Spaceborne Global Navigation Satellite Systems Reflectometry (GNSS-R) has demonstrated efficacy for global wind speed retrieval. However, its retrieval accuracy in coastal regions remains severely constrained by land signal contamination. To overcome this limitation, this study proposes a novel physics-aware multimodal fusion framework to achieve high-precision quasi global coastal sea surface wind speed based on Cyclone GNSS (CYGNSS) missions. The proposed framework addresses the coastal signal contamination through three modules: (1) a Geo-Spatial Positional Embedding (GSPE) module explicitly parameterizes nearshore distance constraints to endow the network with intrinsic geographic awareness; (2) a Physics-Aware Cross-Attention (PACA) mechanism dynamically aligns discrete GNSS-R observables with auxiliary environmental features to actively isolate land-corrupted features; (3) an Adaptive Gating Mechanism (AGM) functions as a learnable filter to suppress non-physical anomalies and prevent noise propagation. Comprehensive validation against the European Centre for Medium-Range Weather Forecasts Reanalysis v5 (ERA5) dataset demonstrates that the proposed framework achieves an overall Root Mean Square Error (RMSE) of 1.42 m/s for the coastal wind speeds, representing a 14.5% improvement in accuracy over the official CYGNSS Level 2 products. Notably, within the challenging 0–20 km buffer zone, the model effectively reduces the RMSE by 0.20 m/s compared to the CYGNSS Level 2 product. Independent testing against in-situ National Data Buoy Center (NDBC) buoys further corroborates the model's robustness across diverse coastal regimes (RMSE: 1.07–2.17 m/s). Finally, interpretability analysis reveals that the retrieval performance of coastal wind speed is jointly influenced by coastal distance, sea surface temperature, ocean currents, and precipitation, which together contribute 22.5% of the overall feature importance, complementing the dominant GNSS-R observables. Collectively, this work advances the understanding of complex coastal signal interactions and highlights the potential of physics-aware fusion for operational coastal wind monitoring.

Global Navigation Satellite System (GNSS) has emerged as a well-established atmospheric observing system, with Zenith Total Delay (ZTD) and integrated water vapor routinely assimilated by several global and regional Numerical Weather Prediction (NWP) centers. While co-derived tropospheric gradients effectively capture water vapor horizontal anisotropy, their assimilation has yet to be widely adopted. Here, we introduce a novel approach for assimilating GNSS tropospheric gradients into the Weather Research and Forecasting (WRF) model by constructing pseudo-ZTD observations from GNSS-derived ZTD and gradient data. Through two comparative experiments, we evaluate the potential influence of GNSS tropospheric gradients on WRF forecasts. The results indicate that assimilating these gradients improves humidity and wind field predictions in the lower-to-middle troposphere (850-500 hPa), with a neutral impact on surface fields. Verification against radar estimates further demonstrates enhanced precipitation forecast skills, particularly for heavy precipitation events, by better resolving the spatial distribution and intensity of precipitation systems. A diagnosis of a precipitation event suggests that the assimilation of GNSS tropospheric gradients is able to adjust the forecast mid-level moisture distribution and modulate the forecast upward motion, thereby influencing the formation of spurious precipitation.

Accurate precipitation nowcasting is one of the most challenging tasks in atmospheric sciences. The current methods of nowcasting primarily rely on inferring precipitation from radar reflectivity, which inevitably leads to uncertainties in forecasts due to the limitations of single radar data in capturing the detailed initial conditions of complex weather systems. Global Navigation Satellite Systems (GNSS) can provide accurate water vapor information of high temporal resolution. In this study, a generative network (GRENet) is designed to integrate GNSS water vapor information with radar observations to improve precipitation nowcasting. A case study on a heavy rainfall event demonstrates that GRENet can predict the range and location of the precipitation center more accurately than a baseline model employing only radar observations. This results in improved performance on critical success index and fractions skill score, indicating that detailed initial water vapor from GNSS contributes significantly to enhancing precipitation nowcasting skill.

