Ocean tide loading (OTL) displacements from global and local grids: comparisons to GPS estimates over the shelf of Brittany, France

In this paper we examine OTL displacements detected by GPS stations of a dedicated campaign and validate ocean tide models. Our area of study is the continental shelf of Brittany and Cotentin in France. Brittany is one of the few places in the world where tides provoke loading displacements of ∼10–12 cm vertically and a few cm horizontally. Ocean tide models suffer from important discrepancies in this region. Seven global and regional ocean tide models were tested: FES2004 corrected for K2, TPXO.7.0, TPXO.6.2, GOT00.2, CSR4.0, NAO.99b and the most recent regional grids of the North East Atlantic (NEA2004). These gridded amplitudes and phases of ocean tides were convolved in order to get the predicted OTL displacements using two different algorithms. Data over a period of 3.5 months of 8 GPS campaign stations located on the north coast of Brittany are used, in order to evaluate the geographical distribution of the OTL effect. We have modified and implemented new algorithms in our GPS software, GINS 7.1. GPS OTL constituents are estimated based on 1-day batch solutions. We compare the observed GPS OTL constituents of M₂, S₂, N₂ and K₁ waves with the selected ocean tide models on global and regional grids. Large phase-lag and amplitude discrepancies over 20° and 1.5 cm in the vertical direction in the semi-diurnal band of M₂ between predictions and GPS/models are detected in the Bay of Mont St-Michel. From a least squares spectral analysis of the GPS time-series, significant harmonic peaks in the integer multiples of the orbital periods of the GPS satellites are observed, indicating the existence of multipath effects in the GPS OTL constituents. The GPS OTL observations agree best with FES2004, NEA2004, GOT00.2 and CSR4.0 tide models.     

Quantifying FES2004 S<Subscript>2</Subscript> tidal model from multiple space-geodesy techniques,GPS and GRACE,over North West Australia

Unmodeled sub-daily ocean S₂ tide signals that alias into lower frequencies have been detected in the analysis of gravity recovery and climate experiment (GRACE) space gravity fields of GRGS. The most significant global S₂ aliased signal occurs off the northwest coast of Australia in a shallow continental shelf zone, a region with high tidal amplitudes at a period of 161 days. The GRACE S₂ aliased equivalent water height grids are convolved with Green’s functions to produce GRACE aliased tidal loading (GATL) vertical displacements. The analysis of hourly global positioning system (GPS) vertical coordinate estimates at permanent sites in the region confirms the presence of spectral power at the S₂ frequency when the same ocean tide model (FES2004) was used. Thus, deficiencies in the FES2004 ocean tide model are detected both directly and indirectly by the two independent space geodetic techniques. Through simulation, the admittance (ratio of amplitude of spurious long-wavelength output signal in the GRACE time-series to amplitude of unmodeled periodic signals) of the GRACE unmodeled S₂ tidal signals, aliased to a 161-day period, is found to have a global average close to 100%, although with substantial spatial variation. Comparing GATL with unmodeled S₂ tidal sub-daily signals in the vertical GPS time-series in the region of Broome in NW Australia suggests an admittance of 110–130%.     

Comparison between the harmonic and response methods of tidal analysis using TOPEX/POSEIDON altimetry

Three years of TOPEX/POSEIDON altimeter data have been processed at Delft Institute for Earth-Oriented Space Research (DEOS) to solve the major diurnal and semi-diurnal constituents of the global ocean tide using the two classical methods of tidal analysis, i.e. the harmonic and response analyses. Some experiments with the parameters in the response formalism show that the tidal admittance in both the diurnal and semi-diurnal band can be adequately described with a lag interval of 2 days and a number of lags of three. Results of both methods are evaluated from the differences with the most recent Grenoble hydrodynamic model (FES95.2) and from the fit with the harmonic constants of a globally distributed set of tide gauges. It was found that the solutions of the two methods differ at the millimeter level and are thus fully equivalent, which is confirmed by the tide gauges and the differences with FES95.2. From the comparisons with the Grenoble model it was found that the M ₂ and S ₂ solutions of that model likely contain bathymetric errors which are of the order of 1–2 cm for M ₂ and 0.5 cm for S ₂. Received: 18 December 1996 / Accepted: 12 May 1997     

潮汐模型对利用卫星测高数据研究海平面变化的影响

利用T/P测高数据反演了中国近海及西北太平洋海域的潮汐参数,构造了CSR3.0、FES95.2和T/P反演的海潮模型改正下的海面高时间序列,通过海面高变化曲线及功率谱的比较确定了利用测高数据发现的海平面季节内变化主要是潮汐模型误差的贡献.     

