A Height Nonlinear Velocity Field Algorithm for CORS Station Based on GARCH Model

In this study, the basic concept of height nonlinear velocity field modeling in the CORS station is described. The noise results in a large deviation between the observation and predicted height. An ARCH testing method for heteroscedasticity of CORS height residual square series was proposed and the non-stationary characteristic of CORS height residual square time series was proved. A CORS height nonlinear velocity field reconstruction method based on the GARCH model was proposed. First, a nonlinear LS periodic fitting model was established for CORS height series data. Then, a GARCH model was established for the fitted non-stationary residual series. Finally, the signal term, linear trend term, and GARCH model noise term of nonlinear LS modeling were combined to reconstruct the nonlinear velocity field of the CORS height. The RMSE of nonlinear LS cycle modeling for 25 CORS stations worldwide ranged from 5 to 10 mm. The differences between the velocity, approximate annual and semi-annual amplitudes, and SOPAC results were 0.73 mm/a, 0.94 mm, and 0.51 mm, respectively. Compared with the centimeter amplitude of the CORS station height, the accuracy of the nonlinear model established in this study met the requirements. The results of height nonlinear velocity field reconstruction at 25 CORS stations worldwide showed that the mean square error of prediction of the one-year height movement reached 9 mm, and the average prediction accuracy of the semi-annual was 7 mm. Compared with the calculation accuracy of the current global CORS elevation component of 3-5 mm, the prediction error in this study was about 3 mm. The expected goal was achieved regarding the accuracy of the CORS station height nonlinear velocity field model.

A Review of GNSS/GPS in Hydrogeodesy: Hydrologic Loading Applications and Their Implications for Water Resource Research

Hydrogeodesy, a relatively new field within the earth sciences, is the analysis of the distribution and movement of terrestrial water at Earth's surface using measurements of Earth's shape, orientation, and gravitational field. In this paper, we review the current state of hydrogeodesy with a specific focus on Global Navigation Satellite System (GNSS)/Global Positioning System measurements of hydrologic loading. As water cycles through the hydrosphere, GNSS stations anchored to Earth's crust measure the associated movement of the land surface under the weight of changing hydrologic loads. Recent advances in GNSS-based hydrogeodesy have led to exciting applications of hydrologic loading and subsequent terrestrial water storage (TWS) estimates. We describe how GNSS position time series respond to climatic drivers, can be used to estimate TWS across temporal scales, and can improve drought characterization. We aim to facilitate hydrologists' use of GNSS-observed surface deformation as an emerging tool for investigating and quantifying water resources, propose methods to further strengthen collaborative research and exchange between geodesists and hydrologists, and offer ideas about pressing questions in hydrology that GNSS may help to answer.

Noise Analysis and Combination of Hydrology Loading-Induced Displacements

Large uncertainties exist in the available hydrology loading prediction models, and currently no consensus is reached on which loading model is superior or appears to represent nature in a more satisfactory way. This study discusses the noise characterization and combination of the vertical loadings predicted by different hydrology reanalysis (e.g., MERRA, GLDAS/Noah, GEOS-FPIT, and ERA interim). We focused on the hydrology loading predictions in the time span from 2011 to 2014 for the 70 Global Positioning System (GPS) sites, which are located close to the great rivers, lakes, and reservoirs. The maximum likelihood estimate with Akaike information criteria (AIC) showed that the auto-regressive (AR) model with an order from 2 to 5 is a good description of the temporal correlation that exists in the hydrology loading predictions. Moreover, significant discrepancy exists in the root mean square (RMS) of different hydrology loading predictions, and none of them have the lowest noise level for the all-time domain. Principal component analysis (PCA) was therefore used to create a combined loading-induced time series. Statistical indices (e.g., mean overlapping Hadamard variance, Nash-Sutcliffe efficiency, and variance reduction) showed that our proposed algorithm had an overall good performance and seemed to be potentially feasible for performing corrections on geodetic GPS heights.

Strain Field Features and Three-Dimensional Crustal Deformations Constrained by Dense GRACE and GPS Measurements in NE Tibet

The continuing impact between the Eurasia Plate and India results in the thickening and shortening of the N-S Tibetan Plateau. There has been strong tectonic movement along the boundary of the zones of deformation of the NE corner of the Tibetan plateau (NET) since the new tectonic period, with its dynamic mechanisms remaining controversial. Here, we use observations of 39 Continuous Global Positioning System (CGPS) gauges and 451 Crustal Movement Observation Network of China (CMONOC) campaign-mode stations to detect the three-dimensional deformation of the crust in the NET. Improved processing procedures are implemented to strengthen the patterns of strain throughout the NET. The principal component analysis (PCA) technique is introduced to decompose the time series into spatial eigenvectors and principal components (PCs), and the first three PCs are used to estimate and rectify common mode errors (CMEs). In addition, GRACE observations are used to detect deformation changes that account for non-tidal oceanic mass loading, hydrological loading, and surface pressure. The rectified deformation of the crust indicates the anisotropic nature of both the subsidence and uplift, and that the highest uplift rate of the Longmen Shan fault uplift reaches 7.13 ± 0.53 mm/yr. Finally, the horizontal velocity is further used to enumerate the strain rates throughout the NET. The results show that the shear band retained property in line with the strike-slip fault along the Altyn Tagh fault, the Qilian Shan faults, the Haiyuan fault, the West Qinling fault, the East Kunlun fault, and the Longmen Shan fault. In addition, the results further indicate that the whole NET shows a strong relationship with the mean principal rates of horizontal shortening strain. Extension and compression of the crust reasonably describe its sinking and uplifting.

Estimation of Terrestrial Water Storage Variations in Sichuan-Yunnan Region from GPS Observations Using Independent Component Analysis

GPS can be used to measure land motions induced by mass loading variations on the Earth’s surface. This paper presents an independent component analysis (ICA)-based inversion method that uses vertical GPS coordinate time series to estimate the change of terrestrial water storage (TWS) in the Sichuan-Yunnan region in China. The ICA method was applied to extract the hydrological deformation signals from the vertical coordinate time series of GPS stations in the Sichuan-Yunnan region from the Crustal Movement Observation Network of China (CMONC). These vertical deformation signals were then inverted to TWS variations. Comparative experiments were conducted based on Gravity Recovery and Climate Experiment (GRACE) data and a hydrological model for validation. The results demonstrate that the TWS changes estimated from GPS(ICA) deformations are highly correlated with the water variations derived from the GRACE data and hydrological model in Sichuan-Yunnan region. The TWS variations are overestimated by the vertical GPS observations the northwestern Sichuan-Yunnan region. The anomalies are likely caused by inaccurate atmospheric loading correction models or residual tropospheric errors in the region with high topographic variability and can be reduced by ICA preprocessing.

