A study of regional gravity field recovery from GOCE vertical gravity gradient data in the Auvergne test area using collocation

Gravity field and steady-state Ocean Circulation Explorer (GOCE) is the first satellite mission that observes gravity gradients from the space, to be primarily used for the determination of high precision global gravity field models. However, the GOCE gradients, having a dense data distribution, may potentially provide better predictions of the regional gravity field than those obtained using a spherical harmonic Earth Geopotential Model (EGM). This is investigated in Auvergne test area using Least Squares Collocation (LSC) with GOCE vertical gravity gradient anomalies (T_zz), removing the long wavelength part from EGM2008 and the short wavelength part by residual terrain modelling (RTM). The results show that terrain effects on the vertical gravity gradient are significant at satellite altitude, reaching a level of 0.11 E?tv?s unit (E.U.) in the mountainous areas. Removing the RTM effects from GOCE T_zz leads to significant improvements on the LSC predictions of surface gravity anomalies and quasigeoid heights. Comparison with ground truth data shows that using LSC surface free air gravity anomalies and quasi-geoid heights are recovered from GOCE T_zz with standard deviations of 11 mGal and 18 cm, which is better than those obtained by using GOCE EGMs, demonstrating that information beyond the maximal degree of the GOCE EGMs is present. Investigation of using covariance functions created separately from GOCE T_zz and terrestrial free air gravity anomalies, suggests that both covariance functions give almost identical predictions. However, using covariance function obtained from GOCE T_zz has the effect that the predicted formal average error estimates are considerably larger than the standard deviations of predicted minus observed gravity anomalies. Therefore, GOCE T_zz should be used with caution to determine the covariance functions in areas where surface gravity anomalies are not available, if error estimates are needed.     

GOCE Quick-Look Gravity Solution: Application of the Semianalytic Approach in the Case of Data Gaps and Non-Repeat Orbits

The satellite mission GOCE (Gravity Field and Steady-State Ocean Circulation Explorer), the first Core Mission of the Earth Explorer Programme funded by ESA (European Space Agency), is dedicated to the precise modelling of the Earth's gravity field, with its launch planned for 2006. The mathematical models for parameterizing the Earth's gravity field are based on a series expansion into spherical harmonics, yielding a huge number of unknown coefficients. Their computation leads to the solution of very large normal equation systems. An efficient way to handle these equation systems is the so-called semianalytic or lumped coefficients approach, which theoretically requires an uninterrupted, continuous time series of observations, recorded along an exact circular repeat orbit. In this paper the consequences of violating these conditions are analyzed. The effects of an interrupted observation stream onto the estimated spherical harmonic coefficients are demonstrated, and an iterative strategy, which reduces the negative influence depending on the characteristics of the data gaps, is proposed. Additionally, the impact of an imperfectly closing orbit (non-repeat orbit) on the gravity field model is analyzed, and a strategy to minimize the corresponding errors is presented. The applicability of the semianalytic approach also to a joint inversion of satellite-to-satellite tracking data in high-low mode (hl-SST) and satellite gravity gradiometry (SGG) observations is demonstrated, where the analysis of the former component is based on the energy conservation law. Several realistic case studies prove that the semianalytic approach is a feasible tool to generate quick-look gravity solutions, i.e. fast coefficient estimates using only partial data sets. This quick-look analysis shall be able to detect potential distortions of statistical significance (e.g. systematic errors) in the input data, and to give a fast feedback to the GOCE mission control.     

基于时空域混合法利用Kaula正则化精确和快速解算GOCE地球重力场

为了研究卫星重力梯度技术对中高频地球重力场反演精度的影响,本文基于时空域混合法,利用Kaula正则化反演了250阶GOCE地球重力场.模拟结果表明:第一,时空域混合法是精确和快速求解高阶地球重力场的有效方法;第二,Kaula正则化是降低正规阵病态性的重要方法;第三,基于改进的预处理共轭梯度迭代法可快速求解大型线性方程组...     

