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The deflection of the vertical (DOV) is the key information in the study of ocean gravity field. However, in most areas, the precision of the prime component of DOV is significantly lower than that of the meridian component. To obtain higher accuracy and resolution of ocean gravity information, researchers have proposed a novel altimeter called the wide-swath altimeter. This altimeter allows for the simultaneous acquisition of high-precision and high-resolution two-dimensional measurements of sea surface height (SSH). In this paper, the Surface Water and Ocean Topography (SWOT) mission with a wide-swath altimeter on board is selected for research. One cycle of SWOT sea surface height data is simulated to inverse the DOV in the Arabian Sea (45°E—80°E, 0°–30°N), and the inversion results are compared with those of conventional altimeter data. The results demonstrate that the difference between the meridian and prime components derived from the inversion of SWOT wide-swath data is minimal, significantly outperforming the inversion results of conventional nadir altimeter data. The advantage of SWOT wide-swath altimeter lies in its ability to use the multi-directional geoid slope at any sea surface measurement point to invert the components in the meridian and prime directions. To investigate the impact of this advantage on inversion precision, this paper employs a method to calculate the gradient of the geoid in multiple directions to invert DOV components. The improvement effect of calculating the gradient of the geoid in multiple directions on the precision of DOV component is analyzed. It is found that the accuracy of DOV inversion has significantly improved with the increase of geodetic gradient calculation direction. In addition, the effects of various errors and grid spacing in SWOT wide sea surface height data on the precision of DOV inversion are also analyzed.

We propose a method for enhancing the accuracy of bathymetry models based on a multilayer perceptron (MLP) neural network that integrates the differences in multisource marine geodetic data (MMGD) (longitude, latitude, reference bathymetry, slope, the meridional and prime components of vertical deflection, gravity anomaly, vertical gravity gradient, and mean dynamic topography). First, we use the MMGD differences between the shipborne sounding control points within 8′ × 8′ grid points and shipborne sounding control points as input data, as well as the differences between the topo_24.1 model and the measured bathymetric values at the control points as output data to train the MLP model. Second, we feed the input data from the central point of a 1′ × 1′ grid into the MLP model to obtain predictions, and then use the topo_24.1 model to recover the predicted bathymetry at the prediction point. We focus on the Caribbean Sea, and construct a Caribbean Bathymetric Chart of the Oceans (CBCO1) model using MLP neural network. The reliability of MMGD, a CBCO2 model using MMGD, and the reliability and effectiveness of the overall method are demonstrated through comparisons with the CBCO2, GEBCO_2022, topo_24.1, DTU18 models at the checkpoints.

The orthometric height variation is evident through changes in the geoid and surface vertical displacements. Hydrological mass change can induce variations in geoid height and surface deformation, consequently resulting in fluctuations in orthometric height. Studying the orthometric height variations in the Mississippi River Basin (MRB) caused by surface mass changes is crucial for understanding crustal uplift and ecological evolution. In this study, the superiority of daily solutions was demonstrated through comparison with the monthly solutions. Based on the spherical harmonic function (SHF) and Green's function (GF) methods, the orthometric height variations in the MRB were calculated by utilizing daily ITSG-Grace2018 solutions and a hydrological model. These results were then compared with the daily solutions obtained from 26 global positioning system (GPS) stations within the study area. The results show that the spatial distribution of orthometric height variations in the MRB is uneven. Except for the western mountainous areas, which show an upward trend, the main trend is a decrease at a rate of 0.1–0.4 mm/yr. The average correlation coefficient between GPS solutions and the orthometric height variations calculated using SHF and GF is 0.71 and 0.72, respectively, indicating good consistency, and hydrological loading was identified as a significant factor contributing to the orthometric height variations. After correcting GPS solutions with global land data assimilation system (GLDAS), vertical tectonic motion rates were calculated at GPS stations. With the exception of a few GPS stations that were uplifted, most of the remaining GPS stations settled at a rate of 0.5–2.6 mm/yr.

ABSTRACTThe Global Navigation Satellite System (GNSS) precise point positioning (PPP) from carrier-phase data is influenced by complex elements. The error sources are divided into two categories according to their relation to the signal propagation path. A new GNSS PPP algorithm based on spherical harmonic expansion (PPP-SH) is proposed, which expresses the error adjustments related to the signal propagation path through the spherical harmonic expansion, such as high-order ionosphere delay, zenith wet delay, phase wind-up delay, multipath delay and so on. Carrier-phase data of multiple continuous epochs are used to achieve the sequential sliding PPP solution, and the truncated singular value decomposition and iteration method by correcting characteristic values are used to solve the ill-conditioned equations in the PPP-SH algorithm. The reliable results can be obtained by using dual-frequency ionospheric-free carrier phase data when spherical harmonic expanding to degree 5. The standard deviations of E, N and U are 0.48, 0.43 and 0.27 cm, respectively. The addition of velocity parameters has positive influence on accuracy of positioning. The best positioning results are obtained by using the precise ephemeris and precise clock bias provided by ESA and the standard deviations of E, N and U are 0.41, 0.43 and 0.26 cm, respectively.

Abstract The precise prediction of polar motion parameters is needed for the astrogeodynamics, navigation and positioning of the deep space probe. However, the current prediction methods are limited to predicting polar motion for specific periods, either short- or long-term. In this study, a sliding multilayer perceptron (MLP) method combined singular spectrum analysis (SSA) and autoregressive moving average (ARMA) for short- and long-term polar motion prediction was proposed. MLP was introduced into PM prediction due to its automatic learning characteristics and its ability to effectively process nonlinear and multi-dimensional data. The SSA was used to extract and predict the principal components of polar motion, while the remaining components were predicted using ARMA. In the meantime, SSA and ARMA were used to provide training data and target learning data for the MLP model. MLP input data were constructed by sliding processing with a window of 7 days, composed of n series of the same length (18 years). Finally, MLP was employed to predict the residuals generated during SSA and ARMA prediction. To evaluate the accuracy of the proposed method, the polar motion prediction was applied for a 364-day lead time based on the IERS EOP 14C04 product. The method outperformed the IERS Bulletin A, as demonstrated by the mean-absolute errors of the x and y components of polar motion on the 30th day, which were lower (5.14 mas and 3.37 mas, respectively) than those predicted by IERS Bulletin A (6.66 mas and 3.94 mas). Similarly, the mean-absolute errors on the 364th day were 17.79 mas and 16.29 mas, respectively, compared to the 19.24 mas and 18.81 mas predicted by IERS Bulletin A. Graphical Abstract

Abstract In recent years, the Global Navigation Satellite System (GNSS) has witnessed rapid development. However, during the sandstorm season, the precipitable water vapor (PWV GNSS ) determined from the GNSS data produces large fluctuations due to the influence of particulate matter, which can indirectly reflect the change in particulate matter concentration. To study the variations of PWV GNSS during the sandstorm season, daily data of PWV GNSS , particulate matter (PM10), and precipitation in Wuhai from 2017 to 2021 were used in this study. The principal components of PWV residual (PWV RPC ) were obtained by using the least-squares linear fitting, singular spectrum analysis, and least-squares spectral analysis on PWV GNSS . The principal components of PM10 (PM10 PC ) were obtained by using least squares linear fitting and singular spectrum analysis for PM10. This study performed a correlation analysis of PWV RPC with PM10 PC and precipitation data. The results showed a strong correlation between PWV RPC and PM10 PC , with a correlation coefficient greater than 0.6. However, it was found that the correlation between PWV RPC and precipitation was not significant. This indicates that during the sandstorm season, PM10 affects PWV determined from GNSS data. Graphical Abstract

Islands and the mainland are separated by seas, and the distances between them might be so long that the height on the mainland cannot be exactly translated to the islands, resulting in different height systems on the mainland and the islands. In this study, we used astrogeodetic deflections of the vertical and ellipsoidal heights of points on the mainland and island near their coastlines to implement height connection across sea areas. First, the modeled gravity and modeled astrogeodetic vertical deflections of segmentation points along connecting routes over the sea between the mainland and the island were determined by Earth Gravity Model (EGM), and the ellipsoidal heights of segmentation points were determined by the satellite altimetry data sets. Second, we used a linear interpolation model to increase the precision of the vertical deflections of segmentation points. Third, we computed the geopotential difference of points between the mainland and the island using a method derived from geopotential theory and the astronomical leveling principle. Finally, we estimated the normal height of the point on the island using the geopotential-difference iterative computation approach. Using observed data of normal heights, ellipsoidal heights, and astrogeodetic vertical deflections referring to height sites in Qingdao, Shandong Province, we conducted a numerical experiment involving the normal height connection across sea regions. We determined the data of the ellipsoidal heights and gravity of segmentation points along the connecting route across the water in the numerical experiment using DTU10. The distance of the height connection across the sea was approximately 10.5 km. According to China's official leveling specifications, the experimental results met the criterion of third-class leveling precision.

