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On the generation of charge layers in MCS stratiform regions
Atmospheric Research 91 (2009) 272–280
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Atmospheric Research j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a t m o s
On the generation of charge layers in MCS stratiform regions A.A. Evtushenko, E.A. Mareev ⁎ Institute of Applied Physics, Russian Academy of Sciences, 46 Ulyanov str., 603950 Nizhny Novgorod, Russian Federation
a r t i c l e
i n f o
Article history: Received 21 January 2008 Accepted 29 July 2008 Keywords: Electric field Charge density Thunderstorm electrification Mesoscale convective system Charge transfer mechanisms Modeling
a b s t r a c t We suggest a quantitative one-dimensional model treating the formation of charge layers near the 0 °C isotherm in stratiform regions of mesoscale convective systems. A number of factors principal for the field generation have been taken into account: both non-inductive and inductive melting charging, light ions, a complicated profile of the vertical air velocity near the 0 °С isotherm, the boundary conditions proper for the horizontally extended systems in the global electric circuit. Non-inductive collisional charging near the 0 °C isotherm was not considered. It was found that both non-inductive and inductive melting mechanisms can contribute; the inductive melting charging of ice aggregates was found more preferable, while the contribution of non-inductive mechanisms might be significant depending on particular conditions. The role of light ions in the formation of the positive charge layer near the 0 °C isotherm may be important. If the advection from the convective region ensures charge inflow to the upper charged layers, the melting charging mechanisms are able to explain an observable electric field structure in the whole stratiform region. It is important that the mutual position of the zero point on the vertical air velocity profile and the point of maximum melting-chargetransfer determines the fine structure of the electric field in the vicinity of the 0 °C isotherm. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Several observational studies have investigated the charge structure of mesoscale convective system (MCS) stratiform regions (e.g., Krehbiel, 1986; Rutledge and MacGorman, 1988; Rutledge et al., 1990; Marshall and Rust, 1993; Stolzenburg et al., 1994, 2001; Schuur and Rutledge, 2000a; Mo et al., 2003; Lang et al., 2004). It was found in particular that the stratiform region of a typical MCS of both A or B types has a number of horizontally extensive charge layers that exist for 6–12 h (Marshall and Rust, 1993; Stolzenburg et al., 1994, 2001). Taking into consideration the vertical shears in the stratiform flow field, the long transport distances, and the long time scales, it is surprising that the stratiform charge layers maintain their integrity (approximately similar charge density and vertical thickness across the stratiform region) and are not destroyed by turbulence. This fact suggests that local charging mechanisms might be at work to stabilize and/or enhance the charge layers advected from the convection ⁎ Corresponding author. Tel.: +7 8314 164792; fax: +7 8314 160616. E-mail address: [email protected] (E.A. Mareev). 0169-8095/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.atmosres.2008.07.010
region. Therefore, as a result of observational studies, two specific hypotheses have emerged: 1) advection of charge from the convective region, and 2) local charge generation within the stratiform region. Since a dominant aspect of the vertical electric structure of the stratiform region (or transition zone) of MCSs is a high-density charge layer at or near the 0 °C level, a problem of particle charging near the 0 °C isotherm is of key importance. It is the more so important that recent studies show that this layer can serve as a reservoir of the very big charge volume for intensive positive cloud-to-ground flashes closely correlated with the transient luminous effects in the middle atmosphere (e.g., Williams, 1998; Williams and Yair, 2006; Mareev et al., 2006). On the other hand, it is an extremely complicated problem due to different microphysical and thermodynamical processes occurring in this region and influencing the charge transfer (e.g., Knight, 1979; Willis and Heymsfield, 1989; Saunders, 2008). Possible mechanisms to explain the large electric field and substantial charges located in this region have been discussed by Marshall and Rust (1993), Rutledge and Petersen (1994), Stolzenburg et al. (1994), Shepherd et al. (1996), Schuur and Rutledge (2000b), Williams and Yair (2006). The recent
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studies emphasize the necessity to account for inherent mechanisms supporting the electrical structure of the stratiform region (Stolzenburg and Marshall, 2008). In particular, most of the data near the 0 °C isotherm were interpreted by Stolzenburg et al. (2007) to fit the inductive melting charging mechanism described by Simpson (1909). Previous work on MCS modeling (Rutledge and Petersen, 1994; Schuur and Rutledge, 2000a) indicated that both in situ charging and charge advection appear to be important contributors to the electrical budget of the stratiform region. But the quantitative and even qualitative understanding of the electrical processes in the stratiform region is far from complete. While charge densities produced by model simulations exhibit many similarities to observations, considerably less agreement was found when the simulated charge distribution was compared to the observed charge structure (Schuur and Rutledge, 2000a,b). Also, melting charging was found to be insignificant in the latter work which is not supported by the recent results of observational data analysis (Stolzenburg et al., 2007). A goal of this work is to suggest a simple 1D model allowing us to explain experimentally observed electric field profiles and to recognize the physical processes which should be taken into account considering the electric structure of the stratiform region. Our model develops a model initially suggested by Mareev et al. (2006). Note that 3D numerical models taking into account numerous fractions and different charging mechanisms in clouds (e.g., Mansell et al., 2005; Schuur and Rutledge, 2000b) represent a powerful tool for the study of thunderstorm electrification. But for lack of detailed information on the microphysical processes involved and due to the extreme complexity of the problem these models do not often allow clear understanding of the physical mechanisms playing dominant roles in particular cloud regions. The use of such comprehensive models is especially difficult when modeling the regions like the 0 °C isotherm where a lot of thermodynamic and electrodynamic processes operate simultaneously leading to the extremely complicated physical picture (Willis and Heymsfield, 1989). Our approach using a simplified representation of cloud components (a few components are considered, space charge densities are the analyzed variables), seems useful for the study of similar systems. We are restricted also by the development of a 1Dmodel because this approach is appropriate for stratiform regions of MCSs. 2. Theoretical model We use a quantitative model treating the formation of the charge layers near the 0 °C isotherm as a result of melting charging process. It is known (Willis and Heymsfield, 1989) that large aggregates with sizes from several hundred µm to several mm, and cloud droplets with sizes of order of 10 µm form near the zero degree isotherm. We assume that previously uncharged precipitation particles (large aggregates of vapor-grown crystals or smaller precipitation particles) acquire negative charge as they melt by shedding smaller, cloud-size particles (either liquid or solid) (Marshall and Rust, 1993; Stolzenburg et al., 1994). In accord with above notions, we have introduced in our model two types of hydrometeors named as “large” and
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“small” particles. The set of equations contains balance equations for the charge densities of several fractions and the Maxwell equation for the quasi-static electric field. In what follows we will present the results of rather simple modeling with the following set of equations: AρQ A VQ þ Vconv d ρQ þ ¼ −Rd f ðzÞ−γd ρQ d Aþ At Az Aρq Að Vq þ Vconv d ρq Þ þ ¼ Rd f ðzÞ þ γd ρq d A− At Az
ð1Þ ð2Þ
AAþ AðVþ d Aþ Þ þ ¼ IðzÞ þ κd Aþ d A− þ γd ρQ d Aþ At Az
ð3Þ
AA− AðV− d A− Þ þ ¼ −IðzÞ−κd Aþ dA− −γd ρq d A− At Az
ð4Þ
e0
AE ¼ ρq þ ρQ þ Aþ þ A− þ ρADD Az
ð5Þ
VF ðzÞ ¼ Vconv F μd E
ð6Þ
IðzÞ ¼ I0 d expðz=hÞ
ð7Þ
Here ρQ, VQ are the charge density and velocity of large (precipitation) particles; ρq, Vq are the space charge density and velocity of small (cloud) particles near the zero isotherm; A+, V+ and A−, V− are the charge densities and velocities of positive and negative (singly charged) ions respectively. The vertical coordinate z in the calculations varied from 0 km to 20 km. The grid step was equal 4 m. Zero point corresponded to the ground surface. The 0 °C isotherm was placed at 4 km above the ground which correspond to the conditions of typical experiments where the electric field near the 0 °C isotherm was analyzed with balloon soundings (Stolzenburg et al., 1994). ρADD is the additional (as compared to the charge generated near the 0 °C isotherm) charge density, which describes the upper charge layers generated either in the convective part of the MCS with the following advection into the stratiform region, or in the stratiform region itself. We have included it into the system “by hand” in the sense that its distribution was chosen specially to reproduce the typical experimental data on electric field profiles (Stolzenburg et al., 1994; Shepherd et al., 1996; Bateman et al., 1999). ρADD should be necessarily taken into account because of an important role of the upper layers in the formation of the whole field structure in the stratiform region and particularly near the zero isotherm, while the study of possible inherent charging mechanisms for these layers is out of the scope of the present study. The setting of ρADD is necessary also for a realistic set of boundary conditions determined by the total voltage U between the top and the bottom of the system and supported by the global circuit operation. Indeed, the electric field strength E determined by charge density distributions is a very important variable connecting all other variables of the set (1)–(7) through the Maxwell Eq. (5). In the modeling we assumed that the voltage U (i.e. the integral of electric field over the height from 0 to the upper boundary of the system at 20 km) was constant. In what follows, the calculations for U = 300 kV are presented. As was noted above, the electrical processes in the vicinity of the 0 °C isotherm are extremely complicated. Dinger and
