A numerical study of aerosol effects on electrification of thunderstorms

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A numerical study of aerosol effects on electrification of thunderstorms Y.B. Tan a,b,n, Z. Shi a,b, Z.L. Chen a,b, L. Peng a,b, Y. Yang a,b, X.F. Guo a,b, H.R. Chen a,b a

Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing 210044, China Key Laboratory for Aerosol-Cloud-Precipitation of China Meteorological Administration, Nanjing University of Information Science and Technology, Nanjing 210044, China b

art ic l e i nf o

a b s t r a c t

Article history: Received 24 January 2015 Received in revised form 7 September 2015 Accepted 9 November 2015

Numerical simulations are performed to investigate the effect of aerosol on microphysical and electrification in thunderstorm clouds. A two-dimensional (2-D) cumulus model with electrification scheme including non-inductive and inductive charge separation is used. The concentration of aerosol particles with distribution fitted by superimposing three log-normal distributions rises from 50 to 10,000 cm
3. The results show that the response of charge separation rate to the increase of aerosol concentration is nonmonotonic. When aerosol concentration is changed from 50 to 1000 cm
3, a stronger formation of cloud droplet, graupel and ice crystal results in increasing charge separation via non-inductive and inductive mechanism. However, in the range of 1000–3000 cm
3, vapor competition arises in the decrease of ice crystal mixing ratio and the reduction of ice crystals size leads to a slightly decrease in noninductive charge rate, while inductive charging rate has no significant change in magnitude. Above aerosol concentration of 3000 cm
3, the magnitude of charging rate which keeps steady is insensitive to the increase in aerosol concentration. The results also suggest that non-inductive charge separation between ice crystal and graupel contributes to the main upper positive charge region and the middle negative charge region. Inductive graupel–cloud droplet charge separation, on the other hand, is found to play an important role in the development of lower charge region. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Aerosol Non-inductive charging Inductive charging Thunderstorms Numerical simulation

1. Introduction Many studies have been devoted to space charge distributions in thunderstorms, which are closely related to the characteristics of lightning discharges (Carey and Rutledge, 1998; Coleman et al., 2003; Qie et al., 2005; Tan et al., 2006, 2012, 2014a, 2014b). A host of observations of soundings of the electric field demonstrate that the complex charge structure usually including four to ten charge layers in thunderstorms (Marshall and Rust, 1991; Rust and Marshall, 1996). However, it is difficult to fully understand the process of charge structure evolution and the origin of charge generation. At present, many cloud models coupled with charge separation mechanism have been explored to discuss the profiles of space electric field and charge structure in the evolution of a thundercloud (Takahashi, 1984; Rawlins, 1982; Helsdon et al., 2002; Mansell et al., 2005). As all various electrification mechanisms are majorly dependent on environment temperature, hydrometeors concentration and size spectrum (Takahashi, 1978; Jayaratne et al., n Corresponding author at: Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science and Technology, Nanjing 210044, China. E-mail address: [email protected] (Y.B. Tan).

1983; Saunders et al., 1991; Ziegler et al., 1991; Saunders and Peck, 1998), the validity of microphysics and hydrometeors is one of the key factors for simulating charge structure. Furthermore, the impacts of aerosols on cloud microphysics and hydrometeors concentration and size spectrum are reasonably well understood (Khain et al., 1999; Yin et al., 2000; Wang, 2005; Fan et al., 2007; Li et al., 2008). Thus, aerosols act as cloud condensation nuclei (CCN) perhaps have greatly effect on the charge structure in thunderclouds. An in-depth study of storm electrification requires numerical simulations. The parameterizations of charging mechanisms by which hydrometeors acquire charge are involved in cloud model. Most of the related electrification parameterizations based on laboratory studies can be classified into inductive charging parameterization and non-inductive charging parameterization. The drop-ice interaction is considered as a primary inductive mechanism (Aufdermauer and Johnson, 1972; Moore, 1975), and the inductive charge transfer between two particles is connect with particles radius, the falling velocities, collision angle and environmental electric field (Mason, 1988). In addition, non-inductive charge separation can be considered as a primary mechanism in thunderclouds, meanwhile several non-inductive parameterizations based on the laboratory results (Takahashi,

http://dx.doi.org/10.1016/j.jastp.2015.11.006 1364-6826/& 2015 Elsevier Ltd. All rights reserved.

Please cite this article as: Tan, Y.B., et al., A numerical study of aerosol effects on electrification of thunderstorms. Journal of Atmospheric and Solar-Terrestrial Physics (2015), http://dx.doi.org/10.1016/j.jastp.2015.11.006i