Haiyang-2A (HY-2A) is the first marine dynamic environment satellite established by China, which has made significant contributions to the marine scientific research field. It carries the satellite-based GPS receiver named HY2, which was independently developed by China. It is an experimental satellite-borne GPS receiver for low earth orbit satellites, and during its operational period in orbit, the satellite-borne GPS data are not made accessible to the public. Therefore, this paper assesses the quality of HY-2A satellite-borne GPS data based on indicators such as satellite visibility, multipath effect, and ionospheric delay. The results indicate that the data acquired by the HY2 receiver are of high quality. The precise orbit determination (POD) uses the reduced-dynamic (RD) method. The adjustment effects of the pseudo-stochastic pulse time interval and a priori sigma on POD are analyzed, and the antenna phase center variation (PCV) is estimated using the direct method and residual method. Furthermore, this paper investigates the impact of PCV models with different resolutions (10° × 10° and 5° × 5°) on satellite orbit determination. To evaluate the orbit precision, three methods are used for validation, including carrier phase residual analysis, external precise science orbit (PSO) validation, and SLR three-dimensional (3D) validation, respectively. The results indicate that the highest orbit precision is achieved when the pseudo-stochastic pulse time interval is configured to 15 min, with the a priori sigma of 1 × 10−8 m/s2. The orbit carrier phase residuals reach the millimeter level. The 10° × 10°PCV model was estimated using the direct method and residual method, respectively; the root mean square of the external orbit validation for both methods show a millimeter-level improvement. The results obtained from the direct method and residual method are comparable. The resolution is increased from 10° to 5°, and the improvement in orbital precision is relatively small. The results obtained from the SLR 3D validation are consistent with those from the external PSO validation. The experimental results contribute valuable information for the POD of the HY2 series satellites.

On 6 February 2023, the MW 7.8 Pazarcik and the MW 7.5 Elbistan earthquakes occurred in southeastern Turkey, close to the Syrian border, causing many deaths and a great deal of property destruction. The Pazarcik earthquake mainly damaged the East Anatolian Fault Zone (EAFZ). The Elbistan earthquake mainly damaged the Cardak fault (CF) and the Doğanşehir fault (DF). In this study, Sentinel-1A ascending (ASC) and descending (DES) orbit image data and pixel offset tracking (POT) were used to derive surface deformation fields in the range and azimuth directions induced by the Pazarcik and Elbistan earthquakes (hereinafter referred to as the Turkey double earthquakes). Utilizing GPS coordinate sequence data, we computed the three-dimensional surface deformation resulting from the Turkey double earthquakes. The surface deformation InSAR and GPS results were combined to invert the coseismic slip distribution of the EAFZ, CF, and DF using a layered earth model. The results show that the coseismic ruptures of the Turkey double earthquakes were dominated by left-lateral strike-slips. The maximum slip was 7.76 m on the EAFZ and about 8.2 m on the CF. Both the earthquakes ruptured the surface. The Coulomb failure stress (CFS) was computed based on the fault slip distribution and the geometric parameters of all the active faults within 300 km of the MW 7.8 Pazarcik earthquake’s epicenter. The CFS change resulting from the Pazarcik earthquake suggests that the subsequent Elbistan earthquake was triggered by the Pazarcik earthquake. The Antakya fault experienced an increase in CFS of 8.4 bars during this double-earthquake event. Therefore, the MW 6.3 Uzunbağ earthquake on 20 February 2023 was jointly influenced by the Turkey double earthquakes. Through stress analysis of all the active faults within 300 km of the MW 7.8 Pazarcik earthquake’s epicenter, the Ecemis segment, Camliyayla fault, Aadag fault, Ayvali fault, and Pula segment were all found to be under stress loading. Particularly, the Ayvali fault and Pula segment exhibited conspicuous stress loading, signaling a higher risk of future seismic activity.

Abstract Polar motion is the movement of the Earth's rotational axis relative to its crust, reflecting the influence of the material exchange and mass redistribution of each layer of the Earth on the Earth's rotation axis. To better analyze the temporally varying characteristics of polar motion, multi-channel singular spectrum analysis (MSSA) was used to analyze the EOP 14 C04 series released by the International Earth Rotation and Reference System Service (IERS) from 1962 to 2020, and the amplitude of the Chandler wobbles were found to fluctuate between 20 and 200 mas and decrease significantly over the last 20 years. The amplitude of annual oscillation fluctuated between 60 and 120 mas, and the long-term trend was 3.72 mas/year, moving towards N56.79 °W. To improve prediction of polar motion, the MSSA method combining linear model and autoregressive moving average model was used to predict polar motion with ahead 1 year, repeatedly. Comparing to predictions of IERS Bulletin A, the results show that the proposed method can effectively predict polar motion, and the improvement rates of polar motion prediction for 365 days into the future were approximately 50% on average.

In order to study the laws of crack evolution in rock and explain its fracture instability mechanism, a series of laboratory tests were carried out with Jinping Marbles. The test results show that the failure degree of marbles under unloading conditions is more severe than that under loading conditions. Based on volume crack strain, five progressive failure stages of crack evolution under different conditions are divided, and the corresponding characteristic stresses are determined. The pre-peak volume crack propagation strain without considering the initial damage is used to evaluate the pre-peak crack growth propagation degree of rock, and it is found that the lower the confining pressure, the higher the strain rate and unloading rate, the less the cracks generated before the peak, and the more the rock is prone to brittle failure after the peak. The starting point of the sharp increase of volume crack strain rate is proposed as the failure precursor point, and stress levels of failure precursor of marbles are in 70%–100%, which decrease as confining pressure, strain rate, and unloading rate rise. Under unloading conditions, failure precursor points appear later and are close to the unloading point, and unloading rocks are more prone to sudden brittle failure.

Altimeter data processing is very important to improve the quality of sea surface height (SSH) measurements. Sea state bias (SSB) correction is a relatively uncertain error correction due to the lack of a clear theoretical model. At present, the commonly used methods for SSB correction are polynomial models (parametric models) and non-parametric models. The non-parametric model usually was constructed by collinear data. However, the amount of collinear data was enormous, and it contained redundant information. In this study, the non-parametric regression estimation model was optimized by using the parameter replacement method of ascending and descending tracks based on the crossover data. In this method, significant wave heights from the Jason-2 altimeter data during cycles 200–301 and wind speed from the ERA5 reanalysis data were used. The non-parametric regression estimation model of Jason-2 was constructed by combining it with local linear regression, Epanechnikov kernel function and local window width. At the same time, based on the significant wave height and wind speed at the crossover points, the SSB polynomial model containing six parameters was constructed by using the Taylor series expansion, and the model was optimized. By comparing polynomial model construction with different parameters, the optimized model was obtained. The SSH of the crossover points and the tide gauge records were used to validate these results derived from two models and GDR. Compared with the crossover discrepancies of SSH corrected by the polynomial model, the RMS of the crossover discrepancies of SSH corrected by the non-parametric regression estimation model was reduced by 7.9%. Compared with the crossover discrepancies of SSH corrected by the conventional non-parametric model from GDR, the RMS of the crossover discrepancies of SSH corrected by the non-parametric regression estimation model was reduced by 4.1%. This shows that the precision of the SSHs derived by after the SSB correction, as calculated by the non-parametric regression estimation model, was better than that of the polynomial model and the SSB correction from GDR. Using the Jason-2 altimeter data, the along-track geoid gradient and the sea level change rate of the global ocean were determined by using two models to correct the SSB. By comparing the results of the two models, the accuracy of the geoid gradient along the orbit that was obtained by the non-parametric regression estimation model was better than that of the polynomial model and GDR. The global average sea level change rate after the non-parametric regression estimation model correction was 3.47 ± 0.09 mm/y, which was the closest to the average sea level change rate that has been published in the international literature within this field.

