Precision assessment of the orthometric heights determination in northern part of Algeria by combining the GPS data and the local geoid model

The main purpose of this article is to discuss the use of GPS positioning together with a gravimetrically determined geoid, for deriving orthometric heights in the North of Algeria, for which a limited number of GPS stations with known orthometric heights are available, and to check, by the same opportunity, the possibility of substituting the classical spirit levelling. For this work, 247 GPS stations which are homogeneously distributed and collected from the international TYRGEONET project, as well as the local GPS/Levelling surveys, have been used. The GPS/Levelling geoidal heights are obtained by connecting the points to the levelling network while gravimetric geoidal heights were interpolated from the geoid model computed by the Geodetic Laboratory of the National Centre of Spatial Techniques from gravity data supplied by BGI. However, and in order to minimise the discordances, systematic errors and datum inconsistencies between the available height data sets, we have tested two parametric models of corrector surface: a four parameter transformation and a third polynomial model are used to find the adequate functional representation of the correction that should be applied to the gravimetric geoid. The comparisons based on these GPS campaigns prove that a good fit between the geoid model and GPS/levelling data has been reached when the third order polynomial was used as corrector surface and that the orthometric heights can be deducted from GPS observations with an accuracy acceptable for the low order levelling network densification. In addition, the adopted methodology has been also applied for the altimetric auscultation of a storage reservoir situated at 40 km from the town of Oran. The comparison between the computed orthometric heights and observed ones allowed us to affirm that the alternative of levelling by GPS is attractive for this auscultation.     

A new high-resolution gravimetric geoid for South Spain and the Gibraltar Strait area: SOSGIS

A new gravimetric geoid is computed for South Spain and the Gibraltar Strait area. This geoid is located just in the junction between two tectonic plates (Euro-Asiatic and African plates) and in the junction of two gravimetric geoids: IGG2005 (the Iberian Gravimetric Geoid obtained in 2005) and MORGEO (the MORoccan GEOid). IGG2005 is the Iberian geoid and MORGEO is the Moroccan geoid, both geoids have been previously obtained. The new geoid is the gravimetric geoid solution that connects the two above-mentioned geoids, getting a more accurate and reliable picture of this area than the other previous geoids. The method used is the Stokes integral in convolution form, which shows to be an efficient method to reach the proposed objective. The terrain correction and the indirect effect have been taken into account. The new geoid is obtained as a regular grid (with a mesh size of 1.5′ × 1.5′) in the GRS80 reference system, covering the study area from 34° to 40° of latitude and from −8° to 0° of longitude. This gravimetric geoid and the previous geoids: IGG2005 and MORGEO; are compared to the geoid undulations derived at the validation points located on the study area (four GPS/levelling points measured on Morocco and five points of the European vertical reference network (EUVN) measured on Iberia). As it is expected, the new geoid is a more precise and reliable model, fitting the geoidal heights of these validation points with more accuracy than the other previous geoids. This new model will be useful for orthometric height determination by GPS in the mountains and remote areas, where levelling has many logistic problems. Also, it can be interesting for other geophysical purposes different to the height measurements, because it can provide a constraint for the density distribution, the thermal state of Lithosphere and the viscosity in the mantle. Such details can be inferred from a geoid model and the seismic velocity structure.     

EGY-HGM2016: an improved hybrid local geoid model for Egypt based on the combination of GOCE-based geopotential model with gravimetric and GNSS/levelling measurements

An improved hybrid gravimetric geoid model for Egypt, EGY-HGM2016, has been recently computed implementing the least-squares collocation (LSC) method through the remove-compute-restore (RCR) procedure. The computation of EGY-HGM2016 involves different datasets in terms of gravity anomalies determined from the GOCE (gravity field and steady-state ocean circulation explorer)-based global geopotential model (SPW-R4) up to d/o 200 and EGM2008 from d/o 201 to 720 combined with terrestrial gravity datasets in terms of 2140 gravity field anomalies and about 121,480 marine surface gravity anomalies. In addition, orthometric heights from 17 GPS/levelling measurements have been considered during the modelling process to improve the determination of the hybrid gravimetric geoid over the Egyptian region. The EGY-HGM2016 model estimated over Egypt provides geoid heights that are ranging from 7.677 to 21.095 m with a standard deviation (st. dev.) of about 2.534 m in the northwest of the country excluding the involvement of the orthometric heights from GPS/levelling measurements. When the later dataset is considered during the implementation of LSC process, hybrid residual height anomalies ranging from ?1.5 to +0.9 m, with a mean of 0.22 m and a st. dev. of 0.17 m, are obtained. Comparison of the predicted hybrid gravimetric geoid with the corresponding ones obtained from EGM2008, GOCE-based SPW R4 model, and GPS/levelling reveals considerable improvements of our EGY-HGM2016 model over Egypt.     

