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.     

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.     

利用GPS动态PPP技术求解海潮负荷位移

受特殊海岸线及复杂海底地形的影响,目前发布的全球海潮模型在局部沿海地区差异较大,需利用其他大地测量手段直接测定沿海地区的海潮负荷位移参数。GPS技术因具有全天候、精度高、成本低等优势,已成为获取海潮负荷位移参数的有效手段。本文基于GPS技术监测测站三维位移变化的灵敏度高于监测48个海潮参数的灵敏度这一基本思想,改进了利用GPS精密单点定位(PPP)技术估计48个海潮调和参数的方法,直接逐历元求解三维海潮负荷位移变化,再利用调和分析方法提取主要潮波(M2、S2、N2、K2、K1、O1、P1、Q1)的海潮负荷位移建模参数(振幅与相位)。利用12个香港连续运行参考站(CORS)8年的GPS观测数据,计算各测站的海潮负荷位移建模参数。与传统方法比较,本文方法可有效加速K1潮波在东西方向的收敛。将GPS海潮负荷位移建模参数估值与中国近海海潮模型值比较,发现除S2、K2和K1潮波的均方根误差较大外,其他潮波的均方根误差均小于1.5mm。将香港2008—2014年验潮站数据反演的潮波参数与海潮模型值比较,结果表明:GPS与验潮站数据反演的潮波参数均与中国近海海潮模型及HAMTIDE2011.11A全球海潮模型符合较好,验证了GPS PPP反演海潮负荷位移的有效性。采用GPS PPP估计的8个潮波的振幅与相位值替换全球海潮模型中对应的潮波值,进行海潮负荷效应改正,可减弱GPS长时间序列中的半周年信号。     

Assessing the accuracy of predicted ocean tide loading displacement values

The accuracy of ocean tide loading (OTL) displacement values has long been assumed to be dominated by errors in the ocean tide models used, with errors due to the convolution scheme used considered very small (2–5%). However, this paper shows that much larger convolution errors can arise at sites within approximately 150 km of the coastline, depending on the method used to refine the discrete regularly spaced grid cells of the ocean tide model to better fit the coastline closest to the site of interest. If the local water mass redistribution approach is implemented, as used in the OLFG/OLMPP software recommended in the IERS 2003 conventions, OTL height displacement errors of up to around 20% can arise, depending on the ocean tide model used. Bilinear interpolation only, as used in the SPOTL and CARGA softwares for example, is shown from extensive global and regional comparisons of OTL displacement values derived from the different methods and softwares to be more appropriate. This is verified using GPS observations. The coastal refinement approach used in the OLFG/OLMPP software was therefore changed in August 2007 to use bilinear interpolation only. It is shown that with this change, OTL displacement values computed using OLFG/OLMPP, SPOTL and CARGA invariably agree to the millimetre level for coastal sites, and better than 0.2 mm for sites more than about 150 km inland.     

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.     

Estimates of ocean tide loading displacements and its impact on position time series in Hong Kong using a dense continuous GPS network

Three-dimensional ocean tide loading (OTL) displacements of eight diurnal and semidiurnal constituents at 12 sites in Hong Kong were estimated using 3–7 years of continuous global positioning system (GPS) observations. OTL displacements were estimated using the precise point positioning (PPP) technique on a daily basis and then combined. The OTL displacements obtained by GPS were compared with predictions using seven recent global ocean tide models. The effect of OTL displacements on GPS position time series was also investigated. The study shows that the GPS-derived OTL displacements (excluding K1 and K2 constituents) agree best with those predicted by the GOT4.7 and NAO99b models. The GPS/model agreement is generally at the sub-millimeter level, except for S2, K1, and K2 constituents with relatively large errors. After systematic biases between the GPS and model values are removed, the misfits of all sites for M2, S2, N2, O1, P1, and Q1 are less than 0.5 and 1.0 mm in the horizontal and vertical components, respectively, while larger misfits (within 2.5 mm) are observed for K1 and K2. Integer ambiguity fixing slightly improves the east component of OTL displacement estimates. The study also finds that GPS-derived OTL corrections, instead of model predicts, can be used in daily data processing with the exception of K1 and K2. Including K2 corrections, a secular vertical rate of up to 1 mm/year in position time series can be induced, which needs to be confirmed by further studies.     

