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.     

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.     

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     

海潮负荷对GPS精密定位的影响

根据海潮负荷理论,利用4种全球海潮模型分别计算了中国及周边地区IGS站的海潮负荷位移系数,分析并比较了海潮负荷位移对GPS单天解和短周期解的影响。结果表明,对于测站的单天解,不同海潮负荷位移改正对测站整体上没有影响,只在局部沿海地区测站的垂向方向存在差异;并且,4种全球海潮模型在黄海和东海的近海区域不够精确,需要利用我国近海区域的海潮资料进行修正;对于测站的短周期解,海潮负荷位移的影响随着测站远离海洋而减弱,特别是在沿海地区能显著提高测站的垂向坐标精度。因此,在短时的GPS精密定位中需要考虑海潮负荷位移改正。     

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)。      

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.     

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.     

Determination of the free core nutation period from tidal gravity observations of the GGP superconducting gravimeter network

This study is based on 25 long time-series of tidal gravity observations recorded with superconducting gravimeters at 20 stations belonging to the Global Geodynamic Project (GGP). We investigate the diurnal waves around the liquid core resonance, i.e., K ₁, ψ₁ and φ₁, to determine the free core nutation (FCN) period, and compare these experimental results with models of the Earth response to the tidal forces. For this purpose, it is necessary to compute corrected amplitude factors and phase differences by subtracting the ocean tide loading (OTL) effect. To determine this loading effect for each wave, it was thus necessary to interpolate the contribution of the smaller oceanic constituents from the four well determined diurnal waves, i.e., Q ₁, O ₁, P ₁, K ₁. It was done for 11 different ocean tide models: SCW80, CSR3.0, CSR4.0, FES95.2, FES99, FES02, TPXO2, ORI96, AG95, NAO99 and GOT00. The numerical results show that no model is decisively better than the others and that a mean tidal loading vector gives the most stable solution for a study of the liquid core resonance. We compared solutions based on the mean of the 11 ocean models to subsets of six models used in a previous study and five more recent ones. The calibration errors put a limit on the accuracy of our global results at the level of ± 0.1%, although the tidal factors of O ₁ and K ₁ are determined with an internal precision of close to 0.05%. The results for O ₁ more closely fit the DDW99 non-hydrostatic anelastic model than the elastic one. However, the observed tidal factors of K ₁ and ψ₁ correspond to a shift of the observed resonance with respect to this model. The MAT01 model better fits this resonance shape. From our tidal gravity data set, we computed the FCN eigenperiod. Our best estimation is 429.7 sidereal days (SD), with a 95% confidence interval of (427.3, 432.1).     

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.     

用东海和南海潮汐资料修正全球海潮模型对中国及邻区重力场负荷计算的影响

利用卫星测高技术建立的全球海潮模型的精度和分辨率均有限,而高精度、高分辨率的近海区域潮汐观测资料,可用于改善和提高全球海潮模型在沿海地区的精度。利用中国东海和南海的近海海潮模型,对HAMTIDE11A.2011全球海潮模型中的中国近海区域进行了替换,并得到了修正前后模型计算的海潮负荷对不同区域GPS测站精密定位的影响。分析可得:(1)确认修正前后的全球海潮模型计算的海潮负荷对GPS测站精密定位的影响存在约5 mm的差异,并通过频谱分析得到修正后的模型在GPS精密定位中剔除海潮负荷影响的效果在半日、周日及半年周期处明显优于修正前的模型;(2)采用高精度近海模型进一步修正全球海潮模型,该成果对近海区域的GPS精密定位海潮负荷改正具有一定参考价值。     

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。     

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.     

