Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 131
Moclels of the Development of the Electrical Structure of Clouds 10 INTRODUCTION ZEV LEVIN Tel Aviv University ISRAEL TZUR National Center for Atmospheric Research Thunderstorms are highly variable in their intensity, dimensions, composition, and electrical structure. Some generalizations can be made about them, however. The lightning activity follows strong vertical air currents and precipitation. As a consequence of this correlation, lightning is most frequently observed in cumulus clouds, rarely in stratus clouds, and never in isolated cirrus clouds. Both satellite and ground observations reveal lightning activity at all latitudes between 60° N and 60° S with the most frequent occurrence at low latitudes and over land. The high occurrence rate over land is be- lieved to be related to the more connectively unstable conditions normally present over land. In high lati- tudes, the lightning frequency decreases because of the reduced convection from colder surfaces and the re- duced absolute humidity. Most thunderstorms contain both water drops and ice crystals, they usually have mass contents (water + ice) greater than 3 g/m3, and they have precipitation rates (involving particles larger than 100 ,um) in excess of 20 mm/in. Although lightning has been observed most often in clouds containing both ice and water, there have been a few observations of lightning from all-water clouds (e.g., Lane-Smith, 1971~. Lightning has been observed in clouds that are completely at temperatures below 131 0°C, but these clouds usually contain both supercooled water droplets and ice. The complexity of the processes leading to the devel- opment of both the precipitation and electrical struc- ture in the clouds makes it impossible to construct or validate theories of cloud electrification from simple field experiments. It is only through the complementary efforts of laboratory experimentation, field observa- tions, and mathematical simulations that we can hope to understand the physical processes involved in thun- derstorms. A recent review by Latham (1981) summa- rized some of the main observations of thunderstorm electrification in a coherent fashion, and we refer the interested reader to it. Improved understanding of the major processes lead- ing to the buildup of strong electrical fields and their mutual interaction with precipitation can lead to better forecasting of thunderstorm activity for use in aviation and protection of forested areas, to the development of methods for artificially modifying lightning activity, and even to the development of more efficient rain-en- hancement operations. As an ultimate test of the various theories of how elec- trical charge separates in thunderclouds, it would be necessary to design a model that simulates as accurately as possible the three-dimensional and time-dependent nature of the cloud and its environment, including the
OCR for page 132
132 microphvsical development of the liquid and solid phases in the cloud and all the possible electrical pro- cesses that are operating. These requirements are not yet attaintable with our current state of knowledge and available computers. The number of processes involved and the large range of scales (from the molecular level to the dynamic scale 1000 m) cannot all be included in a single model. Therefore, attempts have been made to deal with the problem of the development of the electri- cal structure of clouds by emphasizing some processes and ignoring others. A few models, for instance, simu- late the microphysical processes only, neglecting the macroscale dynamics altogether, whereas others have gone to the other extreme and simulate the dynamics in detail while simplifying the microphysics dramatically. To fill in the gap, some modelers have tried to deal with both the microphysics and the dynamics with sacrifices at both ends of the scale. We will review some of these models, try to establish a common denominator from their results and conclu- sions, and d-raw attention to some unanswered points that need further work. GENERAL REQUIREMENTS FROM ELECTRICAL MODELS OF THUNDERCLOUDS The validity of any thunderstorm model is deter- mined by its ability to simulate observed features. Ow- ing to the large natural variability of the various pro- cesses in thunderclouds, it is difficult to find a "typical" storm with which all models could be compared. It is possible, however, to list some common observed fea- tures to use as general criteria for such comparisons. The following summary by Mason (1971) of the basic thunderstorm observations still appears to be valid: 1. The average duration of precipitation and electri- cal activity from a single cell is about 30 min. 2. The average electric moment destroyed in a light- ning flash is about 100 C km, the corresponding charge being 20 to 30 C. 3. In a large, extensive cumulonimbus, this charge is separated in a volume bounded approximately by the - 5°C and - 40°C levels and has an average radius of perhaps 2 to 3 km. 4. The negative charge resides at altitudes just above the - 5°C isotherm. Krehbiel et al. (1979) observed that the negative charge transferred by lightning originates from regions between -10°C and -17°C, indepen- dent of the height above ground and regardless of the geographical location of the thunderstorm. The main positive charge is situated several kilometers higher. An ZEV LEVIN and ISRAEL TZUR other subsidiary small positive charge may also exist near cloud base, centered at or below the 0°C level. 5. The charge-separation processes are closely associ- ated with the development of precipitation, probably in the form of soft hail (particles containing both liquid water and ice). 6. Sufficient charge must be separated to supply the first lightning flash within 12 to 20 min of the appear- ance of precipitation particles of radar-detectable size (d-200,um). MECHANISMS OF CHARGE SEPARATION For space-charge centers to build up in clouds, charge must be separated first in the microscale, and then larger-scale processes can act to separate the opposite charges in space. When accomplished, this dual-scale process leads to the buildup of a space-charge distribu- tion similar to that in Figure 10.1. In thunderclouds the charge separated on a micro- scale by particle interactions is subsequently separated on a macroscale with the help of convection and gravita- tional settling. Convection plays a role in cloud particle growth by forcing the condensation of water vapor until the particles are large enough to coalesce. Some of the interactions between cloud particles, particularly those followed by rebounding, may result in charge separa- tion (as will be discussed later). These charges are then separated by differential terminal settling velocities. The larger particles, which carry predominantly one ~ t ~ Conduction, JE cam--W! t~- 12 km + + + (-25to -60°C)- 1\ 7 km Charge ma/ Separation / Current ~ - l _ _ _ (- 10° to - 20° C ) ~ /~- + + _ (0°to-5°C) Lightning, JL?4/ poloist I I I I I I ~ ~ PreC;P;tOt;On, JP Convection Discharge, l I I ~ 1'', ;; | | ~ ~convection, JC of Wf We'd W/f elf f /7'f elf Wf Wf ,^/7,'7 FIGURE 10.1 A schematic of the main space-charae distribution and currents in a thundercloud.