Different ways to handle topography in practical geoid determination

In this paper two different methods of how to handle topography in geoid determination is investigated. First method employs the Residual Terrain Model (RTM) remove-restore technique and yields the quasigeoid, whereas the second method is the classical Helmert condensation method, yielding the geoid. Both methods were used with the Earth Gravity Model (1996) (EGM96) geopotential model as reference, and results are compared to precise Global Positioning System (GPS) levelling networks in Scandinavia, especially an accurate GPS data set from the very rugged Sognefjord region, where the topography was represented by either a detailed (100 m) or a coarse (1000 m) digital terrain model. The inclusion of bathymetry in the terrain model was also investigated.Even if two different methods were used, they produced almost identical results at the 5 cm level in the mountains, but small systematic differences exist. Results show the importance of comparing the right types of geoid (classical geoid or quasigeoid), since differences in residuals are significant.     

Improving the geoid accuracy by adapting the reference field

In the frame work of the Austrian Geoid 2000 project, the accuracy of the geoid has to be enhanced. One of the possibilities is to use an adapted reference field. The traditional remove/restore technique has the disadvantage of removing a part of the effect of the topography and its compensation twice. In order to avoid this double consideration the effect of the topographic-isostatic masses for the used fixed data window has been subtracted from the reference field yielding an adapted reference field. This adapted reference field has been used for the remove/restore technique. The paper shows a comparison between the geoid computed by the adapted technique using the enhanced reference field, the geoid computed by the traditional remove/restore technique and the geoid based on the RTM-method for the remove/restore process. All the models are checked against a geoid derived by GPS and levelling points. The geoid based on the adapted remove/restore technique shows the best results.     

On the determination of a new Australian geoid

A new, high precision, high accuracy and high resolution gravimetric geoid of Australia has been produced using most updated data, theory and methodology. This paper presents a concise report of the new Australian geoid determination. Some aspects of the new geoid computation, such as data validation, geoid determination strategies and computational procedures, are described. The relative precision of the new geoid is better than 5 cm for average baseline length of 4km~40km and 18 cm for average baseline length of 120km when compared with three local GPS/levelling networks.     

Towards a cm-geoid for Hungary: Recent efforts and results

Some steps were taken recently for Hungary aiming at the determination of geoid heights with a cm-accuracy. The present HGTUB98 gravimetric solution was based on terrestrial gravity data, height data and the EGM96 geopotential model, and was computed with the 1D Spherical FFT method. The gravity data were used in the area 45.5 ° ≤ϑ ≤ 49 °, 16 ° ≤ λ ≤ 23 °, the resolution of the grid was 30″ × 50″. The DTM used had a resolution of 1 km × 1 km.Our solution was evaluated using GPS/levelling data at 340 and 308 points respectively and at 138 vertical deflection points. We have compared our solution to the European EGG97 geoid solution, the gravimetric solution HGR97B developed by A. Kenyeres and the litospheric geoid solution by G. Papp. We have correlated our recent HGTUB98 solution to the Moho model of Central Europe. The comparison with GPS/levelling yielded respectively an accuracy of ±8.7 cm and ±4.4 cm (in terms of standard deviation) when a linear trend was removed. The comparison of the 1D planar FFT solution for the deflections of the vertical with 138 astrogeodetic deflections yielded an accuracy (in terms of standard deviation) of ±0.62″ and ±0.52″ for ξ and η, respectively.     