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1978; Gardiner et al., 1985; Jayaratne et al., 1983; Saunders et al., 1991; Brooks et al., 1997; Saunders and Peck, 1998) are put forward to simulate charge separation via rebounding graupel–ice collisions. Although the comparison of these laboratory-based parameterizations in a full simulation model (with coupled dynamics and microphysics) has revealed significant differences between the results (Mansell et al., 2005), the sign and magnitude of electric charge separated during collisions between ice-phase particles highly generally depends on temperature, relative velocity of the collisions, hydrometeors concentration and the supercooled droplet size spectrum (Takahashi, 1978; Gardiner et al., 1985; Jayaratne et al., 1983; Saunders et al., 1991; Brooks et al., 1997; Saunders and Peck, 1998). In general, charge separation is closely related to microphysics and hydrometeors properties of thunderclouds. It is well-know that aerosols can change dynamical, microphysical, and hydrometeors properties of cloud (Khain et al., 1999; Yin et al., 2000; Wang, 2005; Fan et al., 2007; Li et al., 2008). How aerosols affect electrification process in thunderclouds? However, at present very few previous simulation studies of aerosols effects have been performed in cumulus electrification model. In recent years, considerable progress has been made in understanding aerosols, their microphysical properties, and the factors that enable them to act as cloud condensation nuclei (CCN) (Twomey, 1974; Albrecht, 1989). As a result, aerosols exert a substantial influence on the microphysical properties of warm and cold clouds. Some observations and numerical simulations reveal that greater concentrations of aerosols result in the production of more small cloud droplets and reduced collision efficiencies, which can delay the formation of raindrops (Brenguier et al., 2000; Durkee et al., 2000; Yin et al., 2000; Nakajima et al., 2001; Ramanathan et al., 2001; Feingold, 2003; Jirak and Cotton, 2006). On the other hand, aerosol concentrations have a substantial impact on mixed convective clouds (Khain et al., 1999; Lynn et al., 2005; Seifert and Beheng, 2006; Wang, 2005; Fan et al., 2007; Li et al., 2008). Increase in the concentration of aerosol particles leads to higher vertical velocities; more super-cooled liquid water and increases in large ice-phase hydrometeor particles concentrations (Van den Heever et al., 2006; Yang et al., 2011). Aerosols, therefore, not only affect the microphysical development in clouds but also have influence on the physical characteristics of hydrometeor particles. As the mechanisms of thunderstorm electrification is intrinsically linked to microphysics and hydrometeor particles, the possible effects of aerosols particles on thunderstorm electrification should be studied with cloud models. Some models have discussed below include aerosols and electrification process. A study by Takahashi (1984), who used a spectral bin dynamic model to study the effects of maritime (low) CCN and continental (high) CCN on electrification, suggested that aerosols might be responsible for significant enhancement for electrification for the continental CCN. Mitzeva et al. (2006) performed a 1D bulk-water model to investigate differences between the early electrical development of maritime and continental thunderstorms, and found that updraft enhancement, greater ice production, and stronger electrification with continental aerosol content compared to maritime. The influence of IN (ice nuclei) bacteria on thunderstorm structure and lightning formation has been studied using a regional atmospheric model, and a relationship between lightning rates and maximum cloud updraft was taken into account on the storm dynamics (Gonçalves et al., 2012). A recent study by Wang et al. (2011) revealed the impact of aerosols on precipitation and lightning under polluted aerosol and clean aerosol conditions with a two-moment bulk microphysical scheme. In addition, another recent numerical study by Mansell and Ziegler (2013) investigated the responses of storm precipitation, electrification and lightning to increasing aerosol

concentrations using a 3-D bulk cloud model. The aim of this paper is to present sensitivity studies of aerosol concentration on thunderstorm microphysics and electrification. For this purpose, a two-dimensional cumulus model with detail cloud microphysics and electrification scheme is used. Numerical experiments are mainly tested for the relationship between aerosol concentration and electrification in thunderstorms.

2. Simulation method 2.1. Thundercloud model and simulation background This study used a 2-D Cartesian cumulus model, developed by the Chinese Academy of Meteorological Sciences (Hu and He, 1987). It is a non-hydrostatic cumulus model. Prognostic equations are included for momentum, pressure, potential temperature, and cloud droplet spectral width which is used to calculate the conversion of cloud droplet to rain. There are also conservation equations for mass ratio and concentration ratio of hydrometeors. The microphysics package is a multi-category, double moment scheme. It has five hydrometeor categories, which are cloud droplet, rain, ice crystal, graupel and hail. These particles are all assumed to have a gamma function distribution of diameter (See Appendix A). The main cloud physical processes are condensation and evaporation, collision, autoconversion, nucleation and multiplication, melting and freeze, and the model includes 27 kinds of microphysical processes of cumulus. The 27 kinds of microphysical processes are: condensation and evaporation of ice crystal, rain, cloud droplet, graupel, and hail; collision between cloud droplet and ice crystal, rain, graupel, as well as hail; collision between rain and ice crystal; collision between rain and graupel, and hail; collision between ice crystal and graupel, and hail; nucleation and multiplication of ice crystal; autoconversions of cloud–rain, ice– graupel, and graupel–hail; freeze of rain into hail; melting of graupel, hail, and ice into rain; collection of ice, collection of rain, and welt growth of graupel. To better understand the effect of aerosol on cloud microphysical processes, we made some improvements to the model. As

Fig. 1. Environmental sounding used for the simulation of thunderstorm clouds.

