In order to study and forecast extreme weather, a comprehensive and systematic analysis of the spatial and temporal relationship between Precipitable Water Vapor (PWV), predicted by Numerical Weather Predication (NWP) data, and precipitation, is necessary. The goal of this paper was to study the temporal and spatial relationship between PWV and precipitation during the so-called ‘July 20’ (18–21 July 2021) heavy rainstorm in Zhengzhou. Firstly, the PWV data provided by 120 radiosonde stations uniformly distributed throughout the world, and two IGS stations in China, in 2020, was used to evaluate the accuracy of PWV estimation by ERA5 and MERRA-2 data, and the factors affecting the accuracy of NWP PWV were explored. Secondly, ERA5 PWV and the precipitation data of six meteorological stations were used to qualitatively analyze the relationship between PWV and precipitation during the ‘July 20’ heavy rainstorm in Zhengzhou. Finally, a quantitative study was conducted by an eigenvalue matching method. The main experimental results were as follows. Compared with MERRA-2 PWV, the accuracy of ERA5 PWV was slightly higher. Latitude, altitude and season were the influencing factors of the NWP PWV estimation accuracy. The change trend of ERA5 PWV was consistent with both 24 h cumulative precipitation and surface precipitation during the ‘July 20’ heavy rainstorm in Zhengzhou. The average optimal matching degree and optimal matching time between NWP PWV and surface precipitation during the ‘July 20’ heavy rainstorm in Zhengzhou was 56.6% and 3.68 h, respectively. The maximum optimal matching degree was 80.3%. The spatial–temporal relationship between NWP PWV and surface precipitation was strong.

Step detection for smartphones plays an important role in the pedestrian dead reckoning (PDR) for indoor positioning. Aiming at the problem of low step detection accuracy of smartphones in complex unconstrained states in PDR, smartphone-based unconstrained step detection method fusing a variable sliding window and an adaptive threshold is proposed. In this method, the dynamic updating algorithm of a peak threshold is developed, and the minimum peak value filtered after a sliding window filter is used as the adaptive peak threshold, which solves the problem that the peak threshold of different motion states is difficult to update adaptively. Then, a variable sliding window collaborative time threshold method is proposed, which solves the problem that the adjacent windows cannot be contacted, and the initial peak and the end peak are difficult to accurately identify. To evaluate the performance of the proposed unconstrained step detection algorithm, 50 experiments in constrained and unconstrained states are conducted by 25 volunteers holding 21 different types of smartphones. Experimental results show: The average step counting accuracy of the proposed unconstrained step detection algorithm is over 98%. Compared with the open source program Stepcount, the average step counting accuracy of the proposed algorithm is improved by 10.0%. The smartphone-based unconstrained step detection fusing a variable sliding window and an adaptive threshold has a strong ability to adapt to complex unconstrained states, and the average step counting accuracy rate is only 0.6% lower than that of constrained states. This algorithm has a wide audience and is friendly for different genders and smartphones with different prices.

The serious and frequent typhoon activities can easily cause extreme precipitation weather in the eastern coastal area of China, which is affected by land and sea differences. To explore the temporal and spatial characteristics of Precipitable Water Vapor (PWV) and rainfall during the typhoon period, the data of the conspicuous case named ‘Meihua’ in 2022 is adopted in analysis. In this paper, firstly, the accuracy of the PWV retrieved by ERA5 was evaluated, which met the experimental analysis requirements, compared with the conference value of the Radiosonde (RS). Secondly, the correlation between PWV, rainfall and the typhoon path were analyzed qualitatively and quantitatively, using 16 meteorological stations in the typhoon path. The results indicated that PWV reached its peak value 2–6 h than rainfall, which was an important reference for rainfall forecasting. Then, the ‘Pearson correlation coefficient’ method was used for the quantitative evaluation of the correlation between PWV and the distance of the ‘weather station-typhoon’. The results showed that PWV had an obvious upward trend, with a decrease in the distance between the ‘weather station-typhoon’. The variation in PWV is intense at a reduced distance, and can reach its peak 16 h before the arrival of the typhoon. A strong negative correlation was demonstrated, with an average value of −0.73 for the Pearson correlation coefficient. Analyzing the temporal and spatial changes of the typhoon track, PWV and rainfall, the results show that before the typhoon passes through the region, both the PWV and rainfall certainly reach their maximum. The variation trends of PWV and rainfall in the period of the typhoon are significantly consistent. The center of PWV and rainfall is mainly located on the northwest side of the typhoon center, which showed obvious asymmetry.

Currently, rainfall cannot be accurately forecast because of poor network communication at the ocean. The advantage of the BeiDou Global Navigation Satellite System (BDS-3) precise point positioning (PPP-B2b) signal, which does not rely on network communication to receive data, is that it can provide precipitable water vapor (PWV) retrieval application services for the open seas in eastern China, where the communication system presents difficulties. In this study, data from stations in the coastal region of China were used to establish a rainfall forecasting method for monitoring extreme weather on the sea. First, the service performance of PPP-B2b was explored. Then, based on 17 Chinese coastal stations, the PWV accuracy was evaluated. Finally, based on an analysis of the relationship between PWV and actual rainfall, a threshold rainfall forecasting method based on a sliding window was constructed. The experimental results show that the PWV accuracy varies slightly depending on the geographic location, in which the mean absolute error in the North Sea region is the smallest (2.1 mm), that of the South China Sea region is the largest (2.60 mm), and that of the East China Sea region is in the middle (2.48 mm). The optimal predictors of the constructed 12 h sliding-window threshold rainfall prediction method are a PWV maximum of 49 mm, PWV increase of 5 mm, and PWV increase rate of 1.2 mm h⁻¹. The prediction results can reach a critical success index value of more than 45%, indicating high prediction accuracy and applicability to the coastal region of China during the same period.

Global Navigation Satellite System (GNSS) buoys are widely used to retrieve wave parameters such as significant wave heights (SWHs) and dominant wave periods. In addition to the statistical methods employed to estimate wave parameters, spectral-analysis-based approaches are also frequently utilized to analyze them. This study presents statistical and spectral methods for retrieving wave parameters at GNSS buoy positioning resolution in the Huanghai Sea area. To verify the method’s effectiveness, the zero-crossing method and three spectral analysis techniques (periodogram, autocorrelation function, and autoregressive model methods) were used to estimate wave height and period for comparison. The vertical positioning resolution was decomposed into low-frequency ocean-tide level information and high-frequency wave height and period information with the Complete Ensemble Empirical Mode Decomposition (CEEMD) method and moving average filtering. The horizontal positioning results and velocity parameters were used to determine the wave direction using directional spectrum analysis. The results show that the three spectral methods yield consistent effective wave heights, with a maximum difference of 0.02 s in the wave period. Compared with the zero-crossing method results, the wave height and period obtained through spectral analysis differ by 0.05 m and 0.79 s, respectively, while the average wave height and period differ by 0.09 m and 0.08 s, respectively. The GNSS-derived wave heights also closely match tidal gauge observations, confirming the method’s validity. Directional spectrum analysis indicates that wave energy is concentrated in the 0.2–0.25 Hz frequency band and within a directional range of 0° ± 30°, with a dominant northward propagation trend. These findings demonstrate that the proposed approach can provide high accuracy and physical consistency for GNSS-based wave monitoring under complex sea conditions.

Determining the sea surface height using Global Navigation Satellite System (GNSS) buoys is an important method for satellite altimetry calibration. The buoys observe the absolute height of the sea surface using GNSS positioning technology, which is then used to correct the systematic deviation of the altimeter of the orbiting satellite. Due to the challenging observational conditions, such as significant multipath errors in GNSS code observation and complex variations in buoy position and attitude, gross errors in GNSS buoy positioning reduce the accuracy and stability of the calculated sea surface heights. To accurately detect and remove these gross errors from GNSS coordinate time series, the complementary ensemble empirical mode decomposition (CEEMD) method and the interquartile range (IQR) method were adopted to enhance the accuracy and stability of GNSS sea surface altimetry. Firstly, the raw GNSS sequential coordinate series are decomposed into main terms, such as trend contents and periodic contents, and high-frequency noise terms using the CEEMD method. Subsequently, the high-frequency noise terms of the GNSS coordinate series are regarded as the residual sequences, which are used to detect gross errors using the IQR method. This approach, which integrates the CEEMD and IQR methods, was named CEEMD-IQR and enhances the ability of the traditional IQR method to detect subtle gross errors in GNSS coordinate time series. The results indicated that the CEEMD-IQR method effectively detected gross errors in offshore GNSS coordinate time series using GNSS buoys, presenting a significant enhancement in the gross error detection rate of at least 35.3% and providing a “clean” time series for sea level measurements. The resulting GNSS sea surface altimetry accuracy was found to be better than 1.51 cm.