Performing research on the variation in lake water on the Qinghai–Tibet Plateau (QTP) can give the area’s ecological environmental preservation a scientific foundation. In this paper, we first created a high-precision dataset of lake water level variation every 10 days, from July 2002 to December 2022, using multi-source altimetry satellite SGDR data (Envisat RA-2, SARAL, Jason-1/2, and Sentinel-3A/3B SRAL), which integrated the methods of atmospheric path delay correction, waveform re-tracking, outlier detection, position reduction using a height difference model, and inter-satellite deviation adjustment. Then, using Landsat-5 Thematic Mapper, Landsat-7 Enhanced Thematic Mapper, and Landsat 8 Operational Land Imager data, an averaged area series of Lake Qinghai (LQ) from September to November, each year from 2002 to 2019, was produced. The functional connection between the water level and the area was determined by fitting the water level–area series data, and the lake area time series, of LQ. Using the high-precision lake water level series, the fitted lake surface area time series, and the water storage variation equation, the water storage variation time series of LQ was thus calculated every 10 days, from July 2002 to December 2022. When the hydrological gauge data from the Xiashe station and data from the worldwide inland lake water level database are used as references, the standard deviations of the LQ water level time series are 0.0676 m and 0.1201 m, respectively. The results show that the water storage of LQ increases by 11.022 × 109 m3 from July 2002 to December 2022, with a growth rate of 5.3766 × 108 m3/a. The growth rate from January 2005 to January 2015 is 4.4850 × 108 m3/a, and from January 2015 to December 2022, the growth rate is 8.9206 × 108 m3/a. Therefore, the increased rate of water storage in LQ over the last 8 years has been substantially higher than in the previous 10 years.

The tropical cyclone Idai caused severe floods in Mozambique in March 2019. Sentinel-1 and Sentinel-2 images are processed to monitor the flood disaster in Pungue and Buzi rivers by combining the object-based image analysis approach and the decision tree algorithm. Water is preliminarily extracted from Sentinel-1 image, and shadows of mountain and buildings in the study area are extracted from Sentinel-2 image. Mountain shadow is extracted based on the decision tree classification rules constructed by the digital elevation model and the index model, while building shadow is extracted by constructing the decision tree classification rules using the features of objects. Water extraction results are combined with shadows to eliminate confusing shadows in the preliminary extraction to obtain the accurate flood extent. Sentinel-2 images are used to classify land use types in multiple periods before and after the flood and analyze the disaster by combining with the change information of the water. Land use type changes are analyzed and predicted with the CA-Markov model. The results show that the maximum submerged area was 3.5 times of the normal water area, and that most areas were submerged for more than 10 d. The area between Pungue and Buzi rivers were severely affected, where a large number of crops and villages were submerged. Grassland and cropland were the most seriously submerged. The overall accuracy of extracted water results ranges from 86% to 92%. The results indicated that the combining method can effectively suppress the influence of shadows on water extraction results.

Satellite altimetry is an important technique to derive oceanic deflections of vertical (DOV). HaiYang-2A (HY-2A) is the first Chinese altimetry satellite launched in August 2011 to observe the global marine dynamic environment. To assess the reliability of DOVs derived from HY-2A geodetic mission data, the Bay of Bengal and its adjoining area (0°–23°N, 80°–100°E) are selected as the research area, and the accuracy of HY-2A/GM-derived DOVs is compared with that of DOVs determined from CryoSat-2-measured sea surface heights (SSHs) and SARAL/AltiKa (SARAL)-measured SSHs which are in the same period as HY-2A-measured SSHs. Compared with the along-track DOVs calculated from Sentinel-3B-measured SSHs (from cycle 20 to cycle 33), the RMS of differences for HY-2A-determined DOVs is 0.1 μrad smaller than that for SARAL-determined DOVs and CryoSat-2-determined DOVs. The differences of the along-track DOVs in the frequency domain are also analyzed by power spectral density. In addition, the XGM2019e model is adopted to evaluate the quality of the gridded DOVs model established by least-squares collocation method. Marine gravity anomaly models (SIO V30.1) and ship-borne gravity anomalies are also used to assess the accuracy of gravity anomalies derived from gridded DOVs. The whole results show that the accuracy of HY-2A-determined DOVs is coincident with that of CryoSat-2-determined DOVs and slightly lower than that of SARAL-determined DOVs. Therefore, HY-2A/GM altimetry data can be applied in establishing the global high-precision DOV model.

Ionospheric delay is one of the main errors in precise orbit determination (POD) of Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) with satellite-borne GPS technique. Effective elimination or reduction of ionospheric delay can improve POD precision. For satellite-borne GPS dual-frequency data, the ionospheric-free linear combination is generally used to eliminate the first-order term, while igoring the influence of higher-order terms. To improve the POD precision of GRACE-FO, this paper presents an effective method to calculate higher-order ionospheric delay of GRACE-FO observation. Dual-frequency GPS receiver observation is used to calculate the total electron content on the signal propagation path. The magnetic field strength is calculated according to international geomagnetic reference field model, and the angle between the GPS signal propagation path and the geomagnetic field is calculated. Finally, the delays of second-order and third-order terms are calculated and introduced into GRACE-FO reduced-dynamic POD. The effect of higher-order ionospheric delay on POD of GRACE-FO is analyzed in detail. The results show that the influence of ionospheric higher-order term on satellite-borne GPS observation is in centimeter level. The orbit precision of GRACE-FO can be improved by adding higher-order ionospheric delay, with improvement order of sub-millimeter level.

In order to analyze the influence of mass loading [atmospheric loading (ATML), hydrological loading (HYDL), and nontidal ocean loading (NTOL)] on estimating ocean tide loading displacement (OTLD) parameters by GNSS, the kinematic precise point positioning technique is used to process the GNSS data in Hong Kong to obtain coordinate time series. The 3-D OTLD parameters of eight principal constituents (M2, S2, N2, K2, K1, O1, P1, and Q1) are estimated using harmonic analysis method from the coordinate time series with/without mass loading correction and random noise reduction. The GNSS-derived OTLD parameters are compared with the FES2014 and NAO.99b. The results show that GNSS/model agreement is generally at the submillimeter level (excluding S2 and K1). After mass loading is corrected, the residual between OTLD parameter by GNSS and model of M2, S2, N2, P1, and Q1 have been reduced more than 20%, while the accuracy improvement of other tidal constituents is not obvious. The influence of different mass loading on estimation of OTLD parameters is analyzed. Compared with ocean tide model, root mean square error misfit decreased by 7.52%, 7.76%, and 7.58% in north (N), east (E), and up (U) with ATML correction, respectively. The accuracy is improved little in vertical direction and decreases slightly in horizontal direction with NTOL correction. The HYDL correction has little effect on OTLD estimation. After the random noise reduction, the accuracy of the estimation of OTLD parameters has been significantly improved, and the improvement of the accuracy of the semidiurnal constituents is significantly greater than those of the diurnal constituents.