Please cite this article as: Tan, Y.B., et al., A numerical study of aerosol effects on electrification of thunderstorms. Journal of Atmospheric and Solar-Terrestrial Physics (2015), http://dx.doi.org/10.1016/j.jastp.2015.11.006i

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Fig. 2. Spatial distribution of cloud droplet and water vapor mixing ratio at 27 min of simulation for initial aerosol concentrations: (a),(b) 100;(c),(d) 500;(e),(f) 1000;(g), (h) 3000. (a),(c),(e),(g) illustrate Maximum updraft speed in the towering cumulus growth stage (27 min).

a background field of the initial aerosol spectrum (See Appendix B) and concentration is added to this model, we fit a classic scheme for aerosol activation (See Appendix C for more detail) based on Köhler equation (Pruppacher and Klett, 1997), and the concentration of activation cloud droplets can replace the original constant (400 cm
3). For simplicity, we assume the mixing ratio of activated cloud droplets is related to a minimum activation radius (Yin et al., 2000; Shi et al., 2015). Under these conditions, we use a resolution of 250 m and time steps of 2 s to calculate the microphysical and electrification processes (For more detail see Appendix D) in 76 km  20 km domain. 2.2. Initial conditions Aerosol concentration decreases with height, arising from the effects of Brownian motion and gravitational settling, and assuming that the concentration of aerosol in the horizontal direction is the same. Therefore, the concentration can be expressed as Yin et al. (2000):

Na(z ) = N (Z = 0) × exp( − z/zs)

(1)

where, Zs (the scale height) is set to 2 km in this study. N is the concentration of aerosol on the ground, and we report additional sensitivity studies by changing aerosol concentration from low to high. A sounding profile was used for simulation of thunderstorm clouds, which was in Nanjing, China at PM 12:00 on 12 August 2011. The vertical temperature, dew point and wind profiles (Fig. 1) reveal instability in the atmosphere, with a convective available potential energy (CAPE) of 1137 J kg
1 integrated from the surface, and therefore, the environmental sounding is suitable for simulation in this study. To initiate the cloud, a humid and warm bubble with temperature perturbation of 2 K and relative humidity perturbation of 50% is applied for one time step at t ¼0 at the height of 1 km, in the middle of the domain. 2.3. Statistical methods The mean value averaged over the entire specific region where

Please cite this article as: Tan, Y.B., et al., A numerical study of aerosol effects on electrification of thunderstorms. Journal of Atmospheric and Solar-Terrestrial Physics (2015), http://dx.doi.org/10.1016/j.jastp.2015.11.006i

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Fig. 3. Spatial distribution of ice crystal (34 min) and graupel (29 min) mixing ratio for initial aerosol concentrations: (a),(b) 100;(c),(d) 500;(e),(f) 1000;(g),(h) 3000.

is totally included in thunderclouds. To obtain the cloud area mean, the follow formula is applied to the grid point in each output time step (t).

P¯mean(t ) =

∑ P (x, y, t )/n(t )

(2)

where parameter P can be mixing ratio, number concentration, size of hydrometer particle and charge density. In this study, we calculate a summation of each parameter only grid point included in the cloud profile at a given time step t and magnitude exceeding a given minima. n(t) is the total number of grid point.

3. Simulation results 3.1. Effects of aerosol concentration on microphysical process The concentration of hail is relatively few and rain is not involved in charging, and thus the model electrification primarily comes from non-inductive graupel/ice crystal charging and graupel/cloud droplet inductive charging. To better understand the

process of electrification, studies are performed to investigate the impact of enhanced aerosol on the hydrometeors particles of cloud droplet, ice crystal and graupel. Four cases (N ¼100 cm
3, 500 cm
3, 1000 cm
3, 3000 cm
3) are calculated for thunderstorm cloud. At about 27 min, the cloud droplet mixing ratio reaches a maximum value, and Fig. 2 presents the two-dimensional fields of cloud droplet mixing ratio in the towering cumulus growth stage. the maximum number concentration of cloud droplet for four cases is 26.4 cm
3, 131.9 cm
3, 298.9 cm
3, 896.6 cm
3, respectively, and the more droplet condensation is responsible for the higher cloud droplet mixing ratio, which is consistent with previous observations in warm cumulus clouds (Rosenfeld, 2000; Kaufman and Koren, 2006) and model simulations for deep convective clouds (Khain et al., 2004; Li et al., 2008). With more latent heat released by the process of cloud droplets condensation, the maximum updraft speed at 27 min to 24.6 m/s increases from 19.2 m/s (N ¼100 cm
3) (N ¼3000 cm
3) (Fig. 2a,c,e and g). When aerosol concentration increases, the water vapor mixing ratio decreases significantly in the regions of high cloud droplet mixing ratio.(See Fig. 2b,d,f and

Please cite this article as: Tan, Y.B., et al., A numerical study of aerosol effects on electrification of thunderstorms. Journal of Atmospheric and Solar-Terrestrial Physics (2015), http://dx.doi.org/10.1016/j.jastp.2015.11.006i

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Fig. 4. Charge structure in the early electrical development stage (35 min) for four cases. Isotherms (thin horizontal lines at 0 °C,
13.8 °C, and
40 °C) are respectively in four panels, and thick black lines show contour structure characteristics of thundercloud.