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Gann (1946) proposed a non-inductive charge transfer process associated with melting. Drake and Mason (1966) noted that convection in a melting ice sphere produced negatively charged droplets ejected from bursting air bubbles at the surface. The sign of charge and the conditions under which the charges were separated were highly dependent on the impurities in the melting ice. Drake (1968) found that the melting particle (graupel) gained positive charge. But in the MCS bright band, the dominant particle habit is probably aggregates, not graupel, so the process of melting and break off of small particles is not likely to be the same as for graupel. Note that the production of very large aggregates is dramatic after the onset of melting (Willis and Heymsfield, 1989). We can speculate only how the melting aggregates might be gaining negative charge non-inductively. A natural assumption is that different water phases co-existing on the aggregates can lead to an electric potential between the falling aggregate and sublimating branches that break off (due to a thermoelectric effect in particular). Note that the Hallett–Mossop (1974) ice multiplication process can be involved as well. The process involves the accretion of supercooled water droplets by falling ice pellets, ice crystals or graupel. Hallett and Saunders (1979) investigated this multiplication process with a view to the possibility that the ejected ice fragments were electrically charged and so could contribute to thunderstorm electrification. They found that the growing ice pellet charged positively with a negative charge on an ejected ice fragment of order −10− 16 C. But when the vapor supply used to grow the cloud droplets was turned off, the charge sign reversed. An inductive particle-breakup charging is another candidate for the particle charging near the 0 °С isotherm. When the melting particle breaks, small fragments breaking off the upper side of the particle would be positively charged in the positive electric field (Simpson, 1909; Muchnik, 1946; Canosa and List, 1993). The same process can occur when ice fragments break off the evaporating aggregate (Rydock and Williams, 1991). The positive electric field necessary for this inductive mechanism to initiate and proceed it, can be set up by the charge layers above the level of the breakup (Stolzenburg et al., 1994). The basic signatures that fit the inductive melting charging mechanism are described by Stolzenburg et al. (2007). Overall, we should note that there is no reliable enough experimental data on the charging of melting hydrometeors allowing for rigorous quantitative analysis, and it emphasizes the importance of consideration of both non-inductive and inductive charging in numerical analysis of charge generation. To include the melting charging into account, we describe it by the non-dimensional function f (z) characterizing the effectiveness of this process depending on the height. We considered this function to have Gaussian shape with the maximum at a definite height zm. It is natural to assume that the charging occurs most effectively when the temperature is equal to 1–2 °C when a pronounced but sufficiently thin liquid layer forms on the hydrometeor surface. For the linear profile of temperature in the atmosphere with a lapse rate of 20 °C per 4 km, the level of +1 °C is situated about 200 m below the 0 °C isotherm. Correspondingly, it was assumed that the function f (z) has a maximum at zm = 3850 m and the width σ = 50 m. Note that melting depends on relative humidity at
temperatures close to 0 °C. Note also that a quasi-isothermal layer even deeper than 200 m is sometimes observed (e.g., Shepherd et al., 1996). The parameter R in Eqs. (1) and (2) depends on the mechanism of electrification near the zero isotherm. It was assumed Rnonind = Δq0 · ν · N for non-inductive mechanism and Rind = α · ν · N · E for the inductive mechanism respectively. For non-inductive charging the maximum value of the factor Δq0 · ν, determined by the separated electric charge and the frequency of small particle shedding, was taken as 1.6∙10− 14 C s− 1 in the calculations. Concerning the choice of this value, it should be noted that relatively little (compared to precipitation charges) is known about the charge carried on individual cloud particles inside thunderstorms and their rate of generation (Marshall and Stolzenburg, 1998). Colgate and Romero (1970) found individual charges of +0.2 to −0.4 fC on particles ranging from 5 to 15 μm in diameter. As to the frequency of small particle shedding ν, we did not find any estimation of this parameter in the literature. Our rough estimates give possible values from several units to several tens per second for ν. The number density of melting hydrometeors was equal N = 102–103 m− 3. The sign of the parameter Rnonind was taken as positive. We do not consider in our model the non-inductive collisional charging near the 0 °C isotherm. For the inductive mechanism, the factor α · ν characterized the effectiveness of charging due to polarization of melting particles in the electric field and was estimated as 4·10− 20 C mV− 1s− 1. In Eq. (7) I(z) is the rate of light ion production growing exponentially with characteristic height scale h = 6 km; at the msl it is equal to I0 = 107 m− 3 s− 1. The coefficient of recombination of positive and negative ions was taken as κ = 108 m3/C s. The coefficient of attachment of ions to cloud particles was taken as γ = 107 m3/C s (e.g., MacGorman and Rust, 1998). The velocities of larger components VQ and Vq do not depend on the electric field while the velocities of light ions were varied due to the influence of the electric field. The respective dependence V±(E) in Eq. (6) contains the mobility μ of light ions as the important parameter. A special attention in the calculations has been paid to the account of ions. The atmospheric ions collide with, and attach, to molecules to form small cluster ions, e.g. H+(H2O)n. To quantify this process, the humidity of the air is an important parameter. We are not aware of direct measurements of ion mobility in cloudy air; under laboratory conditions the measurements of ion mobility in saturated air are very scarce. Recent measurements by Harrison and Aplin (2007) gave evidence of some dependence of ion mobility on the water vapor content. We have taken into account in calculations a possible decrease of ion mobility in a cloud but without any rigorous parameterization. The velocity Vconv describes the vertical motion of air. It is known that the vertical velocity is not so big in the stratiform region—updrafts of several tens of cm/s are often observed (Stolzenburg et al., 1994). Respectively, in the first series of calculations we accepted Vconv = 0.5 m/s in the cloud decreasing smoothly to 0 above and below the cloud. This profile is a simplest representation of a slow updraft in a cloud region, smoothly decreasing at the top and beneath the cloud to
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connect it with the actual distribution in the framework of the 1D approach. The change of sign for the velocity is often observed also—the slow updraft is changed with slow downdraft in the vicinity of the 0 °С isotherm. To take it into account as well, in the second series of numerical experiments a more complicated dependence of Vconv(z) with the sign reversal (see Fig. 6 below) was taken. Compared to our previous model (Mareev et al., 2006), the present version includes the ion balance equations, so that the effects of ions are considered in detail in the present paper. Also the dependence Vconv(z) was not taken into account in the previous version. 3. Modeling results First of all, we analyze the dynamics of an initial electric field created by the upper charge layers situated above the 0 °C isotherm. The initial electric field is created by the charges designated as ρADD in Eq. (5). The charges are distributed following the Gaussian law in the height range from 7 to 10 km (positive charges) and from 5.2 to 7 km (negative charges) respectively. The maximum charge densities were taken as 4 × 10− 11 C/m3 and −6.5× 10− 11 C/m3 respectively so that the total integral from these charge densities was equal to zero. This ρADD charge distribution is supported during the run. The ion mobility is equal 10− 5 m2 V − 1s − 1. The first run illustrates just a hypothetical situation when the charging mechanisms near the 0 °C isotherm do not operate, and upper layers are screened by ions. The dynamics of screening is presented in Fig. 1. The process started at the time t = 0. It is seen on the figure how the upper layer is stabilized and at the same time the screening layer is formed. Clearly seen is the electric field maximum of about 60 kV/ m at the altitude between 5 and 10 km. However, this field is screened by the ion layers for about 300 s. The field magnitude in the maximum reaches a quasi-stationary value of about 25 kV/m, while at the ground surface the field is upward and equal to about 1 kV/m. The results of numerical analysis for the layers formed near the 0 °C isotherm due to the non-inductive charging are
presented in Figs. 2 and 3. The velocities of the precipitation and cloud particles in the interaction region (i.e. the region where the charging process occurs) were taken as VQ = −2 m/s and Vq = 0.5 m/s respectively. We are interested mostly in the large particle density in the region where charge transfer
Fig. 1. Electric field profile at the initial moment and the following field screening by light ions.
