Simulation of the Electri fi cation of a Tropical Cyclone Using the WRF-ARW Model:An Idealized Case

XU LiangtaoZHANG YijunWANG Feiand ZHENG Dong

1State Key Laboratory of Severe Weather,Chinese Academy of Meteorological Sciences,Beijing100081

2College of Earth Science,University of Chinese Academy of Sciences,Beijing100049

Simulation of the Electri fi cation of a Tropical Cyclone Using the WRF-ARW Model:An Idealized Case

XU Liangtao1,2,ZHANG Yijun1?,WANG Fei1,and ZHENG Dong1

1State Key Laboratory of Severe Weather,Chinese Academy of Meteorological Sciences,Beijing100081

2College of Earth Science,University of Chinese Academy of Sciences,Beijing100049

Evolution of the electri fi cation of an idealized tropical cyclone(TC)is simulated by using the Advanced Weather Research and Forecasting(WRF-ARW)model.The model was modi fi ed by addition of explicit electri fi cation and a new bulk discharge scheme.The characteristics of TC lightning is further examined by analyses of the electri fi cation and the charge structure of the TC.The fi ndings thus obtained are able to unify most of the previous inconsisitent observational and simulation studies.

tropical cyclone,charge structure,electri fi cation,WRF

1.Introduction

As a devastating weather system,the tropical cyclone(TC)and its dynamical and microphysical characteristics have long been of interest. In recent years,space-borne lightning detectors and the global/regional lightning location network have provided new data for the research on TCs.Observational studies have shown that the spatial distribution of lightning activity in TCs has a unique feature:a strong maximum near the outer rainbands(210–290-km radius),a weak maximum in the eyewall region, and a minimum in 80–100 km outside the eyewall (Molinari et al.,1994,1999).

At the same time,it is found that lightning activity is associated with the formation and development of TCs.Lightning may be used as an indicator of TC formation in the Northeast Paci fi c and Atlantic regions(Price et al.,2007;Leary and Ritchie,2009).In addition,there is a relationship between TC intensity change and lightning activity,in particular the lightning in the eyewall region(Pan et al.,2010;Thomas et al.,2010).The increase in eyewall lightning can occur 24 h ahead of a TC reaching maximum intensity(Price et al.,2009).The outbreak of eyewall lightning sometimes precedes or occurs in the rapid intensi fi cation stage of TCs(Squires and Businger,2008;DeMaria et al.,2012;Zhang and Zhou,2013).Moreover,it hasbeen suggested that lightning activity is related to the movement of TCs(Corbosiero and Molinari,2002; Zhang et al.,2012).

The charge structure is the bridge between lightning activity and the dynamical and microphysical characteristics of TCs.The charge structure in TCs is in fl uenced by vortex dynamics and microphysics (Houze,2010),while any lightning occurs relative to the charge structure.Hence,to further understand the relationship between lightning activity and the internal structure of TCs,it is necessary to examine the bridging role of the charge structure.

At present,there is relatively little research on the electri fi cation and charge structure of TCs.Black and Hallett(1999)presented observations of the vertical electric fi eld of TCs and pointed out that an inverted dipole charge structure dominates in the eyewall.This is,to a great extent,due to the weak updraft in the eyewall.The graupel particles at the levels from 0 to–5℃ and the low liquid water content(LWC)provide the conditions for positive charging of graupel and negative charging of ice crystals,leading to the inverted dipole structure.As observations are limited to altitudes below the –15℃ level(limit of the aircraft),it is difficult to infer a charge structure above that level. Molinari et al.(1994)suggested formation of a dipole with normal sign but outward tilting along the sloping eyewall.However,Fierro et al.(2011)suggested a normal tripole structure in the eyewall based on an analysis of the rapid intensi fi cation of Hurricane Rita using total lightning and narrow bipolar events(NBE) data.

Owing to difficulty in observing the charge structure of TCs,studies on the electri fi cation and charge structure of TCs have been carried out with numerical models incorporating electri fi cation and discharge processes(Fierro et al.,2007,2013;Fierro and Reisner,2011).The results mainly showed a tripole charge structure in TCs. Fierro et al. (2007)simulated the electri fi cation of an idealized TC with the noninductive charge separation scheme of Saunders and Peck(1998)(SP98)and obtained a normal tripole structure in the eyewall and a simple dipole structure in the spiral rainbands.Fierro and Reisner(2011)simulated the rapid intensi fi cation of a hurricane by using a cloud model and indicated that the eyewall is characterized by an inverted tripole structure with a positive charge region sandwiched between two negative charge regions.