Regional Crustal Vertical Deformation Driven by Terrestrial Water Load Depending on CORS Network and Environmental Loading Data: A Case Study of Southeast Zhejiang

Monitoring regional terrestrial water load deformation is of great significance to the dynamic maintenance and hydrodynamic study of the regional benchmark framework. In view of the lack of a spatial interpolation method based on the GNSS (Global Navigation Satellite System) elevation time series for obtaining terrestrial water load deformation information, this paper proposes to employ a CORS (Continuously Operating Reference Stations) network combined with environmental loading data, such as ECMWF (European Centre for Medium-Range Weather Forecasts) atmospheric data, the GLDAS (Global Land Data Assimilation System) hydrological model, and MSLA (Mean Sea Level Anomaly) data. Based on the load deformation theory and spherical harmonic analysis method, we took 38 CORS stations in southeast Zhejiang province as an example and comprehensively determined the vertical deformation of the crust as caused by regional terrestrial water load changes from January 2015 to December 2017, and then compared these data with the GRACE (Gravity Recovery and Climate Experiment) satellite. The results show that the vertical deformation value of the terrestrial water load in southeast Zhejiang, as monitored by the CORS network, can reach a centimeter, and the amplitude changes from −1.8 cm to 2.4 cm. The seasonal change is obvious, and the spatial distribution takes a ladder form from inland to coastal regions. The surface vertical deformation caused by groundwater load changes in the east–west–south–north–central sub-regions show obvious fluctuations from 2015 to 2017, and the trends of the five sub-regions are consistent. The amplitude of surface vertical deformation caused by groundwater load change in the west is higher than that in the east. We tested the use of GRACE for the verification of CORS network monitoring results and found a relatively consistent temporal distribution between both data sets after phase delay correction on GRACE, except for in three months—November in 2015, and January and February in 2016. The results show that the comprehensive solution based on the CORS network can effectively improve the monitoring of crustal vertical deformation during regional terrestrial water load change.

Analysis of GNSS Displacements in Europe and Their Comparison with Hydrological Loading Models

Thanks to the increasing number of permanent GNSS stations in Europe and their long records, we computed position solutions for more than 1000 stations over the last two decades using the REPRO3 orbit and clock products from the IGS CNES-CLS (GRGS) Analysis Center. The velocities, which are mainly due to tectonics and glacial isostatic adjustment (GIA), and the annual solar cycle have been estimated using weighted least squares. The interannual variations have been accounted for in the stochastic model or in the deterministic model. We demonstrated that the velocity and annual cycle, in addition to their uncertainties, depend on the estimation method we used and that the estimation of GPS draconitic oscillations minimises biases in the estimation of annual solar cycle displacements. The annual solar cycle extracted from GPS has been compared with that from loading estimates of several hydrological models. If the annual amplitudes between GPS and hydrological models match, the phases of the loading models were typically in advance of about 1 month compared to GPS. Predictions of displacements modelled from GRACE observations did not show this phase shift. We also found important discrepancies at the interannual frequency band between GNSS, loading estimates derived from GRACE, and hydrological models using principal component analysis (PCA) decomposition. These discrepancies revealed that GNSS position variations in the interannual band cannot be systematically interpreted as a geophysical signal and should instead be interpreted in terms of autocorrelated noise.

A Loading Correction Model for GPS Measurements Derived from Multiple-Data Combined Monthly Gravity

Time-dependent loading deformations of the Earth’s surface, due to nontidal changes in the atmosphere, ocean, land water/ice, etc., contribute significantly to the seasonal and secular Global Positioning System (GPS) site displacements, especially for the up component. While loading deformations derived from general circulation model (GCM) outputs are usually used to correct loading signals in the GPS site displacements, this study aims to provide a loading correction model based on the multiple-data combined monthly gravity products LDCmgm90. We have adopted GPS measurements from 249 IGS reference frame stations and 3 different GCM-based loading models to test the reliability of the LDCmgm90 model. Compared to the GCM-based models, the LDCmgm90 loading correction is more effective in attenuating seasonal (especially annual) loading signals and can bring more significant improvements to most stations for both the data-trend-removed and the data-trend-retained cases. Thus, we have validated the LDCmgm90 model from the loading aspect and proved it to be a reliable loading-correction model for GPS displacements. The relatively better secular loading signals provided by the LDCmgm90 loading model may provide us a chance to study the long-term, nonloading signals in GPS data.

Three-Dimensional Surface Deformation Characteristics Based on Time Series InSAR and GPS Technologies in Beijing, China

Excessive exploitation of the groundwater has resulted in obvious three-dimensional (3D) deformation features on the surface of the Beijing Plain. This paper, by combining Interferometric Synthetic Aperture Radar (InSAR) and Global Positioning System (GPS) technologies, has obtained time-series information of the 3D surface deformation in the Beijing Plain, analyzing its spatial distribution characteristics. On this basis, the relationship between different controlling factors with the 3D deformation of the surface has been analyzed as well. The following results are obtained: (1) From 2013 to 2018, the land subsidence, which generally showed the trend of slowing down, was mainly concentrated in the eastern, northern, and southern regions of Beijing Plain, with multiple subsidence centers. (2) Under the International Terrestrial Reference Frame 2005 (ITRF2005), the horizontal direction of all GPS points in the plain is basically the same, with the dominant movement direction being NE112.5°~NE113.8°. Under the Eurasian reference frame, the horizontal movement rate of GPS points significantly decreases. The movement rate and direction of each point are not characteristic of overall trend activity. (3) The distribution and extent of the 3D surface deformation in the Beijing Plain are controlled by the basement structure. Part of the subsided area corresponds to a Quaternary depression formed at the junction of active faults disrupting the area. Similarly, the distribution of horizontal deformation in the E-W and N-S directions of the plain is controlled by the regional basement structure comprising major faults bounding horizontal deformation. (4) Groundwater exploitation is the main cause of the 3D surface deformation in the Beijing Plain. The groundwater funnels of the second and third confined aquifer are in suitable agreement with the land subsidence. The horizontal movement in the Beijing Plain is either directed toward the center of the groundwater or the land subsidence funnel, and the deformation is directed from areas with higher to areas with lower groundwater levels.

Post-Seismic Deformation Related to the 2016 Central Italy Seismic Sequence From GPS Displacement Time-Series

The 2016-2017 Central Italy earthquake sequence struck the central Apennines between August 2016 and October 2016 with Mw ∈ [5.9; 6.5], plus four earthquakes occurring in January 2017 with Mw ∈ [5.0; 5.5]. We study Global Positioning System time series including near- and far-field domains. We use a variational Bayesian independent component analysis technique to separate the post-seismic deformation from signals caused by variation of the water content in aquifers at hundreds of meters of depth and of the soil moisture. For each independent component, realistic uncertainties and a plausible physical explanation are provided. We focus on the study of afterslip on the main structures surrounding the mainshock, highlighting the role played by faults that were not activated during the co-seismic phase in accommodating the post-seismic deformation. We report aseismic deformation occurring on the Paganica fault, which hosted the Mw 6.1 2009 L'Aquila earthquake, suggesting that static stress transfer and aseismic slip influence the recurrence time of nearby (∼50 km further south of the mainshocks) segments. A ∼2-3 km thick subhorizontal shear-zone, clearly illuminated by seismicity, which bounds at depth the west-dipping normal faults where the mainshocks nucleated, also shows aseismic slip. Since afterslip alone underestimates the displacement in the far-field domain, we consider the possibility that the shear zone marks the brittle-ductile transition, assuming the viscoelastic relaxation of the lower crust as a mechanism contributing to the post-seismic displacement. Our results suggest that multiple deformation processes are active in the first 2 years after the mainshocks.