h). So the supersaturation (with respect to liquid water) decreases with more water vapor consumed in cloud. Despite that both the mixing ratio and number concentration of cloud droplets increase, sharply increasing aerosol concentration results in reducing of the mean size of cloud droplets. For example, the cloud droplet mean size in four cases is about 45.7 μm, 34.5 μm, 26.2 μm, 19.4 μm, respectively. In addition, Fig. 2a,c,e and g also show that smaller cloud droplets in the updraft in 1000 cm
3 and 3000 cm
3 cases extend up above 10 km level, and the distribution of higher cloud droplet mixing ratio (exceed 5 g kg
1) is lifted gradually as aerosol concentration transformed from low to high, probably attributing to the increase updraft. Ice crystals begin to from at 27 min in case of 100 cm
3, at 25 min in case of 500 cm
3, and at 24 min in cases of 1000 cm
3 and 3000 cm
3. The earlier appearance of ice crystals in higher aerosol concentration case is associated with more cloud water content lifted by stronger updrafts, and thus it is favorable for icenucleation. Thereafter, the mixing ratio of ice crystals in four cases increase very rapidly and reach their peak values around 34 min. The comparison of the ice crystals among four cases is given in Fig. 3a,c,e and g. The mixing ratio of ice crystals is higher in case of 1000 cm
3 (maximum is 2.7 g kg
1) than in cases of 100 and 500 cm
3 (maximum is 1.8 g kg
1, 2.4 g kg
1, respectively). This can be explained that the production for ice crystals is related to water vapor supply in updrafts. The supersaturation is relatively higher and the competition of cloud droplets for available water vapor in these cases is not strong, and therefore the formation through vapor deposition and condensation freezing probability

become more favorable. However, at very high aerosol concentration (3000 cm
3), the vapor deposition shows a relatively large decrease because of vapor competition introduced by the increase aerosol concentration, which also result in the production of ice crystals with maximum mixing ratio of 2.1 g kg
1 in 3000 cm
3 case is less than in 500 cm
3 and 1000 cm
3 cases. The similar conclusion is also showed by Saleeby and Cotton (2005) and Yang et al. (2011). It must be stated that the increase in amount of cloud droplet leads to more ice crystals formation from the collision coalescence between cloud droplet and ice crystals. Additionally, secondary ice crystals in low aerosol concentration case produced during graupel riming collection of cloud droplet with diameter greater than 24 μm is larger than that in high (aerosol) cases, this is due to the secondary ice crystals formation is suppressed with the production of large amounts of small cloud droplet in high aerosol concentration case. However the production of ice crystals produced by ice multiplication and collision coalescence between cloud droplets and ice crystals are smaller than other sources. In addition, the mean number concentration of ice crystals for four cases are 0.3 cm
3, 2.5 cm
3, 3.2 cm
3, 5.1 cm
3, respectively. One can infer that the mean size of ice crystals in 3000 case is smaller than those in 100, 500, and 1000 case because of the decrease in ice crystals mixing ratio. Graupel is firstly produced by autoconversion of ice–graupel. The concentration of graupel reaches the peak values at about 29 min. As shown in Fig. 3b,d,f and h, when aerosol concentration increases increase from 100 cm
3 to 3000 cm
3, the graupel mixing ratio is very sensitive to aerosol concentration, with

Please cite this article as: Tan, Y.B., et al., A numerical study of aerosol effects on electrification of thunderstorms. Journal of Atmospheric and Solar-Terrestrial Physics (2015), http://dx.doi.org/10.1016/j.jastp.2015.11.006i

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Fig. 5. Non-inductive charge separation by ice crystal per minute for four simulation cases (N¼ 100, 500, 1000, and 3000 cm
3).

maximum values of 2.5 g kg
1, 10.0 g kg
1, 13.7 g kg
1, 16.7 g kg
1, respectively. The collision coalescences between cloud droplets/raindrop and graupel are majorly responsible for graupel growing. In developing stage, the formation of raindrop has a slightly decrease with aerosol concentration increasing since the conversion of cloud droplet to raindrop is hindered due to the formation of large amounts of small cloud droplets (not shown). Therefore, when aerosol concentration increasing, the enhancement of cloud droplet results in higher cloud water collected by graupel, mainly leading to more graupel produced in high aerosol concentration case, as found by Gilmore et al. (2004). A contributing factor is the increase of graupel number concentration and mixing ratio, so that it indicates mean size of graupel has no obvious change. 3.2. Effects of aerosol concentration on electrification Four cases are performed for charge structure before lightning occur in thunderstorm clouds. The focus here is on the dominant aerosol concentrations relevant to charge structure in the early electrical development stage. The storm at 35 min depicts a triple charge structure with a lower positive charge below a normal dipole, and comparing these figures in Fig. 4 reveals that when the aerosol concentration increases, the charge structure of four cases consistently keep as a triple, but the charge density distribution shows significant differences. The mean charge density magnitudes of upper positive charge region (primarily above 9 km level), middle negative charge region (between 5 km level and 9 km