Fierro et al.(2013)introduced the SP98 noninductive charge separation process and a lightning parameterization into the National Severe Storms Laboratory(NSSL)two-moment microphysical scheme of the Advanced Research Weather Research and Forecasting(WRF-ARW)model(Skamarock et al.,2008). The results showed a normal tripole structure in the eyewall of Hurricane Rita.In the upper cloud region, ice crystals and snow take up positive charge and the small amount of graupel particles take up negative charge.In the middle region,the particles are mainly graupel,which charges negatively,as well as small colliding ice particles with positive charge.In the lower region,particles mainly charge positively while ice and snow charge negatively.This kind of charge structure is conducive to the occurrence of negative cloudground(CG)lightning.

Previous results,including observations and simulations,do not agree with each other.They also do not consider the changes in the charge structure of TCs at di ff erent stages of TC evolution.Outbreaks of eyewall lightning occur in the rapid intensi fi cation stage, while there is little lightning in the quasi-steady stage (Samsury and Orville,1994).Therefore,the charge structure of the TC should vary at di ff erent stages.On the other hand,the clouds in the eyewall and the rainband are in fl uenced by the dynamics of the inner-core vortex to varying degrees.Therefore,several intriguing questions naturally arise:What is the evolution of the charge structure of TCs at di ff erent stages,particularly the intensi fi cation and quasi-steady stages? What di ff erences in the charge structure are there between the cells in the eyewall and spiral rainbands?

The evolution of the charge structure of the TC, including the eyewall and outer spiral rainband cells,is simulated in this work.Although the charge structure of TCs has been simulated in idealized and real cases in previous studies,simulations using di ff erent microphysical and charge separation schemes are essentialto further improving our understanding(Fierro and Reisner,2011).The WRF-ARW model is also used here,but with the non-inductive charge separation scheme based on the work of Gardiner et al.(1985) and Ziegler et al.(1991).The electri fi cation scheme and a new simple bulk discharge parameterization(Xu et al.,2012)are incorporated into the Milbrandt twomoment scheme.

The remainder of this paper is organized as follows.A detailed description of the model is given in Section 2.In Section 3,the idealized test and model setup are introduced.Based on the simulation,Section 4 presents the di ff erences in electri fi cation and charge structure of TCs during the intensi fi cation and quasi-steady stages,and a picture of the evolution of the charge structure of TCs is presented,together with previous simulated and observed results.Finally,the major fi ndings of the study are discussed and summarized in sections 5 and 6,respectively.

2.Description of the model

The numerical experiments are conducted with the WRF-ARW model version 3.4.1 developed by the NCEP/NCAR.The model is fully compressible and non-hydrostatic.

2.1 Microphysical parameterization

The Milbrandt two-moment microphysical parameterization(Milbrandt and Yau,2005a,b)adapted from WRF version 3.2.1 is used in this study.This scheme was introduced into the WRF model in 2010 and includes detailed microphysical processes.Six hydrometeor categories are included in the scheme:cloud droplets,ice crystals,rain,snow,graupel,and hail. The two-moment scheme provides the mixing ratio for water vapor and it can provide both the mixing ratio and number concentration of the other six hydrometeors.Explicit electri fi cation and discharge are implemented in this scheme.

To compute the electrical variables,seven global microphysical variables are introduced into the WRF model:the charge density of cloud droplets,ice crystals,rain,snow,graupel,hail,and the total charge density(or net charge density).These seven variables will be computed as microphysical prediction variables following the other microphysical variables.The vertical electric fi eld and gridpoint fl ash number are diagnosed variables.

2.2 Charge conservation

The particle charge density(ρx)of each hydrometeor is calculated as follows(Altaratz et al.,2005):

The fi rst two terms on the right hand side of the equation represent the advection and turbulent transport of the charge,which can be calculated by following the hydrometeors in the model.The third term on the right hand side represents sources and sinks of the charge,including charge separation and charge loss by the discharge process.Charge transfer between di ff erent particles due to transformation between particles is also considered in this term.We assume that there is no charge transfer involved in evaporation and condensation.The last term on the right hand side represents the charge change caused by sedimentation of the particles.The total charge density at each gridpoint is equal to the sum of the charge densities of all the hydrometeors.

