A preliminary study on the establishment of ocean tide models over the South China Sea from T/P altimetry

On the basis of the characteristic of the perfect spatial distribution of the T/P altimeter data, a spatial harmonic tidal analysis is performed, which transfers tidal harmonic constantsH andg of each constituent into a pair of parameters: the cosine part U and sine partV. And each part is expanded into a polynomial. The polynomial coefficients are estimated with altimeter data upon the least squares criteria. Thus the models of principal tidal waves in the South China Sea are established. 72 cycles of T/P data from cycle 11 through 82 are included in the calculation. The models are evaluated with different approaches and data set. The conclusions are that the tide modes can provide partial tide amplitudes with 3 cm accuracy, and that phase lags deviation of those tides with amplitude large than 10 cm are within ±10°.     

Algorithm for Harmonic Tidal Analysis along T/P Tracks： Taking Differences of Observed Sea Surface Heights at Adjacent Points as Observations

An algorithm （differential mode） is presented for the improvement of harmonic tidal analysis along T/P tracks, in which the differences between the observed sea surface heights at adjacent points are taken as observations. Also, the observation equations are constrained with the results of the crossover analysis; the parameter estimations are performed at 0.1° latitude intervals by the least squares. Cycle 10 to 330 T/P altimeter data covering the China Sea and the Northwest Pacific Ocean （2°-50° N,105°-150° E） are adopted for a refined along-track harmonic tidal analysis, and harmonic constants of 12 constituents in 8 474 points are obtained, which indicates that the algorithm can efficiently remove non-tidal effects in the altimeter observations, and improve the precision of tide parameters. Moreover, parameters along altimetry tracks represent a smoother distribution than those obtained by traditional algorithms. The root mean squares of the fitting errors between the tidal height model and the observations reduce from 11 cm to 1.3 cm.     

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     

基于不同潮汐类型的不同时间尺度分潮结果精度分析

选取4种不同潮汐类型的验潮站实测潮位资料,对验潮零点在一定范围内变动对调和分析结果的影响进行分析,结果表明,一年的潮位数据中若后续6个月的数据发生10 cm、20 cm、30 cm零点漂移,各分潮振幅最大变化量为0.47 cm,迟角为0.16°。采用1~12个月不同中期尺度的实测数据,对调和结果的精度进行分析,结果表明,当潮位观测数据时间尺度小于6个月时,其4个主要分潮O_1、K_1、M_2、S_2振幅综合中误差在2 cm以上,迟角中误差在2°以上,具有显著的不稳定性;相同时间尺度的不同潮汐类型的潮位站潮位资料调和分析得到的主要分潮的振幅精度差异较大,迟角分布相似。当潮位观测数据时间尺度达到或多于6个月时,澳门站、汕尾站的分潮综合中误差分别为1.16 cm、0.61 cm,厦门站、北海站分别为2.90 cm和2.51 cm;各分潮迟角中误差均在2°内。当时间尺度超过9个月后,4个验潮站分潮振幅综合中误差均在2 cm以内,各分潮迟角中误差均在1°左右。     

以相邻点海面高度差为观测量的沿迹调和分析新方法

采用TOPEX/POSEIDON卫星轨迹上相邻点的海面高差作为观测量,在交叉点分析结果的控制下构成同一弧段上观测量在两相邻交叉点间的综合观测方程,以轨迹上纬差0.1°的正常点的潮汐参数构成总体待估参数系列,实施最小二乘综合解算。分析结果表明,这种差分模式可以基本消除非潮汐因素的影响,提高潮汐参数估计的精度和可靠性,可比一般沿迹逐点分析给出更为平滑的沿迹参数分布,更符合海洋潮汐运动的物理背景。     

利用TOPEX/Poseidon和Jason-1高度计数据提取中国南海潮汐信息

基于TOPEX/Poseidon和Jason-1卫星高度计16 a原始轨道、6 a变轨轨道数据,利用同步观测期间测高数据计算中国南海海域的系统偏差,生成基于TOPEX/Poseidon高度计平均海面的统一潮高时间序列,按纬差0.1°间隔提取原始轨道2 184个正常点和变轨轨道1 626个正常点,分别对原始轨道、变轨轨道逐正常点进行调和分析及响应分析,各得到8个分潮（Q₁、O₁、P₁、K₁、N₂、M₂、S₂和K₂）调和常数。利用交叉点处升轨、降轨不符值评估潮汐参数的稳定性,结果表明,变轨轨道交叉点处误差相对较大,多分潮总体综合预报误差RSS值为7.28 cm。通过与全球海潮模型比较表明,该结果与海潮模型在中国南海开阔海域精度表现一致,在半封闭浅水海域差异较大;与验潮站结果进行比较发现,受中国南海复杂的潮波系统、与测高星下点距离等因素影响,中国南海北部海域RSS值较大,海潮模型结果在M₂分潮单分潮预报中误差RMS值较大,为13.64 cm,其余分潮均在10 cm内。     

