The meteorological reanalysis data has been widely applied to derive zenith tropospheric delay (ZTD) with a high spatial and temporal resolution. With the rapid development of artificial intelligence, machine learning also begins as a high-efficiency tool to be employed in modeling and predicting ZTD. In this paper, we develop three new regional ZTD models based on the least squares support vector machine (LSSVM), using both the International GNSS Service (IGS)-ZTD products and European Centre for Medium-Range Weather Forecasts Reanalysis 5 (ERA5) data over Europe throughout 2018. Among them, the ERA5 data is extended to ERA5S-ZTD and ERA5P-ZTD as the background data by the model method and integral method, respectively. Depending on different background data, three schemes are designed to construct ZTD models based on the LSSVM algorithm, including the without background data, with the ERA5S-ZTD, and with the ERA5P-ZTD. To investigate the advantage and feasibility of the proposed ZTD models, we evaluate the accuracy of two background data and three schemes by segmental comparison with the IGS-ZTD of 85 IGS stations in Europe. The results show that the overall average Root Mean Square Errors (RMSE) value of all sites is 30.1 mm for the ERA5S-ZTD, and 10.7 mm for the ERA5P-ZTD. The overall average RMSE is 25.8 mm, 22.9 mm, and 9 mm for the three schemes, respectively. Moreover, the overall improvement rate is 19.1% and 1.6% for the ZTD model with ERA5S-ZTD and ERA5P-ZTD, respectively. In order to explore the reason of the lower improvement for the ZTD model with ERA5P-ZTD, the loop verification is performed by estimating the ZTD values of each available IGS station. In actuality, the monthly improvement rate of estimated ZTD is positive for most stations, and the biggest improvement rate can even reach about 40%. The negative rate mainly comes from specific stations, these stations are located on the edge of the region, near the coast, as well as the lower similarity between the individual verified station and training stations.

Antarctica has a significant impact on global climate change. However, to draw climate change scenarios, there is a need for meteorological data, such as water vapor content, which is scarce in Antarctica. Global navigation satellite system (GNSS) networks can play a major role in overcoming this problem as the tropospheric delay that can be derived from GNSS measurements is an important data source for monitoring the variation of water vapor content. This work intends to be a contribution for improving the estimation of the zenith tropospheric delay (ZTD) obtained with the latest global pressure–temperature (GPT3) model for Antarctica through the use of long short-term-memory (LSTM) and radial basis function (RBF) neural networks for modifying GPT3_ZTD. The forecasting ZTD model is established based on the GNSS_ZTD observations at 71 GNSS stations from 1 January 2018 to 23 October 2021. According to the autocorrelation of the bias series between GNSS_ZTD and GPT3_ZTD, we predict the LSTM_ZTD for each GNSS station for period from October 2020 to October 2021 using the LSTM day by day. Based on the bias between LSTM_ZTD and GPT3_ZTD of the training stations, the RBF is adopted to estimate the LSTM_RBF_ZTD of the verified station, where the LSTM_ZTD represents the temporal forecasting ZTD at a single station, and the LSTM_RBF_ZTD represents the predicted ZTD obtained from space. Both the daily and yearly RMSE are calculated against the reference (GNSS_ZTD), and the improvement of predicted ZTD is compared with GPT3_ZTD. The results show that the single-station LSTM_ZTD series has a good agreement with the GNSS_ZTD, and most daily RMSE values are within 20 mm. The yearly RMSE of the 65 stations ranges from 6.4 mm to 32.8 mm, with an average of 10.9 mm. The overall accuracy of the LSTM_RBF_ZTD is significantly better than that of the GPT3_ZTD, with the daily RMSE of LSTM_RBF_ZTD significantly less than 30 mm, and the yearly RMSE ranging from 5.6 mm to 50.1 mm for the 65 stations. The average yearly RMSE is 15.7 mm, which is 10.2 mm less than that of the GPT3_ZTD. The LSTM_RBF_ZTD of 62 stations is more accurate than GPT3_ZTD, with the maximum improvement reaching 76.3%. The accuracy of LSTM_RBF_ZTD is slightly inferior to GPT3_ZTD at three stations located in East Antarctica with few GNSS stations. The average improvement across the 65 stations is 39.6%.

In precipitable water vapor (PWV) retrieval, results with high spatial coverage but low temporal resolution can be achieved through satellite-borne sensors, such as the Advanced Microwave Scanning Radiometer 2 (AMSR2). Conversely, the ground-based global navigation satellite system (GNSS) can provide PWV with high temporal resolution and high precision but low spatial coverage. To combine the advantages of these two technologies, we introduce a backpropagation neural network (BPNN) to realize PWV retrieval from AMSR2 with ground-based GNSS data. We first detect the optimal configuration for the BPNN. Then, based on the results of the retrieval accuracy from different types of orbits, we find that the descending (De) orbit has the highest retrieval accuracy, with a root-mean-square error (RMSE) of 3.25 mm. Afterward, the influence of brightness temperature (Tb) data at different frequencies on PWV retrieval is analyzed. The results of GNSS- PWV verification indicate that the 18 +23-GHz frequency combination has the highest PWV retrieval accuracy, and the mean RMSE of all 82 test stations distributed globally can reach 3.53 mm. We also analyze the influence of differently located stations on retrieval accuracy, and the results show that the accuracy of high-latitude and polar regions is remarkably higher than that of other areas but with a lower relative error. Finally, we use radiosonde data as another external verification method to assess PWV retrieval accuracy. The results reveal that RMSE can reach 3.87 mm. Through a BPNN approach, we have creatively realized PWV retrieval from AMSR2 using ground-based GNSS data on a global scale.

FY‐3E plays a vital role in the meteorological global earth observing system. Precipitable water vapor (PWV) is an essential parameter for the water cycle and global climate change. Here, we carry out the PWV retrieval using the MERSI‐LL sensor onboard the FY‐3E satellite for the first time. The retrieval accuracy under different cloudage conditions is validated by the extra PWV from ground‐based GNSS and spaceborne occultation. For the results against ground‐based GNSS, the total accuracy shows an RMSE of 2.69–3.36 mm as the clouds increase, and correlation coefficients higher than 0.95. The spatial accuracy distribution indicates that inland stations have higher accuracy than the coast and island stations. As for the results against spaceborne occultation, the verification accuracy varies with the spatial pairing distance, showing poor accuracy in the low latitude area. This study can provide an essential reference for the community to understand the current water vapor inversion performance of MERSI‐LL.

When applying the Global Navigation Satellite System (GNSS) for precise kinematic positioning in airborne and shipborne gravimetry, multiple GNSS receiving equipment is often fixed mounted on the kinematic platform carrying the gravimetry instrumentation. Thus, the distances among these GNSS antennas are known and invariant. This information can be used to improve the accuracy and reliability of the state estimates. For this purpose, the known distances between the antennas are applied as a priori constraints within the state parameters adjustment. These constraints are introduced in such a way that their accuracy is taken into account. To test this approach, GNSS data of a Baltic Sea shipborne gravimetric campaign have been used. The results of our study show that an application of distance constraints improves the accuracy of the GNSS kinematic positioning, for example, by about 4 mm for the radial component.