OCR for page 133
\IODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS sign of charge, fall faster and farther down with respect to the convected air, leaving the oppositely charged smaller particles above. As the charge centers build up, discharging mecha- nisms become more effective, and these should be in- cluded in any complete description of cloud electrifica- tion. Two kinds of discharge are possible: (1) discharge by collisions between drops and ions of opposite polarity and (2) discharge by collision and coalescence with cloud particles of opposite charge (see Colgate et al., 19771. The first mechanism depends on the electrical conductivity of the small ions (\ = nek, where n is the ion number density, e is the electronic charge, and k is the electrical mobility) and on the ion diffusivity. Often ions of different polarities have different diffusivities; those with higher diffusivity attach preferentially to cloud and free aerosol particles. However, after some charge is built up on a cloud particle, further ion diffu- sion to it will be limited. Another factor affecting ion attachment to cloud par- ticles is the electric field in the cloud. Strong fields will move free ions from one region to another. In so doing, they also increase the conduction currents and, hence, the discharge of cloud particles. In addition, when the electric field exceeds about 50 kV/m, corona discharge begins near the corners of ice crystals and high concen- trations of ions are generated. These ions increase the electrical conductivity and help to prevent or slow down the further buildup of the space charge. The other discharge mechanism (collection of oppo- sitely charged cloud particles) takes place at all stages of particle growth. This mechanism is enhanced if the in- teracting particles are highly charged, have opposite po- larity, and when the ambient field is strong. In this case the collection efficiency increases by increasing the colli- sion efficiency (Coulomb attraction changes the trajec- tories of particles relative to each other) or by increasing coalescence efficiency (not allowing bouncing, and hence no charge separation, to occur) or by both. Therefore, for a charge mechanism to be effective, it has to separate sufficient charge at a rate sufficiently high to overcome these discharge processes. The many charge-separation mechanisms and their complexity re- quire a detailed discussion that is beyond the scope of this chapter. We recommend that the interested reader refer to Chapter 9 (this volume) by Beard and Ochs and to Mason (1971~. The various charging mechanisms that have been proposed as possible major contributors to electrifica- tion of thunderstorms can be divided into two major classifications: (1) precipitation mechanisms requiring particle interactions with subsequent space-charge sep- aration by gravitational sedimentation and (2) ion at 133 tachment to cloud or precipitation particles and then charge separation by either gravitational settling or by atmospheric convection (updrafts or downdrafts). Mechanisms from group (1) above are divided into two major subprocesses inductive and noninductive. Most models to date treat these mechanisms with various de- grees of detail. On the other hand, only a few models are available that treat the ion convective process. Conse- quently, since the intention here is to review the present state of knowledge in modeling electrical development in clouds, most of the emphasis is placed on the models dealing with the precipitation mechanisms. As discussed later, there are still a great many questions that these models cannot answer. Inductive Process Charge can be separated by the inductive process dur- ing rebounding collisions of particles embedded in an electric field. This mechanism, which is relatively sim- ple to formulate, was treated intensively in cloud elec- trification models. According to Sartor (1967) and Scott and Levin (1975) the amount of charge that is separated per collision by this process is AQ = t-4~0E~r2cos~ + (co + 1)Q + ~q] [1 - exp(-tc/~] (10.1) In this equation /`Q represents the charge transfer to the large particle as a smaller particle o-f radius r collides and rebounds in an electric field E (defined as positive when a positive charge is overhead), making an angle ~ between the field and the line connecting the centers of the particles at the point of separation; ~ and ~ are con- stants that depend on the ratio of sizes of the colliding particles (Ziv and Levin, 1974~; Q and q represent the initial charge on the particles before the interaction; tc is the contact time of the colliding particles and ~ the relax- ation time of the charge carrier ~ = ccolK' where ~ and K are the dielectric constant and the electrical conductiv- ity, respectively; and c0 is the permittivity of free space). The first term on the right-hand side of Eq. (10.1) represents the charge that is transferred from the small to the large particle because of the inductive polariza- tion effect. One can see that the stronger the field or the larger the size of the smaller particle, the larger is the charge separated. The constant ~ represents the en- hancement of the electric field around the colliding par- ticles, as compared with the the ambient field. Particles may collide at the head-on position but will skid or roll on each other and finally separate at the angle I. For water drops, ~ may vary between 50° and 90° (Levin and Machnes, 1977~. Large liquid particles sometimes
OCR for page 134
134 may also be separated at ~-90°, leading to their dis- charge (Al-Seed and Saunders, 1976~. On the other hand, nonspherical solid or liquid particles can separate larger charges by the inductive process as a result of the much enhanced electric fields near them (Censor and Levin, 1974~. The second and third terms on the right side of Eq. (10.1) represent the limitation of charge transfer due to the initial charge on the large (Q) and small (q) parti- cles, respectively. The constant co then is a geometrical factor that represents the effect of the capacitance of the two on the charge transfer. The last term on the right represents the limitation to charge transfer due to the electrical conductivity of the materials that compose the particles (Sartor, 1970; Caranti and Illingworth, 1983; Illingworth and Caranti 1984~. Ice particles at low temperatures, for example, have low bulk and surface electrical conductivities that lead to longer relaxation times r. This means that in any given collision there is the possibility that not all the available charge will be transferred, since the contact time tc might be shorter than I. Indeed a recent labora- tory study by Illingworth and Caranti (1984) on the de- pendence of charge transfer during ice-ice collisions on the surface conductivity of ice, suggests that for ice-ice interactions the inductive mechanism is not efficient. Interactions of two particles can result in either collec- tion or rebound. To describe the probability of these two end results a collision efficiency, Ed, and a coalescence efficiency, E2, are defined. Ed represents the probability of two cloud particles to interact, and E2 represents the probability of the interacting particles to coalesce. Therefore, the collection probability is Ed E2, and the rebound probability is (1 - EATEN. To separate charge an electrical contact among rebounding particles must be achieved. Only a fraction, E3, of the particles that collide and rebound make such electrical contact. We will refer to E3 as the electrical contact probability. Therefore, the probability for separating charge be- tween two cloud particles is P = EM - E2)E3. The rate of charge buildup on the large particles per unit volume as a result of collisions of particles can be expressed as dQ/dt= 7r(R + r)2(V- v)Nn(Pl\Q - E~E2qj, (10.2) where R and r are the radii of the large and small parti- cles, respectively, V and v are their fall speeds, and N and n are their concentrations. The term P1\Q repre- sents the charge separated per interaction, while E~E2q accounts for the discharge of the large particles resulting from collection of oppositely charged particles (Scott and Levin, 1975~. ZEV LEVIN and ISRAEL TZUR Noninductive Process Many noninductive mechanisms have been proposed to explain the formation of electricity in thunderstorms. Among the most powerful are the thermoelectric effect (Reynolds et al., 1957; Latham and Mason, 1961), freezing potentials (Workman and Reynolds, 1948), and contact potentials (Buser and Aufdermaur, 1977; Caranti and Illingworth, 1980~. All of these rely on the electrochemical nature of water or ice for charge sepa- ration. Thermoelectric Effect Charge separation results from interactions of ice particles of different surface temperatures. On contact the temperature gradient across the surface causes the H + ions to migrate from the warmer particle to the cold one, leaving OH- ions on the warmer ice particle. Subsequent rebound of these particles will result in charge separation. The amount of charge separated in this process depends on the temper- ature and the temperature gradient. In most models, the value of the charge separation per interaction is taken as a constant, regardless of the temperature or tempera- ture gradient. Freezing Potentials Workman and Reynolds (1948) and Pruppacher et al. (1968) observed that high electri- cal potentials develop across an ice-water interface when the water contains small amounts of impurities (~ 10-5 molar). These potentials develop as a result of preferential incorporation of certain ions from the solu- tion into the ice lattice, leaving the ice and the liquid solution oppositely charged. In clouds, if such a situa- tion occurs, fragments of the solution can be thrown off as a result of the impact of other particles. These frag- meets carry away charge of one sign, leaving the ice par- ticle with the opposite charge. Gravitational settling can then separate the two charges in space. These early works suggested that the magnitude and sign of the separated charge depend critically on the amount and type of impurity used. Various laboratory experiments conducted to simulate this charging mech- anism have resulted in a surprisingly wide range of charge transfer. Most investigators (e.g., Weickmann and Aufm Kampe, 1950; Latham and Mason, 1961) measured charging rates that correspond to roughly 3 X Jo- 16 to 3 X 10- Is C per collision. Schewohuk and Iri- barne (1971) observed about 10-~ C per collision for very large water drops (R = 2.9 mm), a value that de- creased as the drop size and impact velocity decreased. On the other hand, they observed very little dependence on impurities but much stronger dependence on temper- ature. In most of these experiments the rebounding
