Comparison of Satellite Altimetric Gravity and Global Geopotential Models with Shipborne Gravity in the Red Sea

The determination of high-resolution geoid for marine regions requires the integration of gravity data provided by different sources, e.g. global geopotential models, satellite altimetry, and shipborne gravimetric observations. Shipborne gravity data, acquired over a long time, comprises the short-wavelengths gravitation signal. This paper aims to produce a consistent gravity field over the Red Sea region to be used for geoid modelling. Both, the leave-one-out cross-validation and Kriging prediction techniques were chosen to ensure that the observed shipborne gravity data are consistent as well as free of gross-errors. A confidence level equivalent to 95.4% was decided to filter the observed shipborne data, while the cross-validation algorithm was repeatedly applied until the standard deviation of the residuals between the observed and estimated values are less than 1.5 mGal, which led to the elimination of about 17.7% of the shipborne gravity dataset. A comparison between the shipborne gravity data with DTU13 and SSv23.1 satellite altimetry-derived gravity models is done and reported. The corresponding results revealed that altimetry models almost have identical data content when compared one another, where the DTU13 gave better results with a mean and standard deviation of ?2.40 and 8.71 mGal, respectively. A statistical comparison has been made between different global geopotential models (GGMs) and shipborne gravity data. The Spectral Enhancement Method was applied to overcome the existing spectral gap between the GGMs and shipborne gravity data. EGM2008 manifested the best results with differences characterised with a mean of 1.35 mGal and a standard deviation of 11.11 mGal. Finally, the least-squares collocation (LSC) was implemented to combine the shipborne gravity data with DTU13 in order to create a unique and consistent gravity field over the Red Sea with no data voids. The combined data were independently tested using a total number of 95 randomly chosen shipborne gravity stations. The comparison between the extracted shipborne gravity data and DTU13 altimetry anomalies before and after applying the LSC revealed that a significant improvement is procurable from the combined dataset, in which the mean and standard deviation of the differences dropped from ?3.60 and 9.31 mGal to ?0.39 and 2.04 mGal, respectively.     

Combined satellite altimetry and shipborne gravimetry data processing

The recovery of quantities related to the gravity field (i.e., geoid heights and gravity anomalies) is carried out in a test area of the central Mediterranean Sea using 5' × 5' marine gravity data and satellite altimeter data from the Geodetic Mission (GM) of ERS‐J. The optimal combination of the two heterogeneous data sources is performed using (1) the space‐domain least‐squares collocation (LSC) method, and (2) the frequency‐domain input‐output system theory (IOST). The results derived by these methods agree at the level of 2 cm in terms of standard deviation in the case of the geoid height prediction. The gravity anomaly prediction results by the same methods vary between 2.18 and 2.54 mGal in terms of standard deviation. In all cases, the spectral techniques have a much higher computational efficiency than the collocation procedure. In order to investigate the importance of satellite altimetry for gravity field modeling, a pure gravimetric geoid solution, carried out in a previous study for our lest area by the fast collocation approach (FCOL), is used in comparison with the combined geoid models. The combined solutions give more accurate results, at the level of about 15 cm in terms of standard deviation, than the gravimetric geoid solution, when the geoid heights derived by each method are compared with TOPEX altimeter sea surface heights (SSHs). Moreover, nonisotropic power spectral density functions (PSDs) can be easily used by IOST, while LSC requires isotropic covariance functions. The results show that higher prediction accuracies are always obtained when using a priori nonisotropic information instead of isotropic information.     

增加近岸船载重力测量数据覆盖的推估方法研究

针对海洋区域离岸距离5～30km的范围内船载重力测量数据覆盖空白的现状,基于已有测线数据,对其进行不同空间距离采样形成对应的采样序列。利用动态时间规整算法计算其与初始测线数据的相关系数,依据相关系数与采样距离之间的关系,确定了最优重采样空间距离新方法。以最优重采样空间距离对测线数据进行重采样,利用拉格朗日插值算法,沿测线方向将测线数据向陆地推估。经过不同测线的内外部检核,结果表明船载重力测量向陆地方向扩展的保守距离约为5～10km,减少了船载重力测量数据在近岸海域覆盖空白的面积。本研究成果可为建立陆海一致垂直基准工作提供更全面的基础数据,技术方法可为航空重力、地磁等测线数据的精细处理及应用提供参考。     