This paper aims to address the limitations of the distribution number and uniformity of Continuously Operating Reference Stations (CORS) and their impact on the reliability of inverting regional groundwater storage (GWS) based on Green’s function method and using global navigation satellite system (GNSS) data. A fusion method on the inversion of regional GWS changes from GNSS and the Gravity Recovery and Climate Experiment (GRACE) was proposed in this paper. Taking the Shaanxi–Gansu–Ningxia (SGN) region as an example, the in situ groundwater level data from ten CORS stations and eight wells were used for test analyses. In this paper, an atmospheric pressure model from the European Centre for Medium-Range Weather Forecasts (ECMWF), a global land data assimilation system (GLDAS), a WaterGAP global hydrology model (WGHM), and mean sea level anomaly (MSLA) data were used to quantitatively monitor the influence of vertical deformation caused by non-tidal environmental load. After deducing these loading deformations from the filtered time series of non-linear monthly geodetic height from the GNSS, the GWS changes in the SGN region from 2011 to 2014 were inverted. Meanwhile, the change in surface water storage from the GLDAS and WGHM models were removed from the terrestrial water storage (TWS) changes derived from GRACE. On this basis, the remove–restore theory in the Earth’s gravity field was introduced to both fuse the inversion results and obtain the regional GWS changes based on the fusion method. The results showed the following: (1) The local characteristics from the fusion results were more prominent than those of GRACE on the spatial scale, such as in the southwest and northeast in the study area. In addition, the fusion results were more uniform than those from GNSS, especially for the sparse and missing areas in which CORS stations were located, and the local effect was weakened. (2) On the time scale, compared with GRACE, the trends in GWS changes obtained from the fusion method and from GNSS inversion were roughly the same as the in situ groundwater level changes. (3) For the in situ groundwater wells “6105010031” and “6101260010”, the correlation coefficients of the fusion result were 0.53 and 0.56, respectively. The accuracy of the fusion method was slightly higher than that from GNSS, which indicates that the fusion method may be more effective for areas where CORS stations are missing or sparsely distributed. The methods in this paper can provide significant reference material for hydrodynamic research, sustainable management of water resources, and the dynamic maintenance of height data.

The traditional altimetry satellites based on pulse-limited radar altimeter only calculate along-track deflection of the vertical (DOV), which results in poorer precision of the prime vertical component than that of the meridian component and limits the precision of the marine gravity field inversion. We expect an improvement in the higher precision prime vertical component using the Ice, Cloud and land Elevation Satellite 2 (ICESat-2) sea surface height (SSH) data. In this paper, the 2′ × 2′ gridded DOVs derived from along-beam DOVs, cross-beam DOVs, and joint along-cross beam DOVs in the South China Sea (SCS; 0°–23°N, 103°–120°E) are calculated with the weighted least squares method, respectively. The inverse Vening–Meinesz (IVM) formula is applied to derive 2′ × 2′ gravity anomalies over the SCS from ICESat-2-derived gridded DOVs. In addition, the XGM2019e_2159-DOV and SIO V31.1-DOV models are used to assess the precision of the gridded DOVs. The XGM2019e_2159-GRA, SIO V31.1-GRA models, and ship-borne gravity anomalies are also adopted to evaluate the quality of gravity anomalies. The results show that the gridded DOVs calculated by the joint along-cross beam DOVs have the highest precision among the three gridded DOVs determined by ICESat-2. The precision of difference between gravity anomalies derived from the joint along-cross beam DOV and the above verification data are higher than those derived from the along-beam and cross-beam DOVs. We conclude that the joint along-cross beam DOV can effectively improve the precision of the gridded DOV, which is conducive to the inversion of a high-precision marine gravity field.

Sea level change is not uniform across the oceans and high-resolution sea level trend (SLT) models reveal that the rate of sea level change differs between different waters. In this study, we developed a new method for obtaining a high-resolution, 1′×1′-grid SLT model, using the time-varying mean sea surface (MSS) of several MSSs calculated from averaged multi-satellite-derived sea surface heights (TOPEX/Poseidon, Jason-1/2/3, ERS-1/2, Envisat, GFO, Cryosat-2, SARAL/AltiKa, Sentinel-3A, HY-2A) over different periods. We applied this model to estimate the mean sea level change in the China seas and their adjacent ocean (0°–41°N, 100°–140°E). This new model revealed the patterning of sea level change within the study region in detail, and detected a sea level change dipole south of Japan. A zonal SLT pattern was identified in three regions: the region of the North Pacific Subtropical Counter Current (an eastward current located in the band of 19.5°–22.5°N, populated with eddies), and the areas east of Taiwan and east of Luzon Island. Moreover, the rate of sea level rise in the offshore zone was found to be ~ 0.67 mm/yr (20%) higher than that in the open ocean. This finding has important implications for coastal protection.

The Tonga volcano erupted on 15 January 2022, at 04:15:45 UTC, which significantly influenced the atmosphere and space environment, at the same time, an unprecedented opportunity to monitor ionospheric anomalies is provided by its powerful eruption. In current studies of traveling ionospheric disturbance (TID) triggered by the 2022 Tonga volcanic eruption, the particular phenomenon of ionospheric disturbances in various parts of the world has not been reasonably explained, and the vertical ionospheric disturbances are still not effectively detected. In this paper, we calculate the high-precision slant total electron content (STEC) from more than 3000 ground-based GPS stations distributed around the world, then we obtain the radio occultation (RO) data from near-field COSMIC-2 profiles and investigate the horizontal TID and the vertical ionospheric disturbances by the singular spectrum analysis (SSA). Horizontal TID propagation captured by GPS STEC results indicates that acoustic-gravity waves dominate the energy input at the beginning of the ionospheric disturbance with an approximate speed of 1050 m/s initially. With the dissipation of the shock energy, lamb waves become a dominant mode of ionospheric disturbances, moving at a more stable speed of about 326 m/s to a range of 16,000 km beyond the far-field. Local characteristics are evident during the disturbance, such as the ionospheric conjugation in Australia and the rapid decay of TID in Europe. The shock-Lamb-tsunami waves’ multi-fluctuation coupling is recorded successively from the COSMIC-2 RO observation data. The shock and Lamb waves can perturb the whole ionospheric altitude. In contrast, the disturbance caused by tsunami waves is much smaller than that of acoustic-gravity waves and Lamb waves. In addition, influenced by the magnetic field, the propagation speed of TID induced by Lamb waves is higher towards the northern hemisphere than towards the southern hemisphere.

On the 15th of March 2021, the strongest sandstorm in a decade occurred in northern China, and had a great adverse impact on the natural environment and human health in northern China. Real-time monitoring of dust storms is becoming increasingly important. In order to effectively analyze the non-hydrostatic delay (ZNHD) anomaly during a sandstorm, the method based on GNSS-derived tropospheric ZNHD residual to monitor the sandstorm is proposed at the same time. We studied the relationship between ZNHD/PWV and PM10/PM2.5 in Beijing, Changchun, Pingliang and Zhongwei before and after sandstorms. The ZNHD time series was then decomposed by singular spectrum analysis (SSA) and the residuals were obtained. The relationship between the GNSS-derived ZNHD residual and PM10 was analyzed. The results show that the impact of the sandstorm on PM10 is greater than that on PM2.5. Before the sandstorm, the correlation between PM10 and ZNHD was low, less than 0.25. When the sandstorm occurred, the correlation between PM10 and ZNHD increased significantly, and the maximum was greater than 0.7. When the sandstorm ended, the correlation between PM10 and ZNHD decreased significantly. Through the relationship between the ZNHD residual and PM10, it can be found that when the peak-to-peak values of the ZNHD residual are all above 80 mm, sandstorms may occur. But Rainfall, snowfall, haze and other abnormal weather can also lead to ZNHD anomalies.

Height variations caused by mass change make an important contribution to the tectonic uplift of the Qinghai-Tibet Plateau (QTP). To study the deformation attributable to hydrological loading and real potential tectonic vertical motion, satellite gravity data from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) with data from the Global Land Data Assimilation System (GLDAS) and Global Positioning System (GPS) are adopted to estimate height variations in QTP. Based on spherical harmonic function (SHF) and Green’s function (GF), the results show the trend of height variations is unevenly distributed in the spatial domain. The SHF indicated that the rate in the southwest of the QTP is ~1 mm/year, while the northern and eastern show a subtle decreasing trend, which indicates hydrological loading is not the main cause of the uplift observed with GRACE. The maximum annual amplitude of height variations is ~12 mm, reaching the annual maximum around February to March. The average correlation coefficients of SHF, and GF height variations with GPS heights are 0.70 and 0.82, respectively. Based on cross wavelet transform, it is concluded that there are annual signals between the height variations derived from GPS with GRACE (-FO) and GLDAS. Finally, the tectonic vertical motion in the QTP is given by removing the effect of hydrological loading, which shows most GPS stations are uplifted at a rate of 0.06 mm/year–1.97 mm/year.