2.3 Non-inductive charge separation

The model considers the non-inductive charge separation between graupel and ice crystals,graupel and snow,and hail and ice crystals.The noninductive charging rate(?ρxy/?t)is calculated as follows(Mansell et al.,2005;Tan,2006):

whereDxandDyrepresent the diameters of the colliding particles;|Vx-Vy|is the fall velocity di ff erence between the two charging particles;Ecolliis the collision efficiency of the colliding particles;Exyis the collection efficiency,which is the product ofEcolliandEagg(fraction aggregated by graupel or hail);nxandnyare number concentrations of the particles;andδQis the representative separated charge per reboundingcollision.Equation(2)can be re-written as follows (Mansell et al.,2005;Tan,2006):

whereβis the force coefficient when the charge transfer is calculated at low temperature,as given by Mansell et al. (2005),andNCLxyis the number concentration collection rate between the particles. The separated charge(δQ)can be calculated by the Gardiner–Ziegler(GZ)scheme(Gardiner et al.,1985; Ziegler et al.,1991),which is based on the laboratory experiment by Jayaratne et al.(1983),as follows:

wherekis a proportionality factor,Direpresents the diameter of ice crystal or snow,δvis the di ff erence in mass-weighted terminal fall speed between di ff erent particles,δLis a parameter related to liquid water content,andf(τ)is a function of reversal temperature and environment temperature.The calculation ofδLand reversal temperature is given in Eqs.(5)and(7), respectively,as modi fi ed by Tan(2006)based on the experiment by Pereyra et al.(2000):

where LWC is the liquid water content,andqcis the cloud water mixing ratio.The functionf(τ)is given by Ziegler et al.(1991)as follows:

whereτ=(-21/Tr)(T-273.16)is the scaled temperature,andTris the reversal temperature(Tan,2006):

Note that the reversal temperature(Tr)used in this study is di ff erent from that used by Ziegler et al. (1991).The reversal temperature determines the sign of charge transfer when graupel(or hail)collides with the ice and snow.The new scheme(Fig.1)speci fi es the reversal temperature under conditions of low liquid water content,while the graupel(hail)would take on a negative charge directly under conditions of low liquid water content in the scheme used by Ziegler et al.(1991).The graupel would charge positively when bounced-o ffice crystals in the regions where reversal temperature is smaller than environment temperature, while the ice crystals would charge with opposite polarity.These regions can be de fi ned as positive graupel charging zones(PGCZ),while the regions where reversal temperature is greater than environment temperature can be de fi ned as negative graupel charging zones (NGCZ).

2.4 Inductive charge separation

Inductive charge separation results from the collision between di ff erent particles in the presence of an ambient electric fi eld.In this paper,the inductive charge separation between graupel and cloud,and hail and cloud,is calculated as follows(Ziegler et al.,1991):

where the subscriptsxand c represent graupel(or hail)and cloud droplets,respectively;DxandDcare the characteristic diameters of graupel(or hail)and cloud droplets,respectively;nxandncare the number concentrations of graupel(or hail)and cloud droplets, respectively;Vxis the mass-weighted mean fall speed of graupel(or hail); Γ(x)is the complete gamma func-tion;n0xis the number concentration intercept for graupel(or hail);〈cosθ〉is the average cosine of the angle of rebounding collision;Ezis the vertical electrical fi eld;Excis the collision efficiency;andEris the rebound probability.All the constant parameters of Eq.(8)are taken from Ziegler et al.(1991).

Fig. 1. Non-inductive charge separation sign-reversal curve used in the present study.The signs represent the polarity of charge taken by the graupel(or hail)in the non-inductive scheme.

2.5 Charge sedimentation

The change in particle charge density that results from the sedimentation of hydrometeors is also considered here.The sedimentation of the particle charge density is calculated by an equation similar to that for the sedimentation of hydrometeors(Milbrandt and Yau,2005a):

whereρairis the density of air andVNXis the terminal fall speed of particles.

2.6 Lightning parameterization

A bulk lightning parameterization(Xu et al., 2012)is used in this paper.When the particle charge density is obtained from the calculation,the electrical potential(Φ)can be calculated by the Poisson equation:

whereρrepresents the total charge density at the gridpoint andεis the electrical permittivity of air (8.8592×10?12F m?1).The electrical fi eld can be calculated by

whereEis the electric fi eld.Equation(10)is solved by successive over-relaxation,with the boundary conditions at the bottom and top set to zero in our model. The discharge initiation threshold(de fi ned asEbreak) is the height-varying electric fi eld,as follows(Marshall et al.,1995):

whereρair(z)is the(non-dimensional)air density varying with height.The unit ofEbreakis kV m?1.

