The accuracy of tropospheric delay correction heavily depends on the quality of the tropospheric model, and the zenith tropospheric delay (ZTD) is an important factor affecting the tropospheric delay. Therefore, it is essential to establish a precise ZTD empirical model. The existing ZTD models are constrained by a single fitting function, lack consideration for daily cycle variations, and rely solely on data with one resolution for modeling. To address these limitations, we proposed a global piecewise ZTD empirical grid (GGZTD-P) model. This model considers the daily cycle variation and latitude factor of ZTD, using the sliding window algorithm based on fifth-generation European Centre for Medium-Range Weather Forecasts atmospheric reanalysis data (ERA5). The ZTD data from 545 radiosonde stations and the second Modern-Era Retrospective analysis for Research and Applications (MERRA-2) atmospheric reanalysis data are used to validate the accuracy of the GGZTD-P model. The results indicate that the GGZTD-P model outperforms the global pressure and temperature 3 (GPT3) model, exhibiting 26 % and 53 % lower bias and rms, respectively, when using radiosonde stations as reference values. Furthermore, when evaluated using MERRA-2 atmospheric reanalysis data, the GGZTD-P model consistently exhibits superior performance across various latitude regions. It is expected that the application of this new model will provide improved services for high-precision global navigation satellite system (GNSS) positioning and GNSS meteorology.

Global Navigation Satellite System (GNSS) offer all-weather and real-time capabilities, enabling the real-time monitoring of precipitable water vapor (PWV). Traditional method for obtaining high-precision GNSS PWV require meteorological parameters such as pressure and the atmospheric weighted mean temperature, which are inconvenient to obtain at GNSS stations, especially in real-time PWV monitoring. To address these challenges, a deep neural network (DNN)-based model, namely D-PWV, has been established to directly convert zenith total delay (ZTD) derived from GNSS signals into PWV without relying on meteorological parameters. The performance of the D-PWV model is comprehensively assessed using GNSS PWV, the fifth generation European Centre for Medium-Range Weather Forecasts reanalysis (ERA5), radiosonde (RS), and data from the 2018 typhoon event Mangkhut in the Guangxi region of China, respectively. The results reveal that the D-PWV model exhibits a bias of -0.25 mm, 0.09 mm, and 0.28 mm when compared to GNSS PWV, RS PWV, and ERA5 PWV, respectively. The corresponding RMSE values are 2.00 mm, 3.37 mm, and 2.74 mm. Notably, when compared to the backpropagation neural network (BP), the D-PWV model demonstrates a smaller range of variation in both Bias and RMSE across the study area and shows greater stability in the latitudinal direction. Besides, the D-PWV model performs stably during Typhoon Mangkhut, with a correlation coefficient of 0.96 with the RS PWV, and the changes on GNSS stations are also highly consistent with the ERA5 PWV, effectively reflecting the PWV variations in the Guangxi region during the typhoon. It shows that the model constructed in this paper can provide real-time PWV values in the absence of measured meteorological parameters.

The atmospheric weighted mean temperature (Tm) is an important parameter in calculating the precipitable water vapor from Global Navigation Satellite System (GNSS) signals. As both GNSS positioning and GNSS precipitable water vapor detection require high-precision spatial and temporal resolutions for calculating Tm, high-precision modeling of Tm has gained widespread attention in recent years. The previous models for calculating Tm have the limitation of too many model parameters or single grid data. Therefore, this study presents a global high-precision Tm model (GGTm-H model) developed from the latest MERRA-2 (Modern-Era Retrospective Analysis for Research and Applications, version-2) atmospheric reanalysis data provided by United States National Aeronautics and Space Administration (NASA). The accuracy of GGTm-H model was verified by combining the MERRA-2 surface Tm data and 319 radiosonde data. The results highlighted that: (1) When the MERRA-2 Tm data was used as a reference value, the mean annual RMSE of the GGTm-H model was observed to be 2.72K. When compared with the Bevis model, GPT2w-5 and GPT2w-1 models, GGTm-H model showed an improvement of 1.5K, 0.33K, and 0.21K, respectively. (2) When the radiosonde data was used as a reference value, the mean bias and RMSE of the GGTm-H model were $-0.41$ K and 3.82K, respectively. Compared with the other models, the GGTm-H model had the lowest mean annual bias and RMSE. The developed model does not consider any meteorological parameters while calculating Tm. Therefore, it has important applications in the real-time and high-precision monitoring of precipitable water vapor from GNSS signal.