Validating ocean tide loading models using GPS

Ocean tides cause periodic deformations of the Earths surface, also referred to as ocean tide loading (OTL). Tide-induced displacements of the Earths crust relying on OTL models are usually taken into account in GPS (Global Positioning System) data analyses. On the other hand, it is also possible to validate OTL models using GPS analyses. The following simple approach is used to validate OTL models. Based on a particular model, instantaneous corrections of the site coordinates due to OTL are computed. Site-specific scale factors, f, for these corrections are estimated in a standard least-squares adjustment process of GPS observations together with other relevant parameters. A resulting value of f close to unity indicates a good agreement of the model with the actual site displacements. Such scale factors are computed for about 140 globally distributed IGS (International GPS Service) tracking sites. Three OTL models derived from the ocean tide models FES95.2.1, FES99, and GOT00.2 are analyzed. As expected, the most reliable factors are estimated for sites with a large loading effect. In general, the scaling factors have a value close to unity and no significant differences between the three ocean tide models could be observed. It is found that the validation approach is easy to apply. Without requiring much additional effort for a global and self-consistent GPS data analysis, it allows detection of general model misfits on the basis of a large number of globally distributed sites. For detailed validation studies on OTL models, the simultaneous estimation of amplitudes and phases for the main contributing partial tides within a GPS parameter adjustment process would provide more detailed answers.     

GPS精密定位中的海潮位移改正

根据海洋负荷潮理论，利用NAO99b全球海潮模型，计算了中国部分IGS站的海潮位移改正，并将海潮位移改正应用到GPS数据处理当中。在GAMIT软件的解算过程中，分别按加入和不加入海潮位移改正，对GPS基线分量和测站坐标分别进行了计算和比较分析。结果表明，海潮位移改正无论是对GPS基线分量还是对测站坐标，都有一定的影响。     

An improved empirical model for the effect of long-period ocean tides on polar motion

Because the tide-raising potential is symmetric about the Earth’s polar axis it can excite polar motion only by acting upon non-axisymmetric features of the Earth like the oceans. In fact, after removing atmospheric and non-tidal oceanic effects, polar motion excitation observations show a strong fortnightly tidal signal that is not completely explained by existing dynamical and empirical ocean tide models. So a new empirical model for the effect of the termensual (Mtm and mtm), fortnightly (Mf and mf), and monthly (Mm) tides on polar motion is derived here by fitting periodic terms at these tidal frequencies to polar motion excitation observations that span 2 January 1980 to 8 September 2006 and from which atmospheric and non-tidal oceanic effects have been removed. While this new empirical tide model can fully explain the observed fortnightly polar motion excitation signal during this time interval it would still be desirable to have a model for the effect of long-period ocean tides on polar motion that is determined from a dynamical ocean tide model and that is therefore independent of polar motion observations.     

利用验潮站资料的中国近岸海潮模型精度评估

针对全球海潮模型在我国近海海域精度较差的问题,该文采用中国沿岸30个长期验潮站的调和常数,对比了3种全球海潮模型DTU10、TPXO7.2、NAO.99b和1个区域海潮模型NAO.99Jb在中国沿岸的准确度。通过海潮模型与验潮站分潮的振幅中误差、迟角中误差以及8个主要分潮的预报误差,对渤海、黄海、东海和南海北部进行了详细的分析。结果表明,NAO.99Jb在中国海域精度最高,NAO.99b次之。在渤海海域,DTU10在Q_1分潮精度最高,NAO.99b在K2分潮精度最高,其余分潮均是NAO.99Jb精度最高;在黄海海域,NAO.99b在Q_1分潮精度最高,其余分潮均是NAO.99Jb精度最高;在东海海域,DTU10在Q_1分潮精度最高,TPXO7.2在P1精度最高,NAO.99Jb在O1、M2分潮精度最高,其余分潮均是NAO.99b精度最高;在南海北部海域,DTU10在N2、S2分潮精度最高,其余分潮均是NAO.99Jb精度最高。     

