My question is regarding RF measurement systems which use antennas signal arrival time as principle of operation e.g. GPS. It is known that impedance of well-matched antenna immersed in lossy dielectric is changed. Like in this case of an antenna covered by snow. Thus the complex input impedance Z of the antenna depends on the surrounding environment. From the circuit theory we know a relation between Z and a phase shift associated to it as: $$ \Theta=atan(X/R) $$ where $$ Z=R+jX $$
So a radar altimeter on airplane passing through a dense cloud would give false altitude reading?
In the literature I see the topic of antenna equivalent circuits vs. lossy dielectric environment is well covered, however no one considered what does it mean from the time domain point of view. Is my reasoning, that antenna intrinsically adds a phase shift, expressed by formula given above, correct?