Airborne Gravimetry Survey for the Marine Area of the United Arab Emirates

The Military Survey Department (MSD) of the United Arab Emirates (UAE) undertook an airborne gravity survey project for the marine area of the country in 2009, especially to strengthen the marine and coastal geoid in the near-shore regions. For the airborne gravity survey, 5 km spacing coast-parallel flight lines were planned and surveyed. These lines were supplemented by cross-lines in order to assess the quality of the airborne gravity surveys. The flight lines were extended 10 km, spacing lines further offshore. A Beech King Air 350 aircraft was used for the surveys, collecting data at a typical flight speed of 170 knots and a typical flight elevation of 900–1500 m, depending on weather conditions and topography. Gravity was measured with a ZLS-modified LaCoste and Romberg gravimeter (S-99), augmented with a Honeywell strap-down inertial navigation system unit. The estimated accuracy for the airborne gravity data is better than 2.0 mGal r.m.s., as judged from the airborne track crossovers. The new airborne gravimetry data changed the UAE coastal geoid by up to 30 cm in some regions, highlighting the importance of airborne gravity coastal surveys.     

空中重力测量数据代表地面数据的误差分析

利用严密的向上延拓公式将地面重力数据上延至空中不同高度,而后与相应的地面重力数据比较从而得到不同高度的代表误差。通过两个不同地形区域的实际算例表明,对于地形平坦区域,在1km高度以下,5＇空中重力数据直接代表地面重力数据的误差小于1mGal,在满足测量规范要求下,空中重力数据可以不用向下延拓而直接使用。对于地形复杂区域,当空中测量高度大于1km时,空中重力数据的代表误差大于3.3mGal,因此必须考虑向下延拓的问题。     

利用空中球面边值问题确定似大地水准面

针对航空重力向下延拓计算过程中的不稳定性,提出了扰动位空中球面边值问题,以航空重力测量数据作为扰动位在空中球面上满足的边值条件,得到扰动位空中球面边值问题,在球外部即为经典的球外边值问题,但对于球内直到地面则没有封闭的解析形式,给出了空中球面球内到地面区域的级数解,对于认识空中重力测量数据向下延拓特征和实际应用具有参考意义。利用地面实测数据计算结果表明,对于1km航高的测量数据,一阶解可满足厘米级高程异常的解算精度。     

Comparison of geosat and gravimetric geoid profiles in the North Sea

Sea surface height profiles derived from 2‐year, repeat track, Geosat altimeter data have been compared with a regional gravimetric geoid in the western North Sea, computed using a geopotential model and terrestrial gravity data. The comparison encompasses 18 Geosat profiles covering a 750 × 850 km area of the North Sea. After a second‐order polynomial was used to model the long‐wavelength differences which cannot be clearly separated over an area of this size, results show agreement to better than ±3 cm for wavelengths between approximately 20 and 750 km. In regions where terrestrial gravity data were not available to improve the geoid, similar comparisons with the OSU91A geopotential model alone show differences of up to ±6 cm. This illustrates the importance of incorporating local gravity data in regional geoid computations, and partly validates the regional gravimetric geoid solution and Geosat sea surface profiles in the western North Sea. It is concluded that, in marine areas where the sea surface topography is known to be small in magnitude, Geosat sea surface profiles can act as an independent control on gravimetric geoids in the medium‐wavelength range.     

Improvement in the Determination of the Marine Geoid by Estimating the Bathymetry from Altimetry and Depth Soundings

Abstract

The contribution of bathymetry to the estimation of gravity field related quantities is investigated in an extended test area in the Mediterranean Sea. The region is located southwest of the island of Crete, Greece, bounded between 33^? ≤ ? ≤ 35^? and 15^? ≤ λ ≤ 25^?. Gravity anomalies from the KMS99 gravity field and shipborne depth soundings are used with a priori statistical characteristics of depths in a least-squares collocation procedure to estimate a new bathymetry model. Two different global bathymetry models, namely JGP95E and Sandwell and Smith V8, are used to derive the depth a priori statistical information, while the estimated model is compared against both the global ones and the shipborne depth soundings to assess whether there is an improvement. Various marine geoid models are estimated using ERS1 and GEOSAT Geodetic Mission altimetry and shipborne gravity data. In that process, the effect of the bathymetry is computed using both the estimated and the original depths through a residual terrain modeling reduction. The TOPEX/Poseidon Sea Surface Heights, known for their high accuracy and precision, and the GEOMED solution for the geoid in the Mediterranean are used as control for the validation of the new geoid models and to assess the improvement that the estimated depths offer to geoid modeling. The results show that the newly estimated bathymetry agrees better (by about 30 to 300 m) with the shipborne depth soundings and provides smoother residual geoid heights and gravity anomalies (by about 8–20%) than those from global models. Finally, the achieved accuracy in geoid modeling ranges between 6 and 10 cm (1σ).     