Improving gravity anomalies over China marginal sea from retracked Geosat and ERS-1 data

The quality of altimeter data and ocean tide model is critical to the recovery of coastal gravity anomalies. In this contribution, three retracking methods (threshold, improved threshold and Beta-5) are investigated with the aim of improving the altimeter data over a shallow water area. Comparison indicates that the improved threshold is the best retracking method over China Sea. Two ocean tide models, NAO99b and CSR4.0, are analyzed. Results show that different tide models used in the processing of altimeter data may result in differences more than 10 mGal in recovered coastal gravity anomalies. Also, NAO99b is more suitable than CSR4.0 over the shallow water area of China Sea. Finally, gravity anomalies over China Sea are calculated from retracked Geosat/GM and ERS-1/GM data by least squares collocation. Comparison with shipborne gravimetry data demonstrates that gravity anomalies from retracked data are significantly superior to those from non-retracked data. Our results have the same order as the other two altimeter-derived gravity models: Sandwell&Smith(V16) and DNSC08.     

潮汐对精密单点定位的影响

基于IERS2003协议,介绍了地球固体潮,海潮,极潮等改正模型,叙述了各潮汐项改正步骤,分析了各类潮汐改正模型的量级及对精密单点定位的影响。     

南极中山站的重力和区域海洋潮汐特征

本文利用中山站弹簧重力仪记录的重力潮汐时间序列、验潮站数据、CATS2008区域和Eot11a全球海潮模型研究重力和海洋潮汐特征。结果表明,在周日频段,潮波O1的海潮振幅达到28 cm,4个主要潮波（Q1、O1、P1和K1）的全球模型与验潮站潮高差之和为4.2 cm,区域模型与验潮站潮高差之和为4.4 cm;在半日频段,潮波M2的海潮振幅达到20 cm,4个主要潮波（N2、M2、S2和K2）的潮高差之和分别为7.7 cm和5.1 cm,说明利用区域模型修正全球模型的重要性。经区域模型修正的全球海潮负荷改正后,重力主波K1、M2和S2的最终残差振幅分别下降了9.84%、56.14%和37.08%,说明区域海潮模型更能反映海洋潮汐的真实特征,用区域模型修正全球海潮模型的有效性得到验证。     

A comparison of GPS, VLBI and model estimates of ocean tide loading displacements

In recent years, ocean tide loading displacements (OTLD) have been measured using the Global Positioning System (GPS) and Very Long Baseline Interferometry (VLBI). This study assesses the accuracy of GPS measurements of OTLD by comparison with VLBI measurements and estimates derived from numerical ocean tide models. A daily precise point positioning (PPP) analysis was carried out on ∼11 years of GPS data for each of 25 sites that have previous OTLD estimates based on data from co-located VLBI sites. Ambiguities were fixed to integer values where possible. The resulting daily estimates of OTLD, at eight principal diurnal and semi-diurnal tidal frequencies, were combined to give GPS measurements of OTLD at each site. The 3D GPS and VLBI measurements of OTLD were compared with estimates computed (by convolution with Green’s functions) from five modern ocean tide models (CSR4.0, FES2004, GOT00.2, NAO99b and TPXO6.2). The GPS/model agreement is shown to be similar to the VLBI/model agreement. In the important radial direction, the GPS/model misfit is shown to be smaller than the VLBI/model misfit for seven of the eight tidal constituents; the exception being the K2 constituent. Fixing of GPS carrier-phase ambiguities to integer values resulted in a marginal improvement to the GPS/model agreement. Statistically, it is shown there is no significance to the difference between the fit of the GPS and VLBI measurements of OTLD to modelled values. Equally, differences in fit of either the complete set of GPS or VLBI estimates to the five sets of model-derived values cannot be identified with statistical significance. It is thus concluded that, overall, we cannot distinguish between GPS and VLBI measurements of OTLD, and that at the global scale, present ocean tide models are accurate to within the current measurement noise of these techniques.     

