The combination of GNSS-levelling data and gravimetric (quasi-) geoid heights in the presence of noise

We propose a methodology for the combination of a gravimetric (quasi-) geoid with GNSS-levelling data in the presence of noise with correlations and/or spatially varying noise variances. It comprises two steps: first, a gravimetric (quasi-) geoid is computed using the available gravity data, which, in a second step, is improved using ellipsoidal heights at benchmarks provided by GNSS once they have become available. The methodology is an alternative to the integrated processing of all available data using least-squares techniques or least-squares collocation. Unlike the corrector-surface approach, the pursued approach guarantees that the corrections applied to the gravimetric (quasi-) geoid are consistent with the gravity anomaly data set. The methodology is applied to a data set comprising 109 gravimetric quasi-geoid heights, ellipsoidal heights and normal heights at benchmarks in Switzerland. Each data set is complemented by a full noise covariance matrix. We show that when neglecting noise correlations and/or spatially varying noise variances, errors up to 10% of the differences between geometric and gravimetric quasi-geoid heights are introduced. This suggests that if high-quality ellipsoidal heights at benchmarks are available and are used to compute an improved (quasi-) geoid, noise covariance matrices referring to the same datum should be used in the data processing whenever they are available. We compare the methodology with the corrector-surface approach using various corrector surface models. We show that the commonly used corrector surfaces fail to model the more complicated spatial patterns of differences between geometric and gravimetric quasi-geoid heights present in the data set. More flexible parametric models such as radial basis function approximations or minimum-curvature harmonic splines perform better. We also compare the proposed method with generalized least-squares collocation, which comprises a deterministic trend model, a random signal component and a random correlated noise component. Trend model parameters and signal covariance function parameters are estimated iteratively from the data using non-linear least-squares techniques. We show that the performance of generalized least-squares collocation is better than the performance of corrector surfaces, but the differences with respect to the proposed method are still significant.     

Comparison of SARAL and Jason-1/2 altimetry-derived geoids for geophysical exploration over the Indian offshore

Satellite with ARgos and ALtika (SARAL) altimeter includes the ALTIKA payload, a 35.75 GHz Ka band radar altimeter. High pulse repetition frequency of SARAL (4 KHz) satellite provides better along-track information. Jason-1/2 data have been extensively utilized as a follow-up of TOPEX/Poseidon altimeter data for its accurate measurements of the sea surface heights, particularly for geodetic mission of Jason-1. In this study, we have compared SARAL and Jason-1/2 altimetry-derived classical and residual geoids over the Indian offshore using Rapp’s, EGM96 and EGM08 gravity model coefficients, which are of interest for better understanding of geological and structural evolution/interpretation. SARAL and Jason-1/2 data have also been used over the two prominent geological features over the Indian offshore, namely the Bombay High in the western offshore and the 85°E Ridge in the Bay of Bengal. The SARAL altimetry-derived geoids could delineate these major geological/structural features with distinct residual geoidal lows.     

卫星测高沿轨海面高的精细结构及其应用技术初探

首先介绍了频域和多尺度域中的两种沿轨测高海面高精细结构，进而提出了利用沿轨测高海面高精细结构计算平均海面高与海平面距平的新方法，最后进一步讨论了沿轨平均海面高和海平面距平的频谱和多尺度分解，以及它们随时间的变化特性。     

The impact of the dynamic sea surface topography on the quasi-geoid in shallow coastal waters

In this study, we examine the impact of instantaneous dynamic sea surface topography (DT) corrections to be applied to altimeter-derived sea surface slopes on the quasi-geoid in the shallow and coastal waters of the North Sea. In particular, we investigate the added value of DT corrections obtained from a shallow-water hydrodynamic model. These corrections comprise the contributions of ocean tides, wind- and pressure-driven (surge), and density-driven (baroclinic) water-level variations including the interactions between them. As a reference, we used tidal corrections derived from the global ocean tide model GOT4.7, surge corrections derived from the MOG2D model, and corrections for the time-averaged baroclinic contribution computed as differences between the DTU10 mean sea surface model and the EGG08 quasi-geoid. From a spectral analysis, we found that the baroclinic and surge parts of the DT mainly contribute to improvements in the signal-to-noise ratio (SNR) at longer wavelengths down to $100{-}200~\hbox {km}$ and that the improvements increase towards the southern North Sea. We also found that the shallow-water hydrodynamic model provides better tidal corrections compared to the GOT4.7 global ocean tide model, which are most pronounced in the southern North Sea and affect almost the entire spectrum. Very small differences (mostly below ${\pm } 2~\hbox {cm}$ ) are observed between the quasi-geoid solutions obtained using the different sets of DT corrections. We showed that the variance component estimation provides too optimistic variance factors for the shipboard data set relative to the altimeter-derived quasi-geoid slopes. Hence, the limited impact of DT corrections is due to the fact that altimeter-derived quasi-geoid slopes hardly contribute to the estimated quasi-geoid if shipboard gravity data are included. When computing quasi-geoid solutions without shipboard gravity data, we found that less accurate or incomplete DT corrections may cause errors in the quasi-geoid with systematic spatial patterns. These systematic patterns disappear or are reduced significantly when using the DT corrections provided by the shallow-water hydrodynamic model. The main contributor to this improvement is the better tidal correction provided by the shallow-water hydrodynamic model compared to the GOT4.7 global ocean tide model. Seen the improvements of the global ocean tide models over the last two decades, we expect that in the near future global ocean tide models perform as well as dedicated regional models such as DCSM. Critical issue is, however, access to high-quality local bathymetric data.     