The M 2 ocean tide loading wave in Alaska: vertical and horizontal displacements, modelled and observed

Crustal deformations caused by surface load due to ocean tides are strongly dependent on the surface load closest to the observation site. In order to correctly model this ocean loading effect near irregular coastal areas, a high-resolution coastline is required. A test is carried out using two GPS sites located in Alaska, where the ocean tide loading effect is large and consequently observed easily by relative positioning with GPS. The selected sites are Fair (Fairbanks) and Chi3 (located on an island that separates Prince William Sound from the Gulf of Alaska). Processing of hourly baseline solutions between Fair and Chi3 over a period of 49 days yields a significant ocean tide loading effect. The data are processed using different strategies for the tropospheric delay correction. However, the best results are obtained when 1-h ZTD (Zenith Tropospheric Delay) parameters for hourly solutions are used. In this case ocean tide loading is not absorbed into the ZTD parameters. Hence, ocean tide loading can be well resolved in the GPS data analysis. In addition, the M ₂ ocean tide wave in the Gulf of Alaska has a very large amplitude. Although the horizontal M ₂ ocean tide loading amplitude in general is only about 1/4 of the vertical M ₂ ocean tide loading amplitude, the differential horizontal M ₂ ocean tide loading displacements are nevertheless measurable using differential GPS (DGPS). When using the GOT99.2 ocean tide model and taking the coastal structure into account, the predicted differential vertical M ₂ amplitude and Greenwich phase lag due to ocean tide loading are 19.3 mm and 110.2 degrees respectively, while GPS measurements yield 21.3 ± 1.0 mm and 99.7±2.8 degrees. Similarly, the predicted differential horizontal M ₂ amplitude and Greenwich phase lag (in the north–south direction) are 4.5 mm and –77.0 degrees, while GPS yields 5.4 ± 0.3 mm and –106.3±3.3 degrees. Only the north-south component of the differential horizontal M ₂ ocean tide loading wave is considered, because the east–west component is too small for the processed baseline and not detectable using DGPS.     

不同海潮模型对东南极沿海地区GPS基线解算的影响

在高精度GPS数据处理中,海潮的影响是一个不可忽略的因素。利用GAMIT软件解算2011年东南极沿海地区中国中山站及其周边6个IGS站的GPS数据,对比分析了FES2004、DTU10、EOT11a、GOT4.7、HAMTIDE11a、OSU12以及TPXO7.2等7个全球海潮模型在不同测站的海潮负荷差异,比较了海潮负荷对于GPS基线解的影响。结果表明,海潮负荷对GPS基线解的影响与测站所处位置及基线方位有关,达到cm级,相对影响达到10-8,因此,在高精度的GPS基线解算中必须考虑海潮的影响;但选用不同海潮模型对东南极沿海地区GPS基线解算的差异可忽略不计。     

利用动态PPP技术确定海潮负荷位移

利用动态PPP对香港12个GPS测站2007—2012年的数据反演了海潮负荷位移,通过与7个全球海潮模型、1个区域模型和静态PPP反演的结果比较发现,相对于另外几个模型,动态PPP反演结果与TPXO.7.2、EOT11a、HAMTIDE和NAO99Jb模型的结果符合得更好。与静态PPP的结果比较发现其RMS与各模型的RMS大体上一致,只是在S2、K2和K1的E方向和M2、S2的N方向稍有增加。此外,除K2和K1潮波外,动态PPP与模型的RMS值在水平方向上均小于1 mm,在垂直方向上均小于2.5 mm,能达到和静态PPP相当的精度。本文反演的结果与NAO99Jb模型值存在明显的系统偏差,当去除系统偏差后,所有潮波的RMS值都有明显的减小,尤其在K1的垂直方向RMS从16.4 mm减少到1.3 mm。此外,通过将香港2012年验潮站数据反演的潮波参数与模型的结果进行比较发现,其结果同样与TPXO.7.2、EOT11a、HAMTIDE和NAO99Jb这4个模型更为符合,这进一步验证了动态PPP反演海潮的有效性,同时说明这4个模型比较适合香港区域。     

