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.     

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.     

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.     

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。     

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.     

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 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.     

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。     

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.     

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.     

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。     

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 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.     

佘山台倾斜固体潮观测的海潮负荷改正

采用FARRELL的负荷理论以及最新的TPXO6海潮模型和中国近海潮汐资料计算了海潮负荷对佘山台倾斜固体潮的影响,采用BAYTAP-G调和分析软件对佘山台倾斜固体潮观测进行了处理,获得不同潮波的潮汐参数。在此基础上进行海潮负荷改正。负荷改正后,东西分量的振幅因子和相位滞后与理论值较为接近,而南北分量的半日波振幅因子与理论值仍有较大的偏离。结果说明,佘山台倾斜东西分量主要受海潮负荷的影响,超过60%,甚至达到96%(O1);而南北分量受到的非潮汐的影响要比东西分量受到的影响大,如N2波甚至高达70%,但是这也可能是和海潮模型在近海的不精确有关。     

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。     

Strategies for High Precision Processing of GPS Measurements with Application to the Amery Ice Shelf,East Antarctica

A number of statistic Global Positioning System (GPS) measurement campaigns have been made on a floating Antarctic ice shelf, the Amery Ice Shelf, as part of ongoing glaciological studies designed to investigate the ice shelf dynamics, grounding zone definition, and ice shelf strain. Such studies ar fundamental to improving out knowledge of the Antarctic ice-sheet mass balance and dynamical models of ice sheet/ocean interaction. This article describes two techniques used to process the statistic GPS data. One approach uses a segmented version of the classical static methodology, and the other approach adopts a new sequential processing technique. Both approaches yield similar results for the station coordinates and demonstrate the potential of GPS for extracting the tidal signal on the ice shelves and giving information on the dynamical motion of the ice sheet. To verify our results for the vertical component, we compare the ice shelf GPS tidal signal with a tidal model derived from tide gauge measurements at nearby Beaver Lake. Comparison of the GPS results with the tide model give good agreement in amplitude at the few cm level (GPS results always larger) but clearly shows evidence of phase propagation of the ocean tidal wave under the ice shelf. Improving the resolution of the tides over the ice shelves will be of tremendous benefit for future satellite missions, such as Ice, Cloud and Land Elevation Satellite (ICESAT), and the integrated use of GPS and satellite data will be fundamental for any on-going Antarctic ice sheet mass balance studies. ? 2000 John Wiley & Sons, Inc.     

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     

Analysis of the first year of Earth rotation parameters with a sub-daily resolution gained at the CODE processing center of the IGS

 The solutions of the CODE Analysis Center submitted to the IGS, the International Global Position System (GPS) Service for Geodynamics, are based on three days of observation of about 80–100 stations of the IGS network. The Earth rotation parameters (ERPs) are assumed to vary linearly over the three days with respect to an a priori model. Continuity at the day boundaries as well as the continuity of the first derivatives are enforced by constraints. Since early April 1995 CODE has calculated a new ERP series with an increased time resolution of 2 hours. Again continuity is enforced at the 2-hours-interval boundaries. The analysis method is described, particularly how to deal with retrograde diurnal terms in the ERP series which may not be estimated with satellite geodetic methods. The results obtained from the first year of data covered by the time series (time interval from 4 April 1995 to 30 June 1996) are also discussed. The series is relatively homogeneous in the sense of the used orbit model and the a priori model for the ERPs. The largest source of excitation at daily and sub-daily periods is likely to be the effect of the ocean tides. There is good agreement between the present results and Topex/Poseidon ocean tide models, as well as with models based on Very Long Baseline Interferometry (VLBI) and Satellite Laser Ranging (SLR) data. Non-oceanic periodic variations are also observed in the series. Their origin is most probably a consequence of the GPS solution strategy; other possible sources are the atmospheric tides. Received: 13 July 1999 / Accepted: 21 March 2000     

应用人卫激光测距技术测定潮汐形变勒夫数

本文讨论了利用人卫激光测距（ＳＬＲ）资料确定分潮波形式的地球固体潮汐形变勒夫数的可能性,并用１１年的Ｌａｇｅｏｓ－１的人卫激光测跨资料直接解算了四个周日波Ｑ、,Ｏ１,Ｐ１,Ｋ１和四个半日波Ｓ２,Ｋ２,Ｎ２,Ｍ２的弹性和粘弹性地球状态下的地球潮汐形变勒夫数ｈ２ｓ,ｌ２ｓ,结果与ＶＬＢＩ结果相符,与ＩＥＲＳ及Ｗａｈｒ的模型值的潮汐响应趋势相符,这证明了利用ＳＬＲ技术确定潮汐形变勒失数是可行的,从而为传统技术和空间技术提供了一种新的有意义的方法和选择。     

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。