RTM Gravity Forward-Modeling Using Topography/Bathymetry Data to Improve High-Degree Global Geopotential Models in the Coastal Zone

We apply the residual terrain modeling (RTM) technique for gravity forward-modeling to successfully improve high-resolution global gravity fields at short spatial scales in coastal zones. The RTM scheme is combined with the concept of rock-equivalent topography, allowing to use a single uniform constant mass-density in the RTM forward-modeling, both at land and sea. SRTM30_PLUS bathymetry is merged with higher-resolution SRTM V4.1 land topography, and expanded into spherical harmonics to degree 2160, yielding a new and consistent high-degree RTM reference surface. The forward-modeling performance is demonstrated in coastal zones of Greece and Canada using ground-truth vertical deflections, gravity from land and shipborne gravimetry, and geoid heights from GPS/leveling, with improvements originating from bathymetry clearly identified. We demonstrate that the SRTM30_PLUS bathymetry carries information on gravity field structures at spatial scales less than 5 arc minutes, which can be used to augment EGM2008 in (rugged) coastal zones, both over land and marine areas. This may be of value (i) to partially reduce the signal omission error in EGM2008/GOCE-based height transfer in areas devoid of dense gravity data, (ii) to fill the gap between land gravity and shipborne gravity along rugged coastlines, and (iii) for the development of next-generation altimetric gravity fields.     

CALCULATION AND ANALYSIS OF THE HEIGHT ANOMALY AND THE DEFLECTION OF VERTICAL IN AN OCEAN AREA

By the analysis of a practical calculation, this paper describes, for the first time in China, the gravimetric method on the calculation of the height anomaly and the deflection of vertical in the ocean by Stokes' and Vening Meinesz's formula. There are 84 calculation points distributed uniformlic in a calculated area of 2°×2° in the Mid-Pacific. In the course of the calculation, the gravimetric data measured by us, the 1° ×1° mean gravity data "published in other countries and the 25-ordeic gravitational coefficients of GEM8 were used. The results (Fig. 2b) show that the calculated area is an uplift of the geoid, with a mean height anomaly of 42 m, the maximum being 45 m and the minimum 39 m. In the whole calculated area, the variation of the deflection of vertical is rather small, with the maximum 7″·1 and the minimum -0″·2. The major causes of the calculation errors are pointed out and the calculation results are compaired with the data from the satellite altimeter.     

On the Influence of Sea Surface Height Variability on Satellite Altimeter Derived Gravity

The effect of sea surface height (SSH) variability is one of the primary factors that limit the accuracy and resolution of altimeter-derived gravity values. We propose a method to estimate the influence of variation of the sea surface height on the accuracy of satellite-derived gravity by simulation technique, with a case study around Indonesian waters. Wederived an Indonesian marine gravity map using the Geosat-geodetic mission (GM). Since most of the area studied is located around coastal and shallow areas, the measurement of SSH of this area is less accurate. To obtain a distribution of SSH variability over the study area, Topex/Poseidon (T/P) data were first processed and assessed. Processing 52 cycles of the Topex/Poseidon data, the root mean square (RMS) of SSH variability for each cycle was found to vary from 1 to 179 cm. Further, for the purpose of estimating the accuracy of altimeter-derived gravity, we derived several levels of Gaussian noise, computed simulation data by adding the Gaussian noise to Geosat data, and determined simulated gravity maps. Based on the distribution of RMS values from T/P data and standard deviation (STD) differences between the simulated and the original gravity maps, we estimated the accuracy of the gravity map. Around Indonesian waters, the accuracy of the gravity map influenced by SSH variation was estimated to be within the range 0.8~93 mgal.     

Bathymetry Inversion with the Gravity-Geologic Method: A Study of Long-Wavelength Gravity Modeling Based on Adaptive Mesh

Modeling of long-wavelength gravity anomaly is crucial for bathymetry inversion with a gravity-geologic method. We propose a new method, named as iGGM, to approximate the long-wavelength gravity anomalies by using a finite element method based on an adaptive triangular mesh which is constructed by uneven control points. The mesh size is suitably controlled to ensure that there are several control points in each grid. By using iGGM, the bathymetry in the South China Sea (Test Area #1: 112°E–119°E, 12°N–20°N) and East China Sea (Test Area #2: 125°E–130°E, 25°N–30°N) is estimated. The performance of the method was evaluated by comparing the predictions with Earth topographical database 1 (ETOPO1) model and shipborne depths in the test points. Results show that the depths derived by iGGM have a strong correlation with the shipborne depths. In the test points, the mean values of their differences are smaller than 10 m. The standard deviations of their differences are smaller than 120 m and their correlation is stronger than 0.98. Meanwhile, the results provided by the iGGM model are comparable with that obtained by the ETOPO1 model, e.g., the differences between iGGM and ETOPO1 models in test points for Test Areas 1 and 2 are 116 and 70 m in standard deviation, respectively.     