Fig. 3. The profiles of the electric field at the time 0, 1000, 2000 s for the noninductive charging with the ion mobility 2·10− 5 V m− 2 s− 1.
Fig. 2. Dynamics of electric field distribution for the non-inductive charging with the ion mobility 2·10− 5 m2 V − 1s − 1 (a) and with the mobility 10− 4 m2 V − 1s − 1 (b).
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Fig. 4. Electric field dynamics (a) and electric field profile at t = 2000 s (b) in a case of regular growth of the upper charge layer.
mechanisms are operating, i.e. in the altitude range of order of 300 m. Here the density N was assumed to be equal to 100 particles per cubic meter. The dynamics of electric field distribution for the noninductive charging is shown in Fig. 2 for two values of the ion mobility: 2·10− 5 V m− 2 s− 1 (a) and 10− 4 V m− 2 s− 1 (b). To represent the field dynamics in a more convenient way, for the first variant of the ion mobility the electric field profiles at the different time moments 0, 1000, and 2000 s are shown in Fig. 3. A narrow layer of the positive charge near the 0 °С isotherm and more extended negative charge layer below are clearly seen in Figs. 2 and 3. The formation of an additional layer of negative charge above the 0 °С isotherm is of a special interest. It forms due to the weak updraft which promotes the upward flow of ions; the latter are negative on average after the primary attachment of positive ions to negatively charged hydrometeors forming the distributed lower negative layer. It is seen from Fig. 2a and b that the shape of the electric field distribution is conserved in general with ion mobility change, but the field magnitudes are substantially different so
that approximately the field magnitude at the same time turns out to be inversely proportional to the ion mobility (5 times in this specific case). In other words, the main result of ion mobility decrease is the increase of time needed for the field development near the 0 °С isotherm. Respectively, the field reaches the same value if the rate of charging increases. It means in particular that the results obtained for the certain (e.g., reduced) ion mobility, can be further used with account for respective scaling in the source function R. It is convenient because the numerical scheme is more stable for the reduced ion mobility in high electric fields. The following step of the model development was the modeling of the field growth near the 0 °С isotherm in the presence of upper layers determined by the term ρADD. A linear growth of the charge density (2.5 times during 2000 s) has been assumed. The mobility of light ions was accepted 0.1 cm2/V·s. The results for electric field dynamics and electric field profile at t = 2000 s are presented in Fig. 4a and b. Along with the characteristic electric structure near the 0 °С isotherm observed on the previous figures, two additional layers between 5 and 9 km are seen also. During the first 600 s the maximum charge density near the 0 °С isotherm grows almost linearly followed by saturation at about 1200 s at a level of about 3 nC m− 3. Note that for the higher velocity of small particles, determined by the convective updraft, the saturation occurs at a lower level. As to the charge of a melting particle, it is growing almost linearly with time for about 600 s, it is then saturated at the level of 10− 10 C, which corresponds well to experimental data (Bateman et al., 1995). The electric current profiles generated by heavy (precipitation and cloud) particles and light ion particles at the time 2000 s are presented in Fig. 5. The contribution of ions is significant even in a case when their mobility is rather small. These calculations clearly illustrate how the electric currents in thunderstorm clouds may be calculated on the basis of microphysical consideration, which is necessary for the analysis of large-scale problems like the global circuit
Fig. 5. The profiles of different components of the electric current density at the time 2000 s. Dotted line—heavy particles, dashed line—ion convective current. Ion mobility is equal 10− 5 m2 V − 1s − 1.
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operation: they can be used for the search of the ionospheric potential perturbation and electric energy of the stratiform region while using a generalized 2D or 3D consideration for the stratiform region. One of the main goals of this study was the investigation of inductive mechanism effectiveness during charge separation near the 0 °C isotherm. Under the action of the electric field on the upper part of the particle the positive charge is formed while an equal negative charge is formed on the lower part of the particle. The dependence of Vconv(z) used in the modeling is shown in Fig. 6. The exponential increase of the mobility from the value 1 cm2/V·s typical for ground level was taken into account. It was assumed however that in the cloud the mobility decreases by 10 times (compared to its values determined by this exponential profile) with the transfer regions 2–3 km and 8–9 km for the bottom and top cloud boundaries respectively. The layer of the negative charge above the 0 °C isotherm distributed according to the Gauss law in the height range from 4.5 to 6 km has been taken into account by means of the term ρADD. The charge density at the center of the layer was growing linearly in time starting from 0 at the initial moment and reaching 5 × 10− 10 C/m3 up to 2000 s. It is assumed that these charges can be advected from the convective region into the stratiform region. The results of calculations are presented in Fig. 7. The noninductive mechanism does not operate in this case. It is obvious that this profile corresponds well to the type B MCS profiles. To demonstrate this fact, a typical example of such a profile, which was initially presented by Marshall and Rust (1993) and then discussed in detail by Stolzenburg et al. (1994), Shepherd et al. (1996), and Evtushenko et al. (2007), is shown in Fig. 8. The temperature zero point coincides in this case with the point of the electric field zero. The absolute magnitudes of the field maxima and even their relation are well reproduced by the model. A sufficiently thin (about 400 m thickness) and dense layer of the positive charge is noted near the 0 °C isotherm. A local maximum of the field just above this layer forms, which is observed in the balloon soundings.
Fig. 6. Vertical air velocity profile used in the numerical modeling. The air velocity zero point: 3.5 km.
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Fig. 7. Electric field dynamics (a) and electric field profile at t = 2000 s (b) in a case of inductive charging near 0 °C isotherm.
Fig. 8. Electric field, temperature and relative humidity versus altitude from the 0659 UTC balloon sounding in the stratiform region of the 8 May 1991 MCS (Marshall and Rust, 1993).
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The result is sensitive to f(z), because the change of its parameters changes the height where the charge separation occurs. N defines substantially the effectiveness of the charging, i.e. the growth rate of the field, while this parameter comes into the charging factor R together with the shedding frequency, so that the growth rate is determined actually by their multiplication. Some additional modeling (the results are presented in Fig. 9) shows that the fine structure of the electric field is determined by the mutual position of the zero point on the vertical air velocity profile and the point of the function f(z) maximum. Electric field profiles at t = 2000 s for the air velocity zero point 4 km and 3 km show that the dense layer of the positive charge near the 0 °C isotherm is much more intense in the second case. When the air velocity zero point is higher than the point of the function f(z) maximum 3.85 km, the sharp peak above the 0 °C isotherm disappears. This circumstance can be used for the model verification when comparing with the experimental data. Describing in detail the fine electrical structure near the 0 °C isotherm, Figs. 7 and 9 illustrate well the sensitivity of the developed model.
Fig. 9. Electric field profiles at t = 2000 s for different positions of the air velocity zero point: 4 km (a) and 3 km (b).
