GPS Time Research Articles

Using the signal-to-noise ratio of GPS records to detect motion of structures

Although major breakthroughs have been achieved during the last decades in the use of Global Positioning System (GPS) technology on structural health monitoring, the mitigation of the biases and errors impeding its positioning accuracy remains a challenge. This paper tests an alternative approach that can increase the reliability of the GPS system in structural monitoring by using the spectral content of the signal-to-noise ratio (SNR) of GPS signals to detect frequencies of antenna vibrations. This approach suggests the potential of using SNR data analysis as a supplement to low-quality positioning solution or as a near real-time alert of excessive vibration proceeding the position solution calculation. Experiments, involving a GPS antenna subjected to vertical vibrations of 0.4- to 4.5-cm amplitude at a range of frequencies between 0.007 and 1 Hz, examine the dynamic multipath-induced SNR response corresponding to the antenna motion. Synchronised fluctuations in the SNR time series were observed to reflect the antenna motion and their spectral content to include the frequencies of motion. SNR records from the GPS monitoring of the Wilford suspension bridge were used to validate the SNR sensitivity to controlled vibrations of the bridge deck. The natural frequency of 1.64 Hz was extracted from SNR measurements using spectral analysis on a 6-mm amplitude vibration, and the frequency of the semistatic displacement (∼0.02 Hz) was revealed in the SNR records permitting, after appropriate filtering, the estimation of a few millimetre semistatic displacement from the GPS time series without the need for any other sensor.

Monitoring geodynamic activity in the Victoria Land, East Antarctica: Evidence from GNSS measurements

GNSS networks in Antarctica are a fundamental tool to define actual crustal displacements due to geological and geophysical processes and to constrain the glacial isostatic models (GIA). A large network devoted to the detection and monitoring of crustal deformations in the Northern Victoria Land (Victoria Land Network for DEFormation control – VLNDEF), was monumented during the 1999–2000 and 2000–2001 field campaigns, as part of Italian National Program for Antarctic Research and surveyed periodically during the Southern summer seasons.In this paper, GPS observations of VLNDEF collected over a more than 15-year span, together with various selected POLENET sites and more than 70 IGS stations, were processed with Bernese Software, using a classical double difference approach. A solution was obtained combining NEQs by means of ADDNEQ2/FODITS tools embedded in Bernese Software. All the Antarctic sites were kept free and a subset of 50 IGS stations were used to frame VLNDEF into ITRF2008. New evidence provided by analysis of GPS time series for the VLNDEF network is presented; also displacements along the vertical component are compared with the recently published GIA models. The absolute velocities indicate an overall displacement of the northern Victoria Land region along the south-east direction (Ve=10.6mm/yr, Vn=−11.5mm/yr) and an average uplift rate of Vu=0.5mm/yr. Two GIA models have been analyzed: ICE-6G_C-VM5a proposed by Argus et al. (2014), Peltier et al. (2015) and W12A_v1 by Whitehouse et al. (2012a,b). Up rates, predicted over the VLNDEF sites by the mentioned GIA models, have been extracted and compared with those observed. A preliminary comparison with GPS-derived vertical rates shows that the Victoria Land ICE-6G_C-VM5 and W12A_v1 GIA models predict overestimated uplift rates of 0.7 and 0.9mm/yr weighted mean residuals respectively. The mean horizontal relative motions within the Victoria Land (VL) area are in most cases negligible, while only a few points exhibit horizontal velocities greater than the confidence level. Such a residual horizontal velocity field could represent some of the tectonic characteristics affecting VL, characterized by block faulting, tilting along NE striking and SE dipping extensional faults. Uplift rates, highlighted in the present paper depict a well defined spatial pattern in the investigated areas. Northward, all sites show a general positive trend up to 2.3mm/yr. In the central and southern areas small negative trends (up to −1.3mm/yr) were detected in the vertical displacements. Only the site VL06, located atop the Mt. Melbourne volcano, does not concord with such a general reading, as it is representative of the volcanic complex’s evolution. Observed and predicted uplift rates increase westward (inland) where the ice-load increases. The same behavior is predicted southward by the GIA models; whereas GPS values decrease toward the south pole, due to the movements of a few sites reflecting the neotectonic phenomena acting in the Victoria Land region.

