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t Charging Mechanisms in Clouds anc! Thunderstorms 9 INTRODUCTION KENNETH V. K. BEARD . University of Illinois at Urbana-Champaigrz HARRY T. OCHS Illinois State Water Survey Since the time of Benjamin Franklin, a major diffi- culty in identifying the causes of cloud electricity has been our inability to obtain adequate measurements within clouds. This observational problem is now being remedied by modern electronics and instrumented air- craft. More quantitative theories of charging have be- come available since the 1940s along with our improved understanding of the atmosphere. In addition, better laboratory simulations of cloud physics in recent dec- ades have led to improved measurements of microscale charge separation. With all these advances we should not be surprised to find that the number of possible charging mechanisms has proliferated. Thus, a modern task has been to sort through the possible mechanisms in trying to identify their relative contribution to cloud electrification (Mason, 1972; Latham, 1981; Taka- hashi, 1982~. A major purpose of this chapter is to de- scribe the mechanisms that charge cloud and precipita- tion particles. We also evaluate their relative role in cloud-scale electrification and assess our state of knowl- edge. A broader evaluation of cloud electrification is found in Chapter 10 of this volume. There are two major categories of charging mecha- nisms: the microscale separators, which ultimately lead to charged cloud and precipitation particles, and the ~4 cloud-scale separators, which can result in field intensi- fication and lightning. The first category includes the creation of ion pairs in the air and charge separation on individual cloud and precipitation particles. These mechanisms are coupled with other microscale separa- tors to produce net charges on cloud and precipitation particles, for example the attachment of ions by diffu- sion to cloud drops and the charging that results from particle collisions. Once the cloud and precipitation particles become appreciably charged, a larger scale separator such as differential sedimentation is needed to create electrification on the cloud scale. Convection can also act as a cloud-scale separator by redistributing ions and particles. Much of the emphasis in this chapter will be on describing the microscale separators that produce the charged cloud and precipitation particles. In discussing the charging mechanisms we consider the electrification of convective clouds. These clouds can produce spectacular displays of lightning and are the most important cloud link in the global electric cir- cuit. We start the discussion of charge separation in the simple environment of a small cumulus cloud. This non- precipitating cloud stage is followed by sections on the rain stage and hail stage. An abbreviated discussion of the charging mechanisms associated with these three stages is found in the evaluation section of this chapter.
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CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS CLOUD STAGE As the first clouds form on a warm summer afternoon, the environment is already set for cloud electrification. The air is filled with ions whose concentrations and mo- bilities determine the effective conductivity of the atmo- sphere. In many practical situations the air is an electric insulator, but the conductivity is large enough to permit a relaxation time of less than 7 minutes for discharging the lower atmosphere (Israel, 1971~. The discharge cur- rent results from the drift of small ions with the mass of a few molecules. Charge separation begins immediately when a field is applied to a mixture of positive and nega- tive ions. Within a cloud the usual result of ion motion is capture by water droplets. The electric background in which the cloud forms contains vertical gradients in ion concentration with a negative charge at the Earth's surface that is maintained by thunderstorms. The electric field above the ground is reduced by a screening layer of positive ions attracted by the Earth. Positive ions from aloft accumulate near the ground because the field-induced drift is reduced by col- lisions as the density of the air increases. Capture of ions by aerosols greatly reduces the drift velocity and, during times of heavy pollution, 500 V/m have been measured between the positive space charge and the ground. A field of 130 V/m is more typical of a summer day with a well-mixed boundary layer. This is reduced by about 1 order of magnitude at a 3 km height. Thus, a fresh cu- mulus cloud forms in an environment of vertical gradi- ents in space-charge density, electric field, ion concen- tration, and conductivity (see Figure 9.1~. The field is oriented toward negative earth with a strong increase in positive space charge below 1 km and a small ion con- centration and conductivity that increase with height. In this electric environment there are several ion cap- ture mechanisms that lead to charged droplets in shal- low cumulus clouds. In the following discussion, micro- scale charge separation is described for diffusion charging, drift charging, and selective ion charging. The cloud-scale separation of charge for these nonpre- cipitation clouds is discussed below under drift charg- ing. Diffusion Charging For the early stage of cloud charging we consider the collection of ions by cloud droplets. The ion-transport equation on the microscale near a cloud droplet gives the charge flux (C/m2 see) or the current density for an ion component as Hi = piU + PiBiE - DiVpi, (9.1) ~5 SPACE CHARGE DENSITY (p), CONDUCTIVITY (A), pC m ~3 pC v-1 s~1 m~1 0.01 0.02 0.05 0.1 0.2 0.5 1 2 5 7 1 1 1 1 / /1 1 I I 3 o q l 11 / ~ 1 2 5 10 20 50 100 200 500 SMALL ION CONCENTRATION (n), ELECTRIC FIELD (E), per 0.01 cm3 V m~1 FIGURE 9.1 Average electric properties of the lower atmosphere during fair weather. The variation of the electric field with height is due to Gish (e. g., see Pruppacher and Klett, 1978~. The space charge density is a direct result of Gauss's law, whereas the conductivity is obtained by assuming a constant current (2. 7.pC m ~ ~ see ~ Id. The con- centration of small ions is proportional to the conductivity and varies inversely with the ion mobility. where Pi is the ion-charge density (C/m3) of a particular species, U is the air velocity, Bi is the ion mobility (about 2 x 10 ~ 4 m2/V see for small ions in the lowest few kilo- meters), E is the electric field, and Di is the molecular diffusivity (m2/sec). The flux term for the microscale airflow (piU) is relatively weak because of the low fall speed for cloud droplets. In addition the field is small enough in the cloud stage to ignore the ion drift term (piBiE). Thus the charging of small cloud droplets is found by evaluation of the standard diffusion equation. An important consequence of diffusion charging is a reduction of ion concentration within the cloud by sev- eral orders of magnitude. The time constant for deple- tion can be obtained from the solution to the diffusion equation for a steady-state attachment of ions to a cloud of similar size droplets. The solution is Pi = Pie expel - 4 7rRDiNt), (9. 2) where R is the droplet radius and N is their concentra- tion. For a typical size and concentration in the cloud
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116 stage (10 ,um, 100 cm-3), the depletion time constant, t = (4,rRDiN) ~ i, is 10 sec. Thus equilibrium is achieved rapidly, and the local concentration in clouds can be approximated by a steady-state balance between pro- duction by cosmic rays and depletion by recombination and attachment to cloud droplets (Chiu and Klett, 1976). The amount of charge on a cloud droplet from kinetic theory is a Gaussian-like (Boltzmann) distribution cen- tered on zero charge for equal concentration of positive and negative ions. As is evident by the positive space charge near the ground, the ion mixture is not always neutral. In such cases a net charge is collected by drop- lets. For the zero-centered distribution the rms Boltz- mann charge can provide an estimate for the magnitude attained in diffusion charging: Q = (8 7re0RkT)~/2, (9.3) where c0 is the permittivity of air (8.85 x 10- 12 F/m), k is the Boltzmann constant (1.38 x 10-23 ]/K), and T is the temperature (Gunn, 1957~. This equation can be in- terpreted as a balance between the stored electric energy on the droplet (1/2 Q214,re0R) and the thermal motion energy of the ions (kT). When the Boltzmann charge is evaluated for a typical droplet size in the cloud stage (R = 10 ,um), the rms charge in number of electrons is ne = 6Ri'2 (,um) = 19. This result is consistent with the spread in droplet charge measured for nonconnective clouds with low electric fields (Gunn, 1957~. Drift Charging Larger-scale transport of ions is characterized by cur- rents from bulk and eddy transport of ions along with the field-driven drift. The charge-flux equation is the larger-scale version of Eq. (9.1) Ji = piU + piBiE - KVpi, (9.4) where K is the eddy diffusivity (m2/sec). If we consider just the drift of ions in the ambient field we find that the vertical drift current (piBiE) at cloud top and cloud base must result in an accumulation of positive and negative space charge, respectively (Figure 9.2~. An electric bal- ance is achieved fairly rapidly as a screening layer forms with the capture of incoming ions by cloud droplets. The field within the cloud is increased by the charge that accumulates at the boundary. The amount of charge on droplets in this region can be estimated by considering diffusion capture by ions of only one sign. The maximum charge captured is found from the amount needed to neutralize the induced KENNETH V. K. BEARD and HARRY T. OCHS a b c 1J+ J / :: ii ~////////// FIGURE 9.2 Electrification of a model cumulus cloud (after Chin and Klett, 1976): a, vertical drift currents reflecting the ion deficits with the cloud; b, resultant charge accumulation and field enhance- ment from ion drift; c, effect of convective transport on charges and field. charge (of opposite sign) from polarization in the elec- tric field: Q= 127re0R2E. (9.5) The capture of ions from the drift current during the cloud stage, for example at cloud base (Figure 9.2b), results in ne = 0.002 R2 (,um) E (Vim) = 20 for R = 10 ,um and E = 100 V/m. This charge is comparable with the Boltzmann charge given by Eq. (9.3). However charge generation from drift into cloud edges increases with R2 in contrast to the dependence of Eq. (9.3). Thus charges of several hundred electrons are readily attained for somewhat larger cloud droplets by diffusion of ions of one sign to polarized drops. Somewhat later in this section we shall find out that the size and field depen- dence given by Eq. (9.5) also applies within clouds for ion capture by polarized drops and for the breakup of these drops. In addition, for the cloud stage we must also consider the role of the bulk and eddy transport terms in Eq. (9.4). For diffusion charging and the simple convective pattern, illustrated in Figure 9.2c, convection trans- ports negative charge upward within the core and car- ries positive charge downward along the edges (Chiu and Klett, 1976). The effect of eddy diffusion in this sim- ple model is to smooth the charge distribution produced by the bulk transport and ion drift. When all three terms in Eq. (9.4) are included, the field is enhanced within the cloud but is not so strong as the pure drift case. For this early stage of cloud electrification, drift charging of droplets with negative charge at cloud base and positive charge at cloud top is apparently the domi- nant mechanism. The current into cloud base from drift
