure 10c).Therefore, an inverted dipole appeared in the Ctrl and polluted cases, with a main positive-charge region located in the middle levels (Figures 8d and 8g).Under clean conditions, graupel was charged negatively with lower supercooled CWC at ∼10 km (<−40°C, Figures 9a and 10a), while cloud ice mainly gained positive charges (Figure 10b).These graupel particles and ice crystals corresponded to the lower negative-charge center and upper positive-charge center in the normal dipole, respectively (Figures 8a-8c).The non-inductive charging rates were clearly enhanced as the CCN concentration increased.By contrast, the charging rate was lower under clean conditions, resulting in lower values of charge density at upper altitudes (9-13 km, Figures 8a-8c).As Figure 9 shows, the averaged non-inductive charging rate was ∼0.3 pC m −3 s −1 for the Ctrl run, about half that of the polluted run.Under polluted conditions, the large ice particle content from 9 to 13 km played an important role in non-inductive electrification.Higher charging rates due to the much larger ice-phase particle content further led to an increase in charge density in the polluted case.Table 2 summarizes the averaged and maximum positive (and negative) charge density of different ice-phase particles.The averaged and maximum charge densities are the average and peak values over the entire simulated domain.The charge density carried by ice crystals and graupel in the polluted case is much larger than in the clean case (Figure 10 and Table 2).Lightning discharges only occur if the charge density is high enough for maximum electric field magnitudes to exceed the breakdown value.This suggests that elevated CCN concentrations may have enhanced the lightning frequency in this storm.Because the charge separation during rebounding collisions is considered between graupel-hail and cloud ice-snow, the polarity of charge carried by hail (and snow) particles and graupel (and cloud ice, figure not shown) were similar.Note that the charge density carried by hail in the clean case was close to zero (Table 2), mainly due to the smaller hail size and corresponding weaker electrification.
Concerning temporal variations, total flashes, including both IC and CG lightning, increased significantly after t = 120 min, peaking at ∼220 min under polluted conditions (Figure 11).The number of total flashes was less in the clean and Ctrl cases.Note that the number and fraction of +CG flashes were increased in the polluted case, peaking at 165 min (19 strokes and 42%, respectively; Figure 11c).As Figure 11 shows, the value of +CG strokes reached 62 flashes in the polluted run, while only 10 and 0 +CG flashes were initiated in the Ctrl and clean runs, respectively.To understand the effect of aerosols on the increase in +CG strokes, we further analyzed time-height variations of positively (and negatively) charged LCCs for different scenarios (Figure 12).Consistent with previous studies (e.g., Fierro et al., 2015;Kuhlman et al., 2006), the evolution of positive and negative LCCs coincided well in time with the maximum vertical velocity (Figure 3a) and the number concentration of ice-phase particles (Figure 5).The peak in LCCs at t = 220 min was associated with the peak in total flash (IC and CG) rate under polluted conditions (Figures 11c and 12c).Positive LCCs reaching the ground at t = 145 min, 165 min, and 220 min were collocated with occurrences in +CG lightning.
The heights of charged LCCs correlated well with the heights of charge layers, with positive LCCs generally located at higher levels than negative LCCs, especially in the Ctrl and polluted runs (Figures 12b and 12c).These correlations are related to the peak in electric potential, which is accompanied by lightning discharge processes (e.g., M01; Mansell et al., 2010).The vertical distribution of the polarities of LCCs chiefly arose  from the arrangement of an upper-level (8-12 km) negative-charge region and a positive-charge region at lower levels (5-8 km) in the Ctrl and polluted cases (Figure 8).Under these conditions, lightning flashes were initiated between 6 and 10 km (Figure 12b), related to the interface between the upper negative-and lower positive-charge regions.The occurrence of IC flashes illustrates that the lightning channels had sufficient electric potential to penetrate these regions.Basically, the downward vertical channel is followed downward as long as the electric field maintains the same sign.In this study, a CG discharge is identified if the following criteria are satisfied: (a) the channel reaches down to −5°C, (b) there is a correct lower-charge region (e.g., negative charge for +CG and positive charge for −CG), (c) the starting point has an electric potential >+50 MV for +CG (<−50 MV for −CG), and (d) |E| > E init -δE init (M01).Only if the difference in the electric potentials of the negative-and positive-charge centers is sufficient to provide a channel with positive potential so that it can propagate to the ground, these charge centers would become the source of +CG flashes.Under polluted conditions, the initiation of +CG flashes indicates that the positive-charge center was the main source of +CG flashes.In the clean run, LCCs were concentrated in the region between about 6 and 12 km (Figure 12a), meaning that the lightning channels between the upper positive-and lower negative-charge centers mainly generated IC flashes.The charge separation in the clean case was insufficient for electric field magnitudes to exceed the breakdown threshold to propagate to the ground.As a result, barely any +CG occurred in the clean case, further indicating that the occurrence of +CG lightning was mainly attributed to the lower positive-charge region (4-6 km) of inverted-polarity charge distribution in the Ctrl and polluted runs.The fraction of +CG lightning was much higher in the polluted run than in the Ctrl run, probably due to the larger ice-phase particle content, higher charging rates, and corresponding greater charge density, as previously discussed.

