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ACOUSTIC RADIATIONS FROM LIGHTNING 58 tion of errors associated with such points. Most of the recent thunder research has used a combination of ranging and ray tracing. The whole-storm studies in which an extended series of channels are reconstructed have proven to be the most valuable use of thunder data to date. They define the volume of the cloud actually producing lightning, the evolution of the lightning-producing volume with time, and the relationship of individual channels with other cloud observations such as radar reflectivity and environmental winds (Nakano, 1973; Few, 1974b; Teer and Few, 1974; Few et al., 1977, 1978; MacGorman and Few, 1978; MacGorman et al., 1981). ELECTROSTATICALLY PRODUCED ACOUSTIC EMISSIONS The concept of electrostatically produced acoustic waves from thunderclouds goes all the way back to the writings of Benjamin Franklin in the eighteenth century; Wilson (1920) provided a rough quantitative estimate of the magnitude of the electrostatically produced pressure wave. McGehee (1964) and Dessler (1973) developed quantitative models for this phenomenonâMcGehee for spherical symmetry and Dessler for spherical, cylindrical, and disk symmetries. The theory developed by Dessler is of particular importance because it made specific predictions regarding the directivity and shape of the wave. The predictions were subsequently verified in part by Bohannon et al. (1977) and Balachandran (1979, 1983). The charge in a thundercloud resides principally on the cloud drops and droplets. In a region of the cloud where the charge is concentrated producing an electric field E, the charged particles will experience an electric force, which is directed outward with respect to the charge center, in addition to the other forces expressed on them. These particles quickly (on the order fo milli Figure 4.11 Low-frequency acoustic pulse thought to have been generated by an electrostatic pressure change inside the cloud during a lightning flash. The higher-frequency signals from thunder have been removed from this record. From Balachandran (1979) with permission of the American Geophysical Union.