4. Discussion The developed model has a number of oversimplifications: 1D approach, a very restricted number of interacting components, rather simple parameterization of particle charging mechanisms and light ion attachment to the hydrometeors, a simplified representation of upper charged layers. At the same time, a number of factors potentially principal for field generation have been taken into account, namely: both non-inductive and inductive melting charging, light ions, a complicated profile of the vertical air velocity near the 0 °С isotherm, the boundary conditions proper for the horizontally extended systems in the global electric circuit. Noted simplifications allowed us to understand an importance of light ions and air flow profile, to compare the peculiarities of non-inductive and inductive melting charging, to reveal a range of parameters for charging effectiveness, to study the fine structure of the electric field determined by the mutual position of the zero point on the vertical air velocity profile and the point of the charging function maximum. We have distinguished, especially in the first runs and respective figures, such physical effects as the charged layer screening, the melting charging development in the close vicinity of the 0 °C isotherm, to make their operation more understandable. The results of our calculations of electric field profiles and their comparison with typical experimental profiles of the electric field demonstrate an agreement of model and measured electric structure; they testify in favor of inherent charging mechanisms operating in the stratiform region of mesoscale convective systems, supporting a respective viewpoint discussed by Marshall and Rust (1993), Rutledge and Petersen (1994), Stolzenburg et al. (1994), Shepherd et al. (1996). After the start of melting charging mechanisms the field magnitude grows reaching 30–100 kV/m in 300–2000 s (depending on the parameters of charge transfer and whether the inductive or noninductive mechanism dominates). An inductive melting mechanism seems to be more promising in terms of the electric structure explanation due to its clear physical sense and an obvious ability to reproduce an electric field shape and even its fine structure. Therefore, the modeling results support the arguments of Stolzenburg et al. (2007) and Stolzenburg and Marshall (2008) on the fitting of experimental data to the assumption on the inductive mechanism operation near the 0 °C isotherm. In our opinion, the main problem with the melting-charging mechanism in the consideration of the layers near the 0 °С isotherm is the absence of reliable microphysical data up to now. The role of ions seems important in the formation of the electric structure of the stratiform region. It is especially important near the 0 °C isotherm leading to the pronounced negative charge layer just above the dense positive layer formed by small particles shed from melting hydrometeors. We have accounted for ion mobility decrease in the cloud region; this effect has no good parameterization so far due to the lack of experimental data, but its scaling can be used for the search of actual values of ion mobility and charging function parameters on the basis of in situ measurements in the stratiform region.
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It is of interest that collisional non-inductive graupel-ice charge separation with respective charge sign reversal is not necessary for the support of intensive charge layers near the 0 °C isotherm if the advection from the convective region ensures the charge inflow into the upper charged layers. Along with that, the further development of the model should include the direct modeling of collisional charging in the stratiform region for a detailed comparison with the advection and melting mechanisms. In our opinion, it would be especially important for the treatment of more complicated profiles of the electric field often observed in the type A stratiform regions (Marshall and Rust, 1993). We have used in our calculations the boundary conditions proper for the horizontally extended systems in the global electric circuit, namely, we have assumed that the integral of electric field over the height from 0 to the upper boundary of the system at 20 km (so called the ionospheric potential) is a given constant determined by the state of the global circuit. It allowed us to calculate in a proper way the electric field near the ground except for the possible influence of corona effects in a strong enough electric field leading to respective conductivity and field perturbations. Note, that the stratiform region itself can contribute substantially (compared to the ordinary thunderstorm and electrified rainy clouds) into the ionospheric potential. This contribution cannot be calculated under framework of the 1D approach, but the charging currents calculated in our model (see Fig. 5) can be used in a generalized 2D or 3D consideration for the search of the ionospheric potential perturbation and electric energy of the stratiform region. 5. Conclusions A quantitative 1D model treating the formation of an intense charge layer near the 0 °C isotherm as a result of melting charging process is developed. In spite of obvious oversimplifications, a number of factors principal for field generation have been taken into account, namely: both noninductive and inductive melting charging, light ions, a complicated profile of the vertical air velocity near the 0 °C isotherm, the boundary conditions proper for the horizontally extended systems in the global electric circuit. It was found that both non-inductive and inductive melting mechanisms can contribute; the inductive mechanism is preferable, while the contribution of non-inductive mechanisms might be significant as well depending on particular conditions. After the start of melting charging mechanisms the field magnitude grows reaching 30–100 kV/m in 300–2000 s (depending on the type of mechanism and the parameters of charge transfer). The role of ionization in the formation of the positive charge layer near the 0 °C isotherm and negative charge layer above it may be important. It is interesting that the mutual position of the zero point on the vertical air velocity profile and the point of the function f (z) maximum determines the fine structure of the electric field in the vicinity of the 0 °C isotherm. Balloon measurements in MCS stratiforms made near the 0 °C isotherm seem to be in accord with the modeling results, while a detailed comparison of the developed model with experimental data is beyond the scope of this paper. Corona near the ground and non-inductive icegraupel charge transfer are the processes to be included in the model as the next step.
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Acknowledgments We thank T. Marshall and M. Stolzenburg for valuable discussions. This work was partially supported by the RFBR (Projects 07-02-1342 and 07-05-13584) and the Russian Academy of Science Program “Physics of the atmosphere: electric processes, radio-physical methods”. References Bateman, M.G., Rust, W.D., Smull, B.F., Marshall, T.C., 1995. Precipitation charge and size measurements in the stratiform region of two mesoscale convective systems. J. Geophys. Res. 100, 16,341–16,356. Bateman, M.G., Marshall, T.C., Stolzenburg, M., Rust, W.D., 1999. Precipitation charge and size measurements inside a New Mexico mountain thunderstorm. J. Geophys. Res. 104, 9643–9653. Canosa, E.F., List, R., 1993. Measurements of inductive charges during dropbreakup in horizontal electric fields. J. Geophys. Res. 98, 2619–2626. Colgate, S.A., Romero, J.M., 1970. Charge versus drop size in an electrified cloud. J. Geophys. Res. 75, 5873–5881. Dinger, J.E., Gann, R., 1946. Electrical effects associated with a change of state of water. Terr. Magn. Atmos. Electr. 51, 477–494. Drake, J.C., 1968. Electrification accompanying the melting the melting of ice particles. Quart. J. Roy. Meteor. Soc. 94, 176–191. Drake, J.C., Mason, B.J., 1966. The melting of small ice spheres and cones. Quart. J. Roy. Meteor. Soc. 92, 500–509. Evtushenko, A.A., Mareev, E.A., Marshall, T.C., Stolzenburg, M., 2007. On the generation and stability of charge layers in MCS stratiform regions. Proc. 13th Int. Conf. on Atmos. Electr., Beijing, Aug 2007, pp. 286–289. Hallett, J., Mossop, S.C., 1974. The production of secondary ice particles during the riming process. Nature 249, 26–28. Hallett, J., Saunders, C.P.R., 1979. Charge separation associated with secondary ice crystal production. JAS 36, 2230–2235. Harrison, R.G., Aplin, K.L., 2007. Atmos. Res. 79. doi:10.1016/j.atmosres.2006.12.006. Knight, C.A., 1979. Observations of the morphology of melting snow. J. Atmos. Sci. 36, 1123–1130. Krehbiel, P.R., 1986. The electrical structure of thunderstorms. The Earth's Electrical Environment. Studies in Geophysics. National Academic Press, pp. 90–113. Lang, T.J., Rutledge, S.A., Wiens, K.C., 2004. Origins of positive cloud-to-cloud lightning flashes in the stratiform region of a mesoscale convective system. Geophys. Res. Lett. 31, L10105. doi:10.1029/2004GL019823. MacGorman, D.R., Rust, W.D., 1998. The Electrical Nature of Storms. Oxford Univ. Press. 380 pp. Mansell, E.R., MacGorman, D.R., Ziegler, C.L., Straka, J.M., 2005. Charge structure and lightning sensitivity in a simulated multicell thunderstorm. J. Geophys. Res. D12101. doi:10.1029/2004JD005287. Mareev, E.A., Evtushenko, A.A., Yashunin, S.A., 2006. On the modeling of sprites and sprite-producing clouds in the global electric circuit. In: Fullekrug, M., Mareev, E., Rycroft, M. (Eds.), Sprites, Elves and Intense Lightning Discharges. NATO Science Series, vol. 225. Springer, pp. 313–340. Marshall, T.C., Rust, W.D., 1993. Two types of vertical electric structures in stratiform precipitation regions of mesoscale convective systems. Bul. Amer. Met. Soc. 74, 2159–2170. Marshall, T.C., Stolzenburg, M., 1998. Estimates of cloud charge densities in thunderstorms. J. Geophys. Res. 103, 19,769–19,775. Mo, Q., Detwiler, A.G., Hallet, J., Black, R., 2003. Horizontal structure of the electric field in the stratiform region of an Oklahoma mesoscale convective system. J. Geophys. Res. 108. doi:10.1029/2001JD001140 NO. D7. 4225. Muchnik, V.M., 1949. Study of drop electrification associated with breaking in electric field. Meteor. Hydrol. 4, 19–25 (in Russian). Rutledge, S.A., MacGorman, D.R., 1988. Cloud-to-ground lightning activity in the 10–11 June June 1985 mesoscale convective system observed during OK PRE-STORM. Mon. Weather. Rev. 116, 1393–1408. Rutledge, S.A., Petersen, W.A., 1994. Vertical radar reflectivity structure and cloud-to-ground lightning in the stratiform region of MCSs: further evidence for in-situ charging in the stratiform region. Mon. Weather. Rev. 122, 1760–1776. Rutledge, S.A., Lu, C., MacGorman, D.R., 1990. Positive cloud-to-ground lightning in mesoscale convective systems. J. Atmos. Sci. 47, 2085–2100. Rydock, J., Williams, E.R., 1991. Charge separation associated with frost growth. Quart. J. Roy. Meteor. Soc. 117, 409–420. Saunders, C.P.R., 2008. Charge separation mechanisms in clouds. Space Sci. Rev. 137, 335–353. doi:10.1007/s11214-008-9345-0. Schuur, T.J., Rutledge, S.A., 2000a. Electrification of stratiform regions in mesoscale convective systems. Part I: An observational comparison of symmetric and asymmetric MCSs. J. Atmos. Sci. 57, 1961–1982.