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CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS is p B E, and the current from convection is U. where p = p + - p is the space charge. (The value of p is ap- proximately one half the small ion concentration, be- neath cloud base, times a unit charge.) The ratio of drift to convection is 7.5 (using the values for p, n, and E on Figure 9. 1 at 1 km and B = 2.2 x 10 - 4 m2/V see and U = 1 m/see) clearly showing the dominance in the drift of negative ions into cloud base over the upward convec- tion of positive space charge. The ratio decreases as the cloud base is lowered and is less than unity for bases be- low about 300 m. The calculations of Chiu and Klett for a cloud base at 10 m show the dominance of convective transport of positive space charge over drift into cloud base. They found a positive core, but drift still domi- nated the charging process in the upper cloud with posi- tive charges at cloud edges similar to Figure 9.2c. Thus, for the majority of cases in the cloud stage, drift charg- ing is the most significant electrification mechanism. Convection and eddy diffusion in the single-cell pattern investigated by Chin and Klett generally weaken elec- trification by redistributing and mixing the drift-gener- ated charge . The charge acquired by droplets in the cloud stage has been from diffusion of ions within the cloud and drift charge at cloud edge. Selective Ion Charging When equal numbers of positive and negative ions are present there can be a preferred attachment of one sign if the droplet is polarized (Wilson effect). The governing equation for the microscale transport t given by Eq. (9.1~] has two classes of solutions (Whipple and Chalmers, 1944~. In the case of "fast ions" the down- ward drift of positive ions exceeds the fall speed of the droplet (B + E > V) and ions of both signs are captured at nearly the same rate (Figure 9.3a). The droplet size where B + E = U in the lowest few kilometers is R = 1 ,um for E = 10 V/m. Since most droplets in shallow cu- mulus clouds are larger than 4 ,um, ions are captured selectively by the Wilson effect. Larger droplets will ac- quire a negative charge by the preferential attraction of negative ions, as shown in Figure 9. 3b for the "slow ion" case (B + E < U). The maximum charge acquired by droplets for the Wilson effect is Q = 2 7re0R2E . (9. 6) This is only one sixth the diffusion charge from the drift current given by Eq. (9.5) and yields a negative charge equivalent to 36 electrons for the largest cloud droplets (R = 100 ,um) and a downward directed field of 10 V/m. ~7 a U t B_E b 1i ~ ll E ~ \, 7 ~ t t |B+E I '~ - I '\' \\~' FIGURE 9.3 Selective ion capture from droplet polarization in a downward-directed field (Wilson effect): a, fast-ion case B+E > By; b, slow-ion case (B. + E < ~ with trajectories Even by dashed curve. Thus the largest cloud droplets are charged for the Wil- son effect to a magnitude of about the rms Boltzmann charge. In our cumulus scenario the cloud is only about 1 km deep with a central updraft speed of 1 to 2 m/see; there- fore the small drops that we are considering are carried upward. When the cloud depth increases to about 3 km, drops become large enough to be detected by radar. This is a common circumstance for summer cumulus clouds in mid-latitudes. The cloud top would lie below the level where droplets readily freeze except over ele- vated terrain or in a more northern climate. The drops associated with the initial radar echo are still quite small and unable to fall out of the cloud. However, we con- sider the time of the first radar echo as the beginning of the rain stage. In the following section we examine the charging mechanisms associated with drizzle drops and raindrops: selective ion charging, breakup charging, and induction charging. RAIN STAGE Selective Ion Charging When we make the transition to the new stage, micro- scale separation of charge becomes more powerful be- cause of the Ret dependence of charge captured by polar- ized drops tEqs. (9.5) and (9.644. As the drizzle drops begin moving downward in the cloud a larger scale sep- aration of charge can result as drizzle drops capture neg
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118 alive ions (Wilson effectJ and the excess positive ions be- come attached to cloud droplets. The enhanced electric field within the cloud would provide a positive feedback to the Wilson effect by increasing the polarization on the drops. If the field should reach about 10 kV/m the ion drift velocity would increase to a few meters per second. This is the situation where the velocity of positive ions is about the same as the fall speed of small raindrops. Con- sequently generation by selective ion charging and the simple feedback mechanism for the Wilson effect is lim- ited. iThe same limit does not apply to diffusion charg- ing at cloud edges, Eq. (9.5~. In the rain stage, microscale separation of charge from ion capture continues while new mechanisms make their appearance. The role of convection remains central to cloud development as well as the motion of charged droplets within the updraft. Transport and drift are important factors in ion movement within the cloud and to droplets at the boundaries. The Wilson ef- fect appears to be responsible for some of the field en- hancement but must be considered along with the addi- tional mechanisms of breakup charging and induction charging. Breakup Charging The collisions between drizzle (R = 100-1000 ,um) and cloud droplets (R = 10-100 Am) usually result in coalescence growth and the production of rain. In con- trast the collisions between raindrops (R = 1-6 mm) and drizzle often result in only transient coalescence fol- lowed by fragmentation. Such events can result in charged drops in the presence of an electric field. The polarization charge of one sign on a spherical drop is Q = 3 7reoR2E. (9. 7) This equation gives the net positive or negative charge that can be separated by "slicing" a polarized drop in half. To apply Eq. (9.7) to the rain stage, consideration of some details of drop collisions and the role of the elec- tric field follows. Four general kinds of breakup phenomena are illus- trated in Figure 9.4 (neck, sheet, disk, and bag) based on the laboratory study of McTaggart-Cowan and List (1975~. The amount of charge separated in bag breakup is given approximately by Eq. (9.7) (Matthews and Ma- son, 1964), but the charge has not been determined for the other cases shown in Figure 9.4. The most frequent kinds of breakup result after a vertical elongation of the coalesced drop pair followed by a neck or sheet that tears into numerous droplets. This is not the ideal "slic- ing" required for Eq. (9.7~. For example, an elongation increases the polarization charge by a factor of 4 if the KENNETH V. K. BEARD and HARRY T. OCHS a b NECK SHEET (27%) (55%) o 0 0 o o c d DISK BAG ( 18%) (< 1/2%) O ~ . O O . O to . · . . · - . - · . ... . . :. ~ : .' .: · . . . .. - . . .e ~ .0 .. .o: .e O o O 00 0~. 0 ~ · 0 0 ~ FIGURE 9.4 The four observed breakup types with percentages of occurrence: a, neck; b, sheet (two views taken perpendicular to each other); c, disk; d, bag (from McTaggart-Cowan and List, 1975). distorted drop is modeled as a prolate spheroid with a major axis of 5 times the spherical diameter. Thus Eq. (9.7) gives a rather conservative estimate of the micro- scale charge separation in breakup. An important feature of breakup collisions is that they occur slowly compared with the charge-relaxation time (i.e., the time required to redistribute the charge). The breakup time is given roughly by the raindrop diameter divided by the velocity difference between the colliding drops (about 0.5 msec). In contrast, the charge relaxa- tion time for pure water is about 100 times faster and for rainwater with impurities, 104 to 106 times faster. Thus, the distribution of polarization charge on a distorting raindrop is in approximate equilibrium with the electric field. In breakup charging, the electric field separates charge on individual drops by polarization, breakup separates charge between colliding drops, and gravity separates charge on a large scale. The sheet breakup shown in Figure 9.4b, with a downward directed field, will result in a positive charge on the large fragment (R > 1 mm) given approximately by Eq. (9.7) and a nega- tive charge of the same magnitude distributed over the small fragments (R ~ 100 ,um). The difference in fall speed between these sizes (6 to 10 m/see) gives the cloud- scale separation rate. Although breakup charging contains the microscale and cloud-scale mechanisms of charge separation neces- sary for cloud electrification, it does not reinforce the existing field. However, it may contribute significantly to drop charging found in both the rain and hail stages.