level) and lower positive charge region (below 5 km level) are defined as ρup , ρmn and ρlp , respectively. As shown in Table 1, the absolute charge density magnitude in middle negative region is larger than the values of upper or lower positive charge region. Furthermore, the charge density increases monotonically as aerosol concentration rises from 100 to 1000 cm
3, but charge density begins to decrease when aerosol concentration increases from 1000 cm
3 to 3000 cm
3. Non-inductive charge separation between ice crystal and graupel contributes to the main upper positive charge region and the negative charge region (Fig. 4). Time evolution of non-inductive charging rates are roughly similar in four cases, as can be seen from in Fig. 5. Non-inductive charge separation started at 27 min and the positive non-inductive charging rates are highest at altitudes of 7–11 km, while the negative non-inductive charge mainly resided at 4 to 7 km (0 °C to
13.8 °C). It is therefore clear that ice crystal charged positively at lower temperatures (o
13.8 °C), and ice crystal gained negative charge in the regions where the temperature is higher ( 4
13.8 °C).The increase in non-inductive charging rate with aerosol concentration increases from 100 cm
3 to 1000 cm
3 is well correlated to the stronger production of ice crystal and graupel in the cloud (Fig. 5a–c). The processes of vapor competition lead to a significant decrease in ice crystals mixing ratio. Since non-inductive charging rate is highly related with the ice particles size (See Eq. (D2)), smaller ice crystals formation results in a slightly decrease in non-induction charge separation in 3000 cm
3 case (Fig. 5d). Inductive graupel–cloud droplet charge separation has a great

Please cite this article as: Tan, Y.B., et al., A numerical study of aerosol effects on electrification of thunderstorms. Journal of Atmospheric and Solar-Terrestrial Physics (2015), http://dx.doi.org/10.1016/j.jastp.2015.11.006i

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Fig. 6. Time–height plots showing the inductive charging rate evolution.(a) 100, (b) 500, (c) 1000, (d) 3000. Positive (thin black) and negative (thick gray) inductive charging rates with contour intervals of 7 1, 7 5, 7 10, 7 15, 7 20, 7 25 pC m
3 s
1.

effect on the negative charge region and the lower positive charge region (Fig. 4). A picture of the inductive charging rates is listed by the time–height plots in Fig. 6. The negative inductive charging rates roughly reside between 7–10 km, while the actively positive inductive charging of graupel makes a greater contribution to the lower positive charge region. This lower positive charge in thundercloud is suggested to trigger the negative CG lightning or the inverted IC lightning formation (Qie et al., 2005; Nag and Rakov, 2009; Tan et al., 2014a). It can be seen from Fig. 6 that the inductive charging rate demonstrates an increasing trend with aerosol concentration increasing, which primary arises from an increase in the amount of cloud droplet and graupel. In addition, the case of 3000 produces time evolution of inductive charging rate roughly similar to that in 1000 cm
3 case. In 3000 cm
3 case, a decrease in vertical electric field arising from non-inductive charge reduction can suppress the charge separation between graupel and cloud droplet, but more production of cloud droplet and graupel leads to stronger inductive charge separation than that in 1000 cm
3 case. Two key factors likely lead to the fact that inductive charging rates in 1000 cm
3 and 3000 cm
3 case are comparable to each other. 3.3. Electrification with high aerosol concentration From the analysis in the previous section, we know that the

Table 1 charge density mean values of upper positive charge region (ρup) middle negative region (ρmn) and lower positive charge region (ρlp) in four thunderclouds at 35 min step. Case

ρup (nC m
3)

ρmn (nC m3)

ρlp (nC m3)

N ¼ 100 N ¼ 500 N ¼ 1000 N ¼ 3000

8.5  10
2 5.0  10
1 6.7  10
1 5.1  10
1


8.8  10
2
5.4  10
1
6.6  10
1
5.0  10
1

7.6  10
3 5.9  10
2 1.5  10
1 5.2  10
2

production of ice crystals at higher altitudes is reduced by vapor competition at aerosol concentration of 3000 cm
3, which is closely associated with the decrease of charge acquired by ice crystals. Of interest here is on the dominant electrification characteristics relevant to higher concentration aerosols (above 3000 cm
3).The mean number concentration of cloud droplet at simulation of 27 min increases with the concentration of aerosols enhancement (Fig. 7a). However, the mean cloud droplets mixing ratio follows the trend of rapidly increasing at lower aerosols (50– 1000 cm
3), with slowly increasing at higher aerosols (1000– 10,000 cm
3) (Fig. 7a), implying that the size of cloud droplet exhibits an obvious reduction. This feature seems to be due to all simulation cases under the same relative humidity condition, and the water vapor content in cloud is certainly, which restricts more

Please cite this article as: Tan, Y.B., et al., A numerical study of aerosol effects on electrification of thunderstorms. Journal of Atmospheric and Solar-Terrestrial Physics (2015), http://dx.doi.org/10.1016/j.jastp.2015.11.006i

Y.B. Tan et al. / Journal of Atmospheric and Solar-Terrestrial Physics ∎ (∎∎∎∎) ∎∎∎–∎∎∎ 3.2 Mixing ratio Number concentration

Ice Crystal

-3

Mean Cloud Droplet Number Concentration (cm )

0.6

200

3.0 150

2.9

2.8

100

2.7 50

2.6

2.5

8

Mean Ice Crystal Mixing Ratio (g kg-1 )

3.1

Mean Cloud Droplet Mixing Ratio (g kg )

10

250

Cloud Droplet

0.4

6

0.3

4 0.2

2 0.1

0

0.0

0

50

0.5

100 500 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

50

Initial Aerosol Concentration (cm )

100 500 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Initial Aerosol Concentration (cm ) 0.40

100

Graupel

Charging Rate

2.0

Positive Non-inductive Charging Rate Negative Non-inductive Charging Rate

0.35

Negative Inductive Charging Rate Positive Inductive Charging Rate

0.25

0.20 1.0 0.15

0.10

0.5

0.05

Charge Separation Rate (pC m s )