OCR for page 135
MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS droplets received positive charge, leaving the target ice negatively charged. In experiments by Latham and Warwicker (1980), these general findings were confirmed, but a maximum charge of only 10- ~4 C per collision was observed with slightly smaller drops, in conformity with most other investigations. It is also clear from these experiments that the charge separation is more a function of drop size than of impurities. Contact Potentials Buser and Aufdermaur (1977) and more recently Caranti and Illingworth (1980) ob- served that a surface potential develops during riming of supercooled water droplets on ice. This surface poten- tial increases steadily with decreasing temperature down to - 10°C and remains constant to - 25°C. Caranti and Illingworth (1980) also observed that im- purities, such as NH4OH, NaCl, or HE, made no detect- able difference in the surface potentials. In clouds, charge could be transferred by collisions and subsequent rebounds of small unrimed ice crystals with a surface potential near zero from the surface of a rimed crystal with negative surface potential. The electric charge buildup by each of the noninduc- tive processes can be expressed as in Eq. (10.1), except that ~Q has the form Q = ~ - A + (co + 1)Q + ~q]~1 - exp( - tclr)], (10.3) where A is the charge transfer per collision resulting from one of the above mechanisms. The value of A for small cloud particles varies from 10- i5 to about 10- i4 C per collision, depending on the type and size of the parti- cles and on temperature (Takahashi, 1978~. Owing to the lack of comprehensive data about the charge trans- fer as a function of size and temperature, all available numerical models take this value as a constant. One should keep in mind that the charge buildup by both the inductive and the noninductive processes de- pends on the interaction probabilities Em, E2, and E3 and on the ratio tclr. In the models, the values of Em, E2, and E3 have to be specified. A detailed discussion of the probabilities and the way they are calculated and mea- sured is beyond the scope of this paper. The interested reader is referred to Pruppacher and Klett (1978, Chap- ter 14) for details. The collision efficiency Em of water drops used in the numerical models is based on calculations of particle trajectories (e. g., Davis and Sartor, 1967~. A few calcu- lations are available for collisions of ice particles with water drops and with other crystals. These are limited owing to the complex geometrical shapes of the ice crys- tals and their dependence on temperature. 135 The coalescence efficiency of water drops or ice crys- tals has not been theoretically evaluated and is deter- mined by experimental measurements. For water drops, the coalescence efficiencies of Whelpdale and List (1971) and Levin and Machnes (1977) are often used. These values vary from almost zero for interac- tions of large drops among themselves to a value close to unity for interactions of very small drops with large ones. The experiments on interaction of ice particles with water drops did not differentiate between collision and coalescence and only measured the end result such as collection (EWES or rebound teat - Ells (e.g., Auf- dermaur and Johnson, 1972, and some other works sum- marized by Pruppacher and Klett, 1978~. Aufdermaur and Johnson (1972) observed that rebound occurred on only about 1 percent of the impacting drops; this im- plied about a 99 percent collection. However, this ex- periment was conducted with a limited range of drop sizes and temperatures. Unfortunately, not enough in- formation is available on this parameter. The values of E3 are the least known, and a large range of values is usually tested in the models. To simplify things, some models do not use the de- tailed formulation of Em, E2, and E3, but rather combine theminto one parameter(P= EN - E2)E3.Therelax- ation time for charge transfer between the interacting particles, I, depends on their electrical conductivity. This conductivity, either surface (electrons) or bulk (ions), is temperature dependent. The relaxation time of ionic charge transfer of pure ice decreases from 6.8 X 10 ~ 3 see at - 10° C to 2.8 X 10 - 2 see at - 19° C (Sartor, 1970~. However, for slightly impure ice (doped with 3 X 10-6 M chloride, for example) this relaxation time will be shortened by two orders of magnitude but be- come more temperature dependent (Gross, 1982~. The relaxation time of charge transfer by surface electrons on the other hand is believed to be about 30 times shorter than bulk ions. It is therefore the surface electrons that are probably responsible for the transfer of charge dur- ing interactions of ice particles (Gross, 1982~. The contact time tc has been estimated to vary be- tween 10-4 to 10-6 see (Sartor, 1970; Caranti and I1- lingworth, 1980~. Therefore, the ratio tclr will vary with temperature by a few orders of magnitude. As the temperature decreases, the factor t1 - exp(- tclr)] in Eqs. (10.1) and (10.3) inhibits the charge transfer. For water drops, this factor is almost unity, because water has a higher conductivity than ice. CHARGING BY ION ATTACHMENT Attachment of ions to cloud particles can also charge them. Three kinds of mechanisms should be considered: ion diffusion, ion conduction, and ion convection. Dif
OCR for page 136
136 fusion of ions through air is a function of the tempera- ture and the sizes of the ion. At altitudes typical of thun- derstorms, negative ions have a diffusivity about 25-40 percent larger than that of positive ions. This would sug- gest that at the early stages of cloud development, when all other charge mechanisms are not effective, charge separation by ions would dominate. At later stages when the strength of the electric field increases, ions can be conducted to the cloud particles because of the electrical forces (ion conduction). At the same time ions can be transported toward the particles because of the relative velocities between them. Wilson (1929) pointed out that ions, which move because of the presence of the electrical forces and the air flow, selec- tively interact with cloud particles moving under the action of gravity and air flow (ion convection). This se- lective ion current depends on the fall speed of the parti- cle, its charge, and the magnitude and direction of the external electric field. The attachment of ions to cloud particles reduces their concentration and the electrical conductivity. Phillips (1967) calculated the electrical conductivity ex- isting in electrified clouds under a quasi-static situation. His calculations were based on the balance between the ion production from cosmic-ray ionization, the rate of ion loss from ion recombination, and ionic diffusion and conduction to cloud particles. Similar formulation was used by Griffithes et al. (1974) for calculating the elec- trical conductivity for three different cloud types cu- mulus congestus, strato-cumulus, and fog. They con- cluded that a decrease in conductivity of about 3 orders of magnitude occurred under highly electrified condi- tions. This decrease was found to be sensitive to varia- tions in the liquid-water content and the electrical field but only slightly affected by changes in altitude, particle charge, and the manner in which the charge is distrib- uted over the size spectrum. When a secondary source of ion production, resulting from corona currents emitted from ice particles under the influence of a strong electric field, was introduced into the calculations, a large in- crease in conductivity was predicted. The process of ion attachment to cloud particles con- tinues until enough charge is accumulated, at which point any additional charge can be quickly neutralized by attachment of ions of opposite charge. Some charge on the cloud particles often exceeds this saturation threshold value owing to charging by other mecha- nisms, so that within the main charge centers of the cloud ion attachments will generally act as discharge processes. When the cloud is electrified the conducting environ- ment reacts. Atmospheric ions that have the same polar- ity as the charge center within the cloud will be re ZEV LEVIN and ISRAEL TZUR pelted, while those with an opposite polarity will be conducted from the surroundings toward the cloud. The ions that enter through cloud boundaries are attached to cloud particles and generate a charged