Surface weather patterns are susceptible to structural variability in the Arctic stratospheric polar vortex, with planetary-scale wave-wave interactions serving as the dominant driving factor of this variability. Nevertheless, the dynamical pathways linking wave-wave interactions, especially in the vertical direction, to the structural variability of the polar vortex remain poorly constrained. To bridge this gap, this study proposes a novel climate network framework constructed from high-vertical-resolution GNSS radio occultation (RO) observations, revealing that the structural variability of the polar vortex is driven by a positive feedback mechanism between the troposphere and stratosphere. Specifically, wave-wave interactions in the stratosphere strengthen those in the troposphere, which in turn subsequently exert positive feedback on the stratospheric wave-wave interactions. In this dynamical process, weakened wavenumber 1-wavenumber 2 (WN1-WN2) interaction tends to enhance stratospheric wavenumber 1 (SWN1) and suppress SWN2, favoring vortex structure displacement. Conversely, strengthened WN1-WN2 interaction triggers vortex structure splitting by diminishing SWN1 and amplifying SWN2. Furthermore, we uncover that the modulation of WN3 on the vortex structure mainly occurs in the stratosphere, where WN3 amplifies the impact of the WN1-WN2 interaction. The presented framework offers robust observational evidence and causal constraints for understanding the structural variability of the polar vortex, while opening new prospects for harnessing GNSS-RO observations in tackling climate change.

Soil Moisture (SM) monitoring using Global Navigation Satellite System-Reflectometry (GNSS-R) has often relied on observations from a single source, thereby resulting in underutilizing abundant reflected signal resources. Moreover, aggregating multi-source observations without considering their heterogeneous characteristics can lead to suboptimal retrieval performance. To address these limitations, this study proposes a dual-branch attention-fusion Transformer model for global SM retrieval by integrating GNSS-R observations from the complementary Tianmu-1 and Fengyun-3 missions. The proposed model learns mission-specific feature representations and adaptively fuses them through attention-based fusion mechanism, thereby enabling effective exploitation of cross-mission complementary information. The integrated Tianmu-1 + Fengyun-3 Level-1 dataset provides an average monthly temporal coverage of 79.7

As Global Navigation Satellite System (GNSS) signals are affected by the atmospheric refraction when transporting through the neutral atmosphere, the resulted tropospheric delay is highly linked to the atmospheric water vapor, promoting the establishment of GNSS as a reliable meteorological observation means of high accuracy and high temporal resolution. Over the past few decades, the advancement of GNSS constellations including GPS, BeiDou, Galileo, and GLONASS has driven progress in tropospheric parameters retrieval, modeling and applications. This paper presents a detailed review of the state of the art in ground-based GNSS troposphere monitoring and applications, covering fundamental concepts, theory, and algorithms. The advances in GNSS tropospheric parameters estimation for both high-precision and low-cost processing are outlined, followed by the progress in tropospheric delay modeling and forecasting. Meanwhile, a recent development on the applications of the external tropospheric models in augmenting GNSS precise positioning is illustrated. Thereafter, progress in the assimilation of GNSS tropospheric data into numerical weather prediction (NWP) models is presented in detail, accompanied by the advances in its direct applications in rainfall forecasting. Furthermore, we outline the key challenges and opportunities ahead, including leveraging Low Earth Orbit (LEO) and smart terminals for advanced tropospheric products, establishing more enhanced delay models in challenging environments particularly cooperating with real-time data transmission, developing more sophisticated data assimilation operators, and coupling deep learning models with physical mechanisms for improved atmospheric simulation. Finally, the paper concludes with some comments and the prospects for future research.

Tropospheric delay is a key metric in weather monitoring and represents one of the primary error sources in precise positioning. Advances in Global Navigation Satellite System (GNSS) and numerical weather models (NWM) present significant potential for enhancing the resolution and accuracy of tropospheric delay models. In this study, a high-resolution (5 km) zenith tropospheric delay (ZTD) model, named the data assimilation model of ZTD (DAM), is developed by assimilating GNSS ZTDs into the fifth-generation of European Center for Medium-Range Weather Forecasts reanalysis background field using the Weather Research and Forecast model. Experiments are conducted in the complex terrain of the U.S. West Coast, using GNSS ZTD data from 35 test stations for validation. Comparing DAM with three other models, the results show that DAM provides the best match with GNSS ZTD, with an RMS of 5.95 mm. DAM also demonstrates high stability across different seasons, with a minimal RMS variation of approximately 0.9 mm and the lowest seasonal average RMS of 5.70 mm. When the number of modeling stations decreases from 62 to 10, DAM maintains good stability and accuracy, with the RMS increasing from 5.95 to 7.03 mm. In cases of uneven station distribution, the RMS value for DAM is 7.55 mm, further highlighting its superior accuracy and robustness to varying station distributions.