0.30 1.5

Mean Graupel Number Concentration (L )

80 Mean Graupel Mixing Ratio (g kg )

Mean Ice Crystal Number Concentration (cm )

8

60

40

20

0

-20 0.00

0.0 50

100 500 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Initial Aerosol Concentration (cm )

50

100 500 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Initial Aerosol Concentration (cm )

Fig. 7. The mean cloud droplets (a), ice crystals (b), graupel (c) mixing ratio, number concentration and the maximum charge separation rate(d) for varying initial aerosol concentration.

small cloud droplets further condensation growth. In Fig. 7b, vapor competition can be explained the reduction in ice crystal mixing ratio at aerosol concentration mediated from 1000 cm
3 to 3000 cm
3, but when the aerosol concentration further increases, the mean ice crystals mixing ratio and number concentration at 34 min will be a stable magnitude of about 0.5 g kg
1 and 5.5 cm
3, which mainly results from the similar supply of water vapor for ice crystals production. In addition, the mean size of ice crystal in higher aerosol cases depending on the mixing ratio and number concentration keeps steady. Since the collisions between graupel and liquid drops (cloud droplet and raindrop) are always a greater source to graupel formation than the initial source of auto-converted ice crystal and cloud droplet (not shown), the production of graupel mainly depends on the graupel–cloud droplet/raindrop collisions, the variation of graupel production with increasing aerosol concentration is correlated with cloud droplets growing. It can be seen from Fig. 7c that the mean graupel mixing ratio and number concentration (at 29 min) significantly increase with aerosol concentration increasing from 50 to 3000 cm
3, while aerosol concentration exceeds 3000 cm
3, the amount of graupel is not very sensitive to aerosol concentration, which shows a nonlinear relationship. The mean mixing ratio and number concentration of graupel exhibit a similar variation characteristic with varying aerosol concentration, implying that the mean size of graupel is

also insensitive to the changes in aerosol concentration. Fig.7d shows the maximum non-inductive and inductive charge separation rates with initial aerosol concentration. From the figure we can conclude that the charge separation increases sharply from 50 cm
3 to 1000 cm
3. The magnitude of charge produced from NI mechanism is mainly associated with ice particles concentration and size spectrum (See Eq. (D2)).Therefore, stronger ice particles formation led to higher NI charging rate. Analogously, the more cloud droplet, graupel formation will lead to a stronger inductive charge separation rates (including positive and negative charging rates). The increasing charge separation produces stronger electric fields, which are more likely to trigger lightning. This simulation is consistent with observational evidences that aerosol may enhance lightning production (Yuan et al., 2011 and Wang et al., 2011). When aerosol concentration is from 1000 to 3000 cm
3, the decrease in ice crystals size is likely to hold the answer to NI charging rate reduce (major about positive charging rates), and the maximum NI charging rate decreases from 93.8 to 64.0 pC m
3 s
1. While aerosol concentration is over 3000 cm
3, the maximum NI charging rate roughly keeps a magnitude of about 60 pC m
3 s
1, because of the stable amount and size of ice particles (see Fig. 7b and c). Moreover, the maximum positive and negative inductive charge separation rates depending on the graupel–cloud droplet collisions have no obvious change when aerosol concentration exceeds 1000 cm
3 (Fig. 7d), which is

Please cite this article as: Tan, Y.B., et al., A numerical study of aerosol effects on electrification of thunderstorms. Journal of Atmospheric and Solar-Terrestrial Physics (2015), http://dx.doi.org/10.1016/j.jastp.2015.11.006i

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contributed to the factor that the graupel and cloud droplets concentration increase insignificantly (Fig. 7a and c).

9

Jiangsu Higher Education Institutions (PAPD) and a program for Postgraduates Research Innovation of Jiangsu Higher Education Institutions (CXZZ13_0515).

4. Conclusions Appendix A. Hydrometeor distributions The hydrometeors are characterized as mass ratio (Qx) and concentration ratio (Nx). The particles are all assumed to have a gamma function distribution of diameter:

N (D) = N0Dα exp( − λD)

(A1)

where D is diameter, N0, λ are two parameters, for different hydrometeors: (1) cloud droplet, α ¼2; (2) rain and graupel, α ¼0; (3) ice crystal, α ¼1; (4) hail, α ¼0.

Appendix B. Aerosol spectral distribution The aerosol distribution of Hobbs et al. (1985) was fitted by superimposing three log-normal distributions function. In Equation (6), the subscript i ¼1, 2, or 3 represents the three modes. rN is the radius of aerosol particle, and ni denotes the aerosol number concentration in mode i, the ratio of ni for three log-normal distributions was 72: 4430: 450. si (s1 ¼1.8, s2 ¼2.16, s3 ¼2.40) is the geometric standard deviation representing the width of the particle size, and the three distributions had respective geometric mean radius (Ri ) of 0.02, 0.16, 6.15 μm. The parameters of the distributions were based on Fig. 8 of Leporini et al. (2004).

dN = d ln(rN )

3

∑ i=1

ni exp( −

ln2(rN / R i) 2ln2(σi)

)

2π ln(σi )

(B1)

10

-3

)

