The construction of high precision geostrophic currents based on new gravity models of GOCE and satellite altimetry data

The new gravity field models of gravity field and steady-state ocean circulation explorer(GOCE), TIM_R6 and DIR_R6, were released by the European Space Agency(ESA) in June 2019. The sixth generation of gravity models have the highest possible signal and lowest error levels compared with other GOCE-only gravity models, and the accuracy is significantly improved. This is an opportunity to build high precision geostrophic currents. The mean dynamic topography and geostrophic currents have been calculated by the 5 th(TIM_R5 and DIR_R5), 6 th(TIM_R6 and DIR_R6) release of GOCE gravity field models and ITSG-Grace2018 of GRACE gravity field model in this study. By comparison with the drifter results, the optimal filtering lengths of them have been obtained(for DIR_R5, DIR_R6, TIM_R5 and TIM_R6 models are 1° and for ITSG-Grace2018 model is 1.1°). The filtered results show that the geostrophic currents obtained by the GOCE gravity field models can better reflect detailed characteristics of ocean currents. The total geostrophic speed based on the TIM_R6 model is similar to the result of the DIR_R6 model with standard deviation(STD) of 0.320 m/s and 0.321 m/s, respectively. The STD of the total velocities are 0.333 m/s and 0.325 m/s for DIR_R5 and TIM_R5. When compared with ITSG-Grace2018 results, the STD(0.344 m/s) of total geostrophic speeds is larger than GOCE results, and the accuracy of geostrophic currents obtained by ITSG-Grace2018 is lower. And the absolute errors are mainly distributed in the areas with faster speeds, such as the Antarctic circumpolar circulation, equatorial region, Kuroshio and Gulf Stream areas. After the remove-restore technique was applied to TIM_R6 MDT, the STD of total geostrophic speeds dropped to 0.162 m/s.     

国际重力卫星研究进展和我国将来卫星重力测量计划

本文首先分别介绍了国际已经成功发射的专用地球重力测量卫星CHAMP、GRACE以及即将发射的GOCE、GRACE Follow-On和专用月球重力探测卫星GRAIL的研制机构、轨道参数、关键载荷、跟踪模式、测量原理、科学目标和技术特征;其次,阐述了当前相关学科对地球重力场测量精度的需求;最后,建议我国在将来实施的卫星重力测量计划中首选卫星跟踪卫星高低\低低模式,尽快开展轨道参数优化选取的定量系统研究论证和重力卫星系统的误差分析,依据匹配精度指标先期开展重力卫星各关键载荷的研制以及尽早启动卫星重力测量系统的虚拟仿真研究。     

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A comparison of GOCE gravitational models with EGM2008

Four new gravity field models from GOCE, two of them combined with GRACE, are compared here with EGM2008. The objectives are to look into the differences in consecutive ranges of the spherical harmonic expansion globally as well as in selected geographical regions and in the regions of the various data sources used for EGM2008. In general, GOCE is able to contribute to improved global gravity models in the spherical harmonic range between 120 and 200 (and above). The agreement between EGM2008 and the GOCE models is very good in well-surveyed regions such as North America, Europe and Australia, with geoid RMS-differences on the order of 4–6 cm. In other regions, where the surface gravity data available for the development of EGM2008 were poor, such as South America, Africa, South-East Asia or China the RMS-differences are on a level of 30 cm. Here GOCE leads to a significant improvement. These findings are confirmed by the analysis of the areas of the various EGM2008 data sources. In the regions of the so-called “fill-in” data of EGM2008 RMS-geoid height differences are high. In Antarctica GOCE also gives important improvements in terms of spatial resolution and accuracy. In general, the agreement between EGM2008 and the GOCE-models up to degree and order (d/o) 200 is good, with a global (excluding the polar gaps of GOCE orbits, throughout) geoid difference RMS of 11 cm, in the ocean areas 8 cm and 20 cm in the continental areas. GOCE models are better suited for ocean circulation studies because no prior ocean information enters into the data reduction process, as it is the case when deducing gravity anomalies from an altimetric mean sea surface. On the other hand, the good consistency between GOCE-models and EGM2008 in ocean areas very likely indicates that the influence of ocean circulation information on EGM2008 is rather small. The four tested GOCE models behave similarly except at the highest latitudes where GOCE lacks data due to its orbit inclination of 96.5° and some form of regularization which has to be applied.     

基于卫星重力梯度数据的密度反演研究

为解决卫星重力梯度大尺度密度反演存在的平面模型误差、病态矩阵正则化、大型矩阵求逆、先验数据融合等问题,依托Tesseroid单元体模型,分别采用广义岭估计、代数重建(ART)、遗传算法完成了附加高斯白噪声的模拟异常体密度反演实验,并将反演结果与原始设定模型进行比较分析。     

利用Wenzel加权谱组合法拓展GOCE重力场模型

根据GOCE和EGM08重力场模型的频谱互补性,利用Wenzel加权谱组合法构建了GOCE和EGM08的组合重力场模型。累积大地水准面误差表明,组合重力场模型具有明显的优势。美国实测GPS/水准检验结果表明,Dir4+EGM08的组合模型精度最高,比EGM08模型精度提高了8%。     

Geoid and high resolution sea surface topography modelling in the mediterranean from gravimetry,altimetry and GOCE data: evaluation by simulation

