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MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS 138 One-Dimensional Models Illingworth and Latham (1975) correctly pointed out that horizontally infinite parallel-plate models overestimate 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 magnitude 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 simple model is its ability to predict the vertical dipole in the cloud and even the small positive pocket at cloud base. Figure 10.3 The variation of the maximum field E m with time for the ice-ice noninductive charging mechanism (curve 1), the ice-ice inductive charging mechanism (curve 3), and the combined ice-ice mechanisms (curve 2). From Illingworth and Latham (1977). Tzur and Levin (1981) developed a much more detailed model that included a macroscale dynamical framework in one-and-a-half dimensions (height as an independent variable and a finite cloud radius with lateral 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-dependent 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 < â 25Â°C), are not likely to contribute greatly to cloud electrification either [see Figures 10.4(a) and 10.4(b)]. This is because of the small value of t c/Ï at these temperatures (low 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 â 10Â°C or warmer) ice particles interact with both ice crystals and water droplets. From the model results, Tzur and Levin concluded that the collisions of the ice crystals with water drops, by a mechanism such as the Workman-Reynolds effect, are very effective charge separators [see Figure 10.4(c)] owing to the large concentration of water droplets 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 rapidly with time once charging starts. On the other hand, the charging rate by the noninductive mechanism is almost constant with time, in agreement with the recent measurements by Krider and Musser (1982). These measurements show that the total currents (Maxwell currents) 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 sec from cloud initiation [see 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 development. However, as opposed to Illingworth and Latham
MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS 139 (1977), who assumed that only ice-ice collisions separate charge, Tzur and Levin (1981) assumed that charge separation by ice-ice collision is temperature dependent, and hence less effective than interactions of ice and water, which occur at warmer temperatures. Although the noninductive mechanism that they considered is the Workman- Reynolds process, any electrochemical process in which charge is separated by interaction of ice pellets and water droplets during riming is applicable to these calculations. Figure 10.4 (a) The charging rate in coulombs per cubic meter per secondby the ice-water inductive process as a function of height and time, from Tzur and Levin (1981). The value of each contour is 6 Ã 10â11 Ã 10âÏ with Î± 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 (noninductive) 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. Ions contributed only slightly to charge buildup, either 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 significant 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 oppositely charged ions to them. A closer look at the charge structure produced by the noninductive process [Figure 10.5(a)] reveals that a "classical" dipole develops with a negative charge center at about â 8Â°C and with the main positive charge center at higher altitudes (about â 18Â°C) (see Figure 10.5 at t = 2400 sec). Large fields are already formed by 2500 sec after cloud initiation (about 10 min after precipitation particles appear), and with precipitation rates less than 20 mm/h. A positive charge pocket develops near the cloud base at temperatures warmer than 0Â°C. On the other hand, the inductive process alone delays the field buildup for about 3000 sec. It produces the negative charge center between about â 10 and â 20Â°C and the positive charge center still higher up at temperatures lower than â 20Â°C [see Figure 10.5(b)]. A positive pocket extending from the â 5Â°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 precipitation rates than does the inductive process.