The grid fl ash number(FN)is counted on the ground grid only.If the value of the vertical electric fi eld at one gridpoint directly above a ground gridpoint exceedsEbreak,the model will reduce the charge density at the gridpoint where the absolute electric fi eld exceeds 30 kV m?1(de fi ned asEend)by 20%.The discharge scheme is one dimensional,so only the grids in the vertical direction of the initiate grid are judged for reducing charge,and one fl ash will be recorded for the corresponding ground gridpoint.The discharge process is calculated independently for each ground gridpoint.If adjacent ground gridpoints all record a fl ash at the same time,the fl ash number will increase in each ground gridpoint,even though they may be considered as the same fl ash.In the mesoscale model, the time step is usually more than 10 s and the discharge can occur many times;therefore,for every time step,up to 12 discharges are permitted in this simulation.The limitation of the number of discharges is sensitive to the time step.

At each time step,the microphysical scheme fi rst calculates the charging,and the transfer and sedimentation of charge density.Then,the electric fi eld is calculated.Lastly,the discharge process is applied and the scheme advances to the next time step.

The lightning code explicitly solves for the electric fi eld in the one-dimensional scheme,so only the vertical electric fi eld can be given by the model.But,the lightning code herein has the Message Passing Interface(MPI)capability to allow for larger mesoscale simulation exceeding the day scale,and it can be used in the real-time simulation.The lightning scheme could efficiently reduce the charge and restrain the increase of the maximum electric fi eld.In a squall line case,the predicted distribution of lightning density is similar to that of the observed CG lightning density.Please refer to Xu et al.(2012)for detail.

The model coupled with the electrical processes is referred to as the WRF-Electric model(WRF-Elec). The charge density of the di ff erent hydrometeor particles and diagnosed grid fl ash number can be simulated by WRF-Elec.

3.Idealized case and model setup

An idealized tropical cyclone,em?tropical?cyclo-ne,is used in this study.This is a three-dimensional default idealized case in version 3.4.1 of the WRFARW model.

The initial vortex is weak and axisymmetric(Fig. 2),and is speci fi ed by an analytic equation from Rotunno and Emanuel(1987).The vortex is placed in the center of the domain,and is in hydrostatic and gradient wind balance with the maximum wind speed at the lowest model level.This low-level vortex has a horizontal radius of 412.5 km and a maximum wind speed of 15 m s?1at a radius of 82.5 km.The initial horizontally homogeneous environment is speci fi ed via vertical pro fi les of the Jordan mean hurricane sounding(Jordan,1958).Anf-plane centered at 20°N is employed in this model with a constant sea surface temperature(SST)of 28℃.

The two domains both have a mesh size of 200×200,with horizontal grid resolutions of 9 and 3 km,respectively.The vertical grid spacing is 1.25 km with the model top at 25 km.Domain 2 is located in the center of domain 1,and both are static nests.The physical options include the Milbrandt twomoment microphysical parameterization with electrical processes,the Kain-Fritsh cumulus scheme(Kain, 2004),and the YSU(Yonsei University)planetary boundary layer scheme(Hong et al.,2006).The lateral boundary conditions are periodic.No cumulus parameterization is used in the 3-km mesh.The default radiation scheme is speci fi ed in the idealized model. The two meshes are integrated for 240 h with a time step of 54 s in the coarse domain and 18 s in the inner domain;see Table 1 for more details.

4.Results

4.1 Overview of the tropical cyclone

Figure 3 shows the time evolution of the minimum sea level pressure(MSLP)and maximum wind speed of the simulated TC in domain 1.The processes of TC development include the spin-up and initial organization,the intensi fi cation stage,the quasi-steady stage,and the TC weakening with oscillation of intensity.The MSLP can reach 920 hPa and the maximum wind speed is 85 m s?1at the mature stage.Four snapshots corresponding to di ff erent stages of the simulated TC are shown in Fig.3.Letters a(t=90 h) and b(t=108 h)denote the intensi fi cation stage of the TC,while c(t=156 h)and d(t=168 h)indicate the quasi-steady stage.The horizontal displacement of the TC is very slow,so the TC is always located within the scope of domain 2.The eyewall can be clearly identi fi ed from the simulated combined radar re fl ectivity at di ff erent times in domain 2(Fig.4). The eyewall shrinks in the intensi fi cation stage.Thespiral rainband is sometimes relatively loose(Figs.4a and 4b),and sometimes has a distinct band structure (Figs.4c and 4d).The eyewall lightning in TCs generally occurs in the rapid intensi fi cation stage rather than in the quasi-steady stage.Lightning activity is di ff erent in the eyewall and the outer spiral rainband region.The charge structure of the eyewall and the outer spiral rainband cell in di ff erent stages of the TC is analyzed in the next section in order to investigate the relationship between the evolution characteristics of charge structure and lightning activity,and the processes driving the evolution.