The determination of local geoid models has traditionally been carried out on land and at sea using gravity anomaly and satellite altimetry data, while it will be aided by the data expected from satellite missions such as those from the Gravity field and steady-state ocean circulation explorer (GOCE). To assess the performance of heterogeneous data combination to local geoid determination, simulated data for the central Mediterranean Sea are analyzed. These data include marine and land gravity anomalies, altimetric sea surface heights, and GOCE observations processed with the space-wise approach. A spectral analysis of the aforementioned data shows their complementary character. GOCE data cover long wavelengths and account for the lack of such information from gravity anomalies. This is exploited for the estimation of local covariance function models, where it is seen that models computed with GOCE data and gravity anomaly empirical covariance functions perform better than models computed without GOCE data. The geoid is estimated by different data combinations and the results show that GOCE data improve the solutions for areas covered poorly with other data types, while also accounting for any long wavelength errors of the adopted reference model that exist even when the ground gravity data are dense. At sea, the altimetric data provide the dominant geoid information. However, the geoid accuracy is sensitive to orbit calibration errors and unmodeled sea surface topography (SST) effects. If such effects are present, the combination of GOCE and gravity anomaly data can improve the geoid accuracy. The present work also presents results from simulations for the recovery of the stationary SST, which show that the combination of geoid heights obtained from a spherical harmonic geopotential model derived from GOCE with satellite altimetry data can provide SST models with some centimeters of error. However, combining data from GOCE with gravity anomalies in a collocation approach can result in the estimation of a higher resolution geoid, more suitable for high resolution mean dynamic SST modeling. Such simulations can be performed toward the development and evaluation of SST recovery methods.     

Error-covariances of the estimates of spherical harmonic coefficients computed by LSC,using second-order radial derivative functionals associated with realistic GOCE orbits

Least-squares collocation may be used for the estimation of spherical harmonic coefficients and their error and error correlations from GOCE data. Due to the extremely large number of data, this requires the use of the so-called method of Fast Spherical Collocation (FSC) which requires that data is gridded equidistantly on each parallel and have the same uncorrelated noise on the parallel. A consequence of this is that error-covariances will be zero except between coefficients of the same signed order (i.e., the same order and the same coefficient type C–C or S–S). If the data distribution and the characteristics of the data noise are symmetric with respect to the equator, then, within a given order and coefficient type, the error-covariances amongst coefficients whose degrees are of different parity also vanish. The deviation from this “ideal” pattern has been studied using data-sets of second order radial derivatives of the anomalous potential. A total number of points below 17,000 were used having an equi-angular or an equal area distribution or being associated with points on a realistic GOCE orbit but close to the nodes of a grid. Also the data were considered having a correlated or an uncorrelated noise and three different signal covariance functions. Grids including data or not including data in the polar areas were used. Using the functionals associated with the data, error estimates of coefficients and error-correlations between coefficients were calculated up to a maximal degree and order equal to 90. As expected, for the data-distributions with no data in the polar areas the error-estimates were found to be larger than when the polar areas contained data. In all cases it was found that only the error-correlations between coefficients of the same order were significantly different from zero (up to 88%). Error-correlations were significantly larger when data had been regarded as having non-zero error-correlations. Also the error-correlations were largest when the covariance function with the largest signal covariance distance was used. The main finding of this study was that the correlated noise has more pronounced impact on gridded data than on data distributed on a realistic GOCE orbit. This is useful information for methods using gridded data, such as FSC.     

Optimal multi-step collocation: application to the space-wise approach for GOCE data analysis

Collocation is widely used in physical geodesy. Its application requires to solve systems with a dimension equal to the number of observations, causing numerical problems when many observations are available. To overcome this drawback, tailored step-wise techniques are usually applied. An example of these step-wise techniques is the space-wise approach to the GOCE mission data processing. The original idea of this approach was to implement a two-step procedure, which consists of first predicting gridded values at satellite altitude by collocation and then deriving the geo-potential spherical harmonic coefficients by numerical integration. The idea was generalized to a multi-step iterative procedure by introducing a time-wise Wiener filter to reduce the highly correlated observation noise. Recent studies have shown how to optimize the original two-step procedure, while the theoretical optimization of the full multi-step procedure is investigated in this work. An iterative operator is derived so that the final estimated spherical harmonic coefficients are optimal with respect to the Wiener–Kolmogorov principle, as if they were estimated by a direct collocation. The logical scheme used to derive this optimal operator can be applied not only in the case of the space-wise approach but, in general, for any case of step-wise collocation. Several numerical tests based on simulated realistic GOCE data are performed. The results show that adding a pre-processing time-wise filter to the two-step procedure of data gridding and spherical harmonic analysis is useful, in the sense that the accuracy of the estimated geo-potential coefficients is improved. This happens because, in its practical implementation, the gridding is made by collocation over local patches of data, while the observation noise has a time-correlation so long that it cannot be treated inside the patch size. Therefore, the multi-step operator, which is in theory equivalent to the two-step operator and to the direct collocation, is in practice superior thanks to the time-wise filter that reduces the noise correlation before the gridding. The criteria for the choice of this filter are investigated numerically.     

利用GOCE卫星轨道反演地球重力场模型

根据积分方程法反演地球重力场的数学模型,利用GOCE卫星2009-11-02～2010-01-02共61d的精密轨道数据反演了几组地球重力场模型。结果表明,GOCE卫星轨道能有效提取地球重力场的长波信息,弥补了GOCE卫星重力梯度带宽的限制,在106阶次的大地水准面误差为±9.6cm,该阶次精度优于EIGEN-CHAMP03S及GRACE卫星两个月轨道反演地球重力场的精度,但由于两极空白,反演的带谐位系数精度偏低。联合GOCE及GRACE卫星轨道反演的模型在106阶次的大地水准面误差为±6.9cm,弥补了GOCE卫星轨道的缺陷。