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MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS 135 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 10â14 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) observed that a surface potential develops during riming of supercooled water droplets on ice. This surface potential increases steadily with decreasing temperature down to â 10Â°C and remains constant to â 25Â°C. Caranti and Illingworth (1980) also observed that impurities, such as NH4OH, NaCl, or HF, made no detectable 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 noninductive processes can be expressed as in Eq. (10.1), except that âQ has the form 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 10â15 to about 10â14 C per collision, depending on the type and size of the particles and on temperature (Takahashi, 1978). Owing to the lack of comprehensive data about the charge transfer 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 depends on the interaction probabilities E 1 , E 2 , and E3 and on the ratio tc/Ï. In the models, the values of E1 , E 2 , and E 3 have to be specified. A detailed discussion of the probabilities and the way they are calculated and measured is beyond the scope of this paper. The interested reader is referred to Pruppacher and Klett (1978, Chapter 14) for details. The collision efficiency E 1 of water drops used in the numerical models is based on calculations of particle trajectories (e.g., Davis and Sartor, 1967). A few calculations 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 crystals and their dependence on temperature. The coalescence efficiency of water drops or ice crystals has not been theoretically evaluated and is determined 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 interactions 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 (E 1 E2 ) or rebound [E 1 (1 â E 1 )] (e.g., Aufdermaur and Johnson, 1972, and some other works summarized by Pruppacher and Klett, 1978). Aufdermaur and Johnson (1972) observed that rebound occurred on only about 1 percent of the impacting drops; this implied about a 99 percent collection. However, this experiment was conducted with a limited range of drop sizes and temperatures. Unfortunately, not enough information is available on this parameter. The values of E 3 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 detailed formulation of E1 , E 2 , and E 3 , but rather combine them into one parameter (P = E1 (1 â E2 ) E3. The relaxation time for charge transfer between the interacting particles, Ï, 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 Ã 10â3 sec at â 10Â°C to 2.8 Ã 10â2 sec at â 19Â°C (Sartor, 1970). However, for slightly impure ice (doped with 3 Ã 10â6 M chloride, for example) this relaxation time will be shortened by two orders of magnitude but become 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 during interactions of ice particles (Gross, 1982). The contact time tc has been estimated to vary between 10â4 to 10â6 sec (Sartor, 1970; Caranti and Illingworth, 1980). Therefore, the ratio tc /Ï will vary with temperature by a few orders of magnitude. As the temperature decreases, the factor [1 â exp (â t c /Ï)] 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
MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS 136 fusion of ions through air is a function of the temperature and the sizes of the ion. At altitudes typical of thunderstorms, negative ions have a diffusivity about 25-40 percent larger than that of positive ions. This would suggest 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, selectively interact with cloud particles moving under the action of gravity and air flow (ion convection). This selective ion current depends on the fall speed of the particle, 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 existing 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 electrical conductivity for three different cloud typesâcumulus congestus, stratocumulus, and fog. They concluded that a decrease in conductivity of about 3 orders of magnitude occurred under highly electrified conditions. This decrease was found to be sensitive to variations 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 distributed 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 increase in conductivity was predicted. The process of ion attachment to cloud particles continues 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 mechanisms, 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 environment reacts. Atmospheric ions that have the same polarity as the charge center within the cloud will be repelled, 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 positive 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 preferentially attach to cloud particles near cloud base, leaving 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 mechanism is probably too weak to produce strong fields during cloud development, since the ion concentration produced 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 depends 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 positive 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 mechanism plays only a minor role in the charging of thunderstorms 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