Global Navigation Satellite System (GNSS) radio occultation (RO), owing to its capability to provide high vertical resolution, high accuracy, calibration-free, and all-weather atmospheric observations, has been widely used in numerical weather prediction (NWP) and climate studies. As China's first commercial GNSS RO constellation supporting all major GNSS systems, Tianmu-1 (TM-1) offers promising observations. However, its data quality and assimilation performance in NWP remain underexplored. This study first evaluates the TM-1 neutral atmospheric refractivity and bending angle profiles collected in January 2024. Compared with the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ECMWF-ERA5), refractivity fractional differences at 5-30 km have a mean and standard deviation within +/- 0.15% and 1.31%, while bending angle differences are within +/- 0.55% and 1.99%. Radiosonde comparisons over 0-20 km show refractivity differences within +/- 0.19% and 1.93%, and bending angle differences within +/- 0.12% and 5.06%. Larger errors are mainly confined to the lower troposphere and low latitudes, with only minor variations across GNSS constellations. After validating data quality, TM-1 refractivity observations are assimilated using the Weather Research and Forecasting (WRF) model and WRFDA 3-D variational (3DVAR) system to assess their impact on regional analyses and short-range forecasts over China. Model outputs are validated against ERA5 reanalysis and radiosonde observations. The results show that assimilating TM-1 refractivity data leads to root mean squared error (RMSE) reductions of similar to 5%-10% for temperature analyses and forecasts in the mid-to-upper troposphere and near the surface, and similar to 5% in specific humidity in the lower troposphere. Wind impacts are mixed, with RMSE improvements of similar to 2%-5% above 600 hPa and degradation in the lower troposphere. Overall, this preliminary study confirms the high quality of TM-1 GNSS RO refractivity data and demonstrates its promising contribution in complementing current operational RO assimilation for regional NWP.

Rainfall forecasting from numerical weather prediction (NWP) models is uncertain due to limited spatial and temporal measurements. Radar and ground-based global navigation satellite system (GNSS) are essential sources for acquiring high spatiotemporal resolution atmospheric water parameters, with complementary strengths in accurately retrieving atmospheric moisture characteristics. Integrating radar-derived precipitation and GNSS zenith total delay (ZTD) into NWP models holds the potential to improve the performance of heavy rainfall forecasts. This study explores the potential of assimilating radar-derived precipitation and GNSS ZTDs on short-term quantitative precipitation forecasting (QPF) using the 4-D variational (4DVAR) assimilation system. A heavy precipitation event in northern Germany on June 29, 2017, is used as a case study, with four experiments conducted involving conventional data, radar-derived precipitation, GNSS ZTDs, and their synergistic assimilation. The results indicate that precipitation and ZTD assimilation individually reduce the root-mean-square error (RMSE) in humidity analysis within the mid-to-low atmosphere and improve forecast accuracy for temperature, wind, and specific humidity to varying degrees. These improvements are further enhanced in the synergistic assimilation scheme, potentially attributed to the additive benefits of radar-derived precipitation for temperature field and the precise humidity modeling enabled by GNSS ZTDs. Furthermore, comparisons of rainfall forecasts with Radar Online Adjustment (RADOLAN)-RW products indicate that synergistic assimilation leverages the advantages of both radar-derived precipitation and GNSS ZTDs, achieving substantial improvements in precipitation representation. This preliminary study underscores the potential of synergistically assimilating radar-derived precipitation and GNSS ZTDs in reducing errors in humidity, temperature, and wind analysis fields and in enhancing short-term forecasts of heavy rainfall events.

Ocean surface wind is vital to the Earth's meteorological system, and their properties can be detected by spaceborne global navigation satellite system reflectometry (GNSS-R) measurements. With the growing number of GNSS-R signal sources, machine learning technology exhibits prominent advantages in wind speed estimation. Currently, the deep learning techniques that establish relationships between GNSS-R measurements and ocean surface wind speeds generally apply grids and sequence structures and lack flexibility and robustness. Additionally, constructing models with individual GNSS-R observations results in the loss of valuable temporal correlation within delay-Doppler maps (DDMs). Therefore, this study proposes a novel spatiotemporal graph-based deep neural network (STG-DNN) for retrieving wind speed, which incorporates a graph module with a transformer module to fully exploit the spatial-temporal dependencies of DDMs. Results demonstrate that the graph module significantly improves both the accuracy and reliability in wind speed retrieval. Meanwhile, the transformer module effectively captures temporal features from various DDMs. Validations with cyclone GNSS (CYGNSS) test data support the superior accuracy of STG-DNN, revealing a correlation coefficient of 0.92 for the wind speeds. The results indicate that the root-mean-square error (RMSE) of STG-DNN for wind speed is 1.27 m/s, representing improvements of approximately 33.2%, 20.6%, and 13.6% over the minimum variance estimator (MVE), convolutional neural network (CNN), and vision graph (VIG) neural networks, respectively. Additionally, a promising agreement is observed between STG-DNN and ERA5 in the spatial distributions of wind speed retrieval, indicating a robust spatial performance in STG-DNN. As for the temporal scale, the daily variations in retrieval accuracy of STG-DNN exhibit smaller fluctuations compared to both CNN and VIG wind data in the test dataset.

