Although the Klobuchar model is widely used in single-frequency GPS receivers, it cannot effectively correct the ionospheric delay. The Klobuchar model sets the night ionospheric delay as a constant, i.e., it cannot reflect temporal changes at night. The observation data of seventeen International Global Navigation Satellite System Service (IGS) stations within and around China from 2011 provided by the IGS center are used in this study to calculate the Total Electron Content (TEC) values using the Klobuchar model and the dual-frequency model. The Holt–Winters exponential smoothing model is used to forecast the error of the 7th day between the Klobuchar model and the dual-frequency model by using the error of the former six days. The forecast results are used to develop the sophisticated Klobuchar model when no epochs are missing, considering that certain reasons may result in some of the observation data being missing and weaken the relationship between each epoch in practical applications. We study the applicability of the sophisticated Klobuchar model when observation data are missing. This study deletes observation data of some epochs randomly and then calculates TEC values using the Klobuchar model. A cubic spline curve is used to restore the missing TEC values calculated in the Klobuchar mode. Finally, we develop the sophisticated Klobuchar model when N epochs are missing in China. The sophisticated Klobuchar model is compared with the dual-frequency model. The experimental results reveal the following: (1) the sophisticated Klobuchar model can correct the ionospheric delay more significantly than the Klobuchar model; (2) the sophisticated Klobuchar model can reflect the ionosphere temporal evolution, particularly at night, with the correct results increasing with increasing latitude; and (3) the sophisticated Klobuchar model can achieve remarkable correction results when N epochs are missing, with the correct results being nearly as good as that of the dual-frequency model when no epochs are missing.

The weighted mean temperature (T_m) is crucial for converting zenith wet delay to precipitable water vapor in global navigation satellite system meteorology. Mainstream T_m models have the shortcomings of poor universality and severe local accuracy loss, and they cannot reflect the nonlinear relationship between T_m and meteorological/spatiotemporal factors. Artificial neural network methods can effectively solve these problems. This study combines the advantages of the models that need in situ meteorological parameters and the empirical models to propose T_m hybrid models based on artificial neural network methods. The verification results showed that, compared with the Bevis, GPT3, and HGPT models, the root mean square errors (RMSEs) of the new three hybrid models were reduced by 35.3%/32.0%/31.6%, 40.8%/37.8%/37.4%, and 39.5%/36.4%/36.0%, respectively. The consistency of the new three hybrid models was more stable than the Bevis, GPT3, and HGPT models in terms of space and time. In addition, the three models occupy 99.6% less computer storage space than the GPT3 model, and the number of parameters was reduced by 99.2%. To better evaluate the improvement of hybrid models T_m in the precipitable water vapor (PWV) retrieval, the PWVs calculated using the radiosonde T_m and zenith wet delay (ZWD) were used as the reference. The RMSE of PWV derived from the best hybrid model’s T_m and the radiosonde ZWD meets the demand for meteorological research and is improved by 33.9%, 36.4%, and 37.0% compared with that of Bevis, GPT3, and HGPT models, respectively. The hypothesis testing results further verified that these improvements are significant. Therefore, these new models can be used for high-precision T_m estimation in China, especially in Global Navigation Satellite System (GNSS) receivers without ample storage space.

The geostationary meteorological satellite Fengyun-4A (FY-4A) has rapidly advanced, generating abundant high spatiotemporal resolution atmospheric precipitable water vapor (PWV) products. However, remote sensing satellites are vulnerable to weather conditions, and these latest operational PWV products still require systematic validation. This study presents a comprehensive evaluation of FY-4A PWV products by separately using PWV data retrieved from radiosondes (RS) and the Global Navigation Satellite System (GNSS) from 2019 to 2022 in China and the surrounding regions. The overall results indicate a significant consistency between FY-4A PWV and RS PWV as well as GNSS PWV, with mean biases of 7.21 mm and −8.85 mm, and root mean square errors (RMSEs) of 7.03 mm and 3.76 mm, respectively. In terms of spatial variability, the significant differences in mean bias and RMSE were 6.50 mm and 2.60 mm between FY-4A PWV and RS PWV in the northern and southern subregions, respectively, and 5.36 mm and 1.73 mm between FY-4A PWV and GNSS PWV in the northwestern and southern subregions, respectively. The RMSE of FY-4A PWV generally increases with decreasing latitude, and the bias is predominantly negative, indicating an underestimation of water vapor. Regarding temporal differences, both the monthly and daily biases and RMSEs of FY-4A PWV are significantly higher in summer than in winter, with daily precision metrics in summer displaying pronounced peaks and irregular fluctuations. The classic seasonal, regional adjustment model effectively reduced FY-4A PWV deviations across all regions, especially in the NWC subregion with low water vapor distribution. In summary, the accuracy metrics of FY-4A PWV show distinct spatiotemporal variations compared to RS PWV and GNSS PWV, and these variations should be considered to fully realize the potential of multi-source water vapor applications.

