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CHARGING MECHANISMS IN CLOUDS AND THUNDERSTORMS 117 is Ï_B_E, and the current from convection is U, where Ï = Ï+ â Ï-is the space charge. (The value of Ï-is approximately one half the small ion concentration, beneath cloud base, times a unit charge.) The ratio of drift to convection is 7.5 (using the values for Ï, n, and E on Figure 9.1 at 1 km and B-= 2.2 Ã 10-4 m2/V sec and U = 1 m/sec) clearly showing the dominance in the drift of negative ions into cloud base over the upward convection of positive space charge. The ratio decreases as the cloud base is lowered and is less than unity for bases below about 300 m. The calculations of Chiu and Klett for a cloud base at 10 m show the dominance of convective transport of positive space charge over drift into cloud base. They found a positive core, but drift still dominated the charging process in the upper cloud with positive charges at cloud edges similar to Figure 9.2c. Thus, for the majority of cases in the cloud stage, drift charging is the most significant electrification mechanism. Convection and eddy diffusion in the single-cell pattern investigated by Chiu and Klett generally weaken electrification by redistributing and mixing the drift-generated charge. The charge acquired by droplets in the cloud stage has been from diffusion of ions within the cloud and drift charge at cloud edge. Selective Ion Charging When equal numbers of positive and negative ions are present there can be a preferred attachment of one sign if the droplet is polarized (Wilson effect). The governing equation for the microscale transport [given by Eq. (9.1)] has two classes of solutions (Whipple and Chalmers, 1944). In the case of "fast ions" the downward drift of positive ions exceeds the fall speed of the droplet (B + E > U) and ions of both signs are captured at nearly the same rate (Figure 9.3a). The droplet size where B + E = U in the lowest few kilometers is R = 1 Âµm for E = 10 V/m. Since most droplets in shallow cumulus clouds are larger than 4 Âµm, ions are captured selectively by the Wilson effect. Larger droplets will acquire a negative charge by the preferential attraction of negative ions, as shown in Figure 9.3b for the "slow ion" case (B+ E < U). The maximum charge acquired by droplets for the Wilson effect is This is only one sixth the diffusion charge from the drift current given by Eq. (9.5) and yields a negative charge equivalent to 36 electrons for the largest cloud droplets (R = 100 Âµm) and a downward directed field of 10 V/m. Figure 9.3 Selective ion capture from droplet polarization in a downward-directed field (Wilson effect): a, fast-ion case B + E > U); b, slow-ion case (B + E < U) with trajectories given by dashed curves. Thus the largest cloud droplets are charged for the Wilson effect to a magnitude of about the rms Boltzmann charge. In our cumulus scenario the cloud is only about 1 km deep with a central updraft speed of 1 to 2 m/sec; therefore the small drops that we are considering are carried upward. When the cloud depth increases to about 3 km, drops become large enough to be detected by radar. This is a common circumstance for summer cumulus clouds in mid- latitudes. The cloud top would lie below the level where droplets readily freeze except over elevated terrain or in a more northern climate. The drops associated with the initial radar echo are still quite small and unable to fall out of the cloud. However, we consider the time of the first radar echo as the beginning of the rain stage. In the following section we examine the charging mechanisms associated with drizzle drops and raindrops: selective ion charging, breakup charging, and induction charging. RAIN STAGE Selective Ion Charging When we make the transition to the new stage, microscale separation of charge becomes more powerful because of the R 2 dependence of charge captured by polarized drops [Eqs. (9.5) and (9.6)]. As the drizzle drops begin moving downward in the cloud a larger scale separation of charge can result as drizzle drops capture neg