Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
ACOUSTIC RADIATIONS FROM LIGHTNING 56 gent point. The shaded zone in Figure 4.10 corresponds to a shadow zone that receives no sound from any point source on the tangent ray beyond the tangent point. Point sources below the tangent ray, suck as source S4 in Figure 4.10, have their tangent ray shifted to the left in this representation and similarly cannot be detected in the shadow zone. However, sources above the tangent ray, S5 for example, can be detected in some parts of the shadow zone. Figure 4.10 Parabolic acoustic ray from sources S1, S2, or S3 tangent to the surface at P. This ray was generated utilizing Eq. (4.8) With T0 = 30Â°C and G = 9.8 K/km. Observers on the surface to the right of P cannot detect sound from sources S1, S2, S3, or S4; an observer at P can only detect sound originating on or above the parabolic ray shown. For each observation point on the ground one can define a paraboloid of revolution about the vertical generated by the tangent ray through the observation point; the observer can only detect sounds originating above this parabolic surface. For this reason we usually hear only the thunder from the higher parts of the lightning channel unless we are close to the point of a ground strike. For evening storms, which can often be seen at long distances, it is common to observe copious lightning activity but hear no thunder at all; thermal refraction is the probable cause of this phenomenon. For T0 = 30Â°C, Î = 9.8 K/km, and h = 5 km we find that l = 25 km; as noted by Fleagle (1949) thunder is seldom heard beyond 25 km. (See also the discussion in Ribner and roy, 1982.) Winds and wind shears also produce curved-ray paths but are more difficult to describe because they affect the rays in a vectorial manner, whereas the temperature was a scalar effect. If you are downwind of a source and the wind has positive vertical shear (âu/âz > 0), the rays will be curved downward by the shear; on the upwind side, the rays are curved upward. Wind shears are very strong close to the surface and can effectively bend the acoustic rays that propagate nearly parallel to the surface. The combined effects of temperature gradients, winds, and wind shears can best be handled with a ray-tracing program on a computer. With such a program one can accurately trace ray paths through a multilevel atmosphere with many variations in the parameters; it is usually necessary in these programs to assume horizontal stratification of the atmosphere. The accuracy of the ray tracing by these techniques can be very high, usually exceeding the accuracy with which temperature and wind profiles can be determined. MEASUREMENTS AND APPLICATIONS A number of the experimental and theoretical research papers dealing with thunder generation have been discussed in earlier sections and will not be repeated here. In this section we describe additional results, techniques, and papers that deal with thunder measurements. Propagation Effects Evaluation The reader should have, at this point, an appreciation for the difficulty in quantitatively dealing with the propagation effects on both the spectral distribution of thunder and the amplitude of the signal. If, however, we are willing to forfeit the information content in the higher-frequency (> 100 Hz) portion of the thunder signal, which is most strongly affected by propagation, we can recover some of the original acoustic properties from the low-frequency thunder signal. If the peak in the original power spectrum of thunder is assumed to be below 100 Hz, then the Ï2-attenuation effects deplete the higher frequencies without shifting the position of the peak. Most spectral peaks of thunder tend to be around or below 50 Hz; therefore, this assumption appears to be safe even with finite-amplitude stretching effects considered. Further assume that the spectra are not substantially altered by turbulent scattering and cloud aerosols. To the extent that these assumptions are valid, the finite-amplitude stretching can be removed from the thunder signal and its peak frequency at the source can be estimated. This technique enables a rough estimate of the energy per unit length of the stroke to be made; the result is corrected for firstorder propagation effects. Holmes et al. (1971) found that the spectral peak overestimated the channel energy using Few's (1969) method; if corrected for stretching