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Schuur, T.J., Rutledge, S.A., 2000b. Electrification of stratiform regions in mesoscale convective systems. Part II: Two-dimensional numerical model simulations of a symmetric MCS. J. Atmos. Sci. 57, 1983–2006. Shepherd, R.T., Rust, W.D., Marshall, T.C., 1996. Electric fields and charges near 0 °C in stratiform clouds. Mon. Weather. Rev. 124, 919–938. Simpson, G.C., 1909. On the electricity of rain and its origin in thunderstorms. Philos. Trans. Roy. Soc. London A209, 379–413. Stolzenburg, M., Marshall, T.C., 2008. Charge structure and dynamics in thunderstorms. Space Sci. Rev. 137, 355–372. doi:10.1007/s11214-008-9338-z. Stolzenburg, M., Marshall, T.C., Rust, W.D., Smull, B.F., 1994. Horizontal distribution of electrical and meteorological conditions across the stratiform region of a mesoscale convective system. Mon. Weather. Rev. 1228, 1777–1797. Stolzenburg, M., Marshall, T.C., Rust, W.D., 2001. Serial soundings of electric field through a mesoscale convective system. J. Geophys. Res. D106, 12371–12380.
Stolzenburg, M., Marshall, T.C., Rust, W.D., Mareev, E.A., Davydenko, S.S., 2007. The stratiform precipitation region of mesoscale convective systems: inductive charging evidence and global circuit effects. Proc. 13th Int. Conf. on Atmos. Electr., Beijing, Aug 2007, pp. 13–16. Williams, E.R., 1998. The positive charge reservoir for sprite-producing lightning. J. Atmos. Sol. Terr. Phys. 60, 689–692. Williams, E., Yair, Y., 2006. The microphysical and electrical properties of sprite-producing thunderstorms. In: Fullekrug, M., Mareev, E., Rycroft, M. (Eds.), Sprites, Elves and Intense Lightning Discharges. NATO Science Series, vol. 225. Springer, pp. 57–83. Willis, P.T., Heymsfield, A.J., 1989. Structure of the melting layer in mesoscale convective system stratiform precipitation. J. Atmos. Sci. 46, 2007–2024.
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Atmospheric Research j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a t m o s
On the generation of charge layers in MCS stratiform regions A.A. Evtushenko, E.A. Mareev ⁎ Institute of Applied Physics, Russian Academy of Sciences, 46 Ulyanov str., 603950 Nizhny Novgorod, Russian Federation
a r t i c l e
i n f o
Article history: Received 21 January 2008 Accepted 29 July 2008 Keywords: Electric field Charge density Thunderstorm electrification Mesoscale convective system Charge transfer mechanisms Modeling
a b s t r a c t We suggest a quantitative one-dimensional model treating the formation of charge layers near the 0 °C isotherm in stratiform regions of mesoscale convective systems. A number of factors principal for the field generation have been taken into account: both non-inductive and inductive melting charging, light ions, a complicated profile of the vertical air velocity near the 0 °С isotherm, the boundary conditions proper for the horizontally extended systems in the global electric circuit. Non-inductive collisional charging near the 0 °C isotherm was not considered. It was found that both non-inductive and inductive melting mechanisms can contribute; the inductive melting charging of ice aggregates was found more preferable, while the contribution of non-inductive mechanisms might be significant depending on particular conditions. The role of light ions in the formation of the positive charge layer near the 0 °C isotherm may be important. If the advection from the convective region ensures charge inflow to the upper charged layers, the melting charging mechanisms are able to explain an observable electric field structure in the whole stratiform region. It is important that the mutual position of the zero point on the vertical air velocity profile and the point of maximum melting-chargetransfer determines the fine structure of the electric field in the vicinity of the 0 °C isotherm. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Several observational studies have investigated the charge structure of mesoscale convective system (MCS) stratiform regions (e.g., Krehbiel, 1986; Rutledge and MacGorman, 1988; Rutledge et al., 1990; Marshall and Rust, 1993; Stolzenburg et al., 1994, 2001; Schuur and Rutledge, 2000a; Mo et al., 2003; Lang et al., 2004). It was found in particular that the stratiform region of a typical MCS of both A or B types has a number of horizontally extensive charge layers that exist for 6–12 h (Marshall and Rust, 1993; Stolzenburg et al., 1994, 2001). Taking into consideration the vertical shears in the stratiform flow field, the long transport distances, and the long time scales, it is surprising that the stratiform charge layers maintain their integrity (approximately similar charge density and vertical thickness across the stratiform region) and are not destroyed by turbulence. This fact suggests that local charging mechanisms might be at work to stabilize and/or enhance the charge layers advected from the convection ⁎ Corresponding author. Tel.: +7 8314 164792; fax: +7 8314 160616. E-mail address: [email protected] (E.A. Mareev). 0169-8095/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.atmosres.2008.07.010
region. Therefore, as a result of observational studies, two specific hypotheses have emerged: 1) advection of charge from the convective region, and 2) local charge generation within the stratiform region. Since a dominant aspect of the vertical electric structure of the stratiform region (or transition zone) of MCSs is a high-density charge layer at or near the 0 °C level, a problem of particle charging near the 0 °C isotherm is of key importance. It is the more so important that recent studies show that this layer can serve as a reservoir of the very big charge volume for intensive positive cloud-to-ground flashes closely correlated with the transient luminous effects in the middle atmosphere (e.g., Williams, 1998; Williams and Yair, 2006; Mareev et al., 2006). On the other hand, it is an extremely complicated problem due to different microphysical and thermodynamical processes occurring in this region and influencing the charge transfer (e.g., Knight, 1979; Willis and Heymsfield, 1989; Saunders, 2008). Possible mechanisms to explain the large electric field and substantial charges located in this region have been discussed by Marshall and Rust (1993), Rutledge and Petersen (1994), Stolzenburg et al. (1994), Shepherd et al. (1996), Schuur and Rutledge (2000b), Williams and Yair (2006). The recent
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studies emphasize the necessity to account for inherent mechanisms supporting the electrical structure of the stratiform region (Stolzenburg and Marshall, 2008). In particular, most of the data near the 0 °C isotherm were interpreted by Stolzenburg et al. (2007) to fit the inductive melting charging mechanism described by Simpson (1909). Previous work on MCS modeling (Rutledge and Petersen, 1994; Schuur and Rutledge, 2000a) indicated that both in situ charging and charge advection appear to be important contributors to the electrical budget of the stratiform region. But the quantitative and even qualitative understanding of the electrical processes in the stratiform region is far from complete. While charge densities produced by model simulations exhibit many similarities to observations, considerably less agreement was found when the simulated charge distribution was compared to the observed charge structure (Schuur and Rutledge, 2000a,b). Also, melting charging was found to be insignificant in the latter work which is not supported by the recent results of observational data analysis (Stolzenburg et al., 2007). A goal of this work is to suggest a simple 1D model allowing us to explain experimentally observed electric field profiles and to recognize the physical processes which should be taken into account considering the electric structure of the stratiform region. Our model develops a model initially suggested by Mareev et al. (2006). Note that 3D numerical models taking into account numerous fractions and different charging mechanisms in clouds (e.g., Mansell et al., 2005; Schuur and Rutledge, 2000b) represent a powerful tool for the study of thunderstorm electrification. But for lack of detailed information on the microphysical processes involved and due to the extreme complexity of the problem these models do not often allow clear understanding of the physical mechanisms playing dominant roles in particular cloud regions. The use of such comprehensive models is especially difficult when modeling the regions like the 0 °C isotherm where a lot of thermodynamic and electrodynamic processes operate simultaneously leading to the extremely complicated physical picture (Willis and Heymsfield, 1989). Our approach using a simplified representation of cloud components (a few components are considered, space charge densities are the analyzed variables), seems useful for the study of similar systems. We are restricted also by the development of a 1Dmodel because this approach is appropriate for stratiform regions of MCSs. 2. Theoretical model We use a quantitative model treating the formation of the charge layers near the 0 °C isotherm as a result of melting charging process. It is known (Willis and Heymsfield, 1989) that large aggregates with sizes from several hundred µm to several mm, and cloud droplets with sizes of order of 10 µm form near the zero degree isotherm. We assume that previously uncharged precipitation particles (large aggregates of vapor-grown crystals or smaller precipitation particles) acquire negative charge as they melt by shedding smaller, cloud-size particles (either liquid or solid) (Marshall and Rust, 1993; Stolzenburg et al., 1994). In accord with above notions, we have introduced in our model two types of hydrometeors named as “large” and