Fig.2.The initial vortex in the center of domain 1,with a maximum wind speed of 15 m s?1at the radius of 82.5 km and a size of 412.5 km.Sea level pressure(hPa;solid lines)contours:986 to 990 by 2 hPa.

Table 1.The model setup

Fig.3.Time evolution of the minimum sea level pressure(MSLP;hPa;red line)and maximum azimuthal wind speed(m s?1;blue line)of the simulated TC.The letters a(t=90 h),b(t=108 h),c(t=156 h),and d(t=168 h)represent four di ff erent times that are analyzed in the following section.

4.2 Eyewall electri fi cation at di ff erent stages of TC evolution

Figures 5a–d show the total charge density in the vertical cross-sections along the red lines marked in Fig.4.The charge structure of eyewall cells is di ff erent at di ff erent stages.In the TC intensi fi cation stage (Figs.5a and 5b),there is an inverted dipole structure in some eyewall cells with a negatively charged region above a positively charged one.However,some cells in the eyewall show a normal tripole structure with a broad negative region between two regions of positive charge.In the quasi-steady stage(Figs.5c and 5d), the negative charge region of the eyewall is widespread and the cells only show the inverted dipole structure. Black and Hallett(1999)also suggested that the inverted dipole structure dominates in the eyewall of TCs.The widespread negative charge region and the inverted dipole and normal tripole structures would be conducive to the occurrence of negative CG lightning (Black and Hallett,1999;Fierro et al.,2013),which is consistent with the polarity of CG lightning observed in the eyewall region of TCs(Lyons and Keen,1994). The formation of the TC charge structure can be affected by the dynamical and microphysical characteristics.

The di ff erence in charge structure is fi rstly due to the di ff erence in updrafts.The updraft in the eyewall is generally weak,even in the intensi fi cation stage. However,there are some extremely tall towers(known as convective burst cells)in the eyewall region during the rapid intensi fi cation stage,which are characterized by the tripole charge structure.Figures 6a and 6b show that the vertical velocity of cells with tripole structure may reach 14 m s?1,while in the quasi-steady stage(Figs.6c and 6d),the updraft in the eyewall cells is much weaker(＜5 m s?1).Note that although the updraft in the eyewall cell can reach very high altitudes(Fig.6a),strong updrafts are always found in the region between levels of 0 and –20℃above the melting level.

Graupel and ice crystals play an important role in the electri fi cation,and their charge density is the primary component of the total charge density.The charge carried by hail,snow,cloud,and rain is smaller than that of graupel and ice in this simulation( fi gure omitted). In a recent TC observational study, Reinhart et al. (2014)demonstrated that the microphysical environments consisting of graupel,very small ice particles,and supercooled water are favorable for non-inductive charging.Figures 7a–d and 8a–d show vertical distributions of the mixing ratio and the charge density of graupel and ice at di ff erent times. Widespread ice crystals are mainly located at the top of the clouds,with some in the layer from 0 to –20℃. The distribution of graupel is concentrated and it is found lower than the ice.In the strong updraft region,as shown in Figs.7a and 7b,the graupel can be lifted into a higher position,resulting in the coexistence of graupel and ice in the middle and upper atmosphere(Figs.7a,7b,8a,and 8b).In the eyewall cells during the quasi-steady stage,the graupel occurs generally between 0 and –20℃ (Figs.7c and7d),and graupel and ice coexist mainly at the middle level.From Figs.5 and 9,it can also be found that the electrically active region mainly accompanies the abundant LWC region.

Fig.4.Simulated combined re fl ectivity(dBZ)in domain 2 at(a)t=90 h,(b)t=108 h,(c)t=156 h,and(d)t= 168 h.The red and blue lines indicate the location of the vertical cross-section of the majority of the plots in this study.