The mean seasonal cycle in relative sea level from satellite altimetry and gravimetry

Satellite altimetry and gravimetry are used to determine the mean seasonal cycle in relative sea level, a quantity relevant to coastal flooding and related applications. The main harmonics (annual, semiannual, terannual) are estimated from 25 years of gridded altimetry, while several conventional altimeter "corrections" (gravitational tide, pole tide, and inverted barometer) are restored. To transform from absolute to relative sea levels, a model of vertical land motion is developed from a high-resolution seasonal mass inversion estimated from satellite gravimetry. An adjustment for annual geocenter motion accounts for use of a center-of-mass reference frame in satellite orbit determination. A set of 544 test tide gauges, from which seasonal harmonics have been estimated from hourly measurements, is used to assess how accurately each adjustment to the altimeter data helps converge the results to true relative sea levels. At these gauges, the median annual and semiannual amplitudes are 7.1 cm and 2.2 cm, respectively. The root-mean-square differences with altimetry are 3.24 and 1.17 cm, respectively, which are reduced to 1.93 and 0.86 cm after restoration of corrections and adjustment for land motion. Example outliers highlight some limitations of present-day coastal altimetry owing to inadequate spatial resolution: upwelling and currents off Oregon and wave setup at Minamitori Island.

Tsunami detection by GPS-derived ionospheric total electron content

To unravel the relationship between earthquake and tsunami using ionospheric total electron content (TEC) changes, we analyzed two Chilean tsunamigenic subduction earthquakes: the 2014 Pisagua M_w 8.1 and the 2015 Illapel M_w 8.3. During the Pisagua earthquake, the TEC changes were detected at the GPS sites located to the north and south of the earthquake epicenter, whereas during the Illapel earthquake, we registered the changes only in the northward direction. Tide-gauge sites mimicked the propagation direction of tsunami waves similar to the TEC change pattern during both earthquakes. The TEC changes were represented by three signals. The initial weaker signal correlated well with Acoustic Rayleigh wave (AW_Rayleigh), while the following stronger perturbation was interpreted to be caused by Acoustic Gravity wave (AGW_epi) and Internal Gravity wave (IGW_tsuna) induced by earthquakes and subsequent tsunamis respectively. Inevitably, TEC changes can be utilized to evaluate earthquake occurrence and tsunami propagation within a framework of multi-parameter early warning systems.

An Analysis of Vertical Crustal Movements along the European Coast from Satellite Altimetry, Tide Gauge, GNSS and Radar Interferometry

The main aim of the article was to analyse the actual accuracy of determining the vertical movements of the Earth’s crust (VMEC) based on time series made of four measurement techniques: satellite altimetry (SA), tide gauges (TG), fixed GNSS stations and radar interferometry. A relatively new issue is the use of the persistent scatterer InSAR (PSInSAR) time series to determine VMEC. To compare the PSInSAR results with GNSS, an innovative procedure was developed: the workflow of determining the value of VMEC velocities in GNSS stations based on InSAR data. In our article, we have compiled 110 interferograms for ascending satellites and 111 interferograms for descending satellites along the European coast for each of the selected 27 GNSS stations, which is over 5000 interferograms. This allowed us to create time series of unprecedented time, very similar to the time resolution of time series from GNSS stations. As a result, we found that the obtained accuracies of the VMEC determined from the PSInSAR are similar to those obtained from the GNSS time series. We have shown that the VMEC around GNSS stations determined by other techniques are not the same.

Coevolving early afterslip and aftershock signatures of a San Andreas fault rupture

Large earthquakes often lead to transient deformation and enhanced seismic activity, with their fastest evolution occurring at the early, ephemeral post-rupture period. Here, we investigate this elusive phase using geophysical observations from the 2004 moment magnitude 6.0 Parkfield, California, earthquake. We image continuously evolving afterslip, along with aftershocks, on the San Andreas fault over a minutes-to-days postseismic time span. Our results reveal a multistage scenario, including immediate onset of afterslip following tens-of-seconds-long coseismic shaking, short-lived slip reversals within minutes, expanding afterslip within hours, and slip migration between subparallel fault strands within days. The early afterslip and associated stress changes appear synchronized with local aftershock rates, with increasing afterslip often preceding larger aftershocks, suggesting the control of afterslip on fine-scale aftershock behavior. We interpret complex shallow processes as dynamic signatures of a three-dimensional fault-zone structure. These findings highlight important roles of aseismic source processes and structural factors in seismicity evolution, offering potential prospects for improving aftershock forecasts.

Seasonal Variation of GPS-Derived the Principal Ocean Tidal Constituents’ Loading Displacement Parameters Based on Moving Harmonic Analysis in Hong Kong

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.

Reconstructing GRACE-type time-variable gravity from the Swarm satellites

The Gravity Recovery and Climate Experiment (GRACE) mission has enabled mass changes and transports in the hydrosphere, cryosphere and oceans to be quantified with unprecedented resolution. However, while this legacy is currently being continued with the GRACE Follow-On (GRACE-FO) mission there is a gap of 11 months between the end of GRACE and the start of GRACE-FO which must be addressed. Here we bridge the gap by combining time-variable, low-resolution gravity models derived from European Space Agency's Swarm satellites with the dominating spatial modes of mass variability obtained from GRACE. We show that the noise inherent in unconstrained Swarm gravity solutions is greatly reduced, that basin averages can have root mean square errors reduced to the order of [Formula: see text] of equivalent water height, and that useful information can be retrieved for basins as small as [Formula: see text]. It is found that Swarm data contains sufficient information to inform the leading three global mass modes found in GRACE at the least. By comparing monthly reconstructed maps to GRACE data from December 2013 to June 2017, we suggest the uncertainty of these maps to be [Formula: see text] of equivalent water height.

Geopositioning time series from offshore platforms in the Adriatic Sea

We provide a dataset of 3D coordinate time series of 37 continuous GNSS stations installed for stability monitoring purposes on onshore and offshore industrial settlements along a NW-SE-oriented and ~100-km-wide belt encompassing the eastern Italian coast and the Adriatic Sea. The dataset results from the analysis performed by using different geodetic software (Bernese, GAMIT/GLOBK and GIPSY) and consists of six raw position time series solutions, referred to IGb08 and IGS14 reference frames. Time series analyses and comparisons evidence that the different solutions are consistent between them, despite the use of different software, models, strategy processing and frame realizations. We observe that the offshore stations are subject to significant seasonal oscillations probably due to seasonal environmental loads, seasonal temperature-induced platform deformation and hydrostatic pressure variations. Many stations are characterized by non-linear time series, suggesting a complex interplay between regional (long-term tectonic stress) and local sources of deformation (e.g. reservoirs depletion, sediment compaction). Computed raw time series, logs files, phasor diagrams and time series comparison plots are distributed via PANGAEA ( https://www.pangaea.de ).

Multidisciplinary Analysis of Ground Movements: An Underground Gas Storage Case Study

The paper presents a multi-physics investigation of the ground movements related to the cyclical and seasonal injection and withdrawal of natural gas in/from a depleted reservoir located in the Po Plain area, Italy. Interferometric Synthetic Aperture Radar (InSAr) data (from 2003) and Global Navigation Satellite System (GNSS) data (from 2008) provided a full and coherent panorama of almost two decades of ground movement in the monitored area (more extended than the field boundary). The analysis of the acquired millimetric-scale movements together with the detailed geological analysis, both at reservoir and at regional scale, represents the focal point for understanding the investigated phenomena. Based on this information, a fully integrated and multidisciplinary geological, fluid-flow and geomechanical numerical modeling approach was developed to reproduce the main geometrical and structural features of the involved formations together with the poromechanics processes induced by the storage operations. The main achievement of the adopted methodology is a deep knowledge of the system and the involved processes, which is mandatory for the safety of the urbanized areas and the effective management of the underground resources.

