In recent years, geographically weighted regression (GWR) models have been widely used to address the spatial heterogeneity and spatial autocorrelation of PM_2.5, but these studies have not fully considered the effects of all potential variables on PM_2.5 variation and have rarely optimized the models for residuals. Therefore, we first propose a modified GWR model based on principal component analysis (PCA-GWR), then introduce five different spatial interpolation methods of radial basis functions to correct the residuals of the PCA-GWR model, and finally construct five combinations of residual correction models to estimate regional PM_2.5 concentrations. The results show that (1) the PCA-GWR model can fully consider the contributions of all potential explanatory variables to estimate PM_2.5 concentrations and minimize the multicollinearity among explanatory variables, and the PM_2.5 estimation accuracy and the fitting effect of the PCA-GWR model are better than the original GWR model. (2) All five residual correction combination models can better achieve the residual correction optimization of the PCA-GWR model, among which the PCA-GWR model corrected by Multiquadric Spline (MS) residual interpolation (PCA-GWRMS) has the most obvious accuracy improvement and more stable generalizability at different time scales. Therefore, the residual correction of PCA-GWR models using spatial interpolation methods is effective and feasible, and the results can provide references for regional PM_2.5 spatial estimation and spatiotemporal mapping. (3) The PM_2.5 concentrations in the study area are high in winter months (January, February, December) and low in summer months (June, July, August), and spatially, PM_2.5 concentrations show a distribution of high north and low south.

Recent decades have witnessed the emergence of the Global Navigation Satellite System (GNSS) Zenith Tropospheric Delay (ZTD) as a pivotal element within the domain of GNSS meteorology. The spatial density of ZTD data is contingent on the number of regional GNSS stations, thereby influencing its application in regional meteorology. This research presents a novel model, GWR-CNN (Geographically Weighted RegressionConvolutional Neural Networks), which utilizes convolutional neural networks to address geographically weighted regression residuals. Utilizing the French region as an illustrative case, this model necessitates solely the acquisition of positional information (comprising precise longitude, latitude, and height) and the ZTD values of the GNSS stations to execute high-precision interpolation calculations for regional ZTD. It is noteworthy that the outcomes of high-precision interpolation for ZTD can closely approximate actual observations, thereby augmenting the predictive capability of the Weather Research and Forecasting (WRF) model for regional rainfall through the process of data assimilation.

To overcome the limitations of long-term prediction of PM_2.5 concentration, a multi-factor information flow causality analysis method is used to screen suitable meteorological and air pollutant-related factors and concatenate them with a PM_2.5 sequence as the dataset. A modal decomposition algorithm is used as a module to be integrated into the autoformer (transformer improved with autocorrelation mechanism) model to improve it, and the modal autoformer (empirical modal decomposition combined with autoformer) is proposed. The constructed model decomposes the sequence into several components by using the modal decomposition module and uses the self-correlation mechanism and decomposition structure to decompose and extract features of different components at the time-feature level. Based on the matching method, the model is adjusted for different component features to improve the long-term prediction effect. The model is applied to three cities in Henan Province, Zhengzhou, Luoyang, and Zhumadian, as examples for experiments, and gated neural unit (GRU), informer, autoformer, and modal GRU (empirical modal decomposition combined with GRU model) are constructed for comparative verification. The results show that the modal autoformer can better cope with the complex characteristics of long-term prediction of the PM_2.5 time series, has strong spatial adaptability and that its various indicators are optimal for the three cities, with R² values being all above 0.96, where the highest is 0.987 in Zhengzhou; MAPE (Mean absolute percentage error) values all being less than 10, where the best is 7.602 in Zhumadian; and MAE (Mean absolute error) values all being less than 4. The prediction effect is stable enough, showing its feasibility and adaptability in long-term prediction.

Tropospheric delay, for which water vapor is a major cause, is a significant source of error in Global Navigation Satellite System (GNSS). This paper presents the GFZTD (Gray Figure-based Zenith Tropospheric Delay prediction) model, which is built on Convolutional Long Short-Term Memory Networks (ConvLSTM) and self-attention mechanisms. The model converts three-dimensional (3-D) zenith tropospheric delay (ZTD) grid products into multi-layer two-dimensional grayscale images for predictive analysis. Utilizing Global Forecast System (GFS) and ERA5 data from southeastern China and its adjacent seas in 2023, the GFZTD model is trained through seasonal slicing and stratification by altitude. This approach generates high spatio-temporal resolution ZTD 3-D grid products in near real-time. To evaluate the grid prediction results, ERA5 is used as the truth, with an overall RMSE of 1.35 cm, representing improvements of 26.5% and 71.0% over ZTD derived from GFS and GPT3 (Global Pressure and Temperature 3), respectively. The model also successfully mitigates regional extreme prediction errors in complex terrain environments for GFS. Additionally, when using VMF3 (Vienna Mapping Functions 3) post-processing products to assess ZTD prediction values at various stations, the GFZTD model shows an average root mean square error (RMSE) of 1.49 cm. This result indicates improvements of 13.1% and 69.4% compared to GFS and GPT3, respectively, underscoring the model's applicability at the station scale.