On the Influence of Sea Surface Height Variability on Satellite Altimeter Derived Gravity

The effect of sea surface height (SSH) variability is one of the primary factors that limit the accuracy and resolution of altimeter-derived gravity values. We propose a method to estimate the influence of variation of the sea surface height on the accuracy of satellite-derived gravity by simulation technique, with a case study around Indonesian waters. Wederived an Indonesian marine gravity map using the Geosat-geodetic mission (GM). Since most of the area studied is located around coastal and shallow areas, the measurement of SSH of this area is less accurate. To obtain a distribution of SSH variability over the study area, Topex/Poseidon (T/P) data were first processed and assessed. Processing 52 cycles of the Topex/Poseidon data, the root mean square (RMS) of SSH variability for each cycle was found to vary from 1 to 179 cm. Further, for the purpose of estimating the accuracy of altimeter-derived gravity, we derived several levels of Gaussian noise, computed simulation data by adding the Gaussian noise to Geosat data, and determined simulated gravity maps. Based on the distribution of RMS values from T/P data and standard deviation (STD) differences between the simulated and the original gravity maps, we estimated the accuracy of the gravity map. Around Indonesian waters, the accuracy of the gravity map influenced by SSH variation was estimated to be within the range 0.8~93 mgal.     

1979-2010年我国大陆海岸潟湖变迁的多时相遥感分析

潟湖是重要的海岸湿地类型,具有丰富的自然资源和独特的生态功能。近几十年来,我国的海岸潟湖遭到了极大破坏,因此,开展我国海岸潟湖遥感监测与分析具有重要意义。本文根据1979年、1990年、2000年和2010年的4期共102景多时相遥感影像数据,利用遥感和地理信息系统等技术方法对我国大陆海岸潟湖进行了遥感监测,首次调查统计了我国大陆海岸潟湖的名称、数量、分布、岸线长度和面积信息,并对近31年来我国大陆海岸潟湖的变迁状况进行了分析。结果表明,1979年我国大陆海岸潟湖共计251个,近31年,共消失19个潟湖,其中辽宁省消失15个,广东省消失3个,广西壮族自治区消失1个;1979年我国大陆海岸潟湖岸线总长度为2 692.26km,总面积为1 092.805 5km2,至2010年我国大陆海岸潟湖岸线总长度共减少337.80km,潟湖总面积共减少204.103km2;31年间,我国大陆海岸潟湖的岸线长度和潟湖面积总体均处在持续减少的状态,各省(自治区)也基本符合该规律;1979-2010年间,我国大陆海岸潟湖大部分处在老年期,死亡期潟湖消失19个。     

The SARAL/AltiKa Altimetry Satellite Mission

The India-France SARAL/AltiKa mission is the first Ka-band altimetric mission dedi-cated to oceanography. The mission objectives are primarily the observation of the oceanic mesoscales but also include coastal oceanography, global and regional sea level monitoring, data assimilation, and operational oceanography. Secondary objectives include ice sheet and inland waters monitoring. One year after launch, the results widely confirm the nominal expectations in terms of accuracy, data quality and data availability in general.

Today's performances are compliant with specifications with an overall observed performance for the Sea Surface Height RMS of 3.4 cm to be compared to a 4 cm requirement. Some scientific examples are provided that illustrate some salient features of today's SARAL/AltiKa data with regard to standard altimetry: data availability, data accuracy at the mesoscales, data usefulness in costal area, over ice sheet, and for inland waters.     

Precise Geoid Determination over Hong Kong from Heterogeneous Data Sets using a Hybrid Method

ABSTRACT

This study attempts to develop a methodology to construct a high-precision geoid model (HKGEOID-2016) over Hong Kong. To achieve this objective, a hybrid method is employed in this article. The proposed method involves three steps: the combination of multisource data; the construction of gravimetric geoid model using the remove-restore technique and Molodensky's theory; and the optimal combination of heterogeneous height data, improved by the evaluation of stochastic models through the variance component estimation method and assessment of the parametric model. The accuracy of the constructed geoid is evaluated with independent GNSS/leveling data. Numerical results indicate that external precision of 1.5 cm level is achievable. Furthermore, compared with the former geoid model HKGEOID-2000, the proposed procedure in this study improves the accuracy of the geoid significantly.     