The Relationship between Surface Displacement and Groundwater Level Change and Its Hydrogeological Implications in an Alluvial Fan: Case Study of the Choshui River, Taiwan

Balancing the demand of groundwater resources and the mitigation of land subsidence is particularly important, yet challenging, in populated alluvial fan areas. In this study, we combine multiple monitoring data derived from Multi-Temporal InSAR (MTI), GNSS (Global Navigation Satellite System), precise leveling, groundwater level, and compaction monitoring wells, in order to analyze the relationship between surface displacement and groundwater level change within the alluvial fan of the Choshui River in Taiwan. Our combined time-series analyses suggest, in a yearly time scale, that groundwater level increases with the vertical surface displacement when the effect of pore water pressure dominates. Conversely, this relationship is negative when the effect of water-mass loading predominates over pore water pressure. However, the correlation between the vertical surface displacement and the groundwater level change is consistently positive over the time scale of two decades. It is interpreted that the alluvial fan sequence in the subsurface is not fully elastic, and compaction is greater than rebound in this process. These findings were not well reported and discussed by previous studies because of insufficient monitoring data and analyses. Understanding the combined effect of groundwater level change and vertical surface displacement is very helpful for management of land subsidence and usage of groundwater resources. The spatial and temporal integration of multi-sensors can be applied to overcome the limitations associated with the single technique and provides further insights into land surface changes, particularly in highly populated alluvial fan areas.

Modeling Seasonal Variations in Vertical GPS Coordinate Time Series Using Independent Component Analysis and Varying Coefficient Regression

Common seasonal variations in Global Positioning System (GPS) coordinate time series always exist, and the modeling and correction of the seasonal signals are helpful for many geodetic studies using GPS observations. A spatiotemporal model was proposed to model the common seasonal variations in vertical GPS coordinate time series, based on independent component analysis and varying coefficient regression method. In the model, independent component analysis (ICA) is used to separate the common seasonal signals in the vertical GPS coordinate time series. Considering that the periodic signals in GPS coordinate time series change with time, a varying coefficient regression method is used to fit the separated independent components. The spatiotemporal model was then used to fit the vertical GPS coordinate time series of 262 global International GPS Service for Geodynamics (IGS) GPS sites. The results show that compared with least squares regression, the varying coefficient method can achieve a more reliable fitting result for the seasonal variation of the separated independent components. The proposed method can accurately model the common seasonal variations in the vertical GPS coordinate time series, with an average root mean square (RMS) reduction of 41.6% after the model correction.

Impacts of Local Effects and Surface Loads on the Common Mode Error Filtering in Continuous GPS Measurements in the Northwest of Yunnan Province, China

While seasonal hydrological mass loading, derived from Gravity Recovery and Climate Experiment (GRACE) measurements, shows coherent spatial patterns and is an important source for the common mode error (CME) in continuous global positioning system (cGPS) measurements in Yunnan, it is a challenge to quantify local effects and detailed changes in daily GPS measurements by using GRACE data due to its low time and spatial resolutions. In this study, we computed and compared two groups of CMEs for nine cGPS sites in the northwest Yunnan province; rCMEs were computed with the residual cGPS time series having high inter-station correlations, while oCMEs were computed with all the GPS time series. The rCMEs-filtered time series had smaller variances and larger root mean square (RMS) reductions than those that were oCMEs-filtered, and when the stations local effects were not removed, spurious transient-like signals occurred. Compared with hydrological mass loading (HYDL), its combination with non-tidal atmosphere pressure and ocean mass reached a better agreement with the CME in the vertical component, with the Nash–Sutcliffe efficiency (NSE) increasing from 0.28 to 0.55 and the RMS reduction increasing from 15.19% to 33.4%, respectively. Our results suggest that it is necessary to evaluate the inter-station correlation and remove the possible noisy stations before conducting CME filtering, and that one should carefully choose surface loading models to correct the raw cGPS time series if CME filtering is not conducted.

Comparative Analysis of the Effect of the Loading Series from GFZ and EOST on Long-Term GPS Height Time Series

In order to investigate the effect of different loading models on the nonlinear variations in Global Positioning System (GPS) height time series, the characteristics of annual signals (amplitude and phase) of GPS time series, loading series from Deutsche GeoForschungsZentrum, Germany (GFZ) and School and Observatory of Earth Sciences, France (EOST) at 633 global GPS stations are processed and analyzed. The change characteristics of the root mean square (RMS) reduction rate, annual amplitude and phase of GPS time series after environmental loading corrections (ELCs) are then detected. Results show that ELCs have a positive effect on the reduction in the nonlinear deformation contained in most GPS stations around the world. RMS reduction rates are positive at 82.6% stations after GFZ correction and 87.4% after EOST correction, and the average reduction rates of all stations are 10.6% and 15.4%, respectively. As for the environmental loading series from GFZ and EOST, their average annual amplitudes are 2.7 and 3.1 mm, which explains ~40% annual amplitude of GPS height time series (7.2 mm). Further analysis of some specific stations indicates that the annual phase difference between GPS height time series and the environmental loading series is an important reason that affects the reduction rates of the RMS and annual amplitude. The linear relationship between the annual phase difference and the annual amplitude reduction rate is significant. The linear fitting results show that when there is no annual phase difference between GPS and loading series, the reduction rates of the RMS and annual amplitude will increase to the maximum of 15.6% and 41.6% for GFZ, and 22.0% and 46.6% for EOST.

Validation of Sentinel-3 OLCI Integrated Water Vapor Products Using Regional GNSS Measurements in Crete, Greece

Water vapor is one of the essential variables in monitoring the Earth’s climate. The Ocean and Land Color Instrument (OLCI) on-board the Copernicus Sentinel-3 missions measures the Integrated Water Vapor (IWV) column over land and ocean surfaces. Post-launch calibration and validation of satellite measurements constitutes a key process in the operational phase of Earth observation satellites. This work presents the external and independent validation of OLCI-A IWV product using the regional network of continuously operating Global Navigation Satellite System (GNSS) comprised 10 stations distributed over the island of Crete in the eastern Mediterranean. The Sentinel-3A/-3B OLCI imagery that captures in a single scene the entire area of Crete has been examined. For each OLCI image, the IWV value of cloud-free pixels containing the GNSS stations have been derived and compared against simultaneous GNSS-derived measurements. The absolute as well as the relative bias between OLCI-A and OLCI-B IWV measurements have been determined. There is a good agreement between OLCI and GNSS with a bias of −0.57 mm ± 2.90 mm for OLCI(A) and +2.42 ± 3.41 mm for OLCI(B). The results of this regional validation activity are compared against other studies and the regular validation carried out at the Sentinel-3 Mission Performance Center. This work concludes that the accuracy of the OLCI IWV products is within its design requirements. The potential synergy between Sentinel-2 and Sentinel-3 IWV products is also discussed.