Comparison of observed and modeled seasonal crustal vertical displacements derived from multi‐institution GPS and GRACE solutions

AbstractEleven GPS crustal vertical displacement (CVD) solutions for 110 IGS08/IGS14 core stations provided by the International Global Navigation Satellite Systems Service Analysis Centers are compared with seven Gravity Recovery and Climate Experiment (GRACE)‐modeled CVD solutions. The results of the internal comparison of the GPS solutions from multiple institutions imply large uncertainty in the GPS postprocessing. There is also evidence that GRACE solutions from both different institutions and different processing approaches (mascon and traditional spherical harmonic coefficients) show similar results, suggesting that GRACE can provide CVD results of good internal consistency. When the uncertainty of the GPS data is accounted for, the GRACE data can explain as much as 50% of the actual signals and more than 80% of the GPS annual signals. Our study strongly indicates that GRACE data have great potential to correct the nontidal loading in GPS time series.

An Intelligent Framework to Manage and Control an Autonomous Platform for Detection, Inspection and Monitoring Applications in Chemical Environments

Implementing an intelligent framework using an autonomous robotic platform offers an effective and versatile solution for monitoring chemical environments. The robotic platform can be customized by adding different types of sensors depending on the desired application. The intelligent control system is realized using a PID control line tracker algorithm allowing it to cover a larger area for data acquisition for further analysis. The data is logged in terms of platform position based on GPS coordinates and time stamp and time interval between sampling. We were able to test the behavior of the developed robot in aggressive chemical environments- acid and base- as well as in experimental ambient conditions (variable concentrations of O2 and CO2). The only limitation we found this moment is the concentrations of acids and bases to be used (Perchloric acid, Hydrochloric acid, Sulfuric acid, Acetic acid, Methanesulfonic acid, Sodium hydroxide, Potassium hydroxide, Sodium carbonate, Sodium sulfate, Sodium fluoride) starting from the observed and proved damage on the plastics of the wheel.

Assessment of seismic hazard of the Japanese islands based on fractal analysis of GPS time series

Based on the fractal analysis of the time series of the Earth’s surface vertical displacements in the region of the Japanese Archipelago, the maps of the estimates of seismic activity in the region over 2015 are constructed. The analysis of the maps revealed several segments of the territory which are prone to the emergence of significant earthquakes. The characteristic peculiarity is noted in the change of the behavior of the geophysical dynamic system—the Earth’s crust—before the occurrence of seismic events: the mechanism of transition to the critical state demonstrates the energy preservation of the low frequencies with the simultaneous energy decay of the middle and high frequencies, which differs from the behavior of the other dynamical systems.

Structural evaluation of dynamic and semi-static displacements of the Juarez Bridge using GPS technology

Global Positioning System (GPS) naturally produces position estimates representing a considerable advantage in comparison with others assessment instruments such as accelerometers, where double integration is required. Several investigations have demonstrated that GPS is an accurate and efficient tool for the evaluation of civil infrastructure. Therefore, an alternative bridge structural evaluation focused on in-service conditions of the Juarez Bridge located in Culiacan, Mexico by using GPS is addressed in this research. The Juarez Bridge connects two important zones of the city, it is a reinforced concrete structure constructed approximately 45years ago, and it has a length closely to 200m. The assessment process consisted in collecting continuous GPS data during one consecutive hour at three different periods of the day (rush hours) from Monday to Sunday under critical traffic loading. Since the response of a structure subjected to loads may result in different types of displacements, GPS time series were used for the proper calculation of dynamic and semi-static displacement at the center deck of the Juarez Bridge. However, GPS displacements obtained in terms of coordinates may not accurately reveal the behavior of the bridge without considering prior filtering of the data. Hence, two post-processing reliable filtering techniques: the moving average and Chebyshev filter were applied to improve the time series. It was observed that the vertical displacements were critical during the evaluation. Hence, vertical semi-static displacements were compared with respect to the AASHTO (American Association of State Highway and Transportation Officials) deflection limits, and probability of failure was properly calculated.

