Range errors due to ionospheric and tropospheric effects for signal frequencies above 100 MHz

Range and range rate measurements play an important role in geodetic applications of electromagnetic waves (terrestrial as well as from space, including Very Long Baseline Interferometry (VLBI)) Recent developments of measuring, techniques have led to the situation that the measuring accuracy is no longer the limiting factor in the final accuracies of range and range rate measurements. The main error stems now from the influence of the atmosphere and from assumptions and approximations in context with the derivation of refractive index used to describe the wave propagation properties of the atmosphere. Only in the case that the geometrical optics approximation holds is it possible to calculate or to measure range error for wave propagation in the atmosphere of the earth (troposphereand ionosphere) from knowledge of the refractive index as a function of space (location) and time. Otherwise we have to consides additionally scattering and/or diffraction effects. A discussion of the formulae for the refractive indices in the troposphere and in the ionosphere is followed by a review of the propagation of electromagnetic waves described by the geometrical optics approximation and on the limitations, of geometrical optics. A comprehensive discussion of range errors in the non-ionized atmosphere (troposphere) and in the ionosphere follows. For this purpose we use the elevation of the “ray” at a ground station for division into four domains: a) vertical incidence (as a special case), b) elevation between 90° and 30°, c)elevation between 30° and 5°, d) elevation smaller than 5°.