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MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS 137 these calculations are confirmed experimentally, the 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 contributions 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 separated in the charging volume is accumulated on two parallel plates, simulating the centers of the space charges in the cloud. Therefore, the models cannot predict 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 stochastic 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 attachment of ions of opposite signs) that exponentially depends on the field. All these models tested the effectiveness 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 powerful 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 thundercloud 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 separation. For ice-ice collisions, on the other hand, this efficiency could be as high as 0.9. There is still great uncertainty as to its value for water drops colliding with ice pellets. As mentioned before, the charge transferred per collision of ice particles should decrease with decreasing temperature. Ziv and Levin (1974) simulated this feature for ice-ice collisions and found greatly diminished charge and field buildup. 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 efficiency. The values of ÏF correspond to the time constants during the time of the maximum growth rate of the electric field. Other important factors determining the electrical development in clouds are the relative sizes of the colliding 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 increases 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 intense precipitation occurs (rates > 30 mm/h) 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.