Pluto occultation on 2015 June 29 UTC with central flash and atmospheric spikes just before the New Horizons flyby

We observed the occultation by Pluto of a 12th magnitude star, one of the two brightest occultation stars ever in our dozen years of continual monitoring of Pluto's atmosphere through such studies, on 2015 June 29 UTC.At the Univ. of Canterbury Mt. John Observatory (New Zealand), under clear skies throughout, we used a POETS frame-transfer CCD at 10Hz with GPS timing on the 1-m McLellan telescope as well as an infrared camera on an 0.6-m telescope and three-color photometry at a slower cadence on a second 0.6-m telescope. At the Auckland Observatory, we used a POETS and a PICO on 0.5-m and 0.4-m telescopes, with 0.4s and 2s cadences, respectively, obtaining ingress observations before clouds moved in. The Mt. John light curves show a central flash, indicating that we were close to the center of the occultation path. Analysis of our light curves show that Pluto's atmosphere remains robust.The presence of spikes at both sites in the egress and ingress shows atmospheric layering. We coordinated our observations with aircraft observations (Bosh et al., 2017) with the Stratospheric Observatory for Infrared Astronomy (SOFIA). Our chords helped constrain the path across Pluto that SOFIA saw. Our ground-based and airborne stellar-occultation effort came only just over two weeks of Earth days and two Pluto days before the flyby of NASA's New Horizons spacecraft.

A REGISTRATION METHOD OF POINT CLOUDS COLLECTED BY MOBILE LIDAR USING SOLELY STANDARD LAS FILES INFORMATION

Abstract. In the last few years, LiDAR sensors installed in terrestrial vehicles have been revealed as an efficient method to collect very dense 3D georeferenced information. The possibility of creating very dense point clouds representing the surface surrounding the sensor, at a given moment, in a very fast, detailed and easy way, shows the potential of this technology to be used for cartography and digital terrain models production in large scale. However, there are still some limitations associated with the use of this technology. When several acquisitions of the same area with the same device, are made, differences between the clouds can be observed. The range of that differences can go from few centimetres to some several tens of centimetres, mainly in urban and high vegetation areas where the occultation of the GNSS system introduces a degradation of the georeferenced trajectory. Along this article a different method point cloud registration is proposed. In addition to the efficiency and speed of execution, the main advantages of the method are related to the fact that the adjustment is continuously made over the trajectory, based on the GPS time. The process is fully automatic and only information recorded in the standard LAS files is used, without the need for any auxiliary information, in particular regarding the trajectory.

The Potential of High‐Rate GPS for Strong Ground Motion Assessment

We show that high-rate GPS can have a vital role to play in near real-time monitoring of potentially destructive earthquakes. We do this by investigating the potential of GPS in recording strong ground motions from earthquakes in Switzerland and Japan. The study uses finite-fault stochastic ground motion simulation based on Fourier amplitude spectra and duration models previously developed for both countries, allowing comparisons in terms of both Fourier and time domain characteristics (here the Peak Ground Velocity, PGV). We find that earthquakes of magnitude Mw>5.8 can be expected to be recorded by GPS in real-time at 10 km distance, i.e. their Fourier spectrum exceeds the noise of the instruments enough to be used in strong motion seismology. Post-processing of GPS time series lowers the noise and can improve the minimum observable magnitude by 0.1-0.2. As GPS receivers can record at higher rates (> 10 sps), we investigate which sampling rate is sufficient to optimally record earthquake signals and conclude that a minimum sampling rate of 5 sps is recommended. This is driven by recording events at short distances (below 10 km for magnitude 6 events and below 30 km for magnitude 7 events). Furthermore, the Maximum Ground Velocity derived from GPS is compared to the actual PGV for synthetic signals from the stochastic simulations and the 2008 Mw=6.9 Iwate earthquake. The proposed model, confirmed by synthetic and empirical data, shows that a reliable estimate of PGV for events of about magnitude 7 and greater can be basically retrieved by GPS in real-time and could be included for instance in ShakeMaps for aiding post-event disaster management.

Status and results from cabled hydrophones arrays deployed in deep sea off East Sicily (EMSO-ERIC node)

Since 2005 a cabled deep-sea infrastructure is operative at 2100 m water depth, 25 km off the port of Catania (Sicily). The infrastructure, under continuous improvement, is the first operative cabled node of the EMSO-ERIC, hosting several multidisciplinary observatories built in collaboration by INFN, INGV, CNR, CIBRA, and other scientific partners. Hydrophones antennas, sensitive in the range of frequencies between 1 Hz and 90 kHz, have been installed on seafloor observatories. Acoustic data are continuously digitized in situ at very high resolution, time-stamped with absolute GPS time and sent to shore in real time, through optical fiber link. Together with biological sounds, noise pollution study and monitoring were the main goals of the research. Results of multi-year monitoring of anthropogenic noise are discussed. Focus of the analysis is the noise level in the octave bands centered at 63 Hz and 125 Hz, in compliance with the EU Marine Strategy Framework Directive. The contribution of ship noise was modeled, based on their data recorded via proprietary AIS antennas, and compared to data. Noise at higher frequencies was also investigated. Detection of air-guns emissions and recorded noise levels is reported. Status and coming activities at the infrastructure is also presented.

