Abstract
Abstract. In Global Navigation Satellite System (GNSS) tomography, precise information about the tropospheric water vapor distribution is derived from integral measurements like ground-based GNSS slant wet delays (SWDs). Therefore, the functional relation between observations and unknowns, i.e., the signal paths through the atmosphere, have to be accurately known for each station–satellite pair involved. For GNSS signals observed above a 15∘ elevation angle, the signal path is well approximated by a straight line. However, since electromagnetic waves are prone to atmospheric bending effects, this assumption is not sufficient anymore for lower elevation angles. Thus, in the following, a mixed 2-D piecewise linear ray-tracing approach is introduced and possible error sources in the reconstruction of the bended signal paths are analyzed in more detail. Especially if low elevation observations are considered, unmodeled bending effects can introduce a systematic error of up to 10–20 ppm, on average 1–2 ppm, into the tomography solution. Thereby, not only the ray-tracing method but also the quality of the a priori field can have a significant impact on the reconstructed signal paths, if not reduced by iterative processing. In order to keep the processing time within acceptable limits, a bending model is applied for the upper part of the neutral atmosphere. It helps to reduce the number of processing steps by up to 85 % without significant degradation in accuracy. Therefore, the developed mixed ray-tracing approach allows not only for the correct treatment of low elevation observations but is also fast and applicable for near-real-time applications.
Highlights
For the conversion of precise integral measurements into 2or 3-D structures, a technique called tomography has been invented
While in most tomography approaches, observations gathered at low elevation angles are discarded (Bender et al, 2011; Champollion et al, 2005; Hirahara, 2000), straightline signal path reconstruction is sufficient for the determination of the path lengths
Where SWD is the observation vector of size (l, 1), N w is the vector of unknowns of size (m, 1) and A is a matrix of size (l, m) which contains the partial derivatives of the slant wet delays with respect to the unknowns, i.e., the traveled distances dk in each voxel
Summary
For the conversion of precise integral measurements into 2or 3-D structures, a technique called tomography has been invented. A variety of tomography approaches based on raw GNSS phase measurements (Nilsson, 2005), double difference residuals (Kruse, 2001), slant delays (Flores Jimenez, 1999; Hirahara, 2000) or slant integrated water vapor (Champollion et al, 2005) have been developed for the accurate reconstruction of the water vapor distribution in the lower atmosphere. Bender and Raabe (2007) showed that especially low elevation observations can be a very useful source of information in GNSS tomography. In addition to their information content about the lower troposphere, the additional observations strengthen the observation geometry and therewith contribute to a more reliable tomography solution.
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