One centimeter-level observations of diurnal ocean tides from global monthly mean time-variable gravity fields

A method of analyzing GRACE satellite-to-satellite ranging data is presented which accentuates signals from diurnal ocean tides and dampens signals from long-period non-tidal phenomena. We form a time series of differences between two independent monthly mean gravity solutions, one set computed from range-rate data along strictly ascending arcs and the other set computed from data along descending arcs. The solar and lunisolar diurnal tides having alias periods longer than a few months, such as K ₁, P ₁, and S ₁, present noticeable variations in the monthly ascending and descending ‘difference’ solutions, while the climate-related signals are largely cancelled. By computing tidal arguments evaluated along the actual GRACE orbits, we decompose and estimate residual tidal signals with respect to our adopted prior model GOT4.7. The adjustment in the tidal height is small yet significant, yielding maximum amplitudes of 4 cm mostly under the Antarctic ice shelves and ~1 cm in general at spatial scales of several hundred kilometer. Moreover, the results suggest there are possible 1-cm errors in the tide model even over oceans well-covered by decades of radar altimetry missions. Independent validation of such small adjustments covering wide areas, however, is difficult, particularly with limited point measurements such as tide gauge.     

近海潮汐效应对上海地区精密定位的影响

针对全球海潮模型在不同沿海地区存在差异性以及在中国近海精度不高的问题,利用全球海潮模型FES2004和NAO99b计算上海地区(经纬度范围为120.85°E～122.2°E,30.6667°N～31.8833°N)S₂、M₂、K₁和O₁四个分潮的海潮负荷位移在垂直分量上的差异;并利用中国近海模型osu.chinasea.2010对全球海潮模型FES2004中相应的区域进行替换,计算近海效应对SHJZ站(上海金山)、SHJBS站(上海宝山)、SHAO站(上海佘山)以及DCMD站(上海崇明)四个测站精密定位的影响。结果表明:1) 全球海潮模型FES2004和NAO99b在上海地区存在较明显的差异,尤其是垂直分量,最大接近4 mm,且两个模型的差异随离海洋距离增大而减小;2) 利用修正前后的全球海潮模型FES2004经过计算分析得出,近海效应对上海地区GPS测站精密定位的影响达到5 mm,对测站垂直分量的位移影响从大到小分别是DCMD站(5.1 mm)、SHBS站(4.9 mm)、SHJS(4.2 mm)、SHAO(3.6 mm)。      

Rotational evaluation of a long-period spherical harmonic ocean tide model

By exchanging angular momentum with the solid earth, tidal variations in ocean currents and sea level cause the rotation of the solid earth to change. Observations of earth rotation variations can therefore be used to evaluate ocean tide models. The rotational predictions of a spherical harmonic ocean tide model that is not constrained by any type of data are compared here to the predictions of numerical ocean tide models and to earth rotation observations from which atmospheric and non-tidal oceanic effects have been removed. The spherical harmonic ocean tide model is shown to account for the observed variations at the fortnightly tidal period in polar motion excitation but not in length-of-day. Overall, its long-period polar motion excitation predictions fit the observed tidal signals better than do the predictions of the numerical ocean tide models studied here. It may be possible to improve its agreement with length-of-day observations by tuning certain model parameters, as was done to obtain the close agreement reported here between the modeled and observed polar motion excitation; alternatively, the discrepancy in length-of-day may point to the need to revise current models of mantle anelasticity and/or models of the oceanic response to atmospheric pressure variations.     

Separation of residual ocean tide signals in a collinear analysis of Geosat altimetry

The effects of residual ocean tide signals on altimetric mesoscale variability estimates are analyzed in the north east Atlantic region using one year of Geosat Exact Repeat Mission data. The variability is evaluated along collinear tracks and covariance functions are determined. Initial results show that the average variability is about 10 cm. Variability values of 15–20 cm are found between Iceland and the Faeroe Islands and values up to 1/2 m are found near the coast of the UK. Then a procedure for estimation of ocean tide signals combined with the collinear analyses was tested. A separation of the estimated tide residuals associated with M₂, S₂, and N₂ resulted in a significant reduction of the variability. The average variability decreased to 5 cm and the temporal correlations vanished. A reduction of the large variability values from 15–50 cm to 5–10 cm demonstrates that significant residual ocean tide signals can be estimated and removed efficiently in a collinear analysis of the mesoscale ocean variability.     

