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. In Global Navigation Satellite System (GNSS) tomography, precise information about the tropospheric water vapordistribution is derived from integral measurements like ground-based GNSSslant wet delays (SWDs). Therefore, the functional relation betweenobservations and unknowns, i.e., the signal paths through the atmosphere, haveto be accurately known for each station–satellite pair involved. For GNSSsignals observed above a 15 ∘ elevation angle, the signal path is wellapproximated by a straight line. However, since electromagnetic waves areprone to atmospheric bending effects, this assumption is not sufficientanymore for lower elevation angles. Thus, in the following, a mixed 2-Dpiecewise linear ray-tracing approach is introduced and possible errorsources in the reconstruction of the bended signal paths are analyzed in moredetail. Especially if low elevation observations are considered, unmodeledbending effects can introduce a systematic error of up to 10–20  ppm , onaverage 1–2  ppm , into the tomography solution. Thereby, not only theray-tracing method but also the quality of the a priori field can have asignificant impact on the reconstructed signal paths, if not reduced byiterative processing. In order to keep the processing time within acceptablelimits, a bending model is applied for the upper part of the neutralatmosphere. It helps to reduce the number of processing steps by up to 85 %without significant degradation in accuracy. Therefore, the developedmixed ray-tracing approach allows not only for the correct treatment of lowelevation observations but is also fast and applicable for near-real-timeapplications.

Atmospheric bending effects in GNSS tomography