Di ff erent dynamical and microphysical conditions may a ff ect the particle charge polarity and value, thereby a ff ecting the charge structure. The noninductive scheme plays the leading role in this simulation,especially the charge separation between graupel and ice crystals,while the electri fi cation due to the inductive scheme is weak.The results given by Takahashi(1978)have shown that the collisions between riming graupel and lighter ice crystals exchanged a sufficient amount of charge per collision to account for the observed electric fi eld.The graupel and ice charge density at di ff erent stages is therefore analyzed in order to understand the formation of the charge structure of the eyewall.

Fig.5.Vertical cross-sections of total charge density(nC m?3;shaded)at(a)t=90 h,(b)t=108 h,(c)t=156 h, and(d)t=168 h along the red lines of Figs.4a–d;and(e)t=90 h and(f)t=156 h along the blue lines of Figs.4a and 4c.The horizontal lines represent the isotherm lines of –20℃, –10℃ (dashed line),and 0℃ (solid line).The solid line with “5” represents the contour line of 5 dBZ.

First,we consider the particle charge composition of the tripole structure in the eyewall.The graupel takes a negative charge at the upper level and a positive charge at the middle level(Figs.7a and 7b), while the ice crystals are oppositely charged(Figs.8a and 8b).The sign of the particle charge is determined by the environment temperature and reversal temperature which is a ff ected by the LWC when graupel collides with ice. The LWC(Figs. 9a and 9b)above the –13.8℃ level is not large enough (＜1 g m?3)to a ff ect the reversal temperature.Therefore,the –13.8℃ level could be considered as the reversal temperature level.The NGCZ is above the reversal temperature level(HRTL)and PGCZ is below the HRTL.These results indicate that the charging process occurs above and below the HRTL at the same time.The sign of the particle charges is consistent with the tripole results simulated by Fierro et al. (2013).

The particle charge distribution of the inverted dipole charge structure is simpler than that of the tripole structure.Att=156 h andt=168 h(Figs. 7c,7d,8c,and 8d),the graupel particles only charge positively and the ice crystals only charge negatively. Each hydrometeor particle takes one polarity. This indicates that the non-inductive graupel-ice charging process only occurs in PGCZ.This is due to the weak updraft and the relatively low position of the coexistence region of graupel and ice in the eyewall,as seen in observations(Black and Hallett,1999).The LWC(Figs.9c and 9d)in the –10 to –20℃ layer is too low(＜0.5 g m?3)to lift the PGCZ,so the graupel becomes positively charged when ice crystals are bounced o ff,as the particle collisions occur below the–13.8℃ level.

Fig.6.As in Fig.5,but for vertical velocity(m s?1;shaded).

The results of Fierro et al.(2007)showed a normal tripole structure in the eyewall and they considered that the simulated updraft is stronger than the observations.The results of our study suggest that only extremely tall towers have updrafts strong enough to generate the tripole structure.Fierro et al.(2011) analyzed the rapid intensi fi cation stage of Hurricane Rita using lightning and NBE data.They captured the simultaneous occurrence of negative CG lightning at the lower level and positive NBE at the upper level. Positive NBEs are produced between a main negative charge layer and upper positive charge layers(Wu et al.,2012).Therefore,it can be inferred that normal tripole charge structures occur in eyewall cells.These observed and simulated tripole results support di ff erent aspects of our simulations.In turn,our simulations help to understand recent results from observations and other simulations.

From the positions of the region of maximum charge density(Fig.5a)and maximum vertical velocity(Fig.6a),we can see that the maximum total charge densities occur at the same time as the maximum vertical velocities,but they are separated spatially.The maximum vertical velocity occurs at a position with very low total charge density.In observations,the lightning hole(lightning-free region)is also associated with the strong updraft in thunderstorms (Zhang et al.,2004).

4.3 Outer band cell electri fi cation at di ff erent stages of TC evolution

Fig.7.As in Fig.5,but for graupel mixing ratio(g kg?1;shaded)and charge density of graupel(nC m?3;red contours of±0.1,±0.2,±0.3,and±0.5 nC m?3).Solid lines indicate positive values and dashed lines indicate negative values.

Figures 5e and 5f show the total charge density in the vertical cross-sections along the blue lines marked in Fig.4.The charge structure in the outer spiral rainband displays the same structure in all stages:a dipole with positive charge above the negative.The cross-sections of the vertical velocity(Figs.6e and 6f) show that the convective cells in the spiral rainbands generally have the greatest vertical velocity(＞12 m s?1).In some cells,the center region of greatest vertical velocity is mainly located at the upper level(Fig. 6e).

