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MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS 140 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 Â± 4 Ã 10â9 Ã 10âÎ± with a displayed next to each one. Note that the maximum charges are produced around t = 2500 sec with negative charge near â 10Â°C and positive charge around â 25Â°C. Another small positive charge appears just below the 0Â°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. Specifically, a strong field develops early (t ~ 2500 sec) but is enhanced later (t ~ 3000 sec). Since the inductive process begins to operate when the field is stronger, a new space- charge center (negative charge) is produced at the cloud top. This charge center, as with all other charge centers, then descends as precipitation falls. At a particular 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 certain space-charge volume are rapidly charged oppositely 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-dimensional, time-dependent models is their poor simulation of the air circulation within the cloud and the entrainment of air from the environment on the sides and top. Since in this model any mixing in of drier air, or detrainment 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 nature, 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 improve the simulation of the macroscale dynamics and its effect on the charge distribution and electrical development. Chiu (1978) simulated a vortex-type thunderstorm in a two-dimensional, time-dependent axisymmetric model. 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 permitted to take place, and the total net charge at each ât 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
MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS 141 shown in Figure 10.6. The effect of ions, either by diffusion in the early stages or by conduction at the later stages, was found to be relatively small and did not significantly alter the charging of the cloud. The entrainment of ions from cloud sides and tops did not greatly modify the electrical development. Figure 10.6 Evaluation of the radial electric field, from Chiu (1978). (a) At 14 min. Contour interval is 2 V/m, and the range is â 14 to 0 V/m. (b) At 18 min. Contour interval is 10 V/m, and the range is â 70 to 30 V/m. (c) At 22 min. Contour interval is 200 V/m, and the range is â 1000 to 200 V/m. (d) At 26 min. Contour interval is 103 V/m, and the range is (â4 â2) Ã 103 V/m. (e) At 30 min. Contour interval 2 Ã 103 V/m, and the range is â6 to 6 Ã 103 V/m. Heldson (1980) used the same model for a two-dimensional slab cloud and simulated the effect of artificial chaff seeding for the prevention of lightning. The introduction 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 conductivity 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 Chiu and Heldson are therefore limited 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-dimensional 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 configuration. Precipitation ice particles were introduced about 1 km above the cloud base and allowed to be moved with the airflow. During their ascent and descent they grew by collecting cloud droplets and separated charge through rebounding collisions of either water droplets or small ice crystals. The model did not consider ion attachment or particle growth by condensation. 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 conditions such as those observed in the field. The results of this model point out that the noninductive process, incorporating ice-water and to some extent ice-ice interactions with an average value of observed charge separation 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 efficiency with which the inductive process operates when large precipitation particles appear. As these large particles descend through a space-charge center and become 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 involving 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