A theoretical model of the shock wave from a lightning discharge ranging from the strong blast wave region out to the acoustic limit is given for the first time. The trajectory and overpressure of the strong shock wave are described by the well‐known equations for cylindrical blast waves. In the intermediate shock strength region (1.1 < M < 3.3), the shock trajectory is given by the ‘correct limit’ equation of Vlases and Jones. We derive an additional ‘correct limit’ equation for overpressure that is valid out to the acoustic limit. The correct limit equations predict a much slower decay of the intermediate shock wave; thus, the shock wave is much stronger at large distances from the discharge than was previously believed. Consequently, the range of action of the lightning discharge via its shock wave, as it affects the shattering and freezing of supercooled hydrometeors, may be large.

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A comparison of 5 to 20 years of qualitative and quantitative observations of hailfalls and hailstorms by three of the most active hail research groups in the world, shows very similar characteristics in a number of aspects of the hail phenomenon. The main similarities are that (a) the frequency of hailstorms decreases with increasing intensity, (b) the characteristics of hailstones (maximum size, number density) and hailswaths (length, surface area, energy) increase with increasing hailstorm intensity (i.e. lifetime, volume), (c) the single and multi-cellular type storms are most frequent, whereas the supercell is rare, (d) the hail flux is not constant but pulsating, (e) the spatial structure of large hailswath is not uniform but contains 'hailcores' and (f) the post embryonic trajectories of common hailstones are often simple and similar.A number of differences are also observed between some of the regions, the main ones being (a) the upper limit of intensity of the more severe storms, (b) the succession and scale of cells in the storm development and (c) the percentage of various embryo types.A major conclusion of this comparative study is that the severe hailstorms, which cause most of the damage, are exceptional and show little similarity in the three regions. For the more requent light and moderate damaging ones, the study suggests that dynamics may be the result of pulsating phenomena.

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