Long-wavelength global gravity field models: GRIM4-S4, GRIM4-C4

Summary.  GFZ Potsdam and GRGS Toulouse/Grasse jointly developed a new pair of global models of the Earth's gravity field to satisfy the requirements of the recent and future geodetic and altimeter satellite missions. A precise gravity model is a prerequisite for precise satellite orbit restitution, tracking station positioning and altimeter data reduction. According to different applications envisaged, the new model exists in two parallel versions: the first one being derived exclusively from satellite tracking data acquired on 34 satellites, the second one further incorporating satellite altimeter data over the oceans and terrestrial gravity data. The most recent “satellite-only” gravity model is labelled GRIM4-S4 and the “combined” gravity model GRIM4-C4. The models are solutions in spherical harmonics and have a resolution up to degree and order 60 plus a few resonance terms in the case of GRIM4-S4, and up to degree/order 72 in the case of GRIM4-C4, corresponding to a spatial resolution of 555 km at the Earth's surface. The gravitational coefficients were estimated in a rigorous least squares adjustment simultaneously with ocean tidal terms and tracking station position parameters, so that each gravity model is associated with a consistent ocean tide model and a terrestrial reference frame built up by over 300 optical, laser and Doppler tracking stations. Comprehensive quality tests with external data and models, and test arc computations over a wide range of satellites have demonstrated the state-of-the-art capabilities of both solutions in long-wavelength geoid representation and in precise orbit computation. Received 1 February 1996; Accepted 17 July 1996     

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.     

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.     

Temporal and spatial variability of the bias between TOPEX- and GPS-derived total electron content

Total electron content (TEC) predictions made with the GPS-based la plata ionospheric model (LPIM) and the International Reference Ionosphere (IRI95) model were compared to estimates from the dual-frequency altimeter onboard the TOPEX/Poseidon (T/P) satellite. LPIM and IRI95 were evaluated for the location and time of available T/P data, from January 1997 to December 1998. To investigate temporal and spatial variations of the TEC bias between T/P and each model, the region covered by T/P observations was divided into ten latitude bands. For both models and for all latitudes, the bias was mainly positive (i.e. T/P values were larger); the LPIM bias was lower and less variable than the IRI95 bias. To perform a detailed analysis of temporal and spatial variability of the T/P-LPIM TEC bias, the Earth’s surface was divided into spherical triangles with 9°-sides, and a temporally varying regression model was fitted to every triangle. The highest TEC bias was found over the equatorial anomalies, which is attributed to errors in LPIM. A significant TEC bias was found at 40°N latitude, which is attributed to errors in the T/P Sea State Bias (SSB) correction. To separate systematic errors in the T/P TEC from those caused by LPIM, altimeter range biases estimated by other authors were analysed in connection with the TEC bias. This suggested that LPIM underestimates the TEC, particularly during the Southern Hemisphere summer, while T/P C-band SSB calibration is worse during the Southern Hemisphere winter.     

联合TOPEX/Poseidon与Geosat/ERM测高资料建立区域潮汐模型的研究

利用近十年的T/P测高数据来反演南海(8°~23°N,109°~120°E)九个主要分潮的潮汐参数,并计算了Geosat/ERM卫星对应的各主分潮的混叠周期及Rayleigh周期。根据潮汐参数提取的要求,选取了7个主分潮,为了克服混叠影响,将T/P沿迹点处的主要分潮间的5组差比关系引入到Geosat沿迹点处,并利用T/P提供的Sa模型去除Sa对M2的扰动影响。精度估计的结果表明,Geosat/ERM反演的潮汐参数的精度与传统的月分析结果的精度相近;因差比关系的捆绑,整个全日和半日潮族迟角偏差相近,这主要和Geosat/ERM的轨道设计有关。本文的方法可以应用于利用轨道调整后的T/P卫星的测高数据提取潮汐参数。     

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.     

