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MODELS OF THE DEVELOPMENT OF THE ELECTRICAL STRUCTURE OF CLOUDS 143 allowed for, will restrict charge transfer during particle collisions regardless of the process considered. Figure 10.7 The vertical distribution of space charges on precipitation, Qp, 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 ineffectiveness of the inductive process under the assumptions of this model. 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 conductivity. These parameters do become important during the early stages of cloud development and below the cloud base during rain. They are probably also important just at the onset of lightning or immediately afterward, 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 produce strong horizontal displacement of charges. These are often found in clouds and frequently lead to horizontal lightning strokes. It was shown that such numerical models could also be used to test the feasibility of preventing lightning by limiting the electric field growth. Multidimensional models can also greatly aid interpretation 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 framework that combines air circulation and precipitation growth, however, reliable values for some of the various parameters are desparately needed. In particular, the electrical contact probabilities of the various particles (primarily ice with water and ice with ice), the coalescence 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 laboratory experiments. Despite the uncertainties in the values of the main parameters 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 [either 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 suggest that the charging rates in thunderclouds are independent of the field and fairly constant with time [Fig