Global navigation satellite systems (GNSS) have been proved to be an excellent technology for retrieving precipitable water vapor (PWV). In GNSS meteorology, PWV at a station is obtained from a conversion of the zenith wet delay (ZWD) of GNSS signals received at the station using a conversion factor which is a function of weighted mean temperature (T_m) along the vertical direction in the atmosphere over the site. Thus, the accuracy of T_m directly affects the quality of the GNSS-derived PWV. Currently, the T_m value at a target height level is commonly modeled using the T_m value at a specific height and a simple linear decay function, whilst the vertical nonlinear variation in T_m is neglected. This may result in large errors in the T_m result for the target height level, as the variation trend in the vertical direction of T_m may not be linear. In this research, a new global grid-based T_m empirical model with a horizontal resolution of 1^∘ × 1^∘ , named GGNTm, was constructed using ECMWF ERA5 monthly mean reanalysis data over the 10-year period from 2008 to 2017. A three-order polynomial function was utilized to fit the vertical nonlinear variation in T_m at the grid points, and the temporal variation in each of the four coefficients in the T_m fitting function was also modeled with the variables of the mean, annual, and semi-annual amplitudes of the 10-year time series coefficients. The performance of the new model was evaluated using its predicted T_m values in 2018 to compare with the following two references in the same year: (1) T_m from ERA5 hourly reanalysis with the horizontal resolution of 5^∘ × 5^∘; (2) T_m from atmospheric profiles from 428 globally distributed radiosonde stations. Compared to the first reference, the mean RMSEs of the model-predicted T_m values over all global grid points at the 950 and 500 hPa pressure levels were 3.35 and 3.94 K, respectively. Compared to the second reference, the mean bias and mean RMSE of the model-predicted T_m values over the 428 radiosonde stations at the surface level were 0.34 and 3.89 K, respectively; the mean bias and mean RMSE of the model's T_m values over all pressure levels in the height range from the surface to 10 km altitude were −0.16 and 4.20 K, respectively. The new model results were also compared with that of the GTrop and GWMT_D models in which different height correction methods were also applied. Results indicated that significant improvements made by the new model were at high-altitude pressure levels; in all five height ranges, GGNTm results were generally unbiased, and their accuracy varied little with height. The improvement in PWV brought by GGNTm was also evaluated. These results suggest that considering the vertical nonlinear variation in T_m and the temporal variation in the coefficients of the T_m model can significantly improve the accuracy of model-predicted T_m for a GNSS receiver that is located anywhere below the tropopause (assumed to be 10 km), which has significance for applications requiring real-time or near real-time PWV converted from GNSS signals.

One of the challenges in the innovative application of global navigation satellite systems (GNSS) lies in real-time single-frequency precise point positioning (RT-SFPPP). The well-known problems associated with SFPPP are its slow convergence and lower positioning accuracy due to the effects of various errors inherited by the GNSS positioning, including the atmospheric error. In order to mitigate the two above-mentioned problems, several scenarios for the reduction of the atmospheric delays in RT-SFPPP, including the ionospheric constraint and tropospheric constraint, were investigated in this research. The performance of the RT-SFPPP utilizing the above-mentioned methods was evaluated using one-week observations from multi-GNSS experiment stations in a simulated kinematic mode. Results showed that the convergence time of the RT-SFPPP was significantly shortened when the slant ionospheric delays derived from the real-time ionospheric products provided by Centre National d’Études Spatiales were applied as the pseudo-observations. Results also showed that the convergence time of GPS + GLONASS RT-SFPPP can be reduced by modeling the frequency-dependent part of the GLONASS receiver uncalibrated code delay as a quadratic polynomial function of GLONASS frequency number. The a priori zenith wet delays (ZWDs) derived from forecast Vienna Mapping Functions 3 (VMF3_FC) were compared to the reference ZWDs from globally distributed radiosonde stations. The mean root mean square error of the a priori ZWDs resulting from VMF3_FC at 381 radiosonde stations in 2020 was 1.53 cm compared to the radiosonde-based ZWDs. When the ZWDs derived from VMF3_FC were used as pseudo-observations in the position estimation system, the convergence time for the vertical positioning reaching a 0.3 m accuracy was considerably shortened.