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CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS Induction Charging In addition to coalescence and breakup, the collision between drops can result in interactions where the two drops bounce apart. The amount of charge transferred between drops that are polarized depends on the contact angle relative to the field, the contact time, the charge relaxation time, and the net charge on the drops as well as the magnitude of the polarization. Induction charg- ing was first considered by Elster and Geitel (see Chalmers, 1967) for contact between a large and small sphere along a line parallel to the field. Later studies included the effects of image charges, contact angle, and net charge with extensions of theory to ice particles. In the rain stage we will consider only induction charg- ing for drops while reserving the ice aspects of this mech- anism for the had! stage. The importance of contact angle is immediately obvi- ous from the induced surface charge on a conducting sphere in a uniform electric field given by 3,rcoE cos ~ and shown schematically on Figure 9.5a. However, the contact angle is a hydrodynamic problem of two defor- mable bodies in a gaseous medium with its own set of governing parameters. Even in the absence of electric effects, such interactions are understood only in terms of broad categories in a manner similar to the breakup phenomena. For example, contact angles of 50-90° are associated with bouncing drops, and angles of 60-80° with partial coalescence. These phenomena occur over sizes intermediate to the ranges for coalescence and breakup. Laboratory experiments indicate bouncing between large and small drizzle drops and partial coa- lescence between drizzle and large cloud drops. We will emphasize the charge transfer between dissimilar sizes, as the above ranges suggest. Interactions between simi a _> E b E - . 1 +/ FIGURE 9.5 Charge transfer by the induction mechanism for collid- ing drops in a downward-directed field: a, charge distribution on a polarized drop; b, contact at moderate angle; c, charge generation after separation. 119 tar size drops are relatively unimportant because their similar fall speeds lead to infrequent collisions. The maximum charge on a large drop (R) acquired by collision with a small drop (r) for dissimilar sizes is given approximately by Q = 12 cos ~ 7re0r2E. (9.8) If we assign an average contact angle of 70 (whereby 12 cos ~ = 4), the result is similar to Eqs. (9.6) and (9.7) except for the scaling by r2 instead of R2. It should be obvious from the r2 dependency that the induction mechanism is not a powerful means of direct charge sep aration. However, as Figure 9.5 demonstrates, the mi croscale charge separation followed by differential sedi mentation reinforces the existing field. Therefore the induction mechanism may be capable of significant charge separation on the cloud scale through positive feedback to Eq. (9.8~. There are several possible limitations on induction charging between drops. First, charge transfer must oc cur on a time scale compatible with contact. When we consider the interaction between drizzle drops and large cloud droplets, appropriate for partial coalescence or bouncing, the contact time ranges from 1 to 50 ,usec. This is several orders of magnitude longer than the charge-relaxation time for cloud and rain water. There fore the contact time is not a limitation for charge trans fer between drops. A second possible limitation occurs because an elec tric field can transform partial coalescence (or bounce) into complete coalescence. This effect has not been stud ied in detail; however, laboratory simulations of induc tion charging (Jennings, 1975) showed that the separa tion probability is reduced by an order of magnitude when the field is increased from 10 kV/m to 30 kV/m. Other studies with charged drops of similar sizes show suppression of bounce at charges comparable with those induced by the above fields. Hence, there is evidence suggesting a limit on induction charging but at fields well above those found in the rain stage (typically less ,2~, than 1 kV/m). JO A third possible limitation, one that applies to bounc ,' ing drops but not to partial coalescence, is that charge transfer must occur across an air gap. Transfer mecha nisms such as field emission or corona, in a small air gap, usually require very high fields (greater than 107 V/m). Since the field between drizzle drops is enhanced by in duced charges by a factor of only about 50 to 500, thun derstorm fields appear to be required for charge transfer across the air gap between bouncing drops. However, neither charge transfer between bouncing drops nor the limitation of field-induced coalescence have been ade quately investigated.