Marine gravity field recovery relies heavily on satellite altimetry. Thanks to the evolution of altimetry missions and the improvements in altimeter data processing methods, the marine gravity field model has been prominently enhanced in accuracy and resolution. However, high-accuracy and high-resolution gravity field recovery from satellite altimeter data remains particularly challenging. We provide an overview of advances in satellite altimetry for marine gravity field recovery, focusing on the impact factors and available models of altimetric gravity field construction. Firstly, the evolution of altimetry missions and the contribution to gravity field recovery are reviewed, from the existing altimetry missions to the future altimetry missions. Secondly, because the methods of altimeter data processing are of great significance when obtaining high-quality sea surface height observations, these improved methods are summarized and analyzed, especially for coastal altimetry. In addition, the problems to be resolved in altimeter data processing are highlighted. Thirdly, the characteristics of gravity recovery methods are analyzed, including the inverse Stokes formula, the inverse Vening Meinesz formula, Laplace’s equation, and least squares collocation. Furthermore, the latest global marine gravity field models are introduced, including the use of altimeter data and processing methods. The performance of the available global gravity field model is also evaluated by shipboard gravity measurements. The root mean square of difference between the available global marine gravity model and shipboard gravity from the National Centers for Environmental Information is approximately 5.10 mGal in the low-middle latitude regions, which is better than the result in high-latitude regions. In coastal areas, the accuracy of models still needs to be further improved, particularly within 40 km from the coastline. Meanwhile, the SDUST2021GRA model derived from the Shandong University of Science and Technology team also exhibited an exciting performance. Finally, the future challenges for marine gravity field recovery from satellite altimetry are discussed.

On 15 January 2022, a violent eruption and tsunami of the Hunga Tonga-Hunga Ha’apai (HTHH) volcano in Tonga, South Pacific, caused widespread international concern. In order to detect the anomalous environmental response caused by the HTHH volcanic eruption based on GNSS ionospheric data, GNSS tropospheric data and GNSS coordinate time series, a new method combining the zenith non-hydrostatic delay difference method and the extreme-point symmetric mode decomposition (ESMD) method, was proposed to detect tropospheric anomalies. The moving interquartile range method and the ESMD method were introduced to detect ionospheric anomalous and coordinate time series anomalies, respectively. The results showed that 9–10 h before the eruption of the Tonga volcano and 11–12 h after the eruption of the Tonga volcano, obvious total electron content (TEC) anomalies occurred in the volcanic eruption center and its northeast and southeast, with the maximum abnormal value of 15 TECU. Significant tropospheric anomalies were observed on the day of the HTHH volcano eruption as well as 1–3 days and 16–17 days after the eruption, and the abnormal intensity was more than 10 times that of normal. The coordinate time series in direction E showed very significant anomalies at approximately 2:45 p.m. on 14 January, at approximately 4:30 a.m.–5:40 a.m. on 15 January, and at approximately 3:45 a.m. on 16 January, with anomalies reaching a maximum of 7–8 times daily. The abnormality in the direction north (N) is not obvious. Very prominent anomalies can be observed in the direction up (U) at approximately 4:30 a.m.–5:40 a.m., with the intensity of the anomalies exceeding the normal by more than 10 times. In this study, GNSS was successfully used to detect the anomalous environmental response during this HTHH volcano eruption.

Global warming has resulted in the melting of glaciers in the southeastern region of Tibet. This study used the InSAR time series obtained from ALOS PALSAR data to investigate the melting glacier over Southeast Tibet during 2007 - 2010 with the small baseline subset (SBAS) technique. Additionally, GRACE (Gravity Recovery and Climate Experiment) gravity field model issued by the Center for Space Research (CSR) was used to extract the equivalent water height (EWH) with the deduction of glacial isostatic adjustment (GIA). The results revealed that the monitoring results by InSAR were basically consistent with the EWHs from GRACE. The glacier deformation in the study area presents a downward trend overall. From the InSAR measurements, a 900-km2 area within the belt subsided -1.6 cm yr-1 during 2007 - 2010, and the subsidence exceeded -24 cm yr-1 in some regions. On the other hand, as an auxiliary data source, the monitoring result of GRACE is large space scale and comprehensive, the rate is about -0.01 cm yr-1 from GRACE. With the variations of glacier shape obtained from MODIS (moderate-resolution imaging spectroradiometer) data, the changing rate of surface temperature was about 0.014°C yr-1. The surface temperature change is negatively correlated with the rate of the glacial subsidence with the correlation coefficient of -0.237, which reflects that the melting glacier is influenced by the temperature rising to a certain extent.

The bright stars in the clear night sky with weak background lights should be observed in the traditional deflection of the vertical (DOV) measurement so that the DOV cannot be observed under all-weather conditions, which limits its wide applications. An all-weather DOV measurement method combining three-dimensional (3D) laser tracking free-fall and multi-GNSS baselines is proposed in this paper. In a vacuum environment, the 3D laser tracking technique is used to continuously track and observe the motion of free-fall with high frequency and precision for obtaining 3D coordinate series. The plumb line vector equation is established to solve the gravity direction vector in the coordinate system of the laser tracker at the measuring point using least squares fitting coordinate series. Multi-GNSS observations are solved for obtaining the precise geodetic cartesian coordinates of the measuring point and GNSS baseline information. A direction transformation method based on the baseline information proposed in this paper is used to convert the gravitational direction vector in the laser tracker coordinate system into the geodetic cartesian coordinate system. The geodetic cartesian coordinates of the measuring point are used to calculate the ellipsoid normal vector, and the angle between this and the gravity direction vector in the geodetic cartesian coordinate system is estimated to obtain the astrogeodetic DOV. The DOV is projected to the meridian and prime vertical planes to obtain the meridian and prime vertical components of the DOV, respectively. The astronomical latitude and longitude of the measuring point are calculated from these two components. The simulation experiments were carried out using the proposed method, and it was found that the theoretical precision of the DOV measured by the method could reach 0.2″, which could realise all-weather observation.

Abstract Generally, the dynamical model is used to estimate coordinates of satellite laser ranging (SLR) stations. In this paper, we put forward a kinematic method to estimate the coordinates of SLR stations by using global navigation satellite system (GNSS) technique onboard a low Earth orbiting (LEO) satellite. We applied it to the processing of SLR and GNSS observations of the GRACE-A satellite from January to December 2012. We found that the LEO satellite as a space-based connection between SLR and GNSS techniques allowed the precise estimation of SLR site positions with the agreement level of 2–3 cm with respective to SLRF2014. The SLR network can be attached to the IGS network at the centimeter level. The results show that the proposed method is feasible for determining the coordinates of SLR stations as an idea for the satellite-based integration of different space geodetic techniques.

For the first time, HY-2A/GM-derived gravity anomalies determined with the least-squares collocation method and ship-borne bathymetry released from the National Centers for Environmental Information (NCEI) are used to predict bathymetry with the gravity-geologic method (GGM) over three test areas located in the South China Sea (105–122°E, 2–26°N). The iterative method is used to determine density contrasts (1.4, 1.5, and 1.6 g/cm3) between seawater and ocean bottom topography, improving the accuracy of GGM bathymetry. The results show that GGM bathymetry is the closest to ship-borne bathymetry at check points, followed by SRTM15+V2.0 model and GEBCO 2020 model. It is found that in a certain range, the relative accuracy of GGM bathymetry tends to improve with the increase of depth. Different geological structures affect the accuracy of GGM bathymetry. In addition, the influences of gravity anomalies and data processing method on GGM bathymetry are analyzed. Our assessment result suggests that GGM can be widely applied to bathymetry prediction and that HY-2A/GM-derived gravity data are feasible with good results in calculating ocean depth.