screening layer. This process was first recognized by Grenet (1947) and independently by Vonnegut (1955~. Brown et al. (1971) and Klett (1972) presented detailed calculations of the charge distribution and accumulation process in the screening layer. Recently it has been suggested (Wahlin, 1977) that negative ions not only have higher mobility than posi- tive ones but also have higher electrochemical affinity to surfaces and will rapidly attach to cloud particles. Therefore, negative ions that are brought, along with positive ions, into the cloud by an updraft, will prefer- entially attach to cloud particles near cloud base, leav- ing the free positive ions to be carried to cloud top. This mechanism also relies on falling precipitation particles and updraft for charge separation to occur. Without large precipitation particles falling with respect to the updraft, all the charges (negatively charged particles and positive free ions) would occupy the same volume and mask each other completely. However, this mecha- nism is probably too weak to produce strong fields dur- ing cloud development, since the ion concentration pro- duced by cosmic rays below the cloud base is too low to produce extensive charge separation (Wormell, 1953~. A mechanism that also relies on atmospheric ions for the charging but does not require gravitational settling of precipitation particles for charge separation, is the convective model proposed by Vonnegut (1955~. It de- pends on air currents to bring abundant positive ions from the ground up to cloud level. Cloud droplets that collect these ions at the cloud base carry them to the cloud top in the updrafts. The resulting region of posi- tive charge, according to Vonnegut, will preferentially attract negative ions from the free atmosphere above to form a screening layer at the cloud top. Downdrafts, produced by the vortex circulation of the air in the cloud, which is enhanced by the negatively buoyant air created by overshooting the thermal equilibrium point and by the evaporation of cloud particles at the cloud top, will transport the negative ions down to the cloud base, forming a vertical electrical dipole. Latham (1981) suggested that the convective mecha- nism plays only a minor role in the charging of thunder- storms because rates of ion production by cosmic rays are far too small to produce enough charge that can be separated and produce lightning. On the other hand, calculations by Martell (1984) suggested that the ion pair production over continental surfaces is greater than that produced by cosmic rays by more than an order of magnitude because of the decay of radioisotopes. If
OCR for page 137
MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS these calculations are confirmed experimentally, the IOOO relative contribution of the convective mechanism will have to be re-examined. SURVEY OF THEORETICAL MODELS Parallel-Plate Models Parallel-plate models are the simplest models of cloud electrification. They completely ignore the contribu tions of the air motions and focus on the microphysics. However, even in this area they consider only a small fraction of the microphysical processes that take place. To simplify things, they assume that any charge sepa rated in the charging volume is accumulated on two parallel plates, simulating the centers of the space charges in the cloud. Therefore, the models cannot pre dict the vertical structure of the charges in the cloud. The cloud is assumed to be composed of water drops alone, ice crystals with hail pellets, or a combination of them. The simplest of these models allows the particles to grow with time at preassigned rates (Mason, 1972), whereas the more detailed models allow the growth to proceed by semicontinuous (Ziv and Levin, 1974) or sto chastic interactions (Scott and Levin, 1975~. These models do not explicitly consider the effect of ions on the charging but assume discharge of particles (owing to at tachment of ions of opposite signs) that exponentially depends on the field. All these models tested the effec tiveness of the inductive process only. Mason (1972) and Sartor (1967) assumed that charge is separated by collisions of ice crystals and hail pellets. They concluded that the inductive process is a very pow erfu] one and is capable of separating enough charge for the field to reach a few kilovolts per centimeter in about 500-600 sec. Scott and Levin (1975), who treated the particle growth in more detail, concluded that the inductive process could account for the first lightning of a thun dercloud provided the electrical contact probability, E3, is greater than 0.1 (see Figure 10.2~. That is, of the cloud particles that do make contact and then rebound, about 10 percent need to separate charge in order for the process to be effective. For water drops, the value of the charge separation probability, which contains E3 in it, is thought actually to be lower than 0.1, thus making this process ineffective in producing enough charge separa tion. For ice-ice collisions, on the other hand, this effi ciency could be as high as 0.9. There is still great uncer tainty as to its value for water drops colliding with ice pellets. As mentioned before, the charge transferred per colli sion of ice particles should decrease with decreasing 137 500 100 - ' ' ' ' 1 ' ' ' ' I ' ' ' ' 1 ' ' - rF=40, E3 =1~ 1// ~0.3 _ E3 -0.8 111 / TF =54. E3=O.S / F<=ll93 E3 =0.1 / OF = 173, E3 =0.05 0 500 1000 1500 TIME (s) FIGURE 10.2 The growth of the electric field as a function of time under the inductive process with water drops only and calculated by the infinite cloud model of Scott and Levin (1975~. The different curves represent different values of E3, the electrical contact effi- ciency. The values of IF correspond to the time constants during the time of the maximum growth rate of the electric field. temperature. Ziv and Levin (1974) simulated this fea- ture for ice-ice collisions and found greatly diminished charge and field buildup. Other important factors determining the electrical development in clouds are the relative sizes of the collid- ing particles and the number of concentrations of the cloud elements. The first factor affects the charge that is separated per collision, since the charge transferred in- creases with increasing size of the rebounding particle. The second factor affects the number of collisions and, hence, the rate of charge (and field) buildup. When in- tense precipitation occurs (rates ~ 30 mm/in) the field can develop to large values with the inductive process only. However, for smaller precipitation rates (smaller particles and lower concentrations) it takes longer than the times set by the criteria above for the field to buildup.
OCR for page 138
138 One-Dimensional Models Illingworth and Latham (1975) correctly pointed out that horizontally infinite parallel-plate models overesti- mate the electric-field development because they lack a finite horizontal extent for the cloud. They constructed a simple one-dimensional model in which precipitation ice particles descended from the cloud top downward and interacted with smaller ice crystals (Illingworth and Latham, 1977~. During these interactions, charge was separated by either inductive or noninductive processes. The linear dependence of the charge separation in the noninductive process [Eq. (10.3~], and its independence of the ambient field, caused the field to grow early in a linear fashion (see Figure 10.3~. The inductive process, on the other hand, started later since it relies on the mag- nitude of the ambient field. Superposition of the two processes led to both a rapid linear field development in the early stages as a result of the noninductive process and a subsequent enhancement of the field owing to the inductive process. One of the important results of this 300 I00 30 10 1 1 1/ 1 / _ // 0 400 800 1200 1600 2000 t (s) FIGURE 10.3 The variation of the maximum field Em with time for the ice-ice noninductive charging mechanism (curve 1), the ice-ice in- ductive charging mechanism (curve 3), and the combined ice-ice mechanisms (curve 2). From Illingworth and Latham (1977~. ZEV LEVIN and ISRAEL TZUR simple model is its ability to predict the vertical dipole in the cloud and even the small positive pocket at cloud base. Tzur and Levin (1981) developed a much more de- tailed model that included a macroscale dynamical framework in one-and-a-half dimensions (height as an independent variable and a finite cloud radius with lat- eral mixing) and fully interactive microphysics of the precipitation development. Electrically the model treated in great detail free ions and their attachment to cloud particles and inductive and some noninductive processes with both ice and water, all in a time-depen- dent frame. From the results of the model Tzur and Levin concluded that charge separation in the liquid section of the cloud is not likely to be effective since the efficiency of bouncing and charge separation by water- water interaction is probably low. Similarly, collisions between ice particles and ice pellets in the absence of water droplets, either by the inductive or thermoelectric effects, namely, near the cloud top (temperatures ~ - 25°C), are not likely to contribute greatly to cloud electrification either tsee Figures 10.4(a) and 10.4(b)~. This is because of the small value of tilt at these temper- atures (Iow surface and bulk electrical conductivities in ice) . Also, at these altitudes the number of ice particles is relatively low, reducing the collision frequency and the charge separation. At higher temperatures (about -10°C or warmer) ice particles interact with both ice crystals and water droplets. From the model results, Tzur and Levin con- cluded that the collisions of the ice crystals with water drops, by a mechanism such as the Workman-Reynolds effect, are very effective charge separators isee Figure 10.4(c)] owing to the large concentration of water drop- lets as compared with that of ice. Comparison of Figures 10.4(a) and 10.4(c) shows that the charging rate by the inductive process changes rap- idly with time once charging starts. On the other hand, the charging rate by the noninductive mechanism is al- most constant with time, in agreement with the recent measurements by Krider and Musser (1982~. These mea- surements show that the total currents (Maxwell cur- rents) below electrified clouds remained fairly constant with time while at the same time the electric field in the cloud increased by a few orders of magnitude. Testing the inductive process revealed that very high fields and large charges can be produced only after 3000 see from cloud initiation isee Figure 10.5(a)] or about 20 min after precipitation particles appeared in reasonable concentration for radar detection. As in the case of the simpler model of Illingworth and Latham (1977), the noninductive process produced linear field develop- ment. However, as opposed to Illingworth and Latham