Distributions of hydrometeors(Figs.7e,7f,8e, and 8f)show that widespread ice crystals are mainly located at the upper level and that graupel can reach the upper level,transported by the updraft.The major region of coexistence of graupel and ice is in the upper level.Under these conditions,the graupel mainly charges negatively and the ice crystals charge positively(Figs.7e,7f,8e,and 8f).This indicates that charging only occurs in NGCZ while in the extremely tall eyewall cells,charging occurs in both NGCZ and PGCZ.From Eq.(7),it is inferred that if the environmental temperature of collision position is lower,the LWC needed for charge sign reversal is higher.Figure 9f shows that the LWC between –10 and –20℃ level is high(＞1 g m?3),which would easily make the graupel charge positively,but the graupel also charges negatively.We can further infer that the collision position is relatively high.

Although the extremely tall towers in the eyewall and the cells in the spiral rainband both have strong updraft,the total charge density is di ff erent in the two types of convective cell.This is because the coexistence regions of ice and graupel are at di ff erent heights.In the simulation by Fierro et al.(2007),the eyewall cells show a normal tripole and the cells in the rainbands show the simple normal dipole.The charge structure of the spiral rainbands is consistent with the present results.

Fig.8.As in Fig.7,but for ice mixing ratio(g kg?1;shaded)and charge density of ice(nC m?3;red contours).

5.Discussion

The electri fi cation of TCs is in fl uenced by vortex dynamics.The di ff erences in the dynamical and microphysical features between the eyewall and outer spiral rainbands lead to di ff erent charge structures. In particular,the eyewall cells show di ff erent charge structures at di ff erent stages.Only one case is analyzed in this study,but a picture of the evolution of the electri fi cation and charge structure of TCs can be inferred from the results.

The simple discharge parameterization is one shortcoming of this study. A one-dimensional discharge scheme is used and the scheme cannot reproduce the branched pathways of lightning.Flashes at neighboring gridpoints may belong to the same fl ash but they have been considered as isolated fl ashes.The discharge scheme can lead to errors in the lightning parameterization but it can reduce the charge successfully.A simple discharge scheme also means that the computation is very efficient.A relatively complex discharge scheme was used by Fierro et al.(2013), and their discharge scheme was implemented in a separate module in the model.The discharge scheme used in our study is incorporated in the microphysical scheme.If the WRF-Elec is to be used for predicting lightning,a proper discharge scheme would be needed.Developing adequate parameterizations of lightning in mesoscale weather models is one of the important goals of atmospheric electricity in the near future(Qie,2012).

There are many two-moment microphysical parameterizations in the WRF-ARW,and many charge separation schemes.The charge structure could be a ff ected by our choice of microphysical and charging schemes.The present study is based on just one non-inductive charge separation and microphysical scheme. Hence,future studies employing di ff erent schemes are planned.

Fig.9.As in Fig.5,but for liquid water content(g m?3;shaded).

In the simulation of an idealized TC by Fierro et al.(2007),the charge structure was a normal tripole in the eyewall,while in our simulation the eyewall cell shows an inverted dipole in the quasi-steady stage. Other than the di ff erent non-inductive schemes used in the two cases,the di ff erence of the simulated strength of updraft may be the main reason.Strong updrafts (＞10 m s?1)can support a deep mixed-phase layer containing abundant supercooled water,which is conducive to TC electri fi cation(Black and Hallett,1999). The observational study by Reinhart et al.(2014)further proved that strong updrafts of 10–20 m s?1are a favorable factor for TC electri fi cation.

Given that lightning mainly occurs in the deep convective cells,the internal deep convective structure of TCs might be deduced from lightning data(Fierro et al.,2011).Assimilation of lightning data could be used to improve the initial structure of TCs.In this study,the distribution and strength of the updraft and microphysical characteristics determine the electri fi cation.Strong electri fi cation accompanies the outbreak of eyewall lightning corresponding to the strong updraft.Cells in the outer spiral rainband with a normal dipole structure correspond to strong updrafts and the coexistence of di ff erent particles at upper levels.This suggests a relationship between the lightning data and TC cell structure.It is evident that the updraft is separated from the strong electri fi cation region,and this represents an obstacle to establishing the relationship between lightning and vertical velocity.

The eyewall in our simulation is de fi nite and strong,while the spiral rainband is relatively loose at times.One possible reason is that the eyewall istoo strong to restrain the development of the rainband;this may be related to the initial vortex.There is strong vortex advection in TCs and charge can be transported by the advection.Therefore,the charge density in one cross-section does not result only from the local charging process but also from the advection, which can also a ff ect the charge structure.

