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PHYSICS OF LIGHTNING 36 measure a dE/dt signature on a 10-nsec time scale, it is essential that the field propagation from the lightning source to the measuring station be entirely over saltwater; otherwise there can be a significant degradation in the high-frequency content of the signal due to propagation over the relatively poorly conducting earth. It is possible that strikes to saltwater contain inherently faster rise times than lightning strikes to ground, but Weidman and Krider (1978) argued that this is probably not the case. If Eq. (2.1) is valid, then the dE/dt values in Figure 2.8 can be used to infer the maximum dI/dt in the lightning channel, i.e., If a typical dE/dt is 33 V/m/Âµsec at 100 km and Ï is 108 m/sec, then Eq. (2.2) implies that the maximum dI/dt is typically 1.5 Ã 1011 A/sec during a return stroke, a value that is about a factor of 20 higher than the tower measurements. At this point, it should be noted that, if return strokes do contain large current components with dI/dt on the order of 1.5 Ã 1011 A/sec, then, if these currents interact with an inductive load, the overvoltage will be substantially larger and faster than has previously been assumed and the lightning hazard will be greater. (See Chapter 5, this volume, for further discussions of lightning protection.) As a final point, we note that the electromagnetic fields that are produced by lightning are now known to be large and to change rapidly; hence, these fields themselves can be deleterious. For example, Uman et al. (1982) showed that, if an object is struck directly by lightning, then the associated electromagnetic disturbance may be substantially more severe than the electromagnetic pulse (EMP) produced by an exoatmospheric nuclear burst at all frequencies below about 10 MHz. Also, Krider and Guo (1983) showed that the typical peak field from a return-stroke at 100 km corresponds to a peak electromagnetic power at the source of at least 20,000 megawatts. Locations of Lightning Radio Sources The radio-frequency noise that is generated by lightning in the HF and VHF bands appears in the form of discrete bursts, and within each of these bursts there are hundreds to thousands of separate pulses. If the difference in the time of arrival of each pulse is carefully measured at four widely separated stations, the location of the source of each pulse can be computed, and the geometrical development of the rf bursts can be mapped as a function of time (Proctor, 1971). Unfortunately, the physical processes that produce HF and VHF radiation in lightning are not well understood. Proctor (1981) reported that the pulses in most bursts are produced by a regular progression of source points, and, therefore, he suggests that bursts are produced by new ionization processes and extensions of old channels. If the source location of each rf pulse within a burst is plotted, the width of the associated "radio image" of the channel ranges from about 100 m to more than 1 km (Proctor, 1981, 1983; Rustan et al., 1980). Figure 2.9 shows the paths of the central cores of six successive lightning discharges that were reconstructed by Proctor (1983). By combining reconstructions such as these with measurements of the associated changes in the electric field at the ground, Proctor inferred that in-cloud channels usually have a net negative charge and that the average line charge density is about 0.9 C/km. Also, by dividing the length of a channel segment by the time required for that portion to develop, Proctor determined that the average velocity of streamer formation ranges from 4 Ã 104 m/sec to 8 Ã 105 m/ sec with a mean of (1.4 Â± 1.2) Ã 105 m/sec. If Proctor's average charge density is multiplied by the velocity of channel formation, then the average current in developing channels would appear to be on the order of 100 A, a value that is in reasonable agreement with other estimates (Brook and Ogawa, 1977). In an analysis of the locations of the first rf sources in 26 lightning flashes, Proctor (1983) found that most discharges begin within or near precipitation, i.e., those regions of the cloud that produce a radar reflectivity greater than 25 dBZ. He also reports that all stepped-leaders begin in a narrow range of altitudes where the ambient air temperature is â5 to â16Â°C. The average altitude of the initial rf sources in the flashes studied by Proctor was about 4 km above ground level (â10Â°C), and the standard deviation was only 440 m. The geometrical forms of intracloud discharges range from concentrated "knots" or "stars" a few kilometers in diameter to extensive branched patterns up to 90 km in length. Proctor (1983) reports that successive discharges in a storm often form an interconnected system and that some flashes seem to extend the paths of earlier discharges. In one case, two flashes that were separated by just 1.6 sec produced tortuous channels that ran parallel to each other for almost 2 km, but the channels remained about 300 m apart. Although more data will be required before Proctor's results can be generalized, it is clear that time-of-arrival methods offer great promise for future research, particularly for those phases of lightning that occur within a cloud (see also Taylor, 1978; Rustan et al., 1980). Radio