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.     

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。     

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.     

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。     

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.     

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。     

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.     

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.     

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。     

高精度大地测量中的海潮位移改正

鉴于目前IERS规范中缺乏海潮对多数中国测站位移的改正，基于表面负荷形变理论，本文采用CSR3．0全球海潮模型和Farrell的格林函数结果，计算了中国测站的海潮位移改正。部分结果同IERS公布结果引比，符合很好，可以用于高精度大地测量，对中国地壳形变监测特别是沿海地区地壳形变监测具有重要的实用价值。     

S<Subscript>2</Subscript> tide aliasing in GRACE time-variable gravity solutions

Errors in high-frequency ocean tide models alias to low frequencies in time-variable gravity solutions from the Gravity Recovery and Climate Experiment (GRACE). We conduct an observational study of apparent gravity changes at a period of 161 days, the alias period of errors in the S₂ semidiurnal solar tide. We examine this S₂ alias in the release 4 (RL04) reprocessed GRACE monthly gravity solutions for the period April 2002 to February 2008, and compare with that in release 1 (RL01) GRACE solutions. One of the major differences between RL04 and RL01 is the ocean tide model. In RL01, the alias is evident at high latitudes, near the Filchner-Ronne and Ross ice shelves in Antarctica, and regions surrounding Greenland and Hudson Bay. RL04 shows significantly lower alias amplitudes in many of these locations, reflecting improvements in the ocean tide model. However, RL04 shows continued alias contamination between the Ronne and Larson ice shelves, somewhat larger than in RL01, indicating a need for further tide model improvement in that region. For unknown reasons, the degree-2 zonal spherical harmonics (C₂₀) of the RL04 solutions show significantly larger S₂ aliasing errors than those from RL01.     

Comparison between geodetic and oceanographic approaches to estimate mean dynamic topography for vertical datum unification: evaluation at Australian tide gauges

The direct method of vertical datum unification requires estimates of the ocean’s mean dynamic topography (MDT) at tide gauges, which can be sourced from either geodetic or oceanographic approaches. To assess the suitability of different types of MDT for this purpose, we evaluate 13 physics-based numerical ocean models and six MDTs computed from observed geodetic and/or ocean data at 32 tide gauges around the Australian coast. We focus on the viability of numerical ocean models for vertical datum unification, classifying the 13 ocean models used as either independent (do not contain assimilated geodetic data) or non-independent (do contain assimilated geodetic data). We find that the independent and non-independent ocean models deliver similar results. Maximum differences among ocean models and geodetic MDTs reach >150 mm at several Australian tide gauges and are considered anomalous at the 99% confidence level. These differences appear to be of geodetic origin, but without additional independent information, or formal error estimates for each model, some of these errors remain inseparable. Our results imply that some ocean models have standard deviations of differences with other MDTs (using geodetic and/or ocean observations) at Australian tide gauges, and with levelling between some Australian tide gauges, of \({\sim }\pm 50\,\hbox {mm}\). This indicates that they should be considered as an alternative to geodetic MDTs for the direct unification of vertical datums. They can also be used as diagnostics for errors in geodetic MDT in coastal zones, but the inseparability problem remains, where the error cannot be discriminated between the geoid model or altimeter-derived mean sea surface.     

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。     

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。     

顾及海岸线地理弯曲特征约束的可控分形插值方法

针对海岸线分形插值缺乏地理特征约束和分形过程不可控的局限,提出了一种顾及海岸线地理弯曲特征约束的可控分形插值方法。首先,根据不同海岸地貌类型所呈现的不同弯曲特征和分形特征,对海岸线进行地貌单元划分,将传统的整体分形插值变换为以海岸线地貌弯曲特征为划分单元的分段插值组合;其次,利用一维随机中点移位法对各划分单元分别进行插值,并结合各划分单元的弯曲特征对分形参量分别进行约束控制,以保持海岸线不同地貌单元的弯曲特征;最后,将各插值单元顺次连接起来得到最终插值曲线。实验结果表明,所提方法能够很好地顾及海岸线不同地貌单元的弯曲特征和分形特征,且分形插值过程可控。     

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     

联合机载LiDAR数据和潮汐数据自动提取潮位线

首先,联合机载激光雷达(LiDAR)数据提取的海岸带数字表面模型(DSM)与验潮站数据提取的高、低潮面进行相交运算,生成"水陆二值图像",然后对其以提取边缘的方式提取高、低潮潮位线;针对LiDAR光束无法穿透水体导致低潮线附近DSM为无效值的缺陷,采取移动趋势面拟合法外推概略低潮线附近DSM,在此基础上重新提取更精确的低潮潮位线。实验表明,该方法能在较少人工干预的情况下有效提取高、低潮潮位线。