Microphysics, Charge Structure, and Lightning Activity
A clear +CG flash occurred at around t = 145 min in the polluted case (Figure 11c).To explore the relationships between microphysical and electrical processes, Figure 13 shows vertical cross-sections of different variables from the occurrence of this +CG flash for the polluted case.In the clean case, barely any +CG strokes occurred.Vertical profiles during a similar period are shown in Figure 14 to analyze the effects of aerosols on these processes, which correspond to the occurrence of an earlier −CG event under clean conditions (at t = 120 min).
There were two major charge regions in the polluted case, namely, an upper negative-charge region (above 6.5 km) and a lower positive-charge region.This positive-charge region mainly arose from graupel particles acquiring positive charges in the presence of larger liquid water contents (Figure 13b; Saunders & Peck, 1998).
Charged ice and snow particles led to the negative-charge region in upper levels.An additional negative-charge center appeared at 3-5 km, corresponding to the negatively charged graupel.Stronger updrafts transported more supercooled CWCs to upper levels (above ∼4 km), leading to a further increase in ice-phase particles, with 45-dBZ echo tops reaching 12 km (Figure 13c).These increased charged ice-phase particles further led to higher charge densities in the upper levels of the thunderstorm (Figure 13a).By contrast, the simulated charge distribution under clean conditions resulted from snow and ice particles charged positively between 8 and 13 km, and graupel and hail charged negatively between 5 and 8 km (Figures 14b and 14d).The polarities of charged hydrometeors at different levels were mainly due to the different temperatures and supercooled CWC for different CCN concentrations.Concerning the charge density, the peak positive-charge density in the upper levels The Domain-Averaged Characteristics of Hydrometeors in the polluted run reached +1.0 nC m −3 .The maximum of that in the clean case was much less (Figures 13a  and 14a).As previously discussed, convection in the polluted run was stronger than in the clean run.Therefore, more ice crystals and graupel particles with larger sizes could be lifted to the upper levels.Collisions of these particles strengthened electrification processes, further contributing to the higher charge density above 10 km (Figure 13a).Under polluted conditions, graupel and other ice-phase particles were mainly charged positively at upper levels (<−40°C) in the presence of stronger updrafts and higher supercooled CWCs.This explains the formation of the stronger positive-charge center at 4-6 km in the core of convection, important for the occurrence of +CG flashes under high CCN concentration conditions.
We attempted to investigate the source of +CG flashes by examining vertical profiles of LCCs at the pre-mature stage for the clean (t = 120 min) and polluted (t = 145 min) runs (Figure 15).In the clean case, there were fewer positive and negative LCCs than in the polluted run.Both positive and negative LCCs in the polluted run were about four times that of the clean run.
