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 A (dB), frequency f (GHz) and slant path elevation angle thetas (degrees), given by tau = (860.4 4.82 thetas)f^-1.71A^0.73, for 20deg les thetas les 44deg, and by tau = 648.3 f^1.71 A^0.73,for 44deg les thetas les 90deg. The formula allows estimating the phase delay due to rain attenuation, with overall average (normalized) error -3%, standard deviation 11.1%, rootmean square 11.5 % for 20deg 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.