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ACOUSTIC RADIATIONS FROM LIGHTNING 51 the acoustic waves from the extended line source can no longer catch up with the shock wave. Somewhere in this mesotortuous range the divergence of the shock waves makes the transition from cylindrical to spherical. Whereas the mesotortuous channel segments are important in the formation and shaping of the individual pulses being emitted by the channel the macrotortuous segments are fundamental to the overall organization of the pulses and the amplitude modulation of the resulting thunder signature. Few (1974a) computed that 80 percent of the acoustic energy from a short spark was confined to within Â± 30Â° of the plane perpendicular to the short line source. A macrotortuous segment of a lightning channel will direct the acoustic radiations from its constituent mesotortuous, pulse-emitting segments into a limited annular zone. An observer located in this zone (near the perpendicular plane bisecting the macrotortuous segment) will perceive the group of pulses as a loud clap of thunder, whereas another observer outside the zone will perceive this same source as a lower-amplitude rumbling thunder. This relationship between claps, rumbles, and channel macrotortuosity has been confirmed by experiment (Few, 1970) and in computer simulations (Ribner and Roy, 1982). Loud claps of thunder are produced, as mentioned above, near the perpendicular plane of macrotortuous channel segments; there are three contributary effects (Few, 1974a, 1975) to the formation of the thunder claps. The directed acoustic radiation pattern described above is one of the contributing factors, and this effect is distributed roughly between Â± 30Â° of the plane. A second effect, which occurs only very close to the plane, is the juxtaposition of several pulses in phase, which increases the pulse amplitude to a greater extent than would a random arrival of the same pulses. The third effect contributing to thunder clap formation is simply the bunching in time of the pulses. In a given period of time more pulses will be received from a nearly perpendicular macrotortuous segment of channel than from an equally long segment that is perceived at a greater angle owing to the overall difference in the travel times of the composite pulses. In this section we have examined the complex nature of the formation of individual pulses from hot lightning channels and how a tortuous line source arranges and directs the pulses to form a thunder signature. The resulting thunder signature depends on (1) the number and energy of each rapid channel heating event (leaders and return strokes); (2) the tortuous and branched configuration of the individual lightning channel; and (3) the relative position of the observer with respect to the lightning channel. Perhaps the most convincing discussion of thunder generation as described above comes not from analytical evidence but from research using sophisticated computer models of thunder. Ribner and Roy (1982) synthesized thunderlike acoustic signals utilizing computer-generated waves formed by the superposition of N wavelets from tortuous geometric sources. The resulting "thunder" is highly similar to natural thunder (see Figures 4.8 and 4.9). Where the computer models are used to simulate laboratory experiments, there is also close agreement. PROPAGATION EFFECTS Once generated, the acoustic pulses from the lightning channel must propagate for long distances through the atmosphere, which is a nonhomogeneous, anisotropic, turbulent medium. Some of the propagation effects can be estimated by modeling the propagation using appropriate simplifying assumptions; however, other effects are too unpredictable to be reasonably modeled and must be considered in individual situations. Three of the largest propagation effectsâfinite-amplitude propagation, attenuation by air, and thermal refraction âcan be treated with appropriate models to account for average atmosphere effects. Reflections from the flat ground can also be easily treated. Once the horizontal wind structure between the source and the receiver are measured, the refractive effects of wind shear and improved transient times may also be calculated. Beyond effects, elements such as vertical Figure 4.8 Schematic depiction of the synthetic generation of thunder by computer by the superimposition (upper trace) of N wavelets from a tortuous line source (Ribner and Roy, 1982); the summed signal is shown on the lower trace.