RTM-based omission error corrections for global geopotential models: Case study in Central Europe

The aim of this paper is to evaluate the effects of residual terrain model (RTM) on potential and on gravity and to point out how significant can the omission error of global geopotential models (GGMs) be and how it can influence their testing. The RTM for Central Europe is computed in the spherical approximation. The topography is modelled by spherical tesseroids and the gravitational effect of the topography is obtained as a sum of their partial gravitational effects. A detailed picture of RTM in Slovakia is shown. The testing of GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) global geopotential models in Central Europe published earlier is re-evaluated with the more rigorous omission error estimation. Experimental results show significantly better agreement between the gravity anomalies computed from global geopotential models with the omission-error estimation and gravity anomalies obtained from the direct measurements. On the other hand, for height anomalies such an improvement is not observed. The results are discussed in context of the other previously published studies.     

GRACE/GOCE扩展重力场模型确定我国1985高程基准重力位的精度分析

高精度高程基准重力位的确定往往依赖于高精度全球重力场模型,其对全球和区域高程基准的高精度统一非常关键,GRACE、GOCE卫星重力计划极大地提高了全球重力场模型中长波的精度.本文首先对GRACE/GOCE卫星重力场模型的内符合和外符合精度进行讨论分析,结果说明卫星重力模型的截断误差影响可达到分米级水平,在确定高程基准重力位时该影响不可忽略.利用EGM2008模型扩展GRACE/GOCE卫星重力场模型至2190阶,可有效减弱卫星重力模型的截断误差影响,但不同模型扩展时的最优拼接阶次不同,其中DIR-1、DIR-5模型对应的最优拼接阶次分别为180阶和220阶,以GPS水准数据检验,扩展模型在中国区域的精度均优于18cm.最后,基于最优拼接阶次获得的扩展重力场模型对我国1985高程基准重力位进行了估计,DIR-5和TIM-5模型对应数值分别为62636853.47m~2·s~(-2)和62636853.49m~2·s~(-2),精度均为1.51m~2·s~(-2);发现在中国区域模型大地水准面与GPS/水准数据的差值存在微弱的系统性倾斜,东西向倾斜约为9cm,南北向倾斜约为1.4cm,考虑倾斜改正后基于DIR-5和TIM-5模型估计我国1985高程基准重力位的精度提高了0.16m~2·s~(-2).     

On High-Frequency Topography-Implied Gravity Signals for a Height System Unification Using GOCE-Based Global Geopotential Models

National height reference systems have conventionally been linked to the local mean sea level, observed at individual tide gauges. Due to variations in the sea surface topography, the reference levels of these systems are inconsistent, causing height datum offsets of up to ±1–2 m. For the unification of height systems, a satellite-based method is presented that utilizes global geopotential models (GGMs) derived from ESA’s satellite mission Gravity field and steady-state Ocean Circulation Explorer (GOCE). In this context, height datum offsets are estimated within a least squares adjustment by comparing the GGM information with measured GNSS/leveling data. While the GNSS/leveling data comprises the full spectral information, GOCE GGMs are restricted to long wavelengths according to the maximum degree of their spherical harmonic representation. To provide accurate height datum offsets, it is indispensable to account for the remaining signal above this maximum degree, known as the omission error of the GGM. Therefore, a combination of the GOCE information with the high-resolution Earth Gravitational Model 2008 (EGM2008) is performed. The main contribution of this paper is to analyze the benefit, when high-frequency topography-implied gravity signals are additionally used to reduce the remaining omission error of EGM2008. In terms of a spectral extension, a new method is proposed that does not rely on an assumed spectral consistency of topographic heights and implied gravity as is the case for the residual terrain modeling (RTM) technique. In the first step of this new approach, gravity forward modeling based on tesseroid mass bodies is performed according to the Rock–Water–Ice (RWI) approach. In a second step, the resulting full spectral RWI-based topographic potential values are reduced by the effect of the topographic gravity field model RWI_TOPO_2015, thus, removing the long to medium wavelengths. By using the latest GOCE GGMs, the impact of topography-implied gravity signals on the estimation of height datum offsets is analyzed in detail for representative GNSS/leveling data sets in Germany, Austria, and Brazil. Besides considerable changes in the estimated offset of up to 3 cm, the conducted analyses show that significant improvements of 30–40% can be achieved in terms of a reduced standard deviation and range of the least squares adjusted residuals.     