卫星测高数据的沿轨迹重力异常反演法及其应用

本文给出了一套基于直角坐标系下的垂线偏差求解重力异常公式 ,并将之发展成为一套新的沿轨迹重力异常求解公式。与其他方法相比 ,本方法无须求解交叠点处沿轨迹和跨轨迹方向的海面高斜率 ,仅需计算沿轨迹方向的海面高斜率 ,因而更为简洁、有效 ,而且分辨率可以更高并可与真正的沿航迹实际船测重力相比较、验证。据此 ,利用 Geosat/GM、ERS-1 /35天及TOPEX/Poseidon三种测高数据 ,反演了南中国海域 (0°～ 2 5°N,1 0 5°～ 1 2 2°E)的 2′× 2′重力异常—— IGG-S。通过与实际船测资料和国际同行提供的重力模型相比 ,IGG-S总体精度达到1 0× 1 0 - 5ms- 2。     

我国陆海统一似大地水准面构建的三维重力矢量法

基于重力场水平分量-垂线偏差对地形信息敏感的特点,根据边值理论由重力与地形数据确定格网垂线偏差模型,在此基础上,首先利用三维重力矢量-格网垂线偏差与格网重力异常,联合格网高程数据求得格网点间高程异常差,然后通过GPS/水准点的控制,构成紧密的几何条件,进行严密平差,从而获得高分辨率、高精度似大地水准面的数值模型。按照本文方法,利用我国6600多个GPS/水准点、1'×1'的格网垂线偏差、格网重力异常、格网高程数据,整体平差计算了我国陆海统一的似大地水准面模型,经GPS/水准点检核,全国似大地水准面的绝对精度达到了4 cm,相对精度优于7 cm。     

应用双输入单输出法确定局部似大地水准面的实例研究

利用了双输入单输出法,融合处理了我国某地区的重力异常和地形资料两类数据,结合WDM94地球重力场模型和63个高精度GPS水准数据,计算了该区域的似大地水准面。     

综合利用海岸带GNSS水准和重力数据精密确定中国高程基准偏差

综合利用中国海岸带GNSS水准和多源重力测量数据,通过精化陆海统一的重力似大地水准面计算高程异常零阶项,精密确定了中国1985国家高程基准相对于重力大地水准面的偏差。结果显示:中国1985国家高程基准相对于国际地球自转服务（International Earth Rotation Service,IERS）的IERS2010标准W₀对应的重力大地水准面的偏差为30.4±1.0 cm;中国1985国家高程基准于20世纪80年代经琼州海峡传递到海南岛后,在1 cm精度水平上未发现明显差异;计算的重力似大地水准面经全球导航卫星系统（globa navigation satellite system,GNSS）水准外部检核,标准差约为4 cm,12个省市和陆海交界处在厘米级精度水平上无缝衔接。在近10 a内,天津市除西北角外,大部分地区存在地面下沉,东南部地面下沉约7 cm,上海市地面下沉约7 cm,浙江省、江苏省和福建省等沿海省份局部地区也出现地面下沉。     

Gravity recovery using COSMIC GPS data: application of orbital perturbation theory