Geoid modelling based on EGM08 and recent Earth gravity models of GOCE

In this paper an estimator for geoid is presented and applied for geoid computation which considers the topographic and atmospheric effects on the geoid. The total atmospheric effect is mathematically developed in terms of spherical harmonics to degree and order 2,160 based on a recent static atmospheric density model. Also the contribution of its higher degrees is formulated. Another idea of this paper is to combine one of the recent Earth gravity models (EGMs) of the Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission with EGM08 and the terrestrial gravimetric data of Fennoscandia in an optimum way. To do so, the GOCE EGMs are compared with the Global Positioning System (GPS)/levelling data over the area for finding the most suited one. This comparison is done in two different ways: with and without considering the errors of the EGMs. Comparison of the computed geoids with the GPS/levelling data shows that a) considering the total atmospheric effect will improve the geoid by about 5 mm, b) GOCO03S is the most suited GOCE EGM for Fennoscandia, c) the errors of some of the GOCE EGMs are optimistic and far from reality. Combination of GOCO03S from degree 120 to 210 and EGM08 for the rest of degrees shows its good quality in these frequencies.     

Modelling the geoid and sea-surface topography in coastal areas

This paper looks at the relation between the time-averaged level of the sea surface and a gravimertic geoid, as determined in coastal areas. Measurements in local regions can now be accurate enough to demonstrate that the geoid and mean sea level are not even parallel to each other, let alone identical. The accuracy and pattern structure of surface gravity data in some shelf seas is comparable with those on land, so that a marine geoid can be derived from surface data without using satellite altimetry. The geodetic objective is then to combine the two to determine sea surface topography. In principle, gravimetric studies provide the absolute datum so that local oceanographic models on the shelf can be combined with sea surface topography models related to the global ocean circulation. In contrast, sea surface topography information near deep ocean coasts must come from external sources and satellite altimetry used to give the gravity data needed to offset the less good coverage by ship-borne gravimetry.Marine Bouguer anomalies enable two specific problems of gravity anomaly patterns near the continent ocean transition to be overcome. The necessary extension of Stokes' condensation reduction is developed and illustrated along a north-south profile from the Mediterranean across the Cote d'Azur. The effect on gravity of deep ocean water introduces a geoid correction in the form of a dipolar ridge whose amplitude at the shore is about 11 cm. In addition to geostrophic currents, a semi-quantitative model for the thermohaline effects on sea surface topography is discussed in relation to sea level differences between the Atlantic and Mediterranean.In considering appropriate algorithms for local geoid computation, Kirby's Iterative Fourier Combination routine for combining altimetry and surface gravity is extended to account for global sea surface topography. The impact of very fast spherical harmonic analysis algorithms is discussed and a simple physical model is given which explains the short coherence lengths found for the global gravity field. This necessary assumption for any local geoid computation was hitherto purely empirical.Finally, the use of land data such as tide gauges, ellipsoidal heights from GPS, and orthometric heights from first order levelling are reviewed as ways of corroborating geodetic estimates of sea surface topography and its relation to levelling datums. Successful examples are given from southern England.     

Local geoid computation and evaluation

A local geoid solution for the northern part of Greece is presented based on a recent processing of newly available gravity data in the area 40.25 ≤ /o ≤ 41.00, 22.5 ≤λ ≤ 24.25. The derived gravimetric geoid heights are compared with geoid heights computed at recently measured GPS/ leveling benchmarks. A 4-parameter transformation model is applied to the differences between the two aforementioned geoid height sets, and a discussion is given on the current state of the leveling datum in the test area and the Greek territory. Regional and local transformation parameters are computed and some numerical tests are performed. A common adjustment of gravimetric geoid heights and corresponding GPS/leveling heights will be carried out in another study following an integrated procedure in order to study problems arising from the combination of different height data sets for geoid determination. Finally, some conclusions are drawn on the problems related to the optimization of a local geoid solution.     