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120 Drop charging occurs in the rain stage from drift charging at cloud edges and selective ion capture within the cloud. The latter mechanism enhances the electric field by gravitational separation of negatively charged precipitation drops and positively charged cloud drop- lets. In addition, breakup charging of colliding drops may result in significant charges on raindrops and driz- zle drops. Since fields are weak in the clouds we have considered, induction charging is ineffective. However, under the special circumstance of deep (warm) convec- tion, as discussed in the evaluation of charging mecha- nisms, induction may lead to higher fields through a positive feedback. As the cloud top rises above the freezing level the newly formed cloud droplets, as well as drizzle drops carried in the updraft, remain in the liquid state. Soon some of the larger drops freeze until, at about the - 15°C level, the cloud top takes on a fuzzy outline indi- cating a substantial number of ice particles. Such a gla- ciated cloud usually undergoes a growth spurt from the release of latent heat. If the air above is not too warm, convection may continue up to the base of the strato- sphere, resulting in an intense thunderstorm. Typically on a day that has isolated thunderstorms, the first cumulus clouds in the early afternoon reach only the cloud stage. Somewhat later cloud tops are higher and reach the rain stage. It is often not until mid- dle afternoon that cloud tops are high enough to glaci- ate. This is the onset of the hail stage, since what follows is the beginning of hail-like precipitation as droplets col- lide and freeze onto larger ice particles. HAIL STAGE The glaciated portion of the cloud contains ice crys- tals in a saturated vapor environment maintained by the presence of more numerous cloud droplets. Since the saturation vapor pressure for ice is less than water, the ice crystals grow rapidly by vapor diffusion. As the ice crystals grow larger than about lOO ,um, they begin to collect cloud droplets. This riming process continues within the upper portion of the cloud until the particles are transformed into soft hail (also termed "snow pel- lets" or "graupel"~. These ice particles are not nearly so dense or large as typical hailstones. When the size and liquid water concentration are large enough, the accre- tion of water occurs too rapidly for immediate freezing. Water will then infiltrate the rime structure and in- crease the particle mass, fall speed, and growth rate. In a strong updraft the water in soft hail may refreeze higher in the cloud, resulting in ice pellets (i.e., small hailstones). Further growth by riming may be followed by a descent to a region where wet growth can again KENNETH V. K. BEARD and HARRY T. OCHS occur. A cycle of wet and dry growth may be repeated several times to produce the multiple layering found in larger hailstones (see also Chapter 7, this volume). The above description for the growth of soft hail and hailstones indicates the complexity of particle interac- tions in the hail stage. Although the growth of ice pre- cipitation is governed by the collection of cloud drop- lets, the charging of ice precipitation appears to be linked to collision with smaller ice particles (Gaskell and Illingworth, 1980; Latham, 1981; Jayaratne et al., 1983~. Therefore, we will consider the separation of charge for collisions of precipitation, such as soft hail and hailstones, with frozen drops and ice particles. First, the induction charging discussed for the rain stage will be extended to drops and ice particles rebounding from ice precipitation with dry or wet surfaces. Then we discuss thermoelectric charging and interface charging. Induction Charging The concept of induction described for the rain stage can be applied in the hail stage after considering a few alterations. Of primary importance is the charge relaxa- tion time for ice that is a factor of 1000 slower than for liquid water. Theoretical estimates by Gaskell (1981) for charge transfer between a 100-,um ice sphere and a much larger one, including the effect of a surface con- ductivity, yield a relaxation time constant of ~ = 100 ,usec, which is much longer than an estimated contact time of less than 1 ,usec. Since-the amount of charge transferred during contact is proportional to 1 - e- tie, an ice sphere charges at less than one hundredth the rate of a comparable water drop. This would increase the induction-charging time from a few minutes for drizzle drops to several hours for ice pellets. However, induc- tion charging of wet hail would proceed to the maxi- mum amount in Eq. (9.8) about as rapidly as in the wa- ter-drop interactions. Another aspect of induction charging is the effective contact angle found from the average over the range of bouncing interactions. In the rain stage the average is about 70° for collisions between large and small drizzle drops. Experimental measurements of charge separa- tion for larger precipitation particles (both water drops and ice spheres) colliding with cloud droplets indicate that the average contact angle is greater than 85 (e.g., see Jennings, 1975; Gaskill, 1981) . In contrast, ice parti- cles almost always separate after colliding with hail, re- sulting in an average contact angle of 45°. When we consider both the effects of contact angle and charge relaxation, we can compare the strength of induction charging for various particle interactions in the hail stage. For collisions between dry hail and ice
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CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS particles the relaxation time is too long to permit charg- ing to the maximum value given by Eq. (9.8~. As stated above, the charge attained by an ice pellet is less than one hundredth that of drizzle in a comparable time. In addition, the average contact angle of 45° yields only a factor-of-2 increase over the 70° angle assumed for driz- zle. Thus, induction charging between dry hail and ice particles is severely limited by the long relaxation time for ice. In collisions between wet hail and cloud drops or ice crystals, charge relaxation should be controlled by liq- uid water and the charging rate comparable to induc- tion in the rain stage. The maximum charge attained would be governed by the average contact angle in Eq. (9.8) of over 85° for wet hail and cloud droplets (or small drizzle drops) and 45° for wet hail and rebounding ice crystals. Thus, the most powerful interaction for induc- tion charging in the hail stage would appear to be colli- sions between wet hail and ice crystals. Thermoelectric Charging Up to this point, we have discussed mechanisms that depend on the ambient electric field. We now turn to charge transfer between cloud and precipitation parti- cles where an external field is unnecessary. This class of microscale separation mechanism originates from in- trinsic charge carriers and their relationship to bulk properties. Thermoelectric charging is the result of a thermally induced gradient in the concentration of car- riers that transport positive and negative charges. For a linear gradient in temperature, the steady-state balance between carrier diffusion and drift produces a field of E = kdTldx with an empirically determined coefficient of k = 2 mV/°C (Latham and Mason, 1961~. The corre- sponding surface charge density from Gauss's law is about (10- is C/cm °C) dT/dx (where the gradient is in degrees per centimeter). We can estimate the steady- state charge (in coulombs) for a short ice cylinder of ra- dius r by Q= 10-isr/`T (9~9) for a temperature difference AT (°C) across a length of err (cm) and a surface charge on an area of errs. In the hail stage a temperature gradient would occur during the contact between a precipitation particle, warmed by the freezing of rime (e.g., soft hail) and a smaller particle. A negative charge would be transfer- red to the precipitation particle with Q = 10- i6 C for a small particle using r = 100 ,um and with a rather large temperature difference of /i T = 10°C. Thus, the charg- ing in a single collision is rather insubstantial when com 121 pared with values of greater than 1 pC measured for soft hail in thunderstorms. These estimates of thermoelectric charging are fur- ther reduced when we account for the limitation im- posed by transient contact. Both theory and experiment show that about 10 msec are required to reach a maxi- mum charge comparable to Eq. (9.9) (Latham and Stow, 1967~. Since the contact time between precipita- tion and cloud particles is many orders of magnitude smaller we can reasonably expect that our estimate of 10-16 C for a single collision would be reduced to well below 10- i~ C. Even under the most favorable condi- tions (i.e., 104 collisions within 20 minutes for high ice crystal concentrations at 100 per liter), the accumulated charge would be less than 10- i4 C. In contrast to the estimate of considerably less than 10- i~ C per event for thermoelectric charging, recent laboratory studies have yielded up to 0.3 pC per colli- sion between a small ice particle and a simulated hail- stone (Gaskell and Illingworth, 1980~. Thus, there is ev- idence to demonstrate that mechanisms far more powerful than thermoelectric charging are at work in the hail stage. Interface Charging Two types of interface charging will be discussed: freezing potentials involving impurities and contact po- tentials. Charge can be transferred across a freezing interface by selective incorporation of ions, originating from dis- solved salts and gases, into the advancing ice. In the steady state, a balance is reached between the selection process and the relaxation of charge in the ice. A tran- sient in potential is observed when a plane interface ad- vances past an electric probe. Early workers measured large potentials in the freezing of aqueous solutions con- taining naturally occurring salts over the range of con- centrations found in precipitation (Workman and Rey- nolds, 1948~. Subsequent researchers have made more refined measurements and developed a theoretical de- scription of freezing potentials (e. g., see Caranti and I1- lingworth, 1983a). Others have investigated charge transfer between solution drops and simulated hail- stones (e.g., Latham and Warwicker, 1980~. As a result of these later studies and related ones (Gaskell and I1- lingworth, 1980; layaratne et al., 1983; Caranti and I1- lingworth, 1983b), the role of interface charging in hail- stage electrification is being clarified. As indicated above, two methods are used to study interface charging: (1) potentials are measured as a function of solute impurities and supercooling, with dif- fering growth rates and interface areas; and (2) transfer