 COSMIC is a joint Taiwan–US mission to study the atmosphere using the Global Positioning System (GPS) occultation technique. Improved formulas are developed for the radial, along-track, and cross-track perturbations, which are more accurate than the commonly used order-zero formulas. The formulas are used to simulate gravity recovery using the geodetic GPS data of COSMIC in the operational phase. Results show that the EGM96 model can be improved up to degree 26 using 1 year of COSMIC data. TOPEX/POSEIDON altimeter data are used to derive a temporal gravity variation. COSMIC cannot reproduce this gravity variation perfectly because of data noise and orbital configuration, but the recovered field clearly shows the gravity signature due to mass movement in an El Ni?o. Received: 3 March 2000 / Accepted: 10 November 2000     

由卫星测高数据观测到的印度洋海啸波高

本文介绍了利用卫星测高资料测定的印度洋地震引起的海啸波高的研究成果 ,以及卫星测高数据在对海啸灾害进行预测的应用价值。通过卫星雷达测高可观测到沿卫星星下点轨迹的相距几公里的点上的海面高 ,还提供了特别有价值的对海啸波的连续观测结果     

SZ-4雷达高度计及其在轨测量结果

SZ-4雷达高度计搭乘神舟4号飞船（SZ-4）于2002年12月30日发射入轨,按预定模式工作,获得了大量有效的观测数据。SZ-4雷达高度计是中国第一个上星工作的实验性海洋雷达高度计,为中国海洋动力环境卫星的发展奠定了基础。本文系统地论述了SZ-4雷达高度计系统方案、系统实现和在轨测量结果。     

Role of ocean variability and dynamic ocean topography in the recovery of the mean sea surface and gravity anomalies from satellite altimeter data

Procedures to calculate mean sea surface heights and gravity anomalies from altimeter-derived sea surface heights and along-track sea surface slopes using the least-squares collocation procedure are derived. The slope data is used when repeat track averaging is not possible to reduce ocean variability effects. Tests were carried out using Topex, Geosat, ERS-1 [35-day and 168-day (2 cycle)] data. Calculations of gravity anomalies in the Gulf Stream region were made using the sea surface height and slope data. Tests were also made correcting the sea surface heights for dynamic ocean topography calculated from a degree 360 expansion of data from the POCM-4B global ocean circulation model. Comparisons of the anomaly predictions were carried out with ship data using anomalies calculated for this paper as well as others. Received: 19 August 1996 / Accepted: 14 April 1997     

用T/P测高数据反演海域重力异常

以反解 Stokes公式为数学模型 ,应用由 T/ P测高数据计算的大地水准面高反演了海域平均重力异常 ,并与船测平均重力异常和 OSU91A位模型计算的平均重力异常进行了比对分析 ,得出了一些有益的结论。     

海洋重力似大地水准面与区域测高似大地水准面的拟合问题

研究了将陆地重力似大地水准面与GPS水；住似大地水准面拟合的处理方法推广到海洋的问题．首先从理论上证明了当存在海面地形．则海洋大地水准面与似大地水准面不重合．导出了在海洋上大地水；住面差距与高程异常之间差值的公式．由此给出了求定平均海面相对于区域高程基准的正常高以及测高似大地水准面的计算公式。由于测高平均海面与GPS大地高有相近的精度．提出了将海洋重力似大地水准面与区域测高似大地水准面拟合的处理方法．并利用当前最新的海面地形模型和测高平均海面模型做了数值估计。     

海洋卫星测高及其反演全球海洋重力场和海底地形模型研究进展

海洋卫星测高在全球和区域大地水准面建模、全球海洋重力场反演、海底地形探测、海平面变化监测、构造板块运动研究等大地测量领域至关重要。本文概述了海洋微波测高卫星的简要发展历程,重点梳理了卫星测高在全球海洋重力场和全球海底地形建模方面取得的丰硕成果,对比分析了主流的海洋重力场和海底地形模型;介绍了合成孔径雷达高度计、Ka频段雷达高度计、合成孔径雷达干涉仪3种先进微波测高技术,并分析了其各自的优缺点,表明它们将在未来若干年呈并驱发展趋势;较为系统地阐述了海洋卫星测高的另一新型技术,即GNSS反射信号测量技术的研究动态,给出了GNSS-R(GNSS reflectometry)类(试验)卫星的发展脉络和发展前景。卫星测高的发展趋势之一是多颗测高卫星的组网观测,本文概括了曾经提出的和拟议中的若干组网测高计划,扼要介绍了由我国提出并正在实施的双星跟飞测高模式;最后指出了卫星测高发展的几个主要关注点,包括双星跟飞测高和SWOT(surface water ocean topography)任务的2维海面高(差)测量、卫星测高反演海底地形与高级地形激光高度计观测数据及遥感卫星图像的结合、星载GNSS-R厘米级海面高的载波相位测量、人工智能技术在卫星测高中的潜在应用等。     