World-wide synthetic tide parameters for gravity and vertical and horizontal displacements

The response of the Earth’s crust to the direct effect of lunisolar gravitational forcing is known as the body tide. The body tide is superimposed by surface-loading forces due to the pressure of the periodically varying ocean tide acting on the Earth, called ocean tide loading (OTL). Both body tide and OTL can be decomposed into components of the same frequency known as tidal parameters. However, OTL is more complicated than body tides because of the dynamic effects of the ocean. Estimating OTL requires a model of the ocean tides and knowledge of the elastic properties of the solid Earth. Thus, synthetic tide parameters (amplitude factors and phase leads) have been developed here on a world-wide grid for gravity and positional displacements. The body tide contributions were added to the oceanic contribution to provide the Earth tide response. The accuracy and reliability of the synthetic tidal parameters have been estimated by comparing observed gravity and vertical-displacement tide parameters with those interpolated from our synthetic model, which shows good agreement. Tests also indicate that the synthetic tide parameters provide realistic gravimetric and displacements for practical use in tidal prediction.     

海潮负荷效应对我国及周边IGS站的影响

针对近海区域海潮变化复杂且海潮负荷效应显著,而全球海潮模型在近海区域精度较低的问题,该文提出了将全球海潮模型NAO.99b和区域模型osu.chinasea.2010相结合,分析海潮对中国大陆及周边地区IGS站的影响。使用GAMIT软件解算IGS站实测数据,通过海潮负荷计算软件SPOTL对解算结果进行改正,并对改正效果进行对比和分析。结果表明,海潮负荷对中国及周边区域站点的影响主要体现在垂直方向,对一些站点的影响可以达到厘米级;海潮负荷对站点坐标的改正效果明显,特别是日本的种子岛站改正效果接近30%;站点改正效果从沿海到内陆逐渐减弱。     

潮汐对高精度重力测量的改正分析

分析了固体潮和海洋负荷潮对沿海基准站绝对重力测量的影响,以及利用不同海潮模型计算后的精度统计,结果表明全球海潮模型对我国沿海绝对重力测量的改正不是十分精确。并简要分析了海洋负荷潮对相对重力测量的影响。     

The impact of the dynamic sea surface topography on the quasi-geoid in shallow coastal waters

In this study, we examine the impact of instantaneous dynamic sea surface topography (DT) corrections to be applied to altimeter-derived sea surface slopes on the quasi-geoid in the shallow and coastal waters of the North Sea. In particular, we investigate the added value of DT corrections obtained from a shallow-water hydrodynamic model. These corrections comprise the contributions of ocean tides, wind- and pressure-driven (surge), and density-driven (baroclinic) water-level variations including the interactions between them. As a reference, we used tidal corrections derived from the global ocean tide model GOT4.7, surge corrections derived from the MOG2D model, and corrections for the time-averaged baroclinic contribution computed as differences between the DTU10 mean sea surface model and the EGG08 quasi-geoid. From a spectral analysis, we found that the baroclinic and surge parts of the DT mainly contribute to improvements in the signal-to-noise ratio (SNR) at longer wavelengths down to $100{-}200~\hbox {km}$ and that the improvements increase towards the southern North Sea. We also found that the shallow-water hydrodynamic model provides better tidal corrections compared to the GOT4.7 global ocean tide model, which are most pronounced in the southern North Sea and affect almost the entire spectrum. Very small differences (mostly below ${\pm } 2~\hbox {cm}$ ) are observed between the quasi-geoid solutions obtained using the different sets of DT corrections. We showed that the variance component estimation provides too optimistic variance factors for the shipboard data set relative to the altimeter-derived quasi-geoid slopes. Hence, the limited impact of DT corrections is due to the fact that altimeter-derived quasi-geoid slopes hardly contribute to the estimated quasi-geoid if shipboard gravity data are included. When computing quasi-geoid solutions without shipboard gravity data, we found that less accurate or incomplete DT corrections may cause errors in the quasi-geoid with systematic spatial patterns. These systematic patterns disappear or are reduced significantly when using the DT corrections provided by the shallow-water hydrodynamic model. The main contributor to this improvement is the better tidal correction provided by the shallow-water hydrodynamic model compared to the GOT4.7 global ocean tide model. Seen the improvements of the global ocean tide models over the last two decades, we expect that in the near future global ocean tide models perform as well as dedicated regional models such as DCSM. Critical issue is, however, access to high-quality local bathymetric data.