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“small” particles. The set of equations contains balance equations for the charge densities of several fractions and the Maxwell equation for the quasi-static electric field. In what follows we will present the results of rather simple modeling with the following set of equations: AρQ A VQ þ Vconv d ρQ þ ¼ −Rd f ðzÞ−γd ρQ d Aþ At Az Aρq Að Vq þ Vconv d ρq Þ þ ¼ Rd f ðzÞ þ γd ρq d A− At Az
ð1Þ ð2Þ
AAþ AðVþ d Aþ Þ þ ¼ IðzÞ þ κd Aþ d A− þ γd ρQ d Aþ At Az
ð3Þ
AA− AðV− d A− Þ þ ¼ −IðzÞ−κd Aþ dA− −γd ρq d A− At Az
ð4Þ
e0
AE ¼ ρq þ ρQ þ Aþ þ A− þ ρADD Az
ð5Þ
VF ðzÞ ¼ Vconv F μd E
ð6Þ
IðzÞ ¼ I0 d expðz=hÞ
ð7Þ
Here ρQ, VQ are the charge density and velocity of large (precipitation) particles; ρq, Vq are the space charge density and velocity of small (cloud) particles near the zero isotherm; A+, V+ and A−, V− are the charge densities and velocities of positive and negative (singly charged) ions respectively. The vertical coordinate z in the calculations varied from 0 km to 20 km. The grid step was equal 4 m. Zero point corresponded to the ground surface. The 0 °C isotherm was placed at 4 km above the ground which correspond to the conditions of typical experiments where the electric field near the 0 °C isotherm was analyzed with balloon soundings (Stolzenburg et al., 1994). ρADD is the additional (as compared to the charge generated near the 0 °C isotherm) charge density, which describes the upper charge layers generated either in the convective part of the MCS with the following advection into the stratiform region, or in the stratiform region itself. We have included it into the system “by hand” in the sense that its distribution was chosen specially to reproduce the typical experimental data on electric field profiles (Stolzenburg et al., 1994; Shepherd et al., 1996; Bateman et al., 1999). ρADD should be necessarily taken into account because of an important role of the upper layers in the formation of the whole field structure in the stratiform region and particularly near the zero isotherm, while the study of possible inherent charging mechanisms for these layers is out of the scope of the present study. The setting of ρADD is necessary also for a realistic set of boundary conditions determined by the total voltage U between the top and the bottom of the system and supported by the global circuit operation. Indeed, the electric field strength E determined by charge density distributions is a very important variable connecting all other variables of the set (1)–(7) through the Maxwell Eq. (5). In the modeling we assumed that the voltage U (i.e. the integral of electric field over the height from 0 to the upper boundary of the system at 20 km) was constant. In what follows, the calculations for U = 300 kV are presented. As was noted above, the electrical processes in the vicinity of the 0 °C isotherm are extremely complicated. Dinger and
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Gann (1946) proposed a non-inductive charge transfer process associated with melting. Drake and Mason (1966) noted that convection in a melting ice sphere produced negatively charged droplets ejected from bursting air bubbles at the surface. The sign of charge and the conditions under which the charges were separated were highly dependent on the impurities in the melting ice. Drake (1968) found that the melting particle (graupel) gained positive charge. But in the MCS bright band, the dominant particle habit is probably aggregates, not graupel, so the process of melting and break off of small particles is not likely to be the same as for graupel. Note that the production of very large aggregates is dramatic after the onset of melting (Willis and Heymsfield, 1989). We can speculate only how the melting aggregates might be gaining negative charge non-inductively. A natural assumption is that different water phases co-existing on the aggregates can lead to an electric potential between the falling aggregate and sublimating branches that break off (due to a thermoelectric effect in particular). Note that the Hallett–Mossop (1974) ice multiplication process can be involved as well. The process involves the accretion of supercooled water droplets by falling ice pellets, ice crystals or graupel. Hallett and Saunders (1979) investigated this multiplication process with a view to the possibility that the ejected ice fragments were electrically charged and so could contribute to thunderstorm electrification. They found that the growing ice pellet charged positively with a negative charge on an ejected ice fragment of order −10− 16 C. But when the vapor supply used to grow the cloud droplets was turned off, the charge sign reversed. An inductive particle-breakup charging is another candidate for the particle charging near the 0 °С isotherm. When the melting particle breaks, small fragments breaking off the upper side of the particle would be positively charged in the positive electric field (Simpson, 1909; Muchnik, 1946; Canosa and List, 1993). The same process can occur when ice fragments break off the evaporating aggregate (Rydock and Williams, 1991). The positive electric field necessary for this inductive mechanism to initiate and proceed it, can be set up by the charge layers above the level of the breakup (Stolzenburg et al., 1994). The basic signatures that fit the inductive melting charging mechanism are described by Stolzenburg et al. (2007). Overall, we should note that there is no reliable enough experimental data on the charging of melting hydrometeors allowing for rigorous quantitative analysis, and it emphasizes the importance of consideration of both non-inductive and inductive charging in numerical analysis of charge generation. To include the melting charging into account, we describe it by the non-dimensional function f (z) characterizing the effectiveness of this process depending on the height. We considered this function to have Gaussian shape with the maximum at a definite height zm. It is natural to assume that the charging occurs most effectively when the temperature is equal to 1–2 °C when a pronounced but sufficiently thin liquid layer forms on the hydrometeor surface. For the linear profile of temperature in the atmosphere with a lapse rate of 20 °C per 4 km, the level of +1 °C is situated about 200 m below the 0 °C isotherm. Correspondingly, it was assumed that the function f (z) has a maximum at zm = 3850 m and the width σ = 50 m. Note that melting depends on relative humidity at
