State-of-the-art modelling of the neutral atmosphere delays in GNSS (Global Navigation Satellite Systems), VLBI (Very Long Baseline Interferometry), and DORIS (Doppler Orbitography by Radiopositioning Integrated on Satellite) analyses requires information about the a priori hydrostatic zenith delays (or the pressure values, respectively) and the hydrostatic and wet mapping functions at the sites. We compare empirical models for the pressure (Global Pressure and Temperature, GPT) and for troposphere mapping functions (Global Mapping Functions, GMF) with discrete time series derived from numerical weather models for the hydrostatic zenith delays and mapping functions (Vienna Mapping Functions 1, VMF1) in terms of accuracy, precision and availability for the radio space geodetic techniques. Unlike prior models which have large deficiencies at around Antarctica, the empirical GPT does not cause significant station height biases, but the degradation of station height standard deviations when using the empirical models GPT and GMF instead of the discrete time series from the numerical weather models is by about 3 mm at the equator and 6 mm at +/- 60 degrees latitude.