Sub-daily alias and draconitic errors in the IGS orbits

Harmonic signals with a fundamental period near the GPS draconitic year (351.2 days) and overtones up to at least the sixth multiple have been observed in the power spectra of nearly all products of the International GNSS Service (IGS), including station position time series, apparent geocenter motions, orbit jumps between successive days, and midnight discontinuities in earth orientation parameter (EOP) rates. Two main mechanisms have been suggested for the harmonics: mismodeling of orbit dynamics and aliasing of near-sidereal local station multipath effects. Others have studied the propagation of local multipath errors into draconitic position variations, but orbit-related processes have been less examined. We elaborate our earlier analysis of GPS day-boundary orbit discontinuities where we observed some draconitic features as well as prominent spectral bands near 29-, 14-, 9-, and 7-day periods. Finer structures within the sub-seasonal bands fall close to the expected alias frequencies for 24-h sampling of sub-daily EOP tide lines but do not coincide precisely. While once-per-revolution empirical orbit parameters should strongly absorb any sub-daily EOP tide errors due to near-resonance of their respective periods, the observed differences require explanation. This has been done by simulating EOP tidal errors and checking their impact on a long series of estimated daily GPS orbits and EOPs. Indeed, simulated tidal aliases are found to be very similar to the observed IGS orbital features in the sub-seasonal bands. Moreover and unexpectedly, some low draconitic harmonics were also produced, potentially a source for the widespread errors in most IGS products. The results from this study are further evidence for the need of an improved sub-daily EOP tide model.     

联合GRACE/GOCE重力场模型和GPS/水准数据确定我国85高程基准重力位

GRACE、GOCE卫星重力计划的实施,对确定高精度重力场模型具有重要贡献。联合GRACE、GOCE卫星数据建立的重力场模型和我国均匀分布的649个GPS/水准数据可以确定我国高程基准重力位,但我国高程基准对应的参考面为似大地水准面,是非等位面,将似大地水准面转化为大地水准面后确定的大地水准面重力位为62 636 854.395 3m~2s~(-2),为提高高阶项对确定大地水准面的贡献,利用高分辨率重力场模型EGM2008扩展GRACE/GOCE模型至2190阶,同时将重力场模型和GPS/水准数据统一到同一参考框架和潮汐系统,最后利用扩展后的模型确定的我国大地水准面重力位为62 636 852.751 8m~2s~(-2)。其中组合模型TIM_R4+EGM2008确定的我国85高程基准重力位值62 636 852.704 5m~2s~(-2)精度最高。重力场模型截断误差对确定我国大地水准面的影响约16cm,潮汐系统影响约4~6cm。     

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.     

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.     

联合GRACE与GPS比较山西省垂向地表形变

利用2009-05~2010-12共20 mon的GRACE时变重力场反演了山西省境内陆地水储量变化造成的地表垂直位移,并与同期的GPS高程残差进行了比较。结果显示,对大部分CORS站而言,GRACE反演的水文地壳垂向形变与GPS高程残差时间序变化量均在-6~6 mm之间;由二者提取的年周期信号平均振幅均为2.5 mm左右,但是相位存在较大差异。由于GPS数据处理过程未考虑周日、半周日大气潮汐,高阶电离层,及非潮汐海潮的影响,这三项误差会传播到测站坐标的时间序列,对GPS周年信号产生影响,所以可以认为GRACE与GPS结果的差异更多的是来自GPS数据处理的误差。     

Non-linear motions of Australian geodetic stations induced by non-tidal ocean loading and the passage of tropical cyclones

We investigate daily and sub-daily non-tidal oceanic and atmospheric loading (NTOAL) in the Australian region and put an upper bound on potential site motion examining the effects of tropical cyclone Yasi that crossed the Australian coast in January/February 2011. The dynamic nature of the ocean is important, particularly for northern Australia where the long-term scatter due to daily and sub-daily oceanic changes increases by 20–55 % compared to that estimated using the inverted barometer (IB) assumption. Correcting the daily Global Positioning System (GPS) time series for NTOAL employing either a dynamic ocean model or the IB assumption leads to a reduction of up to 52 % in the weighted scatter of daily coordinate estimates. Differences between the approaches are obscured by seasonal variations in the GPS precision along the northern coast. Two compensating signals during the cyclone require modelling at high spatial and temporal resolution: uplift induced by the atmospheric depression, and subsidence induced by storm surge. The latter dominates ( \(>\) 135 %) the combined net effect that reaches a maximum of 14 mm, and 10 mm near the closest GPS site TOW2. Here, 96 % of the displacement is reached within 15 h due to the rapid transit of cyclones and the quasi-linear nature of the coastline. Consequently, estimating sub-daily NTOAL is necessary to properly account for such a signal that can be 3.5 times larger than its daily-averaged value. We were unable to detect the deformation signal in 2-hourly GPS processing and show that seasonal noise in the Austral summer dominates and precludes GPS detection of the cyclone-related subsidence.     

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。