Satellite gravity gradiometry: Secular gravity field change over polar regions

The ESA Gravity and steady state Ocean and Circulation Explorer, GOCE, mission will utilise the principle of satellite gravity gradiometry to measure the long to medium wavelengths in the static gravity field. Previous studies have demonstrated the low sensitivity of GOCE to ocean tides and to temporal gravity field variations at the seasonal scale. In this study we investigate the sensitivity of satellite gradiometry missions such as GOCE to secular signals due to ice-mass change observed in Greenland and Antarctica. We show that unaccounted ice-mass change signal is likely to increase GOCE-related noise but that the expected present-day polar ice-mass change is below the GOCE sensitivity for an 18-month mission. Furthermore, 2–3 orders of magnitude improvement in the gradiometry in future gradiometer missions is necessary to detect ice-mass change with sufficient accuracy at the spatial resolution of interest.     

GOCE Gravity Field Processing Strategy

A processing strategy and the corresponding software architecture for the processing of GOCE (Gravity field and steady-state Ocean Circulation Explorer) observables is presented and described, with the major objective to compute a high-accuracy, high-resolution spherical harmonic model of the Earth's gravity field. The combination of two numerical solution strategies, i.e. the rigorous solution of the corresponding large normal equation systems applying parallel processing (on a PC cluster) as the core solver, and the fast semianalytic approach as a quick-look gravity field analysis (QL-GFA) tool, is proposed. Such a method fusion benefits from the advantages of the individual components: the rigorous inversion of the system providing also the full variance-covariance information, and the quickness enabling the consecutive production of intermediate gravity field solutions, for the purpose to analyse partial and incomplete data sets and to derive a diagnosis of the performance of the GOCE measurement system. The functionality and operability of the individual components are demonstrated in the framework of a closed loop simulation, which is based on a realistic mission scenario both in terms of the orbit configuration and the coloured measuring noise. Special concern is given to the accuracy of the recovered coefficients, the numerical behaviour, the required computing time, and the particular role of the individual modules within the processing chain. In the case of the core solver, it is demonstrated that the assembling and rigorous solution of large normal equation systems can be handled by using Beowulf clusters within a reasonable computing time. The application of the quick-look tool to partial data sets with short-term data gaps is demonstrated on the basis of several case studies. Additionally, the spectral analysis of the residuals of the adjustment is presented as a valuable tool for the verification of the noise characteristics of the GOCE gradiometer.     

重力卫星精密星间测距系统滤波器技术指标论证

本文基于重力卫星精密星间测距测量模式,从星间测距观测值与地球重力场频谱关系的角度,建立了距离观测值关于重力位系数的敏感矩阵,分析了各阶次重力场位系数对应的敏感矩阵的频谱特性,讨论了星间测距信息中能反应地球重力场信息的有效信号频带,给出了能最大限度保留地球重力场信息的低通滤波器的通带截止频率、通带增益波纹和频率采样率技术指标设计方案,可为我国首期卫星跟踪卫星重力测量计划的主要技术指标的初步设计提供参考.     

Impact of GOCE Level 1b data reprocessing on GOCE-only and combined gravity field models

The reprocessing of Gravity field and steady-state Ocean Circulation Explorer (GOCE) Level 1b gradiometer and star tracker data applying upgraded processing methods leads to improved gravity gradient and attitude products. The impact of these enhanced products on GOCE-only and combined GOCE+GRACE (Gravity Recovery and Climate Experiment) gravity field models is analyzed in detail, based on a two-months data period of Nov. and Dec. 2009, and applying a rigorous gravity field solution of full normal equations. Gravity field models that are based only on GOCE gradiometer data benefit most, especially in the low to medium degree range of the harmonic spectrum, but also for specific groups of harmonic coefficients around order 16 and its integer multiples, related to the satellite’s revolution frequency. However, due to the fact that also (near-)sectorial coefficients are significantly improved up to high degrees (which is caused mainly by an enhanced second derivative in Y direction of the gravitational potential — V_YY), also combined gravity field models, including either GOCE orbit information or GRACE data, show improvements of more than 10% compared to the use of original gravity gradient data. Finally, the resulting gradiometry-only, GOCE-only and GOCE+GRACE global gravity field models have been externally validated by independent GPS/levelling observations in selected regions. In conclusion, it can be expected that several applications will benefit from the better quality of data and resulting GOCE and combined gravity field models.     

The seismically active Andean and Central American margins: Can satellite gravity map lithospheric structures?