This paper proposes a new Asian single site tropospheric correction model called the Single Site Improved European Geostationary Navigation Overlay Service model (SSIEGNOS) by refining the European Geostationary Navigation Overlay Service (EGNOS) model at a single site. The performance of the SSIEGNOS model is analyzed. The results show that (1) the bias and root mean square (RMS) error of zenith tropospheric delay (ZTD) calculated from the EGNOS model are 0.12 cm and 5.87 cm, respectively; whereas those of the SSIEGNOS model are 0 cm and 2.52 cm, respectively. (2) The bias and RMS error show seasonal variation in the EGNOS model; however, little seasonal variation is observed in the SSIEGNOS model. (3) The RMS error decreases with increasing altitude or latitude in the two models; however, no such relationships were found in the bias. In addition, the annual predicted bias and RMS error in Asia are −0.08 cm and 3.14 cm for the SSIEGNOS model, respectively; however, the EGNOS and UNB3m (University of New Brunswick) models show comparable predicted results. Relative to the EGNOS model, the annual predicted bias and RMS error decreased by 55% and 48%, respectively, for the SSIEGNOS model.

Tropospheric delay is recognized as one of the main error sources affecting Global Navigation Satellite System (GNSS) positioning accuracy. Previous studies have only employed artificial intelligence-based weather models with low temporal resolution for comprehensive assessments. Therefore, this study proposes an ensemble forecasting approach based on multiple initial conditions from the Pangu-Weather model to obtain hourly resolution tropospheric delays. The ZTD data from 250 Crustal Movement Observation Network of China (CMONOC) GNSS stations across China in 2020 are used to validate the accuracy of the Pangu-Weather model. The findings show that the Pangu-Weather model exhibits strong performance under both forecast lead times compared to the traditional Global Forecast System (GFS) product, particularly in southern China. However, the Pangu-Weather model provides slightly inferior forecast accuracy compared to the GFS product in dry, low-humidity regions at stations located between 2 and 4 km in altitude, and for forecast lead times of less than 9 h. Nevertheless, a lower error accumulation trend is exhibited by the Pangu-Weather model, as its RMSE is larger than that of the Global Pressure and Temperature 3 (GPT3) empirical model after 240 h (10 days), demonstrating more stable accuracy over longer forecast periods. In summary, the Pangu-Weather model shows significant advantages in Chinese regions with complex climates and terrains, and it is of great potential in GNSS real-time positioning and meteorological monitoring.

Ocean tidal variation is a key parameter for ensuring coastal safety, monitoring marine climate, and maintaining elevation datum. Recently, the ground-based global navigation satellite system reflectometry (GNSS-R) technique has been applied for regional tidal measurements, which is somewhat restricted in terms of temporal and spatial resolutions. A convenient method to improve temporal resolution of measurements is to combine multi-GNSS observations. This paper proposes a new sea-surface altimetry method using the posterior errors (PE) of dual-frequency carrier-phase signals derived from the ionosphere-free Precise Point Positioning (IF-PPP). Considering that the number of initial retrievals is obviously unsuitable for minute-level tidal measurements, both the time sliding window based on the Lomb–Scargle periodogram and a weighted cubic spline smoothing function are significant processing steps for estimating the reflector heights between the sea surface and antenna center. Measurements from two coastal GNSS stations with different tidal amplitudes are used to test the proposed method and compare it with the tide gauge and the signal-to-noise ratio (SNR) methods, respectively. The experimental results show that the multi-GNSS PE combination method can be used to estimate a minute-level sea level time series, and its root-mean-squared errors (RMSE) are about 12.5 cm. In terms of correlation, for all results, the corresponding coefficients exceed 0.97. Moreover, this combined PE method demonstrates a significant advantage in increasing temporal resolution, which is beneficial for application on high-frequency sea-level monitoring.