A crucial factor limiting convective weather nowcasting is the lack of timely updated and accurate atmospheric water vapor observations. The Global Navigation Satellite System (GNSS) can accurately sense water vapor with high temporal resolutions, which is adequate to observe many meso- and small-scale variations associated with convective weather. In this contribution, an hourly cycling data assimilation system is established to investigate the influence of assimilating GNSS zenith total delays (ZTD) on severe convective weather nowcasting. The contributions of assimilating ZTD with different temporal resolutions are discussed in detail by validating with the radiosonde observations. The results demonstrate that the assimilation of ZTD significantly improves the moisture distribution of the middle and lower troposphere. Furthermore, model simulations become wetter or drier as the frequency of ZTD assimilation increases. Verification of the precipitation forecasts is performed by comparing them with the radar-estimated precipitation. The results indicate that assimilation of GNSS ZTD improves the accuracy of precipitation forecast in the nowcasting range of 0-6 h. Compared to the control experiment, the hourly ZTD assimilation experiment reveals the highest precipitation forecast skill scores, followed by the experiments of assimilating ZTD every three and six hours, indicating that the rapid update of water vapor information could contribute to improving the precipitation nowcasting in a rapidly developing convective system.

Accurate precipitation nowcasting with high spatiotemporal resolution is essential for various applications, including meteorological services, ecological conservation, and atmospheric research. The current nowcasting models, which are primarily based on single radar echo data, exhibit limitations in accurately capturing the complex and fast-evolving nature of precipitation patterns. Consequently, there is an urgent need to incorporate supplementary data sources that offer high spatiotemporal resolution and the capability for all-weather, all-day monitoring. In this study, we propose an enhanced precipitation nowcasting model, named radar-satellite-GNSS generative adversarial network (RSG-GAN), based on the GAN. It effectively combines the strengths of radar quantitative precipitation estimation (QPE), geostationary operational environmental satellite-16 (GOES-16) split window difference (SWD), and global navigation satellite system (GNSS) zenith total delays (ZTDs) to improve nowcasting performance. The American west coast (36 degrees-48 degrees N, 118 degrees-124 degrees W) is considered the experimental area. The RSG-GAN model is compared with the traditional optical flow method as well as two deep learning models: one utilizing solely radar data (radar-only model) and other integrating radar and satellite data (Rad-Sat model). Results of the cases studies exhibit that, compared to the optical flow model, the deep learning models demonstrate enhanced ability in capturing rainfall intensity variations, spatial shifts, and achieving outstanding performance in both image quality and precipitation nowcasting metrics, with the RSG-GAN model showing the most notable improvements. Statistical analysis across 189 precipitation periods reveals that the RSG-GAN model achieves the lowest average mean absolute error (MAE) of 0.34 mm/h and root mean square error (RMSE) of 0.61 mm/h over a 120-min lead time, with reductions of 36.3% and 41.6%, respectively, compared to the optical flow method. In addition, at intermediate and higher rainfall intensity thresholds, the RSG-GAN model consistently outperforms other methods, with significant improvements in critical success index (CSI) and fractions skill score (FSS), while maintaining robust nowcasting performance even when other models struggle to predict precipitation. Compared with three deep learning-based methods (CM-STJointNet, MM-RNN, and MM-STMixGAN), the RSG-GAN model consistently shows superior performance in both prediction accuracy and event detection. Furthermore, transfer learning experiments on the publicly available dataset storm event imagery (SEVIR) also demonstrate the remarkable generalization capability of RSG-GAN model.