OCR for page 139
MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS 11 1O 91 8 _ 7 --3o I 6 ~ I 5 _-20 -lo O _ 4 3 2 _ 11: 10~ 9L TIC 7 _ ~ I 6 5 8 4 3 2 11 1O 9 8 _. 7 I 6 5 4 3 , . . . , _ INDUCTIVE CHARGING (a) _ DROPS - ICE _ 6XIo-llXlo-a(cm-35 T°C it_ o l - ~1 1 1 1 1 1 - I I I ~I I TllERMOELECTRIC EFFECT ~ b ~ _ 2.5 x 10-~3 x 1O-a ~ C m~3 5-1, -30 -20 -10 n ~~ _ WORKMAN-REYNOLDS EFFECT ( C) 7 x 10- 1 1 x 1O-a (C m~3 ~ I T.C --3o _ _-20 ~ ~x _ -10 _ O _ 2 _ - _ 1- , 1 , 1 , I , - 1000 2000 3000 TIME ( s) 139 (1977), who assumed that only ice-ice collisions separate charge, Tzur ant] Levin (1981) assumed that charge sep- aration by ice-ice collision is temperature dependent, and hence less effective than interactions of ice and wa- ter, which occur at warmer temperatures. Although the noninductive mechanism that they considered is the Workman-Reynolds process, any electrochemical pro- cess in which charge is separated by interaction of ice pellets and water droplets during riming is applicable to these calculations. Ions contributed only slightly to charge buildup, ei- ther by diffusion to charged particles or by conduction. Their contribution can be pronounced, on the other hand, in the early stages of the cloud buildup, when droplets are very small, and during rain below the cloud base. This latter charging of raindrops becomes signifi- cant when the field near the ground passes the threshold for corona discharge. During this stage the charge of raindrops can be greatly modified by attaching of oppo- sitely charged ions to them. A closer look at the charge structure produced by the noninductive process iFigure 10.5(a)] reveals that a "classical" dipole develops with a negative charge center at about - 8°C and with the main positive charge cen- ter at higher altitudes (about -18°C) (see Figure 10.5 at t = 2400 see). Large fields are already formed by 2500 see after cloud initiation (about 10 min after pre- cipitation particles appear), and with precipitation rates less than 20 mm/in. A positive charge pocket de- velops near the cloud base at temperatures warmer than O°C. On the other hand, the inductive process alone delays the field buildup for about 3000 sec. It produces the neg- ative charge center between about - 10 and - 20°C and the positive charge center still higher up at tempera- tures lower than - 20°C isee Figure 10.5(b)~. A positive pocket extending from the - 5°C isotherm to the cloud base is also found. This means that the noninductive mechanism produces space-charge centers at slightly lower altitudes, at earlier times, and with lower precipi- tation rates than does the inductive process. FIGURE 10.4 (a) The charging rate in coulombs per cubic meter per second by the ice-water inductive process as a function of height and times from Tzur and Levin (1981~. The value of each contour is 6 X 10- ~ x 10-~ with ax displayed near each one. Note that the charging rate rapidly varies with time and reaches a maximum value at about 3000 sec. (b) The charging rate by the ice-ice thermoelectric (nonin- ductive) effect. Note that the values of the contour are two orders of magnitude smaller than in (a). (c) The charging rate by the ice-water (noninductive) Workman-Reynolds effect. Note that the values of the contours are similar to those of (a). Also note that charging starts early and tends to remain fairly constant with time for most of the lifetime of electrical production.
OCR for page 140
40 10 1 1 1 1 DROP AND ICE CHARGE (a)_ + 4 x 10-9 x 1O-a ( C / ma ) NONINDUCTIVE PROCESSES _ 8 t T C 2.5_ ¢ E ~ ~o ~ '°r 9L 8 7 Y 6 I 5 llJ 3 1 1 1 1 1 1 DROPS AND ICE CHARGE (b) + 6 x 10 9 x 10 a ( C / ma ) INDUCTIVE PROCESS 3.5 ( All, (` " ~7 1000 2000 3000 4000 TIME (s) FIGURE 10.5 (a) The net charges in coulombs per cubic meter on cloud and precipitation particles (ice and water) resulting from the ice- water noninductive process, as a function of height and time, from Tzur and Levin (1981~. Solid lines represent net positive charges, and dashed lines represent net negative charges. The value of each contour is given by + 4 X 10 ~ 9 X 10 ~ ~ with ax displayed next to each one. Note that the maximum charges are produced around t = 2500 see with negative charge near - 10°C and positive charge around - 25°C. An- other small positive charge appears just below the 0°C level. (b) As in (a) except for the inductive (ice-water) process. Note the delay in the development of the space charges as compared with (a). A combination of the two processes produced strong field and space-charge distributions, which are almost a linear superposition of the two individual cases. Specifi- cally, a strong field develops early (t ~ 2500 see) but is enhanced later (t ~ 3000 see). Since the inductive pro- cess begins to operate when the field is stronger, a new space-charge center (negative charge) is produced at the ZEV LEVIN and ISRAEL TZUR cloud top. This charge center, as with all other charge centers, then descends as precipitation falls. At a partic- ular height it seems as if the charges switch signs with time. This implies that at this stage the inductive process is so effective that charged particles falling below a cer- tain space-charge volume are rapidly charged oppo- sitely owing to the reversal of the field direction below the charge center. Had the effectiveness of the inductive process been reduced, the charge centers might have spread out over a greater cloud depth and would have prevented the field reversal. One of the limitations, of course, of the one-dimen- sional, time-dependent models is their poor simulation of the air circulation within the cloud and the entrain- ment of air from the environment on the sides and top. Since in this model any mixing in of drier air, or detrain- ment of cloudy air, is immediately averaged over the entire layer of the cloud, it actually affects the whole cloud development in the model, as compared with na- ture, where relatively smaller effects are produced by mixing at cloud edges only. For a better simulation of these effects, two- or three-dimensional models are needed. Two-Dimensional Models Two-dimensional models have been developed to im- prove the simulation of the macroscale dynamics and its effect on the charge distribution and electrical develop- ment. Chin (1978) simulated a vortex-type thunderstorm in a two-dimensional, time-dependent axisymmetric mod- el. In his model, only water drops were considered, and charge was allowed to develop via the inductive process and ion attachment. Cloud microphysics was not dealt with in detail, and cloud water was converted to precipitation particles, of a preassigned distribution, by a parameterized formulation. In each time step in the model, the number of possible particle interactions was calculated based on known collision efficiencies. From it a net charge separation was derived. Simultaneously, ion attachment by diffusion and conduction was per- mitted to take place, and the total net charge at each At was found. Chiu's results also indicate that the inductive process could be a very effective charge separation mechanism, provided that large precipitation rates are present. The results also indicate the development of a vertical dipole of a proper "classical" polarity with an additional small positive space charge near the cloud base. As in the one-and-a-half-dimensional model of Tzur and Levin (1981) large charges and strong fields developed only after rain formed. The evolution of the horizontal electric field, with a maximum at 30 min. is
OCR for page 141
MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS RADIAL ELECTRIC FIELD ( V m~l) ' 1 ' I I l l l l l 7_2 ~ (a) 14min. _ ~ (b) 18 min. ~ ~ (c) 22 min. 6.4 _ 5.6 4.8 _ E 4.0 FIGURE 10.6 Evaluation of the radial elec- A trio field, from Chiu (1978). (a) At 14 min. 3.2 Contour interval is 2 V/m, and the range is - 14 to 0 V/m. (b) At 18 min. Contour inter- 2.4 vat is 10 V/m, and the range is - 70 to 30 V/ m. (c) At 22 min. Contour interval is 200 V/ I.6 m, and the range is - 1000 to 200 V/m. (d) At 26 min. Contour interval is 103 V/m, and the ° ~ range is ( - 4 - 2) X 103 V/m. (e) At 30 min. O Contour interval 2 X 103 V/m, and the range is -6to6 x 103V/m. shown in Figure 10.6. The effect of ions, either by diffu- sion in the early stages or by conduction at the later stages, was found to be relatively small and did not sig- nificantly alter the charging of the cloud. The entrain- ment of ions from cloud sides and tops did not greatly modify the electrical development. Heldson (1980) used the same model for a two-dimen- sional slab cloud and simulated the effect of artificial chaff seeding for the prevention of lightning. The intro- duction of chaff into the cloud creates centers for ion production by corona discharge as the electric-field strength approaches that needed for lightning. The results of the model suggest that the presence of excessive ions at this stage increases the cloud electrical conduc- tivity and enhances the discharge of the cloud particles. This in turn prevents the further buildup of the electric field and charges. The results of this model demonstrate one practical use for modeling of electrical processes in thunderclouds. Thunderstorms usually contain both water and ice. The models of both Chin and Heldson are therefore lim- ited since no ice formation was simulated even though the clouds in their models reached heights where ice is usually found. Kuettner et al. (1981) developed another two-dimen- sional model. Their model superposes a kinematic flow model, including cloud particle growth, on an electrical charge separation model. The cloud model uses either vortex or shear flow to simulate a steady-state flow con- figuration. Precipitation ice particles were introduced about 1 km above the cloud base and allowed to be moved with the airflow. During their ascent and de- scent they grew by collecting cloud droplets and sepa- rated charge through rebounding collisions of either wa , ~ 0 0.8 1.6 2.4 0 0.8 1.6 2` 141 M ... ~F JO 0 0.8 t.6 2.4 0 0.8 1.6 2.4 0 0.8 1.6 2.4 r (km) 1 1 1 ~ g,0 min.~ it_ 1~~o~ 411~\ \ \ 1' 1 \ 41 ~1_ - ~ 400 / ~ _ ~_ '0%, 1, I, ter droplets or small ice crystals. The model did not consider ion attachment or particle growth by conden- sation. Particle growth by collection was calculated with a constant probability of charge separation. The model also did not address the problem of entrainment or turbulent diffusion. However, the merit of this model is its relative simplicity and the capability of testing the electrical development under different airflow condi- tions such as those observed in the field. The results of this model point out that the noninductive process, in- corporating ice-water and to some extent ice-ice interac- tions with an average value of observed charge separa- tion per collision, can produce an electrical dipole at realistic altitudes but cannot enhance the field to a value comparable with the breakdown value. On the other hand, the inductive process, involving charge separation by ice-water interactions, produced very high fields but generated a very complex space- charge configuration. The complex field and space- charge structure arises as a consequence of the high effi- ciency with which the inductive process operates when large precipitation particles appear. As these large par- ticles descend through a space-charge center and be- come exposed to an electric field of opposite direction, their charge polarity reverses in response to the reversal of the electric field. Combination of the inductive with the noninductive mechanisms produced both a proper charge distribution and a rapid growth of the field. The results of Kuettner et al. (1981) suggest that charge separation processes in- volving ice-ice collisions are not very powerful, being limited by both the long relaxation time of the charge carriers and by the relatively low concentration of ice crystals (resulting in low collision rates). In addition, in
OCR for page 142
142 agreement with the other two-dimensional models, this model demonstrates that both strong horizontal and vertical fields can be produced by charge separation mechanisms that depend on precipitation. The horizon- tal fields are generated by horizontal displacement of the charged particles by the air circulation. Even under very weak shear conditions the space-charge centers were found to be displaced horizontally and produce very strong horizontal fields even close to the cloud base. The presence of the shear was found to smooth the de- velopment of the charge centers by limiting mixing of precipitation particles of opposite charges. Takahashi (1979) developed a two-dimensional, time-dependent mode! of a small warm cloud, which treats the microphysics and the macroscale dynamics in detail. Electrification due to the inductive mechanism and to ion attachment by diffusion and conduction is considered in a way that seems to explain the weak elec- trification of warm maritime clouds. The most impor- tant mechanism responsible for charging in such clouds, according to this model, is the attachment of ions to cloud and precipitation drops. This attachment is signif- icantly enhanced during condensation and evaporation. During the former, positive ions are preferentially in- corporated into the growing drops, whereas during evaporation negative ions are preferentially attached. In an attempt to evaluate the effectiveness of the con- vection electrification process, Ruhnke (1972) and Chiu and Klett (1976) developed two-dimensional, axisym- metric steady-state models. Ruhnke calculated the elec- tric fields and charges that arise from ion attachment to cloud water in solenoidal flow, intended to represent the flow in an isolated convective cloud. The actual cloud volume (where liquid water exists) was assumed to be spherical and to be entirely within the updraft. Space charge arises owing to local differences in electri- cal conductivity. These differences stem from attach- ment of ions to cloud particles (assumed to depend only on liquid-water content), which form ion currents con- sisting of both conduction and convection currents. By assigning a specific liquid-water content and a relation between it and ion conductivity, Ruhnke avoided deal- ing with interactions between ions and cloud droplets. The steady-state assumption precludes any detail of the initial development of the convective electrification. His results show that only very small fields can be devel- oped by this process. Chiu and Klett (1976) improved on this model by us- ing a more realistic convective circulation in which the updraft was within the cloud and the downdraft was at its edges. They also considered the effect of turbulent diffusion in addition to conduction and convection cur- rents on the transport of ions. Attachment of ions to ZEV LEVIN and ISRAEL TZUR cloud drops was affected by the liquid-water content and by the ambient electric field. Chiu and Klett's results show that convective electrification by itself can- not explain the strong electrification in thunderclouds. One should bear in mind that the terms that are highly variable with time such as the rate of charge buildup, especially at the later stages of thunderstorm develop- ment, are ignored in these steady-state models. In a fully developed time-dependent model, such terms may mod- ify the above conclusions. In addition, the dynamics used in the convective models is parameterized and may not be realistic enough to simulate the real convective charging process that is highly dependent on cloud dy- nam~cs. Three-Dimensional Models To date, only one three-dimensional, time-dependent model of an electrical cloud has been developed (Rawlins, 1982~. This model uses pressure as the vertical coordinate with grid spacings of 50 mbar vertically and 1 km horizontally. The microphysical parameterization of Kessler (1969) is used to describe the growth of cloud particles into precipitation size. Ice, initiated by ice nu- clei that freeze the supercooled water drops, is repre- sented by three size classes: 0-100,um, 100-200,um, and 200-300 ,um in radius. Hail is designated as ice greater than 300,um in radius, and it is forced to be distributed exponentially in size (Marshall and Palmer, 1948~. With this model Rawlins tested the effectiveness of various electrical processes, such as the inductive and the contact surface potential (noninductive) mecha- nisms. He assumed that ion attachment to cloud parti- cles can be ignored altogether. He concluded that the noninductive process is able to produce fields of high enough intensity to initiate lightning within about 20 min after precipitation begins. This process produced a "classical" dipole tsee Figure 10.7(a)] but without the small positive charge center closer to the cloud base. The inductive process, involving ice-ice collisions, was capable of producing strong fields only in the pres- ence of high concentrations of ice particles and only 30 min after precipitation particles appeared. With this process, a very complex space-charge structure emerged isee Figure 10.7(b)] as was also found by Kuettner et al. (1981~. Allowing ice crystals to rebound more than once from ice pellets reduced the calculated maximum field to below that needed for lightning "compare the values of E- in Figures 10.7(a) and 10.7(b)~. However, one should note that the same restriction of multiple collisions was not applied to Rawlins's calcula- tions of the noninductive process. Multiple collisions, if
OCR for page 143
MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS 400 600 700 A, 500 LL cr ~ 600 An I3J 700 (a) E SOD -50 0 50 -50 0 50 100 -200 0 200 Qp(C)Qc(C) Ez(kV m~l ) (b 400 _ I \T I I _ ~ -10 0 10-10 0 10 20 -50 0 50 Qp(C)Qc (C) Ez(kV m~') 1 FIGURE 10.7 The vertical distribution of space charges on precipi- tation, Qy, and cloud, Qc, particles and the vertical electric field, from Rawlins (1982~. (a) Ice-ice noninductive charging mechanisms after 36 min of cloud growth with charge separation per collision of Q = 10 fC. (b) Ice-ice inductive process after 44 min of cloud growth. Note the simple dipole structure and the intense field in (a) as compared with the more complex structure and weaker field in (b), implying the inef- fectiveness of the inductive process under the assumptions of this model. allowed for, will restrict charge transfer during particle collisions regardless of the process considered. DISCUSSION From this survey, it is clear that present models can describe both the electrical development and the growth of precipitation in some detail. An interesting common conclusion of all the models is the insensitivity of the results to small changes in free ion concentration or con- ductivity. These parameters do become important dur- ing the early stages of cloud development and below the cloud base during rain. They are probably also impor- tant just at the onset of lightning or immediately after 143 ward, but none of the models described here has dealt with this complex problem. The emergence of the more complex models of two or three dimensions provides a clear visualization of the ability of the precipitation charging mechanisms to pro- duce strong horizontal displacement of charges. These are often found in clouds and frequently lead to horizon- tal lightning strokes. It was shown that such numerical models could also be used to test the feasibility of pre- venting lightning by limiting the electric field growth. Multidimensional models can also greatly aid interpre- tation of the results of field experiments such as chaff dispersal in real clouds because they incorporate more realistic air circulations than do one-dimensional models. One of the main purposes of all the models discussed here is to test the various proposed mechanisms of charge separation in clouds. It seems that now that the models are capable of simulating the main features of the electrical charge separation in the cloud in a frame- work that combines air circulation and precipitation growth, however, reliable values for some of the various parameters are desperately needed. In particular, the electrical contact probabilities of the various particles (primarily ice with water and ice with ice), the coales- cence probabilities, the relaxation time of the charge carriers on ice as a function of temperature, and the length of time the particles actually make contact before rebounding are all essential, and not yet known, for evaluating the effectiveness of the various mechanisms. Such parameters can only be obtained by careful labo- ratory experiments. Despite the uncertainties in the values of the main pa- rameters involved in the precipitation processes of cloud electrification, it is still impressive to see that virtually all of the models appearing within the past 10 years, regardless of their complexity, agree that precipitation mechanisms can explain the main features observed in thunderclouds. They explain the presence of the space- charge centers at the proper altitudes and temperatures. They show that strong fields can be developed within 20 to 30 min of the appearance of precipitation in the cloud. Some show that noninductive charge separation processes teither ice-ice (Rawlins, 1982) or ice-water (Tzur and Levin, 1981~] can produce very strong fields with low precipitation rates as is sometimes observed in nature (Gaskell et al., 1978~. In addition results with noninductive processes show that the electric field grows linearly with time, as observed by Winn and Byerly (1975~. These results also agree with the recent measurements of Krider and Musser (1982), which sug- gest that the charging rates in thunderclouds are inde- pendent of the field and fairly constant with time iFig
OCR for page 144
144 ure 10.4(c)~. However, the observations of Williams and Lhermitte (1983) pointed out that the Musser and Kri- der results can also be explained by the convective charge transport. Their observations showed that fall- ing precipitation may not be the only cause for the elec- trification of thunderstorms. All the models agree that the inductive process requires higher precipitation rates in order to operate effectively. Some models show that the most effective method to produce strong fields is to let both inductive and noninductive mechanisms oper- ate simultaneously. While noninductive mechanisms can be powerful, particularly early in the development of the electric field, it is difficult to see how one can ignore the inductive process altogether. This process should operate in general whenever an ambient electric field is present. In some cases, it may discharge the par- ticles, while in others it will charge them, but it should always operate. If, on the other hand, its effectiveness is very low, as reported by Illingworth and Caranti (1984), it will not be felt in the cloud. Thus if a charge greater than that predicted by Eq. (10.1) is found on some of the particles (Christian et al., 1980), the induc- tive process should have discharged them. Since such charges were observed, it must be concluded that in these cases the inductive process did not effectively oper- ate. Most investigators seem to feel that charge separation through interactions among water drops only is not ef- fective since most collisions result in coalescence, thus limiting the possibilities for charge separation. Never- theless, laboratory experiments (Levin and Machnes, 1977; Beard et al., 1979) suggest that the coalescence efficiency is far from being understood, so the role of water-drop interactions should not yet be ignored com- pletely. Laboratory measurements of the surface potentials of ice under various growth conditions (Buser and Aufder- maur, 1977; Caranti and Illingworth, 1980) reveal the complexity of the charge-transfer problem. Again, ad- ditional experiments are needed to resolve the depen- dence of charge separation by this process on tempera- ture and on the strength of an external electric field. In spite of the fact that the numerical models thus far rule out convective electrification as an effective mecha- nism for producing strong fields by itself, it must be em- phasized that these models are only quasi-static and con- tain parameterized dynamics. To simulate this mechanism effectively, more detailed cloud dynamics, ion convection and conduction, and precipitation pro- cesses must be included. Thus far, no such model has been developed. Such a detailed model is urgently needed, especially following the recent experiments by Vonnegut et al. (1984) that reversed the polarity of a ZEV LEVIN and ISRAEL TZUR thundercloud by emitting negative ions from a long ca- ble electrified to 100 kV and suspended below the cloud. Their observations suggest that the negative ions pene- trated the cloud, ascended to the cloud top, and at- tracted positive ions from the free atmosphere above and were carried down by the air currents to the cloud base thus reversing the previous polarity of the cloud. If the ion concentration was too small to produce this effect, it is still possible that the additional ions changed the initial conditions of the cloud electrification, which led to the reversal in the cloud polarity. With the newly available data and faster computers we can look forward to a new generation of models in- corporating cloud microphysics and dynamics together with the convection and precipitation electrification mechanisms. REFERENCES Al-Saed, S. M., and C. P. R. Saunders (1976~. Electric charge transfer between colliding water drops, J. Geophys. Res. 81, 2650-2654. Aufdermaur, A. N., and D. A. Johnson (1972~. Charge separation due to riming in an electric field, Q. J. R. Meteorol. Soc. 98, 369-382. Beard, K. V., H. T. Ochs III, and T. S. Tung (1979~. A measurement of the efficiency for collection between cloud drops, J. Atmos. Sci. 36, 2479-2483. Brown, K. A., P. R. Krehbiel, C. B. Moore, and G. N. Sargent (1971~. Electrical screening layers around charged clouds, J. Geophys. Res. 76, 2825-2835. Buser, O., and A. N. Aufdermaur (1977~. Electrification by collisions 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, 44-46. Caranti, J. M., and A. J. Illingworth (1983~. Frequency dependence of the surface conductivity of ice, J. Phys. Chem. 87,4078-4083. Censor, D., and Z. Levin (1974). Electrostatic interaction of axisym- metric liquid and solid aerosols, Atmos. Environ. 8, 905-914. Chiu, C. S. (1978~. Numerical study of cloud electrification in an axi- symmetric liquid and solid aerosols, J. Geophys. Res. 83, 5025- 5049. Chiu, C. S., and J. N. Klett (1976~. Convective electrification of clouds,J. Geophys. Res. 81, 1111-1124. Christian, H., C. R. Holmes, J. W. Bullock, W. Gaskell, J. I1- lingworth, and J. Latham (1980~. Airborne and ground-based stud- ies of thunderstorms in the vicinity of Langmuir Laboratory, Q. J. R. Meteorol. Soc. 106,159-174. Col~ate, S. A., Z. Levin, and A. G. Petschek (1977~. Interpretation of thunderstorm charging by polarization induction mechanisms, J. Atmos. Sci. 34,1433-1443. Davis, M. H., and J. D. Sartor (1967~. Theoretical collision efficiencies for small cloud droplets in Stokes flow, Nature 215, 1371-1372. Gaskell, W., A. J. Illingworth, J. Latham, and C. B. Moore (1978). Airborne studies of electric fields and the charge and size of precipi- tation elements in thunderstorms, Q. J. R. Meteorol. Soc. 104, 447 - - 460. Grenet, G. (1947~. Essai d'explication de la charge electrique des nuages d'orages, Ann. Geo phys. 3, 306-310.