The "inverted" polarity charge distribution was manifested in the discharge processes, with positive (and negative) channels at T < −30°C, generating IC flashes between the upper charge regions (Figures 13a and 15b).As noted by Mansell et al. (2002), a lower negative-charge region is required for the initiation of simulated + CG flashes like the role of the lower positive-charge for -CG flashes.The main positive-charge center was significant enough to initiate +CG strokes in the presence of a lower negative-charge region at 4-6 km, showing positive channels in the 0°C to −20°C layer between these charge regions (Figure 15b).Figure 15b shows a few negative-channel volumes near the ground.These near-ground channels may have come from IC flashes, which can get fairly low, but the potential surface was likely too large in this situation and maybe unrealistic.In the clean case, it is difficult to reach the breakdown threshold of the electric field due to the much lower charge density (Fierro et al., 2015).Positive and negative lightning channels mainly arose from the charge regions in the upper levels (6-8 km) in this case.Fewer LCCs were produced, with even fewer reaching the ground, which explains the weaker lightning discharge and fewer CG flashes in the clean case.

Conclusions and Discussion
To illuminate the aerosol effects on the intensity and polarity of lightning activity, a three-dimensional lightning scheme (MacGorman et al., 2001) was coupled in the WRF model to simulate an idealized supercell thunderstorm.
In addition to a baseline run representing a real situation, sensitivity experiments were conducted under clean and polluted conditions by changing the CCN concentration.The similarity of convective and lightning behaviors between observed and simulated (Ctrl run) storms suggests that our idealized simulation provided at least some of the critical storm characteristics in the 2 June 1995 thunderstorms.Our results indicate that lightning flash rates were enhanced by the elevated CCN concentration, accompanied by a significantly increased percentage of +CG flashes in the polluted case.Figure 16 illustrates these gained insights.
Differences in lightning activity between different aerosol scenarios mainly resulted from microphysical processes.Increased CCN concentrations increased the number of cloud droplets and ice-phase particles.The formation of more cloud water strengthened the convection under polluted conditions, with stronger updrafts at upper levels and a larger 55-dBZ echo volume.Smaller droplets suppressed the collection-coalescence process, leading to less rain water under polluted conditions.These droplets not accreted by raindrops were lifted to higher levels.This enhanced mixed-phase processes, with more ice-phase particles generated at upper levels, mainly resulting from the homogeneous freezing of smaller cloud droplets.The release of latent heat associated with freezing further invigorated convection in the polluted case.The graupel and snow particle contents were less under polluted conditions due to the smaller rain water content and thus less effective collection of raindrops by graupel and snow particles.However, the sizable amount of ice crystals and larger graupel (and hail) particles in the upper levels ensured sufficient charge separation in the presence of supercooled liquid water under polluted conditions.
As indicated by the non-inductive charging mechanism (Saunders & Peck, 1998), graupel particles are mainly charged positively at upper levels, where there are stronger updrafts and higher CWCs.Here, the gross charge distribution resembled an "inverted" polarity charge structure under polluted conditions, with negative charge above the main positive-charge region.Electrification was evidently strengthened due to sufficient collisions between larger graupel (and hail) and other ice-phase particles, leading to a higher charge density in the polluted case.As a result, positively charged ice-phase hydrometeors led to a stronger positive-charge region at lower levels.Lightning discharges occur only if the charge density is sufficient for electric field magnitudes to exceed the breakdown value.The higher charge density partly explains the enhanced lightning activity (IC and CG flashes) owing to the elevated CCN concentration.This main positive-charge center is significant for the occurrence of IC and +CG flashes.Under polluted conditions, positive channels originating from the main positive-charge region can propagate to the ground due to the higher charge density, forming +CG flashes.Therefore, total lightning flashes increased with the added CCN concentration, as did the percentage of +CG strokes.The lower negative-charge region under the main positive-charge center was also important for the initiation of +CG flashes in the polluted case, noted by Mansell et al. (2002).Under clean conditions, lower charge density resulted in fewer lightning discharges.The normal polarity charge structure, with mid-level negative charge below the positive charge, mainly generated IC flashes between these charge regions.The main positive-charge region of the inverted charge structure in the polluted case played a critical role in the initiation of +CG flashes.Even if there were CG flashes in the clean case, it would be difficult to initiate +CG flashes without the existence of a mid-level positive-charge region.
