A Relationship Between Phase Delay and Attenuation Due to Rain and Its Applications to Satellite and Deep-Space Tracking

We present and discuss two main results concerning the relationship between phase delay due to rain and rain attenuation, useful in calculations concerning high precision tracking of satellites and deep-space spacecrafts using interferometry techniques. We have found these two results with the Synthetic Storm Technique [SST] applied to a large data bank of rain rate time series collected at three sites in Italy. The first result concerns a formula that provides the extra signal phase delay tau (picoseconds) due to rain as a function of rain attenuation ( dB), frequency (GHz) and slant path elevation angle (degrees), given by tau = (860.4 - 4.82 theta) f(-1.71) A(0.73), for 20 degrees <= theta 44 degrees, and by tau = 684.3 f(-1.71) A(0.73), for 44 degrees <= theta <= 90 degrees. The formula allows estimating the phase delay due to rain attenuation, with overall average (normalized) error -3%, standard deviation 11.1%, root-mean square 11.5% for 20 degrees slant paths. The second result concerns a method to predict phase delay from the probability distribution of rain rate (SST probability model), very useful when only the probability distribution of rain rate is known.