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122 of charge is measured for collisions between particles and a much larger "target" electrode coated with ice as a function of solute impurity, supercooling, and speed of impacting drops. Other conditions have also been var- ied, such as the target temperature and the riming rate of the target for a mixture of supercooled drops and ice crystals. Investigation of these various parameters cov- ers many of the conditions found in the hail stage and helps to sort out contributions of freezing potentials from contact potentials and the thermoelectric effect. Recent studies have shown that interface potentials for bulk solutions near 0°C are substantially reduced by supercooling, apparently from the effects of the den- dritic interface (Caranti and Illingworth, 1983a). Po- tentials could not be measured for 100-,um-diameter droplets, in the range - 1 to - 20°C, impacting on an ice substrate because the potential was either too small (less than 100 mV) or it decayed too rapidly (in less than 5 msec). A reduction in charge transfer was also found by Latham and Warwicker (1980) for millimeter-size drops splashing from ice targets in comparison with ear- lier findings for drops not completely cooled by the air (Workman, 1969~. In fact, the charging was of the wrong sign for the freezing of sodium chloride solutions and independent of concentration, indicating that the freezing potential was not the dominating mechanism. A more likely cause was a common form of interface charging associated with the disruption of an air-water interface (i.e., spray electrification). The charges on the air-water interface are readily overwhelmed by polar- ization charges. For example, Latham and Warwicker (1980) found that charge transfer was substantially in- creased by applying a field of only 100 V/m. As the above comparisons demonstrate, the relative importance of charge transfer during the freezing of aqueous solutions is greatly diminished by supercooling. The effect of dissolved ions on charging seems to be neg- ligible in the splashing of supercooled solution drops from ice targets. However, the above considerations do not rule out the freezing potential as a factor in the transfer of charge for a target collecting solution drops and also colliding with ice crystals. Before examining collisions involving ice crystals dur- ing rime formation, we will consider the transfer of charge between an ice-coated target and rebounding ice particles in the absence of droplets. Experiments have shown that a target of ice accumulates either negative or positive charge in collision with ice particles depending on whether the target surface has undergone sublima- tion or deposition (Buser and Aufdermaur, 1977~. It was concluded from an additional experiment that the con- dition of the surface was controlling the charge transfer rather than a thermal gradient as would have been ex- pected for the thermoelectric effect. Buser and Aufder KENNETH V. K. BEARD and HARRY T. OCHS maur (1977) also found that the transfer of charge be- tween ice particles and targets of various metals was proportional to the contact potential. Thus variations in the surface state and, in particular, the free energy of the charge carriers is a major factor in this type of charge separation. The differing signs in the ice-target experi- ments can be attributed to differing surface characteris- tics of the target. The surface exposed during sublima- tion was composed of ice originally formed near 0°C, whereas a frosted surface was produced by deposition at the experimental condition of - 45°C. More recently Gaskell and Illingworth (1980) studied interface charging in the temperature range from - 5 to - 25°C. They also found negative charging for a sub- liming target and positive charging during deposition without any direct evidence of the thermoelectric effect. Frozen droplets of 100-,um diameter transferred charges of about - 0.015 pC for sublimation and + 0.10 pC for deposition. Little variation in charging was found over the temperature range or when the ice target contained ion impurities. These results are consistent with inter- face charging by a contact potential mechanism whereby the surface states of the charge carriers differ between the smooth surface formed near 0°C, exposed during sublimation, and the frosted surface formed by deposition. Additional support for the contact potential hypothesis comes from measurements of the effects of impact velocity and droplet size on charging, since the transfer of charge was found to increase with both of these parameters in a manner consistent with an in- crease in contact area (Gaskell and Illingworth, 1980~. Charging was also examined by Gaskell and I1- lingworth (1980) for a target undergoing simultaneous collisions with ice particles of 100 ,um diameter and su- percooled droplets at low to moderate liquid water con- tents (0.05 to 0.85 gamy. The charge transferred to the target was positive at - 5°C and negative at - 15°C with the transition near - 10°C. The sign reversal was possibly caused by changes in the contact potential with rime structure at different temperatures (Caranti and Illingworth, 1980~. An estimate of interface charging in collisions be- tween various sizes of cloud and precipitation particles can be obtained from the work of Gaskell and I1- lingworth (1980) in which the charge was found to be related to the contact area through the impact speed and ice particle size. In the following formula, we have com- bined their relation for impact velocity (Q ~ Ut 6) with an expression for the velocity of hail (U ~ R08, e.g., see Pruppacher and Klett, 1978) and have included their scaling for ice particle size (Q ~ ri 7~: Q= FR~.3r~.7 (9.10)
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CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS The factor F is a function of the interface potential, de- pends on the nature of the contact surfaces, and may be evaluated from laboratory data. For example, in the riming experiment of Gaskell and Illingworth (1980) the collisional charge was Q ~ - 0.04 pC in the range - 15 to - 20°C for r = 50 Em end R = 0.43 cm (e size with a terminal velocity at the laboratory impact speed, 8 m/ see). Thus, for the interface conditions corresponding to these experiments the factor for the interface potential is F = - 970 (with Q in picocoulombs and the radii in centimeters). The latest investigation of ice crystals rebounding from riming targets provides additional evidence for in- terface charging (Jayaratne et al., 1983~. In this study the target electrode was moved through a cloud of su- percooled droplets that was seeded to produce ice crys- tals. Charging of the target began shortly after seeding and ended after about 4 minutes when the ice crystals settled out of the cloud. At low liquid-water contents the maximum current was positive at a temperature below about - 10°C and negative at temperatures above, in- dicating a reversal in sign of the charge in a manner sim- ilar to that of Gaskell and Illingworth (1980~. The results of Jayaratne et al. are difficult to interpret in terms of charge transfer because of transients in the ice crystal size, the liquid-water content, and the current measured at the target. However, the charge was esti- mated for single events by the investigators from the tar- get current and ice crystal concentration. In one case they estimated Q ~ 0.01 pC for an ice crystal size of 125 Em diameter, where the target speed was 2.9 m/see, the temperature - 6°C, and the liquid-water content 2 g/ m3. The factor for the interface potential that corre- sponds to these experimental conditions is F = 870 (with Q in picocoulombs and the radii in centimeters). The variation in the sign-reversal temperature with liquid-water content was attributed to changes in the freezing process or to variations in the structure and density of the rime. This view is consistent with inter- face charging by the contact potential mechanism. However, sufficient data are unavailable to express the factor for the interface potential as a function of the rim- ing rate or fundamental parameters such as temperature and liquid-water content. Another aspect investigated by Jayaratne et al. (1983) was the variation in charging with solute impurities in the cloud droplets. For cloud water containing natural amounts of sodium chloride they determined that about - 0.003 pC was transferred by ice crystals of 50-,um di- ameter at - 10°C and 1 g/m3. A charge of the same magnitude but of the reverse sign was found for ammo- nium sulfate under the same conditions. At - 20°C the charge was - 0.08 pC for sodium chloride and + 0.08 pC for ammonium sulfate. It should be noted that with 123 these impurities there was no sign reversal in charging over the temperature range investigated ~ - 4 to - 20°C). The factor for the interface potential based on the sodium chloride measurements is F ~ - 1100 for - 10°C and F ~ - 3100 at - 20°C. The corresponding factors for the ammonium sulfate measurements are the same but have a positive value. In contrast to the above study, Caranti and I1- lingworth (1983b) found that solute impurities at natu- ral concentrations did not have a measurable effect on the contact potential of a riming substrate. Thus there seems to be contradictory evidence on the role of solutes in contact charging. A direct comparison between these two studies may be inappropriate because the rime structure and the resultant factor for the interface po- tential may have been affected by differing experimen- tal conditions. If the solute influenced the rime structure in the experiments of layaratne et al. (1983) either di- rectly during the freezing or indirectly by alternating the cloud properties, then their results would have been affected by the contact potential mechanism. In summary, interface charging occurs between rim- ing precipitation particles and ice crystals with a nega- tive charge acquired by the precipitation for tempera- tures below about - 15°C or - 20°C depending on the liquid-water content. The separation of charge appears to result from an interface potential with an amount given by Eq. (9.10) that incorporates the variation in contact area through the ice crystal size and hail size (i.e., impact speed). The interface potential enters Eq. (9.10) through an empirical factor, F. Natural amounts of solute also affect the magnitude and sign of charging. However, it is unclear whether the resultant change in interface potential occurs as a freezing potential or indi- rectly as a contact potential through an altered rime structure. Before applying the results of these laboratory find- ings to the hail stage we first consider the appropriate value of the factor for the interface potential. In the evaluations presented here F was found to be in the range - 3100 to + 3100. Thus the charge obtained by a precipitation particle of R = 1 mm in a collision with an ice particle of r = 50,um has a range, according to Eq. (9.10), of - 0.02 to + 0.02 pC. This range is increased to + O.15 pC for R = 2 mm and r = 100,um. These calcu- lated values also correspond to the measured range pre- sented in this section because the particle sizes corre- spond approximately to the experimental sizes (r) and impact speeds. For a particular application to the hail stage we consider a situation similar to the experiment of Gaskell and Illingworth (1980) at low to moderate liq- uid-water contents and in the temperature range - 15 to - 20°C. For this set of conditions the type of rime is appropriate for soft hail. The estimated charge transfer