Results reported here support the aerosol hypothesis for charge separation and lightning production.We found that total lightning, particularly the percentage of +CG lightning flashes, increased under polluted conditions, consistent with observations (e.g., Liu et al., 2021;Naccarato et al., 2003).However, aerosols have complicated influences on ice production and updrafts, meaning that the relationship between aerosols and lightning is likely non-monotonic.Too many aerosols may inhibit convection or ice production and reduce the number of lightning flashes (e.g., Altaratz et al., 2010;Hu et al., 2019;Mansell & Ziegler, 2013).In this study, we also found a higher percentage of +CG strokes in the polluted case, originating from lower positive-charge regions with stronger  charge densities.Positive lightning channels from this region could propagate to the ground, forming more +CG strokes.There were very few +CG strokes in the clean case.Previous observational studies have reported the enhancement of +CG flashes in polluted scenarios, speculating that it was due to the charge configuration with an enhanced lower positive-charge region (e.g., Yair et al., 2021).Less obvious aerosol effects on simulated storm charge structure polarity were reported by Mansell and Ziegler (2013).More observational and simulation studies are thus needed to further investigate the effect of aerosols on lightning intensity and polarity.
This study simulated a supercell thunderstorm that occurred in western Texas, but whether our findings are also seen in other types of storms or other regions of the world is unknown.Analyzing different types of storms, which can be created by adjusting the environment in idealized configurations (e.g., Storer et al., 2010; Sun, Qie , et al., 2023), may be warranted.Furthermore, an inverted cloud polarity has often been found in the region of specific thermodynamical conditions (Williams et al., 2005).The roles of aerosol and thermodynamics (e.g., cloud base height, dry bulb temperature) are strongly needed to distinguish, based on collaborative observations in both aspects.Note that the current parameterization in the simulations does not use droplet size to determine non-inductive charging.Some studies have found that large droplets lead to more negatively charged graupel (Avila & Pereyra, 2000).On the contrary, Takahashi (1978) suggested that the impact of droplet size on non-inductive charging was negligible.This presents a challenge for the parameterization of electrification in lightning models.It may be that the varied droplet-size dependence of non-inductive charging could influence the aerosol effects on charge separation and associated lightning polarity.
The input data used for the simulations is available in the Zenodo repository (Sun, Li, et al., 2023).Figure 16.Schematic illustration of the aerosol effects on electrification and lightning polarity.In the clean atmosphere (left), there are lower charge density and fewer lightning discharges as a result of less ice-phase particle content.Negatively charged graupel particles at lower supercooled cloud water content (CWC) form a dipole charge structure, leading to discharges dominated by negative polarity.Added aerosols (right) increase the cloud droplet number that can be lifted above the freezing level, leading to higher supercooled CWC.The increased ice particle content and graupel size enhance charge separation, yielding more lightning discharges.Positively charged graupel particles at higher supercooled CWC generate a strong positive-charge region in the middle level, so an inverted-polarity charge structure appears.Lightning channels originating from this positive-charge region propagate to the ground, producing more +CG strokes.Note that the positive (and negative) lightning shown in the figure is mainly to distinguish the differences between the clean and polluted conditions and does not represent all types of lightning.

Figure 1 .
Figure 1.The sounding used to depict initial conditions for the simulations.
, and 2g), developing(Figures 2b, 2e, and 2h), 2f, and 2i), were identified.Convection developed later in the polluted run than in the Ctrl and clean cases.The morphologies of radar reflectivity during the different periods were similar, with a new convective cell developing toward the north under clean conditions (Figure2c).

Figure 3 .
Figure 3.Time evolution of (a) maximum updraft speed (m s −1 ) at all altitudes (dashed lines) and above 10 km (solid lines), and (b) volume of radar reflectivity (km −3 ) greater than 55 dBZ for different cases.The blue, black, and red curves and bars represent clean, Ctrl, and polluted cases, respectively.

Figure 7 .
Figure 7. Temporal variations of domain-averaged mean-mass radii of different species: (a) cloud water, (b) rain, (c) graupel, (d) cloud ice, (e) snow, and (f) hail.The blue, black, and red lines represent the clean, Ctrl, and polluted cases.Shaded areas show the standard error of each parameter.

Figure 14 .
Figure 14.As in Figure 13, but for simulated variables at the pre-mature stage (120 min) in the clean run.