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LIGHTNING PHENOMENOLOGY 27 Studies by Prentice and Mackerras (1977) have summarized much of the available data on the ratio of intracloud to cloud-to-ground flashes (Nc/Ng). From an analysis of 29 data sets from 13 countries, they obtain the following relationship for an average thunderstorm: where T, the number of thunder days per year, is less than or equal to 84 and Î», the latitude in the northern and southern hemispheres, is less than 60Â°. If the number of thunder days is unknown, then the ratio can be estimated from the relation This result is plotted in Figure 1.4. Note that the ratio has the highest value in the tropics where most of the lightning was shown to occur by the satellite data. Recall, however, that the satellite data were composed of both intracloud and cloud-to-ground lightning flashes. There is at the moment no way to distinguish between a ground flash and an intracloud flash from a satellite. Lightning Flash Density The number of lightning strikes per unit time per unit area, or the flash density, is a fundamental quantity of interest. Most of the available information has been obtained with lightning flash counters. Prentice (1977) summarized the values for several geographical areas and reported 5 flashes per km2 per year in Queensland, Australia; 0.2 to 3 flashes per km2 per year in Norway, Sweden, and Finland; and 0.05 to 15 flashes per km2 per year in South Africa depending on the location. Piepgrass et al. (1982) reported the results of studying 79 summer storms at the Kennedy Space Center, Florida, which produced 10 or more discharges, during the years 1974-1980. Using field mill sites covering an effective area of 625 km2, they observed an area flash density for all discharges during June, July, and August to range from 4 to 27 discharges per km2 per month, with a systematic uncertainty of perhaps a factor of 2 in the sample area. The mean and the standard deviation of the monthly area density over the above years was 12 Â± 8 discharges per km2. Approximately 38 percent of the discharges were ground flashes. Therefore, they were able to estimate the ground flash density to be 4.6 Â± 3.1 flashes per km2 per month. The most recent estimate of the ground flash density in the United States has been made by Maier and Piotrowicz (1983) using thunderstorm hour statistics and is reproduced as Figure 1.5. They used thunderstorm duration data from approximately 450 aviation weather reporting stations, each with an uninterrupted 30 years of records. The station density available is twice that of any previous thunderstorm frequency analysis of the United States. The maximum annual ground flash densities of 18 per km2 are found in the western interior of Florida. High flash densities greater than 12 per km2 are found over much of Florida and westward to eastern Texas. Flash densities greater than 8 per km2 are found in most of Oklahoma, Kansas, Missouri, Arkansas, Louisiana, Mississippi, and Tennessee. Most western and northeastern states have flash densities that are less than 4 per km2. Lightning Flash and Related Characteristics Data from two summers at the Kennedy Space Center, Florida, have been used to estimate the flashing rates in thunderstorms (Livingston and Krider, 1978). It was observed that large storms evolve through an initial, an active, and a final phase of activity. Most of the lightning activity was observed to occur in the active phase with 71 percent of the lightning, although this phase of the storm occupied only 27 percent of the total storm duration. During the active phase, 42-52 percent of all lightning was to ground, while during the final storm period, only about 20 percent of the lightning was to ground. The discharge rate for all storms observed in 1975 was approximately 4 flashes per minute with a maximum flashing rate of 26 discharges per minute during any 5-minute period. The highest flashing rate averaged over an entire storm was about 9 discharges per minute for over 200 minutes. More recent data from a 4-year interval indicates that the mean rate of flashes is about 2.4 discharges per minute per storm (Piepgrass et al., 1982). The relationship of rainfall to lightning flash rates has been investigated by Piepgrass et al. (1982). They reported that when the meteorological conditions favor the production of lightning, there is almost a direct proportionality between the total rain volume and the total number of flashes. Maier et al. (1978) noted in an earlier paper that the lightning counts were proportional to the total storm rainfall and that the proportionality increased with the rain volume until the rainfall reached about 1.2 to 2.7 Ã 104 m3 per flash. Beyond these volumes, storms that produced more rainfall tended to produce proportionally less lightning. Piepgrass et al. (1982) point out that, ''Clearly, these problems warrant further study."