基于ICESat-2和GSWD数据获取动态水域地形图的方法

传统的湖泊、海岸带测深主要是基于船载多波束系统或者机载激光雷达测深系统,但这些方式测量成本较高。因此提出了一种仅利用卫星观测数据,实现高分辨率动态水域地形图的获取方法,该方法基于ICESat-2单光子激光点云和Landsat图像数据的全球地表水数据集(GSWD),对所获取的高精度激光沿轨轮廓线与多年期湖泊水域边界等高线进行融合匹配。以美国最大的水库米德湖为实验区域,生成高程范围约为34 m的地形图结果,覆盖面积超过307 km~2,水平分辨率为30 m;在与机载激光雷达数据等现场实测结果的对比中,所绘制地形图均方根误差约为2 m。研究方法有望为水位波动较大或水质相对较好的内陆水体(例如湖泊)和沿海地区(例如潮间带)提供一种新的水陆交界区域地形图获取方法。     

Effect of the Mean Dynamic Topography on the Geoid-to-Quasigeoid Separation Offshore

It is commonly acknowledged that offshore the quasigeoid very closely coincides with the geoid. Nevertheless, the numerical assessment supporting this assumption has not yet been provided. Moreover, the rigorous definition of the quasigeoid surface and consequently the geoid-to-quasigeoid separation offshore is not given in geodetic literature. To address these issues, we define in this study the quasigeoid surface offshore in the context of the mean sea level. We then derive the spectral expressions for computing the geoid-to-quasigeoid separation offshore and apply these expressions estimate the vertical separation between the geoid and the quasigeoid over the world's oceans and marginal seas using the global dataset of the DTU15 mean dynamic topography. By taking the analogy of defining the geoid-to-quasigeoid separation inland by means of the disturbing potential differences of values evaluated on the geoid and at the topographic surface, the computation offshore is practically realized from values of the disturbing potential on the geoid and at the mean sea surface. Our result shows that the geoid-to-quasigeoid separation offshore is completely negligible, with most of the values within the interval ±0.3 mm.     

Improvement in the Determination of the Marine Geoid by Estimating the Bathymetry from Altimetry and Depth Soundings

The contribution of bathymetry to the estimation of gravity field related quantities is investigated in an extended test area in the Mediterranean Sea. The region is located southwest of the island of Crete, Greece, bounded between 33^ˆ ≤ ϕ ≤ 35^ˆ and 15^ˆ ≤ λ ≤ 25^ˆ. Gravity anomalies from the KMS99 gravity field and shipborne depth soundings are used with a priori statistical characteristics of depths in a least-squares collocation procedure to estimate a new bathymetry model. Two different global bathymetry models, namely JGP95E and Sandwell and Smith V8, are used to derive the depth a priori statistical information, while the estimated model is compared against both the global ones and the shipborne depth soundings to assess whether there is an improvement. Various marine geoid models are estimated using ERS1 and GEOSAT Geodetic Mission altimetry and shipborne gravity data. In that process, the effect of the bathymetry is computed using both the estimated and the original depths through a residual terrain modeling reduction. The TOPEX/Poseidon Sea Surface Heights, known for their high accuracy and precision, and the GEOMED solution for the geoid in the Mediterranean are used as control for the validation of the new geoid models and to assess the improvement that the estimated depths offer to geoid modeling. The results show that the newly estimated bathymetry agrees better (by about 30 to 300 m) with the shipborne depth soundings and provides smoother residual geoid heights and gravity anomalies (by about 8-20%) than those from global models. Finally, the achieved accuracy in geoid modeling ranges between 6 and 10 cm (1σ).     

Nonlinear and Robust Location for Low-cost Shipborne Laser Ranging Positioning

ABSTRACT

Without landing on islands, reefs, or facilities, fast locating targets by the reflectorless ranging integrated with Global Navigation Satellite System (GNSS) has a wide range of application. We propose a nonlinear robust location method and modify current nonlinear estimators for achieving shipborne laser ranging positioning of high precision. The Newton method is recommended as a nonlinear estimator for shipborne ranging positioning since the Gauss–Newton method occasionally fails in critical cases when the control points and the unknown point are approximately coplanar. However, it shows that the vertical positioning based on the shipborne laser ranging is generally of low precision, while the vertical angle measurement is used to further remedy this deficiency. The positioning precision and reliability might be significantly decreased with the increased number of gross errors in the observations that are dynamically implemented on a moving shipborne platform; thus a weighting scheme with high breakdown point is recommended to set the preliminary weights, and then Scheme III of the Institute of Geodesy and Geophysics of China (IGGIII) is applied to iteratively updating the weights of distance observations. It shows that the proposed method based on the angle-distance observational data fusion can be used to achieve a three-dimensional positioning of high precision.