Ocean Tide Loading Displacement Research Articles

Analysis of Ocean Tide Loading Displacement Correction for Long-Strip InSAR Measurements in Coastal Areas of France

Analysis of Ocean Tide Loading Displacement Correction for Long-Strip InSAR Measurements in Coastal Areas of France

Estimation of GPS-observed ocean tide loading displacements with an improved harmonic analysis in the northwest European shelf

Estimation of GPS-observed ocean tide loading displacements with an improved harmonic analysis in the northwest European shelf

Comparison of state-of-the-art GNSS-observed and predicted ocean tide loading displacements across Australia

We seek to quantify and understand the residual signal in GPS and GLONASS estimates of ocean tide loading displacements (OTLDs) after removing state-of-the-art model estimates. To consider contributions over a broad spatial scale, we estimate OTLD over the Australian continent using sim 5.5 years of continuous GPS and GLONASS data from 360 sites. We compare these with modelled estimates, with a focus on the lunar semidiurnal M_2 and diurnal O_1 constituents. We observe spatially coherent patterns of residual OTLD in each of the east, north, and up coordinate components after the removal of tidal loading using elastic models. We subsequently assess the impact of including anelastic dispersion in the model and show a 0.2 mm reduction in range of the up component residuals at coastal sites. A similar reduction at all sites is observed in the east and north components. Of the seven ocean tide models used, we find that three recent models, FES2014b, GOT4.10c and TPXO9.v1, perform similarly, noting these comparisons are made in the CE frame. However, we show that the latter contains centre of mass (CoM) biases in amplitude up to 0.2 mm and 0.5 mm for M_2 and O_1, respectively, due to the assimilated altimetry data having not been corrected for geocentre motion. We find OTLD estimates are sensitive to the chosen orbit and clock products used in our analysis, with differences of up to 0.5 mm in the east component between solutions using the JPL and either of ESA or CODE products (GPS-only). Our analysis shows that current GNSS estimates of OTLD over Australia are typically accurate to sim 0.2 mm at which point we are unable to explain spatially coherent residuals when compared to modelled quantities. These may depend on the appropriate treatment of the CoM variation, anelasticity and/or three-dimensional Earth structure. As such, we recommend great care is taken when interpreting OTLD at the level of 0.1 or 0.2 mm, even if it is regionally coherent.

A Novel Method to Improve the Estimation of Ocean Tide Loading Displacements for K1 and K2 Components with GPS Observations

The accurate estimation of ocean tide loading displacements is essential and necessary for geodesy, oceanic and geophysical studies. It is common knowledge that K1 and K2 tidal constituents estimated from Global Positioning System (GPS) observations are unsatisfactory because their tidal periods are nearly same to the revisit cycle or orbital period of GPS constellation. To date, this troublesome problem is not fully solved. In this paper, we revisit this important issue and develop a novel method based on the unique characteristic of tidal waves to separate GPS-system errors from astronomical K1/K2 tides. The well-known credo of smoothness indicates that tidal admittances of astronomical constituents in a narrow band can be expressed as smooth functions of tidal frequencies, while the interference of GPS-system errors seriously damages the smooth nature of observed tidal admittances. Via quadratic fitting, smooth functions of tidal frequencies for tidal admittances can be determined, thus, astronomical K1 and K2 tides can be interpolated using fitted quadratic functions. Three GPS stations are selected to demonstrate our method because of their typicality in terms of poor estimates of K1/K2 tidal parameters related to GPS-system errors. After removing GPS-systematical contributions based on our method, corrected K1/K2 tides at three GPS stations are much closer to the modeled K1/K2 tides from FES2014, which is one of the most accurate tide models. Furthermore, the proposed method can be easily applied to other areas to correct GPS-system errors because their smooth nature is valid for global tidal signals.

A combination constellation mode of kinematic PPP with priori constraints for determining ocean tide loading displacement

To improve the efficiency of estimation of deriving OTLD parameters with higher accuracy and take full advantage of multi-GNSS data, we investigate the potential of using global ocean tide model predictions as prior constraint for GLONASS and combined GPS+GLONASS kinematic precise point positioning (PPP), analyzing one year of GPS and GLONASS data from 20 Crustal Movement Observation Network China (CMONC) sites distributed along China coast. Seven global ocean tide models predictions are employed as prior constraint in kinematic PPP. Compared with the results of GPS-only kinematic PPP with priori information constraint, the result shows that GPS+GLONASS and GLONASS can improve the accuracy of OTLD estimates more than 40% in three components over GPS. The comparison of the effect of OTLD estimates on long-period signals in position time series shows that the correction effect of the kinematic PPP with seven different priori information constraint estimates is all as same as the reference model in three components.

Ocean tide loading correction for InSAR measurements: Comparison of different ocean tide models

With the rapid development of modern Interferometric Synthetic Aperture Radar (InSAR) missions, SAR instruments with wider coverage can be used to monitor the ground surface deformation from regional to global scale. However, the ocean tide loading (OTL) displacement is becoming a primary source of errors. It contributes to a long-wavelength signal in InSAR interferograms, leading to errors from millimeter to centimeter-level in InSAR deformation monitoring, especially over coastal areas. Although the state-of-the-art has applied ocean tide models to mitigate the errors, the difference between them and their impact on InSAR measurements are rarely discussed. In this paper, we compare representative ocean tide models and investigate their effects in the correction of OTL errors. We found that (i) the modeled OTL displacements from different models show little difference over interiors far from the ocean, while disagreement becomes larger over coastal areas; (ii) the magnitude of OTL artifacts may be greater than the atmospheric delays in some coastal areas, and the correction using ocean tide models can effectively attenuate the OTL effects for large-scale InSAR measurements; (iii) when correcting the OTL errors for InSAR measurements, the global model TPXO and FES are recommended because of their better overall performance, while the NAO model performs the worst. The local models with high spatial resolution can help improve the capability of coarse global models in complex topographic areas.

Estimation of the ocean tide loading displacements by GPS and GLONASS kinematic Precise Point Positioning

Ocean Tide Loading Displacement (OTLD) parameters, derived by Global Positioning System (GPS) approach, need more time to converge to a stable state and show poor precision of K1 and K2 constituents. Combining multi-system Global Navigation Satellite System (GNSS) data can greatly improve the positioning accuracy and significantly reduce the convergence time compared to single GPS PPP, combined GPS+GLONASS with ambiguity resolved in kinematic Precise Point Positioning (PPP) is improved on the basis of the algorithm of GPS kinematic PPP. We collected eight years of continuous observations of 11 worldwide sites from International GNSS Service to generate three dimensional OTLD parameters of eight constituents using GPS with ambiguity fixed, GLONASS with ambiguity free and combined GPS+GLONASS with ambiguity fixed kinematic PPP approach. The results show the eight constituents derived by GPS_FX and GPS+GLONASS_FX solution need four years and three years to converge to stable values, respectively. GLONASS can significantly improve the convergence rate of K1 and K2 constituents which needs only two years to converge to stable values, and S2 and P1 constituents which need three years to stable values. The results also show the GPS+GLONASS/reference misfits are the smallest for the most constituents in three components (less than 2mm) except for K2 and K1 in vertical and north directions. GLONASS can improve more than 40% in vertical and north components over GPS and GPS+GLONASS for K2 and K1 constituents and show very close agreement with GPS_FX solution in vertical and north component for S2 and P1 constituents. Ambiguity resolved in OTLD estimation can significantly accelerate the convergence and improve the accuracy for eight constituents, especially for combined GPS+GLONASS kinematic PPP mode, but no single constellation mode solution for all eight major constituents exists.

Improving estimates of ocean tide loading displacements with multi-GNSS: a case study of Hong Kong

Improving estimates of ocean tide loading displacements with multi-GNSS: a case study of Hong Kong

Comparison of GPS-derived ocean tide loading displacements with models in New Zealand

ABSTRACT We investigate the tidal displacement signals of two principle semidiurnal () and diurnal () tidal constituents in New Zealand. We calculate the predicted loading displacements using the latest ocean tide models and Earth models. The results show that, for the constituent, the tide models FES2014b and TPXO9-Atlas have subtle differences, and the vector differences between the Earth models shows that the regularity of the influence of the Earth model is weak. The vector difference of constituent have significant spatial coherence (about 0.2 mm). The residuals of constituent in the up component subtract about 0.2 mm across the entire areas after considering the anelastic dispersion. We find that the clear regional-scale spatial coherence of the residuals exists in both constituents in all models even if spatial water density and compressibility have been considered. However, the spatial coherence of residuals disappears when the network-mean value removed, and the reduction of RMS for constituent is close to the theoretical error of body tide (about 0.5 mm). We also find that for the different ocean tide models, part of the differences in residuals between the observations and predictions would be attributed to the choice of geocentric reference frame.

The sensitivity of ocean tide loading displacements to the structure of the upper mantle and crust of Taiwan Island

Ocean tide loading (OTL) displacements are sensitive to the shallow structure of the solid Earth; hence, the high-resolution spatial pattern of OTL displacement can provide knowledge to constrain the shallow Earth structure, especially in coastal areas. In this study, we investigate the sensitivity of the modeled M2 OTL displacement over Taiwan Island to perturbations of three physical quantities, namely, the density, bulk modulus, and shear modulus in the upper mantle and crust. Then, we compare the sensitivity of the modeled M2 OTL displacement to Earth models with the sensitivity to ocean tide models using root mean square (RMS) differences. We compute the displacement Green’s function and OTL displacement relative to the center of mass of the solid Earth (CE) reference frame, analyze the sensitivity to the three physical quantities in the CRUST1.0 model and the Preliminary Reference Earth Model (PREM), and present their spatial patterns. We find that displacement Green’s functions and OTL displacements are more sensitive to the two elastic moduli than the density in the upper mantle and crust. Moreover, their distinctive sensitivity patterns suggest that the three physical quantities might be constrained independently. The specific relationships between the perturbed structural depths and the distance ranges of peak sensitivities from the observation points to the coastline revealed by the shear modulus can mitigate the nonuniqueness problem in inversion. In particular, the horizontal tidal components observed by the Global Positioning System (GPS) can yield better results in inversions than the vertical component owing to the smaller OTL model errors and the higher structural sensitivity (except for the shear modulus in the asthenosphere).

Anelasticity and Lateral Heterogeneities in Earth's Upper Mantle: Impact on Surface Displacements, Self‐Attraction and Loading, and Ocean Tide Dynamics

AbstractSurface displacement and self‐attraction and loading (SAL) elevation induced by ocean tides are known to be affected by material properties of the solid Earth. Recent studies have shown that, in addition to elasticity, anelasticity considerably impacts surface displacements due to ocean tide loading (OTL). We employ consistent 3D seismic elastic and attenuation tomography models to construct 3D elastic and anelastic earth models, and derive corresponding averaged 1D elastic/anelastic models. We apply these models to systematically study the impact of anelasticity and lateral heterogeneity on M2 OTL displacements and SAL elevation. We find that neglecting lateral heterogeneities highly underestimates displacements and SAL elevation in mid‐ocean‐ridge regions and in some coastal areas of North and Central America. In comparison to PREM, 3D anelastic models can increase the predicted amplitudes of the vertical displacement and SAL elevation by up to 1.5 mm. The increased amplitudes reduce the discrepancy between GPS‐observed OTL displacements and their predictions based on PREM in places like Cornwall (England), Brittany (France), and the Ryukyu Islands (Japan). Applying our results to ocean tides, we discover that the impact on ocean tide dynamics exceeds the predicted SAL elevation correction with an RMS of about 1 mm, reaching an RMS of more than 5 mm in areas like North Atlantic or East Pacific. Due to the fact that such a value reaches the accuracy of modern data‐constrained tidal models, we regard the impact of anelastic shear relaxation as significant in tidal modeling.

Limitations in One‐Dimensional (an)Elastic Earth Models for Explaining GPS‐Observed M2 Ocean Tide Loading Displacements in New Zealand

AbstractGPS observations of ocean tide loading displacements can help infer the regional anelastic properties of the asthenosphere. We estimate M2 ocean tide loading displacements at 170 GPS sites in New Zealand and compare these to modeled values using a range of numerical tide and radially symmetric (1D) elastic and anelastic Earth models. Regardless of the model combination, we are unable to reduce the strong spatial coherence of the M2 residuals across the North Island where they reach 0.4 mm (2%). The best fit in the North Island is obtained when combining the FES2014b tide model with spatially variable ocean density and water compressibility, and the STW105 Earth model. The residuals exhibit a change of ∼0.3 mm in magnitude between the Taupo Volcanic Zone and the east coast (∼100 km), suggesting that this region's laterally varying, shallow rheological structure may need to be considered to explain these observations.

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.

Benefits of combining GPS and GLONASS for measuring ocean tide loading displacement

GPS has been used to estimate ocean tide loading (OTL) height displacement amplitudes to accuracies of within 0.5 mm at the M2 frequency, but such estimation has been problematic at luni-solar K2 and K1 frequencies because they coincide with the GPS orbital period and revisit period, leading to repeating multipath and satellite orbit errors. We therefore investigate the potential of using the GLONASS constellation (with orbital period 11.26 h and true site revisit period of 8 sidereal days distinct from K2 and K1) for OTL displacement estimation, analysing 3–7 years of GPS and GLONASS data from 49 globally distributed stations. Using the PANDA software in kinematic precise point positioning mode with float ambiguities, we demonstrate that GLONASS can estimate OTL height displacement at the M2, N2, O1 and Q1 lunar frequencies with similar accuracy to GPS: 95th percentile agreements of 0.6–1.3 mm between estimated and FES2014b ocean tide model displacements. At the K2 and K1 luni-solar frequencies, 95th percentile agreements between GPS estimates and model values of 3.9–4.4 mm improved to 2.0–2.8 mm using GLONASS-only solutions. A combined GPS+GLONASS float solution improves accuracy of the lunar OTL constituents and P1 (but not significantly for K1 or K2) compared with a single-constellation solution and results in hourly-to-weekly spectral noise very similar to a GPS ambiguity-fixed solution, but without needing uncalibrated phase delay information. GLONASS estimates are more accurate at higher compared with lower latitudes because of improved satellite visibility, although this can be countered by using a lower elevation cut-off angle.

Asthenospheric anelasticity effects on ocean tide loading around the East China Sea observed with GPS

Abstract. Anelasticity may decrease the shear modulus of the asthenosphere by 8 %–10 % at semidiurnal tidal periods compared with the reference 1 s period of seismological Earth models. We show that such anelastic effects are likely to be significant for ocean tide loading displacement at the M2 tidal period around the East China Sea. By comparison with tide gauge observations, we establish that from nine selected ocean tide models (DTU10, EOT11a, FES2014b, GOT4.10c, HAMTIDE11a, NAO99b, NAO99Jb, OSU12, and TPXO9-Atlas), the regional model NAO99Jb is the most accurate in this region and that related errors in the predicted M2 vertical ocean tide loading displacements will be 0.2–0.5 mm. In contrast, GPS observations on the Ryukyu Islands (Japan), with an uncertainty of 0.2–0.3 mm, show 90th-percentile discrepancies of 1.3 mm with respect to ocean tide loading displacements predicted using the purely elastic radial Preliminary Reference Earth Model (PREM). We show that the use of an anelastic PREM-based Earth model reduces these 90th-percentile discrepancies to 0.9 mm. Use of an anelastic radial Earth model consisting of a regional average of the laterally varying S362ANI model reduces the 90th-percentile to 0.7 mm, which is of the same order as the sum of the remaining errors due to uncertainties in the ocean tide model and the GPS observations.

M2 constituent of ocean tide loading displacements from VLBI CONT14 hourly sessions

Several studies prove that ocean tide loading (OTL) displacements can be observed with space geodetic techniques. In this study, the amplitudes and Greenwich phase lags for each coordinate component, i.e., radial, west, and south of the principal lunar semidiurnal tide, M 2 of OTL displacements were estimated at the very long baseline interferometry (VLBI) sites of the 15 days long continuous VLBI campaign, CONT14, carried out by the International VLBI Service for Geodesy and Astrometry (IVS). In the estimation of the amplitudes and Greenwich phase lags of the M 2 tidal constituent, hourly VLBI station coordinate time series were used as observations derived through analyzing 1 hour VLBI sessions of the CONT14 campaign. In the analysis of hourly sessions of the CONT14 campaign, to derive accurate hourly station coordinates, troposphere delays estimated from daily sessions were reduced from the observations a priori to the analysis. The estimated amplitudes and Greenwich phase lags of the M 2 constituent of OTL displacements were compared with the predictions the state-of-the-art ocean tide models, among others, FES2012 [Lyard et al., 2006; Carrere et al., 2012], FES2014 [Carrere et al., 2016], and TPXO8 [Egbert and Erofeeva, 2002; Egbert et al., 2010]. Both the amplitudes and the phases between CONT14 estimates and ocean tide models agree well for the M 2 tide at all the sites and in most of the coordinate components. The RMS misfits of the M 2 tide of OTL displacements in all coordinate components between CONT14 and ocean tide models over coastal sites are found about two times larger than those of inland sites. This result confirms the modeling insufficiencies in shallow waters of ocean tide models which cause an accuracy restriction of OTL displacement predictions around coastal regions.

Ocean Tide Loading Displacement Parameters Estimated From GNSS-Derived Coordinate Time Series Considering the Effect of Mass Loading in Hong Kong

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

Accurate Evaluation of Vertical Tidal Displacement Determined by GPS Kinematic Precise Point Positioning: A Case Study of Hong Kong.

Global Positioning System (GPS) kinematic precise point positioning (KPPP) is an effective approach for estimating the Earth’s tidal deformation. The accuracy of KPPP is usually evaluated by comparing results with tidal models. However, because of the uncertainties of the tidal models, the accuracy of KPPP-estimated tidal displacement is difficult to accurately determine. In this paper, systematic vector differences between GPS estimates and tidal models were estimated by least squares methods in complex domain to analyze the uncertainties of tidal models and determine the accuracy of KPPP-estimated tidal displacements. Through the use of GPS data for 12 GPS reference stations in Hong Kong from 2008 to 2017, vertical ocean tide loading displacements (after removing the body tide effect) for eight semidiurnal and diurnal tidal constituents were obtained by GPS KPPP. By an in-depth analysis of the systematic and residual differences between the GPS estimates and nine tidal models, we demonstrate that the uncertainty of the tidal displacement determined by GPS KPPP for the M2, N2, O1, and Q1 tidal constituents is 0.2 mm, and for the S2 constituent it is 0.5 mm, while the accuracy of the GPS-estimated K1, P1, and K2 tidal constituents is weak because these three tidal constituents are affected by significant common-mode errors. These results suggest that GPS KPPP can be used to precisely constrain the Earth’s vertical tidal displacement in the M2, N2, O1, and Q1 tidal frequencies.

Determination of Ocean Tide Loading Displacement by GPS PPP with Priori Information Constraint of NAO99b Global Ocean Tide Model

ABSTRACTThe published global ocean tide models show good agreement in deep oceans and exhibit differences in complex coastal areas, along with subsequent Ocean Tide Loading Displacement (OTLD) modeling differences. Meanwhile, OTLD parameters (amplitudes and phase lags) derived by Global Positioning System (GPS) Precise Point Positioning (PPP) approach need long time to converge to a stable state and show poor precision of S2, K1, and K2 constituents. Based on the fact that no constraint is imposed in the current kinematic solution, a new method is put forward, in which global ocean tide model predictions are taken as the priori information constraints to speed up the convergence rate and improve the accuracy of the GPS-derived OTLD parameters. First, the data of tide gauge from 01 January 2014 to 31 December 2016 are used to generate the harmonic parameters to evaluate the accuracy of six global ocean tide models and a regional ocean tide model (osu.chinesea.2010). Osu.chinesea.2010 model shows good agreement with the tide gauge results, while NAO99b model presents relatively large difference. The predictions from osu.chinesea.2010 and NAO99b model are employed as reference and the prior information, respectively. Second, continuous observations of 12 GPS sites during 2006–2013 in Hong Kong are collected to generate three dimensional OTLD amplitudes and phase lags of eight constituents using PPP with prior information constraints approach and harmonic analysis. Third, comparing the convergence time of eight constituents from PPP without and with priori information constraints approaches, the results show that the new method can significantly improve the convergence rate of OTLD amplitude estimates which obtain a certain level of stability seven years earlier than that derived by the PPP without priori information constraints. Precision of OTLD parameters derived by the new method is about 1 mm. By comparing with the precision of single PPP approach, the accuracy of eight constituents has been improved, especially for S2, K1, and K2 constituents. Finally, through comparing the different correction effects of OTLD estimates on the coordinates and their time series of the ground GPS stations, the results show that OTLD estimates derived by the new approach have similar influence as the osu.chinasea.2010 ocean tide model. The new method provides an effective means to improve the convergence and precision of the GPS-derived OTLD parameters, and achieve a similar correction as the high precision ocean tide model.

Analysis of ocean tide loading displacements by GPS kinematic precise point positioning: a case study at the China coastal site SHAO

Ocean tide loading (OTL) displacement amplitudes and phase lags of SHAO site are estimated by global positioning system (GPS), kinematic precise point positioning (PPP) and spectral analysis using 19 years of continuous GPS observations. In kinematic PPP, the 66 additional harmonic displacement parameters are replaced by the three time-varying displacement parameters without a priori modelled OTL displacements. By comparing the results with predictions from hybrid regional/global models, we are able to demonstrate that GPS/model agreements are at the level of 0.2 mm (horizontal) and 0.6 mm (vertical) for the four lunar constituents, 0.4 mm (horizontal) and 1.35 mm (vertical) for the four solar/sidereal constituents, and 0.2 mm (horizontal) and 0.3 mm (vertical) for the three long-period constituents. Finally, we conclude that GPS-derived lunar constituents can substitute for the model corrections in GPS data processing and the accuracy of GPS-derived solar/sidereal constituents needs to be improved by further studies.