Global Navigation Satellite System-Reflectometry (GNSS-R), as a favorable technology to provide large-scale soil moisture estimates, contributes to studies in climatology, hydrology, and agriculture. The Tianmu-1 Meteorological Mission (TM-1), currently runs 23 satellites in orbit (including one experimental satellite) with multi-GNSS compatibility, achieve shorter revisit periods and higher data acquisition frequencies compared with single-satellite missions. The hourly TM-1 surface soil moisture (SSM) products, offer affluent information for global soil moisture monitoring. This study provides the first comprehensive characterization and performance evaluation of TM-1 SSM products based on in-situ measurements and products of Soil Moisture Active Passive (SMAP), European Space Agency Climate Change Initiative (ESA CCI), and Global Land Data Assimilation System (GLDAS). The TM-1 SSM demonstrates expected spatiotemporal patterns at both regional and global scales. The in-situ validation results reveal its landcover-dependent accuracy, with superior performance over bare soils (unbiased Root Mean Square Error, ubRMSE of about 0.02 m3/m3) compared to vegetated regions (ubRMSE of around 0.07 m3/m3). Furthermore, Extended Triple Collocation (ETC) assessments using (1) TM-1, active, and ground observations and (2) TM-1, model, and ground observations triplets are conducted. The ETC-derived results present that TM-1 SSM achieve global correlation coefficient of 0.75 and random error standard deviation of 0.035 m3/m3. Overall, this study demonstrates the reliable accuracy of TM-1 SSM product, and provides valuable insights for its refinement and potential applications.

The tropospheric delay is difficult to be modeled accurately resulting from the high variability of atmospheric water vapor, especially under the conditions of sparse station distribution and large elevation differences, which poses challenges for real-time precise positioning. In this contribution, a real-time high-resolution (0.01° × 0.01°) zenith tropospheric delay (ZTD) model considering sparse stations and topography variations (named GFNSS) is established by integrating the information from the Global Forecast System (GFS) and Global Navigation Satellite System (GNSS). GNSS observations and GFS forecasts in the Hong Kong area are selected for the experiments. The performance of ZTDs derived from GFNSS is assessed and validated with the real-time GNSS ZTDs obtained by the precise point positioning method and the IGS post-processed ZTD products. Results show that the root mean square error (RMSE) of GFNSS ZTDs is 5.5 mm and 12.8 mm when validated with real-time and post-processed ZTD, while those for ZTD derived from the low-order surface model (LSM) are 8.8 mm and 19.0 mm, presenting a reduction of 37.5

Atmospheric water vapor plays a prominent role in weather forecasting and climate change, which can be measured accurately with conventional water vapor observing techniques and the global navigation satellite system (GNSS). However, there are limited studies that assess the retrieval of PWV exclusively using Beidou over oceans, as well as for GLONASS and Galileo. In this contribution, we investigate retrieving the real-time precipitable water vapor (PWV) based on shipborne GNSS kinematic precise point positioning (PPP) solutions through an 8-days experiment over the South China Sea. Observations from multi-constellation and single-constellation, including GPS, GLONASS, Galileo, and Beidou are processed. Real-time shipborne GNSS PWV is validated using ERA5 PWV products. The results obtained from the single-constellation analysis indicate that Beidou performs comparably to Galileo in PWV retrieval, surpasses GLONASS, but slightly falls behind GPS. It exhibits an accuracy of 3.19 mm when compared to the ERA5 PWV products after an average initialization time of 43.9 min. Furthermore, it is demonstrated that real-time multi-GNSS PWV achieves an accuracy improvement of more than 15% compared to single-constellation resolutions, reaching an accuracy of 2.34 mm. Real-time shipborne GNSS can accurately sense atmospheric water vapor over oceans and contribute to time-critical meteorological applications.

Introduction: As a successor to Haiyang-2A (HY-2A), HY-2B is China’s second marine dynamic satellite. Equipped with a scanning microwave radiometer (SMR), it can measure the precipitable water vapor (PWV) over the oceans, providing valuable climate and weather insights. This study aims to evaluate the accuracy of HY-2B SMR PWV data from January 2019 to December 2021 using various validation methods. Methods: to validate HY-2B SMR PWV, fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5) data, radiosonde data, and global navigation satellite system (GNSS) observations are used. Results: the validation shows that the HY-2B SMR PWV data agree well with the ERA5 PWV data, with a root mean square error (RMSE) of 1.61 mm and a mean value of 0.71 mm. However, RMSEs of approximately 3.5 mm are observed when comparing the HY-2B SMR PWV data to GNSS and radiosonde data, likely due to temporal and spatial gaps. Geographically, there are greater differences between the HY-2B SMR and ERA5 in lower-latitude areas. The reason could be attributed to a higher water vapor content and more frequent cloudy weather in the areas. Discussion: The results demonstrate that the HY-2B SMR PWV meets requirement (RMSE≤3.5 mm). The HY-2B SMR PWV has a high quality, with a slight observational drift of only 0.1 mm/year, but regular validation and calibration are still necessary.