Toward a 10' resolution geoid for South America: a comparison study

Since the creation of the Sub-Commission for the Geoid in South America (SCGSA) in 1993, many efforts have been carried out in the different countries in order to improve the geoid computations. The validation of the gravity data in Brazil, Uruguay, Argentina and Chile has improved many of the gravity surveys in those countries. GPS observations carried out on benchmarks of the geometric levelling have been facilitated by the SIRGAS (Geocentric Reference System for South America) project and can contribute for testing the gravimetric determination of the geoid. Several countries made available GPS data for SCGSA like Brazil, Argentina, Venezuela and Chile. The Digital Terrain Model (DTM) has been improved considerably in Brazil and Argentina. A great number of topographic maps has been digitized to generate a DTM grid of 3′ resolution (DTM3). New gravity surveys in the Amazonas region have been in progress along Rio Negro and its tributaries. Many different organizations in most of the countries in South America have been involved with local or national geoid computations. This fact has brought attention to the data in several countries facilitating the efforts for a continental geoid. All these activities are strongly supported by Geophysical Exploration Technology (GETECH) — University of Leeds. The objective envisaged at the moment is to produce a 10′ resolution geoid for South America using FFT and to compare the result with that of the numerical integration of the modified Stokes integral.     

The high‐resolution gravimetric geoid of North Iberia: NIBGEO

The gravimetric geoid computed in the northern part of Iberia, is presented in this paper. This computation has been performed considering two study windows fitted to the areas with higher density of gravity data, to reduce the computation errors associated to the scarcity of gravity data, as much as possible. The bad influence of a bathymetry with poorer resolution than the topography is also reduced considering the smallest marine area possible. Moreover, the computation of this gravimetric model is based on the most recent geopotential model: EIGEN‐GL04C (obtained in 2006). The method used in the computation of the new gravimetric geoid has been the Stokes integral in convolution form. The terrain correction has been applied to the gridded gravity anomalies, to obtain the corresponding reduced anomalies. Also the indirect effect has been taken into account. Thus, a new geoid model has been calculated and it is provided as a data grid in the Geodetic Reference System of 1980, distributed for the northern part of Iberia from 40 to 44 degrees of latitude and ?10 to 4 degrees of longitude, on a 161 × 561 regular grid with a mesh size of 1.5′ × 1.5′. This new geoid and the previous geoid Iberian Gravimetric Geoid 2005, are compared with the geoid undulations measured for eight points of the European Vertical Reference Network (EUVN) on Iberia. The new geoid shows an improvement in precision and reliability, fitting the geoidal heights of these EUVN points with more accuracy than the previous geoid. Moreover, this new geoid has a smaller standard deviation (12.6 cm) than that obtained by any previous geoid developed for the Iberian area up to date. This geoid obtained for the northern part of Iberia will complement the previously obtained geoid for South Spain and the Gibraltar Strait area; both geoids jointly will give a complete picture of the geoid for Spain and the Gibraltar Strait area. This new model will be useful for orthometric height determination by GPS over this study area, because it will allow orthometric height determination in the mountains and remote areas, in which levelling has many logistic problems. This new model contributes to our knowledge of the geoid, but the surrounding areas must be better known to constrain the lithospheric and mantle models.     

EGMlab, a scientific software for determining the gravity and gradient components from global geopotential models

Nowadays, Global Geopotential Models (GGMs) are used as a routine stage in the procedures to compute a gravimetric geoid. The GGMs based geoidal height also can be used for GPS/levelling and navigation purposes in developing countries which do not have accurate gravimetric geoid models. Also, the GGM based gravity anomaly including the digital elevation model can be used in evaluation and outlier detections schemes of the ground gravity anomaly data. Further, the deflection of vertical and gravity gradients components from the GGMs can be used for different geodetic and geophysical interpretation purposes. However, still a complete and user-friendly software package is not available for universities and geosciences communities. In this article, first we review the procedure for determination of the basic gravity field and gradient components from the GGMs, then general MATLAB based software is presented and applied as a sample case study for determination of gravity components based on the most recent EIGEN-GL04C GRACE model in Sweden. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

GPS高程拟合方法精度分析

近年来人们往往利用GPS数据来确定大地高,但大地高不同于正常高,为此,利用多项式拟合与地球重力场模型相结合的数学方法,使GPS所测大地高通过这些数学模型直接转换为具有厘米精度的正常高,将该方法得到的正常高与单独利用多项式拟合和地球重力场模型得到的结果进行了比较,其差值的标准差为±38 cm。     