temperatures close to 0 °C. Note also that a quasi-isothermal layer even deeper than 200 m is sometimes observed (e.g., Shepherd et al., 1996). The parameter R in Eqs. (1) and (2) depends on the mechanism of electrification near the zero isotherm. It was assumed Rnonind = Δq0 · ν · N for non-inductive mechanism and Rind = α · ν · N · E for the inductive mechanism respectively. For non-inductive charging the maximum value of the factor Δq0 · ν, determined by the separated electric charge and the frequency of small particle shedding, was taken as 1.6∙10− 14 C s− 1 in the calculations. Concerning the choice of this value, it should be noted that relatively little (compared to precipitation charges) is known about the charge carried on individual cloud particles inside thunderstorms and their rate of generation (Marshall and Stolzenburg, 1998). Colgate and Romero (1970) found individual charges of +0.2 to −0.4 fC on particles ranging from 5 to 15 μm in diameter. As to the frequency of small particle shedding ν, we did not find any estimation of this parameter in the literature. Our rough estimates give possible values from several units to several tens per second for ν. The number density of melting hydrometeors was equal N = 102–103 m− 3. The sign of the parameter Rnonind was taken as positive. We do not consider in our model the non-inductive collisional charging near the 0 °C isotherm. For the inductive mechanism, the factor α · ν characterized the effectiveness of charging due to polarization of melting particles in the electric field and was estimated as 4·10− 20 C mV− 1s− 1. In Eq. (7) I(z) is the rate of light ion production growing exponentially with characteristic height scale h = 6 km; at the msl it is equal to I0 = 107 m− 3 s− 1. The coefficient of recombination of positive and negative ions was taken as κ = 108 m3/C s. The coefficient of attachment of ions to cloud particles was taken as γ = 107 m3/C s (e.g., MacGorman and Rust, 1998). The velocities of larger components VQ and Vq do not depend on the electric field while the velocities of light ions were varied due to the influence of the electric field. The respective dependence V±(E) in Eq. (6) contains the mobility μ of light ions as the important parameter. A special attention in the calculations has been paid to the account of ions. The atmospheric ions collide with, and attach, to molecules to form small cluster ions, e.g. H+(H2O)n. To quantify this process, the humidity of the air is an important parameter. We are not aware of direct measurements of ion mobility in cloudy air; under laboratory conditions the measurements of ion mobility in saturated air are very scarce. Recent measurements by Harrison and Aplin (2007) gave evidence of some dependence of ion mobility on the water vapor content. We have taken into account in calculations a possible decrease of ion mobility in a cloud but without any rigorous parameterization. The velocity Vconv describes the vertical motion of air. It is known that the vertical velocity is not so big in the stratiform region—updrafts of several tens of cm/s are often observed (Stolzenburg et al., 1994). Respectively, in the first series of calculations we accepted Vconv = 0.5 m/s in the cloud decreasing smoothly to 0 above and below the cloud. This profile is a simplest representation of a slow updraft in a cloud region, smoothly decreasing at the top and beneath the cloud to
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connect it with the actual distribution in the framework of the 1D approach. The change of sign for the velocity is often observed also—the slow updraft is changed with slow downdraft in the vicinity of the 0 °С isotherm. To take it into account as well, in the second series of numerical experiments a more complicated dependence of Vconv(z) with the sign reversal (see Fig. 6 below) was taken. Compared to our previous model (Mareev et al., 2006), the present version includes the ion balance equations, so that the effects of ions are considered in detail in the present paper. Also the dependence Vconv(z) was not taken into account in the previous version. 3. Modeling results First of all, we analyze the dynamics of an initial electric field created by the upper charge layers situated above the 0 °C isotherm. The initial electric field is created by the charges designated as ρADD in Eq. (5). The charges are distributed following the Gaussian law in the height range from 7 to 10 km (positive charges) and from 5.2 to 7 km (negative charges) respectively. The maximum charge densities were taken as 4 × 10− 11 C/m3 and −6.5× 10− 11 C/m3 respectively so that the total integral from these charge densities was equal to zero. This ρADD charge distribution is supported during the run. The ion mobility is equal 10− 5 m2 V − 1s − 1. The first run illustrates just a hypothetical situation when the charging mechanisms near the 0 °C isotherm do not operate, and upper layers are screened by ions. The dynamics of screening is presented in Fig. 1. The process started at the time t = 0. It is seen on the figure how the upper layer is stabilized and at the same time the screening layer is formed. Clearly seen is the electric field maximum of about 60 kV/ m at the altitude between 5 and 10 km. However, this field is screened by the ion layers for about 300 s. The field magnitude in the maximum reaches a quasi-stationary value of about 25 kV/m, while at the ground surface the field is upward and equal to about 1 kV/m. The results of numerical analysis for the layers formed near the 0 °C isotherm due to the non-inductive charging are
presented in Figs. 2 and 3. The velocities of the precipitation and cloud particles in the interaction region (i.e. the region where the charging process occurs) were taken as VQ = −2 m/s and Vq = 0.5 m/s respectively. We are interested mostly in the large particle density in the region where charge transfer
Fig. 1. Electric field profile at the initial moment and the following field screening by light ions.
Fig. 3. The profiles of the electric field at the time 0, 1000, 2000 s for the noninductive charging with the ion mobility 2·10− 5 V m− 2 s− 1.
Fig. 2. Dynamics of electric field distribution for the non-inductive charging with the ion mobility 2·10− 5 m2 V − 1s − 1 (a) and with the mobility 10− 4 m2 V − 1s − 1 (b).
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Fig. 4. Electric field dynamics (a) and electric field profile at t = 2000 s (b) in a case of regular growth of the upper charge layer.
mechanisms are operating, i.e. in the altitude range of order of 300 m. Here the density N was assumed to be equal to 100 particles per cubic meter. The dynamics of electric field distribution for the noninductive charging is shown in Fig. 2 for two values of the ion mobility: 2·10− 5 V m− 2 s− 1 (a) and 10− 4 V m− 2 s− 1 (b). To represent the field dynamics in a more convenient way, for the first variant of the ion mobility the electric field profiles at the different time moments 0, 1000, and 2000 s are shown in Fig. 3. A narrow layer of the positive charge near the 0 °С isotherm and more extended negative charge layer below are clearly seen in Figs. 2 and 3. The formation of an additional layer of negative charge above the 0 °С isotherm is of a special interest. It forms due to the weak updraft which promotes the upward flow of ions; the latter are negative on average after the primary attachment of positive ions to negatively charged hydrometeors forming the distributed lower negative layer. It is seen from Fig. 2a and b that the shape of the electric field distribution is conserved in general with ion mobility change, but the field magnitudes are substantially different so
that approximately the field magnitude at the same time turns out to be inversely proportional to the ion mobility (5 times in this specific case). In other words, the main result of ion mobility decrease is the increase of time needed for the field development near the 0 °С isotherm. Respectively, the field reaches the same value if the rate of charging increases. It means in particular that the results obtained for the certain (e.g., reduced) ion mobility, can be further used with account for respective scaling in the source function R. It is convenient because the numerical scheme is more stable for the reduced ion mobility in high electric fields. The following step of the model development was the modeling of the field growth near the 0 °С isotherm in the presence of upper layers determined by the term ρADD. A linear growth of the charge density (2.5 times during 2000 s) has been assumed. The mobility of light ions was accepted 0.1 cm2/V·s. The results for electric field dynamics and electric field profile at t = 2000 s are presented in Fig. 4a and b. Along with the characteristic electric structure near the 0 °С isotherm observed on the previous figures, two additional layers between 5 and 9 km are seen also. During the first 600 s the maximum charge density near the 0 °С isotherm grows almost linearly followed by saturation at about 1200 s at a level of about 3 nC m− 3. Note that for the higher velocity of small particles, determined by the convective updraft, the saturation occurs at a lower level. As to the charge of a melting particle, it is growing almost linearly with time for about 600 s, it is then saturated at the level of 10− 10 C, which corresponds well to experimental data (Bateman et al., 1995). The electric current profiles generated by heavy (precipitation and cloud) particles and light ion particles at the time 2000 s are presented in Fig. 5. The contribution of ions is significant even in a case when their mobility is rather small. These calculations clearly illustrate how the electric currents in thunderstorm clouds may be calculated on the basis of microphysical consideration, which is necessary for the analysis of large-scale problems like the global circuit
Fig. 5. The profiles of different components of the electric current density at the time 2000 s. Dotted line—heavy particles, dashed line—ion convective current. Ion mobility is equal 10− 5 m2 V − 1s − 1.