Results from a triple chord stellar occultation and far-infrared photometry of the trans-Neptunian object (229762) 2007 UK126

A stellar occultation by a trans-Neptunian object (TNO) provides an opportunity to probe its size and shape. Very few occultations by TNOs have been sampled simultaneously from multiple locations, while a robust estimation of shadow size has been possible for only two objects. We present the first observation of an occultation by the TNO 2007 UK126 on 15 November 2014, measured by three observers, one nearly on and two almost symmetrical to the shadow's centerline. This is the first multi-chord dataset obtained for a so-called detached object, a TNO subgroup with perihelion distances so large that the giant planets have likely not perturbed their orbits. We revisit Herschel/PACS far-infrared data, applying a new reduction method to improve the accuracy of the measured fluxes. Combining both datasets allows us to comprehensively characterize 2007 UK126. We use error-in-variable regression to solve the non-linear problem of propagating timing errors into uncertainties of the ellipse parameters. Based on the shadow's size and a previously reported rotation period, we expect a shape of a Maclaurin spheroid and derive a geometrically plausible size range. To refine our size estimate of 2007 UK126, we model its thermal emission using a thermophysical model code. We conduct a parametric study to predict far-infrared fluxes and compare them to the Herschel/PACS measurements. The favorable geometry of our occultation chords, combined with minimal dead-time imaging, and precise GPS time measurements, allow for an accurate estimation of the shadow size (best-fitting ellipse with axes 645.80 $\pm$ 5.68 km $\times$ 597.81 $\pm$ 12.74 km) and the visual geometric albedo (15.0 $\pm$ 1.6 %). By combining our analyses of the occultation and the far-infrared data, we can constrain the effective diameter of 2007 UK126 to 599 - 629 km. We conclude that subsolar surface temperatures are $\approx$ 50 - 55 K.

Extracting seasonal deformations of the Nepal Himalaya region from vertical GPS position time series using Independent Component Analysis

Seasonal variations in vertical GPS time series are mainly caused by the Earth surface mass loading plus bedrock thermal expansion and GPS systematic errors. Relevant surface mass loading phenomena include atmospheric pressure, continental water storage, and non-tidal ocean loading. In regions with significant water storage variations, the hydrological effect makes the greatest contribution to Earth surface seasonal deformation. In this paper, we extract the various seasonal deformations from GPS time series of 17 stations in the Nepal Himalaya region using a blind source separation tool, the Independent Component Analysis (ICA). The vertical displacement components extracted by ICA showed strong correlations with modeled deformation induced by atmospheric and hydrological loading, indicating that independent components may represent different loading effects. Considering the wide application of GRACE in detecting hydrological deformation, we make a comparison between GRACE-derived displacements and the independent displacements contained in GPS. The results show ICA is effective in extracting atmospheric and hydrological deformation.

Inferring regional vertical crustal velocities from averaged relative sea level trends: A proof of concept

AbstractThis study demonstrates that relative sea level trends calculated from long-term tide gauge records can be used to estimate relative vertical crustal velocities in a region with high accuracy. A comparison of the weighted averages of the relative sea level trends estimated at six tide gauge stations in two clusters along the Eastern coast of United States, in Florida and in Maryland, reveals a statistically significant regional vertical crustal motion of Maryland with respect to Florida with a subsidence rate of −1.15±0.15 mm/yr identified predominantly due to the ongoing glacial isostatic adjustment process. The estimate is a consilience value to validate vertical crustal velocities calculated from GPS time series as well as towards constraining predictive GIA models in these regions.