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124 red to a soft hail particle (R = 1 mm) by an ice particle (r = 50 ~m) is - 0.006 pC using F = - 970 (determined previously for this experiment). Since contact charging happens much more rapidly than discharging of net charge between particles by con- duction, a buildup of charge can readily occur in multi- ple collisions. A charge of 20 pC could accumulate un- der favorable conditions with ice crystal concentrations of 100 per liter after 3000 collisions (or about 6 minutes). This amount is comparable with negative charges found on ice precipitation in highly electrified regions of thun- derstorms (e.g., see Latham, 1981~. Thus, interface charging appears to be capable of microscale charge separation in amounts that can account for a major as- pect of thunderstorm electrification. However, the wide range and sign variation for the interface factor (and charge) found in laboratory studies seems to be at odds with observations of the predominantly negative charge center for thunderstorms. It is apparent that additional laboratory measurements along with more detailed field observations are required to sort out the discrep- ancy. The relation of the interface factor (F) to tempera- ture, liquid-water content, and impurities must be known before interface charging can be reliably applied to the variety of conditions in the hail stage. This completes our detailed! discussion of microscale charge separation. We have gone from diffusion charg- ing in the cloud stage to the more complex mechanisms involving precipitation in the rain and hail stages. In the following section we consider the relative importance of these mechanisms, and in particular, we evaluate their contributions by comparison with observations of clouds and thunderstorms. EVALUATION The requirements for a satisfactory explanation of charge separation in clouds and thunderstorms are fairly well known (e.g., Mason, 1972; Latham, 1981; Takahashi, 1982~. Any theory must be capable of ex- plaining microscale and cloud-scale charge separation on a suitable time scale. For a fairly complete assessment of charge-separation mechanisms, we need to take into account the evolution of charges and fields, and their interactions, in at least two dimensions. Such an evalua- tion is well beyond the scope of this paper (see Chapter 10, this volume, on cloud modeling.) What we can do here is reiterate some of the pronounced strengths and weaknesses for the various charging mechanisms. We can also indicate where model studies would be helpful in quantifying our gross conclusions and point to areas in need of further laboratory or field research. In mak- ing our evaluation we consider the major requirements KENNETH V. K. BEARD and HARRY T. OCHS for an adequate theory of charge separation in three stages: (1) the cloud stage for small cumulus clouds that contain only cloud droplets and drizzle drops; (2) the rain stage for larger cumulus clouds that contain rain- drops formed by accretion of cloud droplets; and (3) the hail stage for the upper regions of large cumulus clouds where precipitation (notably, soft hail) is formed by ac- cretion of supercooled droplets. Cloud Stage Electrification is generally weak in the cloud stage. Ion mechanisms dominate because of the absence of pre- cipitation and their associated charge-separation mech- anisms. Charges have been observed to range from about 1 to 20 electrons for small cloud droplets with a normal distribution centered near zero charge. Values of the average charge magnitude are indicated in Figure 9.6 by region Car from measurements in stratocumulus clouds (Phillips and Kinzer, 1958~. The observations agree with a Boltzmann equilibrium (line c) after the ~n-9 ._ ~ ,o-lo~ 10_7, -12 lo-13 E o 10-14 L) la 1n-l5 n-17 1o-l9 _ 2um 5 1 n 20 PARTICLE DIAMETER - . _ 50 100 200 500 lmm 2 5 10 20 I ~j 1 1 1 I I ~6 -100pC -10pC -1pC -0.1 pC -0.01 pC ELECTRIC FIELD Drift Schaive Breakup Charging Ion Charging Charging Line (Eq 5} (Eq 6) (Eq 7) 6 100 kV/m 600 kV/m 400 kV/m S 10 kV/m 60 kV/m 40 kV/m 4 1 kV/m 6 kV/m 4 kV/m 3 100 V/m 600 V/m 400 V/m 2 10 V/m 60 V/m 40 V/m 1 1 V/m 6 V/m 4 V/m 1o-o 1n-1 10-2 /// /.~ /1 - 1e 1 1 1 1 1 1 1 1 Am 2 5 10 20 50 100 200 PARTI CLE RADI US Q(C) - 8.4 x 10-'5 R'~ (mm) 5(C} - 3.8 x 10-39 R0 6(/lm} la' 10-5 10-6 _ 10-7 in-8 _ in-9 ._ 1 1 1 1 500 lmm 2 5 10 FIGURE 9.6 Average charge magnitude for cloud and precipitation particles. Regions C1 and C2 show cloud stage (after Phillips and Kin- zer, 1958; Gunn, 1957), regions Rat and Ret show rain stage for shallow and deep convection (after Takahashi, 1973a, 1978), and regions HI and H show hail stage (after Takahashi, 1973a; Latham, 1981). Lines labeled c, T. and h are from equations given by lower inset. Lines 1 through 6 have ROE dependence on charge (see upper inset for corre- sponding mechanisms and fields).
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CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS rms charge given by Eq. (9.3) is converted to a mean deviation (see lower inset on Figure 9.6 for the corre- sponding Q equation). We can expect that the charge distributions for large cloud drops would be skewed (no longer centered on zero charge) with higher averages as indicated by region C' from the influence of the electric field by drift charging at cloud edges and selective ion charging. Note that charging under the influence of the electric field is depicted on Figure 9.6 by the lines la- beled 1 through 6. The corresponding values of electric field for three mechanisms are found in the upper inset. For example, line 2 shows the charge magnitude for drift charging at cloud base (or top) in a field of 10 V/m and selective ion charging in a field of 60 V/m. For a small cumulus, charge separation in the cloud stage is consistent with microscale ion capture and cloud-scale convective transport of charge. This combi- nation can account for such features in the cloud stage as the negative core and positive edges. It can also explain a positive charge in the base of a cloud very near to the ground. Charging by ion capture appears to be limited by cosmic-ray production within the cloud (Wormell, 1953) and transport from outside, and therefore addi- tional mechanisms are required to produce the fields and charges found in the rain stage and hail stage. Rain Stage Electrification in convective clouds of less than about 3 km deep is characterized by the drop charges for the rain stage indicated in Figure 9.6 by region Rat (Taka- hashi, 1973a). The mean value (Q) is approximated by the straight line proportional to Ri 3 (i.e., line r with equation shown on lower inset from Pruppacher and Klett, 1978~. Since the electric field associated with these clouds is often 10 to 100 V/m, it is apparent from Figure 9.6 that drift charging (lines 2 and 3) and also selective ion charging and breakup charging can pro- duce charges of the observed magnitude (Q) for drizzle and raindrops (R > 100,um). What is not so apparent is how cloud drops and small drizzle drops acquire their relatively high charge in the rain stage. One possibility is by evaporation of drops with higher charge. Other ex- planations involve selective ion capture from the effects of surface potentials (Takahashi, 1973b; Wahlin, 1977~. However, the details of these mechanisms are poorly un- derstood, and consequently their role in drop electrifi- cation remains uncertain. Additional research is needed to clarify the microscale-separation mechanisms respon- sible for charging cloud drops and drizzle drops. Another aspect of electrification in the rain stage is the predominant sign of charge for cloud drops, drizzle, and raindrops. We can consider charge separation for a 125 convective cloud of about 3 km deep (after Takahashi, 1982~. The trajectories of drizzle and raindrops are de- picted in Figure 9.7 to indicate differences for the pre- ferred sign of charge. The drizzle drop is in a region of lower updraft speed (dashed arrow), which results in a shorter growth time within the cloud. Negative charg- ing occurs by the Wilson effect (for a downward-di- rected field) and by drift current at cloud base. In addi- tion, drizzle may be produced by breakup of raindrops, resulting in negatively charged drizzle for the field near and below cloud base. Raindrops become electrified positively by breakup charging. At an earlier time, rain- drops near cloud top may also acquire a positive charge from the capture of droplets. Although this picture of drop trajectories in Figure 9.7 is greatly simplified it does illustrate some essential differences that can occur in growth histories and in the resultant charge-separation mechanisms for cloud drop- lets, drizzle drops, and raindrops. Our conclusions about the predominant sign of charge, based on trajec- tories and separation mechanisms, are consistent with extensive observation of tropical cumulus clouds (e.g., see Takahashi, 1982~. These observations show a pre- dominance of positive droplets near cloud top and nega- tive drizzle drops and positive raindrops within and be- low the cloud. ~DRtFT(+) If// ~ + SELECTIVE tON i, CAPTURE (-} DRIZZLE ~1,,tL.,~ DRIFT (-) ~ ~ . · ~ /~' `~+) tRAINDROPS ~ BREAKUP (do) 1 (3 BREAKUP (-) ~: ~ : ~ ~ ~ FIGURE 9.7 Rain-stage electrification based on simplified growth histories for drizzle and raindrops (modified from Takahashi, 1982). Air currents are shown by dashed arrows and ion drift currents by heavy arrows.