Zhari Namco, a large lake in the Tibetan Plateau (TP), is sensitive to climate and environmental change. However, it is difficult to retrieve accurate and continuous lake levels for Zhari Namco. A robust strategy, including atmospheric delay correction, waveform retracking, outlier deletion, and inter-satellite adjustment, is proposed to generate a long-term series of lake levels for Zhari Namco through multi-altimeter data. Apparent biases are found in troposphere delay correction from different altimeter products and adjusted using an identical model. The threshold (20%) algorithm is employed for waveform retracking. The two-step method combining a sliding median filter and 2σ criterion is used to eliminate outliers. Tandem mission data of altimeters are used to estimate inter-satellite bias. Finally, a 27-year-long lake level time series of Zhari Namco are constructed using the TOPEX/Poseidon-Jason1/2/3 (T/P-Jason1/2/3) altimeter data from 1992 to 2019, resulting in an accuracy of 10.1 cm for T/P-Jason1/2/3. Temperature, precipitation, lake area, equivalent water height, and in situ gauge data are used for validation. The correlation coefficient more than 0.90 can be observed between this result and in situ gauge data. Compared with previous studies and existing database products, our method yields sequences with the best observational quality and the longest continuous monitoring in Zhari Namco. The time series indicates that the lake level in Zhari Namco has increased by ∼ 5.7 m, with an overall trend of 0.14 ± 0.01 m/yr, showing a fluctuating rate (1992–1999: −0.25 ± 0.05 m/yr, 2000–2008: 0.26 ± 0.04 m/yr, 2009–2016: −0.05 ± 0.03 m/yr, 2017–2019: 1.34 ± 0.34 m/yr). These findings will enhance the understanding of water budget and the effect of climate change in the TP.

Haiyang-2D (HY-2D) is the fourth satellite in the marine dynamic satellite series established by China. It was successfully launched on 19 May 2021, marking the era of the 3-satellite network in the marine dynamic environment satellite series of China. The satellite’s precision orbit determination (POD) and validations are of great significance for ocean warning and marine altimetry missions. HY-2D is equipped with a laser reflector array (LRA), a satellite-borne Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) receiver, and a satellite-borne dual-frequency GPS receiver named HY2 that was independently developed in China. In this paper, the quality of GPS data collected by the HY2 is analyzed based on indicators such as the multipath effect, cycle slips, and data completeness. The results suggest that the receiver can be used in POD missions involving low-Earth-orbit (LEO) satellites. The precise orbits of HY-2D are determined by the reduced-dynamics (RD) method. Apart from POD, validation of orbit accuracy is another important task for LEO POD. Therefore, two external validation methods are proposed, including carrier differential validation using one GPS satellite and inter-satellite differential validation using two GPS satellites. These are based on space-borne carrier-phase data, and the GPS satellites used for POD validation do not participate in orbit determination. The results of SLR range validation cannot illustrate the orbit accuracy in x, y, and z directions particularly, so to make validation results more intuitive, the SLR three-dimensional (3D) validation is proposed based on SLR range validation, and the RMSs in x, y, and z directions are 2.66, 3.32, and 2.69 cm, respectively. The results of SLR 3D validation are the same as those of SLR range validation, which proves that the new external validation method provided by SLR 3D is reliable. The RMSs of carrier differential validation and inter-satellite differential validation are 0.68 and 1.06 cm, respectively. The proposed validation methods are proved to be reliable.

[This corrects the article DOI: 10.1371/journal.pone.0176954.].

As the first in-orbit formation satellites equipped with a Laser Ranging Interferometer (LRI) instrument, Gravity Recovery and Climate Experiment Follow-on (GRACE-FO) satellites are designed to evaluate the effective ability of the new LRI ranging system applied to satellite-to-satellite tracking. To evaluate the application of LRI in GRACE-FO, a relative kinematic orbit determination scheme for formation satellites integrating Kalman filters and GPS/LRI is proposed. The observation equation is constructed by combining LRI and spaceborne GPS data, and the intersatellite baselines of GRACE-FO formation satellites are calculated with Kalman filters. The combination of GPS and LRI techniques can limit the influence of GPS observation errors and improve the stability of orbit determination of the GRACE-FO satellites formation. The linearization of the GPS/LRI observation model and the process of the GPS/LRI relative kinematic orbit determination are provided. Relative kinematic orbit determination is verified by actual GPS/LRI data of GRACE-FO-A and GRACE-FO-B satellites. The quality of relative kinematic orbit determination is evaluated by reference orbit check and K-Band Ranging (KBR) check. The result of the reference orbit check indicates that the accuracy of GRACE-FO relative kinematic orbit determination along X, Y, and Z (components of the baseline vector) directions is better than 2.9 cm. Compared with the relative kinematic orbit determination by GPS only, GPS/LRI improves the accuracy of the relative kinematic orbit determination by approximately 1cm along with X, Y and Z directions, and by about 1.8 cm in 3D directions. The overall accuracy of relative kinematic orbit determination is improved by 25.9%. The result of the KBR check indicates that the accuracy of the intersatellite baseline determination is about +/−10.7 mm.

Weihai's urban development model is representative of coastal cities in China. Landsat MSS/TM/OLI images were used to extract the land use types of Weihai from 1985–2015 using the object-oriented support vector machine (SVM) classification method. The landscape pattern indexes were calculated based on the classification results of land use. The temporal and spatial characteristics of land use and landscape pattern were analyzed by considering Weihai’s economic development. The overall kappa (OK) coefficients were greater than 83% and the overall accuracy (OA) values were greater than 85%. Over 80% of both producer’s accuracy (PA) and user’s accuracy (UA) values of different land use types were greater than 85%. Changes in land use and landscape patterns were closely related to the local economic development. The areas of cultivated land and woodland continued to decrease. The expansion of construction land came mainly from the cultivated land and woodland as with as very little from waters. Under the combined effect of economic development and human activities, the landscape pattern of Weihai as a whole has been decentralized. The internal structure is relatively complex and the fragmentation of land use is increasing. The development model of Weihai is the expansion-aggregation-expansion.

From August to October 2020, a serious wildfire occurred in California, USA, which produced a large number of particulate matter and harmful gases, resulting in huge economic losses and environmental pollution. Particulate matter delays the GNSS signal, which affects the like precipitable water vapor (LPWV) derived by the GNSS non-hydrostatic delay. Most of the information of GNSS-derived LPWV is caused by water vapor, and a small part of the information is caused by particulate matter. A new method based on the difference (ΔPWV) between the PWV of virtual radiosonde stations network and GNSS-derived LPWV is proposed to detect the changes of particulate matter in the atmosphere during the 2020 California wildfires. There are few radiosonde stations in the experimental area and they are far away from the GNSS station. In order to solve this problem, we propose to use the multilayer perceptron (MLP) neural network method to establish the virtual radiosonde network in the experimental area. The PWV derived by the fifth-generation European center for medium-range weather forecasts reanalysis model (PWVERA5) is used as the input data of machine learning. The PWV derived by radiosonde data (PWVRAD) is used as the training target data of machine learning. The ΔPWV is obtained based on PWV derived by the virtual radiosonde station network and GNSS in the experimental area. In order to further reduce the influence of noise and other factors on ΔPWV, this paper attempts to decompose ΔPWV time series by using the singular spectrum analysis method, and obtain its principal components, subsequently, analyzing the relationship between the principal components of ΔPWV with particulate matter. The results indicate that the accuracy of PWV predicted by the virtual radiosonde network is significantly better than the fifth-generation European center for the medium-range weather forecast reanalysis model, and the change trend of ΔPWV is basically consistent with the change law of particulate matter in which the value of ΔPWV in the case of fire is significantly higher than that before and after the fire. The mean of correlation coefficients between ΔPWV and PM10 at each GNSS station before, during and after wildfires are 0.068, 0.397 and 0.065, respectively, which show the evident enhancement of the correlation between ΔPWV and particulate matter during wildfires. It is concluded that because of the high sensitiveness of ΔPWV to the change of particulate matter, the GNSS technique can be used as an effective new approach to detect the change of particulate matter and, then, to detect wildfires effectively.

Haiyang-2C (HY-2C) is a dynamic, marine-monitoring satellite that was launched by China and is equipped with an onboard dual-frequency GPS receiver named HY2_Receiver, which was independently developed in China. HY-2C was successfully launched on 21 September 2020. Its precise orbit is an important factor for scientific research applications, especially for marine altimetry missions. The performance of the HY2_Receiver is assessed based on indicators such as the multipath effect, ionospheric delay, cycle slip and data utilization, and assessments have suggested that the receiver can be used in precise orbit determination (POD) missions involving low-Earth-orbit (LEO) satellites. In this study, satellite-borne GPS data are used for POD with a reduced-dynamic (RD) method. Phase centre offset (PCO) and phase centre variation (PCV) models of the GPS antenna are established during POD, and their influence on the accuracy of orbit determination is analysed. After using the PCO and PCV models in POD, the root mean square (RMS) of the carrier-phase residuals is around 0.008 m and the orbit overlap validation accuracy in each direction reaches approximately 0.01 m. Compared with the precise science orbit (PSO) provided by the Centre National d’Etudes Spatiales (CNES), the RD orbit accuracy of HY-2C in the radial (R) direction reaches 0.01 m. The accuracy of satellite laser ranging (SLR) range validation is better than 0.03 m. Additionally, a new method is proposed to verify the accuracy of the RD orbit of HY-2C by using space-borne Doppler orbitography and radiopositioning integrated by satellite (DORIS) data directly. DORIS data are directly compared to the result calculated using the accurate coordinates of beacons and the RD orbit, and the results indicate that the external validation of HY-2C RD orbit has a range rate accuracy of within 0.0063 m/s.

