Data fusion is an effective method to obtain high-precision and high-spatiotemporal-resolution precipitable water vapor (PWV) products, which play an important role in understanding climate change and meteorological monitoring. However, existing fusion methods have some shortcomings, such as ignoring the applicability of the model space or the high complexity of model operation. In this study, the high-precision and high-temporal-resolution Global Navigation Satellite System (GNSS) PWV was used to calibrate and optimize the ERA5 PWV product of the European Center for Medium-Range Weather Forecasts Reanalysis 5 (ERA5) with high spatial resolution to improve its accuracy, and its applicability was verified at the spatiotemporal scale. First, this study obtained accurate GNSS PWV from meteorological data from stations and used it as the true value to analyze the distribution of the ERA5 PWV in mainland China. The results showed that the ERA5 PWV showed significant spatial and temporal differences. Then, a backpropagation neural network (BPNN) fusion correction model with additional constraints was established. The correction results showed that the bias of the ERA5 PWV mainly fluctuated near 0, the correlation between the ERA5 PWV and GNSS PWV was increased to 0.99, and the positive improvement rate of the root-mean-square error (RMSE) was 95%. In the temporal scale validation, the RMSE of the ERA5 PWV decreased from 2.05 mm to 1.67 mm, an improvement of 18.54%. In the spatial scale validation, the RMSE of the four seasons decreased by 0.26–80% (spring), 0.28–70.71% (summer), 0.28–45.23% (autumn), and 0.30–40.75% (winter). Especially in the summer and plateau mountainous areas where the ERA5 PWV performance was poor, the model showed suitable stability. Finally, the fusion model was used to generate a new PWV product, which improved the accuracy of ERA5 PWV on the basis of ensuring the spatial resolution.

The gravity matching algorithm plays a crucial role in gravity matching aided underwater navigation. At present, most matching algorithms are constructed based on correlation calculation between numerical gravity measurement sequence with reference maps that the performance of this single spatial domain feature correlation mode may be constrained under rough marine environments in practical tests. In this paper, a novel gravity matching algorithm based on spatial-frequency multidimensional feature fusion (SFM) was proposed. In this algorithm three new frequency features were extracted to present the complete frequency domain characteristics of the gravity measurement sequence: Spatial-frequency Trend Concordance Degree, Spatial-frequency Joint-Correlation Comparison, and Spatial Directional Similarity. Then they are fused with spatial-domain numerical features to construct a multidimensional feature correlation evaluation index for gravity matching navigation. To verify performance of the SFM algorithm, simulation experiments were conducted across eight oceanic regions exhibiting diverse gravity distribution. The results demonstrated that under different conditions, SFM algorithm maintained much better positioning accuracy and stability than other algorithm. Furthermore, marine measured gravity data from the South China Sea was employed for verification experiments. The results indicated that the SFM algorithm consistently achieved a positioning accuracy better than 2.0 nautical miles along each survey line, while other algorithms suffered from emerging mismatches in segments with increased measurement errors. Benefit from the frequency features extraction and spatial-frequency multidimensional feature fusion, the proposed SFM algorithm shows the advantages of robustness and accuracy even under challenging conditions in both simulation and measured data experiments.

The El Niño-Southern Oscillation (ENSO) event often causes natural disasters in mainland China. Existing quantitative analysis of ENSO event’s effects on climate change in mainland China is insufficient. The monthly scale prediction effectiveness of ENSO events is still low. Global Navigation Satellite System (GNSS) can estimate zenith tropospheric delay (ZTD) with high accuracy, which can study ZTD responses to ENSO and improve the prediction accuracy of ENSO events. This study quantitatively analyzed the response patterns of GNSS ZTD time–frequency variation to ENSO events in mainland China. The monthly multivariate ENSO index (MEI) thresholds for GNSS ZTD anomaly response to ENSO events are (−1.12, 1.92) for the tropical monsoon zone (TPMZ), (−1.12, 1.61) for the subtropical monsoon zone (SMZ), (−1.19, 1.62) for the temperate monsoon zone (TMZ), (−1.26, 1.64) for the temperate continental zone (TCZ), and (−1.22, 1.72) for the mountain plateau zone (MPZ). The ENSO event causes the amplitude of the nine-month variation period to decrease and the amplitude of the 0.8–3-month period to increase for the GNSS ZTD in mainland China. Furthermore, a forecasting model is proposed by integrating fast Fourier transform and long short-term memory extended (FFT-LSTME). The model uses monthly MEI as the primary input and the GNSS ZTD reconstruction sequence that responds to ENSO as the auxiliary input. It can predict ENSO events in the next 24 months with an index of agreement (IA) of 91.56% and a root mean square error (RMSE) of 0.25. The RMSE is optimized by 70.48%, 43.95%, and 11.6% when compared with radial basis function (RBF), LSTM, and FFT-LSTM.

Accurate prediction of PM_2.5 (particle pollution from fine particulate) concentration is crucial for environmental protection and public health. Precipitable water vapor (PWV) in the atmosphere is an important meteorological element with stratification properties, which plays a crucial role in energy transfer, weather dynamics, and PM_2.5 generation. However, past studies tend to use total PWV as an input parameter, neglecting the impact of PWV variations in different altitude layers on PM_2.5 concentration. To overcome this limitation, this study proposes an innovative approach that employs stratified water vapor data (ERA5-PWV) calculated from the ERA5 reanalysis data instead of the total PWV obtained using the traditional method. This approach provides a more accurate representation of the vertical distribution of atmospheric PWV and enhances the prediction of PM_2.5 content. In this study, the stratified ERA5 PWV in the Beijing–Tianjin–Hebei region is integrated with other meteorological elements and atmospheric pollutants, and the FFT-ConvLSTM method, characterized by its spatio-temporal properties, is utilized to predict the PM_2.5 concentration by incorporating the spatio-temporal correlation. The FFT-ConvLSTM model is modeled by extracting spatio-temporal features through ConvLSTM, following the identification of the optimal common change period of each element using the FFT technique. This process mitigates the problem of spatio-temporal heterogeneity among elements, thus, realizing the high-precision prediction of gridded PM_2.5 concentration in the next 24 h. The research results show that among the results of different layers of ERA5-PWV combinations involved in the prediction of PM_2.5 concentrations in the research region, divided into three parts of the research region—plains, mountains, and plateaus—the stratified ERA5-PWV from layers 1–4 with pressure levels consistently outperformed the total ERA5-PWV in accuracy, and the RMSEs of the predicted results for the PM_2.5 concentrations were each reduced by 0.862 μg/m³, 5.384 μg/m³ and 1.706 μg/m³.