Ocean tides from T/P, ERS-1, and GEOSAT altimetry

 Aliasing of the diurnal and semi-diurnal tides is a major problem when estimating the ocean tides from satellite altimetry. As a result of aliasing, the tides become correlated and many years of altimeter observations may be needed to seperate them. For the three major satellite altimetry missions to date i.e., GEOSAT, ERS-1, and TOPEX/POSEIDON (T/P), the alias periods as well as the Rayleigh periods over which the tides decorrelate can be identified. Especially in case of GEOSAT and ERS-1, severe correlation problems arise. However, it is shown by means of covariance analyses that the tidal phase advance differences on crossing satellite groundtracks can significantly reduce the correlations among the diurnal and semi-diurnal tides and among these tides and the seasonal cycles of ocean variability. Therefore, it has been attempted to solve a multi-satellite response tidal solution for the diurnal and semi-diurnal bands from a total of 7 years of altimetry. Unfortunately, it could be shown that the GEOSAT and ERS-1 orbit errors are too large to improve a 3-year T/P tidal solution with about 2 years of GEOSAT and 2 years of ERS-1 altimeter observations. However, these results are preliminary and it is expected that more accurate orbits, which have become available recently for ERS-1, and additional altimeter data from ERS-2 and the GEOSAT Follow-On (GFO) should lead to an improved T/P tidal model. Received: 4 May 1999 / Accepted: 24 January 2000     

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。     

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).     

Ocean tidal parameters from starlette data

Starlette was launched in 1975 in order to study temporal variations in the Earth’s gravity field; in particular, tidal and Earth rotation effects. For the period April 1983 to April 1984 over12,700 normal points of laser ranging data to Starlette have been sub-divided into49 near consecutive 5–6 day arcs. Normal equations for each arc as obtained from a least-squares data reduction procedure, were solved for ocean tidal parameters along with other geodetic and geodynamic parameters. The tidal parameters are defined relative to Wahr’s body tides and Wahr’s nutation model and show fair agreement with other satellite derived results and those obtained from spherical harmonic decomposition of global ocean tidal models.     

Dual-satellite crossover latitude-lumped coefficients, their use in geodesy and oceanography

Latitude-lumped coefficients (LLC) are defined, representing geopotential-orbit variations for dual-satellite crossovers (DSC). Formulae are derived for their standard errors from the covariances of geopotential field models. Numerical examples are presented for pairs of the altimeter-bearing satellites TOPEX/Poseidon, ERS 1, and Geosat, using the error matrices of recent gravity models. The DSC, connecting separate missions, will play an increasingly important role in oceanography spanning decades only when its nonoceanographic signals are thoroughly understood. In general, the content of even the long-term averaged DSC is more complex then their single satellite crossover (SSC) counterpart. The LLC, as the spatial spectra for the geopotential-caused crossover effects, discriminate these source-differences sharply. Thus, the zero-order LLC in DSC data contains zonal gravity information not present in SSC data. In addition, zero- and first-order LLC of DSC data can reveal a geocenter discrepancy between the orbit tracking of the separate satellite missions. For example, DSC analysis from orbits computed with JGM 2 show that the y-axis of the geocenter for Geosat in 1986–1988 is shifted with respect to T/P by 6–9 cm towards the eastern Pacific. Also, where the time-gap is necessarily large (as between, say, Geosat and T/P missions) oceanographic (sea-level) differences in DSC may corrupt the geopotential interpretation of the data. Most importantly, as we illustrate, media delays for the altimeter (from the ionosphere, wet troposphere and sea-state bias) are more likely sources of contamination across two missions than in SSC analyses. Again, the LLC of zero order best shows this contrast. Using the higher-order LLC of DSC for both Geosat-T/P and ERS 1-T/P as likely representation of geopotential-only error, we show by comparison with the predicted standard errors of JGM 2 that the latter's previously calibrated covariance matrix is generally valid. Received: 14 February 1996 / Accepted: 27 March 1997     

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.     

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。     

利用经优化的边界条件开展黄海海州湾潮汐场模拟

受海底地形、开边界驱动水位及底摩擦系数等边界条件的共同影响,当前中国沿岸和近海潮汐场模拟的精度仍显不足。利用精度和分辨率较海图高一级别的水深数据、包含长周期天文气象分潮Sa的由12个主分潮组成的开边界驱动水位及顾及水深空间变化的底摩擦系数等经优化的边界条件,运行二维潮汐数值模式2D-MIKE21,开展黄海海州湾潮汐场模拟。结果表明,天文潮模拟值与海州湾周边6个验潮站1年潮汐表相比,12个主分潮综合预报误差为5.52 cm;与中国海域现有潮汐模型CST1中24个随机点位相比,12个主分潮综合预报误差为7.10 cm。天文潮模拟值和CST1预报值二者与海州湾周边2个验潮站近1个月实测值相比,前者中误差要小于后者。这为在沿岸及近海开展面向海洋测绘应用的潮汐场模拟提供了新思路,同时也表明通过数值模拟的方式构建天文气象分潮Sa是可行的。