To verify the positioning performance and reliability of multi-system combination Precise Point Positioning in landslide monitoring, we carried out a multi-system combination Precise Point Positioning calculation experiment on the monitoring data of a single landslide disaster area in Fujian Province. The coordinates of the monitoring points obtained by a continuously operating reference station and the monitoring station for static relative positioning were used as reference values. The GPS system was used as the standard system and the combined PPP solution mode of G/R/C, G/R/E and G/R/E/C was used to obtain the surface displacement of the landslide area. The research showed that multi-system combination PPP converges to the centimeter level in about 30 min. The average value of internal accordant precision was more than 1 mm after convergence, and that of the external accordant precision was more than 5 cm, which meets the centimeter-level accuracy requirements in rapid landslide deformation monitoring.

GPS radio occultation (RO) technology can fully describe the subtle structure of the ionosphere. This paper discusses the dynamic abnormity observed by the RO data from the Constellation Observing System for Meteorology Ionosphere and Climate (FORMOSAT-3/COSMIC) before the great earthquake case in Concepcion, Chile (27 February 2010, Mw 8.8). Traditional ground-based GPS monitoring was considered as the external conditions and references to the excitation response. Using kriging interpolation, the global Nmf2 map (GNM) was first constructed to study the ionosphere deviation from the normal state. Successively, the ionosphere abnormality in the F2 region (Nmf2), vertical structure (RO profiles), and multiple heights (electron density) of traveling are unfolded. The Nmf2 disturbances in the possibility of seismic influences were excluded from non-seismic noise factors, including the external input (e.g., space weather activity, 15 February) and meteorological events (e.g., lower atmospheric forcing in quiet periods). However, the results show that there were apparent local Nmf2 perturbations for up to 5 h in the epicenter area on 21 and 25 February. The disturbances of the RO profiles and the interaction of other layers of the ionosphere implied the fluctuation signals of prominent long-wavelength fluctuations >50 km in the F layer. The ionospheric fluctuates wildly, and these wave signals considered as the trace of gravity wave propagating upward are mainly distributed at the elevation of 200–300 km. The simultaneous reaction of GNSS TEC further evidenced the potential possibility of acoustic gravity by the COSMIC RO profiles, reflecting the compounding couplings of seismo-ionosphere effects. In terms of the presentation of VLF radiation noise and the aerosol ion clusters, the electromagnetic and chemical channels have been previously completed by DEMETER and Terra/Aqua satellites. These findings implied the great potential of the FORMOSAT-7/COSMIC-2 system (now in the testing phase), with ~5000 soundings to investigate the subtle atmospheric stratification.

Temporal and spatial variation of ionosphere can influence our daily communication activities. By solving the one-year global positioning system (GPS) data of Shandong Continuous Operational Reference System (SDCORS) in 2012, we modeled the single-layer spherical harmonic model of vertical total electron content (TEC) over Shandong Province, China, and analyzed the time series of TEC in 2012. The ionosphere over Shandong in 2012 was in the peak year of solar activity. The ionospheric model over Shandong was calibrated and verified using data of the Center for Orbit Determination in Europe (CODE) and the Crustal Movement Observation Network of China (CMONOC), respectively. The ionosphere is greatly influenced by latitude and solar activity and has the phenomenon of Winter anomaly and semi-annual anomaly as well as the session change, diurnal variation, monthly change and seasonal variations. So we can grasp the regularity of temporal and spatial distribution of ionosphere over Shandong, China.

Shipborne gravity can be used to refine altimeter-derived gravity whose accuracy is low in shallow waters and areas with complex submarine topography. As altimeter-derived gravity only within a small radius around the shipborne data can be corrected by traditional methods, a new method based on multi-layer perceptron (MLP) neural network is proposed to refine the altimeter-derived gravity. Input variables of MLP include the positional information at observation points and geophysical information (from our own South China Sea gravity anomaly model (SCSGA) V1.0 and bathymetry model ETOPO1) at grid points around observation points. Output variables of MLP are the refined residual gravity anomalies at observation points. Training shipborne data are classified into four cases to train four MLP models, which are used to predict the refined gravity anomaly model SCSGA V1.1. Then all of the training shipborne data are used for training an MLP model to predict the refined gravity anomaly model SCSGA V1.2. Assessed by testing shipborne data, the accuracy of SCSGA V1.2 is 0.14 mGal higher than that of SCSGA V1.0, and similar to that of SCSGA V1.1. Compared with the original gravity anomaly model (SCSGA V1.0), the accuracy of the refined gravity anomaly model (SCSGA V1.2) by MLP is improved by 4.4% in areas where the training data are concentrated, and also improved by 2.2% in other areas. Therefore, the method of MLP can be used to refine the altimeter-derived gravity model by shipborne gravity, overcoming the problem of limited correction radius for traditional methods.

Geocenter is the center of the mass of the Earth system including the solid Earth, ocean, and atmosphere. The time-varying characteristics of geocenter motion (GCM) reflect the redistribution of the Earth’s mass and the interaction between solid Earth and mass loading. Multi-channel singular spectrum analysis (MSSA) was introduced to analyze the GCM products determined from satellite laser ranging data released by the Center for Space Research through January 1993 to February 2017 for extracting the periods and the long-term trend of GCM. The results show that the GCM has obvious seasonal characteristics of the annual, semiannual, quasi-0.6-year, and quasi-1.5-year in the X, Y, and Z directions, the annual characteristics make great domination, and its amplitudes are 1.7, 2.8, and 4.4 mm, respectively. It also shows long-period terms of 6.09 years as well as the non-linear trends of 0.05, 0.04, and –0.10 mm/yr in the three directions, respectively. To obtain real-time GCM parameters, the MSSA method combining a linear model (LM) and autoregressive moving average model (ARMA) was applied to predict GCM for 2 years into the future. The precision of predictions made using the proposed model was evaluated by the root mean squared error (RMSE). The results show that the proposed method can effectively predict GCM parameters, and the prediction precision in the three directions is 1.53, 1.08, and 3.46 mm, respectively.

The Mw7.9 Alaska earthquake at 09:31:40 UTC on 23 January 2018 occurred as the result of strike slip faulting within the shallow lithosphere of the Pacific plate. Global positioning system (GPS) data were used to calculate the slant total electron contents above the epicenter. The singular spectrum analysis (SSA) method was used to extract detailed ionospheric disturbance information, and to monitor the co-seismic ionospheric disturbances (CIDs) of the Alaska earthquake. The results show that the near-field CIDs were detected 8–12 min after the main shock, and the typical compression-rarefaction wave (N-shaped wave) appeared. The ionospheric disturbances propagate to the southwest at a horizontal velocity of 2.61 km/s within 500 km from the epicenter. The maximum amplitude of CIDs appears about 0.16 TECU (1TECU = 1016 el m−2) near the epicenter, and gradually decreases with the location of sub-ionospheric points (SIPs) far away from the epicenter. The attenuation rate of amplitude slows down as the distance between the SIPs and the epicenter increases. The direction of the CIDs caused by strike-slip faults may be affected by the horizontal direction of fault slip. The propagation characteristics of the ionospheric disturbance in the Alaska earthquake may be related to the complex conditions of focal mechanisms and fault location.