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operation: they can be used for the search of the ionospheric potential perturbation and electric energy of the stratiform region while using a generalized 2D or 3D consideration for the stratiform region. One of the main goals of this study was the investigation of inductive mechanism effectiveness during charge separation near the 0 °C isotherm. Under the action of the electric field on the upper part of the particle the positive charge is formed while an equal negative charge is formed on the lower part of the particle. The dependence of Vconv(z) used in the modeling is shown in Fig. 6. The exponential increase of the mobility from the value 1 cm2/V·s typical for ground level was taken into account. It was assumed however that in the cloud the mobility decreases by 10 times (compared to its values determined by this exponential profile) with the transfer regions 2–3 km and 8–9 km for the bottom and top cloud boundaries respectively. The layer of the negative charge above the 0 °C isotherm distributed according to the Gauss law in the height range from 4.5 to 6 km has been taken into account by means of the term ρADD. The charge density at the center of the layer was growing linearly in time starting from 0 at the initial moment and reaching 5 × 10− 10 C/m3 up to 2000 s. It is assumed that these charges can be advected from the convective region into the stratiform region. The results of calculations are presented in Fig. 7. The noninductive mechanism does not operate in this case. It is obvious that this profile corresponds well to the type B MCS profiles. To demonstrate this fact, a typical example of such a profile, which was initially presented by Marshall and Rust (1993) and then discussed in detail by Stolzenburg et al. (1994), Shepherd et al. (1996), and Evtushenko et al. (2007), is shown in Fig. 8. The temperature zero point coincides in this case with the point of the electric field zero. The absolute magnitudes of the field maxima and even their relation are well reproduced by the model. A sufficiently thin (about 400 m thickness) and dense layer of the positive charge is noted near the 0 °C isotherm. A local maximum of the field just above this layer forms, which is observed in the balloon soundings.
Fig. 6. Vertical air velocity profile used in the numerical modeling. The air velocity zero point: 3.5 km.
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Fig. 7. Electric field dynamics (a) and electric field profile at t = 2000 s (b) in a case of inductive charging near 0 °C isotherm.
Fig. 8. Electric field, temperature and relative humidity versus altitude from the 0659 UTC balloon sounding in the stratiform region of the 8 May 1991 MCS (Marshall and Rust, 1993).
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The result is sensitive to f(z), because the change of its parameters changes the height where the charge separation occurs. N defines substantially the effectiveness of the charging, i.e. the growth rate of the field, while this parameter comes into the charging factor R together with the shedding frequency, so that the growth rate is determined actually by their multiplication. Some additional modeling (the results are presented in Fig. 9) shows that the fine structure of the electric field is determined by the mutual position of the zero point on the vertical air velocity profile and the point of the function f(z) maximum. Electric field profiles at t = 2000 s for the air velocity zero point 4 km and 3 km show that the dense layer of the positive charge near the 0 °C isotherm is much more intense in the second case. When the air velocity zero point is higher than the point of the function f(z) maximum 3.85 km, the sharp peak above the 0 °C isotherm disappears. This circumstance can be used for the model verification when comparing with the experimental data. Describing in detail the fine electrical structure near the 0 °C isotherm, Figs. 7 and 9 illustrate well the sensitivity of the developed model.
Fig. 9. Electric field profiles at t = 2000 s for different positions of the air velocity zero point: 4 km (a) and 3 km (b).
4. Discussion The developed model has a number of oversimplifications: 1D approach, a very restricted number of interacting components, rather simple parameterization of particle charging mechanisms and light ion attachment to the hydrometeors, a simplified representation of upper charged layers. At the same time, a number of factors potentially principal for field generation have been taken into account, namely: both non-inductive and inductive melting charging, light ions, a complicated profile of the vertical air velocity near the 0 °С isotherm, the boundary conditions proper for the horizontally extended systems in the global electric circuit. Noted simplifications allowed us to understand an importance of light ions and air flow profile, to compare the peculiarities of non-inductive and inductive melting charging, to reveal a range of parameters for charging effectiveness, to study the fine structure of the electric field determined by the mutual position of the zero point on the vertical air velocity profile and the point of the charging function maximum. We have distinguished, especially in the first runs and respective figures, such physical effects as the charged layer screening, the melting charging development in the close vicinity of the 0 °C isotherm, to make their operation more understandable. The results of our calculations of electric field profiles and their comparison with typical experimental profiles of the electric field demonstrate an agreement of model and measured electric structure; they testify in favor of inherent charging mechanisms operating in the stratiform region of mesoscale convective systems, supporting a respective viewpoint discussed by Marshall and Rust (1993), Rutledge and Petersen (1994), Stolzenburg et al. (1994), Shepherd et al. (1996). After the start of melting charging mechanisms the field magnitude grows reaching 30–100 kV/m in 300–2000 s (depending on the parameters of charge transfer and whether the inductive or noninductive mechanism dominates). An inductive melting mechanism seems to be more promising in terms of the electric structure explanation due to its clear physical sense and an obvious ability to reproduce an electric field shape and even its fine structure. Therefore, the modeling results support the arguments of Stolzenburg et al. (2007) and Stolzenburg and Marshall (2008) on the fitting of experimental data to the assumption on the inductive mechanism operation near the 0 °C isotherm. In our opinion, the main problem with the melting-charging mechanism in the consideration of the layers near the 0 °С isotherm is the absence of reliable microphysical data up to now. The role of ions seems important in the formation of the electric structure of the stratiform region. It is especially important near the 0 °C isotherm leading to the pronounced negative charge layer just above the dense positive layer formed by small particles shed from melting hydrometeors. We have accounted for ion mobility decrease in the cloud region; this effect has no good parameterization so far due to the lack of experimental data, but its scaling can be used for the search of actual values of ion mobility and charging function parameters on the basis of in situ measurements in the stratiform region.
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It is of interest that collisional non-inductive graupel-ice charge separation with respective charge sign reversal is not necessary for the support of intensive charge layers near the 0 °C isotherm if the advection from the convective region ensures the charge inflow into the upper charged layers. Along with that, the further development of the model should include the direct modeling of collisional charging in the stratiform region for a detailed comparison with the advection and melting mechanisms. In our opinion, it would be especially important for the treatment of more complicated profiles of the electric field often observed in the type A stratiform regions (Marshall and Rust, 1993). We have used in our calculations the boundary conditions proper for the horizontally extended systems in the global electric circuit, namely, we have assumed that the integral of electric field over the height from 0 to the upper boundary of the system at 20 km (so called the ionospheric potential) is a given constant determined by the state of the global circuit. It allowed us to calculate in a proper way the electric field near the ground except for the possible influence of corona effects in a strong enough electric field leading to respective conductivity and field perturbations. Note, that the stratiform region itself can contribute substantially (compared to the ordinary thunderstorm and electrified rainy clouds) into the ionospheric potential. This contribution cannot be calculated under framework of the 1D approach, but the charging currents calculated in our model (see Fig. 5) can be used in a generalized 2D or 3D consideration for the search of the ionospheric potential perturbation and electric energy of the stratiform region. 5. Conclusions A quantitative 1D model treating the formation of an intense charge layer near the 0 °C isotherm as a result of melting charging process is developed. In spite of obvious oversimplifications, a number of factors principal for field generation have been taken into account, namely: both noninductive and inductive melting charging, light ions, a complicated profile of the vertical air velocity near the 0 °C isotherm, the boundary conditions proper for the horizontally extended systems in the global electric circuit. It was found that both non-inductive and inductive melting mechanisms can contribute; the inductive mechanism is preferable, while the contribution of non-inductive mechanisms might be significant as well depending on particular conditions. After the start of melting charging mechanisms the field magnitude grows reaching 30–100 kV/m in 300–2000 s (depending on the type of mechanism and the parameters of charge transfer). The role of ionization in the formation of the positive charge layer near the 0 °C isotherm and negative charge layer above it may be important. It is interesting that the mutual position of the zero point on the vertical air velocity profile and the point of the function f (z) maximum determines the fine structure of the electric field in the vicinity of the 0 °C isotherm. Balloon measurements in MCS stratiforms made near the 0 °C isotherm seem to be in accord with the modeling results, while a detailed comparison of the developed model with experimental data is beyond the scope of this paper. Corona near the ground and non-inductive icegraupel charge transfer are the processes to be included in the model as the next step.
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