The GNSS data assimilation is currently widely discussed in the literature with respect to the various applications for meteorology and numerical weather models. Data assimilation combines atmospheric measurements with knowledge of atmospheric behavior as codified in computer models. With this approach, the “best” estimate of current conditions consistent with both information sources is produced. Some approaches also allow assimilating the non-prognostic variables, including remote sensing data from radar or GNSS (global navigation satellite system). These techniques are named variational data assimilation schemes and are based on a minimization of the cost function, which contains the differences between the model state (background) and the observations. The variational assimilation is the first choice for data assimilation in the weather forecast centers, however, current research is consequently looking into use of an iterative, filtering approach such as an extended Kalman filter (EKF). This paper shows the results of assimilation of the GNSS data into numerical weather prediction (NWP) model WRF (Weather Research and Forecasting). The WRF model offers two different variational approaches: 3DVAR and 4DVAR, both available through the WRF data assimilation (WRFDA) package. The WRFDA assimilation procedure was modified to correct for bias and observation errors. We assimilated the zenith total delay (ZTD), precipitable water (PW), radiosonde (RS) and surface synoptic observations (SYNOP) using a 4DVAR assimilation scheme. Three experiments have been performed: (1) assimilation of PW and ZTD for May and June 2013, (2) assimilation of PW alone; PW, with RS and SYNOP; ZTD alone; and finally ZTD, with RS and SYNOP for 5–23 May 2013, and (3) assimilation of PW or ZTD during severe weather events in June 2013. Once the initial conditions were established, the forecast was run for 24 h. The major conclusion of this study is that for all analyzed cases, there are two parameters significantly changed once GNSS data are assimilated in the WRF model using GPSPW operator and these are moisture fields and rain. The GNSS observations improves forecast in the first 24 h, with the strongest impact starting from a 9 h lead time. The relative humidity forecast in a vertical profile after assimilation of ZTD shows an over 20 % decrease of mean error starting from 2.5 km upward. Assimilation of PW alone does not bring such a spectacular improvement. However, combination of PW, SYNOP and radiosonde improves distribution of humidity in the vertical profile by maximum of 12 %. In the three analyzed severe weather cases PW always improved the rain forecast and ZTD always reduced the humidity field bias. Binary rain analysis shows that GNSS parameters have significant impact on the rain forecast in the class above 1 mm h⁻¹.

The tropospheric delay is one of the major error sources in precise point positioning (PPP), affecting the accuracy and precision of estimated coordinates and convergence time, which raises demand for a reliable tropospheric model, suitable to support PPP. In this study, we investigate the impact of three tropospheric models and mapping functions regarding position accuracy and convergence time. We propose a routine to constrain the tropospheric estimates, which we implemented in the in-house developed real-time PPP software. We take advantage of the high spatial resolution (4 × 4 km²) numerical weather prediction Weather Research and Forecasting (WRF) model and near real-time GNSS data combined by the least-squares collocation estimation to reconstruct the tropospheric delays. We also present mapping functions calculated from the WRF model using the ray-tracing technique. The performance tests are conducted on 14 Polish EUREF Permanent Network (EPN) stations during 3 weeks of different tropospheric conditions: calm, standard and severe. We consider six GNSS data processing variants, including two commonly used variants using a priori ZTD and mapping functions from UNB3m and VMF1-FC models, one with a priori ZTD and mapping functions calculated directly from WRF model and three variants using the aforementioned mapping functions but with ZTD model based on GNSS and WRF data used as a priori troposphere and to constrain tropospheric estimates. The application of a high-resolution GNSS/WRF-based ZTD model and mapping functions results in the best agreement with the official EPN coordinates. In both static and kinematic modes, this approach results in an average reduction of 3D bias by 20 and 10 mm, respectively, but an increase of 3D SDs by 1.5 and 4 mm, respectively. The application of high-resolution tropospheric model also shortens the convergence time, for example, for a 10 cm convergence level, from 67 to 58 min for the horizontal components and from 79 to 63 min for the vertical component.

Precise positioning requires an accurate a priori troposphere model to enhance the solution quality. Several empirical models are available, but they may not properly characterize the state of troposphere, especially in severe weather conditions. Another possible solution is to use regional troposphere models based on real-time or near-real time measurements. In this study, we present the total refractivity and zenith total delay (ZTD) models based on a numerical weather prediction (NWP) model, Global Navigation Satellite System (GNSS) data and ground-based meteorological observations. We reconstruct the total refractivity profiles over the western part of Switzerland and the total refractivity profiles as well as ZTDs over Poland using the least-squares collocation software COMEDIE (Collocation of Meteorological Data for Interpretation and Estimation of Tropospheric Pathdelays) developed at ETH Zürich. In these two case studies, profiles of the total refractivity and ZTDs are calculated from different data sets. For Switzerland, the data set with the best agreement with the reference radiosonde (RS) measurements is the combination of ground-based meteorological observations and GNSS ZTDs. Introducing the horizontal gradients does not improve the vertical interpolation, and results in slightly larger biases and standard deviations. For Poland, the data set based on meteorological parameters from the NWP Weather Research and Forecasting (WRF) model and from a combination of the NWP model and GNSS ZTDs shows the best agreement with the reference RS data. In terms of ZTD, the combined NWP-GNSS observations and GNSS-only data set exhibit the best accuracy with an average bias (from all stations) of 3.7 mm and average standard deviations of 17.0 mm w.r.t. the reference GNSS stations.

The assimilation of global navigation satellite system (GNSS) data has been proven to have a positive impact on weather forecasts. However, the impact is limited due to the fact that solely the zenith total delays (ZTDs) or integrated water vapor (IWV) derived from the GPS satellite constellation are utilized. Assimilation of more advanced products, such as slant total delays (STDs), from several satellite systems may lead to improved forecasts. This study shows a preparation step for the assimilation, i.e., the analysis of the multi-GNSS tropospheric advanced parameters: ZTDs, tropospheric gradients and STDs. Three solutions are taken into consideration: GPS-only, GPS–GLONASS (GR) and GPS–GLONASS–Galileo (GRE). The GNSS estimates are calculated using the operational EPOS.P8 software developed at GFZ. The ZTDs retrieved with this software are currently being operationally assimilated by weather services, while the STDs and tropospheric gradients are being tested for this purpose. The obtained parameters are compared with the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis. The results show that all three GNSS solutions show similar level of agreement with the ERA5 model. For ZTDs, the agreement with ERA5 results in biases of approx. 2 mm and standard deviations (SDs) of 8.5 mm. The statistics are slightly better for the GRE solution compared to the other solutions. For tropospheric gradients, the biases are negligible, and SDs are equal to approx. 0.4 mm. The statistics are almost identical for all three GNSS solutions. For STDs, the agreement from all three solutions is very similar; however it is slightly better for GPS only. The average bias with respect to ERA5 equals approx. 4 mm, with SDs of approx. 26 mm. The biases are only slightly reduced for the Galileo-only estimates from the GRE solution. This study shows that all systems provide data of comparable quality. However, the advantage of combining several GNSS systems in the operational data assimilation is the geometry improvement by adding more observations, especially for low elevation and azimuth angles.