Tectonic implied results from geoid and topography signals

The topographic surface is a measure of static equilibrium from the actual density distribution within the outmost Earth's lithosphere. The natural height reference of this surface, known as geoid, reflects the mixed mass-density effects, caused by the same sources, without the contribution of topographic mass. Geoid undulation and topography are output signals, which carry in common a large part of the contribution from the causal “sources”. This contribution appears in both types of signal. Comparisons between the signals depict the geographical location and an estimation of the depth occurrence of areas with geophysical and tectonic formations depending on their correlation rate. We present results from the Greek region, known for its complex diversity in topography, tectonics and dynamics. The tests are in point and “surface” concept, from local and global signals of geoid and topography. Local geoid is represented at 91 GPS points and EGM 96 coefficients compute its global representation. The topography is point values within the area, and the ETOPO5 5′X5′ data within the geographical frame.     

Completion of the nationwide GPS-gravimetric geoid solution for Hungary

The establishment of the Hungarian National GPS Network (OGPSH) had been completed in 1997. It is exclusively settled on the traditional horizontal network sites, no leveling benchmarks were included. The OGPSH network consists more than 1100 GPS points, but less than 30% of the sites have trustful leveled heights. Our task was to supply the remaining points with cm-accuracy heights above the geoid in a uniform system. For this purpose a technique had been developed using the GPS data and the geoid information available. A specialized geoid solution, covering the whole country was computed and used for supporting the GPS-heighting procedure.The OGG98B GPS-gravimetric geoid solution made the GPS-heighting very simple and efficient. The accuracy of the technique was extensively tested and proved to be accurate not worse than ±3 cm. Higher residuals were found only at some points, where the height information was questionable. The improved technique is planned to be used in the 3rd order leveling network in Hungary.This paper shortly summarizes the computational procedure of the GPS-gravimetric geoid and presents some results on the GPS-heighting had been performed in the OGPSH network.     

基于EGM2008模型的GPS高程转换法

GPS求得的高程是地面点在WGS84坐标系中的大地高,而我国采用正常高系统的高程,是通过该点的大地高减去该点的高程异常获得。高程异常的获取,惯用的做法是曲面拟合法,这种方法在水准点稀少的测区（特别是山区）实施起来比较困难。EGM2008模型是迄今为止分辨率最高、精度最好、阶次最多的全球重力场模型。首先利用EGM20081′×1′的大地水准面模型计算各点的高程异常,再通过联测一个一等水准点,获取EGM2008模型所表示的全球似大地水准面与我国高程基准面之间的差异,即可将GPS大地高转换为1985国家高程基准的正常高。兴城测区实例表明,EGM2008模型高程转换法在山区仅用一个水准点即可实现GPS大地高到正常高的转换,且高效率、高精度。     

Recent geoid computations for the Hellenic area

New geoid computations for the Hellenic area are carried out using (a) gravity anomalies for the land area available from old and new data bases, and gravity data for the sea area derived from altimetry and a recent digitization of sea gravity maps, and (b) a 1km × 1km digital terrain model. The EGM96 geopotential model is used as the reference field. In order to assess the quality of the computed geoid heights in the continental area comparisons were carried out with GPS/leveling heights and the recently available European Gravimetric Geoid EGG97. In the sea area the geoid heights were compared with sea surface heights of the recent and more accurate TOPEX/POSEIDON (T/P) altimetry mission. At the end of this article the improvement of the data bases is discussed and some plans for further development in the methodological schedule are pointed out.     

应用GPS数据与重力数据确定大地水准面

作为GPS/重力边值问题理论及方法的应用,在对GPS/重力方法确定(似)大地水准面的原理进行简要介绍与分析的基础上,利用收集到的N区的600个GPS/重力数据和48个高精度GPS水准数据,计算出该区域的(似)大地水准面。通过拟合法和系统差直接改正法进行的精度分析表明,应用GPS/重力数据结合水准方法确定的该地区(似)大地水准面的精度达到厘米级精度。     

物化探测地工作采用GPS定位时进行高程异常改正的研究探讨

本文叙述了我国现行高程系统与ＧＰＳ高程系统垢区别,介绍了ＧＰＳ求解的大地高转换为正常高的几种方法,具体提出了１：２０万区域重力调查中用ＧＰＳ定位时所求测点高程应进行高程异常改正及高程异常对区域重力调查精度的影响。对区域重力调查及其它物化探测地工作有一这的指导意义。