Comparison of Several Methods for Outlier Estimation

Computational problem of gross errors estimation is discussed based on the mean shift model, and the gross errors estimation formulas of the observed statistical correlation data snooping method are given. The relationships of gross errors estimation of the data snooping method, the method of simultaneous locating and evaluating multidimensional gross errors (LEGE), quasi-accurate detection of gross errors (QUAD) method and the partial least-squares (PLS) method are discussed. It is proved that ① in the case of correlated observations, calculation of gross errors estimation of the PLS method and the QUAD method are equivalent. However, these two methods are different with the data snooping method and the LEGE method; ② in the case of uncorrelated and unequal weight observations, calculation of gross errors estimation of the QUAD method, the PLS method and the data snooping method are equivalent, but these three methods are different with the LEGE method; ③ in the case of uncorrelated and equal weight observations, calculation of gross errors estimated value of these four methods are equivalent. Finally, the case studies verify the conclusions

An Improved Adaptive IVMD-WPT-Based Noise Reduction Algorithm on GPS Height Time Series

To improve the reliability of Global Positioning System (GPS) signal extraction, the traditional variational mode decomposition (VMD) method cannot determine the number of intrinsic modal functions or the value of the penalty factor in the process of noise reduction, which leads to inadequate or over-decomposition in time series analysis and will cause problems. Therefore, in this paper, a new approach using improved variational mode decomposition and wavelet packet transform (IVMD-WPT) was proposed, which takes the energy entropy mutual information as the objective function and uses the grasshopper optimisation algorithm to optimise the objective function to adaptively determine the number of modal decompositions and the value of the penalty factor to verify the validity of the IVMD-WPT algorithm. We performed a test experiment with two groups of simulation time series and three indicators: root mean square error (RMSE), correlation coefficient (CC) and signal-to-noise ratio (SNR). These indicators were used to evaluate the noise reduction effect. The simulation results showed that IVMD-WPT was better than the traditional empirical mode decomposition and improved variational mode decomposition (IVMD) methods and that the RMSE decreased by 0.084 and 0.0715 mm; CC and SNR increased by 0.0005 and 0.0004 dB, and 862.28 and 6.17 dB, respectively. The simulation experiments verify the effectiveness of the proposed algorithm. Finally, we performed an analysis with 100 real GPS height time series from the Crustal Movement Observation Network of China (CMONOC). The results showed that the RMSE decreased by 11.4648 and 6.7322 mm, and CC and SNR increased by 0.1458 and 0.0588 dB, and 32.6773 and 26.3918 dB, respectively. In summary, the IVMD-WPT algorithm can adaptively determine the number of decomposition modal functions of VMD and the optimal combination of penalty factors; it helps to further extract effective information for noise and can perfectly retain useful information in the original time series

The GNSS PWV retrieval using non-observation meteorological parameters based on ERA5 and its relation with precipitation

The pressure and temperature significantly influence precipitable water vapor (PWV) retrieval. Global Navigation Satellite System (GNSS) PWV retrieval is limited because the GNSS stations lack meteorological sensors. First, this article evaluated the accuracy of pressure and temperature in 68 radiosonde stations in China based on ERA5 Reanalysis data from 2015 to 2019 and compared them with GPT3 model. Then, the accuracy of pressure and temperature calculated by ERA5 were estimated in 5 representative IGS stations in China. And the PWV calculated by these meteorological parameters from ERA5 (ERA5-PWV) were analyzed. Finally, the relation between ERA5-PWV and precipitation was deeply explored using wavelet coherence analysis in IGS stations. These results indicate that the accuracy of pressure and temperature of ERA5 is better than the GPT3 model. In radiosonde stations, the mean BIAS and MAE of pressure and temperature in ERA5 are −0.41/1.15 hpa and −0.97/2.12 K. And the mean RMSEs are 1.35 hpa and 2.87 K, which improve 74.77% and 40.58% compared with GPT3 model. The errors of pressure and temperature of ERA5 are smaller than the GPT3 model in bjfs, hksl and wuh2, and the accuracy of ERA5-PWV is improved by 18.77% compared with the GPT3 model. In addition, there is a significant positive correlation between ERA5-PWV and precipitation. And precipitation is always associated with the sharp rise of ERA5-PWV, which provides important references for rainfall prediction

Response of upper tropospheric water vapor to global warming and ENSO

Abstract The upper tropospheric water vapor is a key component of Earth's climate. Understanding variations in upper tropospheric water vapor and identifying its influencing factors is crucial for enhancing our comprehension of global climate change. While many studies have shown the impact of El Niño-Southern Oscillation (ENSO) and global warming on water vapor, how they affect the upper tropospheric water vapor remains unclear. Long-term, high-precision ERA5 specific humidity data from the European Centre for Medium-Range Weather Forecasts (ECMWF) provided the data foundation for this study. On this basis, we successfully obtained the patterns of global warming (Independent Component 1, IC1) and ENSO (Independent Component 2, IC2) by employing the strategy of independent component analysis (ICA) combined with non-parametric optimal dimension selection to investigate the upper tropospheric water vapor variations and responses to ENSO and global warming. The results indicate that global warming and ENSO are the primary factors contributing to water vapor variations in the upper troposphere, achieving the significant correlations of 0.87 and 0.61 with water vapor anomalies respectively. Together, they account for 86% of the global interannual variations in water vapor. Consistent with previous studies, our findings also find positive anomalies in upper tropospheric water vapor during El Niño years and negative anomalies during La Niña years. Moreover, the influence extent of ENSO on upper tropospheric water vapor varies with the changing seasons

GNSS-TS-NRS: An Open-Source MATLAB-Based GNSS Time Series Noise Reduction Software

The global navigation satellite system (GNSS) has seen tremendous advances in measurement precision and accuracy, and it allows researchers to perform geodynamics and geophysics studies through the analysis of GNSS time series. Moreover, GNSS time series not only contain geophysical signals, but also unmodeled errors and other nuisance parameters, which affect the performance in the estimation of site coordinates and related parameters. As the number of globally distributed GNSS reference stations increases, GNSS time series analysis software should be developed with more flexible format support, better human–machine interaction, and with powerful noise reduction analysis. To meet this requirement, a new software named GNSS time series noise reduction software (GNSS-TS-NRS) was written in MATLAB and was developed. GNSS-TS-NRS allows users to perform noise reduction analysis and spatial filtering on common mode errors and to visualize GNSS position time series. The functions’ related theoretical background of GNSS-TS-NRS were introduced. Firstly, we showed the theoretical background algorithms of the noise reduction analysis (empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD)). We also developed three improved algorithms based on EMD for noise reduction, and the results of the test example showed our proposed methods with better effect. Secondly, the spatial filtering model supported five algorithms on a separate common model error: The stacking filter method, weighted stacking filter method, correlation weighted superposition filtering method, distance weighted filtering method, and principal component analysis, as well as with batch processing. Finally, the developed software also enabled other functions, including outlier detection, correlation coefficient calculation, spectrum analysis, and distribution estimation. The main goal of the manuscript is to share the software with the scientific community to introduce new users to the GNSS time series noise reduction and application