The spatial resolution and quality of geopotential models (EGM2008, EIGEN-5C, ITG-GRACE03s, and GOCO-01s) have been assessed as applied to lithospheric structure of the Andean and Central American subduction zones. For the validation, we compared the geopotential models with existing terrestrial gravity data and density models as constrained by seismic and geological data. The quality and resolution of the downward continued geopotential models in the Andes and Central America decrease with increasing topography and depend on the availability of terrestrial gravity data. High resolution of downward continued gravity data has been obtained over the Southern Andes where elevations are lower than 3000 m and sufficient terrestrial gravity data are available. The resolution decreases with an increase in elevation over the north Chilean Andes and Central America. The low resolution in Central America is mainly attributed to limited surface gravity data coverage of the region.To determine the minimum spatial dimension of a causative body that could be resolved using gravity gradient data, a synthetic gravity gradient response of a spherical anomalous mass has been computed at GOCE orbit height (254.9 km). It is shown that the minimum diameter of such a structure with density contrast of 240 kg m⁻³ should be at least ∼45 km to generate signal detectable at orbit height. The batholithic structure in Northern Chile, which is assumed to be associated with plate coupling and asperity generation, is about 60–120 km wide and could be traceable in GOCE data. Short wavelength anomalous structures are more pronounced in the components of the gravity gradient tensor and invariants than in the gravity field.As the ultimate objective of this study is to understand the state of stress along plate interface, the geometry of the density model, as constrained by combined gravity models and seismic data, has been used to develop dynamic model of the Andean margin. The results show that the stress regime in the fore-arc (high and low) tends to follow the trend of the earthquake distributions.     

High-harmonic geoid signatures related to glacial isostatic adjustment and their detectability by GOCE

The Earth’s asthenosphere and lower continental crust can regionally have viscosities that are one to several orders of magnitude smaller than typical mantle viscosities. As a consequence, such shallow low-viscosity layers could induce high-harmonic (spherical harmonics 50–200) gravity and geoid anomalies due to remaining isostasy deviations following Late-Pleistocene glacial isostatic adjustment (GIA). Such high-harmonic geoid and gravity signatures would depend also on the detailed ice and meltwater loading distribution and history.ESA’s Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission, planned for launch in Summer 2008, is designed to map the quasi-static geoid with centimeter accuracy and gravity anomalies with milligal accuracy at a resolution of 100 km or better. This might offer the possibility of detecting gravity and geoid effects of low-viscosity shallow earth layers and differences of the effects of various Pleistocene ice decay scenarios. For example, our predictions show that for a typical low-viscosity crustal zone GOCE should be able to discern differences between ice-load histories down to length scales of about 150 km.One of the major challenges in interpreting such high-harmonic, regional-scale, geoid signatures in GOCE solutions will be to discriminate GIA-signatures from various other solid-earth contributions. It might be of help here that the high-harmonic geoid and gravity signatures form quite characteristic 2D patterns, depending on both ice load and low-viscosity zone model parameters.     

High-harmonic geoid signatures related to glacial isostatic adjustment and their detectability by GOCE

The Earth’s asthenosphere and lower continental crust can regionally have viscosities that are one to several orders of magnitude smaller than typical mantle viscosities. As a consequence, such shallow low-viscosity layers could induce high-harmonic (spherical harmonics 50–200) gravity and geoid anomalies due to remaining isostasy deviations following Late-Pleistocene glacial isostatic adjustment (GIA). Such high-harmonic geoid and gravity signatures would depend also on the detailed ice and meltwater loading distribution and history.ESA’s Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission, planned for launch in Summer 2008, is designed to map the quasi-static geoid with centimeter accuracy and gravity anomalies with milligal accuracy at a resolution of 100 km or better. This might offer the possibility of detecting gravity and geoid effects of low-viscosity shallow earth layers and differences of the effects of various Pleistocene ice decay scenarios. For example, our predictions show that for a typical low-viscosity crustal zone GOCE should be able to discern differences between ice-load histories down to length scales of about 150 km.One of the major challenges in interpreting such high-harmonic, regional-scale, geoid signatures in GOCE solutions will be to discriminate GIA-signatures from various other solid-earth contributions. It might be of help here that the high-harmonic geoid and gravity signatures form quite characteristic 2D patterns, depending on both ice load and low-viscosity zone model parameters.     