6.Summary

Inductive and non-inductive electri fi cation schemes and a bulk discharge parameterization are introduced into the Milbrandt two-moment microphysical scheme in the WRF-ARW model.The model with electrical processes,referred to as WRF-Elec,is able to simulate the charge density and electric fi eld in the cloud.An idealized TC is simulated based on the WRF-Elec model.The evolution of the electri fi cation of the TC is analyzed fi rst,and then the electrical structures of the cells in the eyewall and outer spiral rainbands are compared.This study makes an attempt to illustrate the evolution of the charge structure of TCs(Fig.10).The results of this study can unify most of the previous observations and simulations.

The cells in the eyewall have di ff erent charge structures in di ff erent stages.In the intensi fi cation stage,the general cell has an inverted dipole structure,but the extremely tall tower cells with strong updraft can display a normal tripole structure.In the quasi-steady stage,the cells only show an inverted dipole structure.Cells in the outer spiral rainband have a similar structure in all stages of the TC.The normal dipole structure dominates in the cells with relatively strong updraft in the rainband.The noninductive graupel-ice mechanism plays a leading role in the electri fi cation.

Fig.10.Evolution of the charge structure of a TC during di ff erent stages of the TC development.

In the intensi fi cation stage,the updraft is strong in the extremely tall towers in the eyewall. This strong vertical velocity at the middle and upper levels of the atmosphere leads to strong electri fi cation both in positive and negative graupel charging zones. Large particles like graupel take a negative charge at the upper level and a positive charge at the middle level.The small particles take on the opposite sign of charge at the middle and upper levels.As a result, the tripole structure,with a negative charge region between two positive charge regions,appears. Extremely tall towers with strong electri fi cation accompany the outbreak of eyewall lightning and these towers are coincident with storm intensi fi cation(Kelley et al.,2004).In the quasi-steady stage,the extremely tall towers disappear and the graupel cannot be transported to the upper level.The weak updraft and low height of the coexistence region of graupel and ice crystals in the eyewall induce charging processes that occur mainly in the PGCZ.Under this weak updraft condition,the intensity of electri fi cation weakens and lightning in the eyewall is rare.

The convective cell in the spiral rainband is di ff erent from the cell in the eyewall.The cell in the spiral rainband generally has a strong updraft but the coexistence region of graupel and ice crystals is mainly located at the upper level.Electri fi cation is strong in the NGCZ,leading to a simple normal dipole structure.Because the cell in the spiral rainband has strong vertical velocity in all stages of TC evolution,the lightning mainly occurs in the outer spiral rainbands.

An idealized TC is simulated in this study whose structure is in fl uenced by the rather arti fi cial conditions.The evolution of the charge structure of TCs under more realistic conditions will be analyzed and simulated in a future study by employing WRF-Elec. This more realistic simulation could be veri fi ed by observations,which would further help to understand the charge structure of TCs.

Acknowledgments.The authors thank Dr. Milbrandt in Environment Canada for guidance on using the two-moment microphysical scheme.We alsothank Drs.Ting Wu and Xi Cao for constructive suggestions.Finally,the authors thank the two anonymous reviewers for their valuable comments.

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(Received December 17,2013;in fi nal form March 11,2014)

Supported by the National(Key)Basic Research and Development(973)Program of China(2014CB441406 and 2014CB441402), National Natural Science Foundation of China(41030960),and Basic Research Fund of Chinese Academy of Meteorological Sciences (2013Z006).

?Corresponding author:zhangyj@cams.cma.gov.cn.

?The Chinese Meteorological Society and Springer-Verlag Berlin Heidelberg 2014

The results indicate that the TC eyewall generally exhibits an inverted dipole charge structure with negative charge above the positive.In the intensi fi cation stage,however,the extremely tall towers of the eyewall may exhibit a normal tripole structure with a main negative region between two regions of positive charge.The outer spiral rainband cells display a simple normal dipole structure during all the stages.It is further found that the di ff erences in the charge structure are associated with di ff erent updrafts and particle distributions.Weak updrafts,together with a coexistence region of di ff erent particles at lower levels in the eyewall,result in charging processes that occur mainly in the positive graupel charging zone(PGCZ).In the intensi fi cation stage,the occurrence of charging processes in both positive and negative graupel charging zones is associated with strong updraft in the extremely tall towers.In addition,the coexistence region of graupel and ice crystals is mainly situated at upper levels in the outer rainband,so the charging processes mainly occur in the negative graupel charging zone(NGCZ).