The classical harmonic analysis (CHA) method only can be used to obtain the harmonic constants (amplitude and phase) of ocean tide loading displacement (OTLD). In fact, there are significant seasonal variations in the harmonic constants of OTLD. A moving harmonic analysis (MHA) method is proposed, which can effectively capture the seasonal variation of OTLD parameters. Based on 5 years of kinematic coordinate time series in direction U of six Global Positioning System (GPS) stations in Hong Kong, the MHA method is used to explore the seasonal variation of the OTLD parameters of the 6 principal tidal constituents (M2, S2, N2, K1, O1, Q1). The influence of mass loading on the seasonal variation of OTLD parameters is analyzed. The results show that there are obviously seasonal variations in OTLD parameters of the 6 principal tidal constituents in Hong Kong. The OTLD’s amplitude’s changes of the 6 principal tidal constituents are around 4–25.1% and the oscillation ranges of OTLD’s phase parameters vary from 8.8° to 20.4°. Among the seasonal variations of OTLD parameters, the annual signal, the semi-annual signal, and the ter-annual signal are the most significant. By analyzing the influence of atmospheric loading on the seasonal variation of OTLD parameters, it is found that atmospheric loading has certain contribution to the seasonal variation of OTLD parameters. Hydrological loading and non-tidal ocean loading have little influence on the seasonal variation of OTLD parameters.

From late 2019 to early 2020, forest fires in southeastern Australia caused huge economic losses and huge environmental pollution. Monitoring forest fires has become increasingly important. A new method of fire detection using the difference between global navigation satellite system (GNSS)-derived precipitable water vapor and radiosonde-derived precipitable water vapor (ΔPWV) is proposed. To study the feasibility of the new method, the relationship is studied between particulate matter 10 (PM10) (2.5 to 10 microns particulate matter) and ΔPWV based on Global Positioning System (GPS) data, radiosonde data, and PM10 data from 1 June 2019 to 1 June 2020 in southeastern Australia. The results show that before the forest fire, ΔPWV and PM10 were smaller and less fluctuating. When the forest fire happened, ΔPWV and PM10 were increasing. Then after the forest fire, PM10 became small with relatively smooth fluctuations, but ΔPWV was larger and more fluctuating. Correlation between the 15-day moving standard deviation (STD) time series of ΔPWV and PM10 after the fire was significantly higher than that before the fire. This study shows that ΔPWV is effective in monitoring forest fires based on GNSS technique before and during forest fires in climates with more uniform precipitation, and using ΔPWV to detect forest fires based on GNSS needs to be further investigated in climates with more precipitation and severe climate change.

Mean sea surface (MSS) is an important datum for the study of sea-level changes and charting data, and its accuracy in coastal waters has always been the focus of marine geophysics and oceanography. A new MSS model with a grid of 1′ × 1′ over the Sea of Japan and its adjacent ocean (named SJAO2020) (25° N~50° N, 125° E~150° E) was established. It ingested 12 different satellites altimeter data (including TOPEX/Poseidon, Jason-1/2/3, ERS-1/2, Envisat, GFO, HaiYang-2A, SRL/Altika, Sentinel-3A, Cryosat-2) and 24 tide gauge stations’ records and joint GNSS data. The latter were used to correct the sea surface height within 10 km from the coastline by using the Gaussian inverse distance weighting method in SJAO2020. The differences among SJAO2020, CLS15, and DTU18, as well as the differences between them and the altimeter data of HY-2A, Jason-3, and Sentinel-3A were introduced. By comparing with tide gauge records, satellite altimeter data, and other models (DTU18, DTU15, CLS15, CLS11 and WHU13), it was demonstrated that SJAO2020 produces the smallest errors, and its coastal accuracy is relatively reliable.

At present, Global Navigation Satellite Systems (GNSS) users usually eliminate the influence of ionospheric delay of the first order items by dual-frequency ionosphere-free combination. But there is still residual ionospheric delay error of higher order term. The influence of the higher-order ionospheric corrections on both GPS precision orbit determination and static Precise Point Positioning (PPP) are studied in this paper. The influence of higher-order corrections on GPS precision orbit determination, GPS observations and static PPP are analyzed by neglecting or considering the higher-order ionospheric corrections by using a globally distributed network which is composed of International GNSS Service (IGS) tracking stations. Numerical experimental results show that, the root mean square (RMS) in three dimensions of satellite orbit is 36.6 mm–35.5 mm. The maximal second-order ionospheric correction is 9 cm, and the maximal third-order ionospheric correction is 1 cm. Higher-order corrections are influenced by latitude and station distribution. PPP is within 3 mm in the directions of east and up. Furthermore, the impact is mainly visible in the direction of north, showing a southward migration trend, especially at the lower latitudes where the influence value is likely to be bigger than 3 mm.

Altimeter waveforms are usually contaminated due to nonmarine surfaces or inhomogeneous sea state conditions. The present work aimed to present how the singular spectrum analysis (SSA) can be used to reduce the noise level in Jason-1 altimeter waveforms to obtain SSA-denoised waveforms, improving the accuracy of a mean sea surface height (MSSH) model. Comparing the retracked sea surface heights (SSHs) by a 50% threshold retracker for the SSA-denoised waveforms with those for the raw waveforms, the results indicated that SSA allowed a noise reduction on Jason-1 waveforms, improving the accuracy of retracked SSHs. The MSSH model (called Model 1) over the South China Sea with a grid of 2′ × 2′ was established from the retracked SSHs of Jason-1 by the 50% threshold retracker for the SSA-denoised waveforms. Comparing Model 1 and Model 2 (established from the retracked SSHs by the 50% threshold retracker for the raw waveforms) with the CLS15 and DTU18 models in the South China Sea, it was found that the accuracy of Model 1 was higher than that of Model 2, which indicates that using SSA to reduce noise level in Jason-1 waveforms can effectively improve the accuracy of the MSSH model.

Polar motion (PM) has a close relation to the Earth’s structure and composition, seasonal changes of the atmosphere and oceans, storage of waters, etc. As one of the four major space geodetic techniques, doppler orbitography and radiopositioning integrated by satellite (DORIS) is a mature technique that can monitor PM through precise ground station positioning. There are few articles that have analyzed the PM series derived by the DORIS solution in detail. The aim of this research was to assess the PM time-series based on the DORIS solution, to better capture the time-series. In this paper, Fourier fast transform (FFT) and singular spectrum analysis (SSA) were applied to analyze the 25 years of PM time-series solved by DORIS observation from January 1993 to January 2018, then accurately separate the trend terms and periodic signals, and finally precisely reconstruct the main components. To evaluate the PM time-series derived from DORIS, they were compared with those obtained from EOP 14 C04 (IAU2000). The results showed that the RMSs of the differences in PM between them were 1.594 mas and 1.465 mas in the X and Y directions, respectively. Spectrum analysis using FFT showed that the period of annual wobble was 0.998 years and that of the Chandler wobble was 1.181 years. During the SSA process, after singular value decomposition (SVD), the time-series was reconstructed using the eigenvalues and corresponding eigenvectors, and the results indicated that the trend term, annual wobble, and Chandler wobble components were accurately decomposed and reconstructed, and the component reconstruction results had a precision of 3.858 and 2.387 mas in the X and Y directions, respectively. In addition, the tests also gave reasonable explanations of the phenomena of peaks of differences between the PM parameters derived from DORIS and EOP 14 C04, trend terms, the Chandler wobble, and other signals detected by the SSA and FFT. This research will help the assessment and explanation of PM time-series and will offer a good method for the prediction of pole shifts.

Zero drift and solid Earth tide corrections to static relative gravimetric data cannot be ignored. In this paper, a new principal component analysis (PCA) algorithm is presented to extract the zero drift and the solid Earth tide, as signals, from static relative gravimetric data assuming that the components contained in the relative gravimetric data are uncorrelated. Static relative gravity observations from Aug. 15 to Aug. 23, 2014 are used as statistical variables to separate the signal and noise with PCA to obtain desired signals. The results of the linear drift extracted by PCA are consistent with those calculated by the least squares linear fitting, and the differences only reach to 10−2 μGal/day order of magnitude. Furthermore, PCA is used to estimate the solid Earth tide from the relative gravimetric data corrected by the zero drift. The statistical results are consistent with the results derived from the solid Earth tide correction provided by the internal software of the CG-5 gravimeter (SCINTREX Limited Ontario Canada). The statistical results of the differences between the two methods are both less than 8 μGal, and the RMSs for 9 days are all less than 5 μGal.