10

dN/dlnr ( cm

Simulations have been performed in order to investigate the impact of varying initial aerosol concentration on the thunderstorm charging. The analyzes of results demonstrate that aerosol concentrations have a significant influence on the thunderstorm cloud microphysical processes and electrification. From these results one can conclude the following: Aerosol concentrations influence the microphysical properties of hydrometeors. The elevated aerosol concentration is responsible for more numerous cloud droplets, while the mean size of cloud droplets tends to decrease. Graupel formation affected by cloud droplet concentration increases with greater aerosol concentration. However, the concentration of graupel increases slowly at very high aerosol concentration. For aerosol concentration increasing from 50 cm
3 to 1000 cm
3, the increase of ice crystals production is attributed to more water vapor supplied by stronger updraft, but ice crystals mixing ratio tends to decrease in the range of 1000–3000 cm
3, because of the effect of vapor competition in this study. Above aerosol concentration of 3000 cm
3, ice crystal concentration keeps as a relatively fixed magnitude. Charge separation tends to increase as aerosol concentration rises from 50 cm
3 to 1000 cm
3. The enhancement of non-inductive and inductive charge separation rate arises from ice crystal, graupel and cloud droplets formation increase. In the range of 1000–3000 cm
3, the reduction of ice crystals size slightly inhibits charge production via non-inductive mechanism. Under this condition, the magnitude of non-inductive charging rate has a slightly reduce. However, inductive charging rate has no significant change in magnitude. A little change in hydrometeor amount at very high aerosol concentration (above 3000 cm
3) can be attributed to the stability of charging rate. In general, the charge separation magnitude in thunderclouds is insensitive to the varying aerosol concentration. This present study reveals that the cloud microphysical and electrification properties depend on the aerosols concentration under the same initial dynamic and thermodynamic conditions, but the effect of aerosols concentration on charge separation in thundercloud is non-linear. Although the association between lightning activity and aerosol has received further strong support from studies (Yuan et al., 2011) which demonstrate strong and quantifiable relationships – obtained from the analysis of data from observations, the key electrification processes associated with further high aerosol concentration are still short of anecdotal evidence. Furthermore, it is believed that aerosol can act as ice nuclei (IN). Because cloud-ice nuclei (IN) interaction is increasingly recognized as one of the factors influencing the microphysical structure of clouds (Levin et al., 2005; Teller and Levin, 2006; Barahona and Nenes, 2009), and ice crystal (nucleation of IN) is of crucial importance in thunderstorm electrification, this process may have an important impact on electrification properties in thunderclouds. Further aspects of this problem will be addressed in forthcoming studies.

10

10

10

10

10

10

10

10

10

10

Aerosol Radius (mm) Fig. 8. initial number distribution functions of aerosol particles used in the simulations.

Appendix C. Activation of aerosols Acknowledgments The work was supported by National Key Basic Research Program of China (973 Program) 2014CB441403 and the National Natural Science Foundation of China (Grant nos. 41475006) and A Project Funded by the Priority Academic Program Development of

The aerosol particles begin to grow by absorption of water vapor. The activation of aerosol particles to form cloud droplets depends on the assumed aerosol composition and local supersaturation. In this study, the composition of aerosol particles is assumed to be isotropic homogeneous distribution of sulfate

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10

particles. Aerosol particles of a certain size are activated when the radius of growing aerosol particles at each grid point exceeds the critical activation radius (rmin) determined by the Köhler equation (Pruppacher and Klett, 1997)

ΔS =

Br 3 A − 3d r r

(C1)

where, rd is dry aerosol particle radius and r is wet aerosol particle radius, A is the coefficient of the curvature effect and B is the coefficient of solute effect.

A=

2δ ρw R vT

(C2)

droplet under the external electric field and non-inductive mechanisms between graupel and ice crystal under the coexist of ice particles and supercooled water. Since contact times of ice–ice collisions are too short for electrical currents to transfer charge, we assume that the lower conductivity of ice makes polarization charging ineffective. Therefore, inductive charging between ice crystal/graupel collisions is not considered in this study. Inductive collision charging parameterization is based on Ziegler et al. (1991). The inductive graupel/hail-droplet charging rate can be given by:

(

∂Q eg ∂t

)p = (π 3/8)(

6.0Vg Γ (4.5)

)EgcErNcN0gDc2[πΓ (3.5)ε(cos θ )cos EzDg2

− Γ (1.5)Q eg/(3Ng )]

B=

iφsεmρ N Mw ρw MN

(C3)

4A3 1/3 ) ⋅ΔS −2/3 27B

(C4)

rmin = (

where, δ is the surface tension of the solution drop, εm is the fraction of water-soluble material of an aerosol particle, i is the number of soluble particles molecules (for (NH4)2SO4, i¼3). Mw and MN are the molecular weights of water and aerosols. ρw and ρN are the densities of water and aerosols, respectively. After reaching the critical sizes, the number concentration of cloud droplets is associated with activated aerosol concentration. In addition, based on Yin et al. (2000), we assume a correspondence relation between cloud droplets quality and the certain size. Mc is cloud droplets quality and is given by:

Mc = ρw .

4 π (krmin )3 3

(C5)

In which, a factor k is used to calculate the ratio of initial sizes of the droplets to aerosol particle radius based on Kogan (1991).