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126 A fascinating aspect of electrification in the rain stage is the reported occurrence of lightning for clouds warmer than 0°C (e.g., see Moore et al., 1960~. The evidence is incomplete because this phenomenon has not been verified by in situ measurements of cloud tempera- ture. Such lightning is apparently restricted to the trop- ics and probably occurs only in clouds that are deeper than discussed above. For warm clouds of about 5 km depth average charges are typified by region R2 shown on Figure 9.6 (Takahashi, 1978~. These charges were measured at the ground with associated fields of less than 1 kV/m. Drift charging, selective ion capture, and breakup charging can probably account for such high charges providing the fields in or around the cloud reach about 1 kV/m. (Fields as large as 3 kV/m were measured from an aircraft in the vicinity of warm cloud lightning by Moore et al., 1960.) There is also the possibility that induction charging could contribute to the field intensi- fication within the cloud, but the enhancement of drop coalescence in fields of 30 kV/m suggests that lightning cannot be achieved by induction alone. We should keep in mind, however, that induction charging has been in- vestigated for only a narrow range of drop sizes and that lightning in deep (warm) convection has not been stud- ied in detail. Therefore, additional research on charge separation mechanisms is required to understand the strong electrification that occurs in deep warm clouds. Hail Stage There are three aspects of charging in the hail stage that must be explained: (1) the observed region of nega- tive charge, (2) the buildup of fields, and (3) the average values of charge. Regions of negative charge lie gener FIGURE 9.8 Schematic diagram illustrat- ing the levels and distribution of charge sources for ground-flash lightning observed for summertime in Florida and New Mexico and for wintertime in Japan (from Krehbiel et al., 1983). KENNETH V. K. BEARD and HARRY T. OCHS ally between the - 10 and - 25°C level even in winter thunderstorms, as illustrated by the location of light- ning sources shown on Figure 9.8 (from Krehbiel et al., 1983~. The space-charge densities associated with the region of negative charge average about 1 C/km3 from estimates based on lightning currents and particle charges (Latham, 1981~. The second aspect of charging in the hail stage is the development of large electric fields. The maximum fields measured in thunderstorms are consistent with estimates of the requirement for lightning initiation (about 400 kV/m). The average magnitude of charge on individual parti- cles (Q) in the hail stage is shown on Figure 9.6 by region Hi for cloud droplets and region H2 for precipitation particles, with line h giving an approximate Q from Grover and Beard (1975~. The charges on raindrops are in the lower portion of H2 (after Takahashi, 1973a), whereas charges on solid precipitation reside in the up- per portion of H2 (Latham, 1981~. In both cases the av- erage for the negative charges usually exceeded the posi- tive charges by a significant amount, with charges on individual particles sometimes in excess of 100 pC. As a result of the high fields found in the hail stage, breakup charging would be highly efficient (Figure 9.6, line 6), with the sign depending on the orientation of the local field. (Note that a variety of field orientations must oc- cur within thunderstorms around charge centers, see Figure 9.8.) Drift charging would also be efficient in strong fields if ion concentrations are enhanced by co- rona from ice crystals (Griffiths and Latham, 1974~. Thus the generally high charges found on cloud and pre- cipitation particles are probably an indication of field- driven mechanisms that separate charge on the micro- scale. For the causes of high fields we will consider the 20 16 12 I I 8 4 SUMMER STORMS \, ~ FLORIDA NEW MEXICO (I O C ~ Act_ /4 0°C / / WINTER STORMS O ~ ~\\\4
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CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS microscale and cloud-scale mechanisms that lead to the negative-charge region observed to occur between - 10 and - 25°C. We first evaluate convection charging, which has held a controversial position among theories of thunder- storm electrification (e.g., see arguments in Mason, 1976; Moore, 1977~. These theories, proposed by Grenet (see Chalmers, 1967) and Vonnegut (1955), rely on the transport by updrafts and downdrafts of space charges and screening layers. In the hail stage, with a highly electrified cloud, the charge from the positive corona at the ground is carried into the cloud base and by the up- draft, to the cloud top where it attracts a negative screening layer. The downdrafts carry the negative charge back toward the cloud base to strengthen the negative field between the cloud base and the ground, thus enhancing the positive corona. The notion of nega- tive charge in downdrafts has been reintroduced in the form of nonrandom mixing from the cloud top by Tel- ford and Wagner (1979) to provide a qualitative expla- nation for a negative-charge region near the - 10°C level. This picture of descending negative charges appears to be at odds with the early stages of convective electrifi- cation modeled by Chiu and Klett (1976~. They found a positive screening layer at a cloud top and positive de- scending charges. Convection and mixing were found to weaken the field within the cloud. Since Chiu and Klett did not expect their model outcome to change apprecia- bly for clouds deeper than 5 km, it is difficult to envision how convective (single-cell) transport could be the source of strong electrification. However, in the hail stage with multicell convection and with corona from precipitation, the ion concentrations would differ con- siderably from the model of Chiu and Klett. Thus, a better model is required to evaluate the importance of convection in highly electrified clouds. Another criticism of convection charging is that up- drafts and downdrafts may disorganize their associated charges through mixing (e. g., see Chalmers, 1967) . The study of Chiu and Klett clearly shows that single-cell convection with eddy diffusion diminishes the electric field within the cloud. If we picture cloud turrets as con- vective cells (similar to Figure 9.2) with interspersed up- drafts and downdrafts, then the possibility for disorgan- ization by mixing between adjacent charge regions becomes rapidly apparent. Questions regarding the im- portance of mixing in cloud electrification probably will not have a satisfactory answer until we have more quan- titative models of turret scale motions and entrainment. In addition, the common occurrence of a negative charge center near - 15°C suggests that transport of ions and charged particles by convection is not so impor 127 tent as microscale charge separation involving ice parti- cles. In evaluating induction charging in the hail stage, we consider that the most efficient microscale interactions are collisions between wet hail and ice particles. The maximum charge according to Eq. (9.8) is about 1 pC in the limiting field of 400 kV/m for a particle of 100-,um radius and 10 pC for a 300-,um particle. Since the wet growth of hail requires sizes larger than about 10 mm diameter, the induction limit of 1 to 10 pC even for R = 10 mm is well below the charge expected from ion cap- ture in high fields (see line 6, Figure 9.6~. Thus, induc- tion charging cannot be directly responsible for the av- erage charges (1 to 100 pC) found on precipitation particles (0.5 to 2 mm radius) in the hail stage. Another aspect of the induction charging of wet hail is its importance to the region of negative charge near the - 15°C level. For hailstones with a maximum charge of 10 pC at a maximum concentration of 1 m ~ 3, the result- ing space-charge density is 0.01 C/km3. This estimate of the maximum charge density is several orders of magni- tude smaller than a charge of about 1 C/km3 found from measurements of particles and from estimates based on lightning currents. Although the induction mechanism provides negative charge on precipitation particles and field intensification through feedback, it appears to be too weak to account for the charge densities associated with the hail stage. Its shortcomings are twofold: the maximum charge is limited by the effects of size and contact angle given in Eq. (9.8), and the charge density is limited by the instrinsically low concentration of hail- stones. The microscale separation mechanism in the negative-charge region is probably associated with smaller precipitation particles (e.g., soft hail), because their higher concentration could lead more easily to a sufficient charge density. For example, particles at a concentration of 100 m ~ 3 carrying 10 pC would result in a more realistic 1 C/km3. The charging of soft hail has been simulated in the laboratory by collisions between ice particles and an ice electrode in the process of riming (Gaskill and I1- lingworth, 1980; Jayaratne et al., 1983~. Although our understanding of the separation mechanism is incom- plete, the evidence points to interface charging from contact potentials with freezing potentials having a sec- ondary role. Investigations of temperature effects in the above studies have ruled out thermoelectric charging. The formula applicable to these results scales with con- tact area and is the same as line r on Figure 9.6 when evaluated for an ice particle of r = 60,um. Thus charge transfer for individual collisions between soft had! and small ice particles is around 0.01 pC. Since contact time is relatively short compared with the time required to