Performance of GOCE and GRACE-derived mean dynamic topographies in resolving Antarctic Circumpolar Current fronts

Presently, two satellite missions, Gravity Recovery and Climate Experiment (GRACE) and Gravity field and steady-state Ocean Circulation Explorer (GOCE), are making detailed measurements of the Earth’s gravity field, from which the geoid can be obtained. The mean dynamic topography (MDT) is the difference between the time-averaged sea surface height and the geoid. The GOCE mission is aimed at determining the geoid with superior accuracy and spatial resolution, so that a more accurate MDT can be estimated. In this study, we determine the mean positions of the Antarctic Circumpolar Current fronts using the purely geodetic estimates of the MDT constructed from an altimetric mean sea surface and GOCE and GRACE geoids. Overall, the frontal positions obtained from the GOCE and GRACE MDTs are close to each other. This means that these independent estimates are robust and can potentially be used to validate frontal positions obtained from sparse and irregular in situ measurements. The geodetic frontal positions are compared to earlier estimates as well as to those derived from MDTs based on satellite and in situ measurements and those obtained from an ocean data synthesis product. The position of the Sub-Antarctic Front identified in the GOCE MDT is found to be in better agreement with the previous estimates than that identified in the GRACE MDT. The geostrophic velocities derived from the GOCE MDT are also closer to observations than those derived from the GRACE MDT. Our results thus show that the GOCE mission represents an improvement upon GRACE in terms of the time-averaged geoid.     

Band-Limited Analysis of Current Satellite-to-Satellite Tracking, Gradiometry and Combined Earth Gravity Models

Several satellite-only gravity models based on the analysis of satellite-to-satellite tracking (SST) data have become available in the course of the last decade. The realization of the satellite missions CHAllenging Minisatellite Payload (CHAMP) and Gravity Recovery And Climate Experiment (GRACE) enabled the practical implementation of two modes of the SST principle, namely the high–low and the low–low SST. Though similar in their fundamental idea, which is the indirect observation of the gravity field based on the position of two satellites orbiting the Earth, the different architecture and geometrical layout of these techniques capture different fingerprints of the observed field. In the last few years, satellite-only gravity models based on the analysis of satellite gravity gradiometry (SGG) data became available and led to a new insight into the gravity field. The implementation of the SGG principle became possible after the launch of Gravity field and steady-state Ocean Circulation Explorer (GOCE), the first gravitational gradiometry mission. Based on the principle of differential accelerometry, GOCE provides the gravitational gradients which can be used in gravity field retrieval as primary observations of the field at satellite altitude. In the present study, we consider some of the current satellite-only and combined gravity models based on the analysis of CHAMP, GRACE, GOCE, gravimetry and altimetry data. In order to perform a thorough analysis of the models, we present an overview of tools for their quality assessment both in an absolute and relative sense in terms of computing spectral quantities, such as correlation or smoothing coefficients per degree and per order, attempting to demonstrate possible non-isotropic features in the models. Furthermore, typical geodetic measures in computing second-order derivatives, such as degree and order variances and difference variances, have been also evaluated for the same models, using the combined model EGM2008 as reference. Apart from these standard spectral assessment quantities, a systematic spatial representation of the second derivatives at satellite altitude has been performed. The combination of the two analysis steps (spectral and spatial) permits a first detailed assessment of the models, focusing especially on the identification of characteristic interpretable bandwidths.     

Book review of Waves in the ocean and atmosphere: Introduction to wave dynamics by Joseph Pedlosky,Springer-Verlag,New York, 2003, VIII + 260 pp., £38.50, $49.95, Euros hardback (ISBN 3-540-00340-1)

We present an analytical, idealized yet precise model of the terrestrial gravity field. The model is meant as a basic ingredient of geophysical fluid dynamics (GFD). We explicitly deal with geopotential coordinates, show in what sense horizontal geopotential coordinate surfaces can be approximated by spherical surfaces and thus provide a clear interpretation of the “spherical approximation” of the equations of motion in GFD. The horizontal component of the gravitational force plays a crucial role in the spherical approximation. It is shown that to leading order in the relevant small parameters, the horizontal components of the gravitational force and the centrifugal force cancel each other in the spherical approximation of the geopotential field.     

