ture. This variation is far greater at low microwave frequencies than at high frequencies. For most of the distribution functions at a frequency of 3.3 GHz, a decrease in cloud temperature from 20 to -20 °C may lead to an increase in the attenuation parameters by up to a factor of three. However, while both extinction and absorption coefficients are highly temperature dependent, the scattering coefficient (/?, = fie - /3a) is almost temperature independent. In the consideration of the size of precipitating elements, there are two scales. Thunderstorms generally consist of very tall clouds (up to 10 km or higher) with widths approximately equal to heights (29). In such cases the cloud width may be approximately equal to the microwave beam diameter. On the other hand, widespread nimbostratus formations generally are of smaller height (up to about 3 km thick), but are much wider than the beam diameter. In both cloud types, temperature, drop size distributions, and rainfall distributions show wide vertical variability (30-37). Microphysical processes are at present so insufficiently known, and measurements of liquid water contents and drop size distributions so imprecise, that no general framework for detailed calculations is available. For these reasons the large number of cases found in Tables 2 and 3, spanning a broad range of possible conditions, are studied in order to adequately represent the variability of drop attenuation parameters found in clouds. For the purposes of the present investigation, scattering and absorption properties are assumed uniform throughout the rain cloud. Attenuation parameters corresponding to T = 0 °C are used unless otherwise noted. While it is recognized that real clouds have drop size distributions and temperature variations which are strongly height dependent, inclusion of these complexities is beyond the scope of the present study. IV. BEAM GEOMETRY The choice of beam geometry for the transmitted microwave power has not been defined. The two most severe restrictions on beam shape are maximum power density at beam center and maximum power density outside of the receiving rectenna. It is generally assumed that the beam will take a Gaussian shape with power densities P defined in terms of the distance r from beam center, as where r0 defines the beam shape. Figure 2 shows beam power density shapes for several possible configurations. Limiting the value of P (i.e., Px in Fig. 2) to 10 mW/cm2 at the edge of the rectenna (r = 5 km), leads to values of r0 = 5.48 km and Er = 21.7 GW. For such a beam shape, the power densities outside of the rectenna decrease slowly with increasing distance, having values of 6.93, 4.50, 2.73, 1.55, and 0.82 mW/cm2 at distances of 1, 2, 3, 4, and 5 km, respectively, from the edge of the rectenna (6, 7, 8, 9, and 10 km from the center of the beam). The Soviet microwave exposure standard is attained 10 km from the edge of the rectenna. Since biological studies have shown that these exposure levels are dangerous, a
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