Water vapor plays an essential role in regulating the earth's weather and climate, and the tropospheric delays caused by water vapor are one of the error sources in space geodetic techniques. Attributing to the enhancement of the spatiotemporal resolution of satellite observations and the availability of model simulation data, the fusion of the two datasets provides a promising opportunity to improve the performance of tropospheric delay modeling and forecasting. In this contribution, a tropospheric delay network (TropNet) model is developed based on deep learning method to forecast the zenith wet delays (ZWD) by combining information provided by the Geostationary Operational Environmental Satellite-R series and the global forecast system (GFS). The performance of the tropospheric delays predicted from TropNet is assessed with tropospheric products derived from GNSS. The results demonstrate that the TropNet predicted ZWD agree well with the GNSS-derived ZWD, and an accuracy of better than 11 mm is achieved for all the forecast lead times, showing an overall improvement of 15.5% when compared to the GFS ZWD. Moreover, intercomparisons with ZWD derived from radiosondes and Vienna Mapping Functions 3 (VMF3) are performed to further evaluate the performance of the TropNet model. Averaged RMS values equal to 14.9 mm and 13.9 mm are obtained when compared to radiosondes and VMF3. Furthermore, the TropNet model is able to forecast high-quality ZWD up to 6 h at a spatial resolution of 2 km and a temporal resolution of 1 h, which indicates a prospective potential for time-critical applications.

In this study, a tropospheric delay model that integrates tropospheric delays derived from the European Centre for Medium-Range Weather Forecasts fifth-generation global atmospheric reanalysis and the Continuously Operating Reference Station (CORS) network observations in mountainous areas is established, which is then applied to improve GNSS precise point positioning (PPP). Observations of GNSS stations in the Great Dividing Range of eastern Australia are selected for the experiments. The performance of zenith wet delay (ZWD) retrieved from the integrated tropospheric model is evaluated with comparisons to precise point positioning (PPP) estimated ZWD values. Results show that the average root-mean-square value for ZWDs of the integrated tropospheric model is 8.03 mm for the eastern Australian CORS network, showing an improvement of 14.0% compared to that of the CORS interpolation model. Besides, the proposed tropospheric model is applied to regional augmentation precise positioning. Results present that the average positioning accuracy of the tropospheric model-corrected PPP solutions is 1.42 cm, 1.39 cm and 2.90 cm for the east, north and vertical components, respectively, revealing an improvement of 14.5%, 11.5% and 18.6% compared to the PPP solutions with regional CORS corrections. Meanwhile, almost all stations can achieve a faster solution convergence by performing the integrated tropospheric model-corrected PPP. All these results demonstrate the promising potential of the proposed tropospheric model in enhancing precise positioning as well as facilitating applications in the meteorological fields.

Accurate modeling of tropospheric delays is crucial for the global navigation satellite system (GNSS), which finds extensive applications in early warning systems of natural hazards and extreme weather forecasting. Zenith tropospheric delay (ZTD) is estimated as a random walk process with a constraint in GNSS processing. The constraint, referred to as random walk process noise (RWPN), holds significant importance in real-time ZTD estimation and exhibits geographical and temporal specificity. Presently, RWPN is treated as either a constant value or derived from a numerical weather model (NWM). To address this, our study presents a global RWPN model (GRM) by parameterizing a decade of NWM-derived RWPN data. Taking into account its spatiotemporal nature, we formulate the RWPN equation for each station by employing trigonometric, exponential, and Legendre functions. The optimum RWPN value is determined by incorporating GRM using latitude, longitude, orthometric height, and time as inputs. To validate the efficacy of GRM, we compare its performance against RWPN values derived from both JRA-55 and ERA5 datasets for the year 2020. The results indicate that the GRM-derived values exhibit enhanced accuracy in comparison with the optimal fixed RWPN values, as well as the yearly and monthly mean RWPN values. Additionally, we assess the efficacy of the GRM model in real-time ZTD estimation across 20 globally distributed GNSS stations. The results reveal an improvement exceeding 10