(D1)

where Qeg is the individual charge from graupel/hail, Dc and Dg are the diameter of cloud droplets and graupel/hail, respectively. Vg is the fall speed of graupel/hail, Nc and Ng are the concentration of cloud droplets and graupel/hail, respectively. N0g is the number concentration intercept for graupel. Γ is the complete gamma function, and the symbols Egc and Er denote graupel/hail-droplets collision efficiency and rebound probability, respectively. Ez is the vertical electric field, and θ is the polar collision angle. According to Mansell et al. (2005), coefficients for inductive graupel–cloud droplet charging (Erc ¼0.01 and cos θ ¼0.4) in this study are between the moderate to strong values which ranged from Erc ¼0.007–0.015 and cos θ ¼ 0.2–0.5. The non-inductive graupel charging rate takes the form:

(

∂Q eg ∂t

)np = βδqEr(1 − Er )−1 × ∞

∫0 ∫0

∞

1 ¯ Vi − V¯g ρ0

π (1 − Er )Egi(Dg + Di)2NgNidDg dDi 4

(D2)

where, Dg and Di are diameters of the colliding particles (graupel and ice crystal). Er is the rebound probability and Egi is the graupel–ice crystal collision efficiency. N is number concentration. V¯i and V¯g are the mass-weighted mean terminal speeds for ice crystal and graupel and β is given similar to Mansell (2005) by:

1

Appendix D. The electrification scheme

T ≥ − 30 °C

β = {1 − [(Τ + 30)/13]2 −43 °C < T < − 30 °C An electrification scheme must be included in numerical cloud model to generate charge acquired by hydrometeors. Similar to Mansell et al. (2002), the electrification parameterizations include inductive charge separation between graupel/hail and cloud

0

T ≤ − 43 °C

(D3)

The scheme of individual graupel charging rate (δq) we adopted is modified from the scheme of Gardiner et al. (1985) based on

4

1

)

0

Cloud Water Content (gm

-3

o Tr=-25 C

f(t)

-1

-2

o Tr=-13.8 C

o Tr=-15 C

-3

-4

-5 -50

-40

-30

-20 o

Temperature ( C)

-10

0

3

+

2

-

1

0

0

-5

-10

-15

-20

-25

-30

o

Temperature ( C)

Fig. 9. Calculated functional relation of environment temperature, cloud water content and f (τ ) . (a) Graupel charge-sign boundary; (b) The isotherms of f (τ ) , environment temperature in conditions of different reversal temperature supply.

Please cite this article as: Tan, Y.B., et al., A numerical study of aerosol effects on electrification of thunderstorms. Journal of Atmospheric and Solar-Terrestrial Physics (2015), http://dx.doi.org/10.1016/j.jastp.2015.11.006i

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the experiment results of Pereyra et al. (2000). The reversal temperature in modified parameterization scheme, replacing the original fixed value, considers the functional dependence on cloud water content (CWC), so not only positive charges but also negative charges may be acquired by graupel when the cloud water content is less then 1 g m
3. The modified parameterization scheme is denoted as follow. The expression of δq following Gardiner et al. (1985) is approximated as: 3 δq = 7.3Di4 V¯i − V¯g δLf (τ )

(D4)

where Di is the diameter for ice, δL is a parameter related to cloud water content (CWC), modified as:

δL = {

CWC qc ≥ 10−3 g kg−1 0

qc < 10−3g kg−1

(D5)

where qc is the cloud water mixing ratio, f (τ ) was adapted from Ziegler et al. (1991):

f (τ ) = − 1.7 × 10−5τ 3 − 0.003τ 2 − 0.05τ + 0.13

(D6)

where τ = ( − 21/Tr )(T − 273. 16) is the scaled temperature used by Ziegler et al. (1991) to allow the reversal temperature Tr to be varied. From Fig. 9(a), we can conclude that most of graupel acquire negative charges in the modified parameterization scheme, and the varing reversal temperature has little impact on the magnitude of graupel acquired positive charges. When the reversal temperature (Tr) is below environment temperature (T), the magnitude of graupel acquiring negative charges increases linearly with the temperature decreasing, and f (τ ) at smaller values of Tr arises in graupel will gain more negative charges. Furthermore, according to the experiment data of Pereyra et al. (2000), we set the relationship between Tr and CWC as:

Tr = {

CWC < 1

g m−3

−5 × CWC − 8.8 CWC ≥ 1

g m−3

−13.8

(D7)

As shown in Fig. 9b, the reversal temperature is assumed to be
13.8 °C when CWC is less then 1 g/m
3. At higher CWC, an approximate fitting line with slope
5 is used to describe the relationship between CWC and temperature which roughly fit the experiment data, although it have some difference with the result from Pereyra et al. (2000). It must be stated that lightning discharge in this study is simulated to restrict the electric field, which would have a great effect on inductive charge separation rate. The lightning parameterization is based on Tan et al. (2006, 2014a, 2014b), which is capable of simulating IC flashes and positive and negative CG flashes under the condition of fine resolution.

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Please cite this article as: Tan, Y.B., et al., A numerical study of aerosol effects on electrification of thunderstorms. Journal of Atmospheric and Solar-Terrestrial Physics (2015), http://dx.doi.org/10.1016/j.jastp.2015.11.006i