Space weather effects on lower ionosphere: First investigation from Bharati station during 34th Indian scientific expedition to Antarctica

We investigate the solar flare effects on the D-region of the ionosphere with the help of VLF (Very Low Frequency) radio waves using a portable E-field system from Antarctica during the summer period of 34th Indian scientific expedition. Two GPS time synchronized VLF receivers, one located at Bharati, Antarctica (geographical latitude 69.40°S, longitude 76.18°E) and another located at Tripura, India (geographical latitude 23.84°N, longitude 91.28°E) were operated simultaneously to infer common mode changes in the lower ionosphere for a number of solar flares events. The two systems constantly monitored the carrier amplitude and phase of the MSK (Minimum Shift Keying) modulated navy transmitter located in Australia (Callsign: NWC, 19.8kHz, geographical latitude 21.88°S, longitude 114.13°E), around 5.6Mm great circle distance from the two receivers. The results are interpreted in terms of Earth-ionosphere wave-guide characteristics. A Long Wave Propagation Capability (LWPC) model study is also performed to infer the changes in the daytime electron density in polar D-region ionosphere during the solar flares. The exponential fit of the modeled electron density change with average X-ray flux change shows an excellent correlation (R2 value 0.95). The exponential fit is utilized to infer the daytime electron density change in the polar ionosphere during solar flare events. The analyses indicate that small solar flares of class ‘C’ can be very effectively detected with the portable antenna system even if the receiver is located in polar coastal region compared to equatorial region. The expedition results also demonstrate the feasibility of using portable VLF receivers from the coastal stations for monitoring the polar lower ionosphere from Antarctica and open up new opportunities for long term exploration.

THE USE OF EDUCATIONAL SEISMOGRAPHS IN THE SEISMOLOGY SCHOOL NETWORK “EGELADOS”

In this paper we attempt to describe the experience we gained, working with a specially designed seismograph as an educational device. It is a modern instrument with short period response, GPS timing and digital recording on personal computer. The installation was done in the frame of the local seismology school network, called “Egelados”. The knowledge of basic concepts of geology, physics and mathematics (Lower High School level - Gymnasium) is a prerequisite for the use of the instrument. Further research of the earthquake phenomenon and the analysis of the recorded data leads to didactic objectives in sciences and mathematics which are included in the Lyceum curriculum. The reliability test of the results obtained using the seismograph has, from the analysis students made, shown up to now declinations of the events magnitude of 0,2 - 0,4 when compared to magnitudes published by National Observatory of Athens-Institute of Geodynamics. Students’ constructions to overcome the calculation difficulties to find the exact location of epicentre are often proposed activating in this way their research mood. Up to now the use of the tool, in the framework of network “Egelados”, not only connects the participating schools but also gives the opportunity for further collaboration among teachers and students that have installed a similar instrument. Finally, everyday use of the seismograph reveals its drawbacks and provides ideas of enhancements.

Multivariate analysis of GPS position time series of JPL second reprocessing campaign

The second reprocessing of all GPS data gathered by the Analysis Centers of IGS was conducted in late 2013 using the latest models and methodologies. Improved models of antenna phase center variations and solar radiation pressure in JPL’s reanalysis are expected to significantly reduce errors. In an earlier work, JPL estimates of position time series, termed first reprocessing campaign, were examined in terms of their spatial and temporal correlation, power spectra, and draconitic signal. Similar analyses are applied to GPS time series at 89 and 66 sites of the second reanalysis with the time span of 7 and 21 years, respectively, to study possible improvements. Our results indicate that the spatial correlations are reduced on average by a factor of 1.25. While the white and flicker noise amplitudes for all components are reduced by 29–56 %, the random walk amplitude is enlarged. The white, flicker, and random walk noise amount to rate errors of, respectively, 0.01, 0.12, and 0.09 mm/yr in the horizontal and 0.04, 0.41 and 0.3 mm/yr in the vertical. Signals reported previously, such as those with periods of 13.63, 14.76, 5.5, and 351.4 / n for $$n=1,2,{\ldots },8$$ days, are identified in multivariate spectra of both data sets. The oscillation of the draconitic signal is reduced by factors of 1.87, 1.87, and 1.68 in the east, north and up components, respectively. Two other signals with Chandlerian period and a period of 380 days can also be detected.

GPS coordinate time series measurements in Ontario and Quebec, Canada

New precise network solutions for continuous GPS (cGPS) stations distributed in eastern Ontario and western Quebec provide constraints on the regional three-dimensional crustal velocity field. Five years of continuous observations at fourteen cGPS sites were analyzed using Bernese GPS processing software. Several different sub-networks were chosen from these stations, and the data were processed and compared to in order to select the optimal configuration to accurately estimate the vertical and horizontal station velocities and minimize the associated errors. The coordinate time series were then compared to the crustal motions from global solutions and the optimized solution is presented here. A noise analysis model with power-law and white noise, which best describes the noise characteristics of all three components, was employed for the GPS time series analysis. The linear trend, associated uncertainties, and the spectral index of the power-law noise were calculated using a maximum likelihood estimation approach. The residual horizontal velocities, after removal of rigid plate motion, have a magnitude consistent with expected glacial isostatic adjustment (GIA). The vertical velocities increase from subsidence of almost 1.9 mm/year south of the Great Lakes to uplift near Hudson Bay, where the highest rate is approximately 10.9 mm/year. The residual horizontal velocities range from approximately 0.5 mm/year, oriented south–southeastward, at the Great Lakes to nearly 1.5 mm/year directed toward the interior of Hudson Bay at stations adjacent to its shoreline. Here, the velocity uncertainties are estimated at less than 0.6 mm/year for the horizontal component and 1.1 mm/year for the vertical component. A comparison between the observed velocities and GIA model predictions, for a limited range of Earth models, shows a better fit to the observations for the Earth model with the smallest upper mantle viscosity and the largest lower mantle viscosity. However, the pattern of horizontal deformation is not well explained in the north, along Hudson Bay, suggesting that revisions to the ice thickness history are needed to improve the fit to observations.

The impact of solid Earth-tide model error on tropospheric zenith delay estimates and GPS coordinate time series

Any unmodelled or mismodelled subdaily signals left in the model may not only affect the instantaneous site positions and the associated estimates, but also propagate into spurious seasonal signals, contaminating the daily coordinate time series. To demonstrate how subdaily ‘error’ in the modelling of the solid Earth-tide affects the estimates of tropospheric zenith total delay (ZTD) and how it propagates into long-period signal in the daily GPS time series, we analyse GPS observations collected between 2009 and 2013 for 13 sites in the coastal regions of Antarctica using the GAMIT/GLOBK 10.6 software. We find that ZTD differenced time series, with amplitude at 2 mm level, have inverse correlation with the input K1 correction, and the corresponding admittances range from 6% to 14%; Propagated spurious annual signals are evident in the vertical component of coordinate differenced time series, with amplitudes at the mm level and admittances of around 2–11%.

Stability Comparison of Fault Location Techniques Against Faulty GPS Time Tagging for Three-Terminal Lines

Fault location techniques based on the arrival times of Traveling Wave (TW) need precise time tagging and synchronization for multi-terminal transmission lines. Although this need can be satisfied by using Global Positioning System, extracting the correct arrival time of the main TW is a troubling task, especially for multi-terminal lines with large number of wave reflections in different directions after fault incident. So, stability of the proposed techniques should be studied when the time tagging has also faced faults. In this paper, three fault location techniques based on TW, Genetic Algorithm (GA) and Artificial Neural Network (ANN) are discussed and then their stabilities against the faulty time tagging are compared. Simulation results show that three discussed methods have relatively close error averages. However, the proposed ANN-based method is twice much more stable than TW- and GA-based methods in about 22.95% of samples.

Annual variations in GPS‐measured vertical displacements near Upernavik Isstrøm (Greenland) and contributions from surface mass loading

AbstractIn response to present‐day ice mass loss on and near the Greenland Ice Sheet, steady crustal uplifts have been observed from the network of Global Positioning System (GPS) stations mounted on bedrock. In addition to the secular uplift trends, the GPS time series also show prominent annual variability. Here we examine the annual changes of the vertical displacements measured at two GPS stations (SRMP and UPVK) near Upernavik Isstrøm in western Greenland. We model elastic loading displacements due to various surface mass loading including three nonice components: atmospheric pressure, ocean bottom pressure, continental water storage, and one ice component, i.e., surface mass balance (SMB). We find that the contribution from atmospheric pressure changes can explain 46% and 78% of the annual amplitude observed in the GPS verticals at SRMP and UPVK, respectively. We also show that removing the predicted loading displacements due to SMB adversely increases the annual variance of the GPS residuals. However, using the GPS data alone, we cannot identify the exact cause(s) of this discrepancy because the annual loading displacements are sensitive to the SMB changes from over 85% of the ice sheet area. Alternatively, by differencing vertical displacements between the two stations, we find a good agreement between the modeled differential SMB loading displacements and the GPS residuals after removing nonice components. Our study highlights the necessity of correcting for nonice loading contributions in the GPS measurements of crustal deformation to infer ice mass changes in Greenland at annual periods.