The gravitational effect of ocean tide loading at high latitude coastal stations in Norway

Gravity measurements close to the ocean are strongly affected by ocean tide loading (OTL). The gravitational OTL effect consists of three parts, i.e. a change in gravity caused by direct attraction from the variable water-masses, by displacement of the observing point due to the load, and by redistribution of masses due to crustal deformation. We compare the OTL gravitational effect of several global models to observed time-series of gravity to identify the best model for four arctic observation sites. We also investigate if the global models are sufficient for correcting gravity observations. The NAO99b model fits the observations best at three stations. At two stations (Tromsø and Bodø) the global models explain the variability in the observations well. At the other two (Honningsvåg and Andøya), a significant periodic signal remains after the OTL correction has been applied. We separate two of the gravitational effects, the direct attraction and the change in gravity due to displacement, to study the local effects. Simple geometric models of the water load and independent measurements from local tide-gauges are used to calculate these effects. This leads to improved correspondence with the OTL signal, hence demonstrating the importance of careful modelling of local effects for correction of gravity observations in coastal stations.     

利用改进的动态PPP技术建立中国香港区域海潮负荷位移模型

利用GPS技术反演海潮负荷信息,相比传统重力及甚长基线干涉测量,有着全球覆盖、测站数多、全天候、成本低等诸多优势,为海潮模型的建立提供了有效的技术手段,也对海潮负荷效应的研究有着重要的理论意义和参考价值。利用动态精密单点定位技术（precise point positioning,PPP）反演海潮负荷位移,同时构建了区域海潮负荷位移模型。利用香港连续运行参考站8 a的GPS观测数据,精密测定了11个测站的三维海潮负荷位移参数,与高精度海潮模型提供的海潮负荷位移参数进行比较,发现除K₂、K₁潮波外,其他潮波的均方根误差均小于2 mm。与已有的动态PPP及静态PPP结果对比发现,采用改进的重叠时段动态PPP算法可有效改善K₁潮波的反演精度;该方法反演的海潮负荷位移精度可达到静态PPP反演海潮负荷位移的精度,且对于K₁潮波,在东西方向,动态PPP算法的反演精度较静态PPP略有改善。利用最小二乘曲面拟合法可有效建立中国香港地区GPS区域海潮负荷位移模型,可有效弥补沿海地区因验潮站稀少而导致的海潮模型适应性差的问题。     

An estimate of the errors in gravity ocean tide loading computations

The error contributions within the ocean tide loading (OTL) convolution integral computation were determined to be able to estimate the numerical accuracy of the gravity OTL values. First, the comparison of four OTL programs by different authors (CONMODB, GOTIC2, NLOADF and OLFG/OLMPP) at ten globally distributed gravity stations using exactly the same input values shows discrepancies between 2% and 5%. A new program, called CARGA, was written that is able to reproduce the results of these programs to a level of 0.1%. This has given us the ability to state with certainty the cause of the discrepancies among the four programs. It is shown that by choosing an appropriate interpolation of the Green’s function, refinement of the integration mesh and a high-resolution coastline, an accuracy level of better than 1% can be obtained for stations in Europe. Besides this numerical accuracy, there are errors in the ocean tide model such as a 1% uncertainty in the mean value of the sea-water density and the lack of conservation of tidal water mass, which can produce offsets of around 0.04 μgal.     

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。     

潮汐改正对精密GPS基线解算的影响

介绍了三类潮汐模型改正,分析了中国及周边地区不同类型、大尺度GPS网,研究了极潮、大洋潮、固体潮模型改正对定位精度的影响,给出了模型的使用方法.     

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。     

南极国际GPS跟踪站的海潮位移改正 (英文)

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 processing. 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.     

南极国际GPS联测的海潮位移改正

根据海洋负荷潮理论,利用CRS4.0全球海潮模型,计算了参加南极国际GPS联测的中国南极长城站和中山站的海潮位移改正,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基线分量进行了计算和比较分析。结果表明,对于南极国际GPS联测,海潮位移改正对GPS基线分量具有不可忽略的影响,数据处理时需要重点考虑。     

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.     

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。