C. Beam Nadir Angle Table 4c shows calculations as a function of beam nadir angle at a frequency of 5 GHz. The effect of increasing beam nadir angle in a horizontally homogeneous cloud which is wider than the beam is to increase total attenuation of the beam and to increase scattering at the ground. Comparison of Tables 4b and 4c shows that increase of beam nadir angle from 0° to 30° has about the same effect on surface scattering as a change in cloud temperature from 0 to +20 °C. However, while absorption within the cloud increases slowly with increasing nadir angle, the total surface scattering increases rapidly, by nearly an order of magnitude as beam nadir angle increases from 0° to 60°. D. The Effect of Cloud Width Figure 4 shows surface power densities for a frequency of 5 GHz as a function of horizontal cloud width and beam nadir angle. The cloud is assumed to be 7 km thick in all cases, and the Rain M drop size distribution is used. The center of the microwave beam is assumed to intercept the center of the cloud (Fig. 5). For a small cloud 4 km in diameter, a large fraction of the beam misses the cloud entirely at nadir angle of 0°, resulting in very small scattered power densities at the surface. However, surface power densities increase rapidly with increasing cloud diameter. Note that increasing cloud diameter beyond about 10 km (the beam diameter) adds very little to surface power density levels at 0°. However, at larger nadir angles surface power density levels are more strongly affected by the cloud shape. For a beam nadir angle of 30°, the maximum scattered power density for a cloud 4 km in diameter becomes very large within the rectenna, but decreases more rapidly outside of the rectenna than at an angle of 0°. With increasing beam nadir angle, a portion of the beam increases its optical path length through the cloud; at the same time, other portions of the beam traverse decreased path lengths through the cloud (Fig. 5). Therefore, the average path length of the beam through the cloud may be less than or greater than the path length at 0°, depending upon cloud shape. Likewise, surface power densities may be larger or smaller than those given for nadir angles of 0°. As the cloud increases in diameter, the peak in maximum surface power density decreases in magnitude, but shifts to the outer edges of the rectenna (Fig. 4). For a beam nadir angle of 30° and cloud diameter of 24 km, surface power densities increase only slightly with further widening of the cloud. Much more dramatic changes occur at large nadir angles. For nadir angle of 60°, the peak in maximum surface power density steadily decreases with increasing cloud diameter, while continuing to shift to larger distances from beam center. In general, surface power density levels outside of the rectenna increase with increasing beam nadir angle and also with increasing cloud width. Comparison of Fig. 4 with Fig. 2 shows that at 60° scattered surface power density levels outside of the rectenna may equal or exceed those density levels of some of the beam geometries at environmentally significant levels (i.e., for surface power densities > 10 g.W/cm2). E. Cloud Vertical Dimensions Table 5 shows calculations of surface power densities outside of the rectenna as a function of distance from beam center for several variations in cloud height and
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