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128 discharge colliding particles by conduction, an accumu- lation of charge can occur in multiple collisions. In this manner an increase of 3 orders of magnitude, well into region H2, may be attained with high concentrations of ice crystals in several minutes. A key result of the above experiments is a reversal in the sign of charging at temperatures of - 10 to - 25°C depending on liquid-water content. Riming particles acquire negative charges if colder than the reversal tem- perature and positive if warmer. Thus, soft hail would be charged negatively above the reversal level in the cloud and positively below this level. Jayaratne et al. (1983) postulated that descending precipitation particles should have their maximum neg- ative charge near the reversal level and that rebounding ice crystals carrying negative charge from below would also contribute to the negative region. The fields di- rected toward the reversal level would intensify during the process of charge separation by differential sedimen- tation. There are many features of interface charging that need clarification before we can feel comfortable with the above description of charging in the hail stage. First, the roles of temperature, liquid-water content, and so- lutes are poorly understood. These appear to influence contact potential through changes in rime structure. TABLE 9.1 Charge Separation in Clouds and Thunderstorms KENNETH V. K. BEARD and HARRY T. OCHS (Solutes may also affect interface charging by transient freezing potentials. ~ Second, the details of charge trans- fer have not been explained, although the charge carri- ers are probably associated with the contact surfaces. This concept is consistent with a rapid transfer of charge that scales with contact area. Finally, our recently ac- quired understanding of interface charging, even though somewhat limited, cannot be adequately as- sessed until it is placed within the framework of a multi- dimensional cloud model. CONCLUSIONS The charging mechanisms in clouds and thunder- storms are varied and numerous. Some are simple and readily appreciated, whereas others are complex. Sev- eral important mechanisms are poorly understood. Feedback readily occurs through changes in ion concen- tration and the electric field making it difficult to iden- tify the primary causes for electrification. However, some simplification can result by considering the charg- ing mechanisms in three stages of cumulus cloud devel- opment: the cloud, rain, and hail stages. The charging mechanisms discussed in this chapter are summarized in Table 9.1. Each mechanism is listed with the microscale and cloud-scale separators (with Mechanism Microscale Cloud Scale Major Roles 1. Diffusion charginga Ion capture by Removes ions within diffusion cloud 2. Drift chargings h Ion capture in Drift currents Charges particles drift currents Convection Enhances field (Sedimentation) 3. Selective ion Ion capture by Sedimentation Charges particles charging' 'I polarized crops (Convection) Enhances fields 4. Breakup charging'' Collisional Sedimentation Charges drops breakup of (Convection) polarized drops 5. Induction charging`' f Charge transfer Sedimentation Charges particles between polarized (Convection) Enhances field particles 6. Convection chargingd ~ h Space-charge Convection Enhances field production (Charges particles) Ion capture in drift currents 7. Thermoelectric charging) Charge transfer Sedimentation (Charges particles) between particles of (Convection) differing temperatures 8. Interface charging) k Charge transfer Sedimentation Charges particles between particles (Convection) Enhances field involving contact potentials (freezing potentials) aGunn (1957); bChiu and Klett (1976); CWilson (1929); dChalmers, (1967); eMatthews and Mason (1964); fElster and Geitel (1913); "Grenet (1947); hVonnegut (1955); 'Latham and Mason (1961); iWorkman and Reynolds (1948); Abuser and Aufdermaur (1977~.
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CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS items of secondary importance shown in parentheses). Charging appears to be well described by diffusion, drift, and selective ion capture for the nonprecipitating cloud stage (mechanisms 1-3~. The situation in the rain stage is complicated by the addition of breakup and in- duction (mechanisms 4 and 5~. We suspect that drift, selective ion capture, breakup, and induction are re- sponsible for charges and fields in shallow clouds. How- ever, it is difficult to find an explanation for the stronger electrification in convective clouds over a few kilome- ters deep. The basis of lightning from clouds with tops warmer than freezing remains a mystery. A major prob- lem in the rain stage is that our knowledge of the sus- pected mechanisms is still rather rudimentary. There is clearly a need for additional research on changing by ions, breakup, induction, and convection to understand the electrification of warm clouds. In the hail stage we add thermoelectric and interface charging (mechanisms 7 and 8~. Recent laboratory stud- ies of charge transfer involving ice particles rebounding from simulated hailstones in the process of riming have shown that interface charging is the dominant mecha- nism. The roles of temperature, liquid-water content, and solutes are most likely important in altering the rime structure and thereby the contact potential and contact area. More research is required to understand these effects and the details of charge transfer. The electrification process becomes more complex as a cloud develops. The cloud stage involves mechanisms 1-3, whereas the rain stage includes 1-6. All the mecha- nisms listed in Table 9.1 may occur in the hail stage. We might ask, as many have before us, which separation mechanisms are essential to cloud electrification. The answers, if we had them, would depend on which aspect of cloud electrification we consider. For example, the essential mechanism for lightning depends on whether we are looking at the field development in the rain or hail stages or whether we are concerned with the charge centers associated with cloud-to-ground, in-cloud, or cloud-to-cloud lightning. Yet another aspect of light- ning is the mechanism that initiates the stroke. Clearly the idea of an "essential" mechanism is an oversimplifi- cation. A more useful approach is to examine the inter- dependencies. We should be asking how the various charge-separation mechanisms are related. Some an- swers should be forthcoming as we incorporate the knowledge gained from recent laboratory studies of in- dividual mechanisms into models of cloud electrifica- tion and compare the findings to field observations. With continued progress in laboratory, field, and mod- eling research we should achieve, in the next decade, a much improved perspective of the charging mechanisms in clouds and thunderstorms. 129 ACKNOWLEDGMENTS We appreciate the helpful comments of Bernice Ack erman, David Johnson, Anthony Illingworth, and an anonymous reviewer. This review was supported in part by a grant from the National Science Foundation under ATM-83-14072. REFERENCES Buser, O., and A. N. Aufdermaui (1977). Electrification by collision of ice particles on ice or metal targets, in Electrical Processes in At- mospheres, N. Dolezalek and R. Reiter, eds., Steinkopff, Darm- stadt, p. 294. Caranti, J. M., and A. J. Illingworth (1980). Surface potentials of ice and thunderstorm charge separation, Nature 284, 44. Caranti, J. M., and A. J. Illingworth (1983a). Transient Workman- Reynolds freezing potentials, J. Geophys. Res. 88, 8483. Caranti, J. M., and A. J. Illingworth (1983b). The contact potential of rimed ice, J. 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Representative terms from entire chapter: