Motivated by the wide applications of empirical global ocean tide models in Earth science,particularly in shallow waters and coastal regions,we proposed an updated global ocean tide model representing all major diurna...Motivated by the wide applications of empirical global ocean tide models in Earth science,particularly in shallow waters and coastal regions,we proposed an updated global ocean tide model representing all major diurnal and semidiurnal tidal constituents.We integrated the development technique of the Technical University of Denmark(DTU10)model and calculated the residual tides using the intermediary FES2012 model.We utilized all available Topex/Poseidon,Jason-1,Ocean Surface Topography Mission(OSTM)/Jason-2 primary and tandem missions to develop the new model.To reduce the discrepancies between the model and in situ measurements estimated S2 tide constituent,the ERA-Interim model was selected for dry tropospheric correction of altimetry data.The newly developed model with an improved spatial resolution from 1/8°×1/8°to 1/16°×1/16°was assessed and compared against contemporary global ocean tide models using in situ measurements in coastal regions,continental shelf waters,marginal seas,and deep waters.The results demonstrate improvements in shallow waters and coastal regions,particularly in representative coastal re-gions such as the Northwest European Shelf and East Asian Marginal Seas.Moreover,the model performs well in simulating S_(2) and K_(2) tides with root mean square differences of 0.355 and 0.234 cm,respectively,against in situ measurements in deep waters world-wide.Compared with that of DTU10,the root sum square of the new model for the eight main tidal constituents decrease by 8.4%to 0.997 cm.展开更多
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.Howe...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.展开更多
This paper describes the ocean loading tides corrections of GPS stations in Antarctica, such as the Great Wall station and Zhongshan station. Based on the theory of ocean loading tides, the displacement corrections of...This paper describes the ocean loading tides corrections of GPS stations in Antarctica, such as the Great Wall station and Zhongshan station. Based on the theory of ocean loading tides, the displacement corrections of ocean loading tides on GPS stations in Antarctica are calculated by using the CRS4.0 ocean loading tides model. These corrections are also applied to GPS data proc-essing. The GPS data are analyzed by the GAMIT software with and without these corrections. We compared and analyzed the GPS baseline components to get the differences. The results show that the ocean tidal displacement corrections have obvious effects upon GPS baseline components. Therefore, we should not ignore the ocean loading tides corrections of GPS stations in Antarctica to obtain precise and reliable results.展开更多
Global Positioning System （GPS） has been widely used to estimate the total zenith tropo- spheric delay （ZTD） and precipitable water vapour （PWV） for weather prediction and at- mospheric research as a continuous ...Global Positioning System （GPS） has been widely used to estimate the total zenith tropo- spheric delay （ZTD） and precipitable water vapour （PWV） for weather prediction and at- mospheric research as a continuous and all-weather technique. However, estimations of ZTD and PWV are subject to effects of geophysical models with large uncertainties, particularly imprecise ocean tide models of inland seas in Turkey. In this paper, GPS data from Jan. 1, 2010 to Dec. 31, 2011 are processed using GAMIT/GLOBK at four co-located GPS stations （ISTN, ERZR, SAMN, and IZMI） with Radiosonde from the Turkish Met-Office together with several nearby IGS stations. Four widely used ocean tide models are adopted to evaluate their effects on GPS-estimated PWV, such as IERS recommended FES2004, NAO99b, CSR4.0 and GOT00. Five different strategies are taken without ocean tide model and with four ocean tide models, respectively, which are used to evaluate ocean tide models effects on GPS-estimated PWV through comparing with co-located Radiosonde. Results showed that ocean tide models have greatly affected the estimation of the pre- cipitable water vapour at stations near coasts. The ocean tide model FES2004 gave the best results when compared to Radiosonde with ＋2.12 mm in PWV at stations near coastline. While other ocean tides models agree each other at millimeter level in PWV. However, at inland GPS stations, ocean tide models have less effect on GPS-estimated PWV.展开更多
By using 11 global ocean tide models and tidal gauge data obtained in the East China Sea and South China Sea, the influence of the ocean loading on gravity field in China and its neighbor area is calculated in this pa...By using 11 global ocean tide models and tidal gauge data obtained in the East China Sea and South China Sea, the influence of the ocean loading on gravity field in China and its neighbor area is calculated in this paper. Furthermore, the differences between the results from original global models and modified models with local tides are discussed based on above calculation. The comparison shows that the differences at the position near the sea are so large that the local tides must be taken into account in the calculation. When the global ocean tide models of CSR4.0, FES02, GOT00, NAO99 and ORI96 are chosen, the local effect for M2 is less than 0.10 × 10-8 m·s-2 over the area far away from sea. And the local effect for O1 is less than 0.05 × 10-8 m·s-2 over that area when choosing AG95 or CSR3.0 models. This numerical result demonstrates that the choice of model is a complex problem because of the inconsistent accuracy of the models over the areas of East and South China Seas.展开更多
The HY-2A satellite,which is equipped with a radar altimeter and was launched on August 16,2011,is the first Chinese marine dynamic environmental monitoring satellite.Extracting ocean tides is one of the important app...The HY-2A satellite,which is equipped with a radar altimeter and was launched on August 16,2011,is the first Chinese marine dynamic environmental monitoring satellite.Extracting ocean tides is one of the important applications of the radar altimeter data.The radar altimeter data of the HY-2A satellite from November 1,2011 to August 16,2014 are used herein to extract global ocean tides.The constants representing the tidal constituents are extracted by HY-2A RA data with harmonic analysis based on the least squares method.Considering tide aliasing issues,the analysis of the alias periods and alias synodic periods of different tidal constituents shows that only the tidal constituents M_(2),N_(2),and K_(2)are retrieved precisely by the HY-2A RA data.The derived tidal constants of the tidal constituents M_(2),N_(2)and K_(2)are compared to those of tidal gauge data and the TPXO tide model results.The comparison between the derived results and the tidal gauge data shows that the RMSEs of the tidal amplitude and phase lag are 9.6 cm and 13.34°,2.4 cm and 10.47°,and 8.1 cm and 14.19°for tidal constituents M_(2),N_(2),and K_(2),respectively.The comparisons of the semidiurnal tides with the TPXO model results show that tidal constituents have good consistency with the TPXO model results.These findings confirm the good performance of HY-2A RA for retrieving semidiurnal tides in the global ocean.展开更多
Previous studies show that the calculated loading effects from global ocean tide models do not match actual measurements of gravity attraction and loading effects in Southeast Asia.In this paper,taking advantage of a ...Previous studies show that the calculated loading effects from global ocean tide models do not match actual measurements of gravity attraction and loading effects in Southeast Asia.In this paper,taking advantage of a unique network of gravity tidal stations all over the Chinese mainland,we compare the observed and modeled tidal loading effects on the basis of the most recent global ocean tide models.The results show that the average efficiencies of the ocean tidal loading correction for O_(1),K_(1),M_(2) are 77%,7 s3%and 59%,respectively.The loading correction efficiencies using recent ocean tidal models are better than the 40 years old Schwiderskis model at coastal stations,but relative worse at stations far from ocean.展开更多
Ocean semi-diurnal tides are suggested qualitatively to be more accurately explained by the vertical tide generating forces of the sun and moon, not by the historically standard horizontal components. It is proposed t...Ocean semi-diurnal tides are suggested qualitatively to be more accurately explained by the vertical tide generating forces of the sun and moon, not by the historically standard horizontal components. It is proposed that the sea level elevations created sequentially at the eastern and then western ocean coastal boundaries propagate seaward as shallow water sur</span><span style="font-family:Verdana;font-size:12px;">face gravity waves and interact without mutual disturbance. In that manner two tides per day</span><span style="font-family:Verdana;font-size:12px;"> are created. Horizontal tide forces generate horizontal ocean currents with speeds of 5 mph at the most. Shallow water tide waves move at about 500 mph in open waters and therefore come much closer to being in tune with the sun and moon transiting across the sky.展开更多
The movement of global ocean circulation in the Earth’s main magnetic field generates a measurable induced magnetic field(about 2 nT at geomagnetic satellite altitudes).However,this ocean circulation-induced magnetic...The movement of global ocean circulation in the Earth’s main magnetic field generates a measurable induced magnetic field(about 2 nT at geomagnetic satellite altitudes).However,this ocean circulation-induced magnetic field has not been previously estimated or incorporated into geomagnetic field models,potentially causing leakage into the core field model.Here,we present a method to account for the circulation-induced magnetic field during geomagnetic field modeling.First,a forward model of the circulation-induced magnetic field is constructed by numerically solving electromagnetic induction equations based on a realistic ocean circulation model.Then,this forward model is subtracted from the observed data.Finally,the core and lithospheric fields,magnetospheric and Earth’s mantle-induced fields,and the ocean tide-induced magnetic field are co-estimated.Applying our method to over 20 years of MSS-1,Swarm,CryoSat-2,and CHAMP satellite magnetic data,we derive a new multisource geomagnetic field model(MGFM).We find that incorporating a forward model of the circulation-induced magnetic field marginally improves the fit to the data.Furthermore,we demonstrate that neglecting the circulation-induced magnetic field in geomagnetic field modeling results in leakage into the core field model.The highlights of the MGFM model include:(i)a good agreement with the widely used CHAOS model series;(ii)the incorporation of magnetic fields induced by both ocean tides and circulation;and(iii)the suppression of leakage of the circulation-induced magnetic field into the core field model.展开更多
Based on the tide gravity observations recorded with LCR-ET20 spring gravimeter at Wuhan international fundamental tidal gravity station, the characteristics of ET20 and atmospheric and oceanic gravity signals are stu...Based on the tide gravity observations recorded with LCR-ET20 spring gravimeter at Wuhan international fundamental tidal gravity station, the characteristics of ET20 and atmospheric and oceanic gravity signals are studied systematically by using international standard data pre-processing and analysis methods and by comparing the results with those obtained by superconducting gravimeter (SG) at the same station. The numerical results indicate that the identical tidal gravity parameters are the same as those with the SG, the instrument can be effectively used to record temporal change of the gravity field, though the ET20 accuracy is one order lower than that of the SG, and has the large drift induced by the spring creep character.展开更多
The global distributions of eight principal tidal constituents, M2, S2, K1, O1, N2, K2, P1, and Q1, are derived using TOPEX/Poseidon and JASON-1（T/P-J） satellite altimeter data for 16 a. The intercomparison of the d...The global distributions of eight principal tidal constituents, M2, S2, K1, O1, N2, K2, P1, and Q1, are derived using TOPEX/Poseidon and JASON-1（T/P-J） satellite altimeter data for 16 a. The intercomparison of the derived harmonics at 7000 subsatellite track crossover points shows that the root mean square （RMS） values of the tidal height differences of the above eight constituents range from 1.19 cm to 2.67 cm, with an average of about 2 cm. The RMS values of the tidal height differences between T/P-J solutions and the harmonics from ground measurements at 152 tidal gauge stations for the above constituents range from 0.34 cm to 1.08 cm, and the relative deviations range from 0.031 to 0.211. The root sum square of the RMS differences of these eight constituents is 2.12 cm, showing the improvement of the present model over the existing global ocean tidal models. Based on the obtained tidal model the global ocean tidal energetics is studied and the global distribution of the tidal power input density by tide-generating force of each constituent is calculated, showing that the power input source regions of semidiurnal tides are mainly concentrated in the tropical belt between 30S and 30N, while the power input source regions of diurnal tides are mainly concentrated off the tropic oceans. The global energy dissipation rates of the M2, S2, K1, O1, N2, P1, K2 and Q1 tides are 2.424, 0.401, 0.334, 0.160, 0.113, 0.035, 0.030 and 0.006 TW, respectively. The total global tidal dissipation rate of these eight constituents amounts to 3.5 TW.展开更多
The Earth’s Free Core Nutation(FCN) causes Earth tides and forced nutation with frequencies close to the FCN that exhibit resonance effects.High-precision superconducting gravimeter(SG) and very long baseline interfe...The Earth’s Free Core Nutation(FCN) causes Earth tides and forced nutation with frequencies close to the FCN that exhibit resonance effects.High-precision superconducting gravimeter(SG) and very long baseline interferometry(VLBI) provide good observation techniques for detecting the FCN parameters.However,some choices in data processing and solution procedures increase the uncertainty of the FCN parameters.In this study,we analyzed the differences and the effectiveness of weight function and ocean tide corrections in the FCN parameter detection using synthetic data,SG data from thirty-one stations,and the 10 celestial pole offset(CPO) series.The results show that significant discrepancies are caused by different computing options for a single SG station.The stacking method,which results in a variation of0.24-5 sidereal days(SDs) in the FCN period(T) and 10^(3)-10^(4) in the quality factor(Q) due to the selection of the weighting function and the ocean tide model(OTM),can effectively suppress this influence.The statistical analysis results of synthetic data shows that although different weight choices,while adjusting the proportion of diurnal tidal waves involved,do not significantly improve the accuracy of fitted FCN parameters from gravity observations.The study evaluated a series of OTMs using the loading correction efficiency.The fitting of FCN parameters can be improved by selecting the mean of appropriate OTMs based on the evaluation results.Through the estimation of the FCN parameters based on the forced nutation,it was found that the weight function P_(1) is more suitable than others,and different CPO series(after 2009) resulted in a difference of 0.4 SDs in the T and of 103 in the Q.We estimated the FCN parameters for SG(T=430.4±1.5 SDs and Q=1.52×10^(4)±2.5×10^(3)) and for VLBI(T=429.8±0.7 SDs,Q=1.88×10^(4)±2.1×10^(3)).展开更多
This research aims to optimize the utilization of long-term sea level data from the TOPEX/Poseidon,Jason1,Jason2,and Jason3 altimetry missions for tidal modeling.We generate a time series of along-track observations a...This research aims to optimize the utilization of long-term sea level data from the TOPEX/Poseidon,Jason1,Jason2,and Jason3 altimetry missions for tidal modeling.We generate a time series of along-track observations and apply a developed method to produce tidal models with specific tidal constituents for each location.Our tidal modeling methodology follows an iterative process:partitioning sea surface height(SSH)observations into analysis/training and prediction/validation parts and ultimately identi-fying the set of tidal constituents that provide the best predictions at each time series location.The study focuses on developing 1256 time series along the altimetry tracks over the Baltic Sea,each with its own set of tidal constituents.Verification of the developed tidal models against the sSH observations within the prediction/validation part reveals mean absolute error(MAE)values ranging from 0.0334 m to 0.1349 m,with an average MAE of 0.089 m.The same validation process is conducted on the FES2014 and EOT20 global tidal models,demonstrating that our tidal model,referred to as BT23(short for Baltic Tide 2023),outperforms both models with an average MAE improvement of 0.0417 m and 0.0346 m,respectively.In addition to providing details on the development of the time series and the tidal modeling procedure,we offer the 1256 along-track time series and their associated tidal models as supplementary materials.We encourage the satellite altimetry community to utilize these resources for further research and applications.展开更多
The synthetic tidal parameters with high spatial resolution for gravity over China and its neighbor area are constructed with Earth＇s tidal model and ocean tide loading calculated using TPXO7 global ocean tide model ...The synthetic tidal parameters with high spatial resolution for gravity over China and its neighbor area are constructed with Earth＇s tidal model and ocean tide loading calculated using TPXO7 global ocean tide model as well as tidal data over China seas. The comparison between synthetic parameters and ones observed by spring gravimeters at some seismic network stations and Hong Kong station and one observed by super-conducting gravimeter at Wuhan station shows that the average differences in amplitude factors and phases are smaller than 0.005 and 0.5° respectively; and that the discrepancies between observational and synthetic parameters are dependent on gravimetric technique in that the synthetic parameters are in well agreement with the superconducting gravimetric observations. This also indicates that the synthetic result is a good estimation for tidal gravity, and the numerical results in the present paper not only can provide ground and space gravimetry such as absolute gravimetry with correction model of tidal gravity, but also provide effective tidal parameters over areas where no observation is carried out.展开更多
To assist the analysis of tsunami hazards for Qatar coastal areas were using numerical model. By Tsunamis waves created from submarine earthquakes of magnitude of (M<sub>w</sub>) 8.6 and 9.0 in Richard sca...To assist the analysis of tsunami hazards for Qatar coastal areas were using numerical model. By Tsunamis waves created from submarine earthquakes of magnitude of (M<sub>w</sub>) 8.6 and 9.0 in Richard scale along the Makran Subduction Zone (MSZ) as well as coastal landslides with soil volume of 1.25 to 2.0 km<sup>3</sup> along Iranian coast inside the Arabian Gulf is considered. TUNAMI-N2KISR model (Al-Salem) was applied in this study to predict the tsunami propagation and magnitude of Tsunami induced wave heights. The model adopts to solve shallow water equations describing nonlinear long-wave theory. The model also incorporate tidal effect inside the Arabian Gulf as a tsunami travel time from Makran Subduction to Qatar coastline takes more than 9 hours with the tidal range of about 1.6 m during Spring Tide event. For coastal landslides, tsunami generation was simulated using a two-layer numerical model, developed by solving nonlinear long-wave equations. Two-layer model was used to determine initial wave deformation generated by a landslide case. Then TUNAMI-N2KISR was use to simulate tsunami wave propagation. Tsunami waves from landslide scenario arrived after 2.5 - 3 hr with maximum tsunami amplitudes along coasts of Ras laffan-Qatar were 0.8 to 1.0 m. Incorporation of ocean tide is found to impose some small effect on tsunami amplitude at Qatar coastline and nearby areas for the Mw 9.0 earthquake due to small tidal range in this area. In addition, it is found that the tsunami arrival time has become shorter.展开更多
The loading tides are calculated by means of the Green's function method based on a high-resolution regional ocean tide model, the TOPO7.0 global ocean tide model, and the Gutenberg-Bullen A Earth model. The resul...The loading tides are calculated by means of the Green's function method based on a high-resolution regional ocean tide model, the TOPO7.0 global ocean tide model, and the Gutenberg-Bullen A Earth model. The results show that the maximal amplitude of M2 vertical displacement loading (VDL) tide in the Bohai, Yellow, and East China Seas exceeding 28mm appears 150km off the Zhejiang coast; the second maximum exceeding 20mm appears in Inchon Bay; and the third maximum exceeding 14mm is located in the northeast of the North Yellow Sea. The maximal amplitudes of S2 VDL tide at the above three locations exceed 10, 8, and 4mm, respectively. The maximal amplitudes of the K1 and O1 VDL tides, exceeding 13 and 10 mm respectively, appear near the central and north Ryukyu Islands; the amplitudes tend to decease toward the inward areas. The phases of semidiurnal VDL tides are basically opposite to those of corresponding ocean tides. The phases of diurnal VDL tides are basically opposite to those of corresponding ocean tides in the most part of the East China Sea and the eastern part of the South Yellow Sea. This anti-phase relationship generally does not hold in the rest parts of the Bohai and Yellow Seas. The distribution patterns of self-attraction and loading (SAL) tides are very similar to those of VDL tides. The SAL tides have amplitudes about 1.2-1.7 times of the corresponding VDL tides and their phases are basically opposite to the corresponding VDL tides. The maximal amplitude of M2 SAL tide also appears off the Zhejiang coast, with a magnitude exceeding 42mm.展开更多
Currently,aliasing error of temporal signal model becomes the main factor constraining the accuracy of temporal gravity field.In provision of three types of satellite formations,i.e.,GRACE-type,Pendulum-type and n-s-C...Currently,aliasing error of temporal signal model becomes the main factor constraining the accuracy of temporal gravity field.In provision of three types of satellite formations,i.e.,GRACE-type,Pendulum-type and n-s-Cartwheel-type,which are suitable for gravity mission and composed of observation in different directions,here we design two cases and conduct a simulation experiment on the feasibility to apply satellite formations for eliminating the influence from the aliasing error of ocean tide models.The result of our experiment shows that,when the aliasing error is disregarded,n-s-Cartwheel formation can provide the best conditions for gravity field determination,which,compared with GRACE-type,can improve the accuracy by 43%.When aliasing error of the ocean tide model acts as the main source of error,the satellite formation applied in dynamic method for gravity field inversion cannot eliminate aliasing or improve the accuracy of gravity field.And due to its higher sensitivity to the high-degree variation of gravity field,the Cartwheel-type formation,which includes the radial observation,can result in the gravity field containing more high-frequency signals for the ocean tide model error,and lead to a dramatically larger error.展开更多
Ground-based magnetic observatories and geomagnetic satellites can observe the induced magnetic field generated by the motion of seawater containing sodium and chlorine ions.Calculating the three-dimensional(3-D)spati...Ground-based magnetic observatories and geomagnetic satellites can observe the induced magnetic field generated by the motion of seawater containing sodium and chlorine ions.Calculating the three-dimensional(3-D)spatial distribution of tide-induced magnetic fields(TIMF)is crucial for inverting the electrical conductivity structure of the oceanic lithosphere.It also serves as an essential basis for designing optimal geomagnetic observatories and satellite orbits.However,existing methods for simulating TIMF suffer from limitations in inaccurately modeling realistic coastlines,heterogeneous land and sea surface properties,and complex deep Earth structures,thereby the interpretational level of TIMF data is reduced.To overcome this issue,we developed a tetrahedral-based finite element method for simulating TIMF,which can efficiently approximate realistic coastlines,heterogeneous land and sea surface properties,and complex deep Earth structures.Firstly,we derived the boundary value problem for the seawater motion-induced electromagnetic field,which was solved using the vector finite element method based on tetrahedral elements.Secondly,using the latest ocean depth and seafloor sediment layer models,we constructed a 3-D conductivity model of the Earth,which includes realistic coastlines,heterogeneous land and sea conductivity distributions.We then computed the TIMF using the M_(2)tidal source as an example and validated our method by comparing it with results obtained from spherical harmonic finite element and integral equation methods.Finally,utilizing the computed high-precision M_(2),N_(2),and O1 TIMF signals,we marked global observatories capable of observing strong M_(2),N_(2),and O1 TIMF signals and predicted alternative stations suitable for tide signal observations.Additionally,we calculated TIMF at heights of 450 and 200 km for the Macao Science Satellite 1 and its subsequent satellites.The results indicate that the amplitude of the tidal-induced magnetic field at 200 km is approximately twice that at 450 km.The maximum amplitudes of M_(2),N_(2),and O1 TIMF at 200 km are eight,two,and three times the measurement accuracy of the magnetic sensing payload(0.5 nT),respectively.The 200 km orbit has great potential for detecting high-resolution electrical structures of the seafloor lithosphere and asthenosphere in regions such as New Zealand,southern Iceland,the southern Indian Ocean,the Ross Sea region of Antarctica,and the Sea of Okhotsk.It also holds the potential for studying large-scale oceanic dynamic processes and properties.展开更多
Ocean tide loading(OTL)displacements of eight principal constituents at 12 sites in Hong Kong were determined using more than eight years of continuous GPS observations.Parameters of the OTL displacements were estimat...Ocean tide loading(OTL)displacements of eight principal constituents at 12 sites in Hong Kong were determined using more than eight years of continuous GPS observations.Parameters of the OTL displacements were estimated using daily GPS solutions obtained with precise point positioning(PPP)technique.The results were compared with predictions from seven latest global ocean tide models.Gravity measurements of OTL in Hong Kong were also used to validate the GPS results.The study shows that the results from both the GPS and gravity measurements agree best with the GOT4.7 and NAO99b models,when the K1 and K2 constituents are excluded.The agreements between the GPS and the model estimates are generally at sub-millimeter level in both the horizontal and vertical directions,except for S2,K2 and K1 constituents that have relatively larger errors.After removing the systematic biases between the GPS and the model estimates,the misfits of M2,S2,N2,O1,P1 and Q1 at all sites are within 0.5 and 1.0 mm in the horizontal and the vertical directions,respectively,whereas K1 and K2 show relatively larger misfits of up to 2.3 mm.Both the GPS and the gravity S2 estimates have large biases with unknown reasons when compared with the modeled values,which needs to be further investigated.The study demonstrates that GPS is capable of estimating the OTL displacements with the same accuracy as the model predictions,especially for coastal areas.展开更多
基金supported by the open funding of the Technology Innovation Center for South China Sea Re-mote Sensing,Surveying and Mapping Collaborative Ap-plication,Ministry of Natural Resources,P.R.China(No.RSSMCA-2024-B001)the National Natural Science Foundation of China(Nos.T2261149752 and 42476172).
文摘Motivated by the wide applications of empirical global ocean tide models in Earth science,particularly in shallow waters and coastal regions,we proposed an updated global ocean tide model representing all major diurnal and semidiurnal tidal constituents.We integrated the development technique of the Technical University of Denmark(DTU10)model and calculated the residual tides using the intermediary FES2012 model.We utilized all available Topex/Poseidon,Jason-1,Ocean Surface Topography Mission(OSTM)/Jason-2 primary and tandem missions to develop the new model.To reduce the discrepancies between the model and in situ measurements estimated S2 tide constituent,the ERA-Interim model was selected for dry tropospheric correction of altimetry data.The newly developed model with an improved spatial resolution from 1/8°×1/8°to 1/16°×1/16°was assessed and compared against contemporary global ocean tide models using in situ measurements in coastal regions,continental shelf waters,marginal seas,and deep waters.The results demonstrate improvements in shallow waters and coastal regions,particularly in representative coastal re-gions such as the Northwest European Shelf and East Asian Marginal Seas.Moreover,the model performs well in simulating S_(2) and K_(2) tides with root mean square differences of 0.355 and 0.234 cm,respectively,against in situ measurements in deep waters world-wide.Compared with that of DTU10,the root sum square of the new model for the eight main tidal constituents decrease by 8.4%to 0.997 cm.
基金This work was supported by the Natural Science Foundation of China(grant Nos.42074008,41804005,42174018).
文摘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.
基金the National 863 Program of China (No.2007AA12Z312)
文摘This paper describes the ocean loading tides corrections of GPS stations in Antarctica, such as the Great Wall station and Zhongshan station. Based on the theory of ocean loading tides, the displacement corrections of ocean loading tides on GPS stations in Antarctica are calculated by using the CRS4.0 ocean loading tides model. These corrections are also applied to GPS data proc-essing. The GPS data are analyzed by the GAMIT software with and without these corrections. We compared and analyzed the GPS baseline components to get the differences. The results show that the ocean tidal displacement corrections have obvious effects upon GPS baseline components. Therefore, we should not ignore the ocean loading tides corrections of GPS stations in Antarctica to obtain precise and reliable results.
文摘Global Positioning System （GPS） has been widely used to estimate the total zenith tropo- spheric delay （ZTD） and precipitable water vapour （PWV） for weather prediction and at- mospheric research as a continuous and all-weather technique. However, estimations of ZTD and PWV are subject to effects of geophysical models with large uncertainties, particularly imprecise ocean tide models of inland seas in Turkey. In this paper, GPS data from Jan. 1, 2010 to Dec. 31, 2011 are processed using GAMIT/GLOBK at four co-located GPS stations （ISTN, ERZR, SAMN, and IZMI） with Radiosonde from the Turkish Met-Office together with several nearby IGS stations. Four widely used ocean tide models are adopted to evaluate their effects on GPS-estimated PWV, such as IERS recommended FES2004, NAO99b, CSR4.0 and GOT00. Five different strategies are taken without ocean tide model and with four ocean tide models, respectively, which are used to evaluate ocean tide models effects on GPS-estimated PWV through comparing with co-located Radiosonde. Results showed that ocean tide models have greatly affected the estimation of the pre- cipitable water vapour at stations near coasts. The ocean tide model FES2004 gave the best results when compared to Radiosonde with ＋2.12 mm in PWV at stations near coastline. While other ocean tides models agree each other at millimeter level in PWV. However, at inland GPS stations, ocean tide models have less effect on GPS-estimated PWV.
基金The Key Knowledge Innovation Project (KZCX3-SW-131), the Hundred Talents Program of Chinese Academy of Sciences and the National Natural Science Foundation of China (40374029)
文摘By using 11 global ocean tide models and tidal gauge data obtained in the East China Sea and South China Sea, the influence of the ocean loading on gravity field in China and its neighbor area is calculated in this paper. Furthermore, the differences between the results from original global models and modified models with local tides are discussed based on above calculation. The comparison shows that the differences at the position near the sea are so large that the local tides must be taken into account in the calculation. When the global ocean tide models of CSR4.0, FES02, GOT00, NAO99 and ORI96 are chosen, the local effect for M2 is less than 0.10 × 10-8 m·s-2 over the area far away from sea. And the local effect for O1 is less than 0.05 × 10-8 m·s-2 over that area when choosing AG95 or CSR3.0 models. This numerical result demonstrates that the choice of model is a complex problem because of the inconsistent accuracy of the models over the areas of East and South China Seas.
基金The National Key Research and Development Program of China under contract No.2016YFC1401801.
文摘The HY-2A satellite,which is equipped with a radar altimeter and was launched on August 16,2011,is the first Chinese marine dynamic environmental monitoring satellite.Extracting ocean tides is one of the important applications of the radar altimeter data.The radar altimeter data of the HY-2A satellite from November 1,2011 to August 16,2014 are used herein to extract global ocean tides.The constants representing the tidal constituents are extracted by HY-2A RA data with harmonic analysis based on the least squares method.Considering tide aliasing issues,the analysis of the alias periods and alias synodic periods of different tidal constituents shows that only the tidal constituents M_(2),N_(2),and K_(2)are retrieved precisely by the HY-2A RA data.The derived tidal constants of the tidal constituents M_(2),N_(2)and K_(2)are compared to those of tidal gauge data and the TPXO tide model results.The comparison between the derived results and the tidal gauge data shows that the RMSEs of the tidal amplitude and phase lag are 9.6 cm and 13.34°,2.4 cm and 10.47°,and 8.1 cm and 14.19°for tidal constituents M_(2),N_(2),and K_(2),respectively.The comparisons of the semidiurnal tides with the TPXO model results show that tidal constituents have good consistency with the TPXO model results.These findings confirm the good performance of HY-2A RA for retrieving semidiurnal tides in the global ocean.
基金funded by The National Natural Science Foundation of China(No.41774015,41704135 and U1939204)National Key Research and Development Project of China(No.2018YFE0206100,2017YFC1500204)。
文摘Previous studies show that the calculated loading effects from global ocean tide models do not match actual measurements of gravity attraction and loading effects in Southeast Asia.In this paper,taking advantage of a unique network of gravity tidal stations all over the Chinese mainland,we compare the observed and modeled tidal loading effects on the basis of the most recent global ocean tide models.The results show that the average efficiencies of the ocean tidal loading correction for O_(1),K_(1),M_(2) are 77%,7 s3%and 59%,respectively.The loading correction efficiencies using recent ocean tidal models are better than the 40 years old Schwiderskis model at coastal stations,but relative worse at stations far from ocean.
文摘Ocean semi-diurnal tides are suggested qualitatively to be more accurately explained by the vertical tide generating forces of the sun and moon, not by the historically standard horizontal components. It is proposed that the sea level elevations created sequentially at the eastern and then western ocean coastal boundaries propagate seaward as shallow water sur</span><span style="font-family:Verdana;font-size:12px;">face gravity waves and interact without mutual disturbance. In that manner two tides per day</span><span style="font-family:Verdana;font-size:12px;"> are created. Horizontal tide forces generate horizontal ocean currents with speeds of 5 mph at the most. Shallow water tide waves move at about 500 mph in open waters and therefore come much closer to being in tune with the sun and moon transiting across the sky.
基金supported by the National Natural Science Foundation of China(42250101,42250102)the Macao Foundation.
文摘The movement of global ocean circulation in the Earth’s main magnetic field generates a measurable induced magnetic field(about 2 nT at geomagnetic satellite altitudes).However,this ocean circulation-induced magnetic field has not been previously estimated or incorporated into geomagnetic field models,potentially causing leakage into the core field model.Here,we present a method to account for the circulation-induced magnetic field during geomagnetic field modeling.First,a forward model of the circulation-induced magnetic field is constructed by numerically solving electromagnetic induction equations based on a realistic ocean circulation model.Then,this forward model is subtracted from the observed data.Finally,the core and lithospheric fields,magnetospheric and Earth’s mantle-induced fields,and the ocean tide-induced magnetic field are co-estimated.Applying our method to over 20 years of MSS-1,Swarm,CryoSat-2,and CHAMP satellite magnetic data,we derive a new multisource geomagnetic field model(MGFM).We find that incorporating a forward model of the circulation-induced magnetic field marginally improves the fit to the data.Furthermore,we demonstrate that neglecting the circulation-induced magnetic field in geomagnetic field modeling results in leakage into the core field model.The highlights of the MGFM model include:(i)a good agreement with the widely used CHAOS model series;(ii)the incorporation of magnetic fields induced by both ocean tides and circulation;and(iii)the suppression of leakage of the circulation-induced magnetic field into the core field model.
基金National Outstanding Youth Foundation of China (49925411) the Knowledge Innovation Foundation,Chinese Academy of Sciences (KZCX2-SW-131).
文摘Based on the tide gravity observations recorded with LCR-ET20 spring gravimeter at Wuhan international fundamental tidal gravity station, the characteristics of ET20 and atmospheric and oceanic gravity signals are studied systematically by using international standard data pre-processing and analysis methods and by comparing the results with those obtained by superconducting gravimeter (SG) at the same station. The numerical results indicate that the identical tidal gravity parameters are the same as those with the SG, the instrument can be effectively used to record temporal change of the gravity field, though the ET20 accuracy is one order lower than that of the SG, and has the large drift induced by the spring creep character.
基金The National Natural Science Foundation of China under contract No. 40676009 and 40606006the Basic Research Project of Qingdao Science and Technology Program under contract No. 11-1-4-98-jch
文摘The global distributions of eight principal tidal constituents, M2, S2, K1, O1, N2, K2, P1, and Q1, are derived using TOPEX/Poseidon and JASON-1（T/P-J） satellite altimeter data for 16 a. The intercomparison of the derived harmonics at 7000 subsatellite track crossover points shows that the root mean square （RMS） values of the tidal height differences of the above eight constituents range from 1.19 cm to 2.67 cm, with an average of about 2 cm. The RMS values of the tidal height differences between T/P-J solutions and the harmonics from ground measurements at 152 tidal gauge stations for the above constituents range from 0.34 cm to 1.08 cm, and the relative deviations range from 0.031 to 0.211. The root sum square of the RMS differences of these eight constituents is 2.12 cm, showing the improvement of the present model over the existing global ocean tidal models. Based on the obtained tidal model the global ocean tidal energetics is studied and the global distribution of the tidal power input density by tide-generating force of each constituent is calculated, showing that the power input source regions of semidiurnal tides are mainly concentrated in the tropical belt between 30S and 30N, while the power input source regions of diurnal tides are mainly concentrated off the tropic oceans. The global energy dissipation rates of the M2, S2, K1, O1, N2, P1, K2 and Q1 tides are 2.424, 0.401, 0.334, 0.160, 0.113, 0.035, 0.030 and 0.006 TW, respectively. The total global tidal dissipation rate of these eight constituents amounts to 3.5 TW.
基金supported by the Open Fund of Hubei Luojia Laboratory (No. 220100033)the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB41000000)+1 种基金National Natural Science Foundation of China (Grant Nos. 42174108, 41874094, 42192535 and 42242015)the Young Top-notch Talent Cultivation Program of Hubei Province。
文摘The Earth’s Free Core Nutation(FCN) causes Earth tides and forced nutation with frequencies close to the FCN that exhibit resonance effects.High-precision superconducting gravimeter(SG) and very long baseline interferometry(VLBI) provide good observation techniques for detecting the FCN parameters.However,some choices in data processing and solution procedures increase the uncertainty of the FCN parameters.In this study,we analyzed the differences and the effectiveness of weight function and ocean tide corrections in the FCN parameter detection using synthetic data,SG data from thirty-one stations,and the 10 celestial pole offset(CPO) series.The results show that significant discrepancies are caused by different computing options for a single SG station.The stacking method,which results in a variation of0.24-5 sidereal days(SDs) in the FCN period(T) and 10^(3)-10^(4) in the quality factor(Q) due to the selection of the weighting function and the ocean tide model(OTM),can effectively suppress this influence.The statistical analysis results of synthetic data shows that although different weight choices,while adjusting the proportion of diurnal tidal waves involved,do not significantly improve the accuracy of fitted FCN parameters from gravity observations.The study evaluated a series of OTMs using the loading correction efficiency.The fitting of FCN parameters can be improved by selecting the mean of appropriate OTMs based on the evaluation results.Through the estimation of the FCN parameters based on the forced nutation,it was found that the weight function P_(1) is more suitable than others,and different CPO series(after 2009) resulted in a difference of 0.4 SDs in the T and of 103 in the Q.We estimated the FCN parameters for SG(T=430.4±1.5 SDs and Q=1.52×10^(4)±2.5×10^(3)) and for VLBI(T=429.8±0.7 SDs,Q=1.88×10^(4)±2.1×10^(3)).
文摘This research aims to optimize the utilization of long-term sea level data from the TOPEX/Poseidon,Jason1,Jason2,and Jason3 altimetry missions for tidal modeling.We generate a time series of along-track observations and apply a developed method to produce tidal models with specific tidal constituents for each location.Our tidal modeling methodology follows an iterative process:partitioning sea surface height(SSH)observations into analysis/training and prediction/validation parts and ultimately identi-fying the set of tidal constituents that provide the best predictions at each time series location.The study focuses on developing 1256 time series along the altimetry tracks over the Baltic Sea,each with its own set of tidal constituents.Verification of the developed tidal models against the sSH observations within the prediction/validation part reveals mean absolute error(MAE)values ranging from 0.0334 m to 0.1349 m,with an average MAE of 0.089 m.The same validation process is conducted on the FES2014 and EOT20 global tidal models,demonstrating that our tidal model,referred to as BT23(short for Baltic Tide 2023),outperforms both models with an average MAE improvement of 0.0417 m and 0.0346 m,respectively.In addition to providing details on the development of the time series and the tidal modeling procedure,we offer the 1256 along-track time series and their associated tidal models as supplementary materials.We encourage the satellite altimetry community to utilize these resources for further research and applications.
基金The Knowledge Innovation Program of the Chinese Academy of Sciences (KZCX2-YW-133)National Nature Science Foundation of China (40730316, 40574034).
文摘The synthetic tidal parameters with high spatial resolution for gravity over China and its neighbor area are constructed with Earth＇s tidal model and ocean tide loading calculated using TPXO7 global ocean tide model as well as tidal data over China seas. The comparison between synthetic parameters and ones observed by spring gravimeters at some seismic network stations and Hong Kong station and one observed by super-conducting gravimeter at Wuhan station shows that the average differences in amplitude factors and phases are smaller than 0.005 and 0.5° respectively; and that the discrepancies between observational and synthetic parameters are dependent on gravimetric technique in that the synthetic parameters are in well agreement with the superconducting gravimetric observations. This also indicates that the synthetic result is a good estimation for tidal gravity, and the numerical results in the present paper not only can provide ground and space gravimetry such as absolute gravimetry with correction model of tidal gravity, but also provide effective tidal parameters over areas where no observation is carried out.
文摘To assist the analysis of tsunami hazards for Qatar coastal areas were using numerical model. By Tsunamis waves created from submarine earthquakes of magnitude of (M<sub>w</sub>) 8.6 and 9.0 in Richard scale along the Makran Subduction Zone (MSZ) as well as coastal landslides with soil volume of 1.25 to 2.0 km<sup>3</sup> along Iranian coast inside the Arabian Gulf is considered. TUNAMI-N2KISR model (Al-Salem) was applied in this study to predict the tsunami propagation and magnitude of Tsunami induced wave heights. The model adopts to solve shallow water equations describing nonlinear long-wave theory. The model also incorporate tidal effect inside the Arabian Gulf as a tsunami travel time from Makran Subduction to Qatar coastline takes more than 9 hours with the tidal range of about 1.6 m during Spring Tide event. For coastal landslides, tsunami generation was simulated using a two-layer numerical model, developed by solving nonlinear long-wave equations. Two-layer model was used to determine initial wave deformation generated by a landslide case. Then TUNAMI-N2KISR was use to simulate tsunami wave propagation. Tsunami waves from landslide scenario arrived after 2.5 - 3 hr with maximum tsunami amplitudes along coasts of Ras laffan-Qatar were 0.8 to 1.0 m. Incorporation of ocean tide is found to impose some small effect on tsunami amplitude at Qatar coastline and nearby areas for the Mw 9.0 earthquake due to small tidal range in this area. In addition, it is found that the tsunami arrival time has become shorter.
基金supported by National Natural Science Foundation of China (Grant Nos. 40676009 and 40606006)Qingdao Science and Technology Basic Research Program (Grant No. 11-1-4-98-JCH)
文摘The loading tides are calculated by means of the Green's function method based on a high-resolution regional ocean tide model, the TOPO7.0 global ocean tide model, and the Gutenberg-Bullen A Earth model. The results show that the maximal amplitude of M2 vertical displacement loading (VDL) tide in the Bohai, Yellow, and East China Seas exceeding 28mm appears 150km off the Zhejiang coast; the second maximum exceeding 20mm appears in Inchon Bay; and the third maximum exceeding 14mm is located in the northeast of the North Yellow Sea. The maximal amplitudes of S2 VDL tide at the above three locations exceed 10, 8, and 4mm, respectively. The maximal amplitudes of the K1 and O1 VDL tides, exceeding 13 and 10 mm respectively, appear near the central and north Ryukyu Islands; the amplitudes tend to decease toward the inward areas. The phases of semidiurnal VDL tides are basically opposite to those of corresponding ocean tides. The phases of diurnal VDL tides are basically opposite to those of corresponding ocean tides in the most part of the East China Sea and the eastern part of the South Yellow Sea. This anti-phase relationship generally does not hold in the rest parts of the Bohai and Yellow Seas. The distribution patterns of self-attraction and loading (SAL) tides are very similar to those of VDL tides. The SAL tides have amplitudes about 1.2-1.7 times of the corresponding VDL tides and their phases are basically opposite to the corresponding VDL tides. The maximal amplitude of M2 SAL tide also appears off the Zhejiang coast, with a magnitude exceeding 42mm.
基金supported by the National Basic Research Program of China(Grant No.2013CB733302)the Basic Research Project of Institute of Earthquake Science,China Earthquake Administration(Grant Nos.2013IES0203,2014IES010102)the National Natural Science Foundation of China(Grant No.41304018)
文摘Currently,aliasing error of temporal signal model becomes the main factor constraining the accuracy of temporal gravity field.In provision of three types of satellite formations,i.e.,GRACE-type,Pendulum-type and n-s-Cartwheel-type,which are suitable for gravity mission and composed of observation in different directions,here we design two cases and conduct a simulation experiment on the feasibility to apply satellite formations for eliminating the influence from the aliasing error of ocean tide models.The result of our experiment shows that,when the aliasing error is disregarded,n-s-Cartwheel formation can provide the best conditions for gravity field determination,which,compared with GRACE-type,can improve the accuracy by 43%.When aliasing error of the ocean tide model acts as the main source of error,the satellite formation applied in dynamic method for gravity field inversion cannot eliminate aliasing or improve the accuracy of gravity field.And due to its higher sensitivity to the high-degree variation of gravity field,the Cartwheel-type formation,which includes the radial observation,can result in the gravity field containing more high-frequency signals for the ocean tide model error,and lead to a dramatically larger error.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.42250102,41830107,42142034,42130810,72088101)the Fundamental Research Funds for the Central Universities of Central South University(Grant No.2023ZZTS0730)+2 种基金the Science and Technology Innovation Program of Hunan Province(Grant No.2021RC4055)the Macao Science and Technology Development Fund(Grant No.0001/2019/A1)the Macao Foundation and the Preliminary Research Project on Civil Aviation and Aerospace Technology funded by the China National Space Administration(Grant No.D020303).
文摘Ground-based magnetic observatories and geomagnetic satellites can observe the induced magnetic field generated by the motion of seawater containing sodium and chlorine ions.Calculating the three-dimensional(3-D)spatial distribution of tide-induced magnetic fields(TIMF)is crucial for inverting the electrical conductivity structure of the oceanic lithosphere.It also serves as an essential basis for designing optimal geomagnetic observatories and satellite orbits.However,existing methods for simulating TIMF suffer from limitations in inaccurately modeling realistic coastlines,heterogeneous land and sea surface properties,and complex deep Earth structures,thereby the interpretational level of TIMF data is reduced.To overcome this issue,we developed a tetrahedral-based finite element method for simulating TIMF,which can efficiently approximate realistic coastlines,heterogeneous land and sea surface properties,and complex deep Earth structures.Firstly,we derived the boundary value problem for the seawater motion-induced electromagnetic field,which was solved using the vector finite element method based on tetrahedral elements.Secondly,using the latest ocean depth and seafloor sediment layer models,we constructed a 3-D conductivity model of the Earth,which includes realistic coastlines,heterogeneous land and sea conductivity distributions.We then computed the TIMF using the M_(2)tidal source as an example and validated our method by comparing it with results obtained from spherical harmonic finite element and integral equation methods.Finally,utilizing the computed high-precision M_(2),N_(2),and O1 TIMF signals,we marked global observatories capable of observing strong M_(2),N_(2),and O1 TIMF signals and predicted alternative stations suitable for tide signal observations.Additionally,we calculated TIMF at heights of 450 and 200 km for the Macao Science Satellite 1 and its subsequent satellites.The results indicate that the amplitude of the tidal-induced magnetic field at 200 km is approximately twice that at 450 km.The maximum amplitudes of M_(2),N_(2),and O1 TIMF at 200 km are eight,two,and three times the measurement accuracy of the magnetic sensing payload(0.5 nT),respectively.The 200 km orbit has great potential for detecting high-resolution electrical structures of the seafloor lithosphere and asthenosphere in regions such as New Zealand,southern Iceland,the southern Indian Ocean,the Ross Sea region of Antarctica,and the Sea of Okhotsk.It also holds the potential for studying large-scale oceanic dynamic processes and properties.
基金supported by the Research Grants Council(RGC)of the Hong Kong Special Administrative Region(Grant Nos.PolyU5157/05E,PolyU5161/06E)the Scientific Research Foundation of The Hong Kong Polytechnic University(Grant No.GY-F81)the Fundamental Research Funds for the Central Universi-ties(Grant Nos.SWJTU09BR029,SWJTU09BR031)
文摘Ocean tide loading(OTL)displacements of eight principal constituents at 12 sites in Hong Kong were determined using more than eight years of continuous GPS observations.Parameters of the OTL displacements were estimated using daily GPS solutions obtained with precise point positioning(PPP)technique.The results were compared with predictions from seven latest global ocean tide models.Gravity measurements of OTL in Hong Kong were also used to validate the GPS results.The study shows that the results from both the GPS and gravity measurements agree best with the GOT4.7 and NAO99b models,when the K1 and K2 constituents are excluded.The agreements between the GPS and the model estimates are generally at sub-millimeter level in both the horizontal and vertical directions,except for S2,K2 and K1 constituents that have relatively larger errors.After removing the systematic biases between the GPS and the model estimates,the misfits of M2,S2,N2,O1,P1 and Q1 at all sites are within 0.5 and 1.0 mm in the horizontal and the vertical directions,respectively,whereas K1 and K2 show relatively larger misfits of up to 2.3 mm.Both the GPS and the gravity S2 estimates have large biases with unknown reasons when compared with the modeled values,which needs to be further investigated.The study demonstrates that GPS is capable of estimating the OTL displacements with the same accuracy as the model predictions,especially for coastal areas.