OCR for page 145
MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS Griffithes, R. F., J. Latham, and V. Myers (1974~. The ionic conduc- tivity of electrified clouds, Q. J. R. Meteorol. Soc. 100, 181-190. Gross, G. W. (1982~. Role of relaxation and contact times in charge separation during collision of precipitation particles with ice tar- gets, J. Geophys. Res. 87, 7170-7178. Heldson, J. H., Jr. (1980~. Chaff seeding effects in a dynamical-electri- cal cloud model, J. Appl. Meteorol. 19, 1101-1183. Illingworth, A. J., and C. M. Caranti (1984~. Ice conductivity re- straints on the inductive theory of thunderstorm electrification, in Conference Proceedings, VII International Conference on Atmo- spheric Electricity, American Meteorological Society, Boston, Mass., pp. 196-201. Illingworth, A. J. and J. Latham (1975). Calculations of electric field growth within a cloud of finite dimensions, J. Atmos. Sci. 32, 2206- 2209. Illingworth, A. J., and J. Latham (1977~. Calculations of electric field growth, field structure and charge distributions in thunderstorms, Q. J. R. Meteorol. Soc. 103, 231-295. Kessler, E. (1969~. On the Distribution and Continuity of Water Sub- stance in Atmospheric Circulation, Meteorol. Monogr. Vol. 10, No. 32, American Meteorological Soc., Boston, Mass., 84 pp. Klett, J. D. (1972~. Charge screening layers around electrified clouds, J. Geophys. Res. 77, 3187-3195. Krehbiel, P. R., M. Brook, and R. A. McCrory (1979~. An analysis of the charge structure of lightning discharges to ground, J. Geophys. Res. 84, 2432-2456. Krider, E. P., and J. A. Musser (1982~. Maxwell currents under thun- derstorms,J. Geophys. Res. 87,11171-11176. Kuettner, J., Z. Levin, and J. D. Sartor (1981~. Inductive or noninduc- tive thunderstorms electrification, J. Atmos. Sci. 38, 2470-2484. Lane-Smith, D. R. (1971~. A warm thunderstorm, Q. J. R. Meteorol. Soc. 97, 577-578. Latham, J. (1981~. The electrification of thunderstorms, Q. J. R. Me- teorol. Soc. 107, 277-298. Latham, J., and B. J. Mason (1961). Generation of electric charge associated with the formation of soft hail in thunderclouds, Proc. R. Soc. London A260, 537-549. Latham, J., and R. Warwicker (1980~. Charge transfer accompanying the splashing of supercooled raindrops on hailstones, Q. J. R. Me- teorol. Soc. 106, 559-568. Levin, Z., and B. Machnes (1977~. Experimental evaluation of the coalescence efficiencies of colliding water drops, Pure Appl. Geophys. 115, 845-867. Marshall, J. S., and W. M. K. Palmer (1948~. The distribution of rain- drops with size, J. Meteorol. 5, 165-166. Martell, E. A. (1984~. Ion pair production in convective storms by radon and its radioactive decay products, in Conference Proceed- ings, VII International Conference on Atmospheric Electricity, American Meteorological Society, Boston, Mass., pp. 67-71. Mason, B. J. (1971~. The Physics of Clouds, Oxford Univ. Press, Cam- bridge, 671 pp. Mason, B. J. (1972~. The physics of thunderstorms, Proc. R. Soc. Lon- don A327, 433-466. Phillips, B. B. (1967~. Ionic equilibrium and the electrical conductiv- ity in thunderclouds, Mon. Weather Rev. 95, 854-862. Pruppacher, H. R., and J. D. Klett (1978~. Microphysics of Clouds and Precipitation, Reidel, Dordrecht, 714 pp. ]45 Pruppacher, H. R., E. H. Steinberger, and T. L. Want (1968). On the electrical effects that accompany the spontaneous growth of ice in supercooled aqueous solutions, J. Geophys. Res. 73, 571-584. Rawlins, F. (1982). A numerical study of thunderstorm electrification using a three dimensional model incorporating the ice phase, Q. J. R. Meteorol. Soc. 108, 778-880. Reynolds, S. E., M. Brook, and M. F. Gourley (1957~. Thunderstorm charge separation, J. Meteorol. 14, 426-436. Ruhnke, L. H. (1972~. Atmospheric electron cloud modeling, Me- teorol. Res. 25, 38-41. Sartor, J. D. (1967). The role of particle interactions in the distribution of electricity in thunderstorms, J. Atmos. Sci. 24, 601-615. Sartor, J. D. (1970~. General Thunderstorm Electrification, National Center for Atmospheric Research, Boulder, Colo., p. 99. Schewchuk, S. R., and J. V. Iribarne (1971~. Charge separation dur- ing splashing of large drops on ice, Q. J. R. Meteorol. Soc. 97, 272- 282. Scott, W. D., and Z. Levin (1975~. Stochastic electrical model of an infinite cloud charge generation and precipitation development, J. Atmos. Sci. 32,1814-1828. Takahashi, T. (1978). Riming electrification as a charge generation mechanism in thunderstorms, J. Atmos. Sci. 35, 1536-1548. Takahashi, T. (1979~. Warm cloud electricity in a shallow axisymmet- ric cloud model, J. Atmos. Sci. 31, 2236-2258. Tzur, I., and Z. Levin (1981). Ions and precipitation charging in warm and cold clouds as simulated in one dimensional time-depen- dent models, J. Atmos. Sci. 38, 2444-2461. Vonnegut, B. (1955~. Possible mechanism for the formation of thun- derstorms electricity, in Proceedings International Conference At- mospheric Electricity, Geophys. Res. Paper No. 42, Air Force Cam- bridge Research Center, Bedford, Mass., p. 169. Vonnegut, B., C. B. Moore, T. Rolan, J. Cobb, D. N. Holden, S. McWilliams, and G. Cadwell (1984~. Inverted electrification in thunderclouds growing over a source of negative charge, EOS 65, 839. Wahlin, L. (1977~. Electrochemical charge separation in clouds, in Electrical Processes in Atmospheres, H. Dolezalek, and R. Reiter, eds., Steinkopff, Darmstadt, p. 384. Weickmann, H. K., and J. J. Aufm Kampe (19SOj. Preliminary exper- imental results concerning charge generation in thunderstorms con- current with the formation of hailstones, J. Meteorol. 7, 404-405. Whelpdale, D. M., and R. List (1971). The coalescence process in rain drop growth, J. Geophys. Res. 76, 2836-2856. Williams, E. R., and R. M. Lhermitte (1983). Radar tests of the pre- cipitation hypothesis for thunderstorm electrification, J. Geophys. Res. 88, 10984-10992. Wilson, C. T. R. (1929~. Some thundercloud problems, J. Franklin Inst. 208, 1-12. Winn, W. P., and L. G. Byerly III (1975~. Electric field growth in thunderclouds, Q. J. R. Meteorol. Soc. 101, 979-994. Workman, E. J., and S. E. Reynolds (1948). Suggested mechanism for the generation of thunderstorm electricity, Phys. Rev. 74, 709. Wormell, T. W. (1953~. Atmospheric Electricity: Some recent trends and problems, Q. J. R. Meteorol. Soc. 79, 3. Ziv, A., and Z. Levin (1974~. Thundercloud electrification cloud growth and electrical development, J. Atmos. Sci. 31, 1652-1661.
OCR for page 146
OCR for page 147
III GLOBAL AND REGIONAL ELECTRICAL PROCESSES
OCR for page 148
Representative terms from entire chapter: