Accurate noise model identification for GNSS time series is crucial for obtaining a reliable GNSS velocity field and its uncertainty for various studies in geodynamics and geodesy. Here, by comprehensively considering time span and missing data effect on the noise model of GNSS time series, we used four combined noise models to analyze the duration of the time series (ranging from 2 to 24 years) and the data gap (between 2% and 30%) effects on noise model selection and velocity estimation at 72 GNSS stations spanning from 1992 to 2022 in global region together with simulated data. Our results show that the selected noise model have better convergence when GNSS time series is getting longer. With longer time series, the GNSS velocity uncertainty estimation with different data gaps is more homogenous to a certain order of magnitude. When the GNSS time series length is less than 8 years, it shows that the flicker noise and random walk noise and white noise (FNRWWN), flicker noise and white noise (FNWN), and power law noise and white noise (PLWN) models are wrongly estimated as a Gauss–Markov and white noise (GGMWN) model, which can affect the accuracy of GNSS velocity estimated from GNSS time series. When the GNSS time series length is more than 12 years, the RW noise components are most likely to be detected. As the duration increases, the impact of RW on velocity uncertainty decreases. Finally, we show that the selection of the stochastic noise model and velocity estimation are reliable for a time series with a minimum duration of 12 years.

To solve the problems of difficult to model parameter selections, useful signal extraction and improper-signal decomposition in nonlinear, non-stationary dam displacement time series prediction methods, we propose a new predictive model for grey wolf optimization and variational mode decomposition and long short-term memory (GVLSTM). Firstly, we used the grey wolf optimization (GWO) algorithm to optimize the parameters of variable mode decomposition (VMD), obtaining the optimal parameter combination. Secondly, we used multiscale permutation entropy (MPE) as a standard to select signal screening, determining and recon-structing the effective modal components. Finally, the long short-term memory neural network (LSTM) was used to learn the dam deformation characteristics. The result shows that the GVLSTM model can effectively reduce the estimation deviation of the prediction model. Compared with VMDGRU and VMDANN, the average RMSE and MAE value of each station is increased by 19.11%~28.58% and 27.66%~29.63%, respectively. We used determination (R²) coefficient to judge the performance of the prediction model, and the value of R² was 0.95~0.97, indicating that our method has good performance in predicting dam deformation. The proposed method has outstanding advantages of high accuracy, reliability, and stability for dam deformation prediction.

Seasonal variations in the vertical Global Positioning System (GPS) time series are mainly caused by environmental loading, e.g., hydrological loading (HYDL), atmospheric loading (ATML), and nontidal oceanic loading (NTOL), which can be synthesized based on models developed by various institutions. A comprehensive comparison among these models is essential to extract reliable vertical deformation data, especially on a regional scale. In this study, we selected 4 HYDL, 5 ATML, 2 NTOL, and their 40 combined products to investigate their effects on seasonal variations in vertical GPS time series at 27 GPS stations in Yunnan, southwest China. These products were provided by the German Research Center for Geosciences (GFZ), School and Observatory of Earth Sciences (EOST), and International Mass Loading Service (IMLS). Furthermore, we used the Cross Wavelet Transform (XWT) method to analyze the relative phase relationship between the GPS and the environmental loading time series. Our result showed that the largest average Root-Mean-Square (RMS) reduction value was 1.32 mm after removing the deformation associated with 4 HYDL from the vertical GPS time series, whereas the RMS reductions after 5 ATML and 2 NTOL model corrections were negative at most stations in Yunnan. The average RMS reduction value of the optimal combination of environmental loading products was 1.24 mm, which was worse than the HYDL (IMLS_GEOSFPIT)-only correction, indicating that HYDL was the main factor responding for seasonal variations at most stations in Yunnan. The XWT result showed that HYDL also explained the annual variations reasonably. Our finding implies that HYDL (IMLS_GEOSFPIT) contributes the most to the environmental loading in Yunnan, and that the ATML and NTOL models used in this paper cannot be effective to correct seasonal variations.

In view of the fact that there is no unified understanding of the GNSS horizontal velocity field in the Beijing Plain and the serious land subsidence in this area, we collected GNSS data from 2011 to 2021 and Sentinel 1A data from 2017 to 2021 and conducted high-precision GNSS data processing and PS-InSAR verification in order to determine the reason for the differences in the GNSS horizontal velocity field in the Beijing Plain. The results show that, under the stable Eurasian framework, the horizontal velocity of GNSS stations in the Beijing Plain is significantly inconsistent. The velocity of all GNSS stations ranged from −1.32 to 10.41 mm/yr in the E component and from −8.83 to 3.00 mm/yr in the N component. From 2011 to 2021, there was significant uneven land subsidence in the Beijing Plain, and the maximum land subsidence rate from 2017 to 2021 reached 107 mm/yr. In analyzing the observation data of the GNSS and InSAR, we conclude that the land subsidence in the Beijing Plain will indeed affect the GNSS horizontal velocity field in the subsidence area. Under the EURA_I08 reference framework, the horizontal deformation field in the Beijing Plain is mainly caused by the tectonic activity-derived overall SEE-direction movement, accompanied by the velocity field anomaly caused by local land subsidence.

The expected acceleration in sea level rise (SLR) throughout this century poses significant threats to coastal cities and low-lying regions. Since the early 1990s, high-precision multi-mission satellite altimetry (SA) has enabled the routine measurement of sea levels, providing a continuous 30-year record from which the mean sea level rise (global and regional) and its variability can be computed. The latest reprocessed product from CMEMS span the period from 1993 to 2020, and have enabled the acquisition of accurate sea level data within the coastal range of 0–20 km. In order to fully utilize this new dataset, we establish a global virtual network consisting of 184 virtual SA stations. We evaluate the impact of different stochastic noises on the estimation of the velocity of the sea surface height (SSH) time series using BIC_tp information criterion. In the second step, the principal component analysis (PCA) allows the common mode noise in the SSH time series to be mitigated. Finally, we analyzed the spatiotemporal characteristics and accuracy of sea level change derived from SA. Our results suggest that the stochasticity of the SSH time series is not well described by a combination of random, flicker, and white noise, but is best described by an ARFIM/ARMA/GGM process. After removing the common mode noise with PCA, about 96.7% of the times series’ RMS decreased, and most of the uncertainty associated with the computed SLR decreased. We confirm that the spatiotemporal correlations should be accounted for to yield trustworthy trends and reliable uncertainties. Our estimated SLR is 2.75 ± 0.89 mm/yr, which aligns closely with recent studies, emphasizing the robustness and consistency of our method using virtual SA stations. We additionally introduce open-source software (SA_Tool V1.0) to process the SA data and reduce noise in surface height time series to the community.