trans “horizon communication. To estimate the scattered power density, we will assume that the hydrometeor scatters isotropically. This is not quite accurate since we know that Rayleigh scattering has an angular dependence of , where X is the scattering angle. Nevertheless, isotropic scattering is a reasonable first approximation. Consider a unit volume at a height h illuminated by the micro - wave beam. If the incident power density is , then the scattered power density at a range r is given by: where the summation extends over all particles (hydrometeors) in a unit volume. The scattered power density is obtained by integrating Equation (3-8) over the volume containing hail and contributing to a point at an average range from the scattering region. If d is the height of the storm cell that contains large diameter hail, then where is a reflectivity or scattering cross-section per unit volume. A 5 GW system at 3 GHz would scatter 3 mW nearly isotropically, if d is 1 km. Thus, at a range of 1 0 km the scattered power density would be about . We conclude, therefore, that scattering from the hail will not significantly increase sidelobe levels or broaden the main beam. 3.3 IONOSPHERE PROPAGATION 3.3.1 AMBIENT REFRACTION The lateral displacement of the power beam due to ionospheric refraction is (10) given by where N is the total electron content in a vertical column, measured in electrons/ , and is the elevation angle. For , probably an upper bound at midlatitudes, and . Thus, the displace ment is entirely negligible. Horizontal gradients are also expected to produce displacement that are less than 100 meters.
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