Intratropospheric range delay for two refractivity models

Closed form expressions for range delay are derived the dual-quartic refractivity model developed by H. Hopfield in 1969. Graphical results are presented as functions of source-to-target slant range and elevation angle for three typical refractivity profiles. Asymptotic, or transtropospheric values of range delay at 0° and 90° elevation angles, are compared for the dual-quartic and more conventional exponential refractivity models. Relating the parameters of the two models via this comparison leads to the demonstration that both models yield results within a few per cent of each other at all the target slant ranges and elevation angles which were investigated