Extracting Seasonal Signals in GNSS Coordinate Time Series via Weighted Nuclear Norm Minimization

Global Navigation Satellite System (GNSS) coordinate time series contains obvious seasonal signals, which mainly manifest as a superposition of annual and semi-annual oscillations. Accurate extraction of seasonal signals is of great importance for understanding various geophysical phenomena. In this paper, a Weighted Nuclear Norm Minimization (WNNM) is proposed to extract the seasonal signals from the GNSS coordinate time series. WNNM assigns different weights to different singular values that enable us to estimate an approximate low rank matrix from its noisy matrix. To address this issue, the low rank characteristics of the Hankel matrix induced by GNSS coordinate time series was investigated first, and then the WNNM is applied to extract the seasonal signals in the GNSS coordinate time series. Meanwhile, the residuals have been analyzed, obtaining the estimation of the uncertainty of velocity. To demonstrate the effectiveness of the proposed algorithm, a number of tests have been carried out on both simulated and real GNSS dataset. Experimental results indicate that the proposed scheme offers preferable performances compared with many state-of-the-art methods.

Multi-Component and Multi-Source Approach for Studying Land Subsidence in Deltas

The coupled effects of climate change and land sinking make deltas and coastal areas prone to inundation and flooding, meaning that reliable estimation of land subsidence is becoming crucial. Commonly, land subsidence is monitored by accurate continuous and discrete measurements collected by terrestrial and space geodetic techniques, such as Global Navigation Satellite System (GNSS), Interferometry Synthetic Aperture Radar (InSAR), and high precision leveling. In particular, GNSS, which includes the Global Positioning System (GPS), provides geospatial positioning with global coverage, then used for deriving local displacements through time. These site-positioning time series usually exhibit a linear trend plus seasonal oscillations of annual and semi-annual periods. Although the periodic components observed in the geodetic signal affect the velocity estimate, studies dealing with the prediction and prevention of risks associated with subsidence focus mainly on the permanent component. Periodic components are simply removed from the original dataset by statistical analyses not based on the underlying physical mechanisms. Here, we propose a systematic approach for detecting the physical mechanisms that better explain the permanent and periodic components of subsidence observed in the geodetic time series. It consists of three steps involving a component recognition phase, based on statistical and spectral analyses of geodetic time series, a source selection phase, based on their comparison with data of different nature (e.g., geological, hydro-meteorological, hydrogeological records), and a source validation step, where the selected sources are validated through physically-based models. The application of the proposed procedure to the Codigoro area (Po River Delta, Northern Italy), historically affected by land subsidence, allowed for an accurate estimation of the subsidence rate over the period 2009–2017. Significant differences turn out in the retrieved subsidence velocities by using or not periodic trends obtained by physically based models.

Seismo-Deformation Anomalies Associated with the M6.1 Ludian Earthquake on August 3, 2014

A time-frequency method retrieving the acceleration changes in the terminal stage of theM6.1 Ludian earthquake in China is discussed in this article. The non-linear, non-stationaryseismo-demformation was obtained by using the Hilbert–Huang transform and followed by aband-pass filter. We found that the temporal evolution of the residual GNSS-derived orientationexhibits a unique disorder-alignment-disorder sequence days before the earthquake whichcorresponds well with the four stages of an earthquake: elastic strain buildup, crack developments,deformation, and the terminal stage of material failure. The disordering orientations are graduallyaligned with a common direction a few days before the terminal stage. This common direction isconsistent with the most compressive axis derived from the seismological method. In addition, theregion of the stress accumulation, as identified by the size of the disordered orientation, isgenerally consistent with the earthquake preparation zones estimated by using numerical models.

Linear and Nonlinear Deformation Effects in the Permanent GNSS Network of Cyprus

Permanent Global Navigation Satellite Systems (GNSS) reference stations are well established as a powerful tool for the estimation of deformation induced by man-made or physical processes. GNSS sensors are successfully used to determine positions and velocities over a specified time period, with unprecedented accuracy, promoting research in many safety-critical areas, such as geophysics and geo-tectonics, tackling problems that torment traditional equipment and providing deformation products with absolute accuracy. Cyprus, being located at the Mediterranean fault, exhibits a very interesting geodynamic regime, which has yet to be investigated thoroughly. Accordingly, this research revolves around the estimation of crustal deformation in Cyprus using GNSS receivers. CYPOS (CYprus POsitioning System), a network of seven permanent GNSS stations has been operating since 2008, under the responsibility of the Department of Lands and Surveys. The continuous flow of positioning data collected over this network, offers the required information to investigate the behavior of the crustal deformation field of Cyprus using GNSS sensors for the first time. This paper presents the results of a multi-year analysis (11/2011–01/2017) of daily GNSS data and provides inferences of linear and nonlinear deforming signals into the position time series of the network stations. Specifically, 3D station velocities and seasonal periodic displacements are jointly estimated and presented via a data stacking approach with respect to the IGb08 reference frame.

Signal Extraction from GNSS Position Time Series Using Weighted Wavelet Analysis

The daily position time series derived by Global Navigation Satellite System (GNSS) contain nonlinear signals which are suitably extracted by using wavelet analysis. Considering formal errors are also provided in daily GNSS solutions, a weighted wavelet analysis is proposed in this contribution where the weight factors are constructed via the formal errors. The proposed approach is applied to process the position time series of 27 permanent stations from the Crustal Movement Observation Network of China (CMONOC), compared to traditional wavelet analysis. The results show that the proposed approach can extract more exact signals than traditional wavelet analysis, with the average error reductions are 13.24%, 13.53% and 9.35% in north, east and up coordinate components, respectively. The results from 500 simulations indicate that the signals extracted by proposed approach are closer to true signals than the traditional wavelet analysis.

Analysis of the Potential Contributors to Common Mode Error in Chuandian Region of China

Common mode error (CME) in Chuandian region of China is derived from 6-year continuous GPS time series and is identified by principal component analysis (PCA) method. It is revealed that the temporal behavior of the CME is not purely random, and contains unmodeled signals such as nonseasonal mass loadings. Its spatial distribution is quite uniform for all GPS sites in the region, and the first principal component, uniformly distributed in the region, has a spatial response of more than 70%. To further explore the potential contributors of CME, daily atmospheric mass loading and soil moisture mass loading effects are evaluated. Our results show that ~15% of CME can be explained by these daily surface mass loadings. The power spectral analysis is used to assess the CME. After removing atmospheric and soil moisture loadings from the CME, the power of the CME reduces in a wide range of frequencies. We also investigate the contribution of CME in GPS filtered residuals time series and it shows the Root Mean Squares (RMSs) of GPS time series are reduced by applying of the mass loading corrections in CME. These comparison results demonstrate that daily atmosphere pressure and the soil moisture mass loadings are a part of contributors to the CME in Chuandian region of China.

Quantitative Evaluation of Environmental Loading Induced Displacement Products for Correcting GNSS Time Series in CMONOC

Mass redistribution within the Earth system deforms the surface elastically. Loading theory allows us to predict loading induced displacement anywhere on the Earth’s surface using environmental loading models, e.g., Global Land Data Assimilation System. In addition, different publicly available loading products are available. However, there are differences among those products and the differences among the combinations of loading models cannot be ignored when precisions of better than 1 cm are required. Many scholars have applied these loading corrections to Global Navigation Satellite System (GNSS) time series from mainland China without considering or discussing the differences between the available models. Evaluating the effects of different loading products over this region is of paramount importance for accurately removing the loading signal. In this study, we investigate the performance of these different publicly available loading products on the scatter of GNSS time series from the Crustal Movement Observation Network of China. We concentrate on five different continental water storage loading models, six different non-tidal atmospheric loading models, and five different non-tidal oceanic loading models. We also investigate all the different combinations of loading products. The results show that the difference in RMS reduction can reach 20% in the vertical component depending on the loading correction applied. We then discuss the performance of different loading combinations and their effects on the noise characteristics of GNSS height time series and horizontal velocities. The results show that the loading products from NASA may be the best choice for corrections in mainland China. This conclusion could serve as an important reference for loading products users in this region.

