Attenuation and space diversity statistics calculated from radar reflectivity data of rain

During the summer of 1973 the rain reflectivity environment in three-dimensional space was routinely recorded on digital tape at Wallops Island, Va. A mode of operation consisted of sampling periodically
60\deg
azimuth intervals over regions in which the rain activities were most intense and widespread. A series of plan-position indicator (PPI) sweeps over these intervals were implemented at a sequence of elevation angles starting from
0.5\deg
up io an angle above which the reflectivity values were below a designated threshold level. Approximately 500 such raster scans were acquired in which each scan was obtained in less than 4 min and covered a range interval of 10 to 140 km. Using the above data base, reflectivity profiles along representative earth-satellite paths were determined from which attenuation and space diversity statistics were calculated at the frequencies of 13 and 18 GHz. Specifically, the form
k = aZ^{b}
was used to deduce the total path attenuation, where
k
is the attenuation coefficient (dB/km), and
Z
is the reflectivity factor (mm
⁶
/m
³
). The constants
a
and
b
were calculated using the raindrop distribution for thunderstorm activity as proposed by Joss. Probabilities that the attenuations exceed given fade depths, diversity gain as a function of fade depths, and diversity gain as a function of site separation distances are characterized and compared at the various frequencies. For the space diversity mode, a site spacing of 15 km is shown to give rise to a near optimum condition for the diversity gain. Furthermore, the diversity gain has been demonstrated to be minimally influenced by the transmitter frequency.