The monitoring of fog density is of great importance in meteorology and its applications in environment, aviation and transportation. Nowadays, vision-based fog estimation from images taken with surveillance cameras has made a great supplementary contribution to the scarcely traditional meteorological fog observation. In this paper, we propose a new Random Forest (RF) approach for image-based fog estimation. In order to reduce the impact of data imbalance on recognition, the StyleGAN2-ADA (generative adversarial network with adaptive discriminator augmentation) algorithm is used to generate virtual images to expand the data of low proportions. Key image features related to fog are extracted, and an RF method, integrated with the hierarchical and k-medoid clustering, is deployed to estimate the fog density. The experiment conducted in Sichuan in February 2024 shows that the improved RF model has achieved an average accuracy of fog density observation of 93%, 6.4% higher than the RF model without data expansion, 3–6% higher than the VGG16, the VGG19, the ResNet50, and the DenseNet169 with or without data expansion. What is more, the improved RF method exhibits a very good convergence as a cost-effective solution.

The accurate measurement of water vapor is essential for research about and the applications of meteorology, climatology, and hydrology. Based on the BeiDou PPP-B2b service, real-time precipitable water vapor (PWV) can be retrieved with the precise point positioning (PPP) software (XTW-PPP version 0.0). The experiment was conducted in Beijing in January 2023. Three solutions were designed with PPP using the BeiDou system only, the GPS system only, and the BeiDou-GPS combined solution. Real-time PWVs for the three solutions were validated with the ERA5 reanalysis data. Between the PWV values from the single BeiDou and ERA5, there was a bias of 0.7 mm and an RMSE of 1.8 mm. For the GPS case, the bias was 0.73 mm and the RMSE was 1.97 mm. The biases were less than 1 mm and RMSEs were less than 2 mm. Both the BeiDou and the GPS processing performed very well. But little improvement was found for the BeiDou-GPS combined solution, compared with the BeiDou system-only and the GPS system-only solution. This may be due to the poor handling of two different kinds of errors for the GPS and the BeiDou systems in our PPP software. A better PWV estimation with the two systems is to estimate PWV with a single system at the first step and then obtain the optimization by Bayesian model averaging.

Accurate measurement of water vapor is essential for researches and applications of meteorology, climatology and hydrology. Based on the BeiDou PPP-B2b service, real-time precipitable water vapor (PWV) is retrieved with the precise point positioning (PPP) software. The experiment was conducted in Beijing in January, 2023. Three solutions are designed with PPP using the BeiDou system only, the GPS system only and the BeiDou-GPS combined solution. Real-time PWVs for the 3 solutions are validated with the ERA5 reanalysis data. Between PWVs from single BeiDou and ERA, there are a bias of 0.7 mm and a RMSE of 1.8 mm. While for the GPS case, the bias is 0.73 mm and RMSE is 1.97 mm. The biases are less than 1 mm and RMSEs are less than 2mm. Both the BeiDou and the GPS processing performs very well. But little improvement is found for the BeiDou-GPS combined solution, comparing with the BeiDou system only and the GPS system only solution. This may be due to the poor handling of two different kinds of errors for the GPS and the BeiDou systems in our PPP software. A better PWV estimation with the two systems is to estimate PWV with single system at first step, and then to obtain the optimization by Bayesian model averaging.

The monitoring of fog density is of great importance in meteorology and its applications in environment, aviation and transportation. Nowadays, vision-based fog estimation from images taken with surveillance cameras has made a great supplementary contribution to the scarcely traditional meteorological fog observation. In this paper, we propose a new Random Forest (RF) approach for image-based fog estimation. In order to reduce the impact of data imbalance on recognition, the StyleGAN2-ADA (generative adversarial network with adaptive discriminator augmentation) algorithm is used to generate virtual images to expand the data of low proportions. Key image features related to fog are extracted, and an RF method, integrated with the hierarchical and k-medoids clustering, is deployed to estimate the fog density. The experiment conducted in Sichuan in February 2024 shows that the improved RF model has achieved an average accuracy of fog density observation to 93%, 6.4% higher than the RF model without data expansion, 3%-6% higher than the VGG16, the VGG19, the ResNet50, and the DenseNet169 with or without data expansion. What is more, the improved RF method exhibits a very good convergence as a cost-effective solution.

Accurate estimation of the weighted mean temperature (Tm) is essential for retrieving precipitable water vapor (PWV) from ground-based Global Navigation Satellite System (GNSS) observations. Machine learning (ML) techniques excel in modeling nonlinear relationships among Tm time series, station geographic coordinates, and surface meteorological parameters, and recent studies have demonstrated that ML and neural network models outperform conventional linear Tm models. However, the full potential of surface meteorological measurements at GNSS stations for high-precision Tm retrieval remains to be fully explored. This study develops regional Tm empirical models using two ML methods—random forest (RF) and Temporal Mixture of Experts with Sequential Attention (TMESA)—to generate reliable real-time Tm estimates and enhance the accuracy of operational GNSS-PWV retrievals over China. A traditional linear model is adopted as the baseline to evaluate the performance improvements of the proposed models. The models are trained and tested using 10-year (2014–2023) hourly ERA5-derived Tm products and in-situ surface pressure, temperature, and relative humidity from 2377 meteorological stations, with Tm diurnal variations, station coordinates, and day of year integrated as auxiliary predictive features. Validation is conducted using 2024 ERA5 reanalysis data and radiosonde profiles from 120 stations across China. Results show that the RF model yields a bias (RMSE) of −0.11 K (2.67 K) against ERA5 and −0.21 K (2.67 K) against radiosonde data, while the TMESA model achieves superior performance with bias (RMSE) of −0.02 K (2.34 K) and 0.09 K (2.46 K), respectively, whose performance levels comparable to state-of-the-art studies. Compared with the traditional linear model, the RF model reduces Tm RMSE by 32% against ERA5 and 25% against radiosonde data, while the TMESA model achieves reductions of 40% and 33%, respectively. These findings confirm that the proposed ML models can provide high-accuracy Tm estimates for reliable GNSS-PWV retrieval. Future work will focus on the operational application of these models for near-real-time GNSS-PWV estimation.

Ground-based BeiDou Navigation Satellite System/Global Navigation Satellite System (BDS/GNSS) observations can be used to retrieve precipitable water vapor (PWV) at high temporal resolution, but the estimates are confined to discrete station locations. We applied the pretrained tabular regression model LimiX, using its 2M variant, to PWV interpolation over the Beijing–Tianjin–Hebei region in 2024. Station spatial features paired with PWV estimates served as context without regional retraining. Comparisons with inverse distance weighting, ordinary kriging, universal kriging, and geographically weighted regression used PWV derived from the ERA5 reanalysis and a separate fixed-station holdout experiment. Against ERA5, LimiX had an annual mean absolute difference of 1.1 mm and a root mean square difference of 1.5 mm. Its spatial correlation coefficient (SCC) was 0.97. LimiX had the lowest root mean square difference relative to ERA5 in all seasons and months. Interpolation validation against observations at 13 withheld GNSS stations gave an annual root mean square error of 1.3 mm, close to both kriging methods. During a heavy precipitation event on 9–10 August 2024, mean PWV began increasing before quantitative precipitation estimation (QPE) rose markedly and remained elevated after the QPE peak. High-PWV and high-QPE areas overlapped locally at some epochs. LimiX combined close ERA5 agreement with station-level interpolation errors comparable to kriging, providing regional PWV fields without retraining for the study area.