Upstream GPS Vertical Displacement and its Standardization for Mekong River Basin Surface Runoff Reconstruction and Estimation

Surface runoff (R), which is another expression for river water discharge of a river basin, is a critical measurement for regional water cycles. Over the past two decades, river water discharge has been widely investigated, which is based on remotely sensed hydraulic and hydrological variables as well as indices. This study aims to demonstrate the potential of upstream global positioning system (GPS) vertical displacement (VD) and its standardization to statistically derive R time series, which has not been reported in recent literature. The correlation between the in situ R at estuaries and averaged GPS-VD and its standardization in the river basin upstream on a monthly temporal scale of the Mekong River Basin (MRB) is examined. It was found that the reconstructed R time series from the latter agrees with and yields a similar performance to that from the terrestrial water storage based on gravimetric satellite (i.e., Gravity Recovery and Climate Experiment (GRACE)) and traditional remote sensing data. The reconstructed R time series from the standardized GPS-VD was found to have a 2–7% accuracy increase against those without standardization. On the other hand, it is comparable to data that are obtained by the Palmer drought severity index (PDSI). Similar accuracies are exhibited by the estimated R when externally validated through another station location with in situ time series. The comparison of the estimated R at the entrance of river delta against that at the estuaries indicates a 1–3% relative error induced by the residual ocean tidal effect at the estuary. The reconstructed R from the standardized GPS-VD yields the lowest total relative error of less than 9% when accounting for the main upstream area of the MRB. The remaining errors may be the result of the combined effect of the proposed methodology, remaining environmental signals in the data time series, and potential time lag (less than a month) between the upstream MRB and estuary.

Akaike's Bayesian Information Criterion for the Joint Inversion of Terrestrial Water Storage Using GPS Vertical Displacements, GRACE and GLDAS in Southwest China

Global navigation satellite systems (GNSS) techniques, such as GPS, can be used to accurately record vertical crustal movements induced by seasonal terrestrial water storage (TWS) variations. Conversely, the TWS data could be inverted from GPS-observed vertical displacement based on the well-known elastic loading theory through the Tikhonov regularization (TR) or the Helmert variance component estimation (HVCE). To complement a potential non-uniform spatial distribution of GPS sites and to improve the quality of inversion procedure, herein we proposed in this study a novel approach for the TWS inversion by jointly supplementing GPS vertical crustal displacements with minimum usage of external TWS-derived displacements serving as pseudo GPS sites, such as from satellite gravimetry (e.g., Gravity Recovery and Climate Experiment, GRACE) or from hydrological models (e.g., Global Land Data Assimilation System, GLDAS), to constrain the inversion. In addition, Akaike’s Bayesian Information Criterion (ABIC) was employed during the inversion, while comparing with TR and HVCE to demonstrate the feasibility of our approach. Despite the deterioration of the model fitness, our results revealed that the introduction of GRACE or GLDAS data as constraints during the joint inversion effectively reduced the uncertainty and bias by 42% and 41% on average, respectively, with significant improvements in the spatial boundary of our study area. In general, the ABIC with GRACE or GLDAS data constraints displayed an optimal performance in terms of model fitness and inversion performance, compared to those of other GPS-inferred TWS methodologies reported in published studies.

An Improved GPS-Inferred Seasonal Terrestrial Water Storage Using Terrain-Corrected Vertical Crustal Displacements Constrained by GRACE

Based on a geophysical model for elastic loading, the application potential of Global Positioning System (GPS) vertical crustal displacements for inverting terrestrial water storage has been demonstrated using the Tikhonov regularization and the Helmert variance component estimation since 2014. However, the GPS-inferred terrestrial water storage has larger resulting amplitudes than those inferred from satellite gravimetry (i.e., Gravity Recovery and Climate Experiment (GRACE)) and those simulated from hydrological models (e.g., Global Land Data Assimilation System (GLDAS)). We speculate that the enlarged amplitudes should be partly due to irregularly distributed GPS stations and the neglect of the terrain effect. Within southwest China, covering part of southeastern Tibet as a study region, a novel GPS-inferred terrestrial water storage approach is proposed via terrain-corrected GPS and supplementary vertical crustal displacements inferred from GRACE, serving as "virtual GPS stations" for constraining the inversion. Compared to the Tikhonov regularization and Helmert variance component estimation, we employ Akaike’s Bayesian Information Criterion as an inverse method to prove the effectiveness of our solution. Our results indicate that the combined application of the terrain-corrected GPS vertical crustal displacements and supplementary GRACE spatial data constraints improves the inversion accuracy of the GPS-inferred terrestrial water storage from the Helmert variance component estimation, Tikhonov regularization, and Akaike’s Bayesian Information Criterion, by 55%, 33%, and 41%, respectively, when compared to that of the GLDAS-modeled terrestrial water storage. The solution inverted with Akaike’s Bayesian Information Criterion exhibits more stability regardless of the constraint conditions, when compared to those of other inferred solutions. The best Akaike’s Bayesian Information Criterion inverted solution agrees well with the GLDAS-modeled one, with a root-mean-square error (RMSE) of 3.75 cm, equivalent to a 15.6% relative error, when compared to 39.4% obtained in previous studies. The remaining discrepancy might be due to the difference between GPS and GRACE in sensing different surface water storage components, the remaining effect of the water storage changes in rivers and reservoirs, and the internal error in the geophysical model for elastic loading.

Optimal Strategy of a GPS Position Time Series Analysis for Post-Glacial Rebound Investigation in Europe

We describe a comprehensive analysis of the 469 European Global Positioning System (GPS) vertical position time series. The assumptions we present should be employed to perform the post-glacial rebound (PGR)-oriented comparison. We prove that the proper treatment of either deterministic or stochastic components of the time series is indispensable to obtain reliable vertical velocities along with their uncertainties. The statistical significance of the vertical velocities is examined; due to their small vertical rates, 172 velocities from central and western Europe are found to fall below their uncertainties and excluded from analyses. The GPS vertical velocities reach the maximum values for Scandinavia with the maximal uplift equal to 11.0 mm/yr. Moreover, a comparison between the GPS-derived rates and the present-day motion predicted by the newest Glacial Isostatic Adjustment (GIA) ICE-6G_C (VM5a) model is provided. We prove that these rates agree at a 0.5 mm/yr level on average; the Sweden area with the most significant uplift observed agrees within 0.2 mm/yr. The largest discrepancies between GIA-predicted uplift and the GPS vertical rates are found for Svalbard; the difference is equal to 6.7 mm/yr and arises mainly from the present-day ice melting. The GPS-derived vertical rates estimated for the southern coast of the Baltic Sea are systematically underestimated by the GIA prediction by up to 2 mm/yr. The northern British Isles vertical rates are overestimated by the GIA model by about 0.5 mm/yr. The area of the Netherlands and the coastal area of Belgium are both subsiding faster than it is predicted by the GIA model of around 1 mm/yr. The inland part of Belgium, Luxemburg and the western part of Germany show strong positive velocities when compared to the GIA model. Most of these stations uplift of more than 1 mm/yr. It may be caused by present-day elastic deformation due to terrestrial hydrology, especially for Rhein basin, or non-tidal atmospheric loading, for Belgium and Luxembourg.