Real-time precise point positioning (RT-PPP) has become a powerful technique for the determination of the zenith tropospheric delay (ZTD) over a GPS (global positioning system) or GNSS (global navigation satellite systems) station of interest, and the follow-on high-precision retrieval of precipitable water vapor (PWV). The a priori zenith hydrostatic delay (ZHD) and the mapping function used in the PPP approach are the two factors that could affect the accuracy of the PPP-based ZTD significantly. If the in situ atmospheric pressure is available, the Saastamoinen model can be used to determine ZHD values, and the model-predicted ZHD results are of high accuracy. However, not all GPS/GNSS are equipped with an in situ meteorological sensor. In this research, the daily forecasting ZHD and mapping function values from VMF1 forecasting (VMF1_FC) and VMF3 forecasting (VMF3_FC) products were used for the determination of the GPS-derived PWV. The a priori ZHDs derived from VMF1_FC and VMF3_FC were first evaluated by comparing against the reference ZHDs from globally distributed radiosonde stations. GPS observations from 41 IGS stations that have co-located radiosonde stations during the period of the first half of 2020 were used to test the quality of GPS-ZTD and GPS-PWV. Three sets of ZTDs estimated from RT-PPP solutions using the a priori ZHD and mapping function from the following three VMF products were evaluated: (1) VMF1_FC; (2) VMF3_FC (resolution 5° × 5°); (3) VMF3_FC (resolution 1° × 1°). The results showed that, when the ZHDs from 443 globally distributed radiosonde stations from 1 July 2018 to 30 June 2021 were used as the reference, the mean RMSEs of the ZHDs from the three VMF products were 5.9, 5.4, and 4.3 mm, respectively. The ZTDs estimated from RT-PPP at 41 selected IGS stations were compared with those from IGS, and the results showed that the mean RMSEs of the ZTDs of the 41 stations from the three PPP solutions were 8.6, 9.0, and 8.6 mm, respectively, and the mean RMSEs of the PWV converted from their corresponding ZWDs were 1.9, 2.4, and 1.7 mm, respectively, in comparison with the reference PWV from co-located radiosonde stations. The results suggest that the a priori ZHD and mapping function from VMF1_FC and VMF3_FC can be used for the precise determination of real-time GPS/GNSS-PWV in most regions, especially the VMF3_FC (resolution 1° × 1°) product.

Although numerous validations for the ionospheric peak parameters values (IPPVs) obtained from the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) have been conducted using ionosonde measurements as a reference, comprehensive evaluations of the quality of the COSMIC-2 data are still undesirable, especially under geomagnetic storm conditions. In this study, the IPPVs measured by ionosondes (Ramey, Boa Vista, Sao Luis, Jicamarca, Cachoeira Paulista, and Santa Maria) during the period 1 October 2019 to 31 August 2021, are used to evaluate the quality of COSMIC-2 data over low-latitude regions of the Americas. The results show that the $N_m{\mathrm{F}}_2$ ($h_m{\mathrm{F}}_2$) from COSMIC-2 agrees well with the ionosonde measurements, and the correlation coefficients for the two sets of data at the above six stations are 0.93 (0.84), 0.91 (0.85), 0.91 (0.88), 0.88 (0.79), 0.96 (0.83), and 0.96 (0.87), respectively. The data quality of COSMIC-2 derived $N_m{\mathrm{F}}_2$ is largely dependent on geomagnetic latitude. It was also found that $N_m{\mathrm{F}}_2$ derived from COSMIC-2 tends to be underestimated over the stations in Boa Vista and Cachoeira Paulista, which are close to the crests of the equatorial ionization anomaly (EIA), whilst that of the other stations is slightly overestimated. A comparison between COSMIC-measured and ionosonde-derived $h_m{\mathrm{F}}_2$ indicates that the former is systematically higher than the latter. In addition, the differences in the two $N_m{\mathrm{F}}_2$ datasets derived from COSMIC-2 and ionosonde measurements at night are generally smaller than those of daytime, when the EIA is well developed, and vice versa for $h_m{\mathrm{F}}_2$, whose RMSE is slightly smaller during daytime (with the exception of Ramey). Furthermore, $N_m{\mathrm{F}}_2$ obtained from COSMIC-2 is shown to perform best in summer at Ramey, Boa Vista, Sao Luis, and Santa Maria, best in winter at Jicamarca and Cachoeira Paulista. Finally, the COSMIC-2 electron densities capture the ionospheric dynamic enhancements under a moderate geomagnetic storm condition very well.

One of the main challenges of Global Navigation Satellite System (GNSS) tomography is in solving ill-conditioned system equations. Vertical constraint models are typically used in the solution procedure and play an important role in the quality of the GNSS tomography, in addition to helping resolve ill-posed problems in system equations. In this study, based on a water vapor (WV) parameter, namely IRPWV, a new vertical constraint model with six sets of coefficients for six different WV states was developed and tested throughout 2019 in the Hong Kong region with four tomographic schemes, which were carried out with the model and the traditional vertical constraint model using three different types of water vapor scale height parameters. Experimental results were numerically compared against their corresponding radiosonde-derived WV values. Compared with the tests that used the traditional model, our results showed that, first, for the daily relative error of WV density (WVD) less than 30%, the new model can lead to at least 10% and 49% improvement on average at the lower layers (below 3 km, except for the ground surface) and the upper layers (about 5–10 km), respectively. Second, the skill score of the monthly root-mean-square error (RMSE) of layered WVD above 10 accounted for about 83%, 87%, and 64%. Third, for the annual biases of layered WVD, the new model significantly decreased by 1.1–1.5 g/m³ at layers 2–3 (about 1 km), where all schemes showed the maximal bias value. Finally, for the annual RMSE of layered WVD, the new model at the lower (about 0.6–3 km) and upper layers improved by 13–42% and 5–47%, respectively. Overall, the new model performed better on GNSS tomography and significantly improved the accuracy of GNSS tomographic results, compared to the traditional model.