Global pressure and temperature 2 wet (GPT2w) is an empirical troposphere delay model providing the mean values plus annual and semiannual amplitudes of pressure, temperature and its lapse rate, water vapor pressure and its decrease factor, weighted mean temperature, as well as hydrostatic and wet mapping function coefficients of the Vienna mapping function 1. All climatological parameters have been derived consistently from monthly mean pressure level data of ERA-Interim fields (European Centre for Medium-Range Weather Forecasts Re-Analysis) with a horizontal resolution of 1°, and the model is suitable to calculate slant hydrostatic and wet delays down to 3° elevation at sites in the vicinity of the earth surface using the date and approximate station coordinates as input. The wet delay estimation builds upon gridded values of the water vapor pressure, the weighted mean temperature, and the water vapor decrease factor, with the latter being tuned to ray-traced zenith wet delays. Comparisons with zenith delays at 341 globally distributed global navigation satellite systems stations show that the mean bias over all stations is below 1 mm and the mean standard deviation is about 3.6 cm. The GPT2w model with the gridded input file is provided at http://ggosatm.hg.tuwien.ac.at/DELAY/SOURCE/GPT2w/ .

Initial objectives and design of the Benchmark campaign organized within the European COST Action ES1206 (2013–2017) are described in the paper. This campaign has aimed to support the development and validation of advanced Global Navigation Satellite System (GNSS) tropospheric products, in particular high-resolution and ultra-fast zenith total delays (ZTDs) and tropospheric gradients derived from a dense permanent network. A complex data set was collected for the 8-week period when several extreme heavy precipitation episodes occurred in central Europe which caused severe river floods in this area. An initial processing of data sets from GNSS products and numerical weather models (NWMs) provided independently estimated reference parameters – zenith tropospheric delays and tropospheric horizontal gradients. Their provision gave an overview about the product similarities and complementarities, and thus a potential for improvements of a synergy in their optimal exploitations in future. Reference GNSS and NWM results were intercompared and visually analysed using animated maps. ZTDs from two reference GNSS solutions compared to global ERA-Interim reanalysis resulted in accuracy at the 10 mm level in terms of the root mean square (rms) with a negligible overall bias, comparisons to Global Forecast System (GFS) forecasts showed accuracy at the 12 mm level with the overall bias of −5 mm and, finally, comparisons to mesoscale ALADIN-CZ forecast resulted in accuracy at the 8 mm level with a negligible total bias. The comparison of horizontal tropospheric gradients from GNSS and NWM data demonstrated a very good agreement among independent solutions with negligible biases and an accuracy of about 0.5 mm. Visual comparisons of maps of zenith wet delays and tropospheric horizontal gradients showed very promising results for future exploitations of advanced GNSS tropospheric products in meteorological applications, such as severe weather event monitoring and weather nowcasting. The GNSS products revealed a capability of providing more detailed structures in atmosphere than the state-of-the-art numerical weather models are able to capture. In an initial study on the contribution of hydrometeors (e.g. cloud water, ice or snow) to GNSS signal delays during severe weather, the effect reached up to 17 mm, and it was suggested that hydrometeors should be carefully accounted for within the functional model. The reference products will be further exploited in various specific studies using the Benchmark data set. It is thus going to play a key role in these highly interdisciplinary developments towards better mutual benefits from advanced GNSS and meteorological products.

An extensive validation of line-of-sight tropospheric slant total delays (STD) from Global Navigation Satellite Systems (GNSS), ray tracing in numerical weather prediction model (NWM) fields and microwave water vapour radiometer (WVR) is presented. Ten GNSS reference stations, including collocated sites, and almost 2 months of data from 2013, including severe weather events were used for comparison. Seven institutions delivered their STDs based on GNSS observations processed using 5 software programs and 11 strategies enabling to compare rather different solutions and to assess the impact of several aspects of the processing strategy. STDs from NWM ray tracing came from three institutions using three different NWMs and ray-tracing software. Inter-techniques evaluations demonstrated a good mutual agreement of various GNSS STD solutions compared to NWM and WVR STDs. The mean bias among GNSS solutions not considering post-fit residuals in STDs was −0.6 mm for STDs scaled in the zenith direction and the mean standard deviation was 3.7 mm. Standard deviations of comparisons between GNSS and NWM ray-tracing solutions were typically 10 mm ± 2 mm (scaled in the zenith direction), depending on the NWM model and the GNSS station. Comparing GNSS versus WVR STDs reached standard deviations of 12 mm ± 2 mm also scaled in the zenith direction. Impacts of raw GNSS post-fit residuals and cleaned residuals on optimal reconstructing of GNSS STDs were evaluated at inter-technique comparison and for GNSS at collocated sites. The use of raw post-fit residuals is not generally recommended as they might contain strong systematic effects, as demonstrated in the case of station LDB0. Simplified STDs reconstructed only from estimated GNSS tropospheric parameters, i.e. without applying post-fit residuals, performed the best in all the comparisons; however, it obviously missed part of tropospheric signals due to non-linear temporal and spatial variations in the troposphere. Although the post-fit residuals cleaned of visible systematic errors generally showed a slightly worse performance, they contained significant tropospheric signal on top of the simplified model. They are thus recommended for the reconstruction of STDs, particularly during high variability in the troposphere. Cleaned residuals also showed a stable performance during ordinary days while containing promising information about the troposphere at low-elevation angles.

Radio signals transmitted by Global Navigation Satellite System (GNSS) satellites experience tropospheric delays. While the hydrostatic part, referred to as zenith hydrostatic delay (ZHD) when mapped to the zenith direction, can be analytically modelled with sufficient accuracy, the wet part, referred to as zenith wet delay (ZWD), is much more difficult to determine and needs to be estimated. Thus, there exist several ZWD models which are used for various applications such as positioning and climate research. In this study, we present a data-driven, global model of the spatial ZWD field, based on the Extreme Gradient Boosting (XGBoost). The model takes the geographical location, the time, and a number of meteorological variables (in particular, specific humidity at several pressure levels) as input, and can predict ZWD anywhere on Earth as long as the input features are available. It was trained on ZWDs at 10718 GNSS stations and tested on ZWDs at 2684 GNSS stations for the year 2019. Across all test stations and all observations, the trained model achieved a mean absolute error of 6.1 mm, respectively, a root mean squared error of 8.1 mm. Comparisons of the XGBoost-based ZWD predictions with independently computed ZWDs and baseline models underline the good performance of the proposed model. Moreover, we analysed regional and monthly models, as well as the seasonal behaviour of the ZWD predictions in different climate zones, and found that the global model exhibits a high predictive skill in all regions and across all months of the year.

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.