Gravity-field improvement in the Mediterranean Sea by estimating the bottom topography using collocation

The contribution of bathymetry to the prediction of quantities related to the gravity field (e.g., gravity anomalies, geoid heights) is discussed in an extended test area of the central Mediterranean Sea. Sea gravity anomalies and a priori statistical characteristics of depths are used in a least-squares collocation procedure in order to produce new depths, giving a better smoothing of the gravity field when using a remove-restore procedure. The effect of the bottom topography on gravity-field modeling is studied using both the original and the new depths through a residual terrain modeling reduction. The numerical tests show a considerable smoothing of the sea gravity anomalies and the available altimeter heights when the new depth information is taken into account according to the covariance analysis performed. Moreover, geoid heights are computed by combining the sea gravity anomalies either with the original depths or with the new ones, using as a reference surface the OSU91A geopotential model. Comparing the computed geoid heights with adjusted altimeter sea-surface heights (SSHs), better results are obtained when subtracting the attraction of the new depth information. Similar results are obtained when predicting gravity anomalies from altimeter SSHs where the terrain effect on altimetry is based on the new bottom topography. Received: 10 September 1996 / Accepted: 4 August 1997     

高精度海岸带重力似大地水准面的若干问题讨论

本文针对海岸带多源重力数据和地形特点,通过理论分析和试算,对若干影响厘米级似大地水准面确定的关键问题进行了剖析,得出一些有益的结论。我国海岸带Molodensky一阶项对高程异常的贡献在10～30cm,需在Molodensky框架中精化重力似大地水准面;精细处理地形影响是提升多源重力场数据处理水平的重要途径;地球外空间不同高度、任意类型重力场参数的地形影响、地形补偿和地形Helmert凝聚算法可以统一;重力场数据处理中大地测量基准不一致的影响会随数据处理算法的不同而变化,在多源重力数据处理时此类影响易变得不可预测和控制;将地形Helmert凝聚理论引入Molodensky框架,可以解决以其他重力场参数（如扰动重力、垂线偏差等）为边界条件的似大地水准面精化问题。     

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.     

Global mean sea surface and marine gravity anomaly from multi-satellite altimetry: applications of deflection-geoid and inverse Vening Meinesz formulae

 Global mean sea surface heights (SSHs) and gravity anomalies on a 2^′×2^′ grid were determined from Seasat, Geosat (Exact Repeat Mission and Geodetic Mission), ERS-1 (1.5-year mean of 35-day, and GM), TOPEX/POSEIDON (T/P) (5.6-year mean) and ERS-2 (2-year mean) altimeter data over the region 0^∘–360^∘ longitude and –80^∘–80^∘ latitude. To reduce ocean variabilities and data noises, SSHs from non-repeat missions were filtered by Gaussian filters of various wavelengths. A Levitus oceanic dynamic topography was subtracted from the altimeter-derived SSHs, and the resulting heights were used to compute along-track deflection of the vertical (DOV). Geoidal heights and gravity anomalies were then computed from DOV using the deflection-geoid and inverse Vening Meinesz formulae. The Levitus oceanic dynamic topography was added back to the geoidal heights to obtain a preliminary sea surface grid. The difference between the T/P mean sea surface and the preliminary sea surface was computed on a grid by a minimum curvature method and then was added to the preliminary grid. The comparison of the NCTU01 mean sea surface height (MSSH) with the T/P and the ERS-1 MSSH result in overall root-mean-square (RMS) differences of 5.0 and 3.1 cm in SSH, respectively, and 7.1 and 3.2 μrad in SSH gradient, respectively. The RMS differences between the predicted and shipborne gravity anomalies range from 3.0 to 13.4 mGal in 12 areas of the world's oceans. Received: 26 September 2001 / Accepted: 3 April 2002 Correspondence to: C. Hwang Acknowledgements. This research is partly supported by the National Science Council of ROC, under grants NSC89-2611-M-009-003-OP2 and NSC89-2211-E-009-095. This is a contribution to the IAG Special Study Group 3.186. The Geosat and ERS1/2 data are from NOAA and CERSAT/France, respectively. The T/P data were provided by AVISO. The CLS and GSFC00 MSS models were kindly provided by NASA/GSFC and CLS, respectively. Drs. Levitus, Monterey, and Boyer are thanked for providing the SST model. Dr. T. Gruber and two anonymous reviewers provided very detailed reviews that improved the quality of this paper.