Upward continuation of Dome-C airborne gravity and comparison with GOCE gradients at orbit altitude in east Antarctica

An airborne gravity campaign was carried out at the Dome-C survey area in East Antarctica between the 17th and 22nd of January 2013, in order to provide data for an experiment to validate GOCE satellite gravity gradients. After typical filtering for airborne gravity data, the cross-over error statistics for the few crossing points are 11.3 mGal root mean square (rms) error, corresponding to an rms line error of 8.0 mGal. This number is relatively large due to the rough flight conditions, short lines and field handling procedures used. Comparison of the airborne gravity data with GOCE RL4 spherical harmonic models confirmed the quality of the airborne data and that they contain more high-frequency signal than the global models. First, the airborne gravity data were upward continued to GOCE altitude to predict gravity gradients in the local North-East-Up reference frame. In this step, the least squares collocation using the ITGGRACE2010S field to degree and order 90 as reference field, which is subtracted from both the airborne gravity and GOCE gravity gradients, was applied. Then, the predicted gradients were rotated to the gradiometer reference frame using level 1 attitude quaternion data. The validation with the airborne gravity data was limited to the accurate gradient anomalies (T_XX, T_YY, T_ZZ and T_XZ) where the long-wavelength information of the GOCE gradients has been replaced with GOCO03s signal to avoid contamination with GOCE gradient errors at these wavelengths. The comparison shows standard deviations between the predicted and GOCE gradient anomalies T_XX, T_YY, T_ZZ and T_XZ of 9.9, 11.5, 11.6 and 10.4 mE, respectively. A more precise airborne gravity survey of the southern polar gap which is not observed by GOCE would thus provide gradient predictions at a better accuracy, complementing the GOCE coverage in this region.     

GOCO05c: A New Combined Gravity Field Model Based on Full Normal Equations and Regionally Varying Weighting

GOCO05c is a gravity field model computed as a combined solution of a satellite-only model and a global data set of gravity anomalies. It is resolved up to degree and order 720. It is the first model applying regionally varying weighting. Since this causes strong correlations among all gravity field parameters, the resulting full normal equation system with a size of 2 TB had to be solved rigorously by applying high-performance computing. GOCO05c is the first combined gravity field model independent of EGM2008 that contains GOCE data of the whole mission period. The performance of GOCO05c is externally validated by GNSS–levelling comparisons, orbit tests, and computation of the mean dynamic topography, achieving at least the quality of existing high-resolution models. Results show that the additional GOCE information is highly beneficial in insufficiently observed areas, and that due to the weighting scheme of individual data the spectral and spatial consistency of the model is significantly improved. Due to usage of fill-in data in specific regions, the model cannot be used for physical interpretations in these regions.     

顾及多方向观测值权比反演地球重力场的动力积分法

考虑到不同坐标系下各个方向观测值对反演地球重力场的频谱贡献不同,建立了顾及多方向观测值权比的动力积分法,并利用该方法反演了高精度的GOCE HL-SST卫星重力场模型.首先,分析了不同坐标系下各个方向观测值与地球重力场信息的响应关系,其中惯性系(IRF)下X、Z方向的观测值分别对扇谐系数、带谐系数最为敏感,Z方向的解算精度在全频段均略高于X、Y方向;地固系(EFRF)下各个方向的独立解算精度均与能量守恒法的解算精度相当;局部指北坐标系(LNOF)下X、Z和Y三个方向的解算精度依次递减,且Y方向在47阶附近有明显"驼峰"现象.其次,比较了不同坐标系下顾及三个方向观测值权比的加权解算模型,其中加权联合解算模型精度在20至70阶次均明显优于等权解算模型,在带谐项和共振阶次精度提升明显,且LNOF下的加权联合解算精度要优于IRF和EFRF.最后,比较了GOCE和CHAMP卫星的模型解算精度,采用本文计算方法,仅利用2个月GOCE轨道观测值解算的模型精度优于包含更长观测时段信息的AIUB-CHAMP01S和EIGEN-CHAMP03S模型,且略优于ASU-GOCE-2months模型.     

由GOCE引力场模型和CNES-CLS2010平均海面高计算的稳态海面地形

利用欧空局发布的三组GOCE引力场模型及CNES-CLS 2010平均海面高数据,计算得到了全球的稳态海面地形,进而得到了全球地转流速度图.在此基础上重点对黑潮进行了对比分析.结果表明:GOCE不同组解的稳定性较好,所计算的稳态海面地形的差异基本在厘米量级内,这间接表明了GOCE引力场模型提供的大地水准面的精度达到了厘米量级.此外,通过将GOCE与GRACE相应结果进行对比发现,GOCE可提供更多的局部信息,特别是对于流速快、水流窄的边界流,如黑潮、墨西哥湾流等,GOCE所得结果更加清晰,速度也更精确.