The Noise Properties and Velocities from a Time-Series of Estonian Permanent GNSS Stations

The aim of this study was to estimate the noise properties, velocities, and their uncertainties from a time-series of selected (~9 years long) Estonian continuously operating Global Navigation Satellite System (GNSS) stations. Two software packages based on different processing methods, Gipsy–Oasis and Bernese, were used for daily coordinate calculations. Different methods and software (Tsview, Hector, and MIDAS) were used for coordinate time-series analysis. Outliers were removed using three different strategies. Six different stochastic noise models were used for trend estimation altogether with the analysis of the noise properties of the residual time-series with Hector. Obtained velocities were compared with different land uplift and glacial isostatic adjustment models (e.g., ICE-6G (VM5a), NKG2016LU, etc.). All compared solutions showed similar fit to the compared models. It was confirmed that the best fit to the time-series residuals were with the flicker noise plus white noise model (for the North and East component) and generalized Gauss–Markov model (for Up). Velocities from MIDAS, Tsview, and Hector solutions within the same time-series (Gipsy–Oasis or Bernese) agreed well but velocity uncertainties differed up to four times. The smallest uncertainties were obtained from Tsview; the MIDAS solution produced the most conservative values. Although the East and Up component velocities between Gipsy and Bernese solutions agreed well, the North component velocities were systematically shifted.

Time-Series InSAR Monitoring of Permafrost Freeze-Thaw Seasonal Displacement over Qinghai–Tibetan Plateau Using Sentinel-1 Data

Permafrost is widely distributed in the Tibetan Plateau. Seasonal freeze–thaw cycles of permafrost result in upward and downward surface displacement. Multitemporal interferometric synthetic aperture radar (MT-InSAR) observations provide an effective method for monitoring permafrost displacement under difficult terrain and climatic conditions. In this study, a seasonal sinusoidal model-based new small baselines subset (NSBAS) chain was adopted to obtain a deformation time series. An experimental study was carried out using 33 scenes of Sentinel-1 data (S-1) from 28 November 2017 to 29 December 2018 with frequent revisit (12 days) observations. The spatial and temporal characteristics of the surface displacements variation combined with different types of surface land cover, elevation and surface temperature factors were analyzed. The results revealed that the seasonal changes observed in the time series of ground movements, induced by freeze–thaw cycles were observed on flat surfaces of sedimentary basins and mountainous areas with gentle slopes. The estimated seasonal oscillations ranged from 2 mm to 30 mm, which were smaller in Alpine deserts than in Alpine meadows. In particular, there were significant systematic differences in seasonal surface deformation between areas near mountains and sedimentary basins. It was also found that the time series of deformation was consistent with the variation of surface temperature. Based on soil moisture active/passive (SMAP) L4 surface and root zone soil moisture data, the deformation analysis influenced by soil moisture factors was also carried out. The comprehensive analysis of deformation results and auxiliary data (elevation, soil moisture and surface temperature et al.) provides important insights for the monitoring of the seasonal freeze-thaw cycles in the Tibetan Plateau.

The Magnitude of Diurnal/Semidiurnal Atmospheric Tides (S1/S2) and Their Impacts on the Continuous GPS Coordinate Time Series

The site displacement due to diurnal and semidiurnal atmospheric tides (S1/S2) is often neglected in the routine precise GPS data processing. We recall the S1/S2 modeling method and show the magnitude of the S1/S2 tides under the Center of Mass (CM) frame. The results show that the annual amplitudes caused by both S1 and S2 tides exceed 1 mm for stations near the equator. The impact of S1/S2 on the 24-h Global Positioning System (GPS) solution is typically at the sub-mm level, and the scatter of the S1/S2 caused displacement difference increases with the decreasing latitude for northern hemisphere stations, among which the maximum Standard Deviation (STD) reaches up to 1.5 mm, 1 mm and 0.7 mm for the Up, East and North components, respectively, at low-latitude stations. We also find that 65% of the stations’ vertical velocity change caused by S1/S2 is larger than 1%, among which the maximum velocity variation rate reaches more than 40% for some coastal/island stations, while stations with the weighted root mean square reduced account for 65%, 39%, and 38% for the up, east, and north components respectively, in particular for most coastal/island stations. Furthermore, the S1/S2 correction could partly reduce the annual and the semi-annual signals of the global stacked vertical component together with the semi-annual amplitude of the east component. The power of some anomalous harmonics of 1.04 cycle per year also decreased a lot. These results further prove the benefits of S1/S2 correction in the precise GPS data processing.

Effect of Helmert Transformation Parameters and Weight Matrix on Seasonal Signals in GNSS Coordinate Time Series

Seasonal signals caused by the Earth’s surface mass redistribution can be detected by Global Navigation Satellite Systems (GNSS). The authors analyze the effect of Helmert transformation parameters and weight matrices, as well as the additional draconic signals on seasonal signals, in the GNSS coordinate time series. Moreover, the contribution of environmental loading models to the GNSS position series is assessed. Position time series of 647 global stations, with spans of 2–21 years are collected to generate six cumulative solutions using different parameters estimated in a deterministic model, as well as weight matrices. Comparison among the different solutions indicates that Helmert transformation parameters and weight matrices can result in a root mean square of 0.1 mm and 0.3 mm for seasonal signals, respectively. Compared to the displacements obtained from environmental loading models, seasonal signals estimated with the Helmert parameters and full weight matrices considered seems to have the best agreement with the results of the loading model. Meanwhile, the additional draconic signals are not effective to be parameterized in the deterministic model with an observation time span less than 15 years, marginally. There are 62%, 72% and 90% of 647 stations with weight root mean squares (WRMS) reduced by removing the loading-model-induced changes from the GNSS residual series for the east, north and vertical components, respectively. Finally, to obtain a velocity estimation with a bias of less than 0.1 mm/yr induced by seasonal signals, the position series with a time span greater than seven years is suggested.

Temporal-Spatial Surface Seasonal Mass Changes and Vertical Crustal Deformation in South China Block from GPS and GRACE Measurements

The solid Earth deforms elastically in response to variations of surface atmosphere, hydrology, and ice/glacier mass loads. Continuous geodetic observations by Global Positioning System (CGPS) stations and Gravity Recovery and Climate Experiment (GRACE) record such deformations to estimate seasonal and secular mass changes. In this paper, we present the seasonal variation of the surface mass changes and the crustal vertical deformation in the South China Block (SCB) identified by GPS and GRACE observations with records spanning from 1999 to 2016. We used 33 CGPS stations to construct a time series of coordinate changes, which are decomposed by empirical orthogonal functions (EOFs) in SCB. The average weighted root-mean-square (WRMS) reduction is 38% when we subtract GRACE-modeled vertical displacements from GPS time series. The first common mode shows clear seasonal changes, indicating seasonal surface mass re-distribution in and around the South China Block. The correlation between GRACE and GPS time series is analyzed which provides a reference for further improvement of the seasonal variation of CGPS time series. The results of the GRACE observations inversion are the surface deformations caused by the surface mass change load at a rate of about -0.4 to -0.8 mm/year, which is used to improve the long-term trend of non-tectonic loads of the GPS vertical velocity field to further explain the crustal tectonic movement in the SCB and surroundings.

Monitoring ground water storage at mesoscale using seismic noise: 30 years of continuous observation and thermo-elastic and hydrological modeling

Groundwater is a vital freshwater resource for both humans and ecosystems. Achieving sustainable management requires a detailed knowledge of the aquifer structure and of its behavior in response to climatic and anthropogenic forcing. Traditional monitoring is carried out using piezometer networks, and recently complemented with new geophysical or satellite-based observations. These techniques survey either local (small-scale) water systems or regional areas (large scale) but, to date, adequate observation tools are lacking at the water management scale (i.e. several tens of kms), which is generally explored by modeling. Using 30 years of continuous recording by four seismic stations of the Gräfenberg Array (Germany), we demonstrate that long-term observations of velocity variations (approximately 0.01%) of surface waves can be extracted from such recordings of ocean-generated seismic noise. These small variations can be explained by changes to mechanical properties of the complex aquifer system in the top few hundred meters of the crust. The velocity changes can be interpreted as effects of temperature diffusion and water storage changes. Seismic noise recordings may become a new and valuable tool to monitor heterogeneous groundwater systems at mesoscale, in addition to existing observation methods.

Annual variations of monsoon and drought detected by GPS: A case study in Yunnan, China

The Global Positioning System (GPS) records monsoonal precipitable water vapor (PWV) and vertical crustal displacement (VCD) due to hydrological loading, and can thus be applied jointly to diagnose meteorological and hydrological droughts. We have analyzed the PWV and VCD observations during 2007.0–2015.0 at 26 continuous GPS stations located in Yunnan province, China. We also obtained equivalent water height (EWH) derived from the Gravity Recovery And Climate Experiment (GRACE) and precipitation at these stations with the same period. Then, we quantified the annual variations of PWV, precipitation, EWH and VCD and provided empirical relationships between them. We found that GPS-derived PWV and VCD (positive means downward movement) are in phase with precipitation and GRACE-derived EWH, respectively. The annual signals of VCD and PWV show linearly correlated amplitudes and a two-month phase lag. Furthermore, the results indicate that PWV and VCD anomalies can also be used to explore drought, such as the heavy drought during winter/spring 2010. Our analysis results verify the capability of GPS to monitor monsoon variations and drought in Yunnan and show that a more comprehensive understanding of the characteristics of regional monsoon and drought can be achieved by integrating GPS-derived PWV and VCD with precipitation and GRACE-derived EWH.

Physical applications of GPS geodesy: a review

Geodesy, the oldest science, has become an important discipline in the geosciences, in large part by enhancing Global Positioning System (GPS) capabilities over the last 35 years well beyond the satellite constellation's original design. The ability of GPS geodesy to estimate 3D positions with millimeter-level precision with respect to a global terrestrial reference frame has contributed to significant advances in geophysics, seismology, atmospheric science, hydrology, and natural hazard science. Monitoring the changes in the positions or trajectories of GPS instruments on the Earth's land and water surfaces, in the atmosphere, or in space, is important for both theory and applications, from an improved understanding of tectonic and magmatic processes to developing systems for mitigating the impact of natural hazards on society and the environment. Besides accurate positioning, all disturbances in the propagation of the transmitted GPS radio signals from satellite to receiver are mined for information, from troposphere and ionosphere delays for weather, climate, and natural hazard applications, to disturbances in the signals due to multipath reflections from the solid ground, water, and ice for environmental applications. We review the relevant concepts of geodetic theory, data analysis, and physical modeling for a myriad of processes at multiple spatial and temporal scales, and discuss the extensive global infrastructure that has been built to support GPS geodesy consisting of thousands of continuously operating stations. We also discuss the integration of heterogeneous and complementary data sets from geodesy, seismology, and geology, focusing on crustal deformation applications and early warning systems for natural hazards.

Development of Autonomous Mobile Robot that Can Navigate in Rainy Situations

[abstFig src='/00280004/02.jpg' width='300' text='Navigation under strong rainy condition' ] The Real World Robot Challenge (RWRC), a technical challenge for mobile outdoor robots, has robots automatically navigate a predetermined path over 1 km with the objective of detecting specific persons. RWRC 2015 was conducted in the rain and every robot could not complete the mission. This was because sensors on the robots detected raindrops and the robots then generated unexpected behavior, indicating the need to study the influence of rain on mobile navigation systems – a study clearly not yet sufficient. We begin by describing our robot’s waterproofing function, followed by investigating the influence of rain on the external sensors commonly used in mobile robot navigation and discuss how the robot navigates autonomous in the rain. We conducted navigation experiments in artificial and actual rainy environments and those results showed that the robot navigates stably in the rain.

Seasonal Mass Changes and Crustal Vertical Deformations Constrained by GPS and GRACE in Northeastern Tibet

Surface vertical deformation includes the Earth’s elastic response to mass loading on or near the surface. Continuous Global Positioning System (CGPS) stations record such deformations to estimate seasonal and secular mass changes. We used 41 CGPS stations to construct a time series of coordinate changes, which are decomposed by empirical orthogonal functions (EOFs), in northeastern Tibet. The first common mode shows clear seasonal changes, indicating seasonal surface mass re-distribution around northeastern Tibet. The GPS-derived result is then assessed in terms of the mass changes observed in northeastern Tibet. The GPS-derived common mode vertical change and the stacked Gravity Recovery and Climate Experiment (GRACE) mass change are consistent, suggesting that the seasonal surface mass variation is caused by changes in the hydrological, atmospheric and non-tidal ocean loads. The annual peak-to-peak surface mass changes derived from GPS and GRACE results show seasonal oscillations in mass loads, and the corresponding amplitudes are between 3 and 35 mm/year. There is an apparent gradually increasing gravity between 0.1 and 0.9 μGal/year in northeast Tibet. Crustal vertical deformation is determined after eliminating the surface load effects from GRACE, without considering Glacial Isostatic Adjustment (GIA) contribution. It reveals crustal uplift around northeastern Tibet from the corrected GPS vertical velocity. The unusual uplift of the Longmen Shan fault indicates tectonically sophisticated processes in northeastern Tibet.

Modeling and Assessment of GPS/BDS Combined Precise Point Positioning

Precise Point Positioning (PPP) technique enables stand-alone receivers to obtain cm-level positioning accuracy. Observations from multi-GNSS systems can augment users with improved positioning accuracy, reliability and availability. In this paper, we present and evaluate the GPS/BDS combined PPP models, including the traditional model and a simplified model, where the inter-system bias (ISB) is treated in different way. To evaluate the performance of combined GPS/BDS PPP, kinematic and static PPP positions are compared to the IGS daily estimates, where 1 month GPS/BDS data of 11 IGS Multi-GNSS Experiment (MGEX) stations are used. The results indicate apparent improvement of GPS/BDS combined PPP solutions in both static and kinematic cases, where much smaller standard deviations are presented in the magnitude distribution of coordinates RMS statistics. Comparisons between the traditional and simplified combined PPP models show no difference in coordinate estimations, and the inter system biases between the